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@nickstanisha
Created April 23, 2016 04:36
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2 dimensional hexagonal extension of [this](https://fivethirtyeight.com/features/can-you-solve-the-puzzle-of-your-misanthropic-neighbors/) FiveThirtyEight riddle!
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Neighbor Bees\n",
"An extension to [this FiveThirtyEight riddle](https://fivethirtyeight.com/features/can-you-solve-the-puzzle-of-your-misanthropic-neighbors/) summarized below\n",
"\n",
"> Suppose there is a row of some number, N, of houses in a new, initially empty development. Misanthropes are moving into the development one at a time and selecting a house at random from those that have nobody in them _and_ nobody living next door. What’s the expected fraction of occupied houses as N approaches infinity?\n",
"\n",
"The code below simulates a visualizes a 2 dimensional version of the problem with hexagonal bins, reminiscent of honeycombs.\n",
"\n",
"Notebook by [Nick Stanisha](http://nickstanisha.github.io). Final result [here](https://twitter.com/sticknanisha/status/723670601043456000)."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"from __future__ import division\n",
"import matplotlib.pyplot as plt\n",
"from matplotlib.path import Path\n",
"import matplotlib.patches as patches\n",
"import numpy as np\n",
"import itertools, random\n",
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"class HexGrid(object):\n",
" def __init__(self, rows, cols):\n",
" if rows % 2 == 0:\n",
" # Odd row counts are more aesthetically pleasing in the final GIF\n",
" rows += 1\n",
" self.rows = rows\n",
" self.cols = cols\n",
" self.available = np.ones((self.rows, self.cols), dtype=bool)\n",
" self.honey = np.zeros((self.rows, self.cols), dtype=bool)\n",
" \n",
" def reset(self):\n",
" self.available = np.ones((self.rows, self.cols), dtype=bool)\n",
" self.honey = np.zeros((self.rows, self.cols), dtype=bool)\n",
" \n",
" def hex_patch(self, cx, cy, fillcolor='white'):\n",
" \"\"\" Draw a single patch of 'radius' 1 centered at (cx, cy) \"\"\"\n",
" x = np.pi*(30/180.)\n",
" top, bottom = (cx, cy+1), (cx, cy-1)\n",
" rtop, rbottom = (cx + np.cos(x), cy + np.sin(x)), (cx + np.cos(x), cy - np.sin(x))\n",
" ltop, lbottom = (cx - np.cos(x), cy + np.sin(x)), (cx - np.cos(x), cy - np.sin(x))\n",
" \n",
" verts = [top, rtop, rbottom, bottom, lbottom, ltop, top]\n",
" codes = [Path.MOVETO,\n",
" Path.LINETO,\n",
" Path.LINETO,\n",
" Path.LINETO,\n",
" Path.LINETO,\n",
" Path.LINETO,\n",
" Path.CLOSEPOLY\n",
" ]\n",
" p = Path(verts, codes)\n",
" return patches.PathPatch(p, facecolor=fillcolor, lw=4, edgecolor='#ffdf99')\n",
" \n",
" def draw_grid(self, fig=None, ax=None):\n",
" \"\"\" Draw a grid of hexagons, filled appropriately \"\"\"\n",
" cx, cy = 0, 0\n",
" x = np.pi*(30/180.)\n",
" \n",
" return_fig = True\n",
" if fig is None:\n",
" if ax is None:\n",
" fig, ax = plt.subplots(figsize=(8,8))\n",
" else:\n",
" return_fig = False\n",
" elif ax is None:\n",
" raise Exception(\"fig must have accompanying axis if defined\")\n",
" \n",
" for row in range(self.rows):\n",
" for col in range(self.cols):\n",
" color = '#e69900' if self.honey[row][col] else 'white'\n",
" ax.add_patch(self.hex_patch(cx, cy, fillcolor=color))\n",
" cx += 2*np.cos(x)\n",
" if row % 2 == 0:\n",
" cx = np.cos(x)\n",
" else:\n",
" cx = 0\n",
" cy -= 1.5\n",
" \n",
" offset = 2\n",
" ax.set_xlim([-offset, ((self.cols-1)*2+1)*np.cos(x)+offset])\n",
" ax.set_ylim([-3*(self.rows//2)-offset, offset])\n",
" ax.set_xticks([])\n",
" ax.set_yticks([])\n",
" \n",
" if return_fig:\n",
" return (fig, ax)\n",
" \n",
" def valid_coords(self, row, col):\n",
" return (row >= 0 and row < self.rows and col >= 0 and col < self.cols)\n",
" \n",
" def get_neighbors(self, row, col):\n",
" \"\"\" Return a list of adjacent cells in a hexagonal grid \"\"\"\n",
" neighbors = list()\n",
" if col > 0:\n",
" neighbors.append((row, col - 1))\n",
" if col < self.cols - 1:\n",
" neighbors.append((row, col + 1))\n",
" \n",
" for new_row in [row-1, row+1]:\n",
" if row % 2 == 0:\n",
" for new_col in [col-1, col]:\n",
" if self.valid_coords(new_row, new_col):\n",
" neighbors.append((new_row, new_col))\n",
" else:\n",
" for new_col in [col, col+1]:\n",
" if self.valid_coords(new_row, new_col):\n",
" neighbors.append((new_row, new_col))\n",
" \n",
" return neighbors\n",
" \n",
" def run_experiment(self):\n",
" \"\"\" Randomly fill available cells, return fraction filled \"\"\"\n",
" order = [i for i in itertools.product(range(self.rows), range(self.cols))]\n",
" random.shuffle(order)\n",
" \n",
" for x, y in order:\n",
" if self.available[x][y]:\n",
" self.honey[x][y] = True\n",
" self.available[x][y] = False\n",
" for i, j in self.get_neighbors(x, y):\n",
" self.available[i][j] = False\n",
" \n",
" return len(np.nonzero(self.honey)[0])/(self.rows*self.cols)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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KJeQPPIpW3t0CLzmYRHLNNxEZ5q3y5FRDdjZWjuqPLrHm2kFz4wM32SfpRpSS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\n7eJOFA8/5XiijdgOXl+UAqW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Xq6flUArJ1d9ExPKYkYnYMj1oOARXTQPKR2iOm1m16/ii\nFCjdrJ5ulfRAfM72Y+ZqiI+E6IKbkFhxH6d93rHRIUnvsjFPVVLD4V5wO5fmULVP0ZmycCOY3Jyk\nooJXtYN8WeX0Kygd/zfnx/8kv161322/JiSQoQTYadEWYFu1TyMbfJnDoh9V0X0ZuwOJkfs8idJ/\nugETmG45ZT8EYAo2gT79RHuc4OUO3h6XGncGb24nzBVxs3AShQOPQSl7yKoB+ONzkVr3XQRTJofh\nVA1xbWxTBpnfDcvACI3QjR9Ie7KRN3hVpY7S0WdRPfuW9bvskANILLsXsUV3QDIv3AjP1wObx+fa\neC0nOURzTfGVnjJIu6q9fnkPCoeehNrgtLc4hPrXIbn2QfgjphvTbsGbHe06BaSyNfuvXvgQxcNP\nQ2u5WBVsIDy0mdrnYdMYYU1ZuLKxSoGd1ZqLr6HVlT4Pi340jea5J9+ztPCV6jhVQ9lDnkyUQ31I\nrX0Q4cENpncYUxZubSwfAiY/gNWXeUjSjbSKlAxbVuoypixc2ahSIpzbCXNR0SqeRv7AY1BK3hZ4\n+WMj5MvS5hXrHpL0Lhs7HUjGYiHzlIVbGhPA5FvWuemRr7kL5DqffsDsUDsPXH5u+t++ODD/gd6f\nodE04Oyj3VnuwC3kQHsl/zGQ3z71z1bpLCY++Fv0vqOIhOFb/1t3ljv0Re/OyUj2Q72NrBOaA8y5\n15tDNqKpwOmfw5goTOz4v9HK9/7wcmrdnyA67/rpFyIL6Xf3aqOqAGd+3v3a3G/wW7puuPxiV/uz\ndmE78p/83OYP7JF8IQzf+uPuxS7zvw34Y73bePG3Xd2Zypk3UDz0y95tDCYw55b/p/vFhf9pZisL\nz/+6O+FKbXZ+VMKO+jhw6dmpf6qtGi6/9b/PaDOUwRv+Fv6oIZnp+yyQMgdRD1RO0sriDr4oMP9b\nM/Rlj3Uvyuu/CUis7t3G4if6891Eq3wBEx/8n1Nz8d6RMHzr/wfZb5gXHLzD2/PXZnI7qZXcITgE\njHx1Zr7s/K+6k+tZCphXf2s8c6tH9s/sgVNJguVnzHBJsTmT05QGZrb9lmbdxmmmNkqmbFMO9D7A\nAGZmqCn8dqAbtLZpkY8cnJmNsh+WHVNm+TyqM/7NjPbkjG3svj9mbKPl76VZsHG270FTxae1Z7Zz\nGGCdH51tG6VZ8GWzfR6lbhu1dnMGwRIgX2b6+z9EXzaDHYXsEHvJCgQCgUDgAhEwBQKBQCBwgQiY\nAoFAIBC4QARMgUAgEAhcIAKmQCAQCAQuEAFTIBAIBAIXiIApEAgEAoELRMAUCAQCgcAFn37AnNFD\ntJ1jzPJuRGa8bPf0aTEb53FGmzO4OfwfoI2WsTODB6avFFd6fM/GOTXbOOs2X4HrMts2Cl82O8yK\nn7gyXN2zpzb1PVANKEXaI1Tt8STldwOaSd9x8l2g4U2MeopmASh02xhILUFixX29HQ9AfMXXIJk3\nfx5/g76rF5qT1j1Q6+dJxLUXVJX25DU5zvSGv4Ac5EjtOOBPLkZkrkm8tnpS3xy5RxvHX7e+fvll\nQPEo9Nyhdh6od6uCROd/HpG5n+vteJDRt/GvrC9ffoHGfi9UTlpEC2KLbkdoaHNvx5ODyGz6ofX1\nyy84CwrwKB+1bqJd2EPSdL3QrluutRSIIr3hL9Cry4rMuxE+syBAbgdQcxYUYKJUab9bI+0yMP7W\nDHzZXutm+5PvkUJTL7RKutbwNIHEAiRW/nFvxwMQX/YVSGbFmYk3SRezF5o5q09oXNT3wO0BTQPK\nx0hX9wpw9faStdF1BECbaA/eCURc7MYP0AUae8Feniq2kvZiNG8AzkJVaaNrnvA1gHY9j+yev3O9\nabE/sQCZzT/giErrJNbTnpZubZx8B6hw9N8A2pt3+B4g6HID9volYOxljqg0oGltlI+/gPKJ37s7\nHmSkN/wpwsPb+Irz/rSu3O5yA/bqWWD8NY6eJkDi158B0hvdHU9VaA/QGvs6apqGVukscrsfgdp0\nJ38WGtqM9Pr/DNnP22hcJtWO5BqXNjZpn1uOnqamaWjmjyO75yeuE4bIyOeQWvsgJB9nKzPJR8o5\ncZeSWEpdF2G2cejhebr4tcuNw4v7SZ2GIweoKjXk9/0cjYl9zPfNyMEUMlsfhj8+jz8eI4uBwVvd\n25jbDRQYG4ZPfWkIGLy9W9fWjmZB92UcXV6AtFD7b3HnJwBd9P5j7tvtRgHZ3T+FUmLr3prxx0bQ\nt+Vh+CM2+zbH15L+pFtfln3PXoXIFweG73K/V7SdNN6/m83X2zXa/NetBqHT4FVVOl551N3x5CBt\nDmw3eOtjpGJvI6XUQdM01C5+iMInj8JO4zO1/j8hMvJZ/k3aZWOEnErYRq2ldoGcvJ2UkpH4GnLQ\nvMGrKsDE60D1lKvDKbVJ5Hb/xFbiKzSwHukNf969MTMXXQM0cx3/I6pC18Wt7qI/CQzdDdhVxeVj\npDZdfXYAACAASURBVGZgJ6Wko6ltlI7/DpWTL9p8ZxiZzT9CML3M3bUOZChZsNuMvXiQnIkLDVlN\nVVA8/GtUz77B/YwciKNvy8MIJBe6szE4SOfRThKr8DFVaK7auT5SQklwhKwBcnaXngcU50pF0zQ0\ns4eR3fNT28o9vvRexJfdDcnN/q6SHxj4gv0m4s08VeJtd0kUIgspcNr5MockvdvGIDB4GxC1kSFr\njNM940JDVtM01C/tRH7/P8PWl639LiLzrnfpy8LA0J32ai21i8D4yx582WoSzOb5Mk0DSqM0Hlni\n64E+YPhLbC1WDlc/YDqo3Cu1SfiCSUg+xia5kp8UR2ImGZn6ZT2wsTJqiVS+eVkaa/CqKjDxhq5s\nzsCfoBuZ4RTUVhW5j/8HmtnuDCmYWY2+jX/JEeuVSAuRVxVHlwIDt3YPDFUBxl/lCgor1TH4IgNs\nVXTe4K2cpN/NFOv1kUI5UxVdQ+38eyiMPmb6niAym3+AYGYV+6byp/hK8L4oMHSXVauudISqaYbe\nqarUoSk1fuWevAZIX9d9Hp2qIRsbleo4Jnc/AtUkIh2ZfzNSq+9nawRKQarYmEmYpKt5bDN9UYUc\nMk8j0MbGVvkCsrt+DLXRHXBiS+5CYtlX2JqschiAxnFcEgkVm9U8WkWykXc97a51cICutdlxZXfo\n1RDD1/gidA8wHKHWbqFw6JeonX+3+09iI8hs+RH8kX7vNoaGKXk1ikg7JOntehZyIM6u3HlVu1OS\n7k/yfRmraldVYPJNkkZjHi9B44sRGFWlhtzH/4jmZPc0T7BvJfo2fg9ykJXcOfmyJZSAdNmoUKu9\ndsrGRra/par9DiBiErK21Vr2oKdp4uoGTBtFdk1TUTn1CkrHfw9fuA+ptQ8hlOFknp3BK/n1wHaS\n/blAhsRVgwMkZ5Pfya4gjIO3cgaYeI2dkUAmLc3UJuqFT7zFdLSapqExOYrc3p8BAPo2/hVCA+vY\nQSM4SJqfgZSuZ7kHzKxOClDQjC3Sq6G3mYFNazdROvY7VM68hkBiAamiJziZZ2fwQrVt803pafri\npFFX3AdmstAsI/vx36OVO4rIvM8jtfpbnMQnQHqIibX0nSw9yw6xFXRt1Dow9iJXyLs+cQDF0Seg\ntspIrPgaogtu5iQLhqq9sE+vhhjn26inWT9Hc7nMZEFF5exbKB36JeRQGpmtf81XoY8uoepekoHc\ndqDMaaEbW065j3SJI5aziAD9n6fjVk9R9cmoIDRNRfnkiygf+y3kyCD6t/41/FFOGyq2goSiofL1\nLAEKLsN362NiO38OuqOnGVlITjv7Pj8Qp7fR/dWYoGvNq4bia6gDoTa5rTZN06CUziG7+xGozSKS\nax9CdN4NnMQtSVqs4bmkZ5ndzmnzy3Rukutspyw0TUXl9GsoH/8d5GCSfFk/p+UeGgIG76KOl12S\nHuijaaTQIK1TyO3kJ7b9NwKJlUDtHCXVzGrboKeplLjBRdM0NCcPIbv3ZwBU9G34S4QGr+H4sgFd\nqzKj61nuBiux7aranZL09FZKzppZtp5lh8giqrIlyd6PhuboNnrUBu6YflUCZke0NP8R88S0imeQ\nP/CoaQ5QQmTe9Uiu/Aa/KpNkTguNk0HYBGz6sxC/HcASLtVU28GrtSnocqvl9LV08xkdu21mZG9j\nY/IQCqOPoV0zBBVJRmzxF5FY+iW2HfCBnDEnSGc+S60P4w3CE2MF3WBqq0yZNeumiiwkB+qPT7+m\nKhQUCnvBbuX5QTceO0gXDj2F+qUdXa8HUkspWeAFLykEaJxrHV1Kws5GyTm1pSu3f8K0o92qQvaH\n2UHaF6VAaW7r1c7TteZl41KQPz8bX0WVnrHiaTf0QMwWUlZbVUhcG+OUFEVMyVX1NAUl3hoDKcBJ\nLgEk1pH2pVHmqV2j7hKv4rH7zf4UJcBhw3oGTaOgPvk+syrT1DY0tdWtOTv9ZdT+T2/trniUCiUf\nvGkJm3uwVTqHwoHH0Cp2/21k7vVIrvoG5ACnKrP1ZXqS3uXLSrovO+fZxqkk3TgH6NC+tPdlHNH7\nVp6SYV4ibncPskTvNZWS9fwuTuHjp84D636SAnS/JNbMSCLsygfMVoHKbVYl1m6idPz3qJx+lbtk\nWA6lkFz9TUSGt7j7PqcMQtNIqT73obteubEa4p1op8FrJjyfskDe4han3rsJtVVB8fCvUbvwPvcz\nvuiwXrW7FNCOLiYnz5tT01SqKvIfuZr3gxzWq6Gl/PPYnKQbzG6xiIHahe0oHn4aasta+QEAJD/i\nS+5CfOnd7PaoGV9Mt3Ex/zONMbKR1x41E1+tBzbOoh9V0QPxfria9/MnaHzbzr1foIqYV7WbSa6n\n5I2nFag2aSyWXK4PCKTJRrv5qupZfbEf59p1YaiGeNexXad7unzEnY3BfupcmFv+Riongey7FOQd\n0NotlE48h8qpl/i+LJhEcvUDiMzZxnzfAitJ7/pSzaFqNyH5KYFJmJJ0I0qZrgtn4ZuF8DzdlyX5\nNpYP6lW7C91SKUjdA3OSbqRV0P3tBXc2spL0HrnyAbN0UJ9z6qaRPYzC6ONom+Z/eISHNiO5+pvw\nhTmB0GsG0a7at5wAyrb7b3R3ot0MXjlELZ3YCnc22q3u0qld+gjFQ09BbdqspJtCQmTeDUiu/Drk\nAGcBji9CE+luldLdDN74Smpv+mwWi3Rw6EYANM9dPPgEGhMHmO+b8cdGkFr3XQTTS/kfSqylxMiN\n6K3WNrScOIsi/CnKkMOcCtdMY5yqTV7LCZI+B7vN3apNVaHHoAqcOUCA2nwDN1Nb0A31S2Rji7cA\nR6bAlt7sbm5IbVF3xm5xS3BQn1bhzDuaqZ2j8cit2vU2X3KDu2cPHap2AGjkjqJw4DG0q5yukInQ\n4Aak1jzIn2t3k6R32ehQtQPOSboRTaPFmNn3uavku6YsXPmyiu7LbFbfOiXpZhvLh/XCh9ORkCPU\nKbJL0j1y1QOm2qqieOTXqJ1/z+aPON/rjyCx4j7EFtzU/UZkkZ5BuDjRZqqn6NlHY/Yjh2kZdGyZ\n9xPNG7yxZXRMn5uVogY6LafxN2GcD2jXcygcfBKNcf4ScR5yKI3UmgcRHjI9buFUDdnZWO4sxjEE\nEH+CbtLIfM82olWk57gM7RxNU1E98wZKx34Lre1yJd0UEqILbkZy1f3dC13cVEM8mnl6rKVlDHIS\nTQWktrh/HKFDp+WU624vUzV0k6fl79M2TgJjr5gWivS+6AFam+aHTM8kIzQ0PX/llcYY2Whs+0o+\nfcpivfeH6tWWYa7dQHiuHjR6eIa4dkGfD5wOIGqrhtLRZ1A99y68bvIg+cJIrPgaYgtv6X7DS5Ju\npnqGunnGlrYc0n3Z8h58WR3IfghUTFV7dCkd08PqUgC6Lzup+zJDMuw1STeiVPX2uWkdi5ck3QO8\ngHnFNi6oX97VU7AEAE2poXjwCViC9cDNvQVLgLKa8HD3a/FVtACol6zEF6HHX8wM3Oo9WAJkQ2wZ\nEOrOsCtn3+wpWAKA2sijcPAXpu8JUCbvNVh2bEyssrZlkht7C5YAHavvM10vtes5FA8/3UOwBAAN\n1bNvom1aLYrUlt6CJUBt//Sm7tcCfXql6jFYAhQYUpvIyRlJf6a3YAlQsE2s7X4tNEwB02uwBOhv\n+rZRe89I3+d6C5YABdvYiu7XwvNpsUcvO9DI+ty72Y1lbugtWAK0CjOyqOul+tgeVM9ZN/Zwg9au\no3joSWjm9m3/zb23DqMLrR2N2Aog7rKjZcYXBgZvsb4++AXvwRLQfdlSaxs8sba3YAmQHQNfML0o\n09MUsxws7fh3sE+SQCAQCAQmZqn96gURMAUCgUAgcIEImAKBQCAQuEAETIFAIBAIXCACpkAgEAgE\nLhABUyAQCAQCF4iAKRAIBAKBC0TAFAgEAoHABSJgCgQCgUDggisYMK/AQ6WczY5do5r2LG27U6rn\nH49hzyzbKPey00YXpp1aNJVttxdU0ybsvH0oezye3MsuRGbMu9u4FavlYR47Mz0eYB0rNmLI7o43\ny9cFYNjoYmNt2+OZ/n6m9yAd1PRP9t7E7g/XbaPEVB6ZIW6EDGz/fpbPI8snmO9zr5ivw0xtNJ8z\nTaVt+K4iV2wvWU1to3LqJZROPGd1Ng4E0iuQ2fQ9yEHT1lE8MVYnVAWYeJ0t48MSY3VD5TQd0zxw\njXqWXm0ce8kiSaZpGupje5H/+H/AThWdRWh4G/rW/4lV2JYnxupEu042siTJYsuB/lv4qug8igdp\nj0jTb2s3Csju/imUks0mzgzkQBx9Wx5GILnQKjsWX0t7Y3q1sfCxvu+r6V7wxUgr0utWcUoZuPQ8\noJg3N5dom8HMZ5h/ZkvuI+u+r8C0niVPZYJHM0+C25bNzSXa1DztUlWog6oC+Q912TQTgQzZ6HXb\nS66epkxb5iXXe7dx8h2g0q1fqmkaWoWTmNz9E9rT1AOB1FL0bf4+fEHzZug+2hc7wdECtrNx4nW2\nmER4RPdlLoQFjFTP0l7JZrk1o56lJxsVYPwVthJKZCEweHsP/vYE7TltDsLhEdrbuNetEDl8amol\nSuUSCqOPo5k76nwM2Y++DX+B0OBGtsZih+AgMHQ3wNS+M2ErXNrBw+BVmyQo6yQ542XwljobmvMz\nOlWpI//Jz9EYc7GvrD+K/i0/QiC1xP48ehm8xU9og2a7oC0FgaHbrFqLLJQKcPkFW/ksTdNQv7QT\n+f3/bP+9OrHFX0Ri+Ve7N103I4eBoTvd7SvbKpKNTvJZsVW0kbabQJzdARRtlEUA0tUcutuyrzCT\nZpZEwZ3ks5LXAOnrnG1UVVKvKDtIfPkTZKMbgd76GCVaDB3LaSTa77dvq/PxVJV0WisOPiWQBobv\ncbdna+0COXmbzoGmKige+Q2qZ15zPh5kpDf+BcJDmx182QAwdJe7PVt5Sbrpe5H5PJDkCFkb4STp\nFkJzSOjcjS8rH6NrY1dBS34Kcm4KH7skfep4HpVpXHDlA2a7CkwydpPXqZx9C6Wjv4GmsMvy0NBW\npNf/CWS/23acRJtfpzay31ab5Eh4oqYsnAYvpxri4zB4lSplyM0J9vsmNE1DM3cM2b1/B3DOY3Th\nbUiuvM+dLiTgPHiVMnD5eRupJwbh+RSUeDbkdunVkLuxpSo15Pf9ExoTbHkoOTKI/q0Pwx91KV8F\nANEllD2zbFRVIL9d1650iVPVzq2GbIitoI4KK8ipKmk42shRWW2MkOPjbfBev0TJoJdWbmIt0Mep\n2lWVktXqcffH88XJRl7VXjunq4m4bV/rqjJ9nKpdVeh4NtJ6ZpTyJUzufgRqnS3RFhraiPT6P+WI\nWXNsTG8juTSmjS6TdCNOVXvpMMlw2STp3cgkWZhcx35bqVNHwqXGLQDajH/wLn7h4yZJNzITtR8T\nVz5gdqicpKDCcAxMqSp/FP2bf4hAeik7EwvPpaqAp2fJajkVD5D0FuNEq60qqufeQWTe9Yw2CcAc\nvEqFgm+Lo2EYWUj/5d10rMGb30NakKygIYdIgqt0kKlKr6kKCoeeRu3cW9N/Eu5H/5YfwR8fsXwe\nAEn1qA1+Nhkc0pMFw+DN7eDrLPqi1IYtjXKqdx9VXQmDkHUzRxUbrxqKrSB5KkY2qWkamtlDyO75\nWZezTKx+ALEFt0BiZZa+OLWTiqNgOgZWy6kxTteaUQ1pmora+fcQSC5EIMlpuUcWAYO3TQdip2rI\nn6KKvHQA7LEQpC6AUQ3GthqSKIjVz/OTnOgyPVnQz5mq6IGNnewikKGKvHSQY2OYuilGNSCbakhT\nFVTOvonw4Eb4oxznFl9NqiNGG8de5ou3BwcpyJYPs99nVe3lY6T7yRq/ko8EmCvHu+XIOr9BU1E5\n/SpKR54xfEcYmc0/QLBvBduXhUbIB/D0LFlVu12SLgVIF7h8lFO9M6p2pyQ9soB+O2v6CiCVnuG7\nu6t23pQFSPS+eu5dROffAJk5FyyT1GDqGoONvCkLnehiGg/MseBRT5bD1QuYgC7GuoMUuBnULu9C\n8eAvEZ6zFcmV32BXQ3KQpIQ6wqXV05QRMQYvADpJifU0GFo55kfql/egcOhJqI0CpEAMyVX3Izr3\ns+zjdQZv5Ti/GjIKlwIU1Cfftx+8sWVko8IRgo4tp0zOF6FAnX2PO3hb5fPI7voxYgtvQ2zxHZyg\nEaN2c3TRtJ5l7kOOs5UpEw/P06shzrk26mm2SrqwNM+RDQCDXwQKu/jVkD9BmWFkHtlYGqXxw3K2\n7RYKh55Eq3wemU0/gC/EmZtLriedRTlAgWPiHaBxkf3Z0Bxg8E79XLOroVb5AgoHHkOrcAKQZMQW\n3obE8q9Y54cBPRDfTIkPtxqSSOIrtZlu7OYkMPE2P0OPzAf6b6XgyxPnDfZTRRoa0MWv91JixnO2\ng7fR57hTFj6DnqZMepYTb/Pb6NElFOQmXuNWQ83cMRRGH4dSuQjIASSW3csfu52qvV2m68dLevqu\npeAmyfS9E+/w2+ixldSanniJfg+L8DxdTzNJ1y63g8Ykg3Yjj+zunyKQWozU6gfYvkwKApnr6L6R\nJJoznHyHnzgm1tFc9tiL/HMdWahrA8epbZn7kO5tFr44BbnqKZsk3aQNXDlJHYw2z5dtpN9jM2VR\nu7gDxcNPQ22WIAeTSK5+AJE529g2+lPUPi8d5E9Z+KLUsYst0cWvj+ni1wxfNhONXlztgNnBZvBq\nqsJvG/KES9Wmrtx+wJMZ7UYBxYNPoj62x/JeqH8dkmsfhD8ywPhLG3jCpU6Dl4cvThc4ypj/s6na\nNU3jz5Ek1uqajSan3q5SYOdV7Tz8KWDgRqsWn9Pg5WKTDSplXbndWrV3xiTzdwf6KFiFhsx/RAE7\n+6HDHJDpz1QF5ZMvoHziRUtQ8UUGkFr7HYT6V7s+HgCqhgZuogDX/WXUhsp/5G2lp+Sjc5i8xjqH\n08xSFcULDjxCI3StA6Y5Sq1NFUV+N7wsQlOVOkpHn0X17FswO0N/YgHS676LQHKhNxvD8/XAZuoU\nqQolubzuCA85RPd0J0k3Ur9E55FRtdveg9HF5OTNrVG1BeR3shdB2dpoSNLN31k7R4HYslDLgdhy\nXfTe7MsaQG67t7Y/gHY9i8LoL9CYsE5phAY3ILXmQfjCfd5sjK8hX2ZeQd+uUTeRV7X3KDD96QRM\nwNvg9UX1amix/edsBq+Z6rl3UDzyDDSFv+BA8oUQX/4VxBbeys50jbjNXLwM3sR6ypLlAP8zXgZv\nIE0Vm9PCluopmnfmVZJT6Bllaot9m8Np8BpxM9+gaXrV/p6LeTXZUA3ZLPpxqNqNNPMnUDjwKFVD\nNkTmXo/kqm9wWk4GJL8e2NbbL05oFSlZ4FXtRsJz9aBhs0pQU/WqfadzsiDposydaohHM68HYuc1\nAvXxff8/e+8VJcd1pgl+Eel9ZVl4V3BVoAEBUhRJUZRoRIryLcpLnJ3eme6WNC2dmXN2z87Zc2Yf\nZh5mdx92ZLrV29PqbZGiDFtNmZbo1KIVKRIkAAKEBwjvqyq9z8iIffgjUZER90bciCpAren7nYMH\nREZF/hnx39/e+D+UD/wAeptd+aHvVZFafS8ykx9hZ+1WqDEzG/Igf/fK2q3gBelWGD3K2MtvwTNY\nCCUo2/baYdq+DMy+yK2KDUDE+OsaBVyVt+Ftb12CdCua5+lZ86piJgxDR+PMi6ge/RkMl1dIlHAc\nmQ2fQGrl+9y/F+AH6XY0TptZO8OWqQlg2cfJdgvi9+cw+/BSXl42xIOH8mr1S+buXPFML5Jbg9z0\nw4hkljM+7WdD290dmxVeysvLhtzQPG86YlYZRKUy39BN7k5jQEb3khM3G3JD47RZPmeUnILsaPPK\n2mNLyPmK7Njsw6Xk5JYN8eBZcoqvoGBQ9PUOw6C+Z+F37KxdjZrZ0CZxIl2tRrrD2u4P8LMhNxlr\nB4HC60xH3OtUUDn4Y7QuvSl2PQChxBhyW76I2DAna7e2LIRk9MjaQylg5A7vIN0Kr6zd2rIQktEj\naw9SXmzPmOVzzr4La8tCBB6JT7d2HuUD30e3JL7BKzI0iaHpL3H2XQgG6QMyduj1qioja1/6CV+b\ngX7/DhMg5S3uACp7LV8SpV1xItv8WegUgAs/HdjG3Dj7MsqHfhzsJWslhNx1/xOSSy276rx2F3qh\nPQNc+DkGFkP2egoQRB2bFawNEF67C73Qughc/EcMLIbcNsragmzV1rvApV8NGpXIEG0OCfrOVPMs\n7di1Iv9usxQZYFBGr02/2dIn6lZOofDWd6C3BCJ+BmJjNyK/9cuDJbqRu9hlPiEZm8CFnw1WKmJL\naCNQkKEWhkGbROZeGDw+di+QWuf/egBl7eefGOjdt2b3ofT238LoelUv2Eitvg/ZTQ9Zjqi08zrp\ns2zbR7cCnP8pYFiCj+Ras9fs871FgGxZYQdQtdqyCOm33/eb++iUgAtPDDr21EYKtIJsYDF0cpp1\nS6Cpxk1b5iNIt6I9S/posWX1U8+hcuQfgg2MUMMYuuHfIjG+df5YKGXaMh9BuhWtS9T/tQaai+Qw\nr+1oPEWliNiKcDK4swTIQSiDCt+a2Rt8IonRc74zGskubKtybMzpGJNrgjlLgBaPXeGj+eDOEjCf\ngU0/UuuCv9ekRoCITeGjowt7wTixAmwZA06VCsUcPbpO6URgZwlgcAd4HwuSMeEsJcWXBnOWAMnh\ncIysYz4QTjmy0s7cocDOEgCa9vuoRoI7S4DWsL2UmVgZzFkCtC6StowvlAjuLAGqkNjlSa4KvttT\nUUlXrAhngjtLgDaU2eRpzewJPl1J19At2fZSRIaCO0uAdmv7KL/6gZwlKyEhISEhIQDpMCUkJCQk\nJAQgHaaEhISEhIQApMOUkJCQkJAQgHSYEhISEhISApAOU0JCQkJCQgDSYUpISEhISAhAOkwJCQkJ\nCQkBSIcpIfEvHos4zUtC4n9gXHuH2bHR1WhVoOPBaO8GreWYtRkb5ZCcCiKSXTN4oFOk8V9BodWd\nkzB48zxF0bbN5G3PckmlhdCtwDHHsikw/NsNHdscy/ZFH8S/rOsV4DDuTQ+2eDfouoM+KZrfuCAe\nvXCGwZPph/jXDl03n40FzbN0PChajGHyLR9E63boGs2ptWChazA2ZCM01zuk40Gha062n+bpBd5H\n2z3T6jTeLih6LRrXaIUPYmsm7PNuuyXHs/IFreGYohYbmQ5+PcDJLduZo+8JCr3jkzVJHNdulqze\nBUo7B+fIWpG5ngYWs5jbeSjvNYlLGcPXGzPEit4QpzVSY0MY3v51RNKs8VYKcRfmOcO1eSi+CZR3\ngz18fYg44KxkrF7olIjZnMmCophkrDeIX0/XgdLr5oB4BqKjJrG0j1Fs7VmTT5Ol9CoN+M5O+ZOx\n8Fs+U0tsgmZ4+qHwaV0CLj/DZEExem2U9j3ia2g4oGLo+n+N+JJbOEToK2gWqh9n3DhLfJoMEnEo\nEWD0HiDlY1ycrtH1eEY4udYklvYhY/0El09T79RQ2PMddIsC7DV9qFEiYR7exL6PqQ00m9ePnage\noaHzLD5NNUH6Hfcx+lJr0RrkEUmkp4n5xI+MlX1EPccavh5kTrRWJ65KJp+mOdg8/y7GZy4o7SIb\nzrBlWu0C5nZ9C3qLM+ydATU+ipHtf45wijUaVSFmn6Gb/MlYP2mSKthszx/U8HVRqis1YTK3e8w6\n7FZciUv7MAwd9TMvonroR54iptd/DOm1D3jTe4kqb6cAXHqaTxJ7BYLKq+tA8VU+q4gV4RwRxnox\nY7RnSEYm4bVNRhHl1XUiOK4fdT8PACLDJnO7BzNG8zww82uBiFElFousR2aja2TgGydcTzMMA93y\ncczt+rZntBsd2YL8jf8WatiDQUMJAcN3ApmN3jLah+vzEF9mOmKPmai1Y/RsDIbTGJAxTE7Ti5ZK\nbwOXnvGk9zIMA+2ZvSju/Wv6XS5ILL8Duc2fgxLyYNBQozQs3ou9Q2tQ4NYRyEyTk2aw4LH+y3uJ\nZs+rjK3GTVs24SFjjQgFBKgKkd5MlGFeMroF6VaEUhQsxDzmtroG6fMwDB31k79G9egT7tcDkNn4\nEFKr7xGgU8ySjF5MRFrDpO3jrOtlD/kKOH4/DrPXoqip7pNM2U15C6/xs1SeGO0KCm/9BbTyScdn\n4fRyDG/7dwjFfQ4u5ymvVzbEQygJjH+Qrbwu2ZArstcTuzxLxrnngbo4FQ8Ad+VtmtmQr5KrQowo\n+e3Oj3QNmPkN0DzlT8ZI3nTEjKzdJRviwdA1VI48gcbp3zg/VKMY3voVREc28wmEWYiO0rNmOdjq\nEaDwsrdjGxSEGC0yDEosrQXMPB2AQHoJBYYsR1zZT7Rjvgik2yjt+x7al3c6PlOjWQxv+xrCmRX+\n7mNiBTDGydpLu4nSy09/VokAY/ewh7wLBukOuGXtxR3BSK7H7mMPeRcO0m1IbSR6PKYtexWoCQTp\nFvRaJRR2fxta1dl2CmdWY3jbVxGK+SRhyGwB8rc5ZTQMoHaY6P9YtiecI3pC+xB6D1xbh3mF+PdV\ndvYSShMHXWeWFJu18Owlp/YMOQ1mmQ/Ep5lcSwuZUYYwDAOtSztR2vvdK9+Xm34YieW3sxdpOEfM\n5s1zfD5Lu/I2LwAzz3KyIZNPM7Gc7gtv4VlLTnoPmH2OHzVF8lT6aZzgZ54hs+TUL0c0TpMjYvAX\nGrqG2omn0K2cRnbzZxBOjLKvmZkG8mbJSdfoN/P6ndExYPhW4rLk8VmG0uTkoiYLe/0dItVlObY+\nn2Y4S4uZqQ+2rF3vkCHhZUOxJXRuZR/pLQNUcvom9BbpVmLZ7chNfZ6dDSkRk9s1wuezhEJ8hEMm\nrZHWNMt87GyoNbsfteO/QnrtA4iPcUrukREzWDDL5y4tC6gxKt/DoCCUSSxty9q1mlnm47C5JNcQ\nz2npTWbf1jAMdEvvYG73t+n3AkivexDpdR+GojKYe9QEfX+vweezVEJk7NMb6P+dEmWVPLLjXdq3\nRwAAIABJREFU1HogM0VZIi+IsGbthkHGmNeyCKWoxdAt8PkslQgw+r75rL09Z7Ys2Psi6mdeQuvi\nG8hu+hQiWU7JPbGanLsa9g7SwxmSsX2R76DVqGnLTC5g1yBdIT7NxEpag4zs2DAMNC/sQHnf34Hu\niUfLIjJk2rLTbD5LwJm1d8tUuWTuEVCIGzh3U6A9CdfOYWo1Ig/m9Uky1wF5C3Fpp2iSsV5inx9b\nStlXg5MNRYZowfQpwjzIWHWthfqJp5Facx/UCKscyCAubc9SOcu+iaWP+Cr6uxYnG4qOkIx9p+VB\nxgo1CqSvJ649niEb2kZy9inCWhfpPvJKO4l1pPxt9gaUTuk4yvsfgVanDSFKKIb0+o8itepudtlE\njZPjrOxhZ0NKmMq42evmKcK8SvOpjSR/x8WQjdw5TxHWa5Ph4xmKUIquWdkDriEbvhVIT83TbzVO\nAnOvMI2ZYeion34B0fx6RDIr2Qs/sZJk7Ge4vSY5zTqnjxfOAom1Jq+iUxf0Tg2Vw4+jeeH1+duw\n5GZkN38GoSir5G4as8ZpflCWXEfGqe9Ytbq5Zjn6G8kD8eVAdT9TRoQSVG3pOwSPqN/QNdROPoPE\nklsRTnKCsvRG4jrt96W7FZKRV6aOjND64upCmp5LcmVfCAoyi29w1liI1lftkHuQbiW975RMW8YJ\nzKITQCTD1QUivX90nl5QUZFafS8ykx+BEmJk+koYyN5IDsYtSB+6ed6WdeYoGOWVqeMr6LrNk+zP\nI8OUsfUpwoweJT3lt8C0t90GaieeRXrt/VAjrJaFSq2e3NZ5W9a+TDJyA7N1ZFPLu9i2JwjpvQ1X\n32EahqmAO9gKGMmbjo1R0/f6W7Z0FD3ktrIjCC/lZSE6SoSyrBtt6FQKLu0UL5f1s6HsDWxeyc4c\nEbzyNg+wEFtC95FVFvVQXhZ0rYXq0Z+hceYFsIxhJLcGuemHEcksF5cxvtx0bAyDrmuULfCydhbU\nKBnP9CY2r2TzvOmIfZTLEqupjMnqoeod0kWRfvEVGePkhFKTbBkbp0lGTlbBQvPC66gcehx611li\nUyIpZDc+hOTy28VlDKWospNc4/zMMKhSUXiFnLwo0pspUw3FnJ9pDcpAOFk7E+EM6Q6rP2kY1B/n\nZu0c2IP0ARlr9Fz87Fq3B+l2GasHKZATtGWG3kP95LOoHv8Vk8c3lBxHbvqLiA1vYvw1B/YgffAL\nqZpSesNH6Z8RpFvRKZi2zEfpPzZu2jJGO8wj8WGCFaQHxNV3mNXDlIU54HGjrRBV3ui4GUF49B1F\nlVcJUXlM5EZ3y+SIWVvzrYgvJWXwIkwWVV4lQoYpM8U2yFYIKm9r5m2UDz7mTZishJBecz/Skw9C\nYRmdPtQYldBSG7xlbM+QjF2PXXXJtVRO8tql65W1X5ExYTqNtd4yemXtfaQ20O/22qWrd2hDBq/k\nZKLXLKB88DG0Z93PA4Do8BRyW77IL5/3Yc+GuF/epsywdtj9vHCW9FuEMLlxkrJDXqYGYD4b2s52\nbAMyNskRe/XgI3kKgL0Ikw2DrlV41WOfgEoB+tBNArbMI2s30SmfospOzXuDV2L5HchufAhqxGUt\neAXpVnQrZknT49UstyDdiitZ+w73fQJKhAKYzLS3jF4VyD7cgvQAuAYO86C5dduC2IR5o/Pikrop\nrxI2b/QWfxGEm/IGudH9klPhNeeWfyUKDLtkQzy4KW9iNRl5P6+f9JW38Drs2+l7nSoqh36M1sU3\nxK8HIJScwNCWLyGa3+D8MDVJGVbIY6eoXcbyXnNzhi2KDCXNMt8aXzJS+fwldskpvcks8zGyIR50\njTL28i7nZ27ZkBtal0xHPBioGIaOxunnUT32cxj29/FcoISiSE9+lL3rMJwjp8HKhtzQPGdm7fZe\nIKNlIQK9Q4Fr9aDzs8iIWebz8WoH4JK1+wjSrei1zPI5Y5e3aJBuRT9rn3vFsZfD6HVQPfZz1E8/\nR+tAEGo0i+zUZ5GYYGyUEw3S7TLysnY/QboVWtW0t4zEx96yEJWRl/j4CdJ94No7zMRqapwH/RG9\nFnDmkcFjPrcGD8AwgAu/ADqWSCW1gZrxQWXUGsDZ7w8eW/EF71cl3GQ8/5NBQ5rZQo4oqIyty8DF\nn81/Ra+DSy/9bzC6QQcxKBh7z39GOGkxbrlt/t9PtaJ+gl4d6UONAys+650N8WDowJnHBo1U/t3+\n3k+1o7wfKL4y//9whvTRKxviytgDTj8yYABK+76H5vlXA4uYnvwoMpMfmj8QGQaWfjz4IAZdA05/\nDwMB19h93q+cuGH2ZaBmcZqxCWDJR4KX0PSOKaPFTk18WCzz5eHSr4GmZaNdYiVtNgkqY68NnPne\nwKGZ3/0X5i5SUQxv//eIjVh2RSfX0SagwPa2AZyx2bLln6OeaxAYBnD+icEKUnqK2iBBZexWgHPW\nVwQVYOUX/QXpguA5zKs36SeUWJjHZ5W3Qj5enrdDUQD7jsZQcmEyssqEC5XRboAXWUZD7y3AWQKA\nAcPeZ1nIbwacCq+EgztLgAybPbNYqIxhmz4qkeDOEiD5bAZYby9g4hXg7HWqsQVNLYIadureQu+j\nasvu1fjC+k1qFMBiy2jTPTWxMBkZFY0FP2vN1mdeqJ1g3TM/w0rsYNmy8CLLqKhXxVm6Qc6SlZCQ\nkJCQEIB0mBISEhISEgKQDlNCQkJCQkIA0mFKSEhISEgIQDpMCQkJCQkJAUiHKSEhISEhIQDpMCUk\nJCQkJAQgHaaEhISEhIQA/mU5TPvUosUgx15s/CHIeLWxGL/5at83KePiYFGu/4cg41XGP0cZr7Yt\n+z385qvnMNuXiDEkCHSd5i/aMfuiJ2s7X54ZmuFpRe0gMV0Ega4DM887j8++QJ8FQfO8k0Ks+jbJ\nHgS6RjMdLVDCcWQ2fybY9QBER7YgnLQxzpR30cD3INA1k8Heeqxu8jgGRP0duoYVxR00WisI9I7J\n22qBVnQe84PqIccc4symh6BGg40iUyNppFbdPXiwc4nInoOivBf2OcQovEKk1EGg1ZxD3Vtn+Typ\nIijuhMNhzr3kk8jcgk6JhsVb0ThO4xuDQNdNsu1B5Ka/5G/OrQXh9HLERqYGD9YP8zlpvaDrRIRg\nx8wLwW1Z65KTham6z2mDRaHrZFsHD5LuXEPHeXWHrwcZguxKXAoamzb6fvF5lroOzD3vzmxgJWMV\nQfMsMPNP/EWpRoGxe8WHcusakTq7MRukJoGR9zsZx3monyAF47C09NoVFN76C2jlk2LXU6MY3vpl\nREem2DyQAFE9Db9HXMbaUTJuPJaWUMokvxbktdNawMzTfGJggBgx8u8WH9FV2W8aPI7hCGdJRi8m\nhysyNkwSZjZLi6H3UHvnl6ideFLsegBSaz6AzPqPs0mYAWLtmPig+MDrboVk5NKlqcQjmr1eWEYU\nd7gzyURHgfEHnSMIeegUScaek/qMECLCgsxmzuc26DpQfNWd0i22BJh4QHxsY3vGJIpm06XpWhul\nfX+H9mXGYH8OclseRmIZh/QeIJsz9gEftuw8zXHm0aUpUWDsbiDJIbK2Q9eA2ef5pPcAzb0dvduH\nLTsNzLJJ7wEQh+fIncHn3jJw9Yevty4Qqz2PC9OLZkfXgdnnxLnzRJS3cRqYec7JKMKCEiYZU5Mu\nMmqkXKLceSLKWz9uOjaBzFmJkGN3U169Q89BgAfUMAy0Lu1Eae934cY5l1h6G3LTn2eT2Nqhxug3\nJ5byz9FawOUn+SS2dqQ2EguD2wKrvG0yswhExKEkDdN2Y8fQaqZj86A+6yOzBcjf5i5jcRdQZmRE\nrK9vzGJu1zegN/jOX42PYmT71xFOedBXAbjCQJ+/xf20wmvE+yqCcA6YeNDdUHXmSB+FeEAVYOhd\nwNCN/FN0nbLcGoP1hIXoCDD+Qfe5qF5B+gBUIkPITrvL6BWkmzAMA93SO5jb/S3XzD2a34T81j/l\nkN7boIRovaQZrEJXZBQI0q2IL6c142rLTpCzFLVlo3cDqdUuMnaAy88CLYEqoBI2KRp9MlnxLnfV\nHSZg8ln+FmieZn/OI3KtnyJnyXC2ht6FoWtQwxy27uHb6CZZoWu0AHg8b2qcvzhiE6QY9uHvLtmQ\n0evAgAGVRRvFU95ei2Tk8by5yRhfRkww9mChcoBo0VhOQ4mYsjNY0bUWSnu/i/bsoKFUoxnkt30N\nkcxKdkTrJiMvay/tAUo7wHIaercOJRRnZ0pqlJgyEjYi627VzIY45X83GVPrgZH3OZ1c8Q2ThJuh\n+2qMH42rcdIdO0m6VzbEkdEwdDTOvITKoR86Psts+jRSq97vpPPykjGUokDTTpLeniF95HBW6p0a\n1CgrQ1WIe3H4Vtsf6LRe6pxyq9tzCWfJyUVtNFXNC8DMs5zfppCO8D7LbQfy25wyugTpvU4VIV6J\nnJe1uwbpJikA085pqBz5CRqnbW0eNYz8jX+G2Oh1/tdgdMwMFmy2rP4OtbcYjs3odWAYOlRmph8i\ntpGMjcjaK0h3tWVLTUdss2XVQ2Y7iWPLoLMrU9Exk4ZNsCrFwbVxmIDJAXfc5IBj3KRQmtLn5Eoz\ngniGS8bcKR5D+cCj0LUWclOfQ3x8K/s7rcpbPWzeaMbNVMJEopuZptp38TVOWdVSctJawOWnnPV4\nE+3ZAygffAyAgdzUFxEb5USeVuWt7KNInqkMfT7NjR5krBbl1erApSf52VBiNZ2rd00yVqdiG4aB\nTvEICrv+EtBbSK19AJnJj3KcV5yi7NQ6ykZKO9nKq4SJPi21DuiU6T46+BUJzQs7UDn8ONRoDrkt\nDyOa40SeiZXkONUwZZSVvWA6tlCSfnNiJfUay2+Be7/7JSevbKjPp6mVyeDw7ne/5AS4Z0N9Ps3Y\nBN3DytvM39LrVFHc/Zfolo8jnF2D4Zu+ilCMw9/aD0rbM/SsOfcbqU303QAw9wJQP8Y8TatdQOnA\no9Bq55DZ8AmkVr6PfT1r1t48Z5b5WGvLwqfZOs/hs7T+lncD0MkJNU+yz+vzaYYzfD5LAAhlyE5E\nhzyD9No7T6J28hnEx29EdvNnEYqxOCYtWbuuUfmVlw31+TTVOOkEp2TZrV1AYed/g94uIb7kFgxt\neZhd2bGS3tePsfks+zLm30X33CNIbxcOobz/+4DRQ3bq84iPcUru1qzdK0gfvpVaNdVDbD5LAGRv\n7wCyU54tiyt8mkaP+q5tlu8wn0vupsBsPdfOYfbRa5nM7ZwIM7bMNNysjKeJ6pEn0Dj7MqwGJD5+\nE7JTn+MoLyh65i2+xEoyoGFLxKg1XJUXatLkVGRnQ5XDj6N5/rXBr1n6bmQ3fYoTjYMMC495PrmW\nFMdaPtJqZFR4ZeBQyrweKxtKUB8nuXa+Z+dGxgrA6HWhd+sIxTk9udQGyuqtGXi3TMaZE/gglOZm\nV71mAeWDj6E9u2/+oKIitepuZNZ/jFMGVs1sghO1ZqaI+NYatXYKtMA6nBJnKAP0quzPwlmTKNqS\n3Ro96smVdoFdBg5TaYiZaSgUjA1tH6y2tGdMR+zcQGUYBrTmDMKJMXamEclTJcOa3eqa6Yg5QYVi\nfjfTafRQO/EUaieeGthoFxlaj6EtX0I4xSGkdruP0VGSMTZqkbFDGX2VszlJiQHQOH3uEN3D3A2D\nZbjmWZP8miOHi4yd4lGU9j+KXmPeqSjhJLIbP4nkivewr6fGzeCA5TQsQbpVxvpJoPBbpi0wDB29\nZgGhxAj7WbNI73tNcly8MnAoQbycLHvbraNy+CcOLtb4kluQ3fwZfpbtam/NIN3KDexVgXS1Zf0g\nfXLQltUOU/LBWmfhHAUpcZf2EAfX3mH24aW8NrRm9qJ84AfQ2+zo3VN57WDdaDtclJeFfjakd9i/\nSY1mkN30aSSWvktMxlCSHCVvI5