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Investigating colourings of graphs on seven or fewer vertices.
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{ | |
"metadata": { | |
"name": "" | |
}, | |
"nbformat": 3, | |
"nbformat_minor": 0, | |
"worksheets": [ | |
{ | |
"cells": [ | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"0. Configuration\n", | |
"----------------" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"This section not reproduced in the blog post." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"import networkx as nx" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"output_type": "stream", | |
"stream": "stdout", | |
"text": [ | |
"Couldn't import dot_parser, loading of dot files will not be possible.\n" | |
] | |
} | |
], | |
"prompt_number": 1 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"def setfigsize(n, m):\n", | |
" pylab.rcParams['figure.figsize'] = n, m" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [], | |
"prompt_number": 2 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"def first_available(G, node, palette):\n", | |
" \"\"\"Returns the first colour in palette which is not used in G on any\n", | |
" neighbours of node, where D is the maximum degree.\"\"\" \n", | |
" used_on_neighbours = []\n", | |
" for v in G[node]:\n", | |
" used_on_neighbours.append(G.node[v].get('colour'))\n", | |
" available_colour_set = set(palette) - set(used_on_neighbours)\n", | |
" return sorted(available_colour_set)[0]\n", | |
"\n", | |
"def vcolour(G, choose_colour = first_available, nodes = None):\n", | |
" \"\"\"Visits every vertex in G and assigns a colour from [0..D] given by\n", | |
" the choose_colour function object, where D is the maximum degree\"\"\"\n", | |
" if nodes == None:\n", | |
" nodes = G.nodes()\n", | |
" degseq = G.degree().values()\n", | |
" if degseq!=[]:\n", | |
" palette = range(max(degseq) + 1)\n", | |
" else:\n", | |
" palette = range(1)\n", | |
" for node in nodes:\n", | |
" G.node[node]['colour'] = choose_colour(G, node, palette)\n", | |
"\n", | |
"def colours(G):\n", | |
" \"\"\"Returns a list of colours used on vertices in G.\"\"\"\n", | |
" return [x.get('colour') for x in G.node.values()]\n", | |
"\n", | |
"def clear_colouring(G):\n", | |
" \"\"\"Removes a colouring of vertices from a graph.\"\"\"\n", | |
" for v in G.node:\n", | |
" if G.node[v].get('colour')!=None:\n", | |
" del G.node[v]['colour']\n", | |
" \n", | |
"def ncolours(G):\n", | |
" \"\"\"Counts the number of different colours used on vertices in G.\"\"\"\n", | |
" return len(set(colours(G)))" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [], | |
"prompt_number": 3 | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Improved Greedy Vertex Colourings\n", | |
"=================================" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Source code: https://gist.github.com/MHenderson/658e3bb656357cd948d5\n", | |
"\n", | |
"Notebook viewer: http://nbviewer.ipython.org/gist/MHenderson/658e3bb656357cd948d5" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"In the previous post we showed that a greedy vertex colouring of a graph $G$ uses at most $\\Delta(G) + 1$ colours. This sounds good until we realise that graphs can have chromatic number much lower than the maximum degree." | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"The **crown graphs**, sometimes called Johnson graphs are complete bipartite graph $K_{2n, 2n}$ with a one-factor removed." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"import networkx as nx\n", | |
"\n", | |
"def one_factor(n):\n", | |
" \"\"\"The one-factor we remove from K_{2n,2n} to make a crown graph.\"\"\"\n", | |
" return zip(range(n),range(2*n - 1, n - 1, -1))\n", | |
"\n", | |
"def crown_graph(n):\n", | |
" \"\"\"K_{n, n} minus one-factor.\"\"\"\n", | |
" G = nx.complete_bipartite_graph(n, n)\n", | |
" G.remove_edges_from(one_factor(n))\n", | |
" return G" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [], | |
"prompt_number": 4 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"G = crown_graph(6)\n", | |
"nx.draw_circular(G, node_color = 'black', **options)" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"ename": "NameError", | |
"evalue": "name 'options' is not defined", | |
"output_type": "pyerr", | |
"traceback": [ | |
"\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mNameError\u001b[0m Traceback (most recent call last)", | |
"\u001b[1;32m<ipython-input-5-9ac466a8a6b9>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m 1\u001b[0m \u001b[0mG\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mcrown_graph\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m6\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[0mnx\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdraw_circular\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mG\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mnode_color\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;34m'black'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0moptions\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m", | |
"\u001b[1;31mNameError\u001b[0m: name 'options' is not defined" | |
] | |
} | |
], | |
"prompt_number": 5 | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Crown graphs are bipartite and hence 2-colourable." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"setfigsize(6,6)\n", | |
"\n", | |
"options = {\n", | |
" 'with_labels': False,\n", | |
" 'node_size': 250,\n", | |
" 'width': 0.5,\n", | |
"}\n", | |
"\n", | |
"G = crown_graph(6)\n", | |
"vcolour(G)\n", | |
"nx.draw_circular(G, node_color = colours(G), **options)" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"metadata": {}, | |
"output_type": "display_data", | |
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4c+YM7/PkzWr++eefcfToUaU7UBWWk5ODM2fO4Pvvv+fdDk0zNjZGVlaWrptB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\nCSGEEJFR+BJCCCEio/AlhBBCRPZ/X2nYS2rX9PEAAAAASUVORK5CYII=\n", | |
"text": [ | |
"<matplotlib.figure.Figure at 0x2eef9d0>" | |
] | |
} | |
], | |
"prompt_number": 6 | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"However, the maximum degree of a crown graph $G$ of order $2n$ is $n - 1$ and, with some vertex orderings, a greedy colouring of $G$ uses $\\Delta(G) + 1 = n$ colours." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"import itertools\n", | |
"\n", | |
"def bad_order(n):\n", | |
" \"\"\"Visit nodes in the order of the missing one-factor.\"\"\"\n", | |
" return itertools.chain.from_iterable(one_factor(n))\n", | |
"\n", | |
"G = crown_graph(6)\n", | |
"vcolour(G, nodes = bad_order(6))\n", | |
"nx.draw_circular(G, node_color = colours(G), **options)" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"metadata": {}, | |
"output_type": "display_data", | |
"png": 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KlVC+fHltNyVPfHw8AgMD0b59e94FNMaMGYMtW7bwWnqUkpKCO3fuoH379nmv\naTOAs7KyEBgYiLVr16JDhw6YMGGCSs9Y7ezscPr0ad7nyZrV/Mcff+Dw4cMKd6DKLysrC6dPn8av\nv/7Kux3qZmhoiIyMDG03g5QgFL5EJYwxbNy4ERMmTNB2U/Lkf8ZrYmLCewazrq4uBgwYgD179nA+\nZ/Xq1VKLimgjgI8dO4Y5c+bAzs4OCxYsEGTmeZ06dRATE8PrHHnLiUQiEcaOHYt///2X8/WCg4OL\n7c5Q1tbWiIyM1HYzSAlC4UtU8r///Q+9evXiXGhf3QpPrmrXrp1SFZq6dOmSt2RIkZiYGOjp6cms\nLaypAH706BGcnZ0BAKtWrcLPP/8s6PX5zOrlso63WbNmePPmDach20+fPiEhIQENGzbk1WZN6dCh\nA4Uv4YXCt4TLyMhASEgI/ujTB53btoWttTXGjRqFyMhIpTcy5yozMxNnz55Fz5491XofrqTNalal\nQtO0adMQGBio8DgutYXVGcCJiYlYtGgRTp8+DW9vb7UNyzZv3pzTrF4+BTQU1X2W8Pf31/iuRXwY\nGRkhMzNT282QSywW49SpUxg6fAw6dO6NdtY90X/gCOzbtw/Z2dnabt4Ph8K3hEpLS8NMZ2dUqVAB\n3tOmQXTsGGpeu4bKkZF4u307BvXsiV9++gk7d+5UWxuCgoIwefJktV2fD1nLiVSp0FSrVi3k5OTg\nzZs3Mo85d+4c2rZty6m2sNABnJubiw0bNmDFihWYMmUK7O3t1ToRicusXr6VqypUqIAKFSrgwYMH\nMo+Jjo5GjRo1UK5cOd5t1iQLCwskJCRouxlFMMawZs06VKvZAANHzcZ/96xwOdMeV3OccPhZN4xx\nCkDFKrWwaLEnhbAGUfiWQAkJCbBu0wZh69ZhVEoKhqSkoBmAugDqA+jAGCalpqJ1TAxcJkzAbBcX\nwXvBsbGxSE5ORv369QW9rjIUreNVZd9VBwcHmb3f3NxcHDhwAIMGDeJ8PaEC+Ny5c5gxYwZatWoF\nT09Pjax5NTc3lztErGzJSHm1tRlj2Lx5c4nYGcrGxkapGdzqlJubixF/jcPsJf/iQ80QpLS+BdSa\nDlT6FajYG6g5Hl9bnEdi45Pw3ngRtj36IS0tTdvN/iFQ+JYw6enp6G1rC5MnT9A/MxOydokVAfgJ\nwKi0NOwOCsIyT09B2xEQEFAshgG5FNDo1q2b0hWaTExM0LRpU6nP8/7991+MGTOG9wQgVQL45cuX\nmDlzJj5MeLJ9AAAgAElEQVR9+gQ/Pz+Nl1c0NDSUOpKgSq1mfX199OrVC0ePHi3y3r59+/D777+r\nNFNbU5o2bYo7d+5ouxkFTJ3ujEPnXiKt5TnAvD0g62e1TGOkNz2CqFfl0X/AMLkbkxBhUPiWMEHr\n1iH1yRPYZmeDy6/8UgAGp6XBy9NTsGeNN27cwE8//QQzMzNBrqcsrpWrVK3QNHz4cISGhhaYbJSY\nmIiXL1+iefPmSl2TbwCnpKRg2bJl2Lt3L5YsWYLBgwdrZdavtFm9QmyS0KtXL4SFhRWYmZ6eno4r\nV64ovTZZ03R0dCAWi9U+14Kr69evY/vug0hrsh/QM1F8go4eMn75F5dvv8e+ffvU38AfHIVvCSIW\ni+G/ciXapadzCl6JMgCaiMUIUqGqkARjDFu3bsXo0aNVvpYquAYvoHqFJpFIhJEjR2Lbtm15rwlR\nVIRLAEuqZi1ZsgR//fUXZs6cqZW9ayU6duyIS5cu5X0tRPBKTJkyBevWrcv7uiTtDCVRt27dYrPR\nwkq/tcioOg3QL8v9JB0DpFrOxHLfdYqPJSqh8C1BwsPDIU5ORnUlzm2ZlYXgoCCld+2RCA0NxeDB\ng7U6DMgneCWqV6+uUs+/TZs2ePjwIZKTk/Ho0SOYm5sL8pxVXgBfu3YNTk5OqF27Nry9vWUuZdIk\nQ0PDvFm9QgYv8G0zjKSkJMTGxuLdu3fIzMxEnTp1VL6uJilbjERonz9/xsGDByCuOpb/yVX+wIOH\nj+ROgiOqo/AtQS5evIjaKSm8er0S5QEYMoZnz54pff+0tDTcuHEDnTp1UvoaqkpLS+MdvMC3fVdV\n/aXo6OiI1atXY/369YLWFi4cwO/fv8fcuXPx6NEj+Pn5oUOHDoLdSwgWFha4ePGioMEr4ejoiICA\ngGIzp4CvGjVqyJ0dryk3b96EoUVzwLAC/5N1DCCq2JvWLauZnrYbQLj7/OkTVKlVZKyjg6SkJKXP\nDwwMlFrFSVPi4+Nx7tw5hIWF8S4ZWadOHV7VlKSpUqUKXr16hTZt2gi+pMfIyAiLFy9Gv3790K5d\nO3h4ePD+HjWlVq1aWLFiBfbv3y/4CIiZmRkYYzA1NeW041JxpKOjg9zcXK2ODiUmJoLpKb80K0un\nnEq/K4hi1PMtQUqXKQPulXCLymYMpUqVUurc169fgzGGGjVqqNAC5UmGmu3s7JQOJVX3Xc3KyoKh\noSEePnyo9DWkYYzhwIEDWLJkCdavX4/MzExBNq9Xh/v37+PKlSto3LixWsJFLBYjOTkZcXFxxWbi\nEl9WVla4ceOGVttQqlQpiMTKrW8HAD2WpvTvCsINhW8JUr9BA3xSsjeQDuBzVpbS4RkYGKiwipO6\n5H/Gq0qPs1mzZiotBQkODsbUqVNhbW2NM2fOKH2d/O7cuQNnZ2eUKVMGK1euxC+//FIsdkOSRvKM\nd9myZQCglnDcsWMHRo4ciUGDBuG///4T/Pqa0K1bN5w9e1Zr909KSsLLly+RGhsFiJUrmqGfch11\n69YVuGUkPwrfEmTw4MF4JRZDmcGg2yIRevfsqVSVoIiICLRo0QImJhyWKwhMmclVsnTr1k3pfVfj\n4uLyagv//vvvOHLkCK8deQqLj4+Hu7s7Ll++DB8fH9ja2ua9V1y2I8yv8OSqunXr4vnz54Le4+vX\nr7h//z7atWuHzp074/r16yWy4IOZmRmSk5M1dr+srCxERETA09MTbm5uCAoKQqtWrdCkcWPg4wH+\nF0yMgjESCvxMEuHRM98SxMTEBH/99RdubNoEGx6/+MUArunqYpkSNX/FYjH27t0LPz8/3ueqSsjg\nBVTbdzUgIAAuLi4Avg1fjx8/Hhs3buRdXjM7OxvBwcGIi4uDs7MzzM2ll0mRBPDs2bMxc+ZMrQ33\nA9JnNdvZ2eF///ufoL2jwjtDTZ8+HWvWrMGsWbMEu4emlCpVCqmpqWr5g5UxhgcPHuDMmTOIi4uD\nvr4+2rVrBycnpwL369OzE+4F+SC7ymDZxTWkMH63Gk4Ok0tEYZOSjMK3hJk5dy6sdu5Eja9fweXX\nHgNwwsAAzdu2haGhIebOnQsHBwdYWlpyul9ISAhGjRql8YIOQgevhGTfVT7b7EVHR6NmzZoFRg2a\nNGmC//77DwkJCbCwsOB0nZMnT+L48eOYMGECGjVqpPD44hDAspYTVa9eHW/fvhXsPi9evIChoSGq\nVq2a91rNmjUhFovx5s0bVK+uzAI77encuTMiIiLQq1cvQa73/v17hIWF4dGjRwCARo0a4c8//0Sl\nSpWKHPvs2TOsW7cO7du3R52Kx/Ds+WLk1l3A6T6id9tQOu0CJk3U/B/bPxoK3xKmVq1aOHTsGPr1\n6gW71FQ0AmQuPcoGcMrICK9LlcJxf3+0aNECX79+RUBAAIyMjDBt2jS5IZScnIwnT57g77//VsN3\nIpu6ghf4ViQiMjKS85CapLawr69vkfcky2IWLVok9xpPnjxBUFAQunXrhlWrVvH6Q0abAaxoHa+Q\ns3rXrFkDTyklUKdPn45FixZh+fLlKt9Dk9q2bYt//vlH6fBNSUnB+fPnce3aNeTk5KBKlSqws7PD\nyJEjZf78JCcnIyAgACYmJvD09ISRkRFKly6NIcP+RgbLRPZPiwAdGVt/MjF0Xq+D6dulOHvhjMwR\nGSIcCt8SyNraGuERERjUvz+ufvmCZikpaALAEN96up8BROvr4wZj6NyxI079X0nC0qVLo169enBz\nc8Pz58/h5uaGjh074o8//pD6H1ob27ipM3iBb/uurlixgnP4yqstXL58eVSqVAn379+X2pNNSkpC\nQEAAypQpg2XLlsHQ0FCpNmsjgLkU0GjVqhVu3LiBNm3aqHSv8PBwdOjQQeofgiYmJmjevDkuXrwI\na2trle6jSQYGBrx2CMrJyUFUVBTOnTuHlJQUmJiYoEuXLpg/f77CvbLFYjFCQkLw+PFjODg4oEqV\nKgC+lZe8dOkSnj2+gx6/DsDDc9UgrjEFOVXHAUb/V7AlKwGidyEo9XEdalQpiyPXLuKnn35S+vsm\nPDBSYonFYnb69GnWp0cPpq+ry/R0dJiujg4zNTZmfw0fzu7cucNmzZrFGGMsOzubzZgxgz158qTA\nNc6cOcMcHBzY7du3C7z+5MkTtmrVKo19L4wx9unTJzZ16lSWnJws85gFCxaofB83NzdOx6WlpTEX\nFxe5x2RlZTFHR0cmFovzXsvJyWGbNm1i8+bNYx8/flSprfmlp6cze3t79urVK17n8f3M7t27x2bP\nns1ycnLkHpeYmMi8vLx4Xbuw7Oxs5uDgUODzK0wsFjN7e3uWm5ur0r34EOLnzM/PT+a/v1gsZo8f\nP2aBgYHM1dWVeXh4sMOHD7OkpCRe94iMjGT29vbs2rVrBV6Piopi7u7uTCwWM7FYzBwcHFh0dDQb\nN2EqMy5dluno6jMdXQNmYFiKDRg8kl26dEnuvwERHoXvd0IsFjNfX1/25s0blpCQwHx8fBhjjO3Y\nsYNFREQwxmQHcHZ2Nlu/fj2bP38++/TpE2OMsRkzZrCMjAyNtZ9L8DImzC/FlStXsvj4eIXHrVix\ngr148ULhcSdOnGCHDh1ijDF24cIFZm9vz65fv65yO6VRJoD5fGZcg1fC1dWV87WlWb9+PYuOjlZ4\nXFRUFNu8ebNK9+JDiJ+ze/fusR07duR9HRcXx3bt2sVcXV2Zq6sr27JlC3vz5o1S1379+jWbNWsW\n27FjR5HQzB+8jDH233//sbNnzxY45tq1a2zXrl1K3ZsIg4advxMikQiGhoYwMDCAubl5XpGGYcOG\nwdHRER06dICenh68vb0xZ84cTJ48GfXq1QMA6OnpYeLEifj8+TMCAgIQHx8PGxsbpYdJ+VL3UHNh\nkk3hBw8eLPOYt2/fIjs7G7Vr11Z4vZ49e2L8+PEIDw9Hu3bt4O/vr7YJauocglamVrMqs3o/f/6M\nN2/eYOLEiQqPbdWqFfbt24fk5GSUKVOG9720oXbt2li6dCmePHmC7OxsVKhQAba2thg6dKjSPx9p\naWlYs2YNcnNzsWDBgiKf+/Xr13H48GEsWrQIIpEI6enpuHr1Knx8fAocZ2BgoLH/30Q6Wuf7nZLM\n6hWJRBg1ahS2bt0KAHkBHBQUhKdPnxY4x9zcHG5ubkhKSsKFCxdw4sQJtbdT08ELcNt3tfCyF1lS\nU1Ph7e0Nc3NzWFpa4s8//1T7zHB1rANWdpOEzp0748KFC0rdk2/9ZgcHBwQEBCh1L03Izc3F9evX\nsWLFCri5ucHX1xe6urqYO3cuPD094eTkhCZNmij188EYQ2hoKBYsWIDBgwdj7ty5CoMX0G5xHCIf\nhe93ytraGhcvXgTwrdfw5MmTvIX/8gJ448aNmDNnDlatWoXs7Gw4OzvjyZMnammjNoIX+DZLl8mp\nznT58mU0adJEbm1hxhh27dqFRYsWYdiwYVi+fDkyMzPx8eNHdTS5CCEDWJXdidq1a4erV6/yvueD\nBw9Qvnx5VKjAvfB/lSpVYGJiUuRnVptiYmIQHBwMNzc3LFy4EK9fv8b48ePh6emJ+fPno2fPnnj5\n8qVK97h58yYcHR1RuXJlrFixArVq1SpyjLTgffv2LXJycqQeT4oBLQ97EwGtWbOGxcbGMsYYy8jI\nYIsWLcp77/3792zJkiUFji/8DPjTp0/M3d29wDEZGRnM39+fLVq0iCUmJgrWVq7PeAsT4lkcY4xt\n2rSJPXv2rMjrubm5Cif3REVFMXt7+7xn6RKJiYls3rx5grSPKy7PgOV9Znyf8UrD97mvWCxmjo6O\nLCsri/e9MjIy2IwZM3ifx5eszywhIYHt3buXubm5MVdXV7ZhwwYWExMj8zrv3r1jq1evVqoNsbGx\nbN68eWzjxo1y/30KP+OVmD17Nvv69avUc6Kjo9n+/fuVahcRBj3z/U4ZGhoW2Ls3f68h/7Pe/M+A\nt23bBicnpyLXcXBwQGxsLLy9vVG3bl2MHj1apbWd2urx5mdnZ4djx44VWVaxfft2jBgxAjo6RQeF\nPn78CH9/fzRo0ACrVq0q8hmYmZmhXr16uH79Olq1aqXW9kuo8gxYqP14K1WqhI8fP6Jy5cqcjj96\n9Ch69eqlcAmNNIaGhujcuTNOnz6N7t278z6fr8zMTFy6dAkXL15ERkYGypUrBxsbG/zxxx9Sf0YK\ns7S0xIcPH3jdMysrC0FBQUhMTMTs2bNRtmxZmcdK6/ECwKVLl9C0adMSuzPUD0Hb6U+Ek7/nyxhj\nvr6+ebOXGZPda8jOzmajRo0q0FOW5caNG8zBwYGdP39eqTYq2+OVEKrny1jRHltycjKbM2dOkeMy\nMjLYqlWr2OLFixUuBcnJyWH29vYaX7Yhrwcs7TMToscrcf/+fbZ9+3ZOx2ZmZjInJyeV7ifpOWdn\nZ6t0HWlyc3NZdHQ069GjB3N1dWWLFi1ip0+fZmlpaUpf08PDg1MvXywWsyNHjjBnZ2f26NEjhcfL\n6vFyGb2hnq/20TPf75hkVq+EpNdw6tSpAsfp6urCzMwMX758Ufg8rWXLlvDz88OHDx8wa9YsvHr1\ninN7ikOPNz9dXV3k5ubmfb169eoCE4AYYzh06BDmzZuHPn36wN3dXeFMW11dXQwePBihoaFqa7c0\nfJ4BC9XjlWjYsCEePHjA6digoCDe9bALk9TW3rBhg0rXkXj79i02b94MNzc3eHh44NGjR2jWrBk8\nPT3h4eEBOzs7GBsbK339Nm3a4Nq1a3KPefjwIWbMmAFdXV34+vqiQYMGco+X1eMFgG3btmHkyJGc\neuZEe+hf5zvWpEkT3L17t8Brv/32G44dO1ZgR55Dhw7ht99+w4oVK6ROwipMJBJh6NChWLRoEUJD\nQ+Ht7Y3U1FS55xS34AW+7bt68+ZNAN9qCxsZGeXVvL537x6cnZ1hbGwMX1/fvKF6Ljp16oQbN25o\nfEceLgEsdPACyPvlzxRsMRgbG4vExESFwcJF48aN8eHDByQkJPA+Nzk5GYcOHYK7uzvc3Nxw5MgR\nWFtbY+nSpVi6dCmGDh0q6F62Xbp0wfnz56W+9+XLFyxcuBBhYWFYvnw5evfurfB68oL369evePjw\nocpVx4gGaLvrTYRTeNiZsW/VnAoPS929e5etXbuWMVZ0KFpWIQ55Xr16xWbNmsV27twpdbhV1aHm\n/IQcdk5MTGTe3t6MsW9FRdLT01lCQgJzd3dna9euVWpCkMSrV69Urv6krMJD0JLPTMih5sJCQkLY\ngwcP5B7j6urKvnz5Itg94+Pji0wQlCYrK4tFRESwpUuXMldXV+bl5cWuXLkid9hayJ8zxoo+4shf\n2CYuLo7zdWQNNUssXbqUvXv3TuF1aNhZ+2jC1Xfup59+wvPnzwts/da4ceO8HXm2bduGKVOm5L0n\nqxCHPDVq1MDy5ctx8eJFODk54a+//sqbcFQce7wSZmZmSEpKQlhYGNq1a4fNmzfjw4cPcHR05LxT\nkSySiU+vX7/W+G5EhSdhAerp8eZnZ2eHvXv3omHDhlLfv3nzJurUqSN38hBfFhYWqFKlCu7du4fG\njRvnvc4Yw8OHD3HmzBnExsZCX18fbdu2haOjo9YmIJmamuYVCAkPD8ehQ4cwduxYTgVGJOT1eAHg\n+fPnMDY25rxjGdEuCt/vnJ2dHY4ePVpk31VHR0d4enrCwsKiyHvKBDDwbW1xhw4dsHXrVuzbtw8j\nR47E2rVri2XwShgZGcHf3x+1a9fG+PHj0aRJE8GubW9vjwULFmDFihWCXZOr/AGcmJio1uAFvs2m\nl7XGmTGGrVu3St0ZSlUTJkzAzJkzMWfOHISFheHhw4cAvj2HHjJkCOcZ2OrWtWtXhIaG4vHjx2jf\nvj38/Px4FdtQFLwAsHbtWqk7Q5HiicL3Oydr31ULCws8ePAACxculHqesgGso6ODMWPGICYmBn/+\n+ScGDBgAAwMDVb4FtXn27BkOHToEKysr3r8MuShVqhSsrKwQERGBTp06CXptLoyMjPD333+jb9++\niIyMVPvm6Hp6esjOzi6yhOi///7DwIEDBb1/amoqLly4gCtXriAuLg4eHh5wdnbGiBEjNL73tCJf\nv37F6dOnceHCBRw+fJj35C0uwXvmzBlYW1vz2qeaaBdNuPoBFJ7VCwBRUVEYMmQIdu3aJXOijLxK\nWPLEx8fDx8cHZ86cwYABA+Dq6opDhw4pnJCjKcnJyVi6dClCQ0NhY2MDS0tLtf3CHjp0KPbs2VPk\n89eE+/fvIzQ0FGPGjMGqVasEK0UpS9u2bYvM6k1LS8P169fRuXNnla6dk5ODq1evwsvLC25ubvD3\n94epqSnmz5+PnTt3wtTUFD/99FOxCl6xWIxt27bB09MTY8eORZs2bdQSvDk5OThy5Ah+//13IZpN\nNITC9wdgZWWFGzdu5H3NGMP27dvzekWHDx+WeS7fAC78jLdevXpYuXIljI2N4eTkhHv37gnyPSlD\nLBZjy5YtWLZsGcaNG4fs7GzMmjWL176rfIlEIowePRohISFqu4c0+Z/x6uvrC14LWprOnTsXmdW7\nZs0aTJs2jfe1GGN4+vQp1q1bBzc3NyxevBixsbGYMmUKPD094erqCmtr67xe9tSpU7F27VpBvg8h\nXLlyBU5OTqhXrx68vLxQtWpVWFpaSh2FkoVL8ALApk2bMG7cuGL1hwdRjML3B9ClSxecO3cu7+td\nu3Zh6NCh0NHRQffu3XH+/HlkZmbKPJ9rAMubXNWjRw/4+PggIiICHh4eSi0RUUVkZCScnZ3RqFEj\nLFu2DF++fEGFChVQoUIFVKxYEbGxsWq7t5WVFZ4+fYqkpCS13SM/aZOr1LEZQ2GlS5cusOTszZs3\nyM3N5VxbOD4+HqGhoXBzc8P8+fNx8eJF9O3bF56enli8eDF+++03mJmZST23bt26SE1N5V1NSmjv\n3r3DnDlz8PTpU/j5+aFdu3Z573Xv3h1hYWGcrsM1eD9//oy3b9+iadOmKredaJg2p1oTYUlbaiQh\n2UA+JSWFzZ49u8B7T58+Zb6+vgqvL28ZEp/lRJIlImvXruVdpYjvEhBp+54Wri1ceN9Vdfjw4QNb\nvHixWu/BmPTlRPk/M2X2A+Zj2bJleVXAZs2axVJSUmQem5aWxk6dOsUWLlzIXF1dma+vL7t9+7bc\nykzyJCUlCVZbm+/PWVpaGvPx8WGenp4y6ymLxWJOdbAVLSfKz8PDo0AVO65oqZH20YSrH4Rk39XA\nwMAiW+Xl7zVUqVJF5jVkTcLiu5zIwsICixcvxt27dzFz5kz06dNH8Dq98vY9/d///ofevXvnDVn+\n8ssv2LVrl6D3L6xy5cowNTUtUFtbaFyWE6lzP2Dg26zec+fOwcLCAs2bNy/wuYvFYkRHRyM8PBxf\nvnyBkZERrK2tMXfuXEH2li1Tpgzq1auHqKgotG7dWuXrccEYw759+3DlyhVMnToVderUkXls/mIk\nsnqzXHu8wLd/70qVKqF8+fLKfwNEe7Sd/kQ48nq+ERERbMuWLWz58uVS3+fTa8jfA1a1gIZYLGYH\nDhxgzs7O7OnTpwqPV9QjEYvFbPfu3WzmzJlSd5vJyMiQWltYWjESoWVkZDBnZ2e1XFteAQ1pn5m6\nesDZ2dls/vz5efWtY2Ji2IYNG5irqyubP38+27t3L0tISBD0nvlJ6hqr+m/JpecbHR3NHBwcWHh4\nOOfr7tq1i925c0fqe3x6vKrsDMUY9XyLAwrf74i88M3KymIdOnRgqampMs/fvHkzu3btGqd7ZWdn\nsylTprDhw4cLUrkqIyOD+fr6siVLlsjdvEDeL0Uumz74+fmxx48fF3k9JCSEPXz4kFeblXHo0CF2\n4sQJQa+pqHKVrM9MHQH8+fNnZmVlxcaMGcNcXV3Z+vXr2YsXLwS7PhcXL15U+TGCvJ+zuLg45ubm\nxoKDg3k/NomNjWWrVq0q8jqf4GWMscOHD6v0c0Thq3007PyDuHz5MipVqiS3Zu2oUaPg5OSEVq1a\nKRzySkxMBGMM5ubm+Pjxo8pFNAwNDeHs7IwPHz5g2bJlqF+/PkaPHs2pOHxsbCwCAgJQp04d+Pr6\nyhxyjY2NRVJSEurXr1/kPTs7O+zbtw8///yzSt+HIv369YOzszNsbGyU2lKvMFUqVwkxBJ2ZmYnL\nly8jIiICGRkZMDIygp6eHhYsWICaNWvyvp4QOnbsiEOHDqF///4Fhr1VlZWVheDgYMTHx8PFxQXl\nypXjfY2KFSvi06dPBV7jM9QMfPvMz549q5aiJURzaLbzDyA3Nxf79+9H165dZVYhAr4VyBg6dKjC\n55+SZ7zLly/HqlWreK8DlqdKlSpYtmwZGjduDCcnJ0RGRso8NisrCwEBAVi/fj1mzZqFcePGyQ0g\nf39/ODo6yryvJmbKikQiTJgwQZAdeYQoGcl3FjRjDHfv3oWfnx/c3Nzg5eWFrKwsuLi4wNPTEyKR\nCCtXrsTZs2eVao9Q7O3tERgYKNj1jh8/jjlz5sDW1hYLFy5UKnglDAwM8lYX8A1eQJidoYj2Uc/3\nB7BlyxaMHj0ahoaGCAsLw4gRI2Qeq6jXIG1ylTKVsBRp3bo1WrVqhV27duHQoUOwt7dH9erVAXwL\ngKNHjyI8PByTJk3itEvOjRs3ULduXZlLVQBAX19faoUmoTVq1Aj//fcf4uPjlZ4sI2StZkU94Hfv\n3uHMmTN48uQJRCIRGjdujOHDh6NixYoFjnv27BlMTEzQoUMHHDt2TKU2qap69eoQiUR49eqVSj3w\nx48fIygoCHZ2dvD19RVkLW379u1x+fJllC5dmnfwfvz4EcnJyVJHb0gJo+VhbyIgac98v3z5kre8\nQSwW5y05kuf169dSd+SRN7lKmd2QuEpJSWFeXl7M29ubTZw4kTk6OrJjx45xPl8sFjN7e3uFu/kc\nPXqURUZGqtpcTiS7JymD7+5EXJfNSJ4B37t3jx0+fJi5u7szV1dXFhgYyB4/fqzweaRkZyjGvu3i\no+4JbIqkpqaymTNnKnXunDlz2MKFC1lAQADLzMwUtF1paWls8uTJvJ7xSsybN48lJiaq3AZ65qt9\nNOz8nQsICMjbIJ7rvqv5ew0SipYTKVuKkgsTExNMnDgR79+/x+nTp9GmTRv06tWL8/n//fcfBg0a\npLCHKK1Ck7qYm5vD0tKyyH7Liqhjd6Ls7GxERkbC19cXxsbGmDhxInJzc+Hh4QFPT09MmzYN9evX\nl9s7O336NDp16pRXW1jaXtKaVqpUKbRq1QoXLlzgfE5ubi42btyIS5cuYcqUKbC3txe8Nvn9+/dx\n7949Xj1egNvoDSk5KHy/Y48fP0bZsmVRqVKlvNd+/vlnPHr0SOG506dPz3tmxnUdrzoCOCcnB8HB\nwfD19YWbmxtGjRqFatWqwcnJCTdv3lR4Pp/awqVLl0ZKSooQzeZk/Pjx2LhxI+ea10IFL2MMjx49\nQmBgINzc3LB06VIkJibCwcEB3t7eCAsLQ3h4ON6/f8/pejk5OTh69Cj69++f95qtrS3nak7qNGTI\nEOzbt49Tbe3z589jxowZsLKygo2NTZFhdSFInvH269cPiYmJnM9j/7cz1OjRowVvE9ES7Xa8iZAK\nDzs7OzsXGTL78OEDCwgI4HS93bt3s8OHD/NexyvUEHRYWBhzcHBg0dHRea9JhlBzcnLYxo0bmaur\nK/v48aPMa3h7e7OXL19yvmf+Ck2acObMGU7Df3yHmvNbsGAB+/jxI9u+fTtzdXVlrq6uLCQkRO6m\n63yWIa1du5bdvXu3yOtcqjlpwo0bN9imTZtkvh8TE8NmzpzJQkND84aB+Va44iL/cqLr16+zffv2\ncT53165d7MKFC4K1hYadtY8mXH2njh8/Dltb2yJDZpUrV+Zcx9jGxga2tra4cOECr6VEym5HKPHi\nxQusXbtW7r6nurq6GDduHJKSkuDv7w8zMzNMmTKlwPf7+vVrMMZ4Tbjp2rUrzp8/j379+vFqs7Js\nbaD/bJAAACAASURBVG3h4uKC3r17y9wOTpkeb1paWt6We+Hh4ShXrhzs7OwwfPhwTkOdXJchJSQk\n4MOHDwU2s5eQzOoVonqVKlq2bIm9e/ciKSmpwJBtamoqAgICoKenh8WLF/PecYiPwrOamzdvjoMH\nD2LAgAEKz01LS8ONGzfw559/qq19RAu0nf5EOJKeb1ZWFnNycpI5mWPBggUKK+NIJldduHCBbdy4\nUan28O0BJycnM09PT+bj45M3cacwWT2SR48eMWdnZ3bkyJG871tRbWFZbfbw8OB1jqrk1dbm2uPN\nyclhV69eZV5eXszV1ZUtXbqUXbhwgWVmZqrUi1PUA/bw8GDx8fFS3zt16hQ7e/as0vcW0sePH9mi\nRYsYY98m4G3fvp3Nnj2bvX79WurxQvZ8ZRXQ4Doy4O3tLXglMur5ah/1fL9DwcHBmDhxoswejmTf\n1Y4dO0p9v/Az3hMnThTpNXDBtQcsFouxfft2PHjwAPb29qhatSqv+wBAgwYN4Ovri+PHj8PZ2Rmt\nWrUqUluYa5s1vfeupLb2+/fvYWlpmfe6vB4vYwwvXrzA6dOn8ebNG+jo6MDKygqTJk1C2bJlBWub\nvB7wvXv3ULlyZVhYWEg919raGj4+Pujatatg7VFWpUqVYGZmhj179iAiIgJDhw6Vu+ROKPLW8das\nWRMvX76Uu+uTZPRG6BrcpBjQdvoT4axZs4bdv39f4V/tKSkp7J9//pH6nrTlRPl7DcqQ1wO+fPky\ns7e3Z5cvX+Z0LS49koyMDNalSxfm4eHBPn/+zLe5bM2aNezNmze8z1NFcnIymzt3bt7X0nq88fHx\nLDQ0NO+57aZNmzj1iIToxRXuAXOtLVxcnvu+f/+ezZw5k/Xs2ZPTrklCfGaKSka+ePGCbdiwQe41\nlBm94YJ6vtpHPd/vzMaNG+Hu7i73GBMTkwL7rkrImtUs6TU8fvyYU0GLwqT1gN+9e4eAgAA0adIE\nfn5+nMpIcrVz5074+PigZs2a8PX1RfXq1TF27Fjo6XH7cbezs0NYWJhGZ5aampri559/xrVr12Bi\nYoKQkBB4eHjg3LlziIyMRGZmJszNzWFra4tBgwYJ+nlxUbgHfOvWLfTp00dhQZJy5crhy5cvKlWE\nUkVGRgbWrVuHtLQ0uLu74/z58zh16hSvpWrK4FK5qnbt2oiJiZF5jYiICLRo0ULQEpmk+KDw/Y68\nffsWVatW5fSLztTUFMnJyShTpgwAxcuJpkyZgrlz5ypdT1YSwC4uLjAyMkLZsmXh7u6O0qVLK3U9\nWZKTk/HkyROMGTMGALBkyRLcvn0bLi4u6N+/P2xsbBReo169eti6daug7eJixIgR+O2335Ceno52\n7drB19cXHTt2xOzZs2VOxtIkSQC7uLggMzMTGzduVHhOt27dEB4ejoEDB2qghf8fYwwHDx7ExYsX\nMWXKFNStWxcA0LdvXzg7O8PW1lZtlcz4lIwUiUQQi8VF/pjKzc3Fnj174O/vr5Y2Eu2jdb7fCcYY\nLl++jGHDhnE6XjKrF+C2jtfAwAA2NjY4fvy40u07ePAgdHV1kZCQgEGDBgkevMC3oiKF6zc3a9YM\nfn5+SExMhIuLC168eCH3GiKRCCKRiPP6W1W8fv0amzZtgqurK6ZNm4aUlBQMGTIEy5Ytg7u7O2xs\nbIpF8EoYGRmhVq1ayMrK4lQLukWLFrh165YGWvb/3b17F05OTjA1NcXKlSvzghf49m87ceJEBAcH\nq+XefGs1t2jRAtHR0UVeDwkJwahRowQpZ0mKJwrf78T+/fvRtGlTzkOrrVq1wvXr1zkX0ACAPn36\n4OTJk8jOzubVtujoaDg5OcHCwgK+vr4ICgpSSyWsp0+fwsTEBJUrVy7ynkgkwoABA+Dp6YkDBw7g\nn3/+wdevX2Veq3Hjxrh3756g7QO+7QZ14MABuLu7w83NDcePH0fXrl0xYsQIlC1bFmfPnkVMTIxG\ni33w8fHjR2RkZCA4OJjTZgw6Ojoa+SMG+PZHpLu7OyIjI7Fy5UrY2dlJPe6XX35BXFxckd2FVKXM\nJgmSkYH8JKM3rVq1ErR9pJjR6hNnIoj09HTm4uIidz9faZydnXkX0Lh//z4LDAzkdKy8fU+VLcQh\nbyLMjBkzWEZGBqfrvH37ls2ZM4dt3bpV6gScuLg4qfuu8pWZmcnOnz/PlixZwlxdXZm3tze7du1a\ngYlUhSdXvXnzhi1btkzle0sIuWxm7ty5eUVIuBbiCA4OVuuevllZWWzNmjVylz0V9vnzZzZ//nyZ\n7/P9zPjux5tf4UlpixcvZh8+fOB9HT5owpX20TPf78DatWsxdepUnDhxgvM58fHxuHHjBtavX8+r\ngMYvv/yC0NBQfPr0CRUqVJB6jGTf04SEBJn7nqpaiKOwU6dOoXPnzpwLOlStWhVeXl64evUqnJyc\nMHz4cLRr1y7v/QoVKijVM2KM4f79+wgLC0NcXBz09fXRvn17ODs7S504I205UbVq1aCrq6twGYqm\nRUVFoX79+nnzBLgW4ujevTtOnz6NCRMmCN6mU6dO4dixY5gwYQIaNWrE+bxy5cqhWrVquHPnDpo2\nbapSG5Tp8eZnZGSE9PR0GBsb4+nTpzA1NZU6ekO+M9pOf6Kat2/f5i0b4trzlSwnunXrFtu8eTPv\ne8rrNRw7dow5OTmxBw8ecLoW3x6wtB5JVlYWc3R0VHoXndzcXLZt2zY2e/Zs9vbt27zXFy5cyKkn\n/e7dO7Z169a8JUA7duyQW/JSQl4BjbS0NKV35ClMiJ6vZGcoaaMEXHrAQi85evLkCXN2dmaHDh1S\n+t89OzubOTg4SD2f62emSo9XIjw8nJ06dYox9m00iuvojSqo56t91PMt4VavXo358+dzPj7/M97S\npUtj7969vO9Zrlw5VK9eHbdv30azZs0AKL/vqRA94I0bN2L8+PFKT07R0dHByJEjkZKSgtWrV0Nf\nXx/Tpk1D+/btceXKFXTp0qXA8V+/fsX58+dx7do15ObmwtLSEnZ2dvjrr784t0FRyUhjY2O0bt0a\n58+fL3J/bdi9ezeGDBkidYkTlx6wrFm9fCUlJSEgIABlypTBsmXLVCpdqaenh99++w0HDhzgVOax\nMFV7vBIdOnSAl5cXGGPo0qWL1stxEs2g8C3Brly5gkaNGnGeNSxtcpVkVi/fXx5jx46Fi4sLFi5c\niICAAJibm8Pb21up7ddUCWB5tYX5Kl26NObNm4eYmBi4u7ujZcuWeP78OTp27IioqCicO3cOKSkp\nKF26NLp06QIPDw/OE9zy41qrefDgwXBycoK1tbVg2wcqIzU1Fbdu3ZI7k15RAEtmPVtZWSnVhtzc\nXISEhODp06dwcHAQbFhWUlv7119/5TWrXKjgBQBDQ0NkZGTg2LFjWLVqlUrXIiWItrveRDm5ubnM\nwcGhwDCgvGFnaZWrGPu2c9Ht27d53z8nJ4fNmDGDDRgwgNckL3m4DEEXHg50d3fnPMmGK7FYzB49\nesQcHBxYlSpV2MSJE9mRI0d4TUyThe/uRDdv3lRYBUkRVYedvby8ONcWljUE/fnzZ7ZixQql7h8R\nEcHs7e1ZVFSUUucr8vz5c+bj41PgNXmfmRBDzYUNHDhQ0F2LFKFhZ+2jpUYl1M6dOzFs2DBOw3jy\nlhMps+/quXPn4OzsjJEjR6JWrVp5E3BUxXc/4Lt376JKlSoyawvzERcXh127dsHNzQ3z58/HlStX\nMHv2bDg4OPw/9s4zLIqz6+P/BRERscSCvfeoUbErsYDd2FKMRuNjTTTSQWQXabICKtJEsbdYsGMM\nNopdUQk2INhQAUGkSGeB3fv9wLP7wLJlZnYWzJv5XZcfmLnbjAtnz7nPff7o27cv7t27h9LSUo3m\nYKJONGjQICQnJ9PSfmWTt2/fgsfjUa4tLPWA5Y8hSStd0eHdu3dYu3YtUlNTERAQoLWjN127dkVp\naSkl/WI2PV4pWVlZaN68OWX9ZI7/J9S19eegT0FBAXF0dKxxXZHnq8zjrYpAIKA0b3JyMrGzs6um\ne6rIa9AUVR6w1COR1haWP8JElaKiInLp0iXi6upK+Hw+8fPzI0+fPq3hzUh1V3NycoibmxsJCgqq\noZFMBU30eD98+EDc3Nxo95Oiiedrb29PioqKaPdT5AF7eHiQ4uJitX2LioqIt7c38fHx0UpdY0Xk\n5+dX+51S9M604fESUhm9+fjxI+XfQzbgPN+6h9vz/QcSGBgICwsLte2oFtBQp7taVfd0w4YN1XRP\nu3btCpFIhLS0NEZqRIqgsgccFhaGGTNmUN5zFYvFiIuLQ1RUFPLy8mBgYABTU1Pw+XyV+9RVdVdd\nXV2RmJgIR0dHTJo0CVOnTqU0NxOPtyqtWrVCs2bNGNfWZsrNmzdhYmKChg0b0u6raA/Y1NQUt27d\nwsSJExX2IYQgNDQUsbGxsLCwqFUlHyMjI/Tt2xcxMTEYPnx4jfva8HiByuhN27Zt0aJFCxBCGOVf\ncPxDqWPjz0GT169fK/U0q3q+VDxeKcp0V8VisVrdU0Jqeg1socgDdnV1JaWlpcTW1lZt/1evXpGQ\nkBDi5OREnJ2dyZkzZxipHMl7JBKJhFy4cIFYW1uTxMRElX018XirIhKJiLW1NaO+TDzfiooKYmFh\nobGXV9UDLi0tVerBP3z4kFhYWNTqvqc8YrFYdpyq6jvTlscrH73Zt28f7aIzTOE837qH83z/YWzf\nvh0eHh4q29ApGQlU6q76+vpW0129f/8+fv/9d/z4449qdU/VeQ1MUeYBb9++HatWrarRPicnB1FR\nUXj06BEIIejSpQsmT56scaEKed1VHo+H6dOnY+LEidi5cydCQ0NhZWVVQ0dXU4+3KvXr14e5uTnC\nw8Mxbdo0jcaiwsGDB7F48WKNvTB5D7isrKza/YyMDAQGBqJHjx7w8/Or06xuHR0dzJ8/H0ePHpVd\n05bHC9SM3pibm+PChQsaF5zh+GfAGd9/ENHR0RgxYkS1sK882dnZ2LZtG2XDC1SeKZUmE71//x6B\ngYHo06cPLam/hQsXwtraGkOHDmVV7k7eABcWFqJevXro3r07RCIRbt++jVu3bskk9yZMmIC5c+ey\nugZzc3NERERg+fLl1a7Xr18fFhYWyMzMxObNm9GlSxcsWbIEurq6rBpeKdOmTYOtrS3Mzc0ZHemi\nSl5eHl6+fImlS5eyMl5VA9y0aVN8/PgRjRs3xo4dO1BQUABHR0c0adKElbk0ZeTIkTIBEG0a3tLS\nUty8eRO+vr6yax06dEBqaiqr83B8vnDG9x9CRUUFwsLCVJ4DLCwsxKZNmxAYGEirZCRQecbV09MT\nPB4PfD6fdgZzVa9h4cKFtPqqQ2qA165di0uXLmHhwoUQCATQ19fHqFGj4ODgoPILiaao011t1aoV\nhEIh4uLiYGtri0GDBiExMZFVwwtUV+RZs2YNa+PKExAQUEMZSlOkBnjp0qVwdnaGoaEhVq1a9Vl6\neRYWFpg7dy7q1aunFcMLADt27FAYvdHV1YVYLK7TCABH7cAZ338I+/fvx5IlS5T+IcjKysKff/6J\n/fv30zK85L9Sf8+ePcOoUaOwevVqxmuUeg3SQhRskJKSgqtXr+Lly5fIyclBTk4OzM3NMWzYMFbG\np4qOjo7aCk2DBg2Cnp4eBAIBunfvjpSUFNZrM/fp00dtbW1NeP78OZo0aQJjY2PWx3716hWaNWuG\nq1evIiIiolYTquiQkZGBrKws/Oc//9GK4U1PT0dRUVE1qUMpUrUxNrdvOD5PuHO+/wByc3Px9u1b\nWSlHeaR7vLNmzaJl9Krqnh46dAjp6ekar9XS0hJBQUGM++fl5SEsLEwmuXfhwgV8/fXX8PT0ROPG\njbFixQqEhoayLkeojoEDByrUXa1KfHw8Dh8+jDNnzsDT0xMnT56El5cX6/KAVlZWWhNZDwkJwa+/\n/srqmDk5OXBxccH169fh7++P2bNnU5IjrAukoeb58+dj+/btWpkjMDAQlpaWCu+NHTsW165d08q8\nHJ8XnOf7D0CRQLyUqslVhw8fpjReVlYWAgIC0L59e/j6+soSPggLuqvt2rWDnp4ekpOT0aVLF7Xt\ny8vLce/ePdy4cQPFxcVo3Lgxxo8fDzc3t2qht6NHj2LevHm4evUqq2pIVJkwYQL27t2LwYMHK7wv\nv8drYGAABwcHpKSkYMOGDRgwYADloijqaNasGTp27IhHjx5h4MCBGo8n5dKlSxg/fjxrtYUrKiqw\nZ88epKWlwcrKCi1atABQqYw1ZMgQbNmyRaUaUm1TdY/X3d0dgwYNQnR0NMaPH8/aHA8ePECvXr2U\nbus0adIE+fn5rM3H8RlTx9nWHGpISEhQqp8rf5xInapRVd3T7OzsGvd3795NkpOTNV5zcXExsbOz\nU3hPIpGQZ8+ekYCAAMLn84mrqysJDw9XWUyhsLCQODg4EEL+d2yGqR6wJigrgkDlONHt27eJhYUF\niYmJYWUtFRUVShV55KFy1EhTZSh5rl69SiwtLcmTJ09q3EtJSSHBwcGU9YBrA/njRK6urkQikRBL\nS0uNj4lJUaUMVRWhUEgKCgpYmVMZ3FGjuoczvp8xEomEWFtbk7Kyshr3FJ3jVWV8L126RKysrMiz\nZ8+UzpecnEx27dql+cIJISdPniRRUVGEEELev39PDh06RJycnAifzye///47LbFwLy8v2Tnjqoak\ntg2wogpNdM7xisVicuDAAeLo6EjS0tI0Xk9UVBQ5efKk2nZUjO+2bdtIfHy8xmt6+fIlsbGxIWfO\nnFFpyKUSg5+DAVZ0jlf6zuLi4lj7nThy5Ai5ffu22nY3b94k4eHhrMypDM741j3cnu9nTHh4OCZN\nmgQ9Pb1q1+mc433+/DlsbW0hEong5+enUnC8c+fOePv2rcbrLiwshIGBAdatW4d169bh1KlTGDJk\nCIRCIYRCIX766SfKqjRv3ryBrq4uOnToUOMe3VrQmjJmzBjcvn1b9jPd40Q6OjpYvHgxBAIB9u/f\nj61bt2pUL3r8+PG4d+8eSkpKGI8BVH6eMjMz0bdvX8ZjFBQUwNPTE+fPn8fGjRsxZ84clclKurq6\nqKioUFoLurZQd5xo4MCBePPmDe261PIUFRXh8ePHGDVqlNq2w4cPR0xMjEbzcfwDqGvrz6EYkUhE\nbGxsalxXVbmqquf76dMn4uHhQfz9/WmJczs7O6sNi8lTXl5O7t69S7y8vAifzydCoZDcunWLPHjw\nQGOvQb62sCIvrrY84NLSUuLu7k4IYady1cuXL4mtra1aL1EVVGprq/N8nZ2dFW5DUEHqza9bt46W\nNx8WFkbu3r0r+7kuPGBVlauqvrPMzEyNamsTUj16QwVpZEBbcJ5v3cMlXH2m7Ny5E7/88ku1a1Q8\nXrFYjP379zPWPR00aBAePXqkNLEIqEzMevHiBSIiIpCWlgZdXV0MGTIEq1evrpFIcvbsWeTm5qJZ\ns2a01gEAN27cwJAhQ9TWFtZED5gO+vr6EIlErBXQ6NatG3x9fREREQFra2ssX74c/fv3pzWGprW1\nnzx5gvbt2+OLL76g3ffOnTs4fvw4Fi5ciMWLF9PqO27cOGzfvh0jRowAoF4PmG3oFNBo2bIlmjdv\njsTERPTp04f2XKqiN8owNjZGRkYGa7rFHJ8hdW39OWry4cMHmYclhUqtZhsbG7J8+XLy8OFDxnMr\n013NzMwkx44dI3w+n/D5fLJ//36SkpKidjymXoOyhCJVXlxteMBr164la9asYS0JR0p5eTkJCQkh\nzs7O5OPHj7T6FhQUkLVr1yq9r+ydSROK6CpDpaSkEAcHB3LkyBHaUZKqKPLuasMDplKrWf6daVJb\nm4kyVHx8PDl8+DCj+ajAeb51D+f5foYEBgbC3t5e9rM6j/fdu3cICgrCp0+f4OXlpVGBhGbNmuHT\np08oKSnBrVu3cOfOHYhEIrRs2RJmZmaYN28ercIDTL2GAwcO0K4trG0POD4+HpmZmZg0aRLrFYjq\n1auHX375BTk5OQgICICxsTFWrFhRY79fEY0aNUK/fv1w7949mSdJhbNnz2LmzJmUlaFKSkqwbds2\niMViuLi4aFxIxdDQsEZBFm17wExLRtavXx8TJ06kXVv7+vXrGDp0KG1lqD59+uDIkSO0+nD8w6hr\n689Rnb/++ovs2bNH9rMqj7ewsJB4e3sTb29vUlRUpPaokSrEYjF5+PAh2bRpE/n666+Ji4sLiY6O\nprVfrAyp10B1XzM3N1fpnheVzF1teMDSPd6ysrJa0V199uwZsbKyIpcuXaLUvqoijzyK3llJSQkl\nZShCKj3kEydOEDs7O1aOokm5desW+fPPPxXe04YHTEedSNnnzNramrKeM53jYIrg8/msKylJ4Tzf\nuoczvp8R8ucKlRleiURCjh49ShwcHKr9caJrfF+/fk127dpF+Hw+cXZ2JqdOnSI5OTkkOjqaXLly\nhZ2H+i9//vknuXDhAqW27u7uJCMjQ+E9qvJ4bBpg+eQqbf5RrIpEIiFhYWHExsaGJCUlqW1/9+5d\ncujQoRrXFb0zX19f8vLlS7Vj/vXXX8TS0pJcu3aN0prpUFZWRlxcXJTeZ9MA05UFVPY5S0xMJIGB\ngZTG2LNnD4mNjaW6xBocPnyYleNfiuCMb93DhZ1rmdTUVBw9ehTvXr9GWVkZWrZujekzZmDkyJE4\ndeoU5s6dC11dXaWh5ocPH+LQoUP4/vvvMX/+fFpz5+bmIioqCnFxcSCEoHPnzjA3N69RiWrkyJHw\n8fFRKnrOhGnTpsHGxgYTJ05UqciTlJTESm1htkLQipKrunfvjlevXimszcsmPB4PM2fOxOTJkxES\nEoLQ0FBYWloqVQAaMWIEzp07h4KCApVH0N6/f4+SkhJ069ZNaZvMzEwEBASgS5cu2Lp1q1YK/evp\n6aGiokLpfbZC0GyqE/Xu3RuhoaHIzMxEq1atlLb79OkTXr9+jWXLljGey9zcHCdOnNDoCJi2kUgk\niIqKwtWrkfjwIQuGhgbo1as7FixYIKtoxqGEurb+/xbu3LlDZkyeTIwaNCDD9fXJFIBMA8jXPB5p\nbWhIenftSiZPmkTEYrFCjzc9PZ2sW7eO7Nu3T2myj7znW1paSqKjo4mHhwfh8/lk8+bN5OHDh5SS\nZLQRWqXiNdjY2KgM69EVhtfEA1Z2nCglJYVs376d9niakp6eTpycnMjevXuVfgZSU1OJUCisdk3+\nnTk6OipN3BOJRCQgIIC4ubmR3NxcVtatisDAQPL+/XuVbTTxgOl6vFJUfc5UbYtIURW9oYO2jhxp\n6vmKRCKydasfadu2M2nUqAMBxhNgOgEmEwODIaRBg0bk229/VFjhjKMSzvOtBXbv2oW11tYYXVKC\nNQCqVc4lBOOLivD69WvcSk/H9MmT0bFrV2zZsgVGRkYQiUTYsWMHCgsL4eTkpFLqjxCChIQEHDly\nBFlZWahfvz5GjRoFe3t72pJ7LVq0YF05R53XcPHiRUyYMIFVrVqmHrCq40Tt27evE93V1q1bY+PG\njYiNjYWNjQ2+//57mJqaVmvTrl076Ovr4/Xr1+jatWuNMWJiYtCnT58anjEhBOHh4YiIiMAvv/yC\n3r17a/VZpEi1khctWqS0DVMPWFt6vE2bNkXnzp2V1tZOSkpC06ZNWVGG0tPTQ3l5OaXEu9ri06dP\nmDx5Bp49y0Fx8QQAHQD87/1W1nyZgLNnH+HiRVMcOXIAs2fPrpO1fs5wFa60zJEjR8C3scGikhIM\nhZzh/S88AN0A/FRSgjfR0Xj/9i0aNmyIsLAw8Pl8TJ8+Hc7OzgoNb2pqKg4cOAA+n48//vgDSUlJ\nWLhwIYRCIVxdXTFx4kRGWrdmZmaIioqi3U8dyhR5ysvLcfnyZUyfPp31OelWwqJyjlequ1oXmJiY\nICAgAGlpaXBwcKhRGWr16tUKFXkkEgmOHDlSw9AlJibC1tYWPB4Pfn5+tWZ4gcovZH///bfadnQr\nYWnL8EpZunQp9u/fr1CMZOfOnawpQ31u1a5EIhEmTpyOR48qUFz8PYCOqGp4/0dDSCSjUFw8DwsW\nLEFEREQtr/TzhzO+WiQrKwurVqzAD8XFaE6hfT0A34nFeHrjBqZNmwYDAwP4+vpW89by8/Nx/vx5\nuLi4QCAQ4Pz58xg9ejSEQiFmzpyJOXPmsOKt9uvXD0+fPtV4HHmaNm2KLl26IC4urtr1Xbt2YeXK\nlVr5QwlQN8BUC2hIdVfrCh6Phx9//BHu7u44fvw4fHx8UFRUBAAwMDDAyJEja3x5OnbsWDVlpdzc\nXLi5uSEyMhI+Pj60jtCw+RwANUUtqgZY24YXqPzyNWfOHJw6daradbajN19//TVu3LjBylhssHnz\nFsTHf0JZ2RRQMx9tUVIyG99+O0+jUqr/H+GMrxbZu2cPegNQnpZRk3oARpeU4MO7d5g0aRLKy8tx\n69YtbNy4EQKBANu3b0erVq3g4uICoVCI1atXo0ePHqz/kaHzR5EuS5YswYEDB2Rjf/z4UePawlRQ\nZ4DpVK76XHRXGzZsiLVr12L+/Plwd3fHsWPHQAjB3LlzERYWJktoKiwsxJMnTzBy5EiIxWLs2rUL\nvr6++O2337BmzRpWQ/106du3LxITEym1VWeAa8PwShk3bhxiYmJktbW1Eb0xNDSUfamqa8RiMfz9\nt6GkxBSKvV1ldIZEYlzji8q/Hc74agmxWIxtfn4YyKDofXcAb1+/xtKlS+Hp6Yn8/HxYWlpCKBRi\n3bp1GDFiBOXCCJrQo0cPvHz5kvVx5b2GwMBAWFtbsz6PIpQZYLolI5s0aYKCggJtLpUWHTt2xKZN\nm9C+fXtYWVkhNjYWS5cuxb59+wAAQUFBsLCwQHR0NGxtbTFs2DB4enqyuqfPFDMzM1phSWUGuDYN\nr5Q1a9YgODgYwP9KwrI9t5GREfLy8lgdkwl//vknysoaAmhDu29h4Vfw8fFjf1H/YDjjqyVe7m3J\nYwAAIABJREFUvHiBsqIi0K+2W/mf8qVYjG7dusHd3R3Tpk3TuJoQE8zNzXH16lWtjC31GmJiYtCh\nQwdGtZ+ZIm+AmdZqbtiwIQoLC7W4UvqYmprCz88PT58+xfHjx5GQkICMjAzk5+fDz88P2dnZ8Pf3\nV5goVFe0bt0aHz58oNVH3gDXheEFKpXAysvL8fjxY2RlZTGq/ayO8ePH4/r166yPS5dz5y6goIBp\n1bie+PvveOTn57O6pn8yPKKNuCIH7t69i0VTp2IRw2+stwGIRo/GzDlzKPe5c+cO+vfvr1ZmkA4X\nL17E1KlTWRuvKtnZ2Th27BhWrVpF2ehduXIFkyZNYmV+sViMkydPQldXF99++61sL5QqycnJEIlE\ntZqgRIfS0lJcuXIFd+7cgZmZGcaNG/dZZc1W5cqVKzAzM6N9nri8vBzHjx+HkZERZs2axZrhpfM5\nE4lE2LVrF5YtW0a7jCQVJBIJrly5gilTprA25vv375GdnU1LyGPv3sNITOwGYACjOQ0NtyE+/iE6\nderEqP//N7ijRlqifv360CQXVgzAZOhQrFy5knIfHo+H2bNnsxpKzMrKwtKlS7US5g4LC8PXX3+N\nmTNnUlbkyc7OpvVOVJGYmIi0tDSIxWJMnDhRZdEJRZSXl2PLli2srYdNJBIJTpw4gVatWqFTp05o\n3rw5OnfujGnTptWqZ0iVzp07o1GjRpT0bqvy119/ISsrC4WFhZg2bRot5SBV0PmcPX36FH///TdG\njhyJ4cOHszK/PJmZmax+zp4+fYo3b97gm2++odznxo17SExUXhRFHRJJBfT1FZ33+HfCGV8t0b59\ne2SVlqIcABNf41PDhujRsyctL7ZBgwZo1KgRq57vqFGj8Pz5c9b/qJSWliIuLg7BwcHYsGEDfHx8\nKPWrX78+K88XHx+P06dPY+vWrSCEMK6ExePxWH3fbBATE4MjR45g3rx5ePbsGXr37o2CggI0a9YM\nLi4uWLFiBb788su6XmY1pkyZAn9/f0yePJlyn4cPHyIyMhKbN2+GSCRiVYyB6ueMEILQ0FDs2bMH\n9vb2mDBhAu0IChW6du2KT58+sfblwtDQEAYGBpQ/uyKRCIaG+tDReQ+JhMmMhZBIyhhJV/5/hdvz\n1RLGxsYYMXw44hn0LQbwXCLBDz/8wPayaDNu3DitZPUGBwfjt99+Q6NGjTBgwADcuXOH9TmUIb/H\nS/cccFVat26NjIwMLa2UHmlpaXB0dMTz58/h7++PhIQELFmyBLq6upgyZQrKy8uxefNm3LhxAy4u\nLsjJyanrJcswNDREcXEx5fbye7x0zwGzxZkzZzBr1izUr18fCxcuxO+//66VeaTFSGoLiUSCx48f\nY+vWrRAIBPDx8cGkSeaoXz8eAH3vV1f3Eb777oc6zar/3OCMrxaxXrsWj42MQHdTPU5HB7NmzULz\n5lROB2sXIyMj1rN609LSIBKJZBWY5s+fj+PHj0PC7Cs1LZQlVzE1wLX9R1ERpaWl8PX1xcGDB+Hs\n7IxFixYhPz8fb968kSVWTZkyBZGRkSCEYNWqVbC0tIS/vz9CQkJU1leuTRo3bkwpq1dZclVtG+DS\n0lLcvXsXEyZMAAAMGzYMCQkJWsmC7969u1ZOHlQlJSUF+/fvB5/Ph4uLC5KSkvDzzz9DKBTCxcUF\nixcvRqdOHQHaLoUE+vqPYGtroY1l/2PhjK8WmTJlChq2bo27NJJI0gE8aNAAjgKB9hZGE6nuKltI\nj71I0dHRwcKFC3H48GHW5lCEuqxmJga4d+/elM+osg0hBKdPn4azszPmzJkDPp8vCyMGBATAysqq\nWvtff/0VISEhACrLh3p4eGD06NGws7Or8y8QQGVWr7ooi7qs5to0wMHBwVi9enW1a5aWlggMDGR9\nLh6PBx6Px+oX1OLiYoSFhckK9ly4cAGmpqYQCoXw9PTEDz/8IBNHePr0KWxsbLBs2SIYGFwDkEt5\nHn39SAwePACDBw9mbe3/H+CMrxbR1dXFpagoPGveHHfq1VPrAacCOGFggF0HDtDKQtQ2bFbZuXfv\nHvr27Vtjr2nYsGFITEzU2tlZqseJ6BpgbRYjUcXjx49hbW2NZs2aYcuWLdXqOP/999/44osvatTP\n7tWrFz59+lTtWE///v3h7++PwsJC2NnZad27UoWJiYnKqmFUjxPVhgGWj95Iadu2LQwMDPDq1SvW\n5+zfv79GVeeqFuwJCgrCpUuX0KZNG7i6ukIoFGLVqlXo3r17tXeblZWF9evX486dO9iyZQscHBzw\n449zUL/+IQAf1cxIUL9+BNq1y8L581yBjRrUhZrDv43U1FTSv1cv0snIiHwDED5A3P77zxUgPwPk\nK0ND0sTQUKm4OBXo6vlSpaysjLaakCJUCb4TQkhaWhrx9PRUOQaTdShTJ1IFHTWkw4cPk4SEBNrr\nYkJmZiZxdnYmO3fuJOXl5QrbyAu+V31nqhR5SkpKyNatW8mGDRuUqh5pG2VrY6JOpIkakrrPmSpl\nqJKSEmJra0t7TnV8/PiR+Pr6Um4vkUhIfHw8CQgIIHw+n7i6upLw8HBSWFioVtWorKyMBAcHExcX\nF5KdnS27fvLkSbJv3z6yf/9+oqdnQBo0GEyA5QRwJYDbf/85Eh5vCmnUqA0ZPnwMycnJ0ei5/7/C\nZTvXAu3atcOjhARERkbCf9MmBNy8iSb160OXx0N+eTlaGxvDau1aLFy48LPLnAXU665S5ejRo9Vq\nC8tT1Wuge+xHGUwLaNBRQzI3N8fJkye1UmBBSnl5OXbu3ImPHz/CxsZGadZoeHi4Ss3kpk2bomvX\nrvjrr79qhAEbNGgAGxsbvH//HkKhEL1798bPP/+slexdZbRv3x4pKSnVsnqZFtBgSw9Ynnv37uHL\nL79U+rvaoEEDjB49GpGRkTAzM2NlTqByqyA7O1tlm/T0dERGRsq2Qvr27YsffvgBrVu3pjzP5cuX\ncfHixRpZ8adOnUJBQQGWLFmC7OxsWFo+g7Fxa/j5BSEvrxD16jUCIRUoK8vDtGnTYW9/CiNHjvws\nj7Z9FtS19f83kp2dTRISEsijR4/Iu3fvaGuNKkNbni8hhAQFBanVXVVFQUEBWbt2rdp26rwGOp4v\nE49XHqoesLZ0Vwkh5OLFi8TKyorEx8erbCcSiYi1tXWN6/LvrKKiglhYWKj93MXExBALCwty+/Zt\n2mtmyosXL8i+fftkPzPV460KEw9Y2edMLBYTS0tLtZrYEomEWFpaKo1OMMXNzY2UlpbKfi4oKCB/\n/vkncXFxIXw+nwQGBpKEhAS170uR5/v8+XNiY2NDwsLCavSXerxS1q9fT7Kysgghle8kOTmZxMXF\nkcTERJKXl6fpY/4r4DzfOuCLL774x513Mzc3R2RkJBYuXMiof2BgICwtLdW2a9CgAcaMGYOIiAiY\nm5szmgtg7vHKQ9UD1obualJSEkJCQmBmZgY/Pz+1HoRUGUod0opeJ0+eVHmcbdiwYRg6dCiOHj2K\nc+fOwcLCgrVzpsro1q0b9u/fD4C9Ws1sesDqojdSeDweli1bhr179+KXX35hPJ88w4cPx969e1FQ\nUID8/HwYGhpi7NixcHZ2ZvzZy8vLQ2BgIBo3bgwvL68ahTCqerwA8OzZM7Rp00Z2GkNHRwedO3fW\n6Ln+jXDGl4MSvXr1YnyGMTk5Gfr6+pSrWM2ePRvW1tYYN24co8pabBleKVQMsFR3dcyYMRrP9+nT\nJwQGBqJp06bw8fGhdDYyMzMT2dnZlEPfY8eOhYODA2bMmKGyJCKPx8NPP/2EWbNmYdu2bdDV1cVv\nv/2mlTKK0vl4PB7u37+PCxcusFarmQ0DXFhYiKdPn1L+AjpgwACcPHkSOTk5jL9sE0Lw8uVLXL16\nFWlpaZBIJHj37h127NihUN+bDhKJBPv378eLFy9gaWmpMDQtb3gJIdizZw+2bNmi0dwc4MLO/5/Q\nZtiZEEIEAgGj8J+dnR0pLi6m1efx48ckJCSkxnV1YWc2Qs3KUBWCLiwsJEKhUKPxKyoqyJ49ewif\nzycZGRm0+goEAqWJLcreWXJyMtm0aROteZKTk4m9vT0JDQ1lbbtEno0bN5KVK1dqZXyqIWhF70wo\nFJLU1FRa8338+JG4uLjQ6pOZmUmOHz9OBAIB4fP5ZP/+/eTdu3ey+2xscezbt49MmzaNPHjwQGkb\n+VAzIYScO3eOXLlyReP5OQjhjhpxUIaO7qqU6OhojBgxAgYGBrT6DRgwAKmpqbSqMLHt8cqj6hiS\nprqrN27cgK2tLQYNGgShUAhjY2PKfR89eoROnTrRVobq3LkzxGIxUlJSaPXZvHkzjI2NYW1tjbi4\nOFpzquPhw4fIzs5Gz549tZKow/QY0uvXr2lFb6S0aNECrVq1Qny88sIUJSUluHr1Ktzd3SEQCPD7\n77+jT58+2LBhA4RCIf7zn/9UC/c3a9aMcXWyd+/ewcHBAZmZmVi2bBmGDBmisJ28xwtUlpi8fv06\nJk6cyGhuDjnq2vpzsIe2Pd+MjAwSEBBAuX15eTmxtLRk7MEo8hqUeXHa9HjlUeYBe3l5kU+fPtEa\n682bN8TOzo6xJylN7FH13KqiBYWFhcTBwYH2vIT8z1N3cnJi5XNXNblKmwlshKj3gOXfGZPojZSy\nsjJiZWUl+/8Vi8Xk4cOHZPPmzYTP55MNGzaQ6OjoaolUqoiNjSWnTp2itYaioiLi7e1NvL29SVFR\nkcqjRoo8XkII2bp1K3nx4gWteTmUw+35clDG2NgYmZmZlNvv378fS5YsYezBtGjRAsbGxoiPj1cp\nBKBtj1ceZXvAUt3VmTNnqh2jqKgIQUFB0NXVhYeHB+M91NOnT2P27NmMn9vQ0BBfffUVbt++jdGj\nR9Pqq6uri2XLllXbo/71118Z1e+VT67S19dHaWkpGjRoQHssKtDZA2YavZGip6eHwYMHw8LCAk2a\nNIGOjg4GDhyIZcuWMdKxHjhwIM6cOYNvv/1WbVtCCI4fP46//voLFhYWave6FXm8QOURpqKiInTv\n3p32ejkUw4WdOWhRr149lJeXq22Xm5uLt2/faizavmLFCuzevVtpBanaNrxSFIWghwwZorJCE1D5\nx/DIkSNwd3fHTz/9BAcHB8aGt6SkBPfu3cP48eMZ9ZeyYMEChIaGMi5d2LRpU7i4uGDy5MlwdHTE\nhQsXaFX8UpTVPGrUKK2LbVAJQVdUVODcuXOUDF1VcnNzcebMGaxfvx4CgQAikQglJSVwcXHBhg0b\n8O233zIyvEBldjGV9xsbGwsrKyu0b98emzdvZmx4AeqnFTiowxlfDlqMGDECMTExatspqi3MBD09\nPUydOhUXLlyoca+uDK8UeQOsq6sLsVi5ivODBw9gZWWFzp07Y9OmTRof25EqQ2kKj8fDokWLcOjQ\nIY3G6dWrF/z8/KCrqwtbW1tK+QHKjhONGTMGt2/f1mg9VFBngKlGb0QiEa5du4YNGzZAIBBg7969\n6NSpE9zd3SEUCrFixQo4OjrKamtrSpcuXZCcnKzwXkZGBpycnPDkyRP4+fnB1NRU7XiqDO+DBw/Q\ns2dPjbOrOarDGV8OWpiamqqt85yYmIgWLVqgZcuWrMw5efJkREdHQyQSya7VteGVIm+A27dvj9TU\n1Gpt0tPT4eTkhPj4ePj7+9MO7yoiNTUV5eXl6NKli8ZjAcDQoUORlJSE/Px8jceaOnUqNm3ahMjI\nSLi5uSE3V3ERflXneBs0aIDS0lKN10IFZQZYVfSGECIzbgKBAN7e3igvL4e9vT2EQiHs7e1hYmJS\n7Txwz549kZeXV622NlPMzc1x9erVatdEIhH8/f2xe/durFu3TiYnqQ5VhpcQgsOHD2Px4sUar5mj\nOtyeLwct1OmuEkKwa9cu+Pj4sDpvVUWez8XwSqm6BzxlyhRcvXoVS5YsQWlpKXbs2IHi4mI4OTmx\n6jkEBQVh/fr1rI0H/E+Rx9nZWeOx9PT0sGbNGnz8+BFbt25Fhw4dsHTpUtm5bSoFNL744guNzsjS\nQX4PGKgMtVaN3qSmpiIiIgIvXrwAj8dDv379sHDhQlpfMq2srODj44ONGzdqtN7OnTvj7du3ACp/\n5/744w9cu3YNq1atUlkKVR5VhhcAjh07hnnz5tVqidF/C5zx5aCNVHe1SZMmNe6Fh4dj0qRJrItm\n9+zZE6GhoXj79u1nZXilVDXAxcXFaNasGW7evClTimGTu3fvon///mjUqBGr47Zp0waGhoZ4+fIl\na2tu2bIlNmzYgMePH8POzg6zZs1C48aNKVWumjBhAqKiovDdd9+xshZ1VDXAeXl56N+/P+7du4cH\nDx5ALBajXbt2mDhxIhYvXsw4ibBJkybo3r07YmNjYWJiotF6dXR08OTJE+zbtw9Tp07F1q1bafW/\nc+cO+vbtq9TwFhUV4dGjR1iwYIFG6+RQQp3lWXOwjraPGkmJiYkh586dq3FdWW1htrh79y5p3759\nrRwnYkpcXBwxNjYme/fu1cr46pShFEGnHra2FHkIqTwW5ePjQ0aMGEFevnyptr1YLCYCgUAra1FE\nWVkZuXXrFnF1dSWGhobEzs6O3L17l/X6zFRra6siOzubfPfdd8TR0ZGUlZXR7r9582ayZs0alW28\nvLyqFffgYBculsBBGxMTE8TGxta4HhISgl9//VUrc8bHx+Ps2bMYNGgQHj16pJU5NCE7OxsuLi64\ne/cuNm/ejGvXrlHSA6bL77//jp9++klrYcAGDRrA1NS0xn4iG8TGxqKwsBCRkZE4d+4cNm7ciMLC\nQqXtqWb1MoUQgsTERAQFBUEgEMDT0xN5eXno168fvvnmG5SVlaFt27aMSpyqQldXF99//z1CQ0Np\n962oqEBISAj8/f3h5eWF5s2b067pfOrUKRQVFWHChAlK27x9+xY6Ojpar+X9b4YLO3PQRldXt8ax\nlMzMTOTm5qJXr16sz1d1j9fd3R0HDx7E4MGDPwupsvLycuzZswcZGRmwsrJC8+bNkZWVhQ8fPsi+\njNDZg1NFQUEBEhIS8PPPP7MynjJmzZoFGxsbjB8/njXDI7/Ha2dnh7S0NHh6euLLL79U+oWiS5cu\neP36dQ3ReqZ8+PABERERSEhIAAD07t0b3333Hdq0aQMAKCsrg6OjI3r16oV169axLkcoxdTUFA4O\nDpg5cyblo2YRERG4cOECli1bhv79+wOorANOB+ke7+zZs/H69Wul7bZt2wZ3d3daY3PQg/N8ORgh\n1V2VwtbRInnkk6t0dHQYew1sc/XqVTg4OMDU1BTu7u4ylZcWLVogNzdXaSlKptTWWUupIs+ePXtY\nGU9ZclW7du3g7e2NHj16wNraGvfu3avRd+LEiYiIiGA8d1FRES5evAg3NzcIBAKEhoZi0KBB8PT0\nhFAoxKJFi2SGF6gevWFaipIqa9aswbZt29