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@MHenderson
Last active November 2, 2015 16:55
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Graph colouring IPython Notebook.
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"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"0. Configuration\n",
"----------------"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def setfigsize(n, m):\n",
" pylab.rcParams['figure.figsize'] = n, m"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 1
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Introduction to Vertex Colouring\n",
"===============================\n",
"\n",
"In this notebook we demonstrate some of the basic ideas of vertex colouring. In particular, we demonstrate the following result.\n",
"\n",
"**Theorem**\n",
"\n",
"For every graph $G$, $\\chi(G) \\leq 1 + \\Delta(G)$.\n",
"\n",
"One proof of this result is found on p.182 of \"Chromatic Graph Theory\" by Chartrand and Zhang where it appears as Theorem 7.8. The proof is no more than a precise version of the observation that if we apply a greedy vertex colouring then we only need at most $\\Delta(G) + 1$ colours because if we have that many colours then when it comes time to colour a certain vertex one is bound to be missing from the at most $\\Delta(G)$ \n",
"neighbours of that vertex.\n",
"\n",
"Source code: https://gist.github.com/MHenderson/641c18aab2bd52932b44\n",
"\n",
"Notebook viewer: http://nbviewer.ipython.org/gist/MHenderson/641c18aab2bd52932b44"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Greedy Vertex Colouring\n",
"-----------------------\n",
"\n",
"The greedy vertex colouring algorithm starts with the vertices of a graph listed in some order $v_{1},v_{2},...v_{n}$. It begins with the first vertex and assigns that vertex colour 1. To colour a vertex $v_{j + 1}$ further along in the sequence we choose the first colour which is not used on any of the already coloured vertices $\\{v_{1},...v_{j}\\}$.\n",
"\n",
"Below is an implementation of the greedy vertex colouring algorithm for NetworkX graphs. In fact, this implementation is a little more flexible than the one described in the previous paragraph. It allows for some customisation of the algorithm's behaviour. Specifically, it allows use to specify both the ordering of the nodes and the strategy used to select which colour to use one a particular node.\n",
"\n",
"Here we have only implemented one strategy, the `first_available` strategy of the greedy algorithm which chooses the first colour not used on already coloured neighbours."
]
},
{
"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)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Notice that this implementation colours graphs in-place. It adds a `colour` attribute to every vertex and the value of this attribute is the colour given to that vertex.\n",
"\n",
"Below is an example of using the greedy colouring algorithm to colour $K_{9}$. By the earlier theorem we would expect a colouring with 9 colours, as $\\Delta(K_{9}) = 8$."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import networkx as nx\n",
"setfigsize(5, 5)\n",
"\n",
"options = {\n",
" 'with_labels': False,\n",
" 'node_size': 300,\n",
" 'width': 1,\n",
"}\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",
"K9 = nx.complete_graph(9)\n",
"vcolour(K9)\n",
"nx.draw_circular(K9, node_color = colours(K9), **options)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Couldn't import dot_parser, loading of dot files will not be possible.\n"
]
},
{
"metadata": {},
"output_type": "display_data",
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ZsXD5F3vz5g3q16+PiIgIifcZNmwY1q9fX+E2koRLUVERjI2N8fDhQ6HXQ0JC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\n",
"text": [
"<matplotlib.figure.Figure at 0x4c81490>"
]
}
],
"prompt_number": 3
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The `colours` function gets a list of colours used on vertices which is then passed to the `draw_circular` function as the argument of a keyword parameter `node_colour`.\n",
"\n",
"We put other options into a dictionary object so that we can reuse the same options in other drawings below.\n",
"\n",
"Colouring a complete graph doesn't pose much of a challenge to any colouring algorithm. All that is needed to assign a different colour to each vertex so algorithms even simpler than the greedy algorithm will succeed in this case to find a minimal colouring.\n",
"\n",
"A slightly more challenging graph is a complete bipartite graph. If we consider $K_{5,6}$, for example, the above Theorem only guarantees a colouring with 7 colours. A minimal colouring, however, uses only 2 colours.\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"K56 = nx.complete_bipartite_graph(5,6)\n",
"vcolour(K56)\n",
"nx.draw_circular(K56, node_color = colours(K56), **options)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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wNW7cmAwNDeno0aPV7vv69Wvq3LkzDR06VKqpr8JUDGLyqjqL6927d7Rs2TJq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\nx8Pa2hoeHh7YsGGDqFNJurq6C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"text": [