Nh0EIovCrYZ4GZDd3K5hUFTOV9RbyHEUoDo3dS4MGT0U15Hafr\naJx5EdWjP4XRY5cPQ4lR5Ka/gNiIS7/ICq8FYugeWbsdZrlxaDs/Uu0UzaxdcPdfZNjs53P6p4Zu\nccSczVADENhY154lGQV7xp3ScZQPPAqtxsmW1DDSax9Eeu0D/I1GVlizIV5/qXWJZBTtGceW0rOO\ncIJnvQuU3qRqjkDPmBekWxEd3oTc9BcRTor0jMEO0ge+tENVEtF+rBqjYDW1gW/LGqfIKQn1jIHm\nxZ2oHPoR9A67EqFEUshu+jSSy94tKCMjSLfiSgXy1UGCdzewgnQrtLqZ+Jxkf56ZokqFD/7a35/D\nBEzl5ZecANq1WTn0I7Qu7RS6ZDS/kZQ3NcE/KbWenCXvRg/I2KGsq8pX3l6rgPKBH6A9+7aQjLHR\n65Cb+gJCiWH+SekpikBZ/U+nAO4lJ4CdDfFgGJRdz73iorwKGbqhm8UUzitrB9CtnUd5/6PolsU2\neCWWvRvZTZ922fDgswSjVc1I12XzFisb4sEjayeELI5NYFNCtwTMvswpOZmITZCM0byAjDqtv9Kb\n3F3JutZC9djP0Dj9AkScTDi9zCyfu+xYZ2VDXBl7VDov7QZ389aVlsUmsZ3O7ctUWWBk7X20Lu9B\n+eAPoLcFXoNTI8hMfgSp1ffygwWRIH1AgAskI3dXMuhaw7eJkWN7Ze0Aeq0iygd/iPbMHu/rAYiO\nTCM3/QWEEy7rod+yELVlbhVIYL5lIfq2Qf0E2R5W4rP0E+6b/Gz4/TrMPtoz1IuwKUbj3CuoHP4J\nDE0sw7sCNYLM5IeRWnP/YOnC2if1i9YFktESoYlkQzwooRgyGz6B5Mr3Dcq4gHIBmmfoHdCBbFMg\nG+Kh1yJjb39HLjJMMrrtbuahfsLcWDCfbRq6htrxp1A78bRghjcPbtYeHaOMLeoSlLDQz9rnXhqU\nRQlRcJC93v9uO17JKbaUsvOI4KsnVhlrhygat2abSoSqB5kp/wz23YrZ+xnMHluz+1A58Bh6Lb/v\n0ypIrno/shs/CcWqdyLZEA+dIu0ct+8bYLUsRHAla38T1kCAgvQfonVJ/LWOPsKZlRi67o8RySwb\n/MArG+JB14DybvpnRShFWWrSZTcpD62Lpi0bbIfUz7yI6tEnYPh8n1YJxZBe/1GkVt1js2U+gnQ7\nmudIxoGA3WeQbkWvbdqyQ4PHF8lhXttJP7Exej/RAq12AeX9j/h3lgCgd1E9+lNnaXTk9mDOEiAH\nlhvcXNQtn0Dl0I98O0sAMHpt+lu7cgZ1lgCVejK2MmViBTXYgzS5Q3FyOnZ1GHt/MGcJUHnZ9opO\n69Iu1I7/0rezBAC9U0Xp7e/CMGyZx/h9/p0lQEY8vd5ZYk5vEs8C7QinaeOLHRP3+3eWfRkzU85d\nt9kt9FqDX0cEUKY38cDAIcPQUdz1rQDOEgAMNE4/h27V9tJ8bittXAsiYzRPm8WsUGP0rP06S4Ce\n5dBNZNgtqB77eSBnCQBa9Qwqh388eDCcoTXj11kCtG7ztzgzyOHbgjlLAIgvoQDagk75FCoHf+Db\nWQJky6qH/95pq0feE8xZAvR32esGj8WX0e/26ywBym4XYZcsD9d+NJ7NEBmLMtZKjsa6Oghg7Fzx\nz/FZL/JvZDqIxb6Pi3y9f5b6vdj3jIUF/m7HfbsWMi8UV+NZ/3P83VdHpn9Zs2QlJCQkJCQCQjpM\nCQkJCQkJAUiHKSEhISEhIQDpMCUkJCQkJAQgHaaEhISEhIQApMOUkJCQkJAQgHSYEhISEhISApAO\nU0JCQkJCQgDX3mHaXvZVRNnL3WAfOs2ZlSkM2zQZJSwwG9ETthdp7RNr/ML+9zpvhqmvi9r+u8j3\nMcgEFAfs93GhL5/bpg4tyn20f8dCn7XtOTBps/xcz3bPgkzjscO+Bhd6H+33bKG6yLrmQm2PfRoU\nd46wDyz273aswcWwZfbf7X9y1+DfXwNbtki4tg6zMwfM/mbgUDg5itHb/xNUO1msCNQ4hm/+D86h\n3DPPA2WxAekOVA/TLEKrjOkVGLn1PwYbyxVOYuTW/+h0upeeIo64IKi8DVRsQ5PbF4ELvwhmTLUa\ncO7v4VCyi/8oxBrPRHEXUB+cTRsbuwH5m/480Pg+NT6KsTv+s5Mw+fxPiLQ3CAqvOee+1o8Cl389\nQGkljPYccOYx5/FzPyLyY7/QdXPuq40JpbofmHmBPveL1iXg3CAhtaKoGH/v/4lwJsg4SdWcqWob\nkF3eZTJSBJCxeRa4+PPBY4YGnPkBzZn1C10DLj3joPTKbf400pMf9X89ALHRG5Df+uXBg70mcPbH\nRGruW8YOcPGXTjai2ReA0luBZETtCA0jtyCcWoKRd//vUHmUXW4IJzFyy/8KxU4uffnXxIsZBJX9\npCtWdC4DF35OM679Qu+S3nU4fJoLxDViK+kPFuaw2IPmWdaOP4XaO78QumRi+XuQ2/xZKCGXeYPh\nHDDxIBARUA6tYRJF82+0ofdQPfoz1E89KyRjcvV9yG74hDsFUmTEJL8WcMbdKjlazY1VQSWmhKwg\nJVbxDdfnAoBYMcbvF5uR2SkRmTWH/xIgVvfS/kfQuviGkIiZTZ9GatX7nc7SivgyYPwDYllDe4aI\ndN3o3JSISX7twsTRh67TEPe6C/MCACTWEFm1SMDQvADMPMshBTahRolMW2SOp65TsOrCImMYBpoX\nXkd53/fAZQuxIDoyjfwNfwI1knCRMU66Y5+Hy5RRI+JpNxYZgBh+hu8AVIF4v36cnI5LFqQ1Cyju\n+ia0ukBQo8YxvO0riOY3srkqAVwhQhi+1ft6gDvpfR/hLJE2iyQWWgu4/KQrnZuh91B95xeon3ha\nSEQasP/Q4IB9OyJ5srdhHquQVcaaSRTtFgCpxExjnzXLQ+O0SW3GsD1/MGwlItQ1FpDyfgtanc3F\np0azGN7+dYTTy10U1obsje7KW9wFlHdCNI3X6pcwt/Ob0FtshVTjoxjZ/jV36rEBKEBuO5Dfxj+l\n8DqfCJiFSN50xBwi684ccOlpYd48Ut5bicWDBV2naFaQ288wDHTLJzG365sUrDAQzqzG8Lav8gnD\nHQjRIOjMJr6Mcy8QQ70oYktoWDnPETfPkZEXzeyVsOmI13Fk1ICZ34jzlAI0QH7sPr4jrp8EZp8X\nLhnq3QaKe/47OgVO1qBGMLz1K4iOTImvweQ6YPRuvpOrHTWZYwRLkGoMGLsfSHCIrHstCooEeUoN\nw0Dz3CsoH3iUe05i+Z3ITX0GiuhQ8FCSggWeoRYI0h3IXGdyO3LuY+ktoPQGhG1ZYwZzu74JvcEm\nVlfjwxjZ9jWE06JEEQrR7OVv5p9S3EHsMaK2LDwELHmQb8t6TZP2kLOu0xspifBRgr/2DtOLXzKx\nmjj/GI6UlPdVlA88MnA8ve7DSE8+CIVFlKsmKNLm3TSW8nZKpLA8cuvkOuLTY0QshqGjfup5VI88\nPnA8s/EhpFbfw86GQinK1hocHshQhpxc1MJs0Z4FLj/NzYaaF15HdHgzx6mYPJH5W+YP6ToRetvK\npVcQzpKz5Rns8BDJaM3aWxeBy89yyK0V4iVtnmZmS4beQ+XoT9E49WvLURVDN/wx4hM3sw1yJE+L\nh5eJREcoGrdm7Y0z5IiY5NYKkN5AlGRMp8LI2nUNmPknLnt8p3wKRq+F2DDHebOydrdsSAkR+0v9\nHbZTUULAyF3EwHJFxg6VInmcmrEl1D/qOI2lYRhozx1A8a2/HChPJ5behtz056GEGMZHCVMgUDsG\nZoaqRMhppizsG1rLdBozzvMBtOcOQI1kEMlyysWsrL3yNgWYLBnUKP1N/ShYBlvv1FHY8x10i0ct\nf5LD8Pav8YP0xCqgW+YnBan1wMj7Bp2cW5Cuxol9iGfL1ISZtVuYhDpl05axiaCRXEOOmWHrDEMn\nyq9DPxo4ntnwCaTWfCCgLUtToGllEvII0psXdiCa34BQnMXvqpiJj4XezzDoHhVeZVdi/PJpWr/t\nmjrMxkkzNWYY+VCSyimptWapdhc32tA7dRT3/BV6nSqGt/05wgkOZUt6E/EDhuJkvOdeImfMQmo9\nMHwXUPwdUONE0NYbrXeA4ptAdR/z1F67jMKuvwAA92wos4UclxqlHs3cy3xHnZ4G8rcBhZe4ZNFa\n/SJK+x9Ft3QMSjiJ7MZPIrniPezrhVLk5HotMxtilflsfJpuz9B67uxzfKbzyDDRhsXGzCjwVW5P\nlLL2byCSXoqhG/4N1DCrzKfOkzBDpWsVXuU76qHtJOflZ4DWObaM0XGTDmiYmNvnfssPFvolp9YF\nYO5FpuMyeh1Uj/0c9dPPAYaOxPI7kN34ENQIq+RulpxS692zofhSIoqO5IjPcu5ll98zRsFCwyTT\n5TmuPp8mDKB6gKJ+hqM2eh2UD3wf7dn9yG/7GiLZVRynsZLWTDhNfcY5Ru/V+nvG7zdJt3eAvfZr\nqBz+ezQvvAYoKlKr70Nm8iPsFowSBkbfT3p28Ul+y8LKp9meJRkZZUvDMNCe2Yvi3r9Ges0D7kH6\nyB10XaPn3nZSosD4PRQUuwXpVj7N1iXTlnHKlsl1wMj7gfLrQIVtn4hP804guYr6e6U3zXOdMvba\nFRTf+ksYuobhm/4dQnEOJV1mmkjv1ShVWOZe5jvq9GYgfwdQ+C03SNfql1A+8H10ikeghOPIbPgj\npFbexfk9SdJvNWqug7OMkxSqhA1tD0YRhmvlMLUGLVJenyQ9RTfavlPLQ3n7P8CBcIYMib2Ho2uk\nuOXd8LdbyoW41EV5XWWM5ElGew/HQ3l5MPQeaieeRu3Ek46NKdHhTchNfxHhpE8Oy+goyRizsal7\nVQm4CM07Nnt02jhNis6IMonrUmHfx9gEyRi1RZ+9llmOYQcWXCgm/2Bmy6CMhkH6O/eKjdTWG+25\nAygfeAy95qAeq9EsslOfRWJiO+cveTJGyaGmNw3uZDUM+r2F37n3OFlIrCYjby9vaVUzWHBm7a76\nrcYp+05NOmWsHiT98bl7tHlhByqHH3fw3IaS48hNf5GftfMQSgLD7wFSawaPGzplo6VxtDkGAAAg\nAElEQVQ32cGPofP75ulNVBq127JOgYjTORkzF7xsyOiRLSvthkhfeQDWIN2K9mVqk3Wd/Kfu9jZH\nAXDcVgbXNaC001/LCGTL6iefRfX4rxw7Y6P5DWTLUpySO1Qw70dkxCS9F+9XsnD1HWbrIpUOWb2c\ncI4Y5+PLnJ/1YejkPEpvCPQx+hHEze4bKPwob2TYvNEuzsaX8pqktbmtzi33Vrgorx2d8gmU9z8C\nrcbu79LXRpCZ/DBSq+9z32wEkFxDN9O9dNtQ46cPHVtKz9qNMFnv0Gaj6n7v6ykRCrIyHoTJzTPA\n7Muum42uIL6CjJPbZrBey2Ru55SuLdC7dcqGzv/O9bzY+FbkNn+OH7lbYc2GuDI2aEcgryxmhTUb\n4t1HrxKXHdZsiAetZjpi753MvVYB5QM/QHvWbYe7Ymbtn+Rk7Takp0xidZf+lVfWbkU4azo2l41W\nhk66XXxD4JULlyDdCq+s3QpekG6XsbwHKO2C62ajvoy5rdSbdLO37VmqvAj0ZLuVUyjtfwSanXjc\nCjWM9LoPIb3mfm9bhhBllLkbgpG/23D1HWb1ICnd4BUoy8htE3+VwLPkNEK9Gns2xIOn8vbLfFvF\nb7SX8vKyITcZXZRX77VRPfpzNE4/B9EILpxZiaEtDyOSXcU+Ib7MLPNl2Z87hPDY6axEzGxos/h7\nfV7l88Qq2sTDa/Y7ZOxSwMUrT6kxMxtaLy5j8xzJyCmhNS+8gcrhHzuyIR6UcMIsn9/JPsHashBF\n45RZPuds4EpvNLMhwfdgvTZRhNJmmU/wNRTDIKc+9wqzfG4YOhpnXkT16E9h9MQyZjWWQ27z5xCf\nuIl9QjhHAXBccLOKYdBrGMXfcTZw2VoWIuhWXcqGEAvS7TJeKZ9zeu0iQfqAjCXz1aWL7M+jY5RV\nWnuRrjLqlGmWdrq0LH6B+unfCL+fHE6vQG7LlxDNrWGfIBKk+8S1d5jhHDB+Lzk4v+gr79yLg8eH\nbvbn2KzoVum9QmsGEhkBxu4Z3GTjR8bqAcd7Thi+3cyGgshYMt+lnDcqndJxlN7+G/SaAd4rUlSk\n1j2I7ORHrAfJ2NnLfKLozNF9tBqV+DLqIYlsJ7fD6JFxrlr6yf0NLPYynyjal+mdNmuAlFhFCz/k\n8goED7pGm3EsmZyuNVF6+2/Rntnr/3qgktPw9q8P7rhMTVLpMMjL5XqH3oezBppqnDbEBNj0AIDK\n55efwUCAlN5MWWWQ3lCvRZs+LJuMeq0iinv/O7qlYO/7xsdvwtCNfzJYOs1eDwzdEuh9X2gNei3K\nWvEJZ4Gxe8WDdCv6Wfvs84PHc9vIuYk6tgEZa8CFXwI9S98wkicZRYN0u4y1g+arLRbkzVc6Atmy\nMnDhHwF9fg9Ep3wCpb1/42hZCEFRkVp1D7KbHho8PnKnvyBd9Os4DvPqDS6ILw3mLAH68axXA4I6\nIoDKb3bHmFgRzFkCJGN2i/O4vSfmB5EhR8bXmtkTzFkCgKGjeda2CJQwkFmAgkVHKAuyIrkumLME\nzN2f6wePqQna7RlUxtg4OQsrUuuDOUuADK8t4+s1ZwM7SwDoFI9C12zZVmpjMGcJmLs/bRlfJB/c\nWQK0UcRu0NObAm+kQCjuaMt0K6cCO0sAaF3e7cxU0lPBnCVAJfCorf8VWxLMWQKkw+kNzuOZ6WDO\nEqCKiz3jiy8P5iwB094y3tvOLsSW5Ry2rD2zL5izBABDR/3MC7aDIdq4tsjO0g1ylqyEhISExB8e\nrp2fvALpMCUkJCQkJAQgHaaEhISEhIQApMOUkJCQkJAQgHSYEhISEhISApAOU0JCQkJCQgDSYUpI\nSEhISAhAOkwJCQkJCQkBSIcpISEhISEhgKvnMPUWjVwKCtbsToEB5a7o2gZzty8TP2RQdBgzUHlz\nUUWg60QxZUEk62OmKAPhpG3av6HRmMCg0HUacWZFm00+Kwz7few1uaTSQtB15/DwBcs4yFITio8A\nYcHZrCyoYSgOpgufDBd22HWvW3KwQPiC3nHOA2UwCvmCjXornF6OBZmhcNI5jWbBMtqoqjozC7MT\nGoMQYKG2bLFlZNmyDodWTASG4ZhtHOHNghWEg7nEYNiiq4yrO3w9vsxkheBwRPJQeJ1PFZOaJA44\nHuM4C27EpWrcJGN1mexvh67TDNkah/YqPUUDtP3I2LpEczsZw6m1ZgHFXd+EVucQATOhInfdv0Ji\n6a1sqp7sDTQs3Q+a54g0mUnWmiWeuqiPZ61rwMxzQPMk40MFyG0H8tv8yVg/RRydrOHUkTzxgooO\nc+/LyOHTNHQNlSM/QeP084w/5CO+5BYMbXmYTcLc57P044x7LRc+zRANsGeNmnRD5QCxlrBYeWJL\ngYn7fTHYQ2uYRNHOMY+61kZp3/+H9uXdvkRMrf4AMhs+zmaySKwExu7zNyKvW6U5sixWHiVKc3mT\nHDIDHopv8AkLkuuIUNuXLSuRjCxWHjUOjH/ASb/lBl2ngfM85qDUJrLhfmRsz5A+Mrh0e60iCru+\nDa3mwlLCQG76YSSW3+60ZWoCGLmd7uUijsi7BsPXDxGrg+MighRSANHDXH6aQ1psvaag8uo6OXEO\ncekARJW3dRG4/CyHtNgCNQ6M3+fNlqDrJgmzO0WTYRhonnsF5QOPul8PQHR4Cvkb/8Sb/iiUpGDB\niztO14h4msGV6EDmOhra7HUf68dpoLkX/VEoTaTNXjN/9Y7p2LyCCpOqKH+Lx3kAqofNgdTu9Efd\n2gUUdv436G2P6kI4iZFtX0Mkt4YdxFhlzL/LJMr2QOVtCjC96OaiI6Yj9tAJrQZceopPWnwFKgWF\n2SlvGUu7iL3ChWnHMAx0Su+gsPtbgH3Grv2b46MY2f41hFMeQW5/iH96vft5gHuQbkV8Oa0ZL0fs\nFqQPyBghu5Na7X6eV5BuRXKNacs8ZHQJ0gegxij4SLjQM/ZlnHuBz3JjwjAMNC+8hvK+v3O/HoBo\nfiPyW/8MasRjVrVfZiMPXH2H6cVn6UbLpevETOKXBNhNeZvnycj7Idh1U15dMx3bSX8yuimvWzbE\ngd6po7jnr9ApHnF+qIaR3/oVxEamPQyyDan1wMj72E6udoyejSdHqVWOhJm1M2iLXLMhF6SniQmG\nJWPloMka46MkFUoDEw+waYtcsiEeDENH7cQzqB37GfPz5Op7kd3wCSh+Mp5wjjJiFgWbVgMuPuko\ncbpDoeB1iEOJVXzTP+l6ZNjM2hkGrVMi59sTbwEYuoby4b9H0zFom5DZ+BBSq+/hEzuz4Ja1iwbp\nAwhR1pXZ6PzIT5BuRXypacsYWbtokG6FEiYGIRZNnGCQ7kBiFTGisHS4cZqqRQaLGo0NvdtAcc//\ni07hkPNDNYz8jX+G2Oh14rZMiQD5WxdlIPvVd5h9uPJZMjjlmmfNMp/zRht6D7WTz0DvVJFZ/zGo\nzDKVreSka3Q9HmFtdJSodSp7+Ebbrrz1E0TPw8iGjF4X1eO/BABk1n0YSojB5GBXXr1DC6DFIYKO\nTQDZG4HyLmY/xjAMtGf2orj3r+n3AkgsvRW56S+yy3xKmOiO9DbfICpRWgxJk91CawEzT/N7f/Hl\nxHBQepOfjSQn6Xf3nVxlP1F5sRybEqWsSiubfJYMGe0lJ61uZkPsflDr8h40L7yGzIZPIJzkcA6m\nNwHDlpJTaTf9Jt73528leqoqO9KnktO3oNXOmX8yYmZDnDJZahJIrCayal42kr0eGLp1XsbCDtJf\nhoy9VhGVI/+A2OgWJJfdxr5eOGOWz82svVMwsyEO+XZ6E62JwuuA3mScoBC5cP5m+q+uUzm3doBx\nrvn9+XdRlaFxgnlKt3YehZ3fuJK1hzOrMbztqwjFOCX/zBYKyouvc4JkhZ5d7oZ5Gd2C9HCOqhC1\nw/zKSnQUGH9gPmt3DdJN2xdOu/NZWrN2jyC9Wz2D6ju/RGrV3YgNc0rusSUUGF6xZW5BuskNrIRo\nDbCCZCVMNHmpyXkZOS0LAEB0nCo65d3MHr1hGGjP7kdxz3eu2LL4xM0Yuu5hZ48fmK9YGhqtVWbL\nYIKSs6BMVLiWDhMwOeCOknHk9buGbweq+8hhMtApn0B5/6NXDE8oPozs1OcRH7ue/Z3RESA1DZR+\nxy7z2UvDhkFGr/g6X3nyt9KC5pCrtgtHUD7wKHoNciqh5Dhy0190Ud4JKv0WOSU0JUKGJDNNEZKh\nU8mNo7x6r43ywceRWnknItnV7EgsvsLsI2fo/50CMPsif4NJfAUZx9JOtoxqjEqu6Y2mjD3q0fCU\nV4kA+duB6l4Xx7qGDEU/S2lfJlJb3saI5FognAcqbOffa1dQOfQjtC7tNGWOIDP5YaRW38fud6kx\nIH8bBSj2zRR9pNaTzvZJmFsXSEZGv8swDDTP/w56t87PhkIpCvSSZjVD71C/i9dLUhOkj6Ud3Gyo\nfuZFVI8+AcMsaUZHppGb/gLCCQ41VXqKdIyXDYWzpDuJ5fT/Xot0t8Y5P5SmwKz4O042pBC/4tDN\n8xRh9RNUHWD8Jsran0Y4MYr4klvY+h3JExF6fw9CrwHMvcrPnsI5MuBuRNG5rRQAqOF5PsvCqy6O\ncBvQnXEP0kfeO19d02pU6uedHxmmAKDItmX9IL1+8lmT2kxBYvkdyG78JKcNowJD7wJap/gtCzvp\nfbdCLTZuUD8OpDYAhdfAbFkoYYstU01btt+sQLJ+UwelQ48jtfx2RHJrObZsuWnLzIpLp0gyMhMf\n0/nnbgxEo3ZtHWYfXsrLgN5ro3b056iffg4sYxhfcguymz+DUDQjLkd8GSkDr7TlprwsGbtNVI78\nA5rnfsuQ0Ut5OXCrwbtm7RyoMTLwKQavpKGTYS6ylZeL5DpqsNv5MAEP5eUglCRHySobGTpQ3kP9\nL48eohWNc6+gcvgnMBi7bMOZlRja8jAiWR8bN0JpWqTJlc7PdI0iZ96mDh4yWyh74ZXf5l7ytdta\nq19E+cD30Sk6syUlFEN6/UeRWnW3jzImoxJkRfMcycjayc5DZBgYfS8ZWjt6bdMRM0pzXKhUWs5t\nZRvExila1149RCuiY5Q9scr0vSYlAB79uQG47d8wDLKLc69ysnY27EG6FWosh9zmzyE+wSm5M2V0\nKWMaBlA74hJccJBYadoyho3uVk1b5mPTjxoj0vLUBraM1QP8rD2Sp2fK0jsX/H4cZh+Cytue3Y/y\nwcc8CZOVSArZTZ9GcpnHLk81SplDPxviwYfyti7tRvnQD6G3GTvprF8tqrxqHBi5w3uX1xXlfc27\nL5taTwrmRZgsqryhlCnjGvfzvJTXivRmWqhehMndEjD7MtB238yjNWbIabD6IVYoKlKr70Vm8iPs\n8rUV2esoY/IiTO7MUbbp9VpIZMjMhjx2MRo9ytjLb8GtL9tvWdSO/+pKOYv71bk1yE0/jEhmuft3\nu+01sELXqPJReRvuwULIEul7bag7T8+atUvVCns2xJWxQ7pY5ZSG++i3LEQIkxtnaM3wytd9uAXp\nVvRatKZrjD0JFrgH6bavHr8J2anP8cvXfYhulNEalGF7JT5uQboVXhVIK9yC9AEZa/RceOXzZZ/y\nRbD9+3WYgKvy6p0aKocfR/PC674uGRvZguz059klp+Q6enheuwKtcFHeXruMysEfEsO7D7gqb3oj\nlTdDPl4hcFPeUNos8/nIoLxKTplpKq34eoXAJWsP58wyn8eOO7uMtUNU/rE5YsPQUT/1T6ge+4Wv\ndw5DiTEqn49sdn4YJCq9suntTUbWrlImNHSTv/JQp2Bm7c5solM+abYsfETqSgjpNR9AevJDUOxB\ngBKijDJ7g7fTsKI9QzKyNkjFllBWGfHRS9I1Ko2X32LIb2tZiMIta7e3LIRk7Jrl833Oz0SDdDua\nZ8ngM7J20SDdCiWcQHbjJ5FccSdDxoCvYjROmokPoyUgGqRb4Za121sWIjAMoP6OactsLYGln/B+\nG8CC37/D7KN2lDbQmOi1Sph97b9A7wR7mV4JxTD+3v86WP7M3yq2JZ+Hwg6gMr9gtfolzL7+X5ll\nPiEZwwlM3PV/DWY0I+8FMgxjLYrZFwd7SdERYMlHvbMhHnpN4Mz3MRC9jt0LpNYFu55hAJd/PfiO\nZWwJvSLiZ6eoFVodOPvYwKG5N/8f76zSBcPb/wNiI5aec2IlbSwK0PcAQOXzcz8aPLb0j7wzNh4M\nHTj/U6A775CaF3ag9PbfwlcZ2IJwajnG7vhPgweXf8b/+9JWGc89Ptj/TW8mRxR0t2LjFG0m6UMJ\nA8s/Hfy1AaMHnP3hoLHP3kgOOKiMlYNAwfLuuRoHlj3kL0i3Qu8CZ34AGPOBa+Xoz1A/8VSw6wFI\nrX0Q2Q0fmz8QzpDz8BOkD8jYITthDQqH3wNkpwPLiLlXBnv3kTyw9GP+gnQrei3g/BODVYBFcpjX\nfjRedNBw6FojsLMEAKPXhmHPLIIu/D5sW+T1TjWwswQAQ2vC0G19uIXKGLJt4w8lgztLwIwMbfrh\nJzOwQ1Gc0WY4HdxZAuZzGZRRq/t8PcUG3T71KJwJ7iwBdgluIc9aUR1la605i6DOkv7efs+Uhcto\nN26R3MK29odt8iihhb1jp4QoQ7VioTLas1I1GtxZArR+bZvSeo0F6nfLtnFOjQd3lgD9RnsFYsG2\nLOn8f1BnCdDvW8hvdIGcJSshISEhISEA6TAlJCQkJCQEIB2mhISEhISEAKTDlJCQkJCQEIB0mBIS\nEhISEgKQDlNCQkJCQkIA0mFKSEhISEgIQDpMCQkJCQkJAUiH+T8KFmUi0yJPdXJc/g9Axn+R+AO4\np4uhO4s9texqXF/KePWvvwBcW4fZn/VnQTi1BImlHkPUXRAd3gzVPnGjtMvfdH0rdM3BmhDJrUFs\nfGtACYHY+FYoYduQ8dJOz4HZXOgdx31E6wINhg6K6hE4DGfxDeINDAKt5Zwl2zxFcz2DouKc3Zmx\njv3yCTWaRdROxVY7RqTCQVHa5Ty2kPvYqdC8VguSy++AyuP3FEBm8qPOg8U3A18PnYKTuq2yn2YK\nB4Gum3RxFhgdYq8JitZl58D08h6azRwEug6U3x481qvSuLygaJ5zzEBNr+UQXwtBRWLlewcPdedI\nx4OifspJrLAgW6Y5OUnbF4G6OHuUA+3Z4LrngWs3S7ZTIsJWBv2TYRjoVk6juOub0LuCP1QNI3/j\nlxEb3cJh5LaRsYqgdoxkZHBPGoaBTukYCru/Tc5ABOE4hrd+FdH8BraMSoiYIdLrxWWsHCT+QB6L\nRXy5SX4tOIJOaxDjPIOommSMAKN3AykfQ5DLe03OT47uJNfQNYVlrAGXnuRSXumdGgp7/gpdBr0V\nD+l1H0Z63YNsfkyAqIRG7ponbfZCpwRcfopPeaUm6LnEBR2drgOl1002ECcMQyf+y0M/Yn7OQji9\nHMPb/hyhOIe1IZQmsmEWvRVPxsLLfH5MKDTTOf8uYRnRukjk6kw+TdDIvIkPerOAWGWcfc6FaUMh\nCq4hH5RYjTPAzG/IibMQGSYZbSM2+TK6k94buobyocfRPPuisIix8a0Yuu6PodoD9fkTgLEHxJ2x\n3jGJonmsQSGaHZzZKCwjqodpmDuPvi++jOY6i47J0zVy3pW9cNieP5jh60bPwmvoHmUbeg/Vd36B\n+omnXc+LL3kXhrZ8yZueCRBTXq0FzDzNZIVwyiimvIkV70Vu82egiDiF6Bgw7hFJanXg0lN8UuUB\nCCpvaTexa4iU5OJLTUfscs+7FZLRi54JMJnb38/mwrSiuMPMLNxlNAwD7Zm9KO79a9doN5RaiuFt\nf45wYsRbRjVKA+gTK/jn6DqxI9Q8KKT6SE7S73ZzxK3LZJwEeBJ77QoKb/0FtPJJ1/NyW/4VEstu\n4wSXNqQ300BtNxmb54GZX3vTMwE0G3T8g0DM5Z7rGpEyNE54Xw8gjsmhW91lrJ8iZ+lFNQfQDOHx\nDwJRl/nJumY6DRFeWgXIbQPy291PcwnS7ejWzqOw8xvQ2y5cqeE4hm/6d4gOrRd41ioFM7kb3E/z\nCtKtiI4C4w+4z9TVGhRcshhuWDKKJD7NcybbC4MAXo0RAYIPRprfj8NsXyZWDXu5BgAQAi+y0Boz\nmNv1Teh2ktRwEiPbv45IdjU/Y2MqnkIM6vmbnR+V95JRZikD93p85VWjQxi++WuIpDm8g9xruihv\ncSdRHrGchouMXOXtlCirZCkXAP6z4SivVzbU6/CDm9gSYOJ+Umor2nO0qFhUQn1ZGM9M19oo7f8e\n2pd2Oj7LTn0ByRV3+tQdEAXU+AecGXHrkunYnNmQYeiAobMDJiUCjN4DpGw0bLpuOo13nH/jIqNh\nGGhd2oXS3r+B/Z5Ehzcjf+OfcsjM+/eBoVdqDBi7z0nD5pENud5HXtZeP0G/m0lmzn7O9FGCMmJ7\n5qB3KEttnWf+mas+ZqaB/O1OGatHyCAz1wXflnGzdq8gnfusddROPI3asZ87PkusuAu5zZ/m6JzL\nc+Fl7V5Bupu95WXtLkG663OJjJiJj02Pe22TkpFT5UhNEs2jH9oxXGuH6cYXB5iM3HeSI51lk7Ha\nS06p1R9AZsPH2SW0PiN3YpXJ3M65eVbl9cqG+nya7UsUXTEMt11505MfRXrdB9nM9qEERe3xCSKq\n5pWIrMrbKZKMPLLaPp9m8wyfz9KqvLoOFF/lE+qG0vRconk+nyVgZu0PkvK2Z8j59tjZUP3086ge\n+xniE7cgu/GTUCMsxVXp+WW3kIxzLzr7Gn2Ec8DonSTr3EtMo2gYBrql45jb/W1AayAytB7DW78M\nNcpiu1DMbGUblYhKb7ANtxIChs2s3SMb6lbPorz/URi9NnJbHkZ0iEORZi051U8Ds7/hZEMqPb/s\nDRSUcKo1utZCae930Z7d692yiI4RV6Vh0P3mRfuJ1cDYPRQs1N+hAJh3f4ZuJodT3s2vClizdr0D\nXHqaelYsxJbSs+61+HyWABnFETNrd8mGdK2F6tGfonn+NaTXfwSpVXez16oaN8vnE94tiz6fplbm\n8lkCGMza3YJ0NUZrOrnGtGVs6rpeq4DCrm9Dq53zDtKTayjQ7cwQlVavzj4vewMwbO4nKb5Jz5H5\nDE0+zfgyPp8lAISzFLBHhzxbFo3zr6Fy+HHERqaQ3fwZhKKskrsC5LYD+W2kt40T9HtYlZggfJrW\nb7pmDtONkVyNm4zck/O0OnrXZG7fB9bD6bUrMHodhJMcPkEWcWnzHC0wnvJGR/kLIJQCRu4gJZsX\nwkN5izAAhHm9ofRm4ui00jQ1TplkrBzldZMxnDFJmC2lQjcy1v7vMjR+CS1zHZC/ZZ4izDDIqc+9\nyi8NRkaBLlvGbu08yge+j25pPltSYznkNn8O8QlOvyiUIfmYvSGzH5bbNp/pGQaRfRdfY/4uQ9eg\nVc8izKtIREeIl9SaoXSrpL8tDjFzOEfPjOE0DL2L2ju/Qu3ks5bIW0Fy5V3IbPgEVGbJXSH+P14U\nH5swgxhLhtIpmcTSTkdjGAa02lmEkxPsaF0JA0O3UHDSdxaGTn2f0k5OxhCichbPYcWXmSTMFpqn\nzhww+xIZaRaiIxQQMis7ETLc6c3zdsLoUXZSfov9NwhT24UTALdm9qJ84AfQ2/PVrkhuDXLTDyOS\n4TiayKjJQ8rJwIdvJ/tzxZZppi17m/03SpQCBl4AzCK9b543HbHzdxmGgU75JKK51ZwgPUmO0tr2\n0DvkrHlBs5qg38Or7LBI7xunTVvG+V0udkJrzqJ84DF05ublUSIpZDc+hOTy29nXC6WJepC3RjNb\nTFsWnCLs6jvMXouyHJ7BTm2kRcDjKWtfpgUm1KOD6djuBJKr2J97KS8LmWkqi/JudOs8ZcQiPTqA\njOvInc6y1hUZPZTXgX42dDN/w4xbwMJCJA+M3kWbAFjotcySxxGhyxm6Rln38ac4JTYgPn4TslOf\nQygmyKPXz4ainB6Y1iDd427ssEEJAUPbKaJmGRrDID3mZu1OtItHUd7/KJe/UI3nkZv6AuJj1wvK\nGCFdzEyzORsNA6gdBAqvi/XogPlsiNfL6ZpZEqeU6YAaBfK3kRFlyqhTIFx6k6sLDvSzId6eg07B\nDBa89xsAQK9TQeXgj9G6xNkFrISQXvMBpCc/BEWUT5YVpFvRniEZhXp0YAfpVugatWQEevlXwArS\nrWhddM/a7QhnKLhMcIILr6qiDYaho376OdSO/QJGj73GosNTyE1/AeGk4GadyBDJGF8idr4Lrr7D\nrB40a/w2sLIhHkQ3CGWuo36kSAQhorx+brSQ8jKyITeIKG9khJyGyE4vIeVVqQyZu1GMMLl51r3k\nBKBTOo7ygUeh1bwNrhJOILvxk0iuuNPlpJCZDV3Hdmx2NE66l5wA2rw08l4x0luvrB2ArjVRPfIE\nGmdfhogxiy+52aXkZKLfshAhTNbqZvn8FP+cfssitcGbMNkwqKVRfM391SxWNsRDt2I6YpfNMv2W\nhdcmMIAccfUABZsujrhx7lVUjvwERtdFH/pfn5zA0JYvIZrf4HJS2izzcYJ0u4yuWbsJryDdis4c\nlcR5lSfAO0i3QtcoY+eVXgEIBelWtC6Ztoy1b4XQrZ5D+cAj6HpsVAMAJRRFevIjSK2+l51FA7jS\nsshtXRj5u/V7r73DVMjQDd08X+YTBa/kFMmbjm3C3/X6ylt8A4OKYW4Gym0Vf8Xhiowc5Y2OmmU+\nTgmZK2O/5GR/j8/MhnKcbMgN7cvAzAuAZnPEsSUko9uOQBb0rmXbtuWw1kL16M/QOPMC/L4EH81v\nRG7Lw84oMr7czIYEXx+4Igwna1eiZplvk7fTsKNxGph9wbG5p3X5LZQP/tB91yIDSiSF7KZPIbns\ntsEPWC0LEfT7ObMvOcvZXtkQD1qDeoH2Pm0oaTqNNf6uZxjUl577rdPJeWVDXBlrZHOag+8fa40Z\nKvMV/L4TqSC54k5kNn0Kqr2cbW9ZiKJbNnvtttcxgmZD/azd8dqWzyDdik7BLPZZWksAACAASURB\nVJ/bsnZWy0JIxn7iM5jVs1sWYohkVyO35UuIZFYOfhAbN22Z4KtQguA5zKs3uCC9gRaqXwUDyJAv\n+Yjz+JIP+3eWADma3FbqtViR7WeqPhUMIGVa+nHn8aUf9+8sAYqM8jdT+dGKoZuAoa3+nSVAyjTx\ngO17InRv/TpLgJ7l8LuB8ODfkrN8HkEmxnSKR1Da93eDB0Mp2lTk11kCFKmPvIeuYcXI7UBms39n\nCVBGMTzYT+nWzqP41nd8O0sAMLp1lPf9HfSOrWw+ar6T61dGRQFS65y7EmMTwNjd/p0lQJnj+H3U\n87Ri7F7/zrIvY3ojZVRWJFZR5cSvswQoAx9/AHYzVnzrLwM4SwAw0Dj7EloX3xg8nFpP+hPElkVy\nwMSHnccnHgxWOlRUCp4TNseRmTIz1SC2bBhYyhhmseSj/p0lYFaGtpH+WVA78SxqJ57y7SwBoFs5\nhbkd/7ftqEoyLrKzdMNVnPSzwEszjUYAY+d6zYXKyPr7xZZxoddjyBjEaQz8ve3/ARbA4N/by+/K\nwmV0CLnI+rjQ3wzAcAQYC12Oi/ybhb7DL+wyLfZ6ofe5FwRHVe1q2LKFPhv7318FWxYkSB+8wOB/\nHevcHwz73yvKIsjoD3KWrISEhISEhACkw5SQkJCQkBCAdJgSEhISEhICkA5TQkJCQkJCANJhSkhI\nSEhICEA6TAkJCQkJCQFIhykhISEhISEA6TAlJCQkJCQE8C/LYdpffF2El88XHVdbxgW+PMy8xmK/\nPLwYv9lxHxf4u+0vsweZqOKA/cXuhZK12/5edOC5r2v+M5QxwIQpd9ify2LIuMj4Q7RlizTndf76\ni/3cvXH1HGbjBFA7GuxHaXXg3D84j5//B5p7GASl3U4Whup+oLAj2PW6FeDsj53Hzz1OnwVBcYdz\nNm15tzmMPgA6BeCCnWi2B5z7Cd1jv9B1mgVqI57ObvoUkivfF0jEcGYV8lu/bPueJnD+p0SyG0TG\nmecB3UZPNPcy8V0GQZ9iyYJwcgmGt//7gBRCKoZu/FOoEdv4vtl/IjLlIKifAso2Ro7ODPFN6gEM\nvq4BF38FBzHy5adpEH8Q1I4BVRvJeOsccPk39Nz8otcy9XvQxoy8639BJCcwxJ2BxPL3ILHs3YMH\nG8dp1moQGbUGcP4J5/ELTxBJehCU9wAtG1dt7SARBQSSsQacfdx5/NzjNNc7CIpvOmbTptfdj/S6\nDwW6nJocx9jt/4ftqGmP3EgCFhlXn60ksZJme4Y5lEJ2FHeaA8hdvje1iQZz21nRWeiUaJFrLk4s\nlATGPwjEOPRRVug6UHrdpA1zQfZ6YOhWMRnbc0SuyuOgA+j+jX9QbAasrgOF33L5OwkKDWrOb/e+\nHkAsBJefcQwgt6JbO4/Czm8IzldVMXT9v0Z8yS1srkrzHOTfRbMzRdA8C8z8k/sCio7S/FERlg1d\nA2Z+48oEYvS6KB/6IZrnXhESMTZ+I4au+2MON2b/pCU0A1jEGesd4PKz7pRcSpgGVKfXC8mI6hFz\nLbtkLfEVJvm1QKattUwSZhdKLiUCjN4DpASYQAAaQF54DTxWI8Mw0Lq8C6U9f8M9xwo1msXwtq8h\nnFnB10c1BozdJ8YEAlCQXnoT7rZsAzByl5id8CK9B4jPcuIB8RmwhR1AxYM2LLOFaNyE7G2BgjQX\nekGtOYvCzm9yqfAcX7/5s0itvIvPVuJFjxYAV5+tpFMiY8Xis1TCFm4/zo/uFEkZRHkcvZRX14Hi\n7yiLFIWX8rb7ETuHUNkho4fy6joxGdTFuCYBmHRAt/NlbJ4HZn4tzOOIUBqY+CAQ5ZBf6xow+7yT\ntYIDw9BRO/40au/YM9t5REemkb/hT6BGBIeCh3MkI28Yu64BM8/6yHwUYtGxDyu3ov4OsdEIlOMM\nw4BWPYvCrm9A73Doz9Q4hrd9FdH8BpcAYeAPiLwgu4V/SuUgMYoIOAQANIx/7AGA56y1hunYXOij\nrFBCFLimN/LPKe+lyomojPFlpiPmBAtaDbj0pDCPo661UNr7XbRn93LPSa/7ENLrPgRFFSwZJlYD\nY/fwg4VOiQJgFyq8AahRGmrPo0AUDdKtSE0CI+93sWUCQfqAjHFg/H4++YVQkD4Pw6BB95WDP+Ce\nE8mtRX7rVxCKCZIwJNfRkPyQQDDsgavvMAGqWV/hs2REp9FxkwjYMl1e12nR1zjsAuEMKRSPz5Kl\nvF7ZUGKVSQnEYlJnKK+uA3PPkxFlIWJmfbxFnJwERm3K65INGXoP7bn9iI1ex46qWMrrlQ1FR+i7\neIs4vZn4CK0y1k+Qs2Q6DZXIZG3USn1ozQKKu78NrWbhQFSjGN76FURHNrOdRnSMFjCPzzJ7PbG9\nW/+2dpSCDlYPRwkT/yVHRoSzlG1as/Zei3SnzYl+Y0uIsokRNBl6D7Xjv0Tt+JMDxxMr3ovc5s9A\nYRlYJUKOjMcVGclTsGDlxtQaFFx2OWsivoycHjPTVoHhW+leWlF6CyjZ6e/6fxIDIsNA+4LzM8DM\n2h8cdMTdKjk2TjbUnt2PyNAkJ9MOUVUqs2nwcHEHn4c2lCRbwXhuhmGgUzyKwq6/GLAJoeQEhrd/\nDeEEh10osZIyd55ujb6PWGL68AjSteYs9E4d0dxq/veN3Tdoy7yC9MQqM1BkBCRKhGyjlb9T14G5\nF4lqjSVj/SIMvYdIhkMUnVxLlYABW+YWpCv0uzj2Vu9UUdj9HXTLVtuqYujGf4P4+Da2nYgM0zNh\n6ZYaIxvBIzUXxLVxmH10S8Dsy5wFZlJtDd0EtGaAmWf4Nzp7PXFBKiGKrkpvuijvXUBiLTD7HPUc\nWIjk6bzYuMln+RL1eVjoK2/rPDkiJqu95bcAJp/lW3BV3vgyUi6OEe+UT6K8/1FotbOI5NYgN/2w\nh/LeTU5y9gW2Y1NMPs3sDRTQlN40I1WOYRy7j+jJLj3t5CPtw8qn2TpPz5qhvIZhoHnuVZQPPILE\n0tuQm/48FDvPYP/e5G+h7NnQ2HyWfYSSFCyEMhQh855ffAUZ3UgWaJyhEiOvetEvOdX2A4XXwXx+\natRciJtIX4uvATV2ZUBrzKKw65swtBaGt3/d5fmtAYbvAMIpCk4KvyXSagcU0rP8Le4tCzVulqbW\nmeTXr/LXQniIHLGhm9kQp2XR59NU42RkC7/jr9ehW4iKrvCagzO1j16riPLBH6A9sxdqPI/c1BcQ\nH7ueeS4iIyRjr0mZLy+Q6vNpqlGzl/c6c70aehflgz9G89zLyE59HskV72UbZCvpfbdskl9zSt6x\nCdLHbpkbpBuGjvrp51A79gsYvQ5Sq+5GesPHoLIozZQQra3kpHeQ3ufT7BRM/mBOyTu+nGRsX3QN\n0msnn0Ht+K8Aw0B6zf1ITz4IhUVppkTI7iSWewfpI3eRPWnPkL1lBHlUPn8LpT1/jdjodRi64X/m\nB1J90ntDp3XAC6CC8un2f+I1dZiAydx+iBYPy9moMX7ZMDJCmai9lOmlvFDArsWr8zfaulOrT8Za\nepOTRfGuB3a2DHgrL+eaRq+D6rGfo376ucHdZUoI6TUfQHryQ2zldZMxvpQWVSQ3eLw9QzLysnbe\nNZUIGabM1GD0pmuuymvoGqCE2MYpsZIU25pBAUDrosnc7nPTgRojA5/aYJOxSwTi1X28PwS3bJhc\nR3yY9r5n8yzpIyNrp3VjsCsEoQRl8ynbxpRem4iBuWUtFxnTG8mhh2yGpnGSNkaIlt6uyJg2iaJt\nPcVek5xm/ZhvGeunX0D16E9h9AadSnzJzchu/gxCUZ/GLZwzHZutLaPV6TczDLlhGIDRY2f7V4J0\nG0euYQC1wxQk+dxg0q2eQ/nAI+iWTw4cDyVGkJv6ImKj0+w/dLNl/SDdbsuqByjY9GnLrEH6gIzJ\nCQxt+RKi+Q3+ZLQG6Vb9N3Qq0Zd2glWBNPQeoKhsOxFbQvY2YtvD0Z41bRmjjaCE6Flmr/e9k//a\nO8w+XJTXCfNG527g/0C/yhubMLMhTo8OoGb63Mv8spgVIv1YT+UdRHv2AMoHH0Ovye8deSuvVcYo\nET2nN/HLEoZOWUBpp9iW9MRqc/NWin9OZ476fiI9MDVOTig16SJjzz1rtyM1Sdd0I0xuXyYZu0Xv\n64WSptNYwz9H79I95GXtdvSzITfC5OZ5MgJuG9X6sGZDXBk77lm7HZnrKJt1I0xunDazdu/d1lrt\nAkoHHkW3xMmWACiRFO22XnabgIAKBb+5bfw+omFQ333uFbE9B7wg3QqtQe0jgX6+oXdRe+dJ1E4+\n47q+EkvfjeymT0GNprnnXAEvSB+QsUbPhdeGsEDvtVE7agbpXN1VkFxxJzIb/whqWGDPQXyZmdnl\n+Od0y5Rt8kr8A18foRZCesrDlu2jlgLrXkdHqVLhg0j99+cwgXnlLbzCKTkBiC0FRu90RhA8aA33\nkhMvG3KT0bXkBP87fj2UV+/WUTn8OJrnXxO7nojyJteaZT7Bxne3TMa5xVFeNWGW+dYK3kcP5QUo\n+xu+zZkN8dApmOVzTtYeStEitWdDXBl7ll47xxFnpubLfCJoz5iOmPPaUzhLgZvoDktdMx3xXrCN\nmaVl4ebYrGhdoPvI22UZyZtlPs7GDoeMHTNrZ/fsDL2H2omnUDvx/7P3XkFyXGe+5z8zy/v28N50\nN0CAAEiRougpiUYzMhwZiiI1c0c7uqPRiIrduDdiY2NjN2Lvw+7bXXJGc2PuXO3skKIoR5mRhqRI\niN6CBECC8CA8GkC76vI2K3Mfvix0VuY56RqAlnHPLwIPqKrO+irz5PnMOfn9n/X8aEtkYAzZ8Yf4\n64qRQbIxynnfSqdbPuc9UuQhSLdSPWWUz9lZe2vuGAoHnvC8C1SOpJHZ+FXEF3+C/QEvQboZXadS\nbv5N7j4OCtJ/hE7d26MtcjSH7NiDiA1v5f2I+SULr/Nt5YhRgeQkPl6CdDNOic/iL3nfOYw/tsPs\n0mnSgnPtlOlLFMoKUqPBFmlrp4CpneiZ+GLLKBKzlvk82VgHpl7oXb+TwnThkuv829gdvDMvwTzx\nNSb3onjoSf6uSgfkaA59134Hkewq84s0kVjLfF5trBwhx2kmuc7I2Dw6NjPtEq2DqqaSqpIw1pqX\nB7DRyNrzb/a+7texmWHtzA6laTNHbHEwG4sfGJtnTGS22Mt8XmnO0OYZ88QXzpGN0WH/x9NUChRK\n7/e+nttBpb4gD5c3Juk8mia+dukMCvv/GWrF4XEXDpISQXrDV5Bcfqv5VXIaAcprAID6BK0xmis+\n0RE6j07ZEA+tRQGSKdvUO22UjvwMtXOvIUgzhejgNejb+u8hKaYAKLaE7hmvQbqZToPmxub8NdDU\nBkqHnkL9gtcgvZfYyA7krvlW747i+Aqae7wG6WbUKj0WZd6LIEeNANhjkG5G12lvQf6N3mt9mRzm\n1e30o0RpY4CZUNp7FsgisYpOsJnMeDBnCVDanlzb+1qkH0itD2ajJNHzb1LvZFk5vTOQswQArVlA\nc9qyxTw6HMxZdm1Mj8I2HLLXBnOWAC22W51ObEkwZwnQJJnZDFsXluy2gM0DQGV6q9OJLw/mLAGy\nkfWoSm5H8M5A0UF7CS6xOpizBMiO3HbLi9L85rogxEZsmyvqF3YFcpYAredXTr/Q+6IcMfYgBJyy\n4kupEmEmtTGYs+zakx7reanTnEPt3KsI2nmoOfMhtLZlY1p6PJizBOjeTfUu4ajVi4GdJQA0Jnfb\n1qCRuSaYswQoe7QueUQGafdx0Pk2vdF7pdIn/321xhMIBAKBICDCYQoEAoFA4AHhMAUCgUAg8IBw\nmAKBQCAQeEA4TIFAIBAIPCAcpkAgEAgEHhAOUyAQCAQCDwiHKRAIBAKBB4TDFAgEAoHAA1ffYVq7\nRHTqnvtMMtE0uxpK20PTaiesPSLVCn1PUDTN1lc1FBsIfjwAUsTSoaRdWqCNKmwdStrBOhFdwnoe\n24UF2tiCzUbVvfm3I1YbWw5q9l5QGb07PTQod8R6z/hVcLGiWnug6oDqURSdR6e3/7KS8NiPloNi\n7cCjtX0rhdiw/v1lPo9yOBW8o5OBZG3Kf5nnMiWWw4KnfcnSu9iLSIATtvm2vLB5Qtc8iV4E4er1\nkr3U4+9Nu4OTQtSLMLXO3zHrF4Dp59nN0mPLDOV2HwNY6xh6mgw1ApYYqxdqZ5h6mrquozG5B4V9\n/w2e1egBQA6hb+tfG+LSltZRXT1Lrw2+u1RP8PU0kxvo2vCU21loLb6ephwHRu7x1dcRAFA+Qqo3\nLGHyrp6lHxvVBjD1DFtZRUmRuoGTwg2L4ockz2W7noa6Rh+nuTbXxoohFM1QVgllgZH7gLDPtmlc\nPU2TnqUfWgXSqrRMmrquQy2fRX7PY75bQKbX34/kqs8wpNFk6m2c4UlicWjO8vU0u3qWflpAaho1\nX2fIsOmdFgoHnkDj4i5fJoayq9B/7XehRBkSZ7ElxlzmowWkplH/6ppdIUZTGyjs+yGaM2zNUh6R\n/lH0bf025DCjGXp8Jc2PvuZbB9F7OWLMZRwtWR48oYaPVfN1r/JZ0WFg6J5e5XYWmgpMvwjUTzl/\nTlKoiW9qg7uN1ZOG02AJRZvwOni1FjUV5mp3Gh/zMXhji65HbtM32SLMZrwO3k6DGlIzVOp7kCPA\n0KedJaS6lLoN0l2CgORaYOAOdyen1gyn4aKqIMdo4vOitFF432iQ7jK2U6OkW+lmY7tMDdJ5KiBd\nlCQFCxEP1YW5XXxxXDOZLSTl5gar0TyLUAYYvhewVjCsaBow9xZXqaSLrnVQOf47VE4+42piKL0C\n/du+a2RBDoT7KKBx6xetaSQoUGULfc8jk4RUhiNkbaZ+ngTgeYpGoGChXTqF2d2PMbJ5+3fntnwL\nsZEdbB3ISygkAJHe6G4jJ0i32tiaO4r8nn/gKprMmxhC39bvIDq4ydlGKUTN7JNr3G2sHqfm9W6Z\nYHw5OU63ucxNCvBj4TB1jXQCC+9501wE4Dp4nbIhHpFBYPg+tiN2yoa4uAxep2yIgevgDSUwsP0R\nhLOrXG4qE26Dt/QhKdP7yW6dBq9TNsS10SVrn9sDFHfDVzPrxGpg8C62k2sVgaln/ZWQ5Cgw9Fkg\nzmnInn8HKH3g/XgAkNxIgRzTxlkaj37KuEqCggXWhKBppNxQOeTPxvRmkmti2diYpEDLbaI1odZm\nMLvnUWg1lkSbjNzmv0Bs8Se8j29IJA7Qdz377fo5YHqnvzJuKEeOmJW1O2VDHHStg9KxX6FmbSRv\nEB3cgtyWb0F2SxDMRAYooGE1O/cYpPfY2GmjePgnqE+8znw/tugTyG162D1IN+OUtasNYPo50qX1\niqQAA7fxK5BOYvNS2NAG9qeGdfUdpoMStt5poXz8dwhnViC+6Dr231tLTm7ZUGwxTZaF3Zzoj1Fy\ncsiGNLWOyke/RWRgFLGhLezvtA5etUYTcouTDcWXA7GlhmizPfrTtTaKh36K+sRrl15LrPwMMuu/\n1Cun00WOkspE7RT/JrEO3naZHJvKXr+pX3wP7dIZpNZ+DjJL5FhSjPK5SQVh7l0jsmOMFSUOZHdQ\nlM+7SWJLyMaurmOrYGRD7FJebeJNdOozSK25FxJLC1IKA4N3AMlV9H9NI03E8n729ytJUvAoH3S4\ndpasvTlN45GjiYj0OGXmvCxRjhpZ+9J5G2dfA6ps3Ua1OonKqeeRWvlphFIc551cBwzcPu/knJYs\nunqausY/L3LcyNqH522ceZGvQRvuI0WZ4vu0DmVB1zXUzr6K0uGnLr0WGRhH35a/ghxmqV3IVMru\n1JnlTwD2rF1TKQPkaNC2iqdQn3gdqTWfgxJjldwlI2u/Yf4lpyBdUkjIuj0HVD9ifqdancTs7seg\nNYy5UI6hf/vfINK3gR0gRBdRBaawmxOUSHRP9ZlUZ5yCdClM47txkenwdV2HWplAfvej0FpGMBlK\nYGDH9xHOrGTbGFsGJJZTiZ+pZymTo8psnn/JIUjX2lWUj/8WscEtiA5ySu6RIWO+NeYyN2F0v3qa\nJq6ew3QRvm3OHkTx4JPo1GnwRIe2IDv2IGfwAshspR+cfxvMbEiKGBGEIVzaqZMINGfwIpQhfbnZ\n17nZUGPqfRQPPQWtSU4ltug6ZEa/BiXCWF/oDl4J9LuZk2OM1l6Sa8lGtUrf7zB4iweeQO6av0Qo\nySkxJtcaWpXxeT3Lubc5EbWRtas17nXpNOZQPPQUmtOULSnxAWTHHnIevLkbgdkX+dlQaiNlKUp0\nXs9ybhenOqCQ8HVrBqiwbwC1PoPigR+hladsSUmMILfpYUT61jM/j+himiimXwQ0zqaW9Gag7zpy\nbrpG56ewm10RkUIU6dZP88dXOGeIMC+i/zsEjgBISzA9To6Ice10rYPqqedRPvFvtPFFDiG1+l6k\nVt/LDqKkCAULlSP8JYvwAOnFdjPSxqQRoXOqA4k1QGItMPsyp8wn03nObiUHorWNOeBDMMdaq4y5\nD/4J6dX3IDIwxp6QI8NkY1farH6ebORVB5IbKWjOv8a8dnqnhfJHv0H1zIuArkEKxZBe/yUkl9/O\nPp6SAAbvpNK9U5A+cOu8RFjtDAU9jPtB1zVUT/8BavUisqMP9GpedrGK3ncaxlx2jP39oTQta8y9\n4RykD9xC5Wtdp/0Zs28w7wdd76By/BlonaZzkN7/SRKBlySaU/JvsPd9AJS1D94CzLzmGKSXDv/0\nkrOOL7kRmY1fZa+VdnVRwzmaQ1lzjxKnuSSInmb3W66Kw3QY1Fq7itKRn6F+3q7F5jp4eSRW04lh\nlSccBi+PTrOI0uGfoDG5x25jOInMxq8gseST/mxMrqcBZi1PuAxeLkrSEFdllDHdBi+H6tlXUD72\nS+iMHZ7xxTcis/ErkCM+9EVDGbKRtWCvVui6cDIAFt3JpnL8X6F3rE5FQmLZLUhvuB9yKO7dxnCf\n4dgYAUm7SOO4ccH78SCRNmf2WnvJWteA0n6afD0vTQCt4mkUDz4OtXzO9l4otQTZ8YcRyXlYL7qE\nYghFb7HrSuodQ/x6D3yV6aOL6DxGGOuOzWlap2rnvR9PCtGEmB632+gSjPNozhxE8dB8kG4mnFuH\n3KaHEUou8mGjJUjvsbFFFReXtV0bTtlQ/RzdM4ysnYs1SDfTadDmtAq7msEluc6Yyxj3WfUkzT28\nigsDa5DeY34kjczGryK+2OdGudQoBR2s6pgPrrzDrJ6kUgiD+oVdKB35metuuXBuLXLjD/NLTl2U\nBDlKN8FkrQXMvccvOZmonXsdpaNPQ3dZpI8MjCE7/hBC8UHnA4bShtNw2SjTaVJm6GXwpjfRmo3b\nhqPqKdrF5zJ41epFFA48gXaBky0ZeB+8RjnLTTBZ12nRP/+m6zpYu3wWxQNPoF1yXjuSozlkx76O\n2LDbLk9D5Dl7rbNgcjdrz7/NKTmZsGZDPDxufrNmQ3wkJFbcjvS6L7qvg1mzIR6tOQoW3DaCWbMh\nHrpmcsQuwUJ8ueE0XHb+umXtBlqrgtKRn7sLJsshpFbfh9Tqe9hZlRmnIN2MW9Z+6bvjwICHbEhr\n016Q0n64Bgu8IN1KfcJwxC5r+k5BuplOkypIHtbLq2dfRvnYr5hBupno4DXIjj8IJeZyb4UyNL79\nPiHA4co7zPIhOvkmOo08igd/jObMh94tdSs5pcYoAvUTQTgMXrU2heLBH6GV9x5tSUoEqbWfR3Ll\nXYyt7xLV7XPXza/JecFp8DplQzy0FkWRZfvg1bUOKiefo52LPp6BjQ5uRnbsG1DijMEbGSQboy6B\nhBmHkpPeaaN84neonnrexWn0EhvZjszoA1CiDMcQHTGyIR+Pizhl7VKIApj0Jns2xEPX6ffm32Ku\nLVqXLLygxPqRGf8GYoOb7W86ZUNONpYP0fhhlWDjK2mSd9ulaqZdoLJck5G1O2VDXBudNxR6DdLN\nhFJLkN30TUSyjEBcSdCO6e66uCcbO7SeW9gLZtZuXrLwSnOKHptgZe1eg3Qzblm7ecnCK40LZCNj\n1zgF6Y+jXbA/7sJDUqJIr/8SEstv48y3HoJ0n1x1h9mcO4a5PX8P3frQtUdCqSUY/OT/1ru+MXIv\nRaFB0DvA+V/1DLTG9IeY++AfKXoLQDizEoM3/i+9Ly7+Ij0eEwRNBc7/otdpJtYAQ3c4Z0NOWDJ/\nXWtj5u3/E2rF5REfDpISxdCn/o/erf+pUcoMvDoNK6UD5JQMtHYNM+/8X+jUXLIcno2hBIZu/k9Q\nzGXkzBbKiAKuadDGpr3z/1fiwKIv+n8OskunBpz7Sc96bvmj36Bywv3xCx6ZsQeRXH7b/AuhDLDo\n8+7ZEA+1QjaaJ/v+m4wAIcB51HXauWoOPsL9wKI/8fccpJl2CZj4KcyTfeHD/wf1C+8EOx4k9O/4\nPqIDY/MvRUdo7vHjNMy05oDzP+99bfhuILEy2PF0Dbjw694MO7bUeNzNR5BupjkDXPhl72uLPj+/\nFu8XTQXOP93jNOuTe1D48IeBG9VE+tZj4Pr/0Pvi4vv9Beke4TnMK9bpp1O9GNhZAoBaYez6jPh8\n2N2MpNgmDrVyPrCzBMAuEy7ERjlknzgiA8GdJWB71EDvqIGdJf19E5q1bB0ZDO4sAdtziZpaD+ws\nAUBXa9AtnWfIxoDOErCXW+V4cGcJUMZiua7tovdHFlioVcujUUoyuLMEKIO0XtfIUPDzKEm0+73n\nO9LBnSUAhDOgHXfztIqngh8POjp1ywaaUDa4swTYFY0FzWUyNdcwE+4L7iwBttPx21zEjByyrXWq\n5YkFdXWzXVdJuSLO0gnRS1YgEAgEAg8IhykQCAQCgQeEwxQIBAKBwAPCYQoEAoFA4AHhMAUCgUAg\n8IBwmAKBQCAQeEA4TIFAIBAIPCAcpkAgEAgEHhAOUyAIwuUQVr8cx7jSx7/SNl4WPg42Ci47f4Sx\necUcZii5GNICuozEFjGEYf0qAJjpNKj9U893XAc5ErxbS3zpLfYXedpsqqeKVAAAIABJREFUXlBr\n1EbLTOUoia4GpdTbS1YKxRBb5FMBwIQc64cS7+3Mg8ohf0K9Vsq9fXyVaB+igxwNUg8oiRF7L9ny\nweBdRjQNqFga1KtFUpEISnPa1qc1seJ2LOSWjA1v732hPU19lINSPw9bw/TSfjofQdBUoH6m97XG\neb40lRdqZ2B1mMkVdwQ/nhxCpG9D72v106TRGpQqo29qaQFzmdayN8evnaBWhkEpM/RGSwuZy+pA\nq7ffbXzxJxbUeSphbvsIAND8CVFfBq5s8/VmEaVDT6ExtZfzRwxCCQxsfwTh7Cq2Tl4oAwzfw5YT\n4uEgXKprHVSO/44akXtEjmTRv+MRhNOcJsfhPuo96ac59dweoMjR0+zqWWau8X68VpHErBnN3HVd\nR7t0GrO7HyUn7ZHU+i8hteqzjAbIAKBQQ+70qA8bZ4HJ5zj6gTpac0eR3/MProomZjJjDyKx7Fb2\n2JFCpIWaXOvdxsYkCUXzbIgvB4Y+473xs6YBsy+xJ1FQH925ff+E1qz3ySrStxF91/57jn4gqB/x\n4J3zwtKuNqrA9B+Yeq0ADPHrzwJxF1UhM9WThggzpxVlcgM1xvdsYwuYep4rnN5pFJDf+/dQy95l\n5GKLrkdu0zchKZw2eOnN1Czdq41qA5h+jj+pKylg5D6fc9kBatzPlGCTSIWnj5FscG2skVh7mxO0\nhHLAonvdFWTMFPZSU3zGXKZrHZSO/RK10zs9H06O9WNg+yN8FavMZiB3/cJaA1q48s3Xa6doADNo\nTO5F8fBT0Jr27vVmEis/bQiXeph80puAvk86D161Alx8hitc2vPR2gxm9zwKreYcsaTW/ClSa++F\n5Nrf1ePgbRWAyWeAjofoMJSlG8yph6mmkVyYB0kzXeugfOzXqJ5mX7dLX5tejv5tf9vbcJ1HZMBQ\nRXeIJDWNgququ0KMrrVRPPRT1Cdec/xcOLsGfdv+BoqXikF0hJpfO/Uw1TQSda6dcD+epNBkn+II\nWXepnSExaxe5MF3X0Zw9hLn3f+CcFcsh9G39a0QHN7MDhB4bw+Q0ky4Nv6snDMfmIRuPrwKG7nQO\nFrQWBUXNi/zPdJGjwNCn2TqqZspHSDzYRS5M13XUL7yD4v5/gaPGp1uQ3mNjjMaOm3KQQ5BuIzVG\nkmFuc9nks+5yYQD1EB65111uzjFIN2MogvTf4PyxVgGYes5dLgyAWp3E7O7HoDWcVXnS6+9HctVn\nOEG6CSVFQtVBxTksXB0B6cZFQ0bL7qC0dh2lo0+jPvE6rBdIjg1gYMcj/kRc6Q/5gze/Cyh9YPsu\nJ3RdQ+3sqygdfsr2Xii5GH3bv4eQtRzphpIERu6xNRiHppEeZMVv2cNh8DamjGzIhyA1nAavhOzm\nP0d88Y3uE4nVxtwOILfd/lZ9ghQrGNJWPHRdh1qZQH73Y9Ba1qBLRm7rtxEbvtanjQ5Ze/U0OUtG\nNqTrGv/mjQwZwYLFEWsqXRcXHUzbd3VaKB58kqnn6JoN8YgtpnvG2ky80yAbOTqY3N8thYDB24Ek\nQ8i6dMhQofFZwuVl7WqNqiY+S7hau4a5D/4rWnm71B0F6fe762Da/pCTtatl4OKznoL0HuQYqY2w\n1EHm3iWZML9rtamNQP8tdhv9BOlmlARV96wNz30E6Wa6wvDlo7+wvecrSDfjVQvUhavjMAGS0Srs\nNS6w/UZp5o+gePBH6BiZXHrDlzm6kjCES2+mrvczr/CjK/Pgbc5QlMMTT06PAdkdpP9W+hCsQdhp\nlTG39x/QLlJ2kR1/CPGlN/NLxAO3AJAoWOBFV8mN9DlZpsBi6nlOmc/Q08xsBYp7+Gui5sGracDM\nS0CNozHX1dPUmpTZMUugvYM30j+Gvq3fhhxmZYpG9pweJ8FYhp4l2Zg2It2cUebbaV/D6tLV01RL\nwOwbTKev6x1Ujj+DyonfAQCiw9cit/nfccSTFXLaqXVUwmLpWQJGyek+Kp9rLcOxMTQbAbTmPkLx\n4BMIZ1Yhs/ErkCOskrtEMmJZYw3WKRuSQqTtGl9BjqVuLx9S+fwM5vY8Bq1dcc+GYktpnNXP8fUs\nIVNGkzEkrEr7SSibcb9q7RpKR3+B1twxZMcfQrR/I/Pc9GTtatXIhhiajYChp3kTlWkL7zL1LClr\nv42uH0AC1AVONtTV04z0kw5jy14loqz9IObe/wdAUyHHBo0gnZMpJtfSdawcNcSvGU7fmrXn3+Hr\nSioJYy5LGnMZ59wkVhlzWYjWACef4zu21EbS3S3t53+vHKXgI77ECNLf4Ao8q7VpFA8+CV1rI7fp\nYX4Ck1xP10aW3Zcs0ptpriju5e5B6TSLyO/5AdTyaQCyEaTfwB7f4RzNE3qb9FVZ5yaIvqqFq+cw\nu7Ty/MHbaaN65iXEl9zAFvoFjJLr9fORsN4xKbezItYQRWcNzkaMUBYYvJUi7C7Nae7g1XUdrdnD\nCGeW8ydGq3CpmxirFCHH0GSvuyDcTzaa9TQdxFgB0ATZnOJPjLltNGC7JWStRRGrw+BVq5OI9K1n\nD9jIEK0Dmss99XOG+DVHrDe23Fhr4kyMueso0+sGTZ0mRawVdslWrc9CaxYRzq5m2xhdTOWZsCk6\nrZ4C8q9zAimJspr6OTCdhlpH+egvUTv3GrrXVY6kkdn4VdrIwELJ0LjgOo3lNIF214Z0ndY1828y\nJx9d66AxvQ+xoWvYSxZylCLr5Pr5SUKtkLPmBSmhHP0eztiqT+5G6dBPoLW6QaCE+NKbkNnwZU4g\nJRvn0b4Rh96O0zp3YvW8je0SjR1e9h0eoECP5zSsGYWu0diee5dZVtY7LTRmDyI2tMUhSL8FSKyY\nf601R8EwJ/tGZJjOteYQpPfdYJrLNNNcxiorKzRPcecyI0g3l66bM2Rji1PijC6mscio7FCwvBOV\n47+F3jGWC+QQUms+h9Squ9nZtxSmeYp73Rii9w4VyG5AE8mudgjSjbns0nzbprXS0n4wx1t8OZ0n\nP3tJut921R0mYAzeg5SFeFkTAeYjCJ5wqdvgtWFkQ9lt7LUW18HLIDJAERZPi81t8NpQqHyZ3crW\nldRUitD8lGWiI3QeWVp8AEWGs696WxMBjGzoekM8mGWjy+Bl0c2Gwhn2+/UJwxG7r4mQjREqs6ZG\n2ZGl1qIsgBNhs2hM70Px4I+hNdnnKTp4DbLjD0KJuawXdXGLfjsNcprVj+zv8UiuNZwGY6LRdVqH\nnX3Tc6m+0yigePgpNKfeZ/+EaBaZ0QcQH2GU3HmkNpLTYJXKdJ0yubm3vZfq3das2mXDEfvYyWwN\n0q02XprLPGrosoL0HhsLlCU12RUNO4wgvcdGjapmhffYWTvLhPJZFA88wdb2BRBKLUV208OIZFd7\ntFE2zWUMR6t3aB4r7IXnUn1kmM4jb022OUVJBSs47VZx0uO+NHv/OA6zi1o2Il2nHWsyObbcNnfB\nZF2nXbnckpNBZMg40R7WHb0MXlY2xLXR4+BlZUM8WnnKiFvTDjaGTQPEpRzhdfDGlhmOzcOGGqfB\n20WO0m7D1AZ3G92y9i6JVVRmDHF2ippxy9oBdJollA7/BI3J3a6Hk5QY0uu/iMTy25w3JyTXkbP0\nsr5SO2uUzx3WmbpLFgmXjTwAOeK5t8kxOVA9+wrKx34FXXV3rrHhbciMPuC8zhRKU+DmtpEHoOx/\n9k2XjVbGkkXuOvddkbpOgUf+TWdH7Bakm3HL2rs2OgXpVhsrh6kk7jiXuQTpZtpFI1jgVLJAVb7y\nid+heup5mqsckZBccSdS678AWYnyP+YWpJtp5Y3Ex2GTpVuQbsatArn4S74Esf+4DhOYLznNvm7f\nJRgdNk60xyi9C2/wSiHDsW32FVVcGryzb8KWbcaWGE6DU0Lm0S7RwLAOXikM9N/Iz4a4Nmq0tXyO\nsQMvvsIo8/ksQfCydjlqZEPr/NtY/IC9tTyxho7p93ms5gww+4p9w4cSB/pvBpJeI2CDS1m7/ZGn\n2sSbKB35OXQfj9wAQDi3FtnxhxBOLbHYmDLKfD538GltWuMrMTZTpMcpMGJlQ07Uz1GwYHHEanUS\nxYNPoDXHWY/mIIXiyGz4MySWWZ9JliiwzF3n/ZGbLrVTwMzr9hIna8nCC506rWPbsnbGkoUXuln7\nzGv2ucxPkG5GrdL6Yu1U7+t+gnSrjZUjFCxYqnvN/FEUDz5xaR+JV5T4ALJj30B0cJPFRh9Beo+N\nRgUy/w7s862PIN1Mq2DMZZZd2R87h9mlcRG4+K/z/w+lgaVf8zcYzOg6cPaJ3nWfobv8PWtnpbiP\novEukQFg8f2BF5Ch68CZf+4duCP3AXHOc5xeyO8CSqaSWWwJMPK5hdl4+ofoccKLv+h/cjIz80rv\nOmRiFe0EDIquGTaaxuTSr3rLznlM/r7necPaxBsoHng8+PGkEBZ9+u9711aXP0yOPSgX/rV3Ashc\nQyXYoHQawNn536jrGi7+4XvBGzsAGLzxf0U4YwoIctexd0l7pTkDXPjl/P+lCLDiYX+Ozcq5n/SW\n9/tvoqA6KLUztMGwi5IEln09+FwGAGee6C2dD95OlZigWJ6Pb5cnMPPWf8JCuiON3PGfe9cZh+/2\nVuXgUdhtbOgyiI4Aiz6/sLns/C96l5suk8O8+q3xZEtKLykLG2CSBMDyuxZyU7H+XgoFv3jAFbLR\ncs4k5TLYaH3NZ2Zgw2rjAo/He6xhQcfsvQ56x+P6FA/WWv3l/t0LPp7l73V9Qc6SDmHJEBY8vi02\nStLCj2m7By/3dVngXAbY78PLfA/qWhsLbyVo+fsrMU8sdC5b8FhhI3rJCgQCgUDgAeEwBQKBQCDw\ngHCYAoFAIBB4QDhMgUAgEAg8IBymQCAQCAQeEA5TIBAIBAIPCIcpEAgEAoEHhMMUCAQCgcADf3yH\n6drH0MsxdOf/L/j4HpuyOx7jcttk/c2XwcYFP9BsPZzVxstwra+0jQt98PxKcEXO4+XG8qD5ZR/v\nH4d54mNg45V4oH+hNl6RuezKcHVnh06Duv2bUUvA1AuAFuAkdUWYdYsc0uyrQN2rAoCF5jQw917v\na60ZYPpl+r4gNk6/AsDSSWVqJ31XEOoX7WKtjfOGIkVAG6d2wuaMJp+jPrNBqJ2162TWTpLsUhA0\nlTQWrVz8N1KmCEL1RE9bPABILP0UEis/E+x4cgz91/1PdsmxC/9K4sdBKB+x98UsfQiU/AqPG6gN\nsseEJCsYuP4/2oWvPZJYcUdvWzyAWp1VfCiu9NhYIY1FM3qbrnXQjkRze4CORfVm7i0SCw9Cq0it\nH810KsDk88FtzL9jV5SZfY1UewLZOGv0nJ4nnF6G7Oa/gC3A8Uhm7EFI1j7QMy+SeH0QGpNA6YPe\n15oXjV7CAeayrqqMVxUmn1ydXrIuWn/0ZRYxVjcaU4ZwqYOqQnwVMHSnt+bPmgbMvuwsqyRHDDFW\nD8oLAFA/D0y/4KyUkFwHDNxuV0Vn2qjS4LQ2aO6xMU69HWMee8BWT9MxnZQSUmOkBOLVxqnf83Xy\nAOq5OXKP9wbVlY+o8To38jRkj/pv8Ha8ToNsdJCIU6uTmN39GLSGN4m2+NKbkR19AJLCU9CQSJbJ\na39VtQZMPWtvNm8m3E8C3V4UWgBqiD+3C7wsXddUlI78ArWzL3k6nBztQ/+O7yOc4shXAdSMfPhe\n78547l0XGTuFBAbSHCFrK60CBVodh6AqtpjuGS+N7DWN+kxbA1YzUggYvMO7IEBzmsYjT/QeIGGF\noU/7mMteA6psPVmAhMHnPvhHtPKHPZkYzq5F37bvQIk4NENPrDHEr73MExow8we+sDtAUnjDn/Wm\nIgM4K059bJqvqxUjSnKS9jLhNng1DZh5Cagd93Y8KUQNjJNr+J+pnwOmd5JeohfcBq+m0vEcJYDM\nNkaoYbyTmkX1JP1ur7qiboNXaxmOzWMm7mXwlo8ajZ49VguSG0mRgGej2jCchsdMXEkAw/c4SyCV\n9pOUkgctPhLW/QPKR3/B/YwcyaB/x/cRSi1li1lbCaXJgUQcGsYX9hjNqL3ce4awbt91/I+0S+Q0\nHOTMej5eOY/87kehNe1Cv11S676I1Oq7neXMzDb23QBkt/A/0spTRcNJzsxMZJCuNU/1plt9qnjN\nxGUKCjNj/I94CdLNREdoLuPJuXkJ0s1ICkl8pdbxP1OfMOYyd11RXdfRnDmAuQ/+i0NWLCO39duI\nDV/rbXxLYWDwLiC5gv8ZL0G6mcRqCkB4862bpnFkGBi525cAwtV3mC7i0WrlAuRYDnKI9SM4g7d6\nhqIS5omWSYeNF5GzBq+mAlPPc0Vm2+UJhBJDkBSG8+YN3spHVBJmNuFWSFSWpxUZW2oEC6aBobVo\nIrGW5bo2ls4glFoCiTWYeFl76RBJCbGchhSmjIWhig6APXjVGqk28ASzI4PGdWGMJTlqZO0WSazi\nPiMbYtgoR+kfT1g6uZ6ujdkRqxVg8hn+74oMcR1zp1lEfs8PoJZ7y3epNX+C1Jr72Ir0cpyuN88B\npMeBvpt6bWwVKEBQOdmQg41QUkbWbpLI0zSg8A6VcJl/kwSgMzMbXddQOfkcKh/9puf1UGop+rd/\nD0qMo3noZGMoSxmxWTBc04D86ySrx0CtTUMKxTiZjWSoomzrfblxke5rZjVLosoGb6yysnaXIF2t\nXoQcyfQqeFxCJmWZjEUSyzFIl+g6cueyYWDont6s3S1ID/fRuGLMS3qnhcKBJ9C42LtcFh2+FrnN\n/w4yszqgkNQhdy5bQgG2OfFxC9LDA8b9yXB6vKz9CohHA1fbYTqIg+paG5Xj/4bKqechR9LIjj2I\n2PBW9nG6g1cOG46NI4ja1dMM9xkacG/bdeoA9Aze8lEg/xqzzKd1migf+w1qZ14kDbjxhxAd4ESe\n3cELANPP8QVRY0vIxlAKKB+g0hMzW1Qo60pvIN3L/FtgOQ2tXUfp6NOoT7yOUHIRsuMPIdLHiTy7\ng7e7Dtjm3IhdPU0l4RyxmQdvYS9b9xLo1dNszbL1LM3fPfRpmrydsqHEGmDgJsrKi3v55Ts5QseL\nLyPHW/yA/TklQcFZcjVNtLOvMp2qrutoXHwXhQ//GUpiGP07HkEozikppzZSRiUpfD1LwMja7yYn\n45QNKSkSGY8vpwxi9lW+U02Nkj5oa5aCGF42lN5E4ry6TutcHIfVacwhv+fvoFYmkN3054gv+SQ7\n0whlSQcythionSad2k6V/d2Za4DcDRQEcpYsdK2D6umdKB//LWQlivTGryCx5Eb28UIZI9tMGY6N\nU+br6mlGhkjPcvZNzvmRgOx2oG+HY5CuayoqJ55F5eRzkCNJZEe/jtjINsbxQHPTyL10zR2CdNLT\nvM2Yy45S+ZeZLcrkDLJbnJcszHqaatUQlrZ/t67raJdOY3b3owA09F/7t4j0rWNf667ofShrSoo4\nSczAzUB61D1I77sBSI/RfT/D0LO89N2LKDCERPNOaT+Y93V8uaEN7FNPs2vSVXGYeocm0OL7YJ2Y\n5twxFA88gU6td+0oNrKDlNujGdvfEDLzeHSir7dHEDwx1kt/F+KWNpszB1A8+CQ6jd6JPb7kJmQ2\nfhlymLVe1D2vnIm775OkaWcefO0yd/C62diY3Ivi4aegNc1ORUJi+W1Ir/8SJyJ0sjEGDHyKnFGP\njQ5rAi42IrmOghNzGUTXKNspvMdZj+RcZ4CyoYFPkaammdYs3WC8rMbJxtQo3ahmFXm9Q+O3sJdp\ni9ZpQZLDHKeRpqDIusbdnKINIryNCJLCX5/NbAZy11PQeMkI1ZgsPgS7bKuAWxYP58hGa2m9cZ6u\nNSNQ0XUdutaGzKq0QCIB5uw2e2VkbhdNqCwcfnO7dAaFA49DLfcu40QHNiEz/g1+oMIdPwqtHWe3\n9s4TnQY5pMpRjo38sdMqHEfxwBNQq733Rmx4GzJjX4cS5QnN8+ayEF3nzCbLXFajYKp2wreNiC01\nRJhN86qu02a8/FvcQAUAu2oiRWifgFX03m3ZzclGlui9rgOVQ7QJiueIlSgJg9veihlB+toFSYRd\neYfZmqNokRGda+06yseeRu3c6+Cty0ihBDIbv4zE0k95+774choM5hNtpXqSHKfTYnrXxlYFpSM/\nQ/3CO9zPyJEMMqNfQ3yRw3qRmcQauni8dRZdp/WL/Jue1hw6zSJKh55CY2ov38ZoH7LjDyI25LBe\nZCa1Aei7kb/OouuUfeTf9rbmoKToBkg4rGG0i0awwKkYWEmPUzTNW9fWNcrGC7ys3UIoS2PHWgY2\n08qTjQ4bg+aRjKzpOod1lo4pa/ew+6+bDTkJeDenKdt02hh0CZkcW24b/9ECTQWKe/jZuJXIkJGx\nOWzecsjareidFsrHf4vq6Z3cRzQkJYr0ui8gseIOb+un3WzISWS8fo6uNS9rN6GpDZSP/Qq1s6+A\nP5fFkdnwZ0gsu8XdPgCILTMcm0M2VDsFzL7Bz9rNyFG6p61BuplOnZym1/XTxCqqxPA2mHnZ2Nlj\nY5wqRdYg3YxapUqFZSc7l+Q6mm95c5kPrrzDtCh7d2lMvY/ioaccNxCYifSPIjv+EEIJzo4mvxFE\np+lYcgKA+oV3UDr8M2htbxsOokNbkB17kL+Ow8uGuDa6D97auddQOvo0dNXbhoPYyHXIjH0NSoST\ntYfShtNY5s1Gt6wdANKbKeOXeTtFTei6UXJ6i7/ZipcN8XDL2iFRlpHd7m23YXeLOrfkBHIWA7d6\n34HXKhjLFZySE2RTNuThmTldA0r7aJMQL0vtLlmY1zcdbfSQteeuo+zXi9NyqTwBQHP2MIoHf4RO\n3dsGr3B2FbLj30Q4zdmxLoWB/hvt2RAP16wdaEzvQ/Hgj6E1vT2yEOnbQHNZcoT9AfOShScbXbJ2\nwD1It1I7Q/cMzxGblyy80GlQcF3lZO2Ae5BuRtepxJ5/g51RAkaQfovzpkmfXHWH2WmVKBua3OPf\nWjmM9No/RXLVZ3tLXwuJIBiPeHQaeRQPPonmjMMWcQ6SEkN6/ZeQXHF77xvpMSrzedmibqV2Bpju\nXS9Ra9MoHngcrTmHAcizMZxEZvQBJBZ/oveNzBZ6xMGLY7NSPQlMv4iekl+4j9ZdnLIhHmoNmHnZ\n4uSMnZ9O2RCPbtY+8wp6JufIAO2W9vooS4+NFbouPdmmTDtTM1v8Nzvolpxm30DP5Bwdoc1KTjto\nebSL9DyzefPDAjY9kCPeTyVLM6wyn1daeVq/M23W0tp1quycf9P/8SQFqVV3I7Xu873zRHyFUX3y\n+LiNmeY02WhyIFqrguLhp9C4+J7DH3KQw0iv+RySq++xzGVrjbnM+87NS7A2NSkJo7Kzyv/xtBY9\ne259VIa1ZOGV+jkaj+ZA02+QbqbTNMrnlkdlWEsWlwGew7xijQuaUx8Ec5YAoLVRPvZL++sLSbfj\nS2xZQP3Cu4GcJQDonQZKh5+yv9F/czBnCVAZM9KbtdYmXg/kLAFAb1dRPvp074vdyDvoAEuutpeO\n0puCOUuAImHrs4lKkpxRkK4kkgSk1tMEYiazNZizBKjsn9nc+1o4RyXOIJ2BJImcmHWcZLcHc5YA\n7VhMbeh9LTLkPQu02SjThhLJkonnrgvmLAHKcBO9j3e15o4Ec5YAoHdQOfmMPbPuuzGYswRojoj1\nTuiN6X3BnCVAc9lHv4Yta+37ZDBnCVDFJWqpuiTWBHOWAI3DgZvsrw98KpizBMgpWu+31IZgzhIg\nO/qty3Uy+YTL7Cyd+P9hHzCBQCAQCFxYwKaeoAiHKRAIBAKBB4TDFAgEAoHAA8JhCgQCgUDgAeEw\nBQKBQCDwgHCYAoFAIBB4QDhMgUAgEAg8IBymQCAQCAQeEA5TIBAIBAIPXDmHGaRLSw8M07wKjvLo\n9PYslaMBu6pcOgCjH6lXgWceFhuVCE/1wCOypVOH3nEQi/WIZrkOHprbOx+vZf+/5qFBuRPW67BQ\nGzuW36w1LoONlg41XoWJeVjP44Kvi2Zvgu6lsbbjMXtFBuSFjm8A80o87O/wjeU8KrEFzhPMucyj\nWD0P62/00pTd8XiMOcF6n/s+puU3qgu00Tr/64zxeYW5Yr1kdV1D7ewrKB/7FfSOvwEcHd6K3Oa/\nZMhUydTWzdqmzA2txdTT1HUd7eIpzO55jHqa+iC++AZkxx9iiEsrhgbcRn82qg0SD7Y0vNZ1Ha38\nEeT3/oDfpJxn47LbkB39ql1cmifG6mpj1dDTZIi1dvUsvTQ1N8PT05QiwNBd/hsqt0t8Pc3EGhLU\nln3GifldQOl9++tyjHRGvTaH79LKkyg4S1y6q2fpx0ZN4+tpKgnSiowO+rOxMUVivywn3tWz9Gvj\n7MtMgQG1No3Z3Y9C89h4vUu4bz36t34HcsTaBs/oRdznUVXoko0qMPMiU2CgXTmP/O5HPYtIdIkO\nbkZuy/8AOWRtgydRn9asR1Uhs41TvwcaE/b3IoOGLqjHxutduHqaMrWjy3C0gHl0GmQjS+mnq2fp\nt30oT08zMmiIH/gc3y780dRKqMH5j9Gc4ai+m5Fj6N/+XUT61rP1BruEcsCi+5ylvbo4CZca6JqK\n0rFfoXZ6p7uJ4RT6tn8P4cxKZxv9DN7iPlIhcLKx00bx8E9Qn3jd3cZoDv07vo9wykG+CqBm38N3\ne+vPO7ebpJ+cZJ8khZqHpzhC1mZaBQoQ3CSVYkvJRjdHrGlA4R1DbcIBKUxOM7nS3cbmLNnolqkl\nVlMA4sXG/OuOyjkAqCow9Bln+bEurEbcLJLr6dq4OTlNM5wGR3/xko1xYORubz2E62eBqT84ZlW6\nrqF69mWUD//U/XhyCH1bvo3o0Bbne1BJ0eTsRaWlepLEpx0qRLquoXLyOVQ++o0HGyPo3/ZdRPo3\nusxlWRKW9tKft3yE5K54WqcAAIn6/eY4QtZmOEG6jfAAnUcv/XlL+0mtxFHCTiat3MwmDzY6BOmX\n8KlC5IEr7zB53eQN6hd2oXTkZ9Ba7AkyvuxWZEe/Zs+G+NZRQ+0V49aKAAAgAElEQVT+T7DfVmvG\nifaiFWj8SfUiZnc/Bq3B/pvkqruRXvcFtrgqz0anweuUDTHQdR1q+Rzyex6D1ioxP5Na+wWk1tzj\nTSsQgGvW3pojG1nZEI/IsBEsMByxpgFzbzpLFNlQSOUgvYH9dnOaMjY/Jc3YEsoOWZGuplHEXT3m\n/XhuWTtDLceV+ErKsln3hKbSBF876f14coSqALwG2NXT5Cz9LH0k1hrBAmO8aapR2eHJrdnpNEvI\nv/8DqMVTzPejIzuQ2/znkP00BXfK2jtNIxviya0x/qQxh/yev4NaYWR5AOJLb0Z29AFIio+m4E5Z\nu1oDpp4DWjPejxfK0D3Ia+Zf/MAI0j3O75DIIfXtYL+tVoCLzwCqjww83EfBAi/xmXsPKO71bmMo\nS9qnMQ+BpgtX3mF2qU8YYqz2CV1rVVA6+nPUz89LBsmRLGVDPF27xCoqffGiciUBDN8LRE2d8Z2y\nITlOzqF8kFn313UN1dM7e1Q+5PgQBrY/glCSE00njYyKp2cZSpON3cGr6xRc8LIhJUlqFqX9TCeg\nax1UTvwbKif+bf4rUkvRt+1vEYpzounUKGUhPD3LcA4YMWXtLtmQWptGfeJNJFd9GnKYFXnKJC1l\nLjk1Jo0yHycbSm+iccNTbrdm7ZpmOI3jzI+3K+fRuPgekqs+yyjvGzZaS071c8D0Tk752xCKbk4D\nzQtsG60lJ00laTCeCG5kgBxj6QO2nqUUIum05Nr51xyyIb3TRvX0C4gMjCGS5Tjv+DJg6LPzjpiz\nZDH/m0aA2GKqhLAyBylslM9NouGVo8DMa2BmQ1KIZNFqp5iZg67raEzuQWHff5v/vlACA9v+FuHc\nGnbGFltKmWRpP9j3PSNrLx0gHVrmb4rQ2K0cYwa0uq6jfv4tFA/8y/xXRNLo3/59hNLL2DbGV9D9\nxQsW5TiNHbOqEm/JAjSfVk/vRHzZzQjFOSXJ9CZSRuk6YrcgPbmWKkUVjkKSkiInZ1ZVyu+i8cs6\n70qCbCjv5+hZGtlhnynxcVqyAFCbeAOSEkV8EafkvhBZsq5VV81hAoYY624StmWcxObMQRQP/Qjx\nJTchteY+djakxCkq7EbsjQskasu90Osp45zin+ge4VKtBcy9C5QPMD/aaRaQ3/MDxJfciCRP3d0q\nXFo/S5ME7/vTm8jO6ef5Zb70OA0eOUJrAXNvcwevWp9Bfs/fIbXys4gvvYl9k1qjrmpXjJX1/cbg\njS3jZkO6rqF66gWUj/8W0NqQI2lkNn4N8cXXs39PKEtOrrCLnw2F+4HBW6m819WzzL/JycYk0r+L\n9Nu0Qy/ZqKmonHwWlRPPAboKOdqH7PiDiA1x1ovCAzSZzr3h4KyHyMbIgKFneZhKT8xszJAdUqKk\ny8kq80mKIcJ8DUlptYuG+LWD0xq6E5h+iZsNNfNHSYS5NglAQmLFnUiv/wI7G5MUWvvRVP6ShRQ2\n6WlKNJHNvsZemwJojPXfCszs5GdDsWWGnmaaNmwUPwAKe8ByrJraQGHfD6EkBpHZ8Gfs6pMcpXs6\ntYFsbM5QdaDFqSzFV9Lnp58H2hwh6MQqCqRCSTo/xT1kJ8tptauYe/8fEelbi9SaP2FXn+Q4yWcl\n1pCNjYskIt7mZGPJtUBmBzD9HDPxAIDa+bdRPvJzaO0KJCWK1LrPI7niTvY8JccoQKqfdA7SB24G\nEsZSRf2ckfhwlkxSY/Rv+jn+XJYao/GjRI0K5DsOiU8SGLqb1uG5QfoUigefRCtP70eHtiA79iCU\nWJ/9w36Fry1cXYfZxWHw6rrGLxvyIgRNpRS9+D68lxLgLFzqMHh1XeevP/CES7U2UHjXiHR9EM7R\nBMbaQFKfIBsZg5dvo0Nd323wcmiXzqBw4HGoZbtTocH7dSgxD+tFl5BJCzO71b6rulOn6J+XtXNo\nFU6geOBxqFV7Bhgb2YHM6ANQoj70HKWQ4dgYupJqlZwNL2vnEVtC19q6bqXrFBzNveVrg5fWrqN0\n9Gljfbv3vlBiA8iOfwPRQQ/rRWbiK2gCtZbLdJ0ypLld/kq3cpSCiOQ6uyxTu0DBMCMQcLwHE2vI\nEVm1T3WNgvXCbnbWzsNpkm3Nko2M9T5HG81Bes8fdSh7LL4P5/W+XtT6DEoHf4zmrD3QD2dXITv+\nTX61jkd6E9B3vX15QlMpuy19CH/zbZaCy9hi+3v184Yj9rYMBVBFrXp656Ug3YykxJBe/yUkV9zO\n/mNz8OODP47DBPwN3lCGJhK3zQ4Og7cXo4SW2+EsMupn8Ib7qETmttmhOUXZBS+KvYRMQsS5bc6P\n4vgZvOZsyInGecqIXQav3mmhfPy3qJ7e6biNmwbvF5FccYfz9wJUuhy41V0wuXaWbjCXNVRNbaB8\n7FeonX0FTudHCiWQ2fgVJJYyBHOtxJaR03DbkFE9SeVrZsnJhByh8lg3G+Kh1ijDdtt4A6AxuRfF\nw09Bazpfw/jiG5DZ+FXIEZeNcnKMhIO72RDXxgpdF15Gbia5jjZ5OAkm6zpQOQTk33F3xErSsHGV\n8+fcsnYzXsp4ukaBcOE998fHnIJ0M608BcPNKceP6bqG6pkXUfnoX52fOpAUpFbdjdTa+yC5CSs7\nBelmmtM037ruB5FoLstuc95845K1m3EK0s2Ec2uRG38YoRTDSUsRYMn9voTP/3gOs4vj4A2wy8lt\n8IYHjDLfkP09Ho6D1yEb4trYMZWcGI4mMmw4Nh9ZWXOabGSVnCSFsl5WNsTDZfA280eMMp/zDW3G\nefCGaWJKj3kXgNXaRvmcnbU3pj9E8dCT0Bpuwck8kf5RZMcfQijBGB9ylCb45HrvNrpl7Yk1lGH5\n2fJfO0W7Ihklr06ziNKhp9CY2uv5cFQ+/wrii29gf4CXDfHQdaB63CifM9allZRR5lthf4+HWqXf\nzFvzNS9ZeLWxcoSWNlhZeyhrODYfG0XaJWMuY2366Qbp1/mbyy5l7fa5rF2eQPHg42hzNkKxUBIj\nyG16GJG+9Yx3PQbpVhuLRuLDWpf2GqSbac4Yc5m9fO81SO9BDiG1+l6kVt9rL40v/pIvX/DHd5gA\nDd7CHqC4e/41OQqMfC74czTtEnD+F70DLb2Zdn563ilqtlGjaKpqWjdUkrQhJsKolXuhVSAbzU4z\nu50ccFAbp17onVRCGbLRRxTVa+MscP6XMDvN0pFfoHr6hWDHk0Lo3/4IogOm51HD/cauOH/lkUs0\np4ALv+55qXDgcdQn3ghmohJB//X/AZGM6RGT6LDxqI1DNuRE/Tww+bve14Y+DSTXBDue1qLrYlrL\nas4exNwH/wTd57PDXaKDW9C//bu9L47c554N8eg0gPNP926ii68Ehu7w/7wdMF/2zZuvqwIs+pz/\nZ167qDXg/M9718WT6yjDCvIogq6T8yjumX9NipCNfoL0HhsrwMTPezLs6tmXUTr8M3+l5XmDkBl9\noLdcKcfJRj9Bupl2EZj4BXqcZvZaChCCzmXTvY8xqfUZ5N/7v9Hx+Vxul1BqCfp3/I+9Sy+XyWFe\n3dZ4kmSfOJT4wh46DWcoazETXxLs4gH0d9YTG0oFd5YAlR2tkVx86cJstEZy4WxwZwkYx+sdH6x1\nEs/oqn0dMdIf3FkCRhncYuOMn8dTetE7LXRqlpsyMhjcWQLsTCXus/mCGTliW0dsFU8FdpYA0Mxb\nz5kU3FkClJFaz1lsUTBnCdA8EbOsw8mh4M4SoMxetmTOsSXBn9uTJLs9Siy4swToOlvKqK38kYDO\nEgB0tIuWjXahVHBnCdA8Y83eYpd3LuvUpgI7SwBQK+ehNb1Xm/wgeskKBAKBQOAB4TAFAoFAIPCA\ncJgCgUAgEHhAOEyBQCAQCDwgHKZAIBAIBB4QDlMgEAgEAg8IhykQCAQCgQeEwxQIBAKBwAPCYQo+\nZlzGzlMCg4/BOb2cHceuFB8HGwUL4uo7TGuf1naJegoGRa3YZaAqx0krMSh1S4/IVp7a2wWlVbD3\niKyyNRw9oWl2PcbmFJ2LoDRnYO13Gxvh6M15JJyzqD40zlOLsqA07LJSsREPyvJcZITSli48tbPU\n6i0oNYZYsh+RZyuaSiLeJmJDWxakLB8dZMicVc8EPh60ll1Jp3qSbA+KtZes3qa2g0FRG3b92+oC\n54mapSF4pwo0gneogVq1jb2F3oORgbHeF9pzNJ8FpVWyKYYsaC4DbP3Fw5mVkGM+etJakCNpyOH0\nwmzicPV6ybo1p06uBwZuYyuO85jbxe94L8epJ2jMRVXEjItwKVLj1EDbq42aBsy9yReMVVIkGOu3\n+frkc0xhaaYYqxcbZ18BqseYb6vVi5jd/Ri0hptSwTzh3Dr0X/sdjjKGRH0ncz4cnaYaQtF2x6Pr\nOtTyOeT3PAatxdYOZBEZ2IS+rX8FOcRqgydT8/WMD0ksTTVEmBkOE6C2fkP3AEwhaw6Vj+jaMFqj\n6Z0WCgd+hMbFd7wfT4mhf9t3EelbzxFhXgIMf9ZfS7vSIQc9zRAweIc/TUK1Rpq2PD3N+Arqzesn\nYCjuo7mHOU9E6Hh+WgOqFWDyGb6eZWIt/W5fc9l7JF3IsLHTLCH//g+g+mi+LieGSfSeJS4AkDpL\n/83+5rLCO856msP3AFGfzden2Hqal3R3j/3S+/EAxJfciMyGr9jnno9V8/XqCUO02IP8kZfB25o1\nHFvV+XOAt8GraSTP5EUfUo4ZjnjE+XONSWDq92wVByteBq+mAbMveYvmlAQwfK/74K2fA6Z3umov\n0uDdifKxp52PJyno2/ptRIe28vUBu4QydIO5yXtVT5KzdJFT0rUOKid+h8qJZ5yPJ0fQf+3fIDIw\n6m5juM9oFu8iiVU+CuRf89DzU6ZgJssRsu6iNkiY11XySUe7dBr53Y9BV53vhfiyW5Ed/RpbhNlq\n48DNQHrUxcaa4TQ8ZCvRRRQYujniwl5SH3IrEUshkthLrnX+XLsETD7rTXsxvoxElt3Oj1OQ3mNj\nGBi6y12pxS1IN9B1HY3J3Sjs+yHcJAjTow8gufw2vt5wFzlKvznOUBUy05gmx8YM0i0kNxgN7d3m\nMn6QbqbTKCC/9+9d5b2U+ACyYw8hOjjOeFcClnzZVz/wP47DDCqwyxu8mkZyMGYlES9IYWDwLiDJ\nGLz1C6S+bi3rupFYbThiq40dYOZF/2U4OQoMfYbdvLt2Bpj+gz/BXoCftWsq/eY6JxviQIP3B1DL\n9vJddHg7cpv/AnLIQU+QRXoc6GNk7VqLJhKGqLATan0G+d2PoVOzl2/jS25CduxBSIqLTmAPDlm7\nWgemnuVnQzxCWUNZhlE2Ku6jSdmHqLCudVA+9mtUTz9ve0+OZNG/4/v+RYXDA0awwJAjm+uqdPiZ\nGxyy9laBJmTVe4UAAD9r13WS8+JlQzwkhSb7FEMSqzlrZEMegnQzvKzdT5Bu/jO1gcK+H6I5s8/2\nXii7Cv3XftefQDpgKMvcxZ5vZ14Caj5LrnLEmMsYY85jkG5G13XUL+xCcf//C9t9IclIrrgTqXWf\nh8zSMo0M0jX1KfBxdR2mrtNAyL/NnOTVygUUDz2JUHoF0uu/wP6hkkI6dakN9P/6hHGiWY7NmNQS\nq0mbr2mfLAH0Dl5NJSfE0d1rl86geOjHiPaPIrX2c2wxVikMDN4+X3KqngRmXuY4NkNPM7aUbhSW\nniXQO3i1llHmY6/dtAonUDz0FOIj25BcdbddAw6wZ+2VYxR0sLIhKUTl0ugQ6f0xSk66rqNxYRcK\n3cEbimFg2/cQzq3ll/n6bqQgp8TWs7Rl7aWDdB2ZZb4w0H8DZaizr9nXzgwba+deRenQj41TkEbf\n9kcQTi9n2xhfThqdpf38Ccxaciq8DxTeBbvMFzVK92Fg9g3+JJvZQjJ0ANAuU8bGy4YSa2j8FN8H\nqh8xP6JWpzC7+1FoDXLgqbWfR2rNvexMQ4mTEj10spFZCZGA7A6gbzv9tzVHGRt3yWID/abCe/wg\n2Zy1axow9xZQZqviqPVZlA79GHIkg8zGL0MOs5RuZBoPmWvov81pquwwynwAKEBLj5FQNa98HhkE\nhu8jR+wWpHf1NNt50mxl3vuKkbUbUnf188D0C/y5LHMNSY/l32QGjLquozV3FPk9/2BcNxm5Ld9C\nbGQHe3yH++n7mxdJkox37w/ePq8mVT0DzLCDdF1TUTnxLJoz+5EZexCR7ErbZwDQfTX0GWMucwnS\nI0MkCl47Q2Occe9r7Rrm9v0TWrO0xBVKLUN208OIZFcxfo9Cc1nmmkBKKlfPYbYLwMxr9k0pMMpm\nJ59F5eSzlzYEKLEBZMe/geggZ70oPECyOUyxVtgjiK6W3twu/uBNbwQqR5llPhIu/R3pQBrCpUpi\nBNlNDyPKFGMFEDEm+hbHUUcXkY3d8qOuAaV9zoM3tQEoHwFLrFVTGygf+zVqZ19Gd8J2HDwAOepO\nE2hzsqHYUrrxuxJheodKZNzBW0ftwttILruFXeaTI+QoUxvnRZibU8DMK7TxgEV8JWUZTu8P3Dwv\nEaapNDmXPgTLcWmtCuoXdyOx7GZOMBEjx5ZcO29j/bzhiHmOazUFO7xsKLmOMqmu3JXWorHIXcdO\nALFl/AlZSdJEklg1/1rtDNnIcMS6rqE28TaiA6MIxTlr46lRChC6gWqnQcEtzwY5CcQWAzW2o0Yo\nbYgwL+saQRUW7jKMROO7dprpqHVdQ+3MSyh/9BvoHXIqciSDzOjXEF/E2QSjZKnkVj/Ffj+co3uw\nK8ml61QSzL/Fd1ypUcqumNkQQ/RerdB1qXPKh+F+up4NzvuRAWMuG5q3sXyI1l+ZjquN6rnXkFhy\nE2Tm2jhD9L5dpACgYZ+fyYZh+ixj/gaMIP3A4/PSfUaGl173BUgKo+QuKUByFKgedg7SzaL3rTxp\nErfsSxK6rqM5ewhq6QySqz7Dvq9jS+g8LkDu8Mo7TF2j2n5hD1iTfKtwAsWDT0CtsLOl+OIbkNn4\nVc5GEZZxCpC7vvdEm3EbvAya+SMoHvwROjXW2pGExLJbkN5wP2ejCOtPwjQxpcfmJ2QzboOXQWP6\nQxQPPQmtwXAqboOXhRylCT65nm2jw+DlklhN2QurnKd3TOPEq5J63HAaq9k2NqfJxrb3jUlIrjcc\nG2Oi0VQqOXpZq+qiJMlp8NasGhcpWPCyntYlPU6lYNban9aijSJlTtbOIpShiYRV9gco+udk7WyM\nbCi3w6bjCMDY6Pc2UDni2cR2eQLFg4+jzdngEh3aiuzY16HEvK5HyYbA8Ta7Ji1ADj3/pr+dnpFB\nWkO1atIChiM+Tsf0sn8BMOayHZSdM+eyKjD7OrcaxsQapFttrBwxKoDeSqMUpP8KtbOvgHVPKPFB\nSnwGWGuIHGLLKABmOTZdMyU+HndbyxGg75MUjLntT3DhyjvM8mGa/C1oagPlj36D2pmX4Db5yJE0\nMhu/gvjiG5y/y5oN8fA4eLV2DaWjv0B94g3uZy7ZGM0hO/Z1xIavdf5gfCVN8m4bRjwO3k6rjNLh\nn6Jx8V1XG5X4ILJj3+AsgJtIrqUMy00w2evgVRK0eSm5ytVGtAo0XtzWKFMbKVNlle2tNhaNrJ0R\nsF3Cmg050ZwhG93WKNObgb7r3De1aCrthCy+D8d7IZSlCdmLYHJjkmzkZeUAmNkQ18a2kbXvd7Yx\nPAAM3upt52F9wnDE/DVKXWujcuIZVE7+3nXzlBSKIb3+fiSX3+b8vZFhstHLLnSHrH3+i12CdDOd\nBmWvbhtbYouNbCjr/Llu1j77hvPmG7cg3YxaM/aYOO+3cAzSLcSX3EiJD7N8buAWpPfYWDaCBZfE\nJ7GG5jJWkB6Aq+AwD9GAM9GY2Y/SwR+j4+ORBACIDm5GduwbUKwlJTlqlPl8RhAOg7c+uRulQz/x\n9UgCAMRGtiMz+gCUqGWgu2VDPBwGb+38Wygd+Tn0tr8NB/HFNyKzkbHF2i0b4troMHjTY3Sj+nkk\noVtyyr8NwOKIQxnDsfncrMLN2iWa6HLXsbMhro0aOQ/WRpxwn1Hmc9kxbYWbtUtAdhtlRH4em9A7\n5IQLjI04ATc9UPn8VcYuWCMbynKyIR6aSsFM6QPbW625j6j6VPW3wSucW4fcpocRSloCCylEmXl6\n3KeNLVqHZK2peg3SrfCydilC69fmJQsvOGXt1iULr1S75fPedd9Oq4TS4Z95CtLNUOLzVcQXMzbK\nWZcsvOCU+CgJ+s3mJYvLwFV3mPWLu1HY91/9W9r9biWKkTsf7V3EXvrAgurSuPDbntp87dxrKB78\nUXAbQwksuvM/9764/JvsMp9XJn7RM0lVTv7e97NIZkKpJRi66X+ff0FSgOUP+3NsZnQdmPhJ7wSQ\nu97fc5VWqmfoMYouchxY9vXgD+frOnDuyd4JoP9T/p6rtFI6DORNFZRQBlj6FXaZz5ONGnDm8d6q\nwuCdQGpdcBvndgPF3fP/jwzQ82cBNj3M2/jPvRnf8D3+Ay0zs6/3rOc280eQf+8/I3C3ITmERXc+\n1ruWtegL/oMYM1M7gdqJ+f/HV9JmwaBlPq1N59HMkq/4eszBxsVnejctJdfTpp2gNnaawNl/6Xlp\n8uX/6DuRMDNww/+MSNb0DG56MzBwU+DjQa3SfX0JCVjx58HnMgd4DvOKdfrRF9LRBbi02N/DQk+M\nZYFYay/QRtZvlH0+VmH7+14noS3wPNp/o7yw8yhJdiex0N9sXW+VlAV1sqFJwzK0F2yjJSuVQsGd\nJUBOzDq5LXjsWG2MBHeWgPG3l9lGqfda62odC2rNp6n2v1+wjZbzKEcXtibGqmgs2EbL/bFQGxlL\nHgueHzuWjUpuyypuWM+ZtMC5LIgJV/XbBAKBQCD4mCIcpkAgEAgEHhAOUyAQCAQCDwiHKRAIBAKB\nB4TDFAgEAoHAA8JhCgQCgUDgAeEwBQKBQCDwgHCYAoFAIBB44L8vh3k5xLCvNFfaxstxfOsxLrfN\nunctSP4xrvR5FDZeHhbWJPuKcKXH9+Xg42Cjlcs+T1z933zFHGakfyPCGY5Omisycpv/0v7y1Au+\nhEd7qJ+z9RdNrLgD0aGtwY4nKei79jv216d+f0m6zDfVk7ZG36nV9yDSPxrseHIEuS3fsryoAlN/\nIJ2/IFSO2ptoF9+jJuBBUBvUUNqMVqM+pkFtLB0ANEvf3fxbJAIcyMYakN9lea1gSEMFtLGw195s\nf/Y1akofhHaJJOPMtCapXV5Q5nbB1sh+5mVSAgpCaw6oHOp5KTq4GYkVdwY7HoD06NfsHZem/0Di\n3kFoTgP1E72v1Y4DpUPsz7uhacD0S/bXpxcyl523a3lWDwMVjvyaG5pKc6uFvmv/OnDHrejgZkRy\na3pfLO2jJvdB0FTSBu59kfo8X0XHeUWbr+u6hurpnagc/y30jrfBERkYR9+Wv4Ic5nWdl42+oGPe\n7NJUGpycbvckxnoM+T0/8CzHEx3egdzmP4cc4rR6kkKkNpFc69HGFjD5HFe5Q9d1NGcOYO6D/+LZ\nGceX3ITs2IOQrC3dLtkYBgbvApIe+4KqDWDqGWfljsRqYPAO7zdZ6UMS8uXJfMlRQ7mdI0dls7FC\nAsdOyh3JDdSMXPYYK87tJqkvXvs2OQ6M3ONNtQMghzj1nKNyB9KbSKbIi42aBhTeMTRBOSgpEm32\n2ru0OUs2cpU7DPWTPkZzbZ6N+df54twgUfnZPY9Ba1ibvbMJZVeh/9rvQonyektLRo9jF1Uhs40z\nL5Fz5BEeMMSvPSpi1M8Zove8uU+mRuReexy7iN4DAKIjJMbutZ919ST9bo4Kkd5poXDgce8N2OUI\n+rf9DSL9o2wxa4D0Koc/672tXfmo4Vs4KjbREWqM70WVxiNXvvl6Y5JuMoYYq1qbRvHgk2jlHaI0\nOYT+a7+LyMAY/0Sb8TJ4K8dIucJFLgggFfHi4Z+ifs4uUXaJUAwD276HcG6tNxujw8DQPaTczqN0\nkLrwe9CGpMH7BBoXd3E/I0fS6N/+CELp5d5s9DJ4C+8DhXfhqeenFCKnmVzN/0y7DEw+410bMr4S\nGLrL2RHPvesum9VFjgBDn3aW+GrNkfPteMymkmuBgTv4Tk7TgLm32EoYTBtjNPE5NRFvTlNFo+Ox\n52dqjIJNJxtnX+ULSVtRkhQssHQhu9TPG9kUS6S5F13XUD31govYgIzclm8hNrLD2/gOZYDhe4GI\ng3xW7Qw5IqbgvBUJyO4A+rbzP6KpwPTz5DC9EO4z5jIHKcDqcdJT9aQNKQP9N5BWKddG5yDdjK7r\naBdPYXbPY1Rt4RBf+ilkR7/OD9J7UEhlJL2R/xG1Rj7FTV4PgKvuqU+uvMMEDDHWt4AquzRQm3iT\nZKosJz2++EZkx7/BUewO0T9m9scZvGoDmHoWaE2z7QyluSK57fIE8rsfhdbqncwTK+5AZsOXIbEm\nbSlCSzHMSJIzeN2yIY6NToM3ufpepNf+KVuFXI5R4MCcFDiDt1Wk88jJhtTaNEIJTmYVXUSTqdUR\n598xSoeMcaXE6RzylNkHbweSljJPa5ZufE42pNZnEIpzpK3iyymDNV9TTSOpowonuFOSNM5ZAY4U\nAYbutKt5NCaNUr19DOu6hk5jDqE4x+kk1pCKidnJaRow+zL3PiMba2CeYzlKAVJsce/r9QlumVDX\nOtBaRSgxTgSf3EgRfo+NLtmQkuIGI51GAfm9fw+13FsVig5uQW7LtyAzA1CZsipe8JDeTNKAPTa2\n6bo02KL2jmNHSQEj99kFmp2CdEmhMcLUs5Rowu+7vvflToNsbLKXPBzvwVAOWHSf3RGXDtA8zRzD\nYWpqzghwdE1F6divUDu9s+d11yDdYb5FZIACGmvi4xSky1Fan2fNZUEl9yxcHYfZpXaGZHwYN0Sn\nWSIh5Mn3IIdT6Nv+CMKZFewTHV9OE7kUJs1EXuRrHrzFD4y1F86J7gqX1roacPbBq+sdVI4/i8qJ\n30KO5tC/4/