S2e/XqFWxtbVFYWAg/Pz+Z4ZWuUVUCZFXUJVdJuXHj\nBoYMGaI18QyOSjjjy8GIqn8U4+Li0KVLFzRt2pTVOZRlNZuamiI2NpbyHx22efHiBWxtbVFcXAw/\nPz/069evRht9fX2IxWLWDPDr16/RoEEDtG3bVqNxqNK/f3+kpaWpFW9XB5Ws5hEjRsDf3x8vXryA\no6Mj0tLSZPc6deoky+qlglgsxv379+Hj4wOBQICAgAA0atQIfD4fQqEQlpaW6Nu3r8K1KIreaNMA\nd+rUCYQQpeMWFBTA09MT58+fx8aNGzF79uwa6zY1NcWtW7fUzkXV8IrFYpw+fVql1CQHS9TxnjMH\ni9RWwhUhlckzUpUjdbWFmaCsVrM0eejt27fEx8eH1TnVkZeXRzw8PIifn5/aOrxXr14lUVFRhBDV\nakhUsbW1JSUlJYz60km4qkpWVhZtRZ6qVK3VTJWCggIiFArJli1bZLWUnZ2dlX6+JBIJefHiBdmx\nYwfh8/lk/fr15Ny5c7RrbBNSqRaUm5tLCKn5zqiqIdFFUW1tsVhMDhw4QNatW0fS0tJU9i8tLSVu\nbm4q2yiq1aystvOePXtIbGwsxdVzaAK358vBCOk38NDQUMydO5fVYz9UzvF27NhR5jWwvR8nj0Qi\nwcGDB/H8+XNYWVkp1D2VZ/To0diyZYts31SdHrAqIiMjMXr0aK3VOVZG8+bN0bp1azx79kyhd68K\nKh6vIqRe6uvXr7F+/XqMHDkSgwYNQlxcnEyBJzs7G5GRkXjy5AkAoFu3bpg2bZpGnwN10Rs29IAV\nYWhoiEGDBuHmzZswNTXFnTt3cPz4cSxcuJBSYQt9fX2UlZUpvU/V4wWAvLw8vHr1CsuWLaP1DBwM\nqWvrz8Eeten5EkLI4cOHyaJFi1gdU506UVWPRBNFHqrcvHmTWFpaqtQ9VYa8Mg8TD1hTZShCmHu+\nhNRU5KECE49XGVFRUWT58uVk7ty5xN3dnfD5fOLr60sePXpE67iVKhRFb5S9M214wBKJhCxZsoTY\n29uTI0eO0H4uPz8/hb/3ytSJCFHs+bq7u9PWkeZgDrfny8GYly9folOnTqyNR7dyVVWvgW3evXuH\ntWvXIiUlBf7+/kp1T1Uhr7uqSg9YGXv37sWyZcvqLLNbT08P06ZNw/nz5ym1Z+rxVkUikSAuLg6+\nvr6IiIhAu3btkJaWhuLiYlhbW8PW1hZfffUVa8etTp48STl6w/YecElJCbZs2YKGDRuia9euWLBg\nAe3nMjMzQ1RUVLVrdDxeAEhKSkKTJk1o6UhzaAYXduZgREpKCvT19TUSkK8K05KRP/74I6ysrDBq\n1ChWQt/FxcUICgoCALi6usLQ0JDxWBMmTEB0dHQ1RRw6IeicnBykpqZiwIABjNfABpMmTYKtrS2m\nTJkCfX19pe00Mbxv375FREQEkpOTwePx8NVXX2HJkiWy0pL16tXDkiVLEBwcjBYtWmDlypWsVFEr\nKSnB/fv3sWXLFsp92AhBE0Jw8uRJ3L9/H2vWrEHnzp3h5OSE/Px82mVI+/Xrh+PHj+PHH38EQN/w\nAsDOnTvh7e1Na14ODalr15uDPWoz7Lx27VpSWFhI3N3dGScCSVEXaq6KonDgw4cPlYbXqCKRSMix\nY8eIvb09efPmjUZjSRGLxcTZ2VnhPSohaFdXV5KZmanxOjQJO0t5/vw58fPzU3qfbqg5NzeXnDlz\nhjg7OxM+n0927txJXr16pbT9tWvXyKVLlwghhMTHxxMrKysSHh5O7yEUsGnTJpKcnFzjOpV3xjQE\n/ddffxFLS0ty7dq1atfT09OJh4cHrbGk8Pl8IpFIVIaaq1I17Hzx4kVy/vx5RvNyMIcLO3PQ5s6d\nOxgwYAAMDQ0xevRo3L17l/FYbIgkmJiY4Pnz54wVeWJjY2FtbY127dph8+bNrIXSdXR0lGrkqgtB\nJyQkoGXLlqwpQ2lKjx49UFBQgIyMjBr3qHi8ZWVluH79Ojw9PSEQCLB792506NABbm5uEAqFWLly\npcpCGiNHjpR9zvr27Qs/Pz9IJBLY2NggKSmJ0TOlpKSgoqICnTt3ZtSfbgg6MzMTAoEAsbGx2Lp1\nK8aOHVvtfuvWrWFkZMToWFrPnj0RFBRE2+MtLy/HpUuXMGPGDNpzcmhIXVt/DvaoDc9XvrZwSUkJ\n42/rdDxeKco8EiZeQ0ZGBnFyciJ79+7VWr3o3bt3k9evXyu9r8gDlkgkxMrKilHNXkWw4fkSUnnU\nat26ddWuKfN4JRIJefr0KfHz8yN8Pp+4ubmRy5cvk6KiIsbzyyewEVJZTzwgIIC4u7vLjglRRRq9\nUQTdetiqPGCRSEQCAwMprbG0tJTY2NhQnltKSEgI+emnnyi3l3q+27ZtI/Hx8bTn49Acbs+XgxaH\nDx/GwoULZUkhDRo0qKazSxW2ZQGreg3qjvKIRCKEhIQgPz8fjo6OCtWZ2MLc3BxXrlzBypUrFd5X\ntAd84cIFTJ06lXbNXm3TuHFj9OzZEw8fPsSQIUNqeLzv379HREQEkpKSwOPx8OWXX2LBggVo1aoV\nK/O3bNkSmZmZ1carX78+LC0tkZmZic2bN6NLly6UdGyrRm80RdkeMCEE4eHhiIiIwK+//kqp9Kq+\nvj7Gjh2LK1euYNKkSZTmP3XqFOrXr087YpOXl4fMzEz07duXVj8OduDCzhyUyc/PR2JiIoYNG1bt\nunxWrzq0pce7atUq7NixQ+l98l/dUycnJ0ydOhXr16/XquEFquuuKqNqCDohIQHR0dGYPHmyVtfF\nlMWLF+Pw4cN48OABTp06haFDh8LV1RUCgQBnz57F8OHD4enpCU9PT8yfP581wwtUfpGJjIxUeK9V\nq1YQCoUwMTGBra0trl+/rnQciUSC48ePY/78+aytTT4EnZiYCFtbW/B4PPj5+dGqeT5z5kyEh4ej\nvLxcbduqyVW6urqoqKigPM+ff/4Ja2tryu052IUzvhyUCQoKUli/Waq7SgVtGV6g0msYN24cLl++\nXONeQkICbGxsoKenh61bt6Jnz56szq0KHR0diMVilW2kBvi3337DlClTamll9KioqMC9e/eQkpKC\nRYsWoXHjxmjRogVcXFwgFArx22+/oVevXlo7FvXll1/i2bNnKtsMGjQI/v7++PDhAxwcHPDmzZsa\nbeSjN2zRoEEDODk54fvvv8fJkyfh4+ODadOm0R6Hx+Nh+fLlamtry2c1Dx06FA8fPqQ0x/Pnz9Gi\nRQs0a9aM9vo42IEzvhyUePXqFQwMDKoVoZfy1Vdf4fHjx2rH0KbhlfLNN9/g4sWLMq8hJycHrq6u\nuHbtGjZv3lwnho2qDGJ2dja+/vprXL58WStyhHQhhCApKQnBwcFwdnbGhg0bcP/+ffTs2RMzZ86E\nlZUVRo4cybrknjKkRp2okRnk8Xj44Ycf4O7ujpMnT8Lb21t2JE5Z9EZTxGIxdu3aheDgYJw6dQpZ\nWVkKk9Oo0q9fP6SnpyMrK0vhfUXHicaNG4dr166pHZsQgnPnzsHMzIzx+jg0h9vz5aB1OOK6AAAg\nAElEQVTE9u3bIRQKFd6jortaG4YX+J/XsGvXLtSrVw+pqamwsrJCixYttDanOsaPH489e/bAxMRE\nZbuAgAA4OjrC0NCQcSlKTcnMzERERATi4+PB4/HQs2dPzJkzB23btpXt8Xp5eSElJQXbtm2Do6Nj\nra6vZ8+eeP78OaUwbsOGDeHg4ICUlBR4eHhgwIABSE5OZl19Kzo6GufOncOSJUtke/tslKK0srJC\nQEAAPDw8ql1Xdo7XyMgIBQUFasc9e/Ysxo4dq9XfQw71cJ4vh1oiIiIwZswYlbWFpbqriqgtwyvl\nw4cPOHToEHr37o0NGzbUqeEFKvfE1emu/vXXX+jevTuaNGnCqBIWU4qLi3H58mWZ5N6xY8cwYMAA\n2b7tzz//XM3wSpOrOnbsCB6PR0txiA3Mzc1pSwx26NABPj4+0NPTw+XLl5GamsrKWpKTk2FnZ4ec\nnBz4+/tj4MCBsntsVMJq3rw52rRpg6dPn8quqSugYWhoiMLCQqVjlpaW4vbt2xg+fDijNXGwB2d8\nOVRSUVGBP/74A7Nnz1bZTpnuam0a3levXsHOzg55eXkIDw9XmpxTFxgYGKCkpEThPUIIDh48WK2Q\nvrYMsFgsxoMHD7Bp0yY4OzvDz88PBgYGMsk9Kysr9OvXr9q+rbJzvGvWrEFwcDBra6NCu3bt8P79\ne0Z9Y2JicPnyZcTHx2PdunVIT09nNE5hYSE2btyIM2fOwNPTE99++63CfW42DPCKFSuwd+9eEEIo\nVa4aO3asymSz4OBg/Pbbb4zWwsEuXNiZQyV79uzB8uXL1SbRdOzYscYfmNoyvAUFBQgMDISBgQGE\nQqHMQ2/bti2ePn1aTXy8rhgzZgxu3ryp8PjIiRMn8O2339Z4R5qqIUnJzc3Fzp078e7dO+jq6mLw\n4MFYuXIlJf1lVQU0GjZsiMGDB8sUeWoLaVYvnb1mafSmYcOG+M9//oP8/HwEBQWhYcOGWLVqFSXF\nKIlEgiNHjuDZs2ewtLREu3bt1PbRtBRlvXr1MGPGDDg6OqJPnz5qC2gMGzYMnp6emD59eo17aWlp\nEIlE6Nq1K6UcDQ4tU3dHjDnYhu0iG9nZ2UrLIypi/fr1smIVTApoUKFq8QOp7qmjo6NC3VM2FIHY\nQpnualFREbG3t1fZl64aUlZWFjlx4gQRCASEz+eTmTNnMiqZSaVkpEQiIRYWFlorUqKIP/74g9y5\nc4dye1WfgxcvXhBbW1ty5syZavfli2zcu3ePWFhYkLt37zJasyZqSCdPniSTJk2iXMZVUTESQghx\ndHQk+fn5hBDler4ctQcXduZQSkBAAK3kFKnuam14vHfv3oW1tTV69+4Nb29vtG3btkabevXq4Ztv\nvkFYWJhW1kAHZbqr27Ztw5o1a1T2VReCLi0tRVRUFDw8PCAQCHDw4EH06NEDHh4eEAqFGDRoEO0C\nDFRFEng8HhYvXoyDBw/SGl8Txo4dSymrV4qq6E337t3h6+sLIyMjWFtbV9tfBSq9RUdHRzx//hz+\n/v4YMWIEozUzDUFLQ83BwcEqz7BXpU2bNjVC8zExMejbty+MjIxorZtDe3BhZw6FxMfHw9jYmFay\n0vjx4+Hp6QldXV2tGV5pVaoBAwbA399f7VlNc3Nz2NnZYcqUKbUuRi9Py5Yt8fHjR1m95pSUFBBC\nKBnGqiHolStXoqSkBFFRUcjJyYG+vj5GjRqFtWvXsvKMdNWJTExMcPr0aeTl5Wm9aAlQmdWrKqmo\nKjk5OUhLS1O79WBubo5x48Zhz549OHHiBIqKiuDr6wuRSARnZ2dWjBbdELT8Hm9RURHS09MVHveT\nf5bIyEgsWrQIwP/C5f7+/ho/AweL1LXrzcEebIWdmdYWfvbsGRk5cqRWQpDFxcVk06ZNxMzMjBQU\nFNDq++LFC7J161bW10SXJ0+ekGPHjsl+dnBwUFpbWJ53796RvXv3knXr1pHhw4eTgIAAkpWVRakv\nnTrFdNWJpGRkZDCu8c2EjRs3ykKoqnBxcSEfP36kPK5EIiH79+8n7du3J+7u7qzV164KlRC0InUi\nRbW1FSGRSKqFng8fPlwjTM+FneseLuzMUYM//viDdm1haah56tSpjGo9K4P8V/d0/fr1+O677zBm\nzBg0atSI1hjdu3dHUVER4yxZtujXr58srHnr1i0MHDhQaW3hvLw8nDt3Di4uLnB2dkZ4eDjGjh0L\nLy8v3Lp1C2/fvqVV0pMKmujxGhsbo3Hjxnj+/Dmra1KGuqxegH705vHjx7C2tkbHjh2xbNkyzJ07\nF/b29rhy5QobS5ahLgStLKu5cePG6NWrFx48eKBy/KrFSAoLC/H06VOMHDmSvQfgYIe6tv4c7MGG\n58tEVaVqctX169fJ5cuXNVqDlLi4OGJpaUmio6Nl15gq9OTn51PyGrQNn88nFRUVxMLCopp3KRKJ\nyI0bN4inpycRCATEx8eH3L9/X2kUgU4SFpV3xtTjrQpTRR4mlJeXk/Xr1yu9Tyd6k5mZSZydncnO\nnTtJeXk5IeR/70wikZCwsDBiY2NDOeGNKoo8YHV6vFJVMXX/T0eOHCHPnj0jGzduJKmpqTXuc55v\n3cPt+XJUIyQkBKtWraLcXj65asSIEfDy8qKsyKKIzMxMBAQEoHPnzti6dSsre8dGRkYyr2Ho0KEa\nj8eUnj17YtOmTVi0aBESEhIQGRmJzMxM6OnpYfjw4bC2tqaktMPWMSRAM4+3Kvr6+hg/fjwuXbqk\n9TKe9erVU1kvm0r0pry8HDt37sTHjx9hY2ODL774okYbHo+HmTNnYvLkydixYwfy8/NhZWXFyt62\n/B7w/fv31Z7j1dHRwbx583Ds2DEsWLBAaTszMzMEBwejcePGlI5EcdQ+nPHlkJGRkYH8/HzKf8gV\nZTXXr1+fkhqLIsrKyrBz507k5OTAwcGB0jlUOvz888+wtrbGkCFDtFb8XxXp6enIyMjA7t27UVRU\nhL59+2LevHkwNjZmNB4bBpgtwytlxowZsLGxgZmZmdYlEaVZvfKZ7iKRCNeuXcPWrVuV9r106RIu\nXbqElStXUpLU09fXh7W1NTIyMuDj44MePXrg559/1viLodQAz507FxMmTIC9vb3aPqNHj0ZYWBhm\nzZql9IuasbExrly5gujoaI3Wx6E9uD1fDhmBgYGwtLSk1FbVcSKp7iodwsPD4ejoiIkTJ8LV1ZV1\nwwtUeg0//vgjjh49yvrYiigsLMSff/4JV1dXODs74/Tp03j//j2++eYbeHp6YsGCBYwNrxRNKmGx\nbXiBSk9x5cqV2L17NyvjqUJZqcmQkBD8+uuvCvskJSXBxsYGFRUV8PPzo61l27p1a2zcuBH9+/eH\nra0tbt26xWjtVblw4QJmz56Nd+/eUT6GZGFhgaCgIKX3o6Oj0bFjR65+82cMZ3w5AFT+Ie7Rowel\ncJq6c7xmZmaUSzv+/fffsLGxAQD4+fmhd+/e9BZOk1GjRuHx48eUj6rQQSq55+3tDYFAgKCgIDRr\n1gzOzs7w9PTE5MmT0blzZzRp0oSW7qo6mBhgbRheKX379sWHDx+UKvKwRa9evZCUlFTtmjR6Iy8Z\n+enTJ3h4eODy5cvw8fHBjBkzNHruIUOGwN/fH6mpqVi7di3j8pHS5KqVK1fSOgfcoUMH6OrqKpRM\nrKiokAk9xMTEMFoXRy1Q15vOHOzBNOFKIpEQS0tLSkeEqFSukkgkRCAQqBwnJyeHuLq6kqCgICIS\niSivlWnCVVXevXtHvLy8NB5HIpGQpKQkEhwcTAQCAXFxcSF//PGH0iMwtra2pLS0lJw/f55xpSRV\nKEvCkn9nbCRXqYNudTSmCASCas/h5OREPn36JPu5oqKC7Nmzh/D5fJKRkUF5XDqfs8LCQuLj40O8\nvb1JUVER5X6KkqvoVMJSVh1t165dJC4ujhQWFhJPT0+FfbmEq7qH2/PlQGhoKL777ju1ISqqlauq\nHnWQ9y7EYjH27duHt2/fwtLSEq1atdL8AWhS1Wvo3Lkzrb4fP35EZGSkTNS9R48emDVrltqklitX\nruDrr7+Gvr4+xo0bh+DgYMbVkpRBZQ9Ymx5vVb744gu0b98eT548wYABA7Q2T9++fREfH49+/frV\niN7cuHEDp0+fxuLFi7Fs2TKtrcHQ0BBr167F27dv4erqChMTE8ybN0/l+1V2nIhOIY6GDRtiyJAh\nuH79OsaOHQugso73mzdvsGLFCgCVqlUcnyl1bf052IOJ50ultjAh9Gs1Hzx4kCQlJVW7Fh0dTSwt\nLUlcXBytNVaFDc+XEOrPXVxcTC5fvkzc3NyIQCAgfn5+5MmTJ7S8xvLycmJlZVWtj7L6u2wg7wFL\n31lteLzy69B2be2MjAzi7+9frcb0mzdviJ2dHQkNDWU8tyafsxs3bhALCwvy8OFDhffVHScihLoH\nLB+1cnNzI5mZmbL73t7e1SIBUjjPt+7hPN9/OUFBQbCwsFDZhkmtZnNzc5w7dw49e/ZEcnKyzNPz\n9/evk0xjeRo2bIihQ4dW8xqASs/80aNHiIqKQl5eHho0aABTU1M4OTmhfv36jObavXt3jdrCjRo1\nQmFhIe2CIVSQ94CB2vN45dcxc+ZMnDt3DnPmzNHKHMbGxsjMzERoaChmzJiBzZs3Q1dXFx4eHmjY\nsKFW5lSHqakpRo0ahUOHDuH06dOwtLRE69atAajX45VC1QOW1tY+cOAARo0ahebNm8vKlwKVJV+j\no6PVSoJy1D6c8f0XI03sUBXaYiqS0LZtW7x58wZeXl7Q09PDhg0bYGBgoPGa2eT777+HtbU12rVr\nh6ioKLx9+xa6uroYNGgQli9fjmbNmmk8R3Z2NtLT09GvX79q17/++mtcv35dofQbG1Q1wKmpqZBI\nJLVqeKWYmZnBzs4OU6dO1Wpt7UOHDqF///5Ys2YNOnTooLV5qKKrq4slS5YgLy8PgYGBaNy4MVq1\naoXS0lK1hlcKVQM8ePBgnD59GrGxsTXqN5uYmFDS4+aofbhs538x6rxepoZXIpHg999/x+3btzF/\n/nzY29t/VoY3NzcXp0+fhouLC4qKiuDp6YlJkyZBKBTCw8MDc+bMYcXwAsqVoYYNG4b79++zMocy\n6tWrh++//x63b9/GwoUL6yzisHr1amzfvl0rYz948ABnz57FqFGj4OPj81kY3qo0adIE69evB4/H\nw/79+9G8eXMQQij3p6qG1KdPH+Tn59eIzujq6kIikTBeP4f24Izvv5SbN2/CxMREaWiOqeGNiYmB\ntbU1unXrBicnJ6Snp7O1ZMaIRCJER0djw4YNcHZ2xr59+9ClSxe4u7tjz549aNeunVbOFT99+hRt\n2rRB8+bNa9zT09Nj9biRIh4+fIjw8HAsXboUO3fupH0OmC26deuGkpISVmtrp6enw8nJCTdu3MCP\nP/7I2rja4NSpUzAyMsKVK1egr68PGxsbxMfHU+6vzgCXlZUhNjYWw4YNq3H0CqhMMGR6FIpDi9T1\npjMHe1BNuFJUW7gqdJOrCCEkLS2NODo6koMHDxKxWEwIqaynzMaRnqpQSYSRSCTk8ePHZOvWrYTP\n5xN3d3dy9epVUlxcrLB9RkYGcXd3Z3Wd0trC0lrBiggKCiLv379ndV4pVZOrXF1dadWC1gZs1dYu\nKSkhvr6+ZMOGDSQvL4/Y29uToqIi1hPY2ErsU5RcVVZWRoKDg4mLiwvJzs6mPJayJKzAwECSmJhI\nRCKRwtraL1++JHv37q12jUu4qnu4Pd9/IYcOHcLixYsVhiHperylpaXYvn07SktLIRAIqume0tFd\