"<matplotlib.figure.Figure at 0x479fa10>"
]
}
],
"prompt_number": 4
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It isn't really all that surprising that we found a minimal colouring here. If we have managed to colour some of the vertices properly with only two colours in such a way that all vertices of one colour lie in one of the bipartitions and all the vertices of the other colour lie in the other bipartition then it's obvious how to extend this to a similar 2-colouring with fewer uncoloured vertices."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Colouring Some Classic Graphs\n",
"\n",
"In this section we apply the greedy colouring algorithm from the previous section to some well-known graphs and compare the number of colours used with the chromatic number.\n",
"\n",
"First we consider the Petersen graph. It is known to have chromatic number 3 and, indeed, with our greedy colouring algorithm we find a 3-colouring."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"P = nx.petersen_graph()\n",
"vcolour(P)\n",
"nx.draw_shell(P, nlist=[range(5,10), range(5)], node_color = colours(P), **options)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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biIqKQlRUFOLj49GtWzdwuVzweDwMHToUzZo1q/X7kLVXr16Bx+Nh5syZWLZs\nmVzPRTPHFV9aWhrs7Oywe/dujBs3ju04KoGKQ4mJRCKMHTkST/l8jCor++w6Vf8rG8BZDQ2E8/kY\nMmSIVOerqKjAnTt3wOfzERUVhVu3bqFt27aSEQmXy2V9D4u8vDxYW1vDw8MDa9eulfv5qDiUQ3Jy\nMhwdHXH48GG4uLiwHUfpUXEoOYFAgCkeHogPC4NlSQmM8ekbVwUA7mpq4r6ODkzMzGBkZITTp09D\nU7PmVyuFQiGSk5MRFRUFPp+P6OhoNG3aVDIi4XK56NixY42PL63379/D1tYWTk5O+PHHH6Gmpib3\nc1JxKI+EhAQ4OzsjICAADg4ObMdRalQcKkAsFiMwMBDbN2/GsydPYCoQwEAkgiaAcgBP9fSQwzCY\nOnUqlq5YgVatWmHs2LEwMDDAiRMnoKGhIbMcaWlpkhFJVFQUOByOZDTC4/HQrVs3ufxALygogL29\nPYYOHYqffvqpTkoDoOJQNjdv3sTYsWNx5swZWFtbsx1HaVFxqJjExESc+OUX5D59ivKyMhg2a4Yh\n1taYPHky9PT0JF9XVlYGFxcXtGvXDkeOHJHLyqIMwyAzM1MyIuHz+RAKhZIi4XK56NmzZ63PXVxc\nDEdHR/Tp0we7d++us9IAqDiUUWRkJCZMmIALFy5IfbmWfETFUY+VlJRgxIgRMDExwb59++T+A5dh\nGOTk5FQZkbx//x5Dhw6VjEjMzMykunxWWloKZ2dndOnSBQcPHqzzpbWpOJRTaGgovv76a1y+fBmD\nBg1iO47SoeKo54qKiuDg4ABzc3Ns3769Tn9bB4A//vgD0dHRkjLJzc3F4MGDJfdIBgwY8Nl/w/Ly\ncowePRpGRkY4duyYzC65SYOKQ3ldvnwZM2bMwLVr1+jfT0pUHAT5+fmwtbWFnZ0dNm/eXOfl8b/y\n8vIQHR0tGZE8evQIgwYNkoxIzM3NoaOjg4qKCowfPx7a2toIDAys1U3+2qDiUG6//fYbFixYgLCw\nMPTq1YvtOEqDJgASGBgYIDQ0FMOGDYOOjg7Wr1/PWpbmzZvD1dVVsqZUfn4+bt68CT6fj5UrVyI1\nNRV9+vTB+/fv0aRJE1y+fJm10iDKb9y4caioqICjoyOuX7+Or776iu1ISoG+4wgAoGnTplVWFl21\nahXbkQB8LDVnZ2c4OzsD+Pj0lKurKyorK6Guro727dvDxMREMiKxsrJCkyZNWE5NlMnEiRMhEAhg\nZ2eHyMh75LywAAAgAElEQVRIdOnShe1ICo+Kg0gYGRlVWVnU29ub7UhViMViSabU1FTo6OigvLwc\n8fHx4PP52LlzJyZNmoQuXbpUeXLLyMiI5eRE0U2bNg0CgQC2trbg8/no0KED25EUGhUHqaJ169ZV\nVhadN28e25EAfHwia/78+Xj06BFCQkKgo6MDANDW1pYUBABUVlbi7t27iIqKwtGjRzFz5ky0atWq\nyuz2tm1rswUWUVWzZ89GeXm5pDzatGnDdiSFRcVB/qFdu3ZVRh7Tp09nNQ/DMPD29kZSUhJCQ0Or\nzEf5Oy0tLVhYWMDCwgLLly+HSCTCvXv3wOfzce7cOSxatAiNGzeuMimxU6dOrD4QQBTH4sWLq4w8\nWrSoyRKiqo+Kg3xSp06dEB4ejmHDhoHD4WDy5Mms5GAYBqtWrUJ0dDQiIiKgr68v1es1NDTQt29f\n9O3bF0uWLIFYLEZ6ejqioqJw7do1rF69GhoaGlWWSenevTsVST22fPlylJeXw87ODjdu3FDIhTzZ\nRsVBPsvY2BhhYWGwtbVFgwYN4ObmVucZNmzYgCtXruDGjRswMDCo9fHU1dXRs2dP9OzZE3PnzgXD\nMMjOzpbMI/H19UVpaWmVEYmpqWmdTywk7Fq7di3Ky8vh4OCAiIgIeuDib6g4yL8yMTFBSEgIHB0d\nweFwMGrUqDo79+bNm3Hq1ClERkaiadOa7nX479TU1NC1a1d07doVM2bMAPBxA6i/JiXu2bMHeXl5\nsLKykpRJv3796BFgFaempob//Oc/KC8vx/DhwxEWFib1aFeV0QRAUi137tyBk5MTjh8/juHDh8v9\nfDt27MCePXvA5/NZX6r95cuXkkmJfD4fOTk5sLS0BI/Hw9GjR3Hy5ElatkJF/fVQxr179xASEvKv\n+9fUJ1QcpNpiY2MxevRonDp1CjY2NnI7z759+7B161bw+Xy0b99ebuepqXfv3iEmJgZ8Ph/79+8H\nwzCwsLCQjEgsLS2hq6vLdkwiI2KxGF5eXnjy5AmCg4MlT/TVZ1QcRCp8Ph9ubm44f/48rKysZH58\nf39/rF+/HpGRkejcubPMjy9rf63IW1RUJBmRpKSkwMzMTHKzfciQIXSZQ8mJRCJ4enri7du3CAoK\nAofDYTsSq6g4iNTCw8MxadIkXLp0Cebm5jI7bmBgIJYtW4YbN27A2NhYZseVp0+tVVVaWorbt29L\nbrgnJCSge/fuVWa3y+ueDZEfoVAomWV+7ty5ev2zhYqD1EhwcDCmT5+Oq1evol+/frU+3rlz57Bw\n4UKEh4ejZ8+eMkhYN6qzyKFAIEBCQoJkRBIbG4sOHTpUmZTYsmXLOkxNaqqyshLjx49HgwYN8Ouv\nv9bbhySoOEiNXbhwAXPnzkVYWBhMTU1rfJxLly7By8sL165dg5mZmQwTyl9NVscVCoVITEyUrAAc\nHR0NIyOjKo8As3lvp6SkBLdv38b79++hpqaGpk2bwtLSEtra2qxlUiQCgQBjxoyBoaEhjh8//o/l\n/OvF58eoKC0tLUYgELAdQ+WdOnWKadWqFZOenl6j14eEhDBGRkZMQkKCjJPVDTMzMyYpKalWxxAK\nhUxycjKzc+dOZty4cUzz5s2ZDh06MFOnTmUOHz7MZGZmMmKxWEaJPy8jI4OZv3g+o2+oz3Sz6sr0\nGWfGmLmaMV0sOjNNmjdhfFb4MI8fP5Z7DmVQWlrKDBs2jJk+fTojEokYhvn4+c2Zs4DR1dVnGjfu\nxujr9/nzvy5Mw4ZNGG9v1fn8aMRBau348eP47rvvcOPGDXTt2rXar7tx4wbc3d0RFBQES0tLOSaU\nH3nsx8EwDDIyMiQjEj6fD7FYXGV2e48ePWQ2KVEkEmGJzxIE/BqA3jNMYTarNww6NK7yNe8evUfK\ngXtIPZaKhfMXYeP6jfV+dn1JSQmGDx/+5/bHWjh2LACVlWYQCvsC+Ptk1Xdo0CAZ6uop8PZeiP/8\nR7k/PyoOIhMHDx7Epk2bqr2yaExMDFxdXXH27FnweLw6SCgfdbGRE8MwePLkiaREoqKiUFhYWGXL\n3d69e9doB0SxWIwJkyfg3ut7GHPeBdoG/345pfh1Cc67/A6HAQ44sOeAUv/wk4X8/Hx06mSM4mI9\nCIUeAL50OaoYurrn4O5ujyNHlPfzo3UUiEzMmjULS5cuhY2NDXJzc//1a+Pj4+Hq6orAwEClLo26\noqamhs6dO2PatGk4evQosrOzkZSUhPHjxyMjIwOTJk1C06ZN4ezsjK1bt+L27duorKys1rFXrlmJ\n5D+SMf7K2C+WBgA0bKEH94jxCIkNwdb/bq3tW1N6Gzf6oqJCH0Lh1/hyaQBAQ5SWTsTp0yHYvFl5\nPz8acRCZ+umnn3Do0CHw+fxPPimUlJSE4cOHw9/fX7I5kzJTlK1j37x5U2Xv9uzsbMmkRB6Ph