sIpzhlwcRqitoByhRrJ9ifC+WARffS4Jl7j5edilEAACAASURBVISEmTaa9DSrx4x1\nMtbg7aB07Jeond4JOTGMge2P8G+c5Hr63bpKpQ2eGGt38MoxYO4doMwu83XqeRQPPYnmzAEklt2C\n9Ib7IYdY+nam8nlzxijz8SY0Q0+zU+foWRp0S05ShH5LlaELCECtTqJ48EdoFT5CcsWdSK/7Aicg\nU+gGS60HGhdpnYQXnGWuIS1ItczRszSILSUbIQMzL3LHRLsygeKBJ9AunUFq9d1IrbkPEkvZQgqT\n00yuNLKhFzli40aUnb2WArGZV4E2Z902sYqOCTguWbSKp1E8+DjU6iTSaz6H5KrPcgKyqJG1LwWq\nJ2itk5UNSYaeZmYLOYGZV5mVBl3XUb/wNor7/wWQo+jf/jeI9G1gzxPRRXQNQwm+niVA99bw3UBs\nGCgfoTmKUebT1AbKx36N2tmXERkYRXb8Ib7jTI2TcLHWcg7Su3qacpSvZwkYc9k9VF50WLLQ2lWU\njj6N+sQbiA5tRXbs61BirJK7BGS2Av2fcA/Su3qakmQkPuzytFq9iNndj0FrzCK1+j6k1v4JP0jv\nv4mqLzw9y66NuesoO3QJ0i/paeodQ5uXsyaa3kTBR0A1k6vrMAGK3ubeBcr7mW+3iqcQTi93P9Hm\nG4Qnxmr+O946ZHKtIVxqimScxFgBdFoVyOEEJJZEkpIA+m8Gkqt6X6+dMoIFjmOQo/zyVGojRcFm\nGZxOnQYaZ/B2WmXI4STbxlDaEGE2lR6dxFi7SBHmhKzrGmpnXkb5o1/3yK/J0RyyY19HbJizXuR0\nXUJZYPDW3oxH1+ma5N/mOAaJMk5GhKlrHVRPv4Dy8d/RGDRQ4oPIjn0D0cFxjo1xvpJ9uJ/WpM3r\nlLpGuo5zuzhlMpkidcZ7utZG5cQzqJz8fU8mEkouQnb8YUT6OJqYTjZGhuk8mtdxdA0o7iPhZub6\nT/fes7+nd1oof/QbVM+82LPbNpRehtymb/I39DnZGFtMji1sKo9qKgWPnHK6pjYgySFOZSdMQVZ6\nrHeeaExS0MVzDA7jsTH9IYqHnoTWmP9bSYkgtfbzSK68i32fSWHjOrsE6T1z2YQxl3Ecg4ON9Yu7\nUTrcK3ovhWJIr78fyeW3sY8nRYz7hVPZ6WeI3tdOG3OZvXqj6xq0dg2KVZy+S3IDCWSb11I7DcMR\nH+PYGAV0ztzIEr3XdUp8Zt9gjznW33jk6jvMLs0pqr07bcQwk1xHzpK3aK21DeX2D+FpvUpJGorc\nDjt23QavldQYlVl50YvWMjI0jzvrQhnDsS3lf6Z2hmzkbsQwIwGZzRS1sTIWwH3wWmhXzlM2VORk\n0ABiI9uRGX0AStRhvchsY/ZaILuNvzap1qgKUDvpzcbSaRQOPGEr5ZmJL7kRmY1fhRz2okqvALnt\ntMGFpyuplo1Il/+dZlpzH6F48AmoVd7akeSStVs/HqLNN+lxvo3tAjDzWo94uhP/X3vnFS3JVd77\nf1Xn3CfOnMk5B2lGJEkgUEASySSDAEk2xss4gR/vfbpP9+WudV8w2Fz72r4GCQTYCCSMAggJoRwm\nanLW5Dmhw+ncXV11H77dM9XVe1ftqjMzEov9ezvdfaq/rtq1v7Rr/1szB1A+8AN0G4LekaYjteQO\nZFZ9ip+1D3w+SpNneq1Ys7FdoHlClKE5SSylSoyo72d1yQmXdkFmfUC3XaHKl8vilkh2KXIbH0Ak\ns1jOxtRKNpcJrqNpsLlM0KJw2tgsonzwEbSm9gg/Ex1aTRlxar6cjbwgvc/GtnvW7oQXpDtpnKHx\nKLs+ILMJGLpJPN92mzTfirL21EqW3ctnm++cwwTY4N0DlHZCOHhDaRYNSA7G1hRzxC6r6jIbaDKR\nOVEyg5eXDbnRvCAsOREalaby2+VWlsoM3sgw2Rgbl7PRY/BapoHqiSdRPfmU1IIDLZxEds3nkFx0\nq/hD0THK2GRXtdV65XN+1k7Z0OOonf6N1LOHejSD7NovIDHhssozNgGMfhCI5MWfuWyARf3EwsvC\n6oFpNFA58ijqZ1+AzOSox4aQ2/BlxMe2iD/Ua1mEM3I2Vg9RiY+btbMy3+GfoHH+Ve/jgWXtG+5H\nbMRlxXqvZSGzstQyaWwX3xCPNXvLQmbRT7tI2aagBwgA9fOv0NqKjkQwqulILbsbmRUfFy9ukQnS\n7bSmgZnnqR8voHbmeVSOPgrLkFjJr4eRXvFxpJfdza/gAXJBup3mRZa1ix57kgjS7Zgd6lHO8iuQ\nAPz3IxvnyEZeBXLiM/Ir2fFOO8we7SL1X5x9lcwmVm+WWV1lwzKZI3ZEhZE8O9GSUZad1jR7jsvu\n5Ngy+tw2/88lXS457ep/PToCjNwGxAS9ETeaF+k89jk5iWxIaGMHKL058GhCu3Qc5f0PwajJZSZ2\nosPrkN/8Z/3Zphampf7Zjf5t7Lao/OlYjNOaOYTygYfE2ZALsdHNyG/+an+2qUVYNrTOv4K9YNFb\nc2ovygd+CLMlWWWxEZ+3HbmND/YvdNFjrGWxyr+NRo1lxP2LcRoX3sDs4R/DbAvaHS4kFnwAufVf\n6XcgoSQ5SrfV0iI6FeqBOjPi9BqWDUk+MtHDsqh8XngZ9mDFaEzT6v2ZA75NDCXnIbfpq4jlHb8v\naO/MMun+K77W97JRu0i9+KJcJchOOL0Q+S1fQyRtd4o+g/Q+G7uUsZd39r/uN0i305qk58K79nGn\nUz8zd4P/Fa+mYZvLbL7rKjnM67vTT3SIHjmwE8kDIzf7d5YATbr5GynqtDP03mDOEiAHlt3keG2c\nZaoBHuLVw3QDaY7fN3xzMGcJ0G9Lr+l/LbGALakOcEn1CPVZHMOhfODhQM4SANqFQ2hecgQJyWVA\nbnMwG0MxyvgcO8OU9v17IGcJAK3pt9CacZTN06sHe2LSNiZolayD0t5/CeQsAaB5aQc6JUdJOrOB\n7AxiYzhFj+jYsMwuSm/9SyBnCQCN86+gUz3X/2J2czBnCQARVtazo8dolbRfZwnQecpupKzKRvXE\nE4GcJQB065dQPfqz/hfDWcp+gyw00XQKdkP9mXjl2GOBnCUAGNVzqJ10POwfHWXtpABzmRbil0aH\nPxDMWQL0fxnHxizxCXLoQR4P0cMU8Lo96jQHrv/WeEFucoVCoVAo3mH+sPaSVSgUCoUiIMphKhQK\nhUIhgXKYCoVCoVBIoBymQqFQKBQSKIepUCgUCoUEymEqFAqFQiGBcpgKhUKhUEigHKZCoVAoFBJc\nf4fp1IkzOZpmvo/p2D/UlBFZdTue00aRYrqfYzpslBKCdTue00ZvgV6Jg/b/qQXYDcROyPH/XYl9\nMD1x2jjHIezc8WSu59Hk7WU7x806nOdRpPwii3MsXo3NRJw7dc31nhm4X7qCc+vnmP33nBZk1yA7\nzn1ar8FcpgWUp7rM1R7fAGe+nePvvh5z2VXi+u4l27wETD83qAoSSpPieJSn5+aCUWcadM5Ni9ne\nr0Mum2uLEAmXhnOkuRmR2OjaTqdCGnSGc9NijfZVzQsksdwovjG4Ny0AREaYcrvERtd22kWy0bEB\nu2V2UD70YzTOvuDbxMzaLyC15PZB/cKenqXfyao1RUK6jg3YrW4bpf0PoXnxdd825jY8iMTCmwdt\njC8gkWW/k1XjPBNh7r/hTaOJ0t5/RWt6r08LdeS3fA3xedsHbUwspS3u/G5xVj9NeyU7pNHMTg3F\n3f+EdlGg+CA0MYyhrX+J2OimQRtTq4CRD/eLNstQO0HzhHMi1eNMz9KnOLDZJpHxVr9CjGVZqJ/9\nHWYP/tDf8SDYPxegjdfn3eN/azajCUw+AbT7t3m0LBO1U79CxbkNnwTJJbcz0XuHYw9nSfc2KqMq\nZLdRpKepAbntwNA23zaiuAMo7xh8PTJE821YRlXIRrfJ107+vdp8XVYiJr2ONCZlbrDSTqbz52Kf\nn8HrJVzaI7uV9mKUofCat3SPn8HbnqEb31Xiy8fgNU1SAam6y5B1KudQ2PEtmG2R6soVwpmlGN72\ntwjFsi6f0ukcZjfL2Tjz24ENze1YloXO7CnM7Ph7CqI8iA6twdDWv4QedbsZQ6Q4kVkrYaNBTsix\nobnTxnbxCAo7/1EqQ4yNbkF+y9f6N113ooVpf9XUCgkbOxRwNM+72tia3ofinv8jVaWJz38P8hsf\ndJf40qLk2GVUiLpNstFFWQQAkFxB4tcy88Rsb9N1cXbabVdQ3PVddMp8zVk7ejSD4W3fRDizmC9m\n3SO1lklKycxlgiDdbmOzhMKu77hK1122MT5MgvJpD1Wl7CYg/345G4uvk9CF61yWYXOZhMKPIEjv\nRyP5v6GbvI/npfP7e+Mwfek4gim3fxRICC52u8Qcm4+Not0Gr2kCpVfdZWachJIU6YouQGsamHxK\nLCLNI7OJlBhENs68ANR8RP+hDMvaBYO3eRGY/JV0ec+yuqgefxLVE78QfEJHfsufIT7vJveJxE44\nTzaKsvb6GZYNyZX3LLOL2aM/Q/3tXwtMDGNo69cRG90sb2N0hCYBUdZeO0HKGpIldqvbQfnQj9A4\n96LAxjiGt/01okNr5G30ytorh0mhhCsizbOxjdK+76F56U3+B8JJjGz7JiK5ZfI2xheSjaKMePYt\nCjAltCsBkJjB6O1ASiChZdSAS09I6/BaloXm5G6U9vyz0Ib08nuRXvlJsWSWEz0GjN1Fwgg8ZIN0\nm42NC6+ivO97EDmu9OrPIL3so3yha66NCZa1CzZPlwrSnUZsIHEJ0VwmEaT3EUqzxEcgB2hUmQLP\naf77mU2+xTOuv8PsNsjb1/hRW/38K4ikFyKSFahhJ5aR8kPvR5omUHyZZHp4hDOkD1g5CKHy+did\n/fpvzUmKaEUK8el1VMYRacA5S06mSbp2AlFmo3YR7eJRJBbewh/QvMErKPMRGilrNM6IAwjn4DUN\nYPpZoH6K//nICA1M0W9ozKCw89vo2lRMYqObkN/y5wLBY51srJ8UBBBMbsietZsGy4bOcT4PIDpO\nwsF1vpi1UbuEmR3fgtm8UqqPzbsJQ5sehMYTytVCJApeOyYIIDRST8jbsnavbCg+QdkVJ+u0LAtG\ntZe1X5ksEwtvRW7dfXydRS1C2W7liCCA0Emlwa60I2xZ9L5wMfWjOOfZsix0yicxs/PbfVl7cumd\nyK7+DDTe5KPHgNRq0t3kBhCcrN2oAhef4LQsiMalHQhFs4gOreb/hvgEc8S2LLf4JmtZcOaBUAJI\nrmTzxGAAYRpNlPb9G1qTV0Sa9eQ4ZWxJQYCcWkVzRFugmpNYQnOPfS5zC9JDKdLSFMxlZqeO4p5/\nQrtw6PJr4cxiDN/4NwjFBW2t9Bpqa4gCiORKUpLqm8tcgvRwjs599TDXRiqff7RfNapxEZh6mjuX\nWZaJ+tkXEBtZj3BS4LydFciebFvx9YEWAwAq647eFkhJ5fo5TMuiybbwCvfEGPVJ0ncrHCYx1qV3\nIbPyE/yyTq/kFEoxxyaYzOzCpa1pEhF1G7yjt9NgqAtKMHbhUtMg5XbRDahFgfE7yI6pZ7iLHSyz\ni+rJp1A9+QRgGojklpNye1og3ppcQVqZ078RR03RUbIxNsr0LHcMasD16A3eboP1hgSTWX47kNtC\nC2ka55kY62D0a1kW6udexOyh/8DwjX+N6PBafqYRm0c2RodYWf51ccATSgLj9wDtAl0bXjakhSlS\nzGwgG12qF5Zlovb2b1A58QRGtn0Dkdxyvo3xhVR9iGRZ/+MVYbBwueTUPEt9El4mokWZniZzCvWT\nwMxL3KDMMruonvgl6mdfwPD2v0M4vZBvY2IpE4pOkfMqvETH5RHJU++nekTcstDjTE9zJf3tcr9a\npoHZI4+iObkbI9u/iXBKIJuXWknHDCUoeJt5kQI5HtFRutaz+4BZfpmv2yyifPARtKb2ANCQXPRB\nZNZ8VhyUDd9C9+ulp8RlvvRapqcZAzplEnd3am6iVz4/hsKu7yCz+tNILb6NH+CGmQxZYhHTs9xH\npVVn7xWgsTvyIWrBuAXpmU1XJLTaBbKxPcm1sTVzAMXd30Vuw1eQmHg/f+yEc+Q04vPJrvJu0rTk\njt0IMMr64m5Bul0buDVJNnYK/N+TXM7mst8CjVPcj3Rmz6C0//swKqcBPYLMyk8gtfQufibfy9pD\nCRdhcN2mDRxAIgzXy2F2ZmkC40WsZhe1t59B5fgvBlZVhZLjpNw+LNEvsiMSLvUavEJchEtdBq8b\n7fJJlPd/H0bV0TvSQkgvvxvpFR+D5kcLVAtRcJDl6Eq2poDp58WDV0RsgrQmI47yrWkwR8zvw1qW\nxb9JtQgw9D6+rmTzAp1Hw7sf2kdiMXMajvKtR39caKMeIx2/FEdXsnGWxrGfsj9Ak8PwLYPl226T\nhIGr/GhdbGOC9BWTywdtrJ0kx+mn7A/Q7x3+wGD5tltnwQI/iBTaGEqR00gucf6De0/JhdqZ51E5\n+igso///9FgeufVfRnx8q6/jkU7lB/urSz0bq4cp+OFk7cLf7AzS7bjMga7Yg/Q+I0wa28U3uIGu\nq425G6gH6KwGtIsuzsYFe5DutLG8h9aVSJb9AWpPVI7/ArW3fz2w8jacWYz8xgfFFUho4AaD9iB9\nDlx7h9k4T307zkXtzJ5mEYR7wzqx8BZk13weesRrlWfIFkG41Or9DF6ZE+0xeO2Y3RYqR3+O+unn\n4NYoD6cmkNtwP6JDq7xttGdDbjbKDl4tSqXQ9Dr3Rwu8snY7iSXMsaXFnzENytjLu+G5/FuPsWxo\nlbuNzUtko0zPKrmCRMtDLuPM7DDl9n3eNoaS5Ci9BJMb51jWLuGI02sp6HBbTdxtUdYu0w8KpSko\nSngsvqm/TdmhTM8qs5HE0d1WE3ebrDUjXrTVw6hdRGn/Q+iU3D8bn7cd2XX3eSwsAy6X+/Pb3ftX\nRo1l7ac8bRQG6XYsizL84qsSj0i4BOl2OhU2l531tjE6RlmlqOfXs9GtnGlHC9GK/uwmj/m2BEy/\nwM3anbQKh1E+8DC6dZcERNORWnonMis/6b6wDHAP0gNw7R1m5SArpV3B6rZZBPHM4LM7AvRoFtn1\n9yExbzv/A7H5NGCd2ZAIr8GrRWxlPskT7TF4m9P7MXvgB+g2Bb2jQSOQXPwhZFZ/lr8qUo9RKSm9\nxoeNHoM3uYxlQ5LLti2TSr6lN/lZu54gJ5RcIW9ju0AZcXuK/35qFcuGeGU4no0eJadQipx5UrBQ\nhIdXySm9jjk2Tm+Uh2kwRywon4czFLg5syE3mufpWnOzdpdsSGijR/k8kmfZkKA8y6N+hpXPB8ul\nltlF9dTTqJ74pfQz1Fo4iezazyO58Bb+B6IjVAp0ZkNuuGbtkkG6nW4dmHlZ2Gv3nQ1ZFgUehZcF\nc1mYApjMRnkbvRbMyATpThurh1jWPuiIzU4ds0f+E41zL0P2WclQYowqkCPr+B+QCdJ9ct0dZqdy\nDsXd30W3IZgMPYiN34ChrX/ZX24YvpkNhgARRLcOXHisP7qPjgPjdwY70b3BO/1c38ult/4NjQuv\n+T8eAD02hNH3/bf+xn18AfVc/T5b2bOxvBco2e3RaAGCVzYkojMLXPhZ/w2bWMJ6zQEeBLdMmpxn\nbc8oamGy0Vnmk6VdBC78vP+GTa6gQCvIg+AWWwBhL6nqUbaoQbAC0ovWNI1HexUgvY4t0AqwYQTv\n0ZYQW0QWYNEDAFpJffEX6JvYspspwAzSGzI77HnIK0Gc0ZhGcdc/wqj6LGEyosPrMLz97/p7jLlt\n5NyCbGrRbQGX/qt/oVQkT9daNkh3Un+b+pZ2ht7P2ipB5rIGcOHx/gApOkq9Pb/PiQM0T9RP0Pix\nM/IhqnQEsdGo0T1oq1S0ikdR2vt/YbZ8tmMYiYW3Ir/xgf4Xx+7wF6RLInKY12ynn075RGBnCQCt\nyd2DL3qV5dwIJYGI41nH+ETwqETTgPTgyr2gzhIAzFYR3YYjk4kvDOYsAWbjSsdr4eDOEqBI05nx\nJZYEc5YATWrJZf2v6fHgzhKgiF13ZHzJZcGcJUA2Jhb1vxZKB3eWAGU+TseYXB7MWQL0f3HHo1jh\nfHBnCVAG6XSMyRWBF1JAj1BWZcOonA3sLAHQSlFn9Sq1KvgOUKEYEHFkpdHx4M4S4Fc05jSXJajn\naSc2P5izBMiO1MrB19Oc/r4s4dTAeoP2zKHAzhLgzK1aiOy+ys7SDbWXrEKhUCgUEiiHqVAoFAqF\nBMphKhQKhUIhgXKYCoVCoVBIoBymQqFQKBQSKIepUCgUCoUEymEqFAqFQiGBcpgKhUKhUEigHKZC\noVAoFBJcM4epx3KgHeWDEU5xBKT97q5vxzSBtkOqqnmeXg9Kc9CecHZZ8ONBh55wbJjcPDdHGx2b\nG1uGWB9RBtPo00ek75DYENqNlsPGbp3EdYNiGoMKGX7VI5w4z6NRoX04g9JtDqj2zNnGlmNz/E4B\nMPwphfRh1Af3DW6e539WFscG/pHsUtrZKSB6fHhwV5+52ujcwL91SXqPWy5tjtZn62Lw45nmoEZv\n88Lc5okWZ1c255j3g2kOiAxEh9cEPx6ASM6xQ5nVpS34riPXdPN1krZ6yPfWV7kN9yOx8FaBNuBi\n2jPRzxZizYvA5K/4MkNalISq/WzFZppMhHlwU2XLstC89CZKe/8N0urxAKLD6zG09S/4Si16HBi/\na3DrM1cbDdK0E2kSptbSpso8VXQRtROka8dTagkl2b6lApFdro1tJhQt2CA+s4n23PRjY+UwbSbN\nU2oJpUkrMupjmzOjyUSYeds8MgmloffIHw+gjdcLr4E7PsJ5YP7H/G3ZaFSBS08KlFo02vs151MS\nq7RTrKcZHSFdUD9bNrbLdB55+qrdDsqHfoTGuRd9mZhe/Rmkl32Ur1UZm0fj0c+Wje0ZpqfJmYS1\nEG3mnpZQFephmrSZu0hNJr6QiV/7mcsuibWBtQjtO53yIS5gmsDMb8VqMslldEw/NjbOMT3NQck0\ns11FYc//Qaco0JzloiO/9euIj28d9Amyiks+uQ6brx8GZp4feNmPEkFkaBWGt/4V9KjHZKGF2MbA\nAhX2HqbBHNspD+MhP3hrb9MxPSRxTKOB0t5/RWv6Lffj6WEM3fDXiI1sEOja2ZAdvNVjdC28tED1\nGG1y7qWM0W3STSqT4adWASMf9nZyswdpMvEKKnS2gXjcY09Uo84cm0T2nN7ANjn3sLG8l3QsPeW9\n0sC8e9zllABybBefAAxOxtGHBmS3AsPv9fgcgOKbYnFzO+EcMO9eb9WJdomcb9dLgkwjBZT8je4f\nM006hxX3+8CyLBiVsyjs/HuYzkqQg3B6EYa3/W2/SAEXncS8s5u8bZx5Aajx9Ur7iI6xYMHDEbsF\n6X2EKHDNeGRfLkH6APEJNpd57J1cPw1MPcvVAu1DCwOjH/Heg9orSGdYloXW1F4U9/6zp0+Ijd+I\n/KavQg97qAHFJ8gnOPcLD8i1d5geYqxG7SLKBx5GmxdZ6GEMbfkLxMa2eDsNO26Dt3aSlEQ8dCv7\nCZFMTIYjZG226QbwUe6xLAvtwmEUdv0DN9pKTLwPuQ33e2u92XEbvK7ZkAuJJeQ4eY54dh9dUx/Z\nMmXtdwBJjvaiUWPZkE+R6+QKFixwnFxpF0lmScoFAWBZ+0f5ElWdWbLRr8h1ei0wLMjaC68Ds3v8\n2RhKAuP38CWq2gWWDfksC2c3A/n3DdpomiQbVRVIeokIZ+ge5GXtzUmWDTWkD2eZXVRPPIHqif/i\nvp/b9KdITLzf3zwRyVNlgZe1N86zbMhLt9KORpJuuS2Db/kJ0u1ER+la87J2ySC9H53k+7Lr+TZO\nPu2/BRCbT4EhzxHLBul9ZrRQ2v89tC7tGHwzHMfwjd9ANL/Sx7UOkfZpbkvwzfcZ195h9jDqTIz1\nJPdtp5p6bHw78pv+hB9BaCGm4xd3EWN1lJzMNpMQ4vcIWoUjqB7/BVLL70Z8VBB5OgevWzbU09ME\nhGKszpKTHkljaNs3EMku5Q+G+CIq9ZV2iPUsnSWn8l76fp6NPT1NsynWs3SWnIwqcOmJwV5Jj+Qy\nklorvi520M6svbgDKO8E12noCdK+NMpiPUtnyaldYmU+fjZUP/8qGudfRXbt5xDJCISTk8spANHD\n5DRKrzGtSg6hFGWmrUkmR8b7HTFqGSSYkklrmoTVuRqLdD+0pvYgu/YLCKcE+pKp1XRtdJ05thdJ\nc5BHOEvnsXGWxM556Ama+Hrlc9dsiOlpxidI21HkoDMbgKGbr9g4/RxQP87/bGSIMr/aiX7JNBtG\nYwaFnd9Gt0bjPzq8DkNbvy4Ql2el8egIOX3uudZojujdq6YBTD0j1IHszL6N2SOPIrnwViQmBCV3\nZ9buGqQzPc1wCii8Ip7L7Fm7V8siNo8+P/uWWM8yMsyCBXbeXFoWptFE5djPYXUNZNd8DnqEp0Or\n0/jKbqQ/vYL0+EIgdyPd95xkw7IsdEonMLPrO5fXRiQXfwTZtZ+HxgvgeyVY0wBKb/DPdXSEsk0/\n7SHn11w3h9nDRYy12yxi9shPkVr8EUTyKwROYwETLmUpdrdOA60muAnDOZpYyjvBm2zNTgOzR37K\nnBb9pvj89yK37ouCEjBTa2+cBTqCMp9TuNRFjLVXcmpM7UVm+T3QdI5Ekh6jCbkn/XNZjPU1QdlE\nB7I30MQkyoaSK0jYOcRumM4sE78WRJexcZIzquwH1yGEkhS59jJcy6TPFgWDFyGaACqHxJNteg05\n9J7zbxeBmd+JS8CxCcoaBL0hozGN2QM/RGuGOQxNR2rZ3cis+Di0EEdEWQsDue3kBEXZUGYDTba9\n6Lo1TRG1qAQcX0yBXp3fqxmouOhhpFd8HOlldwvGRhTI3gjM7hZPttktFGH3JprmRTqPoqAnsQKA\nCTRO8d+PDJOGaE8izOzQJDW7j/95PU6l5PJOQTak01jI3XBFIqxxjmzkBD2WZaF+7kWEYkOIjW7k\nzxPRMWD0tivl8G6LSsCigCKUpN54eSd3vFrdNirHO9oBbAAAIABJREFUHkft9G8uy4bFxrYgt/5L\nCMUFJffMBqBVANqChTyxCWD0g1ckwroNNpcJ+obhLN0TJf5cNiB639OznHlZMH41ILMZaJ0fWHTV\nozm9j4neU+VHj+WQW/clxOcJSu6RISCxHJgVtAP0GDnW1GrbXHYEKL7CrbZZpoHKiSeQmH8TImmB\nbF5yORO9781lFTaX8RYdaqyaclMgybzr7zABNnhfFze9eehRmjxFwqX1t8kp8RrzApqXdqF86BGu\nFpseSSOz9o+RXPB+HzYmyAnxhEs9B6+A1CoaYE6tSYDKmIWX/JV5Qily5jwtvsuDV5S1C0ivo1JU\niFMNcB28AsIZCoqcWpM9GysHhFk7D8syUTv9LKrHHofVHfxdoeQ8Um73s1ovkqdolVe6tUyK7kVZ\nO89Gj55+OL0QuY0PIOpcEehGdIQyUF7p1upSxl7eDfmyOsuGclv5pa3WJDD9O39l9dg8Oo9RTt/R\nNOgczr4F6ZK1Fgby76FMh2dj8zww/YKvsnpr5iDKBx5GtzHoVLRQHJnVn0Zy8W38RUZcGz0WpNTP\n0D3jp6zuDNLtdJt0T1ePSB+u265g9tCP0bz4Bvf9+PiNyK7/EkIxH73B1Eo2l3GqAUadqgAyvdge\nziDdjmVR4FF4mT+Xuc0xLrwzDrOH7OBNrqAMy2v1ndmmjEZUcmJ0W2XMHnwEzcldnibGRjYiu+HL\nCCc4k44dZzYk/HLJwRtK0wXl9fucuGTtfTizIaGNdXLsXoM3nKMI2Usw2WvwXsZH9OeStdvpVM6h\nfOD76JRPuR8PGhILb3UpOfXQKRPK3+gtmNwps2DBvb8tv2pcQ2rJ7Uiv/iPovODk8sdYyyK72btn\n0y6wrN3jUQFnNiTC6gLlPeIs6LKNjmzIDa+svUd8Eas+eQgmmwZlkmX33rHZqWH28H+icf5l9+MB\niORXIrfhfnEW1CO5jGVDKQ8bPbL2Hm5BupPGWRqPglZFj/r5VzF7+CewOu7JhxZOILvmc0gu+qD7\n97oF6QNffgqYeck78Umvp/Hjdh8A3ln7gs97L8qz8c46TMA2eHcPvhdKshO9zN8xXUpO9bMvYPbI\no7Cczwy6oIViSK/6FFJLbh+MIgNGKq6DN7OJHknQOWVCEW4lJ7dsyA3h4GV9n9w2f2UNt8EbpL9w\nOWt/aaDPZpkdVI//EtVTv/K14MC15BQbZ9mQ/A12edFb8