n1ZTU1FRcvXoVL1++hI6ODvr3749FixZRUrQxNjZG06ZNkZSUhF69erGynvPnz2P69OmoV0/5r5i0\nQpNUd5UtFCVXsVkLmglGRkbo06cP7t+/j2HDhtHuTwhBWFgYbt68iVWrVqF79+64efMmBg8ejIYN\nG6JJkyb49OmTViIYTFGWXKWnp4fVq1cjKysL/v7+aNeuHZYtW6byswIo3gPOzMxETk6OrDjNhAkT\ncPHiRUydOlXWr2vXrti3bx/7D8ihGXVt/TnYg4rn++nTJ+Lk5KTwHh2PVyKRkNOnTxNbW1vy6tUr\npe28vLwo6a5SReqR5OXlkbCwMLJ+/XrC5/PJ9u3byYsXLxgfLRGJRMTa2pqVNVJV95HXXWUDRceJ\nqnpxdekBSxV5pJERqjx9+pRYWVmRK1euyK7JR2/u379Pzp49y9paNfV8qRwnkvLkyRNiaWlJIiIi\nKLWv6gHz+XySm5sru6dMzUkgEFR775znW/dwe77/MpTVb6bj8T558gTW1tZo0qQJfH190bVrV6Vt\nx44dixs3bmi87vLycty6dQs3b96Es7MzQkJC0Lp1a7i6ukIoFMq8IaZJRfXr14eZmRkuXryo8Vq3\nb9+O1atXq21XtRgJG1A5TqRJLWhN0dHRwfz583Hs2DFK7bOzs+Hi4oKbN29iy5YtmDhxouyefPRm\n8ODBiI2N1cq66UL1OJGU/v37w9/fH/n5+bCzs8OrV69Utpd6wI6OjmjcuHE1b5/H4+GXX37Bzp07\nq/UZMGAAnjx5Qv9hOLQGZ3z/Rbx48QJGRkayM4dSqBrerKwsODs74+7du/D19YWZmZnaOYcOHcoo\nq5cQgsTERAQFBcHZ2RlCoRAFBQUYMWIEPD09sXbtWgwbNozVwvHTp0/H5cuXGasyAZWJQEVFReje\nvTul9l9++SUSEhIYzyeFzjneujTAI0eOxJMnT1RuR5SXl2PHjh0IDAyElZUVVq1aVS0km5eXhxcv\nXsDExER27XPJ6qVreKXweDzMmTMHQqEQYWFh8PT0REFBgdL2+vr6+OKLL5CamlojmapPnz7IysrC\nx48fZdfMzMwQFRVF72E4tEtdu94c7KEu7GxjY0NKS0urXaMSai4rKyPbtm0jrq6utBJEpKir8ywl\nPT2dHD58mPD5fCIQCMjvv/9O0tPTq7VhKxFGGQkJCSQoKIhxfycnJ5KXl0e5fUZGBgkICGA8HyHq\nK1cpe2d1FYJOSUkhGzduVHjvypUrxMrKijx9+lRpfw8PjxqfC0IICQkJIW/evGFljUw+Z3RCzepI\nS0sj69atIwcOHFAYpj9x4gSJjo5WmoSVk5NTo7Z21S0OLuxc93Ce77+Ey5cvY9y4cdDX15ddo+Lx\nXrp0CQ4ODhg/fjzc3NwUCo6rQ6q7Kk9RUREuXrwINzc3ODs74+TJkzAxMYGnpyc8PT3x008/1fDS\ntY0ir4EqDx48QM+ePdG4cWPKfYyNjfHhwwfac0nRpHJVXXnA7du3h56eXjVFnpcvX8LW1hbFxcXw\n8/OrUZREirLoDaBcYrA2YOrxKqNt27bw8vJCnz59YGNjgzt37sjulZSUICYmBuPGjVN6DKlZs2bo\n0KEDHj9+LLumr6+P0tJSVtbHwQJ1bf052EOZ51tWVlajtrA6jzcpKYlYW1uTP/74Q+PavH///Tc5\ndOgQqaioIPfu3SPe3t5EIBCQjRs3klu3btVIDlGFtj1fQiq9BqreuhRpbWG6yUSEVD4THWUnKVRr\nNat7Z3XhARcXFxM7OzuSl5dHPDw8iJ+fX42ojCIURW+qwlYCG53PGZseryLEYjE5cuQIcXBwICkp\nKWTTpk0kOTm5WhtFHrB8be2IiAgSGRlJCOE8388B7qjRv4Ddu3djxYoVMs9Ilcebl5eHgIAANG3a\nFN7e3tU8ZboQQvDq1StERkbi6NGjePnyJUxMTLBq1Spa3mFt06xZM3Ts2BGPHz/GV199RanPsWPH\nMG/ePOjo0A8mjRgxAjExMTA1NaXch81azXVxDElfXx/FxcVYtWoVfH19KUU4FEVv5OHxeJBIJIz+\nH5jAtserCB0dHSxYsAAzZ86EUCjEo0ePsGbNmmptFB1D+r/27jMgiqt9G/i19I4CEsWOQY0oYkdF\nRMGaoMYWewxiV0A0GmMMNmKLAoK9EImaqNii0ccEBRV7QWxRIgqKBgSRjpTdeT/4X17Q3WVmdnd2\nwfv3LTtzZg5IuJiZM/etp6eHwYMH4/Dhwxg2bBi6d++ONWvWoHfv3mqbK2GPbjvXcJmZmUhPT4ej\noyMA+cErFouxc+dOrF69GlOnToWvry+v4M3MzMT+/fvxww8/YPHixYiLi8OgQYPg7u6OJUuWYNCg\nQVodvFLe3t7YtWsXq5XIBQUFuH37Nrp3787rXD169OC0IlwdTRKEvAUdFxcHf39/TJw4ETY2NpUa\nAchTWlqKU6dOwcvLS+F+bdu2rXSrVZ2ECN6KzMzMIJFIsHbtWixevBgHDx6s9PMp6xZ07969cenS\nJbx9+xZGRkYoLi4WZK6karpLlixZoulJEOW8fPkShw4dwunTp5GWlobXr1+jSZMm0NPTw6pVq+Dv\n7w9jY2O5wXv+/HmEhISgf//+GDduHKdOO0VFRTh37hz27NmDv//+G//++y86d+6MUaNGwcPDA87O\nzrCwsEB6ejp0dHSU7t8bGxsLd3d3pY7Bho6ODgwNDREfH49WrVop3Dc4OBg+Pj7lfWS5MjAwwOnT\np1mtHucTvGy/Zzo6OvDw8MCqVatgb28vsyymMp49e4agoCCYmJjg22+/RYMGDVCvXj2cPHkS7du3\nVzh269atGDp0aJU/P3Xr1i2v9ayMqr5nQgcvAFy6dAmGhobw9PRE3759kZmZieDgYNStWxf16tUD\n8O6PqF69emHp0qVwdHSEpaUlHBwcEBkZiW7duuHq1atITExEbGws4uPjkZeXh/r162usA9THjG47\nV2OxsbHYuH4NzsTEoF9jPdTTLcLzxycQnW+AKd8AXkOGoJlDS1hZWckM3pSUFISHh6Njx46sW/1J\nJBLcvn0bMTExePPmDYyMjODq6ooFCxYovFL28PDAb7/9Vn4FXh307t0b8+bNw8CBA+U2hkhJSYFI\nJFK6oL+lpSVycnIUBrgQbQHVcQu6sLAQ4eHhYBgGgYGBMDU1Ld/m7OyMqKgohdWpMjMzkZaWxupn\nx9raGllZWUrPWRFNBK9EIsHvv/9eqWtRz5494erqioiICERFRcHPzw+2trYf3IK2t7dHamoqxo79\nGocPH4ZIVB9icW0wDHDw4C2UlU2Hl9cgzJ8/Bx07dhTsa/rYUfhWQxKJBN/NC8DByO2Y16oQO0cC\nFuXNTMQAivFvNhB2ay9CjpigTp06ePz4cXnwFhQUIDw8HCKRCEuXLq3yr97k5GRER0cjOTkZIpEI\nzs7O8Pb25tT5x9bWltcKYk2TduSZO3euzO3h4eFYunSp0udxd3dX2HdVyH68qgpghmFw4MAB3Lx5\nEzNnzkTjxo1l7ufr64vQ0FAEBgbK3L5hwwb4+/uzPq90Va86WhhqIngB4Ndff8W4ceM+eJatq6sL\nHx8fZGdnIzQ0FFZWVpg6dWqlAG7evDm2bo3A27dtwTCTAfz/P/DevdJeiEOHbuPPP/vhxx+/w/z5\n87Si53ZNR+FbDX07xxeXj0TghlchrOX8fnGoBWzoJsGIpvkY5DcDh06cho6ODvbt21e+YENef9Ds\n7GycPXsW8fHxYBgGjRs3hqenJ5o2barUvPX19VFSUsK7Kb0m2Nvbo7i4GC9evED9+vUrbTt//jw6\nduyoklt2ivquChm8UsoG8M2bNxEZGYnhw4fjq6++Urivra0trKys8PDhw/IaxVJ3796FnZ0dp1fc\nXF1dcfHiRVa38bnQVPDm5ubin3/+wddffy13n1q1aiEwMBAPHz7EggUL4OnpiYEDB6JLly6YOHEa\nysrGA/hEzmgTSCTdUFjoiGXL3l1ZL1jwreq/EFIJLbiqZo4fP44Tv/+CPz3lB29FPeoBUR5lGPnl\nIEyfPh2NGjXCmjVrKgVvcXExzp07hxUrVuCHH37Ajh070LhxYyxduhQrVqzA5MmTlQ5e4N2q3itX\nrih9HKHNnj0bYWFhlT4Ti8U4dOgQRo4cqZJzyKvQpIngleKzCCs9PR3ff/89EhISsH79etYruGWV\nRGQYBjt27ICPjw+neXfr1g0XL17kNKYqmgpe4F3fbVklYWVp2bIlgoODIRKJMGXKFPj4TEdZ2TjI\nD96KLFFY+BWWLVuF69evKzVnUjW68q1mNqwJQmCbAtTmsBDZowHgUqcM7du1g6urKxiGwb1793Dm\nzBlkZmbCwMAAXbt2xdy5c9Xa9L5Hjx4IDg6Gm5ub2s6hDubm5nB0dMSVK1fg4uICAPjll1/kdobi\nS9p3VfqHkSaDV4rtFXBxcTG2bNmCnJwcLFiwgPPiMwMDA/Tp0wcnT57EwIEDAQBHjx6Fl5dXld1+\n3qfqVb2aDN6kpCQYGxvDzs6O07iBAwfiwoWLKCtrCYBLoRpLvH3bEWvXhuDAgb2czkm4ofCtRh49\neoQ7dxIwTPFdPJl8WxZjxvIfkZySAl1dXbRu3Rpjx45l9ZqHqpiYmKCoqEiw86nS2LFj4e/vj86d\nOyMvLw9JSUmYNGmSSs/Rp08fREdHw9vbWyuCV0pRADMMgxMnTiAmJgbTpk1D8+bNeZ9n4MCBmDNn\nDjw9PSGRSBAXF4d169bxOpaVlRVev36t9IptTQYv8K5JR1BQEOdxpaWl2LJlO8rKRnAeK5E44/jx\nTSr5/hH56LZzNXL06FF81VQMQx69BDwbAIX5uZg0aRKWL1+Or776StDglZKu6q1upIUO9u7di9DQ\nUPj5+an8HPb29khKStKq4JWSdQv6wYMHmDNnDvT19bF+/XqlgldqypQp2LZtGzZv3ozp06fzPo4q\nGgloOnijo6Ph6urKa+HY1atXIZGYAuDzap8J9PQ+xcmTJ3mMJWxR+FYjGWn/oYExv447OiKgvqUh\nXr9+reJZcdOrVy/ExMRodA58ubi44Pz58zAyMsInn7B5hsaNSCRCWloajh07plXBKyUN4JCQEMya\nNQsxMTFYu3Yt+vfvr7JzfPbZZ0hOTkZ6ejrrzlCyODk5KVVs48GDBxoN3rKyMnmpyZMAACAASURB\nVLkL8Nh492YB/2I2JSWmyMzM5D2eVI3CtxrR0dGBRInWrxIGgpXdk6ddu3a4deuWRuegDJFIpLYq\nQTdu3EBOTg6GDh2qdcELvAuEnTt3olatWpBIJOjbty/09fVVfh6xWKx0e0AdHR1IJBJevZKjoqJQ\nUlKiseAFgJ07d8LHx4f3z4GOjg6U+RESiRiN/66o6ei7W43Urd8ATwr51VoukwDPc4rVcsXGhbb0\nXeXj1KlTGDRoEExMTPDkyROVHlt6q3nLli1aeWfgzJkzmDt3Lrp27YqgoCBs2LBBLaUor127Bmdn\nZzg4OOD27dtKHevTTz/l/O8kvdXs7Oys1LmVkZWVhdTUVLRp04b3MerWrQuJJAsAv7/WDQzyNP67\noqaj8K1GRowYgagnQD6PO89/JAMtmrdQuhKTKkhX9VYnpaWlOH36ND7//PPywhuqUvEZr42NjcYf\nDVT05MkTzJ07Fzk5OQgJCYGTkxMA9dSCZhgGe/bswfjx4+Ht7Y2IiAheV65Snp6e+Pvvv1nvr+ln\nvFKqWFPQqVMnmJiIALzgMToXZWXJ+Pzzz5WaA1GMwrcaadiwIXq69cC+x9zHbkoyx4yABaqfFA/S\nVb3VybZt2zBlyhSIRCIYGxuja9euSi/oAWS/TqQNfVfz8vIQFBSEo0ePIigoSOatcFUH8L59+zBq\n1Cjo6OhAV1cXQ4YMwaFDh3gfr1GjRnj+/DmrfbUleO/fv49PPvkENjY2Sh1HR0cHAQGzYWLC/e6B\nrm48xowZA3Nzc6XmQBSj8K1m/Bf8gGV3TPA8n/2Y3x4Dj4uMMXToUPVNjAN7e3uV37ZVp4yMDLx6\n9apSg4WhQ4fi2LFjKCsr431ceauau3fvXql5upAkEgkiIyMRFBSEb775BgEBAQpX26oqgPPz85GQ\nkFCpIUKvXr1w5coVpV5P09XVhVgsVriPtgQvwzDl7T9VYdIkb+jqJgHg8v/aKxgaxmPuXNWv5ieV\nUfhWMz179oT/gsXo85cJnuZWvf/BJ4DfDTMc/1+0Ur15VU3ad7U6kFVbWCQSld8a5UPR60Tdu3dH\nXFwc7/nydfnyZfj7+6NFixZYtWoV68IOqgjg8PBwmVWcZs6ciY0bN/I6JgC0b98eN2/elLtdW4IX\neFe9bsCAASpbxGZtbY0//jgME5M/ADxlMSIdJib7sXVrGD777DOVzIHIR+FbDc1b8B1mfh+EzieM\nseC6/gchzDDA2RfA8FhTBCRY46+YC0ot3lCHtm3b4s6dO5qeRpUSEhLQsGFDmU0k2rZti5SUFLx5\n84bTMat6j1fovqupqalYsGABkpKSEBISgi5dunA+hjIBnJycDF1dXTRo0OCDbU2bNkVpaSlSU1M5\nzwlQ/GqbNgVvcXExYmNj0a9fP5Ue193dHX/+eQTm5n/A2PgEgFR8uAgrA4aGp2FsvBc7d4Zj3Lhx\nKp0DkYMh1VZiYiIT4DuLsbYwZbo1sWC+/MyC+aKlJfOprSnj+GljZmN4OJOTk6PpacqUmZnJrFu3\njvO4wMBA1U9GDolEwvj6+jKlpaVy93n16hWnOV2/fp1ZvHgxI5FIFO73888/M5mZmayPq4i8+RUW\nFjJr165lfvrpJyYvL08l5yotLWUCAgKYxMRE1mPmzZvHFBQUyN2el5fHzJ8/n/ecvv/++w8+O3jw\nILNr1y65Y4T8OWMYhgkJCWEePXqktuNnZGQwq1atZmxtGzDm5g0ZCwsnxsKiLWNh0ZSxtLRhFi5c\nxDx79kxt5ycfovKS1ZiDgwPWhYZh+crVuHLlCrKysmBgYIAGDRqgXbt2WvmuqJQQfVeVdeTIEQwa\nNEhhbeE6derAxsYGDx48qPRMWBYulat69+6Ns2fPYsQI7uUBq8IwDKKionD16lXMnDlTJU0zpLh2\nQzp37tz/rcyV3xnKzMwMbdq0weXLl9G1a1fOczIxMUFBQUF5H2FtuuIFgLS0NOTm5qqkQpg8NjY2\nWLBgPr79dh6uXbuGtLQ0SCQS2NjYwMXFpVp1GqsxNJ3+5OO1bNkypqioiNMYoa5IioqKmICAAFb7\nlpSUMP7+/gqvZtle8UqJxWJm0aJFrPatSsXvWXx8POPr68vExMSo5NjysLkCLisrY3x9fVl9T8Ri\nMTN79mxGLBZznsv58+eZU6dOMQxT9RWvlJBXvgsXLmSys7MFOx/RDvTMl2hM9+7dVd76TVU2btyI\nmTNnstpXX18fffv2lVsLl0+tZh0dHaXecX1fRkYGFi1ahOvXr2P9+vVwd3dX2bFlYfMMOCIiAhMn\nTmT1PdHR0cHYsWOxZ88eznPp0qULrly5onVXvMC7vscODg6cu0CR6o/Cl2hMt27dNPZKjSIvXrxA\ncXEx7O3tWY8ZMGAAoqOjUVJSUulzZZokqOKVrJKSEly7dg2bNm3CvHnzMHnyZOjq8ujMwYOiAM7O\nzsbTp0/Rrl071sfr0qVLec1lLgwMDHD37l2tC16GYRAZGYkJEyZoeipEAyh8icYIvaqXrbCwMMye\nPZvzuGnTpmHLli3l/61sd6I+ffpwqtD0vpMnT2LBggWwt7dHYGCgzBXb6iYvgDds2MC6QXxFvr6+\n2LBhA6cxUVFRMDQ0LO8TrC3279+P4cOHC/bHENEuFL5Eo6R9V7XF1atX0apVK17VfVq0aIHs7Gyk\np6erpC1go0aNeJXhfPjwIebMmQMACA4OVrpakrLeD+BHjx6hVq1avGoH29nZwcjIiPUdAemt5kWL\nFuHMmTOcz6cuhYWFuHnzJnr06KHpqRANodXORKOkfVfVsaqXK4lEgr179yIkJIT3MXx9fREQEIAG\nDRqopC2gjo4OxGIxq6uj7OxshISEwNraGqtXr9aqFawVV0G/fv0a27Zt432smTNnYtGiRVi3bp3C\n/So+42UYBvv27eN9TlXje3eF1Bx05Us0qk2bNlpTbGPfvn0YPXq0Uq3UHj9+jIyMDAwZMkQlr3q1\nb9++yhaMYrEY27dvx88//4wZM2Zg9uzZWhW8Unp6enB3d0dOTg5SUlJ4H8fIyAjdu3dXeCX7/uIq\n6b+FKhex8SW9m9GoUSMNz4RoEoUv0ShVr+rlKz8/H3fv3uX1HqmU9FbzkSNHsHv3bpV8XYoqNAFA\nbGwsAgIC0LFjR6xYsQK2trZKn1NdSktLcebMGRw4cEDpWtBffvkl/vjjD5m1teWtam7ZsiUePXrE\n+5yqEh4eTle9hMKXaJ69vT2SkpI0OoewsDBeC4CkKj7j1dPTw9ChQ3Hw4EGl51WrVi3k5OR88PnT\np08xb948ZGZmIiQkhNOqYU3ZunUrpk6dCn19faVrQYtEIkyaNAk7d+6s9Lmi14k8PDw03k3rwoUL\naNeuncKiIuTjQOFLNE7TLQafPn0KfX191K9fn9d4WYurevbsievXr6OwsFDp+RkbG5cfJz8/HytX\nrsShQ4ewfPlyDB8+XKsrmUllZGQgMzOzvGC/KpoxODk5ITU1tbxSWlXv8drZ2eG///7j9wWogFgs\nxsGDBzFq1CiNzYFoD1pwRTSuYcOGrPuuqsPGjRuxfPlyXmMVrWqWduT59ttvlZqfm5sbzp07h6ys\nLNy5cwezZ8+W2YRAm4WGhmLu3LmVPuNailIW6atHrVu3ZvUer56eHkpLS1XWOYiLyMhIfP3119Xi\njyWifnTlS7SCdFWv0GJiYuDi4gJjY2POY6t6nahJkyYQi8VK/2Ghq6uLJUuWoGnTpli9enW1C97b\nt2+jUaNGMt8zVvYKuE6dOkhNTcWjR49YFdDo3Lkzrl27xvk8ysrJycG///6LDh06CH5uop0ofIlW\n6NChQ5WrelWtrKwMR48exbBhwziPZfse7+zZsxEeHs5rfi9fvsR3332HpKQkeHh4VGo0X10wDIOI\niAh4e3vL3UeZAI6KikKXLl2QkZHBaoFbz549ce7cOU7nUAW+RUVIzUXhS7SCu7u7wlW96hAREYFv\nvvmG821ALgU0TE1N4eTkxKmG9du3b7F+/XpERERg0aJFmDBhAmxtbZGens5pntrg8OHDGDx4sMLO\nUAC/AJY+4508eTL69++PEydOVDnGzMwMBQUFrI6vKv/++y/Mzc1Rt25dQc9LtBuFL9EKlpaWyM3N\nFex8b968QXJyMpydnTmN41O5asyYMdi/fz8kEonC/RiGweHDh7Fo0SIMHjwYixYtKq+05enpqVUV\nmtgoKirC5cuX0bt3b1b7cwng9xdX9e/fH2fPnv2gtrYsZmZmgv6sbd68GdOnTxfsfKR6oPAlWqPi\nql5127BhA/z9/TmN4VsyUiQSYfz48YiMjJS7z507d+Dv7w9LS0usW7cOzZo1q7Td0dER9+/f5zRf\nTdu0aRNmzJjBaQybAJa3qnn69OnYvHlzledwd3cX7Nbz6dOn4e7uDkNDQ0HOR6oPCl+iNdzc3HD+\n/Hm1n+eff/6BtbU16tSpw3qMsrWaO3XqhEePHn1wxZWZmYnFixfj8uXLWLduHTw8PGSO16YKTWzw\n6QwlpSiAFb1O1Lx5c+Tk5FR5e75Tp064ceMG53lxVVpailOnTsHLy0vt5yLVD4Uv0RouLi64evWq\nWs/BMAy2bduGKVOmsB6jiiYJwLvXYsLCwgC8+8W8adMmhIeHY86cOZg6dWqVz0VbtGiBxMRE3ucX\nkrILjGQFMJt+vH5+fggNDa3y2LIqY6na9u3bMXnyZHq1iMhE7/kSraGvr4/S0lK1nuPkyZPo06cP\n69rHqgpeAKhXrx5MTEwQERGBhIQETJkyBa1atWI93sPDA0ePHkWLFi2Umoe6XblyBa1bt4aZmZlS\nx6n4HnCTJk1gZmZW5etElpaWaNasGW7duoX27dvL3c/Ozg6pqalqe20rMzMTaWlpcHR0VMvxSfVH\nV75Eq6hzVW9JSQmio6NZ93VVZfACQGJiIp4+fYpjx44hODiYU/ACQP369fHy5Uul56FOEokE+/bt\nw9ixY1VyPD09PXTu3BknTpyAq6srqzETJ06ssrZ2nz591LqAjc+aAvJxofAlWsXDw0NtvxSltYXZ\nUGXw5uTkYNmyZTh16hTWrl2LiRMn8i6nKdQtU7727t2LMWPGKNUZqqKoqCgUFhbizz//ZP0akq6u\nLoYNG4YDBw7I3cfBwUFtt/Dv3r0LOzs7WFlZqeX4pGag8CVapVWrVnjw4IHKj/vq1StkZWWhZcuW\nVe6rquAVi8XYtWsXVq9ejalTp8LPzw+GhoYYPHgwTpw4wStEO3XqpJEKTWzk5eXh/v37cHFxUcnx\nKj7j5foesJubG27cuCF39bxIJIJIJFL5AjaGYbBjxw74+Pio9Lik5qHwJVpFXat6Q0ND4efnV+V+\nqgreCxcuYM6cOWjbti1++uknfPLJJ+XbRCIRfHx8sGPHDs7H1VSFJjZU2SBe1uIqrgE8a9YshdXF\nWrdujXv37qlkvlJHjx6Fl5dXlYvnCKHwJVqnRYsWKu27Gh8fj6ZNm6JWrVoK91NF8KakpGDevHl4\n8eIFQkND5dbybdOmDV68eIHXr19zOr65uTny8/N5zU2dnjx5AkNDQ96doSpStKqZSwA3btwYEolE\nbm3t3r17q/QRx9u3bxEXFwdPT0+VHZPUXBS+ROt4enqqrMUgwzD45Zdfqlwlq2zwFhQUYPXq1di/\nfz+WLVuGUaNGVXkcf39/bNiwgfO5zMzMkJeXx3mcOvEpqCELm9eJuATw7Nmzy1/vep+trS0yMjKU\nmm9FVMmKcEHhS7ROvXr1kJaWppJjRUVF4csvv4Surq7cfZQJXoZh8Ntvv2Hp0qUYPXo05s+fz7pR\nurW1NerWrcv51qeQFZrYOHv2LLp27cqrM1RFbIJXim0Am5qawtnZGXFxcTK3GxgYoLi4mPecpV6+\nfImCggJ8+umnSh+LfBwofIlWUsWq3qKiIly9ehXu7u5y91EmeG/cuAE/Pz80bNgQa9asQaNGjTjP\nUfrsl8szbm1adFVWVoZjx45h6NChSh2HS/BKsQ3g0aNH48CBAzJra3ft2hVXrlzhNeeKwsLCWK0p\nIESKwpdoJVX0XQ0PD8esWbPkbucbvGlpaVi4cCHu3buH4OBg1u+fyqKvr48BAwbg+PHjrMfo6elp\npPexLLt27YK3t7dSi9P4BK8UmwAWiUSYMGECdu/e/cG2Hj164MKFC5zPW9G1a9fQsmXL8iYYhLBB\n4Uu0kpubm1K3VlNTU1FWVoYmTZrI3M4neIuLixESEoLt27dj4cKFmDhxosLb2Wz169cPsbGxnG5/\n2tnZ4cWLF0qfWxlv3rzBs2fP0LZtW97HUCZ4pdgEcMeOHZGYmPhBbW1jY2MUFRXxPjfDMNizZw/G\njx/P+xjk40ThS7SSsn1XFb32wjV4GYbBsWPH8P333+Pzzz/H4sWLYWFhwXtusrDtyCOlDS0G2b6+\nJY8qgleKTQD7+vrKXOBWq1YtvHnzhtd59+3bh1GjRqmsqAj5eNBPDNFafFf1Xrp0CU5OTjJrC3MN\n3nv37mHOnDkwNjbGunXr4ODgwHk+bDg4OCAvL4/1QrPmzZur9HUsrh48eAAbGxtOnaEqUmXwSlUV\nwPXq1YOpqekH23r16oWYmBjO58vPz0dCQgK6devGe87k40XhS7QWn1W9EokEv//+O0aPHv3BNi7B\nm5WVhR9//BEXLlzA2rVr0bdvX07z4MPPz4/1q0eabDEo7QzFtlTn+9QRvFJVBfCMGTOwZcuWSp+1\na9cO8fHxnM8VHh6uVOcm8nGj8CVaq2PHjrh+/TqnMb/++ivGjRv3wW1AtsFbVlaGzZs3Izg4GL6+\nvpg+fTr09fV5zZ8rCwsLODg4sO4127p1a9y/f1/Ns/rQn3/+iX79+vH6vqgzeKUUBbChoSHc3Nzw\n119/lX+mq6srcyW0IsnJydDV1VVbVyRS81H4Eq3FdVVvXl4e/vnnH3Tu3LnS52yDNzo6GvPmzYOr\nqyuWL18OGxsb3nPna8KECYiMjGR1Revh4aGyYiRslZSU4MyZMxgwYADnsUIEr5SiAB40aBBOnjxZ\n6VW2xo0bIzk5mfXxN27cqHAlPSFVofAlWo3Lql5ZDdzZBO/jx48xd+5c5OfnIzg4GG3atFF63nzp\n6upi5MiR+P3336vcV9UVmtjYsmULpk2bxnmckMErJS+ApbW1t2/fXv5Znz59WP8hc+7cOXTq1Enp\noiLk40bhS7Qa21KTSUlJMDY2hp2dXflnVQVvbm4uVqxYgePHjyMoKAhDhgxRSd9eZbm6uiI+Pp7V\nam99fX2UlJQIMCsgPT0d2dnZaNGiBadxmgheKXkB3Lp1a/z333/ltbWbNm2Kp0+fVnk8sViMw4cP\nY8SIEWqbM/k4UPgSrebg4MCqg837tYUVBa9EIsEvv/yClStXYtKkSZgzZw6MjIxUPndlVNWRR6pr\n1664fPmyADOSfWehKpoMXil5Aezn54fQ0NDy/9bR0any2W9ERAQmTpyoFX+kkeqNwpdoNTZ9V6Oj\no+Hq6loeoIqC9+LFi/D394ejoyNWrlyJevXqqXX+fElLVT579kzhfqqo0MQG285QFWlD8ErJCmBr\na2vUq1cPd+/eBQA4Ozvj9u3bco+RnZ2Np0+fol27doLMmdRsFL5E6zk6OsptPlBWVobjx49jyJAh\nAOQH7/PnzzF//nykpKQgNDQUnTp1EmTuylDUkUfKxMREqQpNbLDtDFWRNgWvlKwAnjx5cnlt7V69\neuHs2bNyxytbVISQiih8iVbLzc1FyrNkeA32hIWlCVYELUcdW0sMG/EFYmJisGPHDkyaNAkikUhm\n8BYWFmLt2rXYu3cvAgMDMWbMmGpzy9DExAQdOnSo8srW0tIS2dnZapvHwYMHMXToUNalNLUxeKXe\nD2A9PT188cUXOHLkCC5duoQNmyJgZmmDZcuDYGJWG63bdcPu3buRkJCA2rVrw9bWVtNfAqkhKHyJ\nVpJIJAhcugiNm9TD2eshWLjDCCdSGiIuzwF7b9uiea9bmDxzKJYsX4iCgoIPgpdhGBw4cACBgYEY\nMWIEvvvuO5iammr6y+Lsq6++wsGDBxW+csW3QhMbhYWFuH79Onr27Mlqf20OXqn3A7i0tBTjvp6K\n0VOW4bnlfBS4PADTPx9Frkm4b/A9Zv24H526uKG0jNu7wIQoImI0USKHEAUkEgm+/mY07v0bjZ/2\nW6FuQ9nFHBiGQczRfARNzkL/voOxd+9eiEQi3Lp1C7t378awYcPg5uYm8OxV7+bNm0hISIC3t7fM\n7WKxGEuWLMHy5ctlbl+yZAmWLFnC69xr167FiBEj5DaoqKg6BG9FZWVl+PwLL5y/GI+3bX4DbHrJ\n3zn/EUzuDsXk8V8gZP1q4SZJaiw9TU+AkPct+mE+Hjw5g01n6sDIWP7NGZFIhN5fmsOmri4CBh1H\nTEwMoqOj0axZM6xfv14lHYe0QYcOHXDo0CHk5OTA0tLyg+18KjSx8fz5c4jF4hoZvABw/vx5XLgU\nj7cdYwHzlop3NmuBwg5x2P6rK5o0bgh/PyqwQZRDt52JVklPT8fmzZuw9rCVwuCtyKmrCbx/MIV/\nwHTMnz8fkyZNqjHBKyWvI49Uo0aNkJKSotJzhoeHy+0MVVF1DF4A8A1YhKIWG6sOXimD2ihscwSL\nf1yq9kVupOaj8CVaZcfObfAYboHadbjdlBnsbYnnz54r1YZQm9WtWxcWFhZITEyUuZ1LhSY2Ll68\nCCcnpyqfk1fX4L116xaeprwE6g7hNtCsOVC7Mw4cOKCeiZGPBoUv0RoMw2DL1jAMm869bJ+puS76\njbbAjp3b1DAz7TBt2rQPOvJI2dvb48mTJyo5j0Qiwf79+zFmzBiF+1XX4AWADeHbUGw3BRBxv0OS\n/8kMrFkv+9+BELYofInWKCwsROarN/isPb+auU7ddXH/H+6t4aoLQ0NDuLu74/Tp0zK3i0QilTz7\njYyMxPjx4xW+klWdgxcA4hMeQGzZnd/g2t3wNOkf1U6IfHQofInWKCgogLGpAe/xxqY6KCjIV+GM\ntI+XlxdOnTqF0tLSD7Y5OzsjISFBqePn5ubi0aNHCouQVPfgBYCCwgJAj+erZ3qmKH5bMx9vEOFQ\n+BKtYWFhgfzcYt4N4gtyJbC0+HA1cE0iEokwefLkSh15pKqq0MRGWFiYwvrNNSF4AcDC3AIozeE3\nuDQXRiYWqp0Q+ehQ+BKtYWRkhOYtG+P62UJe4y+dFKNLZ3fVTkoLOTo6Ij09HZmZmZU+t7a2RlZW\nFu/jPn78GCYmJnLrXdeU4AWAnj06w+DN//gNzjiFdu07V70fIQpQ+BKtMnPGPBzaVMx5XGZaGS79\nLw9fT/haDbPSPu935JEyNDTE27dveR1z8+bNmD59usxtNSl4AWD2zKnQebEbEHN/Zcg8fRMWzJ1R\n9Y6EKEDhS7TKuLHjcD0mH08fcgvg30JzMGz4ME5dd6ozKysr1K9fH3fu3Kn0uaurK+Li4jgfLzo6\nGj169JDZWrGmBS/wbnV4506dIXq+k9vA1xdgKH6JgQMHqmdi5KNB4Uu0irm5OdasWY85X2Qi478P\nFxXJcmpfLk7vkWBp4E9qnp128fHxwc6dOys9I+/WrRsuXbrE6ThlZWU4ceIEBg8e/MG2mhi8UpvC\n1sD02TIg4292A/ITYXzvK+zaHl7jirgQ4VH4Eq0z2WcKpvl8C++u6bgaXSB3AVZ+rhg7VmQhfP5b\n/O/kWTRo0EDgmWqWnp4eBg0ahKNHj5Z/ZmRkhOJibncNKnaGqqgmBy/w7tn5n39EweyfsRAlh8u/\nBc2Igf+OwPiGG8LWB8HLy0vYiZIaicKXaKWF3/2A4J93YoO/Lka2SsO+0De4daEQD24U4fJf+Vg5\nPQtejZ/jv9sdcPniTbRp00bTU9YIDw8PxMXFVXrOa21t/cFiLHlev36NFy9efPD9q+nBK+Xm5oYr\nF2PganMSRucbQf/RPCDjDJB9E3h9DjpJK2FysRk+K16FY4d+xaRJNfv7QYRDXY2IVmMYBhcuXMC2\nHWFIepKIwsIi1KplCXe3/pg6ZTrs7Ow0PUWNS0pKwrFjxxAQEAAAuH37NhITEzFy5EgAirsaBQYG\nwtfXF9bW1uWffSzB+76kpCSEb9yK2AvXkJuXC1MTU7R1+gx+s6agY8eOmp4eqWGoqxHRaiKRCG5u\nbjWiNaC6NGvWDEVFRXj58iXs7Ozg5OSEqKio8vCV5/79+6hbty4F7/9p1qwZgtev0fQ0yEeCbjsT\nUgP4+voiLCwMAKCjowOJRKKwWAnDMNi+fTt8fHzKP/uYg5cQoVH4ElIDmJubo2XLlrh27RoA4NNP\nP0VSUpLc/Y8fP44BAwZAX18fAAUvIUKj8CWkhhg/fjz27NkDiUQCT09PREVF4cyZM3j48CFiYmKQ\nkZEBACguLkZsbCz69esHgIKXEE2gBVeE1CAXL17E8ePHEf/wAWLOnoVVh9Yo0dOBQUkZcu8kYsDn\nA9HAug5mzpyJ5s2bU/ASoiEUvoTUEHl5efAaORw3niTCImAsLMYOgI6ZSfl2cVYOcn85gZzQffjC\nrRe+HPgF3r59S8FLiAZQ+BJSAxQVFaGbRy+8dKwPq83fQaQn/0UGSWERMkZ9j3ovc3H7yjXoKdiX\nEKIe9MyXkBpgiu8svLS3gdW2RQqDFwB0TIxhe2gN0q2MEbhiuUAzJIRURFe+hFRzr169QpMWzdHw\nyTHo1mbfZ7Yk6TleuXgj/dlzGBsbq3GGhJD30ZUvIdXc9l07YTHMg1PwAoBBs4Yw7tgKBw8eVNPM\nCCHyUPgSUs3t3LsHRpMG8Rqr7zMIW/dGqnhGhJCqUPgSUs1l/JcGg2b8OjoZNGuAtLQ0Fc+IEFIV\nCl9CqjlGIgF0ef6vrKsDsVii2gkRQqpE4UtINWdpbYWyF694jS17kQFraysVz4gQUhUKX0KquRFD\nvkThnlO8xpb8egpjvxym4hkRQqpCrxoRUs0lJSXByaUzGj47AR1jI9bjY5shSAAAAvZJREFUyl5l\n4UWLYUh98hS1a9dW4wwJIe+jK19CqrlmzZrBxcUFOSt/YT2GYRjkfL8Jw0eOoOAlRAPoypeQGiAt\nLQ3tu7kAviNQy3+Mwn0ZhsGbheGodfomrp+Pg7m5uUCzJIRIUfgSUkMkJyej18D+KHBsDBP/UTDu\n1hYikah8OyORoCD6KorW7UP93FL8/ccJ1KlTR4MzJuTjReFLSA2Sm5uLHbt2Yv2mjSgy1oe+mzMk\nZsbQzS1E0V9XUMfUAt/OnIUJ4yfAyIj982FCiGpR+BJSA0kkEsTGxuLevXvIy8uDpaUlOnToABcX\nl0pXw4QQzaDwJYQQQgRGq50JIYQQgVH4EkIIIQKj8CWEEEIERuFLCCGECIzClxBCCBEYhS8hhBAi\nMApfQgghRGAUvoQQQojAKHwJIYQQgVH4EkIIIQKj8CWEEEIERuFLCCGECIzClxBCCBEYhS8hhBAi\nMApfQgghRGAUvoQQQojAKHwJIYQQgVH4EkIIIQKj8CWEEEIERuFLCCGECIzClxBCCBEYhS8hhBAi\nMApfQgghRGAUvoQQQojAKHwJIYQQgVH4EkIIIQKj8CWEEEIERuFLCCGECIzClxBCCBEYhS8hhBAi\nMApfQgghRGAUvoQQQojAKHwJIYQQgVH4EkIIIQKj8CWEEEIERuFLCCGECIzClxBCCBEYhS8hhBAi\nMApfQgghRGAUvoQQQojAKHwJIYQQgVH4EkIIIQKj8CWEEEIERuFLCCGECIzClxBCCBEYhS8hhBAi\nMApfQgghRGAUvoQQQojAKHwJIYQQgVH4EkIIIQKj8CWEEEIERuFLCCGECIzClxBCCBEYhS8hhBAi\nMApfQgghRGAUvoQQQojAKHwJIYQQgVH4EkIIIQKj8CWEEEIERuFLCCGECIzClxBCCBEYhS8hhBAi\nMApfQgghRGAUvoQQQojAKHwJIYQQgVH4EkIIIQKj8CWEEEIERuFLCCGECIzClxBCCBEYhS8hhBAi\nMApfQgghRGD/D8dndCKH3F7GAAAAAElFTkSuQmCC\n", | |
"text": [ | |
"<matplotlib.figure.Figure at 0x2eef290>" | |
] | |
} | |
], | |
"prompt_number": 7 | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"We might ask, what vertex orderings lead to colourings with fewer colours? The following theorem of Dominic A. Welsh and Martin B. Powell is pertinant.\n", | |
"\n", | |
"**Theorem** (Welsh, Powell)\n", | |
"\n", | |
"Let $G$ be a graph of order $n$ whose vertices are listed in the order $v_{1}, v_{2}, ... v_{n}$ so that \n", | |
"$\\operatorname{deg} v_{1} \\geq \\operatorname{deg} v_{2}\\geq \\dots \\geq\\operatorname{deg} v_{n}$. Then\n", | |
"$$\\chi(G) \\leq 1 + \\min_{1 \\leq i \\leq n}\\{\\max{\\{i - 1, \\operatorname{deg} v_{i}\\}\\}} = \\min_{1\\leq i\\leq n}\\{\\max{\\{i, 1 + \\operatorname{deg} v_{i}}\\}\\}$$" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"In the case of regular graphs, like the crown graphs, this theorem reduces to the $\\Delta(G) + 1$ upper-bound on the chromatic number. For graphs that are not regular this result suggests that we can get a tighter bound on the chromatic number by considering orderings of vertices in non-increasing degree order." | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"The Grotzsch graph is an irregular graph that plays an important role in the study of graph colouring. Unfortunately, it is not one of the named graphs in NetworkX. We can, however, download it from the House of Graphs as a file in *graph6* format. Then we can use the `read_graph6` function to lead it." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"G = nx.read_graph6('/home/matthew/workspace/graphs-collection/External/HoG/graph_1132.g6')\n", | |