0GD\nBv3j5mxeXh46deuE2ZkzoWf0+RWHP+XDk3wcHxCAF89e/OtqxaosLy8P7dp1gkAwD4C0n8EH6Ooe\nxZs3yvn50YiDyJSPjw+mTJkCW1tb5OXlVfm7+/fvw8nJCfv371eJ0lAkRkZGGDduHHbu3Ink5GQ8\ne/YMixYtQmFhIXx8fNCsWTNwuVysXbsWYWFhKC4uxmH/w+jh2l3q0gCAJp0M0GFoewT+GiiHd6Mc\nDh06DHV1E0hfGgDQBGpqHRAYqJyfH404iFysWbMGwcHBiIiIgKGhITIyMmBra4uff/4Z7u7ubMeT\nGUUZcXxJUVERbt26JbnhnpiYCGgxmBjugdYDWtXomNmhj5G8IgVpSQ9knFbxiUQitGrVAXl5zgBq\nupZaNrp0uYusrDRZRqsT9XP2CpG7jRs3SlYWPXjwIFxcXODr66tSpaFMGjVqBEdHRzg6OgIAsrKy\n0H9I/xqXBgB0tuuEcxnnUVJSopSXW2rj5cuXKC4uRc1LAwA6IyfntFJ+flQcRC7U1NSwbds2TJs2\nDRYWFti6dSumTp3Kdizyp7KyMug3r936WWrqatDU0cTo0aPr3cJ/hYWFqKys7RNRatDS0kN+fj4V\nByF/efHiBWJiYtCvXz9cuHABM2fOpFVjFUSDBg0gqhDW/kAMMG3aNDRu3PjLX6tCcnNzkZDwPYS1\n/AgZRqiUl9OpOIhcvHr1Cra2tpg7dy68vb3xzTffYOzYsQgKClKtpReUzF9b5169ehVvc9+hsqwS\nWjpaNTpW2YcyiAQiuLu7Q0urZsdQVh8+fMCSJT4AKgHU9L2XQSSqkMnOlnWNnqoiMvf27VvY2dnh\n66+/ho+PDzQ0NODv7w8DAwO4ubmhoqKC7Yj1hkgkQmJiInbs2IGxY8fCyMgIo0aNQlpaGoy7G+PB\nmfQaH/vesfsY7Tqq3pUGADRp0gQDB1oAqPmNbTW1FIwcOVopPz8qDiJTHz58gL29PcaMGYM1a9ZI\n/lxTUxMBAQHQ0NDAxIkTIaztGJ98UmVlJW7fvo0tW7bA2dkZTZs2xeTJk5GRkQE3NzckJycjOzsb\nR48ehe8Pvkjde79G52HEDO7tS8XieUtk/A6Ux4oVS9CwYUoNX81AVzcZPj6LZZqprtDjuERmCgsL\nYWdnBy6Xi23btn1yOQWBQICxY8fCwMAAJ06cqNEyGYqE7cdxy8vLERcXJ3nM9vbt2+jSpYtk4t/Q\noUNhZGT0ydeKRCJ06NoBQ3cPQTfn6q8xBgCpJ+7j4X8fIS0pTWmXzagtkUiE1q074M0bHgBp949J\nQdeuGcjMVM7Pj+5xEJkoLi6Gk5MTBg0a9NnSAAAOh4PffvsNLi4umDlzJo4cOSKzxfrqg+LiYsTG\nxkrWrUpMTISJiQl4PB4WLVqEM2fOoEmTJtU6loaGBk4HnIbzWGfoXtJBG/M21Xrdk4iniFwaBX44\nXyl/6MmKhoYGzp8/DVvbERAI3AG0reYrH0NP7wZ++015Pz8qDlJrpaWlcHFxQY8ePbBz584vfjPo\n6OggKCgII0aMwLx587Bv3z6l/QaSt/z8fNy8eVOylMj9+/fRt29fcLlcrFmzBpaWlmjUqFGNjz9k\nyBCcPHoSX7t8De5WK/Sa1BMaDT49ChSWC5F8JAW3N8Tj97O/o3fv3jU+r6ooLy8Hh6MGNbUzKC+3\nAWAK4HOjaCHU1JKgp3cLly8r9+dHl6pIrZSXl2P06NFo0aIFjh49KtWlp6KiIjg4OMDc3Bzbt29X\nyvKQ9aWqvLw8REdHS0YUWVlZGDRokGQ5dXNzc7nMmbhz5w4WLVuE9Ix0mM3sjR4Tv4JeCz2AAYpe\nFONBQDruHU1F//79sOu/u5Vql0Z5iY6Oxrhx43Du3Dno6upizpzFePAg/c+l1Xvi/5ciKYKW1n1o\naKSgf//+OHBgl/J/fmxsAlIXaCMn+RMIBIyLiwszYcIEprKyskbH+PDhA9OvXz9m+fLldbJZkazV\ndiOnP/74g/n111+ZOXPmMCYmJoy+vj4zYsQIxtfXl7l161ad/z+clpbGzFkwh2nXpR3TyKARo2+o\nz3To1oHx9vFmHj16VKdZFFlsbCzTvHlzJiwsrMqfp6WlMTNnzmFatGjH6Og0YnR19ZmWLTswixap\n1udHIw5SI0KhEB4eHhAKhTh79mytHil89+4dhg0bBldXV6xfv152IeuANCMOhmGQk5MjuezE5/Px\n4cOHKvtqmJmZ1dt9rJVFYmIiRowYgaNHj8LJyYntOKyg/0OJ1EQiETw9PVFaWooLFy7U+jn0pk2b\nIjw8HDweDxwOB6tWrZJRUnYxDIPMzMwqGzBVVFRILjstWbLkz93j6OEAZZGamgonJyccOHCg3pYG\nQMVBpCQWi+Hl5YXXr1/j0qVL4HA4MjmukZERIiIiwOPxoK2tDW9vb5kcty6JxWKkpaVJSiIqKgoN\nGjQAj8cDj8fDunXr0K1bN6W8l0OA9PR0ODo6ws/PD2PGjGE7DqvoUhWpNoZhMG/ePKSlpeHq1aty\nWZjt+fPn4PF48PHxwbx582R+fFkSCoXo2bMnRo4ciaysLMTExMDQ0LDK3uAdO3ZkOyaRgaysLFhb\nW8PX1xdTpkxhOw7raMRBqoVhGHh7eyM5ORmhoaFyW82zXbt2VUYe06dPl8t5aqKiogJ37tyRjChu\n3boFgUCA58+fY+LEidi3bx9at67NMttEET19+hS2trb4/vvvqTT+RCMO8kUMw2DVqlUICwtDRERE\nnSzKlpmZiWHDhmHr1q2YPHmy3M/3KWVlZbh9+7bkslN8fDy6desmGVFYWVnB3t5eKTZyIjWTm5sL\nHo8Hb29vLFiwgO04CoNGHOSLNmzYgCtXruDGjRt1tpKnsbExwsLCYGtriwYNGsDNzU3u5/zfXfL4\nfD6SkpJgamoKHo+Hb7/9FkOGDFHKlUxJzbx8+RI2NjaYN28elcbfUHGQf7V582acOnUKfD4fTZs2\nrdNzm5iYICQkBI6OjuBwOBg1apRMj//hwwfJZLuoqCg8ePAA/fv3B5fLxfr162FhYYGGDRvK9JxE\nOeTl5cHOzg6enp5YunQp23EUDhUH+awdO3bgyJEj4PP5n10oT97MzMxw+fJlODk54fjx4xg+fHiN\nj/X69esqs7IfP34MCwsL8Hg8/PTTTxg0aBDtFULw/v172Nvbw9XVFd999x3bcRQSFQf5pH379mHn\nzp3g8/ms3/AdMGAAgoKCMHr0aJw6dQo2NjbVel1ubm6VORQvX76ElZUVuFwuDh48iH79+inlXghE\nfgoKCuDo6Ah7e3ts2LCB7TgKi4qD/IO/vz98fX3B5/PRrl07tuMAACwtLXH27Fm4ubnh/PnzsLKy\nqvL3DMPg8ePHkstOfD4fhYWFkhvZc+bMQe/evZV+GXciP0VFRRgxYgQsLCywdetWmm/zL6g4SBWB\ngYFYt24drl+/jk6dOrEdpwoej4fAwEC4urri4sWLaNy4cZURhVgslsyf8PHxQY8ePWhWNqmWv1Z4\n7tWrF/z8/Kg0voCKg0icO3cOS5cuRUREBIyNpd2YRr7EYjFSU1Px4MEDdOvWDYMHD0bLli1hb28P\nW1tbbNiwAV26dKFveCK18vJyjBkzBu3bt8f+/fvpl41qoOIgAIBLly5hwYIFuHbtGkxMTNiOA6FQ\niMTERMmIIiYmBkZGRuByuZg7dy48PT2xbt06+Pj4wNTUlO24RElVVFRg/PjxMDQ0hL+/P5VGNVFx\nEFy7dg0zZ85EcHAwzMzMWMkgEAiQkJAguewUGxuLjh07gsvlYsqUKTh06BBatmxZ5TWNGzeGo6Mj\nrl+/ju7du7OSmyivyspKeHh4QEtLCydOnKBViaVAn1Q9d+PGDUyZMgVBQUEYMGBAnZ23tLS0yhao\nd+7cQffu3cHlcjFv3jwEBgZ+cd6Iu7s7BAIB7O3tcePGDXTtKt2+2aT+EolEmDp1KgQCAc6fP09P\n10mJikMFMQyDkpISlJeXw8DA4LO/ScXExMDd3R1nz56FpaWlXDMVFhZW2QL13r17MDMzA5fLxYoV\nKzBkyBDo6+tLfdypU6eivLwcdnZ24PP56NChgxzSE1UiFosxY8YMvH37VqYrPNcnVBwqJCUlBbu2\nb8evp05BJBJBS0MDpRUV6NmtG5asWAEPDw/o6uoCAOLj4+Hq6orAwEDweDyZZ3n37l2VWdkZGRkY\nOHAguFwufvzxR1hYWEiy1NasWbMgEAhgY2MDPp+Ptm3byuS4RPUwDIO5c+fiyZMnuHLlCk34rCFa\n5FAFZGVlYbKbG7IePkTfigr0EYnQ6M+/EwPIBpDcsCFyGQarvvsO9o6OGDFiBPz9/eHs7CyTDK9e\nvaoyhyInJweWlpaSx2MHDhwo99/sfvrpJxw6dAh8Pv8f90PkRdZ7jhP5YRgGS5YsQXx8PEJDQ9Go\nUaMvv4h8EhWHkktMTISjjQ0GFRVhgFiMf3sm5D2A89rayAdwLCAA48aNq/F5nz17VmXDojdv3lTZ\nArVv376s3Gz88ccf8euvvyIyMhLNmzeX+/moOJQDwzBYsWIFrl+/jvDwcFqsspboUpUSe/LkCYbb\n2sKmoADVeYDWEMCU8nKc5HCQcPt2tYuDYRhkZWVVGVGUlpZKSmLBggXo1auXQszKXrNmDcrLy+Hg\n4ICIiAgYGhqyHYkogPXr1+PatWu4fv06lYYMUHEosaULF6J3YWG1SuMvHADuAgEO7NmDaTNmfPIx\nVrFYjPT09CqzstXV1SWXnVatWoWvvvpKYSfbbdy4EeXl5Rg+fDjCwsLQuHFjtiMRFm3atAlnz55F\nZGRkna/wrKroUpWSevnyJYw7dcICgQA1ub13Q1MTpl5e2LV3L0QiEe7duycpiejoaOjr64PL5UpG\nFZ06dVLYovgUhmGwcOFCJCUl4dq1a3JbHp0uVSm2n3/+Gfv37wefz0erVq3YjqMyaMShpA7s24de\namo1Kg0A6CsU4sDhw8jMzkZcXBxatWoFHo+H8ePHw8/PT2EWN6wpNTU17Ny5E7Nnz4aLiwuCg4Nl\n9hQXUQ579uzB7t27qTTkgIpDSZ0NDIRFeXmNX28AwEhNDf369cOJEydY229DntTV1bF//3588803\nGDt2LIKCgujxy3riyJEj2LJli0Kt8KxKaGEWJfX+wwdIP12uquYNGqBHjx4qWRp/0dDQgL+/PwwM\nDODm5oaKigq2IxE5CwgIwPfff4+IiAiFW+FZVVBxKCkxw6C2dxzUGAZisVgmeRSZpqYmAgICoKGh\ngYkTJ0IoFLIdicjJ2bNnsXz5coSGhqJbt25sx1FZVBxKykBfHyW1PEaphgaaNGkikzyKTktLC6dP\nn0ZpaSmmTp0KkUjEdiQiY0FBQVi4cCFCQkIUYoVnVUbFoaScRo1CRi0WZisBkFNRgaFDh8oulILj\ncDg4f/48Xr9+jZkzZ9aL0VZ9cfXqVXh5eSE4OBi9e/dmO47Ko+JQUvMWLkSimhpqetElWV0dY8eM\nqXcT5HR0dHDx4kVkZWVh3rx5UNGn0euViIgIeHp6IigoCP3792c7Tr1AxaGE7ty5g9mzZ0NDQwMp\nNXh9JYBkbW0sWrpU1tGUgp6eHoKDg5GcnAxvb28qDyUWHR2NiRMn4ty5c3Jf4Zn8PyoOJfL48WNM\nnDgRo0aNgru7O8L4fETp6uK5FMcQA7ioqws7J6c63X9D0ejr6yMkJATR0dFYuXIllYcSuv3nsjmB\ngYHgcrlsx6lXqDiUwNu3b7FkyRIMHDgQPXr0QGZmJmbPno2BAwfi1G+/4TddXWRW4zgCAL/p6qLF\nwIE4dvKkvGMrPAMDA4SGhuLq1av44Ycf2I5DpJCYmIjRo0fj2LFjsLOzYztOvUPFocBKS0vh6+uL\n7t27QygU4sGDB1i3bl2V5TOGDx+OK+HhuNG8OQIaNcI94B/3PfIAhDZogN3a2hg8YQKuhIWp7FIs\n0mratCnCwsJw+vRp+Pr6sh2HVENqaiqcnJxw4MABODk5sR2nXqKZ4wpIJBLhl19+wffffw9zc3Pc\nunULxsbGn/16S0tLPHvxAsHBwdixZQt2JCaiCYcDTTU1lIpEEGloYNbcuTg1bx7Nov2EFi1aICIi\nAjweD9ra2vD29mY7EvmM9PR0ODo6ws/PD2PGjGE7Tr1FxaFAGIbBlStXsHLlShgYGODMmTPVvuGn\nqamJ0aNHY/To0Xjz5g1evXoFgUAAAwMDdOjQgUYYX9C6dWtJeXA4HMybN4/tSORvsrKyYG9vjy1b\ntsDd3Z3tOPUaFYeCSEhIwPLly/Hq1Sts2bIFLi4uNV6N1sjISKWXEZGX9u3bIyIiAtbW1tDW1sb0\n6dPZjkT+9PTpU9ja2uL777/HlClT2I5T71FxsCw7OxurV69GTEwM1q9fj2+++YaVnfPIR507d0Z4\neDiGDRsGDoeDyZMnsx2p3svNzYWtrS2WLVsGLy8vtuMQ0M1x1uTl5WHx4sUwNzeHqakpMjMz4eXl\nRaWhAIyNjREaGgofHx+cPXv2k1+Tn5+P2NhYFBYW4s6dO8jKyqrjlPXDy5cvYWNjg3nz5mHBggVs\nxyF/ouKoY6Wlpdi0aRN69OgBsViMBw8eYM2aNdDT02M7GvkfPXv2REhICBYsWICLFy9K/vzu3buY\nMn0K2nVsi8mLJ0PYUojNR30xaOhADBgyACdPnoRAIGAxuerIy8uDnZ0dPD09sbSeTlZVVLQDYB0R\nCoWSJ6UGDx6MTZs2oWvXrmzHIl+QkJAAZ2dn7Nu3D/v99yMlLRlmc3qj93RT6Bn9f9mLhWJkXnqE\n1L338S7tPS6cvYAhQ4awmFy5vX//HjY2NnBxccHGjRvZjkP+hopDzhiGQXBwMFasWIFmzZph69at\nMDc3ZzUTkU5ISAjGThgL00m94LDbDuqa/z5QzwrJxpWpITh1/BSGDx9eRylVR0FBAezs7GBtbY2t\nW7cq1ZbF9QUVhxzFxcVh+fLlePv2LTZv3oyRI0fSN4GSEYlE4NlxITIVwc7Pptr/fs9v5eLC6CBE\nRUTRaq1SKCoqgqOjI/r374+dO3fS94uConsccpCVlYUJEybA1dUVU6dORUpKSq0eryXsCQ4Oxh/F\nf8B2+zCp/v3aDW4Li7Xm+O6H7+SYTrWUlpbCxcUFvXr1gp+fH32/KDAqDhl68+YNFi5cCAsLC/Tp\n0wePHj3CjBkz6EkpJbZj73aYLeoNdQ3pv1XMvjFF5I1I5ObmyiGZaikvL8eYMWPQvn177N+/H+rq\n9KNJkdG/jgyUlJTgxx9/hImJCdTV1ZGeno7Vq1dDV1eX7WikFrKyspCYmAQTtx41ej2nEQe9Jppg\n/8H9Mk6mWioqKjB+/HgYGhrC39+fSkMJ0L9QLQiFQhw6dAjGxsa4f/8+4uLi4Ofnh+bNm7MdjcgA\nn89H1+FdoKld8xFjV9euCI0MlWEq1VJZWQkPDw9oaWnhxIkTNDpXEvSvVAMMw+DSpUtYuXIljIyM\ncOHCBQwaNIjtWETGPnz4AE4zTq2OodtMB/kf8mWUSLWIRCJMnToVAoEA58+fh1YttkImdYuKQ0px\ncXFYtmwZ3r9/j23btsHJyYlu4qkoTU1NMMLaPXQoFoqhqUXfZn8nFosxY8YMvH37FpcuXQKHU7uC\nJnWLLlVV06NHj+Dm5obx48dj2rRpSElJgbOzM5WGCjMyMkLxs5JaHaPgWSGM6NJlFQzDYO7cuXjy\n5Al+//13aGtrsx2JSImK4wvevHmDBQsWwNLSEv369cPDhw8xffp0aGhosB2NyJmTkxOe8J+g+HXN\nyyP9aAa+dqPVXP/CMAyWLFmCe/fu4fLly7TUjpKi4viM4uJibNiwASYmJtDU1ERGRgZWrVpFT0rV\nIwYGBhg3fhzuHblXo9fnP83Hs5vPMXHiRBknU04Mw2DFihW4efMmrl69ikaNGrEdidSQyhQHwzCI\ni4uD50xPDBw6EOq66rAcZonJ0ybj5s2bqO4EeaFQiAMHDsDY2Bjp6emIj4/Hjh070KxZMzm/A6KI\nFs9bjKS9KSh9Wyr1a2/7xmPqlKn0W/Wf1q9fj2vXruHatWswMDBgOw6pBZVYcuT06dP4cduPePP+\nNXrPMUVri9bgNGoAQVEFXt19jXv7UmGgY4CVS1di6pSpn7wvwTAMLl68iJUrV6JVq1bYunUrBgwY\nwMK7IYpm2cplOB/9G8aHuILTqHo3ceP+G4/HR54i/mY8mjRpIueEim/Tpk0ICAhAZGQkbTKmApS6\nOBiGwbfLv8XpS6dgvZ2HLo6doab+iVIQM3hy/Sn430bBaagz9u7cW+UeRWxsLJYtW4aCggJs3boV\nw4cPp5veREIsFmP2/Nm4dvsanE8OR3OTz9/sFhQKcHNDLF5ceokboTfQoUOHOkyqmH7++Wfs378f\nfD4frVq1YjsOkQGlLo6V363E6fDTGH91LHQMdb749eUF5bgwKgiOfYdj947dyMzMxKpVqxAfH4+N\nGzdiypQpdNObfBLDMPDb5Yf/+P4Iwx5NYTqvJzrbdwJHnwNhuRDvMt7h7p4kPDj9AE7OTji45xCa\nNkbGVrMAABAvSURBVG3KdmzW7dmzB//973/B5/PRrl07tuMQGVHa4oiIiMAkr4n4Om4S9JpX/xpy\neX45TpifRN8u/ZCQkAAfHx8sWrQIOjpfLh5CKioq8Pvvv2P73u24l3gPZcVl0NTSRIu2LeA6yhUn\nfjmB58+f030NAEeOHMEPP/wAPp+PTp06sR2HyJDSFofTGCdoOKuhr1cfqV+bevI+En9IRmJsIv1W\nSGpFJBJBXV1dcmlzzJgxGD58OObMmcNyMnYFBARg5cqVuHHjBrp168Z2HCJjSvlU1bNnzxATHYOe\nk0xq9Poe47ujoKAAb9++lXEyUt9oaGhUuR+2ePFi7Ny5s9pP8amis2fPYvny5QgNDaXSUFFKWRwB\nJwNg4tEDDfRqtkmTJkcTpp698MuJX2ScjNR31tbW0NLSQlhYGNtRWBEUFISFCxciJCQEJiY1+8WO\nKD6lLI6nz5+iiUntHnE0NGmCJ8+fyCgRIR+pqalh0aJF8PPzYztKnbt69Sq8vLwQHBxMux6qOKUs\njuLSYmjp1G7hOC1dLZSU1m4dIkI+ZdKkSUhISEBmZibbUerM9evX4enpiaCgIPTv35/tOETOlLI4\nDBsborxAUKtjlOeXo3GjxjJKRMj/09HRwcyZM7F79262o9SJmJgYeHh44Ny5c7C0tGQ7DqkDSlkc\nA/oOwIuIF7U6xqNLWThz8gx4PB7WrVuH8PBwlJTQCITIxrx58xAQEICCggK2o8hVXFwcXF1dERgY\nCC6Xy3YcUkeUsjgmTJiA3Nt/4MOTmm2QU/SiCC9iXiIrKwurVq2CUCjE+vXr0aJFC1haWmLFihW4\ncuWKyn/TE/lp27YtHBwccPToUbajyE1iYiJGjRqFY8eOwc7Oju04pA4p7TyOxUsXI1HzLoZt4Un9\n2pgfbqLzy644vP9wlT8vLS1FXFwcoqKiwOfzER8fD2NjY/B4PHC5XAwdOpQWOyTVFhsbi6+//hqZ\nmZkqtyJBamoq7O3tsX//fowZM4btOKSOKW1xPH36FP0G9cXI087oOKz66wHlxubi/KggxMXE4auv\nvvrXrxUIBLhz5w6ioqIQFRWFW7duoV27duByuZIyobV3yOcwDANzc3OsWbMGo0aNYjuOzGRkZMDG\nxgbbt2+Hu7s723EIC5S2OICPT3K4erhiZKATOtt9eUmDZ9HPEDT+MgL8A+Ds7Cz1+YRCIZKTk8Hn\n8xEVFYXo6Gg0a9YMXC5XUia0qB35XydPnoS/vz8iIiLYjiITWVlZGDZsGDZt2oQpU2iDqvpKqYsD\nAKKiojDWbSw6O3WC2TxTtB7Y+h9f8yr5NVL2piDzQhZOnzwNBwcHmZxbLBbj/v37khEJn8+Htra2\nZDTC5XLRrVs3Wmm3HquoqEDHjh1x7do1mJqash2nVnJycsDj8fDdd9/By8uL7TiERUpfHACQl5eH\nw/6HsWf/Hmg100JL8xbQbKQJYZEQb+7moSS3BPPnzIfXDC+0bNlSbjkYhkFmZqZkRMLn8yEUCqtc\n2jIxMYG6ulI+k0BqaOPGjXj2f+3dfVBVdR7H8U8KiDyYmcouTWEpOmhiPCQPBmRmbpbR5B85jo3r\nNtk46hbbzJbVzOY2O00PYzNupTs61YzV7JT2ZMu2LBEgqDAqpghFJKiASa6IPAnCPftH22nPaOXv\ncuHcC+/X/5zz9a+3v3PP7/yOH9eWLVvcHsVrDQ0NysrKUk5OjtasWeP2OHDZkAjHD/r6+pSfn6+a\nmhqdO3dOkZGRmjJliu644w4FBfVvw6A3LMtSfX29HZHi4mKdPXtWGRkZdkxmzZo15H44hVNzc7Om\nTZumr7/+OiBfrvj222+VlZWllStX6rHHHnN7HPiBIRWOQNDY2Oh4tNXU1KT09HR7RZKUlKSQEO++\nwQX/tWLFCk2dOlXr1q1zexQj3333nW699VYtXbpUTz31lNvjwE8QDpc1NzerpKTEXpHU1tYqJSXF\nXpHMnj2bs0KGgIqKCi1atEh1dXUKDg52e5zLcubMGc2bN0933323nn32WbfHgR8hHH6mpaVFpaWl\n9orkyJEjSkhIsFck6enpioiIcHtMeCEzM1OrV68OiFdYW1tbNX/+fGVlZemFF17gBQ84EA4/197e\nrj179tgrkgMHDmjGjBn2iuSWW27R2LFj3R4Tl2HHjh3asGGDSktL3R7lZ7W3t2vBggVKTEzUxo0b\niQYuQjgCTFdXl8rLy+0VSVlZmaZMmWK//puZmakJEya4PSYuobe3V5MnT9aOHTuUnJzs9jiX1NnZ\nqbvuukuxsbHavHkzbwDikghHgOvp6dH+/fvtH9xLS0sVHR3teAX4mmuucXtM/M+LL76oQ4cOadu2\nbW6PcpHz588rOztbUVFRevPNN4kGfhLhGGL6+vr0xRdf2CuSXbt2aezYsY7d7ZMmTeLxg0taWlp0\nww03qKqqyq8+V9PT06PFixcrPDxcb731liuvryNwEI4hzuPxqKqqyvEKcFBQkGNFMm3aNEIyiFat\nWqWJEydq/fr1bo8i6ftHaPfff788Ho/efffdgHnrC+4hHMOMZVmqra21f2wvLi5WV1eXY0Vy4403\n8phiAFVXV2vu3Lk6duyYRo0a5eosfX19euCBB9Ta2qr333/f9XkQGAgHdOzYMcfu9tOnT9u72zMz\nM5WQkMCjCx9bsGCBli5dquXLl7s2g8fj0YMPPqiGhgbt3LlToaGhrs2CwEI4cJGTJ0/aq5Hi4mId\nP35caWlp9qOt5ORk/mfaT7m5uXr66ae1f/9+Vx4TWpalVatWqbq6Wrm5uQoPDx/0GRC4CAd+0enT\npx2727/66ivNnj3bXpGkpqYqLCzM7TEDisfjUVxcnLZu3aqMjIxBvbdlWcrJyVFZWZny8vIUGRk5\nqPdH4CMcMNba2mrvbi8uLtahQ4c0a9Ysx+72MWPGuD2m33vllVdUWFio7du3D9o9LcvSE088oc8+\n+0z5+flsHoVXCAf6raOjQ3v37rVXJPv27VNcXJxjd/u4cePcHtPvtLW1KSYmRhUVFYN2ANgzzzyj\nDz74QAUFBbr66qsH5Z4YeggHfK67u9uxu33v3r2aNGmS44CrqKgot8f0Czk5OQoJCdHzzz8/4Pd6\n7rnntG3bNhUWFmrixIkDfj8MXYQDA+7ChQuqqKiwVyQlJSWKiopy7CW59tpr3R7TFUePHlVKSorq\n6+sH9Afql19+WZs2bVJRUZFfbTxEYCIcGHR9fX06fPiw4xXgiIgIx4pk8uTJw2ZTYnZ2thYuXKiH\nH354QK7/2muv6aWXXlJRUdGwDTR8i3DAdZZl6csvv3QcuSvJsSKJi4sbsiEpKCjQ2rVrVVlZ6fN/\n4+uvv67169ersLBQ119/vU+vjeGLcMDvWJalo0ePOlYkbW1tjt3tM2fOHDJH7lqWpfj4eG3YsEHz\n58/32XXffvttPf744/r8888VGxvrs+sChAMB4cSJE47vbZ06dUpz5syxVySJiYkB/Y2lrVu36sMP\nP9Qnn3zik+u99957euSRR5Sfn6/p06f75JrADwgHAtKpU6ccu9vr6uqUmppqr0huvvnmgPqERldX\nl2JiYlRaWtrv1cHHH3+slStXKi8vT/Hx8T6aEPgR4cCQcObMGZWUlNgrkurqaiUlJdkrkrS0NL//\nrMaTTz6p9vZ2bdy40etrfPrpp1q+fLlyc3OVlJTkw+mAHxEODEnnzp3T7t277RXJwYMHNXPmTHtF\nMmfOHF155ZVuj+nQ0NCg+Ph41dXVeTVbQUGBlixZoo8++khpaWkDMCHwPcKBYaGzs1NlZWX2j+3l\n5eWaOnWqvSLJyMjQ+PHj3R5TS5YsUWpqqh599FGjvyspKdF9992n7du3KzMzc4CmA75HODAsdXd3\na9++ffajrd27d+u6665zvALsxka5PXv2aNmyZaqpqVFra6saGxvV0dGhMWPGKCYm5pKP28rKyrRo\n0SK98847uv322wd9Zgw/hAPQ96fgHTx40F6R7Nq1S+PHj3e8AjwY35P64au54yIidPjIEY0bNUoh\nV1yh8x6Pzv3vpL61OTn2j94HDhzQnXfeqTfeeEMLFy4c8PkAiXAAl+TxeFRZWenYSxIaGurY3R4b\nG+vTDXvffPON7vnNb/SfEyeU2N2tmyT9/6knbZIqRo7UwZAQJc2erT/95S9avHixNm/erHvvvddn\ncwC/hHAAl8GyLNXU1Dh2t/f29jpWJNOnT/f6yN3Dhw/rtowMpba1Kcnj0c/lqE9SfkiIKvr6tHHT\nJj300ENe3RPwFuEAvGBZlurr6x0rkrNnzzqO3L3pppsua3f7yZMnlRgfrzmnT2umwQz5I0fq/IwZ\nKikv50RGDCrCAfhIY2OjY3d7U1OT0tPT7cdbSUlJCgkJuejvfr96tQ5s2aL5Fy4Y3c+S9PfwcK17\n9VVXzy7H8EM4gAHS3NzsOHK3trZWKSkp9ookJSVFlmXp1xMm6HednfLmLL6vJFXHxamiqsrX4wM/\niXAAg6SlpcU+creoqEiVlZWKjo7WiGPHtNRwtfEDj6TXwsL0z6IiJScn+3Zg4CcQDsAl7e3tunPe\nPE0oL9esflzn30FBuuvPf9a6det8Nhvwc7x7BQRAv0VEROgKSf39gtbo3l79p7nZFyMBl4VwAC4a\nOWKE+rvktySNCAryxTjAZSEcgIsm/OpXOtfPa3SEhGhiVJRP5gEuB+EAXHT/smX6MjLS67/vlVQ9\nYoSys7N9NxTwCwgH4KJ77rlHZ0eO1Ckv/75KUkJCAkfDYlARDsBFwcHBWrVmjfaEhhr/1tEraV94\nuB754x8HYjTgJ/E6LuCytrY2pSYmKrq+Xrf09l7W33gk7Rw9WtfOnasPdu70+htZgDcIB+AHmpqa\nlJWerqiTJ5XV06OLP0zyow5JuWFhmpiYqH/k5Wn06NGDNSYgiUdVgF+Ijo5WeUWFxs+bp7+Ghiov\nJETfSfbjK0vSCUkfh4VpU2ioblu+XP8qKCAacAUrDsDPHD9+XJtffVVb/vY3nW1rU2hwsDp7ehQT\nHa21f/iDfrtiha666iq3x8QwRjgAP9bd3a2Ojg5FRkYqODjY7XEASYQDAGCI3zgAAEYIBwDACOEA\nABghHAAAI4QDAGCEcAAAjBAOAIARwgEAMEI4AABGCAcAwAjhAAAYIRwAACOEAwBghHAAAIwQDgCA\nEcIBADBCOAAARggHAMAI4QAAGCEcAAAjhAMAYIRwAACMEA4AgBHCAQAwQjgAAEYIBwDACOEAABgh\nHAAAI4QDAGCEcAAAjBAOAIARwgEAMEI4AABGCAcAwAjhAAAYIRwAACOEAwBghHAAAIwQDgCAEcIB\nADBCOAAARggHAMAI4QAAGCEcAAAjhAMAYIRwAACMEA4AgBHCAQAwQjgAAEYIBwDACOEAABghHAAA\nI4QDAGCEcAAAjBAOAIARwgEAMEI4AABGCAcAwAjhAAAYIRwAACOEAwBghHAAAIwQDgCAEcIBADBC\nOAAARggHAMAI4QAAGCEcAAAjhAMAYIRwAACMEA4AgBHCAQAwQjgAAEYIBwDAyH8BCAFff6G3aJQA\nAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x4ea31d0>"
]
}
],
"prompt_number": 5
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The dodecahedral graph is a slightly different story. It also has chromatic number 3 but with the greedy algorithm we find a colouring with four colours."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"setfigsize(6, 6)\n",
"\n",
"G = nx.dodecahedral_graph()\n",
"vcolour(G)\n",
"nlist = [[2,3,4,5,6],[8,1,0,19,18,17,16,15,14,7],[9,10,11,12,13]]\n",