dWBkpPZbaF69DHUTj8LP4t+QokR5NZ/\nBbHRjYNvOlsWUjaalLUXXgfgyG61CPUV/S7Pb5eYI+aUI92yITcbZ/fS6l+nI3a2LKRtnKGMmNNn\na1x8E7OHfuy5MrcPLYz0inuRXn7PYJ8tlACGb/VeUeqkNQlMP89/NEg2SLdjdmgNxOzegbcGWhaS\nRIfWILfhfoRT8wbflA3S+2xsUwWpwlloJhukO6mfZlm7Yy6b+IyvOeedd5g9aidpVVqPUApY+Mf+\nTrQdqwucfqivx1c++EPUzww+4iJLasXHkV31qSsvRPJ0wv04NjumAZz5Xv+EPnq7v2e6nEy/2L+i\nMToGTHzKOxsS2tgGTn8PfRP6+D3+nk91MvlMf/YaX0ALEIKuYOs2gTPf73tp+rX/hU7ZR3nHwfC2\nb/Y7pOQyWjEc1EajDpx9uO+lyRf/B7r14JtujLzvv/eXaFNrqG8X9Lmzdgk4/5P+1xZ9xTsbEmFZ\nwLmf9FeQMpuoLBfUxsY54NIvr/ytRYBF9/FbFlI2msDZR/om0srxX6B6nL8aV4b4/PdiaMvXrryg\nJ4CFX/DOhoQ2doEzD/dXZ4Y+AOQ2B7YRpd1A6fXLfxr1SUy/8j+5LQsp9Ajmffh/Q7c/mTD6YXLq\nQZl5pf+xo+gIMP+PAvUeAdBcdv6n/UnKVXKY139rPGepR48Ed5YAOQiHk+g2eQ9wy2O2HdmgHgvu\nLAF24Z0Za8DJqYcz2gzFgztLgF0Dx/jwkxlwj+mYOELJuS33DsXhtHHO19pw9JnnaiOnnWC2vJ67\ndMfqOFavhlNze0h74LpqcxuPmjZ4f8zVxpDDHk0P7ix7/6/1T8BzHjvONRF6JLizBLhz2dznif5z\nZnbqwZ0lHWCwkuO8Vn5xzmV6PLizBGguc849Vwm1l6xCoVAoFBIoh6lQKBQKhQTKYSoUCoVCIYFy\nmAqFQqFQSKAcpkKhUCgUEiiHqVAoFAqFBMphKhQKhUIhgXKYCoVCoVBI8M47zKuxk9DV3o3oWhz/\n98FGP1qNgQ7/h2LjNeaq2/gHMr6VjRjYnOTdyLv4Hry+DtMygYpDucQoA6U9wY9ZPQZY/TuhZFZ/\nBnok4C414ThSSz7S/1p7ijQxgzJ7EAN7dxZeoa3egmDUB3UEm+fpXASlzNF3nHnJUxFdiFEd1ESt\nnyIx3KAU3xx4Kbf+Swg6jPXkOGIjG/pfrB2jbdmCYJp0XR1k13852PEAhNOLEMmv6H+xeoDEmYNg\nmkwP0cH0i/ReEJoXB/dALe+lDd+DYJpMtNyG1WZ74Aakfgbo9u/glV7xcejxkWDH08NIr/pk/2vd\nCtNyDUjtxKDCUfENUisKgtke0HaNZBcjsei2gAaCxLudu1kVXyVdzCAYTZL+s9O6CFTkFVcGaF7w\n3Hg+KNdvL9nWFJMEEigRhLPA+MeAaFbueEYTmHpKqL5gmV1Ujj+O2smnpE1MLLoNuXVf4AuXAkyM\n9V757aqMGnDpSRcZJJ02vM4KhKx5lHaRFJIoK4iOAeP3AmHJjZo7s2SjUEkmRJt8Z3zsFVl83V0h\nIj7BhKUlt0RsF0gUXCCDZBpNlPb9P7QmORv7C8isuw8pN6mmxBLaU1Z2i67mJIn9CiTdzE4dxT3/\nhHZBoNPIIbfpT2mCEm0xl1zJxK8lA4bGedrHWaQko8fpusQ5m2vzMA1g+ll32bn0OtqMXNbG2tt0\nTJGkWyhJexzzpMxENk4+LdR/tSwTtbd/g8qR/5Q7HoD4vJuQ3/QgNNE2eOEM3YNRD8WXHt0m2SjS\nf4VGIsxDN0nb6Cp6D6BTPYfCm38Psy23bSOJ3n8TkewSwXjUafP13BZ5G8t7mOi9aC4bpWvtpV7V\nw2yTdjBPTvL3ZvP1y7vmS2rdZTcD+fe532DlvexEe0fERn0KMzu+BbMhUAQHoEfzGL7pm4ikF3rb\nJzt4izuYmLXEb47kmSq6S1bcLgGTTwGGjKqCRrqVboPXNIHSawMRqBCZwduaIfV1L/kxABQs3AJk\n17vbWHhRLAZsw7IstItHUdj1D66Zezi3DMM3/A1CMYnATAuRzqTbJvmmCUw/RyLeEja2pvejuOe7\nrpl7dHgdhrZ+HXpEYqLQIsDoHUDKZZN80wCmnvGUSLtMcjlzxC7BQu0k/W6uaLgDPQaM3QUkXJQn\nzDYw+StPibTLpFbTtXGbJypHSLkC3io23VYZhZ3fgVFxOUfhJEa2/S0iOYHovZPMBmDoZncbZ/ez\nqoREdh9KA/PucVfR8QzSr2BZJqonnkT1+OOun0stvweZlZ/iC5s7CecoqYi43F+eQbodjSTs8gIh\n6x61UzRX8OaeUBKY+LSvvbHfGYfpIm1ldhrQwjF+hK8naHKOOyKCTgW49IT4ROtRvpq3ZaJ25reo\nHPrxwHvplZ9CesW9Ajv4xwMgHrztIg0GkSis8JhMSmvovf0vmyZQfJkvgQPS8tMjgoxXNHhbU+R8\nuwKBay0iiPAFg9c0ScewdtS/jZFhFiw4nINrNqTRRtocGy3TQPnQj9E4+zvHOzryW76G+Lzt/MnO\n7VrHxoGxewaz9tppYPo3gnOl04bfHIdiddso7X8IzYuOEqMextDWv0JsdKN/G+MLgPGPDmbtteMk\nG8VzbFqIxXMch6KFyWk6ZarMNmX7PDkveFzrxFJg7I5BR+yWDWlhttk3Zx7So1QFcEruGXUa3+1B\nIejL/8edJyw0L76O0lv/PmBLcskdyK75LL/6JLxfIM7ajSpzbPwN4F3PoyhrdwvStWifolOfKY0C\niru+DaPaH6zoiTGMbP87hJOCzMxtPGa3UPXMjkeQ7j6XZcknOLN2o05jx9n+6ZFZT8mDT4GP6+sw\nPcSTGxdew+yhnyCUHEdu4wNiMVZ7yanwKlfbDQATLr0FiC9kyu37wBs03dYsCrv/AUb5FMLpBRi6\n8RsIJwTRWnodnej2NOn9iWrivcEL0IXjlQOAK3qa0TGxnmXvt4zfA8RGgOYlVuYbzJgsy0Tt9LOo\nHnsc0eG1yK3/EkJxwW/JbiY9PcsCZp6jSZRHT08zknMXY7UP3sZZyl54E5DZRe3U06iceALxsS3I\nrrtPkNlppLk5tJ1lQ78BGoJeZ3SEMotQgt0op7gf61TOobDjWzDbZcRGtyC/5Wv9kkSX0YH8NgpW\nqseYniXPSdtKTl7ZUGwenUctzISlzw6eG8tCZ/ZtzOz4FmDUEZ//XuQ3PgAtxLmxtTCQfw+Q3Uhr\nAIqvCyboEN0HmXWeLQvS0/wQAJNaJQIHiNh8Cgz1qGs2ZHYamD3yUzTOv4TU0juRWflJ8W8ZvQ1I\nraTJ7tKT4jZNT0/TbAn1LOlzi4Cxj5IjdmtZXNbTXEGfK+8W/pbi3n9Ge+YA9PgwRrZ9E+H0BP+7\nkytI2NmoivUsAZa13w7oIdeWRbdZwuyhH6E5vQ+ZlZ9EatldgmA+Rr85MeEdpKfXsrmswBKYwYTD\nsiw0zr2M8gGSz8us+yJSiz/M/+5QmrQqY/PEepYAK5/fTaXQ1hQFWpyWhWWZqJ95HpWjP0N0aBWy\n67+CcELQW85sorlM04T6swCYnuaHqP0TgOvjMC8L/b7MPTHdRgHlgz9Aa9qmLq6FkV5+D2V53BJQ\nmG4EjtMAwBcubU2yfulgWcKyLBi1iwin5vOj+HCOCUXbnLhpMEcsKCtr7Lu5EZzGysw39UfWzfPA\nNH/wXrZD8F6ncg7lA99Hp3zqyreE4sis/vTggqUeepwidVE2lLuBMke7vFD9DBNjFdyILja2y6dQ\n3v8QjOoVZ6GFk8iu/WMkF94ssDFB55AnBK2FgPx2ilztN3HtJCvF8G/Ebn0KoeQ4/1rH5jOhaFvU\natSBwsv9Op52Qin2XbxsKEJjMbPhirSVZVHmXXiF64gtswujMYNwcoxvY3wRE4rO2Gys0nVpnBHY\nmGalKY6NepQ0FtNr+m2sHqT+j6iyEEoJx0Hz0i6UDz3SJ3cVSowht/F+xIbX8W0MZ1kQynNscXL8\nyRU2G00KhEtvCsrAOv2fKWgHpFaRPqdd7qpdYOLXg0EFzROXEE6NC5wGC9LtovdWlxxhaSf4JdYw\nSYAJ+twkev9TWDbJuXBmCfIbH0AkKyi5u9yDFKR/CEjYWk2mQVmowGGbnTosy0QoKihfZjdR8GaX\nc2tepPPYEfRD3eay6nmU9z/Up2mrhWLIrPojJJd8RBAsxCmo5/Z8NZrLcjfOSSLs2jtMo8Zu4sEe\ngGWZqJ9+DpVjjwm12MKpCeQ2Poioc0WgiHCOItX4fP77noPXCSuJ5raJT3RrigZGWxARO4mMUJQj\najZ7DF4nltlB9fgTqJ56mu9UAETyK5Hf8IA4InYSHScbRX0Rs0Mr9Sr7+O87bey2UTn2GGqnn6VJ\njveVw+tIuV1U6nESn7iS+fLottyzdidahCLuzHqxZmP9FK0Sdiq3i0gsJscm6pN0G+5ZuxM9RhN8\najXfRsuiSkHhZXEw6SS5gjIsUR/aqNEKWlF276DbKmP24CNoTopXhiYW3Izs2s+LS21O0msog3Bq\nJPbozLKsXXIlcyhNWapICN0yKUMqvi7XjwX4Qbqddok5YkHW7sCoXUL5wMNoFwUrQzUdqaV3IbPy\nE/ysffAf+EG6nRarnInK1k4iQzTfxsb575sGZezlXZCbywxUTz6J6omnhOc9klvOKpAya0tA1bvR\nD1EVao5ce4dZOcga7P3wIggXM5FcfBs9FiJc5ekzgpAZvNFRmpBlVt5ZJpWGSzuETgtg2VDOkQ0J\nbZyhco7L4G0Xj6K0/yF066KVdDa0MNIr7kV6+T3iFb9a2JYNSdjYmnQvOQFoTR9A+eAP0G1434Ra\nKIr0yk8itfRO8UpVLUp9kPRaOTHixnlWPndZGJVYShOozEpns+1ecgIo2h2+mUqMMjbWT7Os3cUR\n87IhEd0mc8T8/jEAKo2N3NqfDYmwLOoHzbwkzISAXjb0KCzDe4GXHs0iu+4+JOZvF3+o17Jw9iNF\nNrpk7ZfJbAKGHNmQCK+sHbjSshAF6U4bKwcpkBP0N6ll8StUTvySAlMPQslx5Dbcj9jwWhcbPYL0\nfgNY1v6Gy1xma1nICNS3C6x8Ln7sqV06gfL+78OoXfA+nhZCevndSK/4GDTRddTCFBxkN81N/N1+\nyOvtMC3TQPXEE6iefMrlYvDR40PIrf8K4mOb+9+IjlGU47ZKjEdv8BZeRl+2qYVYbyjAie6UaXJu\nOi56bIIGrCgbEtrIBm/xNdgjNNNooHLkUdTPvgCZyM1OOL0AuQ0PIpp3LNxILGZOI8P/R6GNvay9\n/3lIs1PD7OGfoHH+VcE/iolklyK38U8RyTj62MnltIpWdkn5ZWN6WbvjERM9wUpoy+Ucm53mRWDq\n2cGSZGo1c2ySj/BctrHNsvb9/a+HUuQ0RNmQG42zwNRzg07OKxsS0W2xdQj9z/t6ZkMuxMa2Irfx\nQUe5r5cNbZdzbH02NuiedvbkI0PMsUk+HtOjl7XP/M6R9bCV8bkb/Jf5jCoFH46svV1+G+UD34dR\nGexve5FYeAuy6+6D3pdt+gzS7Yiydl7LQgbLpLFdeBX9c1kTlaM/R/3Mb+F7LktNILfhfkSHHCvW\n44toLnNblRsAkcO8ZhsXNM6/guqJX/p2lgBgNoso7voOBpz1vHv9O0uAJsjsBlroYCezMdgAA8gh\nzvvE4OvzP+HfWQJkQ24LBQU2qiefRv3s7xBkNxajeh7FPf/s+J4IezzEp7MEWICxDQj330CVY48F\ncpYA0Jl9G+WDD/e/GEoB43f5d5YATWhD76Vj2Bn+AC328OssAcoonKuXI8PA2Ef8O0uAnNfILVR2\ntRPUWQKUmeW29r8Wm6DJxK+zBIBQjIJTrd9BlPb9eyBnCQCtqT1onHNsmpBYQlUEv84SoAx87A4M\nTGNjd/p3lgCNjfQqKl3bSa2ix8iC9MTCaVq97KC46zuBnCUANM69hPaMo+qRWQ/kbwg4l2VppbqT\neR/z7ywBsiG7mRYF2ai9/WvUzzyHQHNZ7QIKO7/leFX3foTlKvPOb413PRlMsOd4vGuwzdTAIee6\ncQRvccpcf7fj77k+qzvw/1fjvF7la3MtrvXgl1yH75grc7vWV20jFFfmeh6d///umyeu+nnk2Xi1\n7Z7zNOE4gKZdp/vyCn9YDlOhUCgUioAoh6lQKBQKhQTKYSoUCoVCIYFymAqFQqFQSKAcpkKhUCgU\nEiiHqVAoFAqFBMphKhQKhUIhgXKYCoVCoVBIoBymQqFQKBQSXDOHGZ9/E5KLb0OQXTK0SAq5jX8y\nKHc0/ZxYl9INywJqJ2hPUDvVQ6TZGWTXDKMOTP568PWpZ+i9IDZWjwCtfiWU1JLbEZ+3zf/xwPbk\n3fig43s6tOdoV1Lhwmnj7AHae9JGevm9iI1uCmRjKDmOzNrP97/YrZL0mUic1tVGEyjvHdzcvPQm\nbc4ehHYBKO7sf61TZJt/e2+aPWhjl1R0nBuHF18lDdQgtKbo2vS9dhEovhloe0qYBpP76leSyK77\nEsIZiQ3SOUTyq5Bc4BAVbpwFSruFyjbuNrZpn1bnblYzz5PoQhAaZwfVWuonaJ/nIDZ2WyRa4CC/\n+asIJSTEHjjExrYObsBePQJUDgWby7oN0qB1MvkMKdj4xbJIW7bVr1+aXHIb4vPf4/94APRYHkNb\n/jzQ/15NrrlaSbt4DOUDD8GoyUndxOffhOy6LyIUFewP6FdlQ0ayKL6QaQ5K7EloWe7CpQDTHPSh\nsiEhWdSc3I3ywUdgtmQmAg3JxR9GZvWnxaovflU2JFRfGhdex+zhn8BsSwQ1MpJFflQ2AKb64iI0\nDDAx3ffTXqleWF1XoWEA/lQ2AHKIM79zVX3xpbJhdkg5R6TVCvhT2QA8VV/8qmxo4Tgyqz+L1OLb\nxB+KjjDFIEnJN0/VF58qGzKqL7Fxthm5xH7WEqovZreF6rHHXaXw7EipvsQXsLlMYj9rGdUXLQIM\nvw9Iu0jh2TEqbL4Vq740p/aifPCHMJsu98AVA5Bc9EFk1nwWetih3qOFgKVfkziGf669WklnljJA\njqinZXaYcolYx1GPDSG34cuIj22R+z4vHUdPUVwHMhIxnTJzbJKZitfg9RTF7cfsNFA56q5c4ltX\n1EvH0aeuqNmuYvbwf6BxQbwZu6corhMv5RKfuqIIJeh4bsolXqK4TlJraBNx0WbsPnVFPXUcAcqG\nZl6Qr7p4KZf41BUl5ZKH0C6KnUxsbAty67+MUHxI4ogSOo4ihRIRXjqOvnVFBWLrdnzqivLE1p0k\nFt6C7JrPyemKisTW7fjVFY3NZypMgs3YfeqKknLJz1A/8zxE92woOQ/5jQ8OKpQAoIDoRvqd14Br\n7zABJqPVO2mDTqpTPce0MU/av8VdAzOcpUibK9osGLydEmUa3GxII0Hi1iW+8+aJkHppYIaHqPLM\nyxpEg9c1G9IpG2heBM9JtYpHUXZqY2phpFfcg/Tye/kamJFhsp2nfK5FKKNxZu2tSbKxU+DYGAbi\n40zebHCMtKb3M21M23XTI8is+pRYAzM6RpF+l+MARFl78zyVb0W/KzoGtAQBTnIZc8S2SchLAzM6\nTiXjLqfsLsra66dpAnXKgwGAFqOgryXQBuRpY3abJJ1UE6iGxOZTcMfLbEIp5oiX9r9eOwEUXiKH\nNPC7ElR94Src97QxfwrLuPK/lA19EYn5NwlsnKBxxctseFm7VzYUSlFFQlRd4GXtRpU5tkHRewAU\n8Lam+AE3L2v3CtLDGVKo4ejeUtb+NMvarzicUGIMuY33Iza8zsXGSb6Tio4AI7f16/x6BenhHM0B\n3ApIiObanEMVpV1g1SeeBqZO823zAnhzWbt0nIIFuzamFkJ62d1IrxRoYMbmsUxfJggLxvVxmD1c\nBqJlmaiffg6VY48hFB/ma5wB6CupQKeot/Cq++CNjVP5rLQLAM8Z2rJS12xRo+/NbSPnO/M832Hb\n9TQB94HYG7yRvHs2FJ+g3xLJuQ5Ey+ygevyXqJ76FdOUfACR9ILB42kRYOh9JP8D0z1bjM1j2WaG\nRGVnBdmQPSttTTHl9sHzY3ZbqB59DLXTzyI6vBa5DfcjnOSU3PQYk99azTJat/PDsnY97p4NJVeQ\n8won3bNFe8mp0XNsnDKfPSu1DPdsMbGEnJIWYmW+Y/zPpdew8nDcPVvUY8wRr2LZ0CsCZ2jLSr2y\nxeQKYORmmuQLLwH1U/zP2bPS+il2fgaDhW6zhNlDP0JzchcSC25Gdu3n+dlQOMec4QKWLUqcH7NN\n39vkZWC2rFQLuWeLoTT77oUssH9DMJ/YslKvbLF3frp1lyDdFthDd23pGLWLpDdaOo7U0juRWflJ\nfsvCHti7Zou282OUxUG6PbAH3LPFyPCV73ZrWdizUpeWDmknP4nqyacQyS5CbsODiGQWcmyM2Npx\n11al5Po6TMCz1NFtFqFHM/xsSBRBeA3eUFoQxQv6nl79yFCKTQ68iVvQ9/QavKEkf0LWolTSc2ZQ\nHqUOozGDUHyIn7ElljKhaMfE5dqP1GkC95NBeWTgRmMaYdECh9RKOmbI0Z9oz9BiCU40Di1E54vr\nNAR9T69+ZDgjLm2K+p6tSbKRW1mI0FiTzaAA736km42ivqdbP1KP0bWTzaAAzwxcfK1tQajznnfr\nR+pxGvfciXuEJmRn39OrHyk8j4K+p1c/MpSgAIU3rkStI6POApWTg/8Dl/MoEr2XycCFc5mgdeTa\nj3SbywR9T8uitS5FfgbuPpd5tI6uMtffYfbwKh/1faEtGxJFEL3BKyofOUksZk7DRTDZY/D2Yc+G\n3Gz0aqbb8erRASxrf8G1mX7FxgQJFLv16DwG7wCp1aw06CKY3CnT5NwUlBfthFLegsmXy0dvyK30\nzKyn8eMmmNwusCibVz5yEM5eyUiENvrp8fai/e3uC3paU8wR80rhDiJDzLG5CCabBnPEe+Hd49WA\nHCu7uQkmNy/QeeSVwp1ER1kFyGVVqNlmWft+7+OBZUNe4u9+eryx+SxIdxFM7rYouK4e9j6e7OLE\n2imgwM/aB5BZnOinxyuzONFvj1cUpNvxKoX32ehzceJV4p1zmD28Bm+vjCUbQXiVnIKcaK/Bm1rJ\nnIaLY+uz0WPwhpLA8K1Aapnc8WQGr59VoAAbvC+Js3a/q0B7WXvhVcASrCLObGTZkItjs+O1QCGc\noyg+PiFpo9cCBY1KU/nt7k7DTrvIsnbBYyGibMjNxsuOmBcs+FwFCgCtaVY+52TtgPdCOiemAZR7\nWTtnnhBlQ254rSK2tyykbOxQm2R2n8BGiSDdSeMcm8v4q4ilgvQ+G9s0l1UO8t+XCdKd1N8WtxeA\n/paFDF5Zu8xCOjsSq4g9F9JdQ955hwnwS056gnopyRXBIgheySm1ipX5Apxo3uAVLZSQhVdySq+n\nsoWs07DDG7wy2ZAI7uDVaKLL3yT3eIMTXtYukw252TiQtWuUCeVulHdsfTZySk4y2ZCbjQNZu2Q2\nJKJTokVN9kVBc1n0YJl0/5Vsz2f6fVTLSbvAyue23pifR7UGbOza1iKwrF3UspCFt4AtsZQqMUHK\nfLysfa7ZEC9rF7UspGzkZO1+H9Vy0jhD49He+vIbpNvpNlniY8va/Qbp14B3h8Ps0ZqigREbubLo\nYS70Bm/9JItyFs/dxuYFcnLxhf6yIaGNbPA2z9FgkM2G3GicISeXXO4vGxLRG7ytKZYNCZbi+6F2\nkspY6TVsdZ1kNiS0sU5OszNLCzNksyERvaz1FrMoAAABUElEQVS9+DqQ3Ugl0yBOw06v5GR2gNEP\nipfi+7GxeoiyzdyN/rIhEb2sXdP9ZUNCG02amMt76X7xkw2J6GXtoaR3y0LWxvIeCmqG3y+fDbnR\ny9ojQ94tCxl6WXvtGDnKoEG6neZFNpfN925ZSNnYoTZJ/QyNnSBBupPGObpnkkuCB+lXkXeXwwRo\nErjaNemrfUxl47vzeNfimNfieICy8d12vGtxTGXju/N4c+Dd5zAVCoVCoXgXInKYavN1hUKhUCgk\nUA5ToVAoFAoJlMNUKBQKhUIC5TAVCoVCoZBAOUyFQqFQKCRQDlOhUCgUCgmUw1QoFAqFQgLlMBUK\nhUKhkEA5TIVCoVAoJPDcfFR7l2xVpFAoFArFO4nr1ngKhUKhUCgIVZJVKBQKhUIC5TAVCoVCoZBA\nOUyFQqFQKCRQDlOhUCgUCgmUw1QoFAqFQoL/Dz2zbMIEnfdxAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10ca00898>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"G = HexGrid(20,20)\n",
"G.run_experiment()\n",
"fig, ax = G.draw_grid()"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def plot_gen(min_size=5, max_size=75, n_trials=1000):\n",
" avg = list()\n",
" animated_grid = HexGrid(20,20)\n",
" for i in range(max_size-(min_size-1)):\n",
" f, (ax1, ax2) = plt.subplots(1, 2, figsize=(16, 7), dpi=80)\n",
" G = HexGrid(i+min_size,i+min_size)\n",
" \n",
" trials = list()\n",
" for _ in range(n_trials):\n",
" G.reset()\n",
" frac = G.run_experiment()\n",
" trials.append(frac)\n",
" \n",
" # Always draw same size view of honeycomb\n",
" if i % 2 == 0:\n",
" animated_grid.reset()\n",
" animated_grid.run_experiment()\n",
" animated_grid.draw_grid(ax=ax1)\n",
" ax1.axis('off')\n",
" avg.append(np.mean(trials))\n",
" ax2.set_xlim([min_size, max_size])\n",
" ax2.set_ylim([0, 0.4])\n",
" ax2.set_ylabel(\"Average Fraction of Filled Honeycomb Cells\", fontsize=14)\n",
" ax2.set_xlabel(\"Honeycomb Size $(N$ x $N)$\", fontsize=14)\n",
" ax2.get_yaxis().grid()\n",
" ax2.plot(np.arange(len(avg))+min_size, avg, linewidth=3)\n",
" f.tight_layout()\n",
" yield f\n",
" \n",
" while True:\n",
" # Hold last frame of the movie for a few seconds\n",
" yield f"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"# Create Animation"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"from moviepy.video.io.bindings import mplfig_to_npimage\n",
"import moviepy.editor as mpy"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"gen = plot_gen()\n",
"\n",
"def make_frame_mpl(t):\n",
" fig = next(gen)\n",
" return mplfig_to_npimage(fig) # RGB image of the figure\n",
"\n",
"animation =mpy.VideoClip(make_frame_mpl, duration=15)\n",
"animation.write_gif(\"honeycomb.gif\", fps=6)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"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": "3.5.1"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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