"\n", | |
"nx.draw_circular(G, node_color = 'black', **options)" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"metadata": {}, | |
"output_type": "display_data", | |
"png": 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+i9WrVyMqKgrOzs4Kj0lKStLZL+CkLmq+zUBKSgqviUXqMjY2VmsjeLFYjB9/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\nQgjP/h8Qzy7gHBJNUgAAAABJRU5ErkJggg==\n", | |
"text": [ | |
"<matplotlib.figure.Figure at 0x2eb2610>" | |
] | |
} | |
], | |
"prompt_number": 8 | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"We can compute the bound from the Welsh-Powell theorem." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"def welsh_powell_number(G, nodes = None):\n", | |
" \"\"\"Calculate bound from Welsh-Powell theorem with nodes in given order.\"\"\"\n", | |
" if nodes == None: nodes = G.nodes()\n", | |
" if len(nodes) == 0: return 0\n", | |
" else:\n", | |
" return 1 + min([max(i, G.degree(nodes[i])) for i in range(len(nodes))])" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [], | |
"prompt_number": 9 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"welsh_powell_number(G)" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"metadata": {}, | |
"output_type": "pyout", | |
"prompt_number": 10, | |
"text": [ | |
"4" | |
] | |
} | |
], | |
"prompt_number": 10 | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"which is a significant improvement over the $\\Delta(G) + 1 = 6$ bound. In fact, the chromatic number of the Grotzsch graph is 4 and a greedy colouring with 4 colours can be found." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"vcolour(G)\n", | |
"nx.draw_circular(G, node_color = colours(G), **options)" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"metadata": {}, | |
"output_type": "display_data", | |
"png": 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cifHjx2s8ho+PT4OhDC+7cOECunfvrvG1mruRI0ciKytL6+SjiooKzlO2NGVq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DlzptBzk5KSoKSkBAcHB3G62qJ8/PgRu3btwsePHzF79uw6G2RkZ2cjOjoag2xssHbtcmwKLcPU\ncUBDyYuVlcCBY8DaCC3s239ErkEVBPE5UnyJFun169fYtWsXqqqqsGDBAlhYWIjd1tWrV3HixAmE\nhoaKnK1LURQCAgIQEREh9Nzg4GD4+flBTU1N3K62OOXl5Thw4ACePn2K8ePHY+TIkWCxWDh16hRm\nz5qIC39Wo38f4e1cvQV8vUALp+IvYMiQIdLvOEEIoSLvDhCENHTo0AEBAQEoLCzEnj17kJOTgxkz\nZoi1V/KwYcNgbGwMDoeDsLAw6Onp0b6WxWJBSUkJNTU1QrNkKysrSeH9goaGBr777jvU1tbif//7\nH7y8vDBkyBCEhXpj70Z6hRcAhg0CNgSXYs3qRUi9Ip+MaYL4HHnyJVqFqqoqHDp0CHfu3MGYMWPg\n4uIi8jByXl4egoKC4O3tLVIow8mTJ2FoaNjkZg/Pnj1DamoqFixYIFKfWqNt27YhJmolMq5WQZS/\nwupqoMtXWjh5KhX9+/eXXgcJggay1IhoFVRVVTF79mxwuVwoKSnBy8sL+/fvR2VlJe02DA0NweVy\n8dNPP+HOnTu0r3NwcMD58+ebPCchIYG8j6Tp0sV4rF5cLVLhBQAVFeD72RX4ZesG6XSMIERAii/R\nqrBYLDg7O4PL5aJv374ICgrCpk2baGf8amhoIDo6GmfOnKEdytCmTRuh22O+e/cO7du3p9Vea3fj\nxnWMHSXegN3Y0TW4cSOZ4R4RhOhI8SVarf79+yMqKgqTJk3Chg0bEBYWhpycHKHXKSkpwcfHR6RQ\nBjMzM7x69arBY0VFRSJlIbd2hUWl0NMV71p9XaCwsITZDhGEGEjxJVo9c3NzBAUFYcWKFTh06BB8\nfX1p7ScsSiiDm5tbo0/KiYmJGDNmjFh9b43aaGmgRMycjeISoE0bTWY7RBBiIMWXIP4/AwMDeHh4\nIDg4GLdu3YKnpyfOnz/fZDiCs7MzJk6cKDSUwcLCAllZWQ0eu337tlizsFsrK6seSL0p3rVXbgFW\nVjSnSBOEFJHiSxBfUFdXx4IFCxATE4PS0lJ4enri4MGDjQa89+3bl1Yog7q6OsrLy+t8jf/EzMS2\nmK3F9z944pf9og/TUxSwdZ82vv/BQwq9IgjRkKVGBEHDjRs3cPToUZibm2PevHkNRv4VFxfD398f\ny5YtQ48ePeodv3TpkiC1qLCwENra2qisrERpaSmmTJkii2+jRaiurkYXCxMc2/ERg0VYMXQuGVge\n2BFPnmaLtVsZQTCJFF+CEEFGRgb27dsHdXV1LFy4sN4MZX4ow5gxYzBy5EgA/+5ylZqaig0xMYiP\nj0dnbW2oA6gE8KKkBPYjR4Lj6wtHR0dSFGj6z/59WBe4FFeOl6K9sfDzX7wChk/UxObNBzBx0iTp\nd5AghCDFlyDE8OHDB+zatQsFBQWYO3dunSddiqKwZcsWGBkZYdKkSZgzcyaSExMxoLQU/SgKn0/3\nqQDwAMBdbW30GjwYR0+caPCpmqgvKjIUv+2IxrEdpbDu3fh5N+4AU5dowWttOH5cuUZ2HSSIJpDi\nSxASKCsrw/79+5GWlgZ3d3cMHz5c8PR6+PBhBPv7QzUnBxPKytDUrtA1AE5raIDVsycuXrkCTU0y\nI5eOvXt2w8dnDXp1r8WyuUWwHwbotAEKi4GkZGDrXh08z1ZBXNwvmC5BOhVBMI0UX4JgQE1NDY4f\nP47U1FQMHz4c7u7uCPD1xbGff8aM8nI0vavzvygAJzQ1YTN9OnaIGBzfmlVWVuLYsWP4ZWsMHjz8\nB0VF5dDV1cCA/n2wbLk3JkyYIHIgBkFIGym+BMGw1NRUHDlyBDu2bsXiykroi3BtKYCtGhp4np0N\nIyMjaXWRIAg5I+sbCIJhw4cPR79+/dBZRUWkwgsAWgB6sljYtXOnNLpGEISCIE++BCEFdkOGwOzm\nTfQU49qXAK506YInmZlMd4sgCAVBnnwJQgrevHkDAzGvNQCQm5fHZHcIglAwpPgShBTU1taK/cOl\nBKBGyF7RBEE0b6T4EoQUGLZtC3ohhfUVAjDQFTO2hyCIZoEUX4KQgulz5uCJlpZY1z5SU8PUb75h\nuEcEQSgSMuGKIKQgLy8PFmZmWFZeDlFKcBWAnzU0cO/JE1hYWEipdwRByBt58iUIKTA0NMTkyZNx\nSV0dony6TVFVxYgRI0jhJYgWjjz5EoSUFBYW4quBA2H88iVGVVVBWGTCNWVlPGrXDrfu3YOxMY20\nAIIgmi1SfAlCit6/f4+xDg4of/4cg0tL0QWoU4QpANkAbmlqoszEBIkXL6Jz587y6SxBEDJDii9B\nSFlZWRn27duHjdHRKMjNhUV1NVQqK1GjqopsVVUo6+pilacnvlu0CDo6oofEEwTR/JDiSxAyQlEU\nrl69ir///hsFBQXQ0dFB3759MWrUKJLjSxCtDCm+BEEQBCFjZLYzQRAEQcgYKb4EQRAEIWOk+BIE\nQRCEjJHiSxAEQRAyRoovQRAEQcgYKb4EQRAEIWOk+BIEQRCEjJHiSxAEQRAyRoovQRAEQcgYKb4E\nQRAEIWOk+BIEQRCEjJHiSxAEQRAyRoovQRAEQcgYKb4EQRAEIWOk+BIEQRCEjJHiSxAEQRAyRoov\nQRAEQcgYKb4EQRAEIWOk+BIEQRCEjJHiSxAEQRAyRoovQRAEQcgYKb4EQRAEIWOk+BIEQRCEjJHi\nSxAEQRAyRoovQRAEQcgYKb4EQRAEIWOk+BIEQRCEjJHiSxAEQRAyRoovQfy/9upYAAAAAGCQv/Us\ndpVEADP5AsBMvgAwky8AzOQLADP5AsBMvgAwky8AzOQLADP5AsBMvgAwky8AzOQLADP5AsBMvgAw\nky8AzOQLADP5AsBMvgAwky8AzOQLADP5AsBMvgAwky8AzOQLADP5AsBMvgAwky8AzOQLADP5AsBM\nvgAwky8AzOQLADP5AsBMvgAwky8AzOQLADP5AsBMvgAwky8AzOQLADP5AsBMvgAwC8g26w3hXhdT\nAAAAAElFTkSuQmCC\n", | |
"text": [ | |
"<matplotlib.figure.Figure at 0x2ef24d0>" | |
] | |
} | |
], | |
"prompt_number": 11 | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"We might suspect then that a good vertex colouring strategy is greedy colouring with vertices in non-increasing degree order. In the next section we devise a small test of this claim." | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Greedy Strategies for Colouring Small Graphs\n", | |
"--------------------------------------------" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"NetworkX comes with a collection of all unlabelled, undirected graphs with seven or fewer vertices. The experiment below colours every graph in this collection using four different vertex orderings: in order, random order, decreasing degree order and increasing degree. In order is the order ordering of vertices in the data representation of the graph. In the case of NetworkX this just means that we colour vertices in the order they appear in `G.nodes()`. Random order just means that we first shuffle this list using `random.shuffle`. The other orderings are defined by the `degree_order` function below." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"def degree_order(G, reverse = False):\n", | |
" \"\"\"Vertices of G, ordered by degree.\"\"\"\n", | |
" return sorted(G.nodes(), key = G.degree, reverse = reverse)" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [], | |
"prompt_number": 12 | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"In the following code extract we iterate over the graphs in `graphs_atlas_g()` colouring each graph with each of the four above mentioned vertex ordering strategies. We calculate the number of colours used by each colouring and, at the end, we print out the totals of these numbers over all graphs.\n", | |
"\n" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"import networkx as nx\n", | |
"import random\n", | |
"\n", | |
"graphs = nx.graph_atlas_g() \n", | |
" \n", | |
"colours_used = {'inorder': 0, 'random': 0, 'decdeg': 0, 'incdeg': 0}\n", | |
" \n", | |
"for G in graphs:\n", | |
" \n", | |
" nodes = G.nodes()\n", | |
" inorder_nodes = nodes\n", | |
" random_nodes = random.shuffle(nodes)\n", | |
" \n", | |
" orderings = {'inorder': nodes,\n", | |
" 'random': random_nodes,\n", | |
" 'decdeg': degree_order(G, reverse = True),\n", | |
" 'incdeg': degree_order(G)}\n", | |
" \n", | |
" for ordering in orderings:\n", | |
" vcolour(G, nodes = orderings[ordering])\n", | |
" colours_used[ordering] += ncolours(G)\n", | |
" clear_colouring(G)\n" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [], | |
"prompt_number": 13 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"from IPython.display import HTML\n", | |
"\n", | |
"s = \"\"\"<table>\n", | |
" <tr><th>Ordering</th><th>Colours used</th></tr>\n", | |
" <tr><td>{0}</td><td>{1}</td></tr>\n", | |
" <tr><td>{2}</td><td>{3}</td></tr>\n", | |
" <tr><td>{4}</td><td>{5}</td></tr>\n", | |
" <tr><td>{6}</td><td>{7}</td></tr>\n", | |
" </table>\"\"\"\n", | |
"\n", | |
"output = s.format('in order', colours_used['inorder'],\n", | |
" 'random order', colours_used['random'],\n", | |
" 'descending degree order', colours_used['decdeg'],\n", | |
" 'ascending degree order', colours_used['incdeg'])\n", | |
"\n", | |
"HTML(output)" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"html": [ | |
"<table>\n", | |
" <tr><th>Ordering</th><th>Colours used</th></tr>\n", | |
" <tr><td>in order</td><td>4278</td></tr>\n", | |
" <tr><td>random order</td><td>4252</td></tr>\n", | |
" <tr><td>descending degree order</td><td>4120</td></tr>\n", | |
" <tr><td>ascending degree order</td><td>4468</td></tr>\n", | |
" </table>" | |
], | |
"metadata": {}, | |
"output_type": "pyout", | |
"prompt_number": 14, | |
"text": [ | |
"<IPython.core.display.HTML at 0x2e5e150>" | |
] | |
} | |
], | |
"prompt_number": 14 | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"We can see that the best ordering to use in this case is the ordering claimed in Welsh and Powell's theorem. Ordering vertices by their degree from highest to lowest. The worst case is the reverse ordering and randomised and natural orderings lie somewhere in between." | |
] | |
} | |
], | |
"metadata": {} | |
} | |
] | |
} |
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