"nx.draw_shell(G, nlist = nlist , node_color = colours(G), **options)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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s7e1Rp04d2Q5C6srOzg5xcXE4ePAgZs+eTYvK5KSnp4dvv/0WsbGxOHbsGFxd\nXXH79m2+Y1VJly5dsHnzZvj7+9MKb1IlGrOzUWWYmZnhyZMnMDMzk3ushIQETJo0CS1atEBgYCCa\nNWvGQULV9OjRI3z11Vd48eIFdu7cia5du/IdiTP5+fnw9/dHgwYNsG/fPnrrDwekUil27tyJb775\nBpMnT8by5cvV6vd1xYoVCA8PR1RUlFrlJvyhGWk1de/eHUlJSXB2doajoyM2bNigcbOaiooKrF27\nFl27doWHhwdu3LihUSUKAObm5ggLCwNjDEKhEO/f09t/5KWlpYXJkycjNTUVmZmZcHBwQHR0NN+x\nKm3FihWwtLTElClTaswVJyIfmpFy4N69e5g8eTJKS0uxY8cOODg4cDo+H5KSkjBp0iTUrl0bW7du\nRevWrfmOpFASiQRz5sxBTEwMQkND0bhxY74jaYwzZ85g+vTp8Pb2xpo1a1CnTh2+I31ScXExevTo\ngeHDh2PRokV8xyEqjmakHLC1tUV0dDQmTpwIT09PfP3112r7gLdIJMLChQshFAoxc+ZMhIeHa3yJ\nAoC2tjY2btyIESNGwMXFBXfv3uU7ksbw8/NDWloaDAwMYG9vrxZrC4yMjGRvwAkJCeE7DlF1vC1z\n4oG8q3Yr4/nz52zo0KGsdevWLDIyUqHn4tqFCxeYlZUVGzlyJMvNzeU7Dm/27NnDGjZsyOLj4/mO\nonHi4+NZu3btmK+vL3v8+DHfcT7p6tWrrH79+rQpC/lXVKQKcubMGda0aVM2fvx49ubNG6Wcs7ry\n8vLY6NGjWYsWLdj58+f5jqMSzp8/z+rVq/fRna9I9ZWVlbEffviB1a1bl61fv17lH5U5ePAga9Gi\nBcvLy+M7ClFRdGlXQQYMGIC0tDQYGxujXbt2CAoKUrnLWYwx7N+/H+3bt0eDBg1w584dCIVCvmOp\nBKFQiHPnzmHy5MnYuXMn33E0Sq1atbBs2TLExcXhxIkT6N69O27dusV3rI8aOXIkRo4ciSFDhtAr\n+ciH8d3kyqTMGemfJSQkMHt7eyYUCll2drbSz/8hDx48YF5eXqxjx47s+vXrfMdRWZmZmaxly5bs\n+++/p40bFEAikbAdO3aw+vXrsyVLljCRSMR3pA+SSCTM39+fTZgwgf4ekH+gGakSODs74+bNm3Bz\nc0Pnzp2xfv163h6VqaiowJo1a+Dk5AQvLy8kJiaiS5cuvGRRB9bW1oiLi8PJkycxbdo0jXvEiW9a\nWlqYOHH4qQylAAAgAElEQVQiUlNT8fDhQ7Rv3x6RkZF8x/oHLS0t7N+/Hzdu3MD69ev5jkNUDD3+\nomSZmZmYMmUKioqKsHPnTnTo0EFp57558yYmTZqEunXrYuvWrWjVqpXSzq3uCgoKMHjwYJiYmODQ\noUMwMDDgO5JGCgkJwfTp0+Hp6YlffvkFdevW5TvSXzx+/Bjdu3fHrl276DYIkaEZqZLZ2NggKioK\nU6dOhZeXF5YsWfLJR2UYY4iJicGY0UPg3M0O9u2aobtzW4wbOxRxcXGfvPdaXFyM+fPno1+/fpgz\nZw4uXrxIJVpFpqamOH/+PAwMDODl5YW3b9/yHUkj/bG2wMTEBPb29jh8+PAn/36XlpbiwIED6CH0\nRetOndHC3gEd3Hpi4dKv8fjxY07zNW/eHMePH8e4ceOQnp7O6dhEjfF6YVnJ+LpH+jEvXrxgn3/+\nOWvVqhWLiIj4x69LpVK2e9cu1q5tc9bG2pht+EHA4k6DpUaCxZ0G+/U7AbNuZcQc2lux/fv2ffAc\nYWFhrEWLFmz06NG06pADEomEzZ8/n7Vt21Zt33SiLv68tuDRo0f/+PXCwkI2b/ESZlyvPjPu0Zdh\n7RGGoESG4BSG3VGs1ri5TL9OXebhO4DzdQC//fYba9WqFXv9+jWn4xL1REWqAs6ePcuaNWvGxo0b\nJ/uHWVFRwaZO+YI5tDNiUcfApDlg7Pk//5M8AwsPAmvXxojNmjmFSSQSxtjvj7SMHDmSWVlZsbCw\nMD6/PY30yy+/sKZNm7Lbt2/zHUWjicVitnLlSla3bl3266+/yh6VefnyJbPt6Mj0BoxiOJ/JkMY+\n/N+NYobvtjHDevXZ8ePBnGZbuHAhc3d3Z2KxmNNxifqhe6QqorCwEMuWLcPRo0fxyy+/4NrVy0hN\nOogze0QwNfn08fnvAd+xhnDtNRHt7B2xaNEijB07Ft999x2MjIwU/w3UQIcOHcLcuXNx7Ngx9OzZ\nk+84Gu3PawvWr1+P8dNm4JFLf1TM+B4QCD49QEYyDL4S4tSBffD29uYkk0Qigb+/PywtLbFlyxYI\nKpODaCQqUhWTmJiIYcOGQSB9huSLEphXIerbd4BDHy3oG1rh6NGjcHR0VFxQAgCIiIjAyJEjsXXr\nVgwePJjvOBqNMYY9e/Zg2tz5qPDwg2Tlb5Ur0T8kxcJotj9eZD+CiUklPp1WQkFBAVxcXDB16lTM\nmDGDkzGJ+qHFRirGyckJ1q0tsHJJ1UoUAOrUBr5fIEUb2yZUokrSp08fhIWFYebMmQgMDOQ7jkYT\nCAQYPHgwBAAk81ZXrUQBwNEN6OqO/fsPcJbJ1NQUISEhWLlyJcLDwzkbl6gXKlIVk5mZidTUVAyp\n5juzh/sDV69eQ3Z2Nqe5yMc5OjriypUrWLduHZYtW6ZyO1hpkr1790GrpxCo17Baxxd/Pg2rNwdy\n+mdkZWWFI0eOYPTo0bh37x5n4xL1QUWqYvbv34NxQyugp1e94w0NgJGDpDiwfy+3wci/atmyJeLi\n4nDx4kVMnDgRFRUVfEfSSAG/7YVoyOTqD+DkgdeiUiQnJ3MXCkDPnj3x448/YsCAAXj37h2nYxPV\nR0WqYp4+uY82rcrlGqNNKzGePXvIUSJSWQ0aNEBUVBRevHgBf39/FBcX8x1J47x89hRo2ab6AwgE\n0GnZBs+ePeMu1P98+eWX8PX1xbBhw1BeLt+/YaJeqEhVTElJMeTdNMdAHygpKeImEKkSY2NjnD59\nGvXq1YOnpydev37NdySNUl5SAujJ9w9EqmcAkUjEUaK/WrNmDXR0dDBv3jyFjE9UExWpijEzq4v8\n9/KN8b4QMDOrx00gUmW6urrYs2cPevfuDVdXV7pfzSFDMzOgMF+uMbQK82Fubs5Ror/S0dFBUFAQ\nIiIisHXrVoWcg6geKlIV07mzKyJi5XvuM/yKMTo5OnOUiFSHQCDAjz/+iBkzZsDV1RUpKSl8R9II\nnRw7AwkR1R+guBClt6+jffv23IX6GzMzM4SEhOC7775DVFSUws5DVAc9R6piCgsL0bx5Q6SGl6BJ\n46of//Ax4NTfCE+e5MHQ0JD7gKTKjh07hunTpyMoKAi9e/f+x6/fvXsXO/b8hoyHj1BYXAxzU1N0\ntW+HSV9OQKNGjXhIrLrCwsIwdMHXKDpys+qPvwBA0Bb0vR2BsJPB3If7m+joaIwYMQKxsbFo3bq1\nws9H+EMzUhVjYmKCkSNGYvtB7Wodv3W/LsaNHU8lqkKGDh2Ko0ePYvjw4Thy5Ijs/589exbdPDzR\nqUcvbHwnQGi3QYj1nYKzjr746fYTWNm1he9nw3Dt2jUe06sWb29vGBW/B1Kr8XvCGIyPBmLhjGnc\nB/sADw8PfPfddxgwYADy8+W7HE1UG81IVdD9+/fh0r0jTuwshptT5Y+LigVGTDfBtcRUtGjRQmH5\nSPWkpqbC19cX8+bNw5MXL7Hj2AkUT/se8BoM1PrA806F7yE4sw8GO1Ziw08/YuKXE5QfWgXt3vMb\nZq5cBdH+eMCsTqWP0934DdqlXkZS3BWlbuc3c+ZMZGVl4ezZs9DR0VHaeYnyUJGqqIsXL2L0KH8c\n2VICD9dKfP1lYPRMQxw5ehYeHh6KD0iq5fHjx+jk1A1F9RqjfEc4YF6J920+ugfDqX0R+N/vMW7c\nWMWHVANzFy3G9vPhEG0+B9T/xOVvxqAb+B0aXDyM5Pg41K9fXzkh/6eiogJCoRD29vZYt26dUs9N\nlIMu7aoob29vHDl6Dp9/ZYzxcw1w/QNrVRgDrt4Exs42wJjZpgg+EUYlquJSUlJQZmhS+RIFACtb\niALPY9r8BcjIyFBsQDXx68+rsHD4EGj5tYVWwLdAbs4/v6hcDIQegfEXPWF9LRQ3Y68ovUSB31fy\nHj16FOfOncPOnTuVfn6ieHSdQYV5eHggLf0h1q9fi95DV8O2tRG6dKiAiVEFCot1kJiii/eFhvjq\nq3lYt+VL1K1byR/MhDffr10H0awfK1+if2jVFuKhU/Dr5kDsCNikmHBqRCAQoHMHBzSrYw53ySsc\nGdweOp1cIG5sBYluLdQqeIuKy+egq62N3QEb4e/vD11dXd7y1q5dGyEhIejZsydsbGzobUEahi7t\nqoE1a9YgPT0dI0aMwP3791FYWAhTU1NYW1ujd+/e0NKiCwvqIC0tDV09vVBy4TFQnR/qL57C4LMO\nyHv6BMbGxtwHVCMlJSVo27Yttm/fDi8vLxQWFuLcuXPIzc2FWCxG7dq10bVrV3h7eyM2NhbW1tZ8\nRwYAhIeHY8yYMUhISICVlRXfcQhHqEhVHGMM7du3R2BgIH2KVXPT587DtjJjSGZ8X+0xjOYMwqYR\nfhg/fjyHydTPihUrkJGRgaNHj/7r182dOxfGxsb44YcflJTs0wICArB161bEx8fD1NSU7ziEAzSV\nUXE3b95ESUkJ3Nzc+I5C5JR+/wEkbTrJNUaxbSc8eFiz91G+f/8+AgICsHbt2k9+7bhx47Bv3z5I\npVIlJKuc6dOnw83NDSNHjoREIuE7DuEAFamK27t3L8aOHUuXbzVAUXExYCDfrlUwNMa7wpq7jzJj\nDLNnz8aiRYvQtGnTT359x44dYW5ujsuXLyshXeUIBAJs2rQJxcXFWLp0Kd9xCAfop7MKE4vFCAoK\nwtix9MiDJjA1MQGKC+UbpKgAdc1q7uXAkJAQPHjwAHPnzq30MePGjcPevar1WkFdXV0cP34cJ06c\nwG+//cZ3HCInKlIVdu7cObRt25YWJai5srIyREZGoiAvF7h+Sa6xjG/Foa2dHTfB1IxIJMLs2bMR\nEBCAWrVqVfq4UaNG4dSpUygqUq2ZfN26dRESEoJFixYhLi6O7zhEDlSkKmzv3r0YN24c3zFINWRn\nZ2PLli3w8/ND/fr18c0338C1mxNqnT8ElFTzFV7ZmRBkpmLQoEHchlUTq1atgpOTE/r06VOl4xo2\nbIgePXogOFjx++tWlZ2dHfbu3YuhQ4fi8ePHfMch1USrdlXUq1evYG1tjSdPntDKPjVQWlqKmJgY\nhIaGIiwsDG/evIGPjw98fHzg7e2NevV+f62de7/+uOw6BBhU9VW3tX6ei5mN9PHLqp+4jq/y7t+/\nD2dnZ6SkpKBJkyZVPv748eMIDAxU2bexrFu3Dr/99hvi4uJq/KNN6oiKVEVt3LgRiYmJOHDgAN9R\nyEc8ePBAVpwxMTGwt7eHUCiEUCiEo6PjBxeIXbp0Cb4jRv2+T2zj5pU/WVIcjOb4I+3mDTRvXoXj\nNABjDL6+vnB3d8eiRYuqNUZZWRksLS1x8+ZNlfz9Y4xh4sSJePv2LYKDg2lxoZqhPy0VRZd1VU9J\nSQnCwsIwe/Zs2NjYwNXVFTdu3MCYMWOQnZ2N+Ph4LF++HF26dPnoD0J3d3f8sHgRDCd7AU8r+RhL\ncjz05wxC8MEDKlkCinbmzBk8evQIc+bMqfYYenp6GDZsGPbv389hMu4IBAJs2bIFb968wfLly/mO\nQ6qK1SCmpqYsPz+f7xifdPv2bWZpackqKir4jlLjZWZmsg0bNjAfHx9mbGzM3Nzc2MqVK1lSUhKT\nSCTVHnfDpgBm2MCCac1dxXAljyGN/fO/sAdM98uFTM+sNmvcuDF78+YNh9+ZeiguLmbNmzdnERER\nco919epVZm1tzaRSKQfJFCMvL49ZWVmxAwcO8B2FVAFd2lVBCxcuhI6ODn76qebdC+ObSCRCdHS0\n7JKtSCSSXa7t06cPzM3NOTtXcnIy1mwKwMkTJyDo2Q8l1h1+f860uADGyVeAO9cx4YsvMGf6NAQE\nBODWrVsIDQ3ldc9YZVu+fDmysrIQFBQk91iMMdjZ2WH37t1wcXHhIJ1i3LlzB71790ZISAi6devG\ndxxSCVSkKqaiogLNmjVDVFQU2rRpw3ccjccYw7179xAaGorQ0FAkJCSgc+fOEAqF8PHxgYODg8Lf\nXfn27VsEBQUh8+EjvC8qRj0zUzjYt8Nnn30GAwMDAIBEIsGAAQNgZWWFzZs3KzSPqsjKykL37t1x\n69YtWFpacjLmTz/9hOzsbGzbto2T8RQlJCQEU6dOxdWrVyu18QThFxWpigkNDcV3332Ha9eu8R1F\nYRhjEIlEKC4uhqmpKfT19ZV6/qKiItmsMzQ0FOXl5bJZp6enp8r+/Xj//j26d++OGTNmYNq0aXzH\nUSjGmOwqwIIFCzgb99mzZ3BwcEBOTo7sQ4qqWr16NYKCgnDlyhUYGcm5IxZRKFpspGI0eZHRo0eP\nMG/eQpiZ1YW5eV00b24NY2NTWFg0w6pVP+P169cKOS9jDOnp6Vi7di369OmDRo0aYd26dbCyskJI\nSAiePn2KHTt2YPDgwSpbosDvHwRDQkLw/fffIzIyku84CnXq1Ck8efIEs2fP5nTcJk2aoHPnzjhz\n5gyn4yrCwoUL0b59e4wbN06l9gom/0QzUhWSn5+PFi1a4OHDh6hTpw7fcTjz5s0bjBw5DjExVyCV\nOkAs7gTgj/dxMgDPYWCQDKk0A6NHj0Zg4MYq7VzzIYWFhYiMjJTd6wQgm3X27t0bJiYmco3Pp0uX\nLuHzzz9XqdeDcUkkEqFt27bYvXs3evfuzfn4Bw4cwKFDh3D+/HnOx+ZaaWkpevfuDS8vL/znP//h\nOw75CCpSFbJ9+3ZcvHgRx48f5zsKZ549ewYXl17IzbWEWNwTwL8tlBHBwCAUHTqYIzIyDIaGhpU+\nD2MMd+7ckRXn9evX4ezsLCvPNm3aKPxepzJt374dv/76K65evcrpAihVsGzZMjx48ACHDx9WyPjF\nxcVo0qQJ0tPT0ahRI4Wcg0u5ublwcnLC6tWr8fnnn/Mdh3wAFakKcXFxwddff43+/fvzHYUTBQUF\ncHR0RnZ2E0gkrpU8Sgp9/bPo0cMCoaFnoK2t/dGvfP/+PSIiIhAWFoawsDDo6urKFgl5eHho/A4x\ns2bNwr1793Du3Dno6OjwHYcTmZmZcHFx4XSB0YdMmDABbdu25fT+qyKlpKTAy8sLoaGh6NKlC99x\nyN/QPVIVkZmZiYcPH6Jv3758R+HMmjVrkZOjB4mkKo8aaKG01Bfx8Wk4derUX36FMYZbt25h1apV\n6NWrF5o0aYIdO3agXbt2iIiIwIMHD7B582YMGDBA40sUAH799VcAUJsy+BTGGGbOnImlS5cqtESB\n/38jjLrMIzp27Ijt27dj0KBByMnJ4TsO+RuakaqIZcuWQSQSyX44qrvy8nI0aGCJ/PzPADSsxgi3\n4eSUhwsXziA8PFx2ydbQ0FB2udbd3b1Kl381UX5+Prp164YFCxZg0qRJfMeRy4kTJ7B8+XKkpKQo\n/FlZqVSKVq1aITg4GI6Ojgo9F5d+/PFHnDx5EjExMSq/6rgmoSJVAVKpFFZWVjhz5gw6dOjAdxxO\nBAcHY/z4JSgsHF3NESqgpbUW+voC9OrVS1aerVu35jSnJsjMzESPHj1w9OhR9OrVi+841VJcXIy2\nbdti7969cHd3V8o5V6xYgfz8fGzYsEEp5+MCYwyjR4+GVCrFoUOHNOq+vzqjS7sq4NKlS6hdu7bG\nlCgAHDp0DIWF8rw3UwcCgQOWLl2K8+fPY+bMmVSiH2FjY4ODBw/i888/x8OHldy/V8X8+OOPcHV1\nVVqJAsDYsWNx+PBhiMVipZ1TXgKBADt37sTDhw+xcuVKvuOQ/6EiVQGa+Ozoy5d5AOR7xEQiMcHb\nt/ncBNJwffr0wfLlyzFgwAAUFBTwHadKMjMzsW3bNvzyyy9KPW+rVq1ga2uL0NBQpZ5XXgYGBjh1\n6hS2b9+uku9YrYmoSHlWVFSE06dPY+TIkXxH4ZREIgEg72Unwf/GIZUxffp09OrVCyNGjFCb37c/\nFhh9/fXXaNy4sdLP/8eiI3XTqFEjnDx5ElOnTkVycjLfcWo8KlKeBQcHo0ePHmjYsDoLclRX/fr1\nARTLNYa2dgkaNqzPTaAaYsOGDSgtLcXixYv5jlIpJ06cQE5ODmbOnMnL+YcOHYqoqCiF7aqlSJ07\nd0ZgYCD8/f3x8uVLvuPUaFSkPNPEy7oA8NlnA2BkdE+OEaTQ07sHHx8fzjLVBLq6ujh27BhOnz6N\nPXv28B3nXxUXF2PevHnYvHkzb2+0MTMzg6+vr8I2f1C0oUOHYsKECfD390dpaSnfcWosKlIePX78\nGKmpqRgwYADfUTh1/fp1hIaGorj4PoC31RzlPpo3t1SrRxNURZ06dXDmzBksXrwYsbGxfMf5qJUr\nV8LNzY33lcbqenn3D99++y2aN2+OSZMmqc1zsZqGipRH+/fvx7Bhw6Cnp8d3FLmVl5cjKCgILi4u\nGDp0KLp06YJJkyZCV/d6NUZjMDK6gcWL53Ces6aws7PDvn37MHToUGRnZ/Md5x/u3buH7du3Y82a\nNXxHgaenJ16+fIm0tDS+o1SLQCDAnj17kJGRgZ9//pnvODUSPUfKE8YYbG1tsX//frV+ee+rV6+w\nfft2bNmyBdbW1pg1axb8/Pygra2N3NxctG/viNevu4Gxyj7aw1CrVjTs7Epw7doVjfiQwacNGzZg\n165diIuLU5mN+hlj6Nu3L4RCIebOnct3HADAkiVLIJVKsXr1ar6jVFtOTg66deuGzZs3Y+DAgXzH\nqVFoRsqThIQEaGlpwcnJie8o1ZKSkoIJEybAxsYGDx8+xLlz5xAdHY1BgwbJ9sdt2LAhLl0Kh7l5\nHLS0EvH7m17+jQR6ehfRpEkeIiNDqUQ5MGvWLHTr1k32EL8qCA4OxosXLzBjxgy+o8iMGzcOBw4c\nQEVFBd9Rqs3S0hInTpzAxIkTkZqaynecGoWKlCd/LDJSp51JKioqcOLECfTq1Qv9+/dH69atkZWV\nhV27dn10M4m2bdsiKekabGyewth4BwSCawD+viiiADo6l2BgEABXV1MkJV1F3bp1PzQcqSKBQIDN\nmzcjPz8f33zzDd9xUFRUxPsCow+xs7NDkyZNEBERwXcUuTg5OWHjxo3w8/NDXl4e33FqDlaDmJqa\nsvz8fL5jMJFIxGrXrs2ePn3Kd5RKefv2LVu9ejVr3rw5c3FxYUFBQUwsFldpDKlUymJjY9nAgZ8x\nPT0jZmzciAkEdZiJSSNmYGDCJk6cytLS0hT0HZBXr16xli1bsn379vGaY8mSJWzUqFG8ZviYgIAA\nNnz4cL5jcOKbb75hrq6urLS0lO8oNQIVKQ8OHz7MvLy8+I7xSWlpaWzKlCnM3NycjR49miUmJnIy\nbn5+Prty5QozNzdn9+7dY8XFxZyMS/7dnTt3WL169VhCQgIv58/IyGB169Zlz58/5+X8n/L69Wtm\nZmamEj8j5CWRSNigQYPY+PHjmVQq5TuOxqNLuzxQ5WdHpVIpzp49Cy8vL3h6esLCwgIZGRnYv38/\nunbtysk5zMzMYGNjA11dXdjY2NT4N7goS7t27bBnzx4MGTIET548Ueq52f92MFq2bJnKvky7bt26\n8PT0xNGjR/mOIjctLS3s27cPSUlJGvNGKZXGd5MrkyrMSHNycpi5ubnKzcLev3/P1q9fz1q1asU6\nd+7M9u3bp9DLQrm5uax+/foKG5983Jo1a1jHjh1ZUVGR0s559OhR1r59e1ZeXq60c1bH6dOnmaur\nK98xOPP48WPWqFEjdvbsWb6jaDSakSrZwYMHMXjwYJWZhWVmZmLWrFlo0aIFEhISsG/fPly/fh1j\nxoyhVbMaav78+ejYsSPGjh2rlJW8f15gpKOjo/DzyUMoFCIrKwv379/nOwonmjVr9r9XGo5X2+dk\n1QEVqRIxxlTisi5jDBcuXICvry/c3NxgYmKC1NRU2YYK6rSSmFSdQCDA1q1bkZubixUrVij8fP/9\n73/h4eGBHj16KPxc8tLV1cWIESOwb98+vqNwpnv37li7di38/PzUck9htcD3lFiZ+L60e+PGDWZl\nZcUkEgkv5y8sLGSBgYGsTZs2zMHBge3cuZOJRCJestClXf7l5uay5s2bs0OHDinsHOnp6axevXrs\nxYsXCjsH15KSkljz5s15+3eqKIsXL2a9evViZWVlfEfRODQjVaK9e/di7Nix0NJS7m/7o0ePsGDB\nArRo0QLh4eHYsmULUlJS8OWXX8LAwECpWYjqaNCgAc6cOYNZs2YhMTGR8/HZnxYYWVhYcD6+onTs\n2BGmpqaIiYnhOwqnVq5cCVNTU8yYMYP25OUYFamSiMViHD58GGPHjlXK+Rhjsp2GunbtCoFAgBs3\nbuDEiRNwd3eny7cEAODg4ICdO3di8ODByMnJ4XTsY8eOIS8vD9OnT+d0XEUTCARqv5H9h2hra+Pg\nwYNISEjApk2b+I6jUVT7zr8GOX/+POzs7NCyZUuFnqekpAQHDx7Exo0bUVFRgVmzZuHAgQMwMjJS\n6HmJ+ho4cCDS09MxcOBAxMTEcLIQrqioCPPnz8ehQ4dUfoHRh4waNQp2dnYICAjQqH87JiYmCAkJ\nQffu3WFra4u+ffvyHUkj0IxUSRS9yOjp06dYunQpmjVrhlOnTmHt2rVIS0vD1KlTNeoHAVGMJUuW\noE2bNhg/fjwnl/1++OEH9O7dWy0WGH2IhYUFXFxccOLECb6jcK5FixY4evQoxowZg7t37/IdRyNQ\nkSrB69evER0djaFDh3I6LmMMcXFxGDZsGDp06ACRSIT4+HjZhgp0+ZZUlkAgwM6dO/H48WP88MMP\nco2VkZGB3bt3q/WbVAD1f0/pv+nRowdWrVqFAQMG4O3b6r4zmPyBilQJDh8+DF9fX5iamnIyXllZ\nGfbt24euXbviiy++gJubG7Kzs7FhwwZYW1tzcg5S8+jr6+PUqVPYuXMnjh07Vq0xGGOYMWMGli9f\njoYNG3KcULn8/PyQnJys9F2glGXChAnw8/PD0KFDUV5ezncctUZFqgRcXdZ9+fIlVqxYgebNm+PA\ngQP4z3/+g3v37mHWrFmclTSp2SwsLHD69GlMmzYNSUlJVT7+6NGjeP36NaZNm6aAdMqlr6+PYcOG\nYf/+/XxHUZjVq1dDT08Pc+bM4TuKWlO/VQAqrLCwEFevXsW7d++gpaWF+vXrw9TUFC9fvoSnp2e1\nx71+/To2bNiAc+fOYfjw4YiKikLbtm05TE7I/+vUqRO2bt0Kf39/XLt27S9745aVlSEhIQGvX7+G\nVCpFnTp14OzsDGNjYxQWFmL+/PkICgpSywVGHzJu3DiMHTsWkyZNQlJSEvLz86Gnp4dGjRrByclJ\n6Y+ycU1bWxuHDx9G9+7dERgY+I8PQHfv3kVWVhaKiopgYmICGxsb2NjY8JRWdWnG33ae3blzB+s2\nb8HhoMOoZdMe0roNIJBIgNxnKH2UBUcHezx//hxNmzat9Jjl5eUIDg7Gxo0b8fz5c8yYMQObNm1C\n7dq1FfidEPK7IUOGID09Hf7+/rh06RLy8vIQEBCIbdt2QiCoDcAEACAQiFBe/hKjR49CRUUZ+vTp\nAzc3N37Dc4QxhoqKCrx/9xw21k3RtZMBaptJIS4X4P4jhlKxEaZOnYvxE75U6/fnmpmZISQkBK6u\nrrC1tUWPHj0QHByMn39eh6ysB9DVtYRUqgstrXKIxc/Qtq0dFi+eA39/f5V6pyyfBKwGPZlrZmaG\nJ0+ewMzMjJPxysvL8eW06Qg+ew7iIZNRMWQi0NDyr1/0IAO1jgRC6/whLF+8GEsXLfzXRUCvXr3C\n9u3bsWXLFlhbW2PWrFnw8/ODtrY2J5lVRV5eHuzt7enlwyqMMYbhw4cjPf0u7t9/BKnUAWKxI4C/\nl8Z7aGsnQyK5ipEjh2Hv3l1qPyMtLCzE8M8HICvzBr4aI8IXwxhqm///rzMGJCYDgfsMEBIOBG7e\nheEjRvAXmAOXLl3CkCFDIBDUglhsjsLCDgBs8dc7gBIAd2Fikgpj4xJERV1AmzZt+AmsQtT7bzuP\nKioqIBw0BAlFEohC7gGGxh/+wlZ2EH+9CZiwGCun90PemzdYv/rnf3xZSkoKNm7ciJMnT2LIkCE4\nd5w1Ev0AACAASURBVO4cOnTooODvgpB/Z2JSG+npLyGVTsYfs9B/MoNE4g6gO06dOomBAz/DmTPB\navvhr6CgAB7uTujSLhuno8vwoc8EAgHQzRHo5liC1HTAd+yXKCjIx+QpXyk/MEdMTExQXCxGWZk7\nAIePfJU2gHYoLGyHoqIUODm5IjY2Gg4OH/v6mkG9L/Dz6KvZc5FQIIZow6mPl+ifWTSBaPcl7Dhx\nBoFbtwH4vYxPnDiBXr16oX///mjdujWysrKwc+dOKlHCu3XrNuDw4XOQSifg4yX6Z3oQiYbi0qUM\nzJkzX9HxFIIxhmFD+6OrfTa2/vzhEv07h7bApeMlWLFiPi5evKj4kArw/PlzeHkJUVbmi4+X6F8x\n1hGFhb3Ru3ffGn9liS7tVsOTJ09g27ETSkMfAiZVHCvrDkwn98GSObOxbds2WFpaYtasWRg8eHCN\nut9Al3ZVW0lJCRo0aIyiojH456XcTxFBTy8Q2dlZarXHLgBcvnwZUyf1x+3IokqV6J+dCgN+2mKH\na4npigmnQPPnL0RAQDzEYu8qH6unF4qFC/vihx/+o4Bk6oFmpNWwedt2SPuPrnqJAoC1PQoaNsf5\n8+dx7NgxxMXF4fPPP69RJUpU39GjRwFYouolCgCGEAjaYdu27RynUrzAzWswfVxxlUsUAAZ4Abkv\nH+PGjRvcB1Og0tJS7NixC2Jx52odX1bWGQEBW2r0s6hUpFUkFouxdedOiIfJcS9kwiIUMQG6du3K\nXTBCOPTzz+tQVFT92wulpZ2wcWMgKioqOEylWC9evMDF8AiM+ax6F+m0tYGpY0oRuHktx8kU6/jx\n4wAsUL0PTQDQABJJbZw+fZrDVOqFirSKHjx4AKmRKdBSjpVqHgOQejUeUqmUu2CEcEQsFuPevTsA\nWssxigXKyiRqtSvQ9evX4dJFD2Zy7G0ywEuKuLjL3IVSgoiIyygstJJrjMLCFoiKUq/vm0u0areK\n3r17B21zOZ8Z060FbT19FBUV0Y5EROXk5+ejVi0jlJbK9zlbW9sI+fn5HKVSvHfv3qGOuUSuMeqY\nAy9evMKAAQM4SqV4iYkpALrJOYoBXr2quXv2UpFWUa1atYBysXyDMAZJufj3sQhRMbVq1YJUKv8l\nWcYq1OrveK1atSAul+/Dg7gcMDTUx+TJkzlKpXivX/+CvDz5PkAAEujrq8+fNdeoSKvIwsICZc+f\nAOXlQHUXCOU9h56BIfT19bkNRwgHTE1NwZgEQDGA6r6CrwJicT4aNGjAYTLFsrCwwKMn8r0x6dET\noEmTRmo1I42KuoTExCTIc6dJR+c9mjXryF0oNUP3SKuoSZMmsLG1BS6FVHsM7RO78Plw9d4FhWgu\nLS0tDB78GbS0bskxSgY6dHBUqyJ1c3NDzkstpMrx9MquIAOMGDGJu1BKMGbMKOjr3wFQ3SaVQFf3\nDkaNqrk/06hIq2HxjGkwPhpYvYPLy6F3fDv+r737jori6t8A/oDSiw2JhVhQQIFQFAUsiF1UwIod\nbGBNoolRY4j9tfeGXRSxEQHhVYqIWFCwIggKAgKKYgHpS937+yO/7BsTC7C7zJbv55ycnBOZmWc1\n+HDvnbmzcJ707oBCZN/PP/8INbU41PUvVy2tR1iyRLreKKKkpAQPj/nwOqFSp+Pf5QLBlxmmTZ8h\n4mTi1aVLF7Rr9y2AZ3U8w1MYG3eS6xdpUJHWwejRo9Eg9TFwt/Z3qSn8cQiG+u3lfkstItm6deuG\nNm1aQkGhLqPSNCgpFcHJyUnkucTNY9ZcnA1WQEpa7Y9dt0sJo0aOQNOmTUUfTMyWLl0IDY0YALVd\nG6+EhkYslixZKI5YUoOKtA5UVFTgd9IHaotcgOT4mh94NRhaB1fj7LEj4gtHiIj4+flCQ+M6gNRa\nHPUKampBCAg4J5Ub17ds2RIbN+zAUFd1vHxV8+N2HVHExau62LR5t/jCidGkSZPQp48ZVFWD8efG\n9DVRBTW1CxgyxBZjxowRZzyJR0VaRwMHDoT33j1Qcx8AXDwNfOnB89ISKB7bgkZrPHA5OIje50ek\ngomJCXbs2AzgLBQUYgB8aeeaagCPoK5+DqdPH4ednV39hBQDd49ZmDN3OXo4q+Py9T/f9PI5uXnA\nz6uUsNu7BULDrkNHR6f+goqQoqIizpzxgbp6Dho2PAkg9ytHvIe6+ln06dMevr7Hv/hGK3lARSoE\nF5exCA/0h1nAXqgNbocG+9cA6U+Bgjwg7x3w5CEU1syFUn892CVdw72bN9C9e3euYxNSI69evcLK\nlSuxc+cW9OpVCVXV3VBSigCQgz/v6C0F8A4NG16HmtoeWFq+RmRkKJydnbkNLgI/L1qCnbt8sHB1\nW+jbNMTOw0B6JpBfAOS8BaLvANMWqqFDTxW8LXbErdtx0NfX5zq2UJYvXw4LCxMsWjQRWlonoal5\nFsATAIUAygAUAEiCpuZpaGufxi+/TMZ//xsAFZW6rSnLFCZHtLW1WX5+vljOHRcXx9zcZzHddvpM\nrVFjptG0GWtlYMQGDR3GBg0aJJZrSrM3b96w5s2bcx2DfEZpaSnr1q0bW7NmjeC/paWlsQULfmYt\nW7Zj6uraTE1Ni+nq6rHp0z1YQkICh2nFp7CwkGloaLCRIwaxNt82Y9raqqy5jiYz+64d27D+P+zt\n27dcRxSJQ4cOMUNDQ5aXl8cYY4zH4zEfHx9mYWHNGjduzlRU1Fnjxs1Z16627NSpU6ysrIzjxJKF\n3v4iZgUFBWjbti3S0tLQrJmQOyLJEHr7i+RijGHixIlQUFCAr6+vXE/bHT9+HH/88QeCg+v+uJuk\nu3btGsaOHYubN2/SslMd0dSumDVq1AhDhw7F6dOnuY5CSI2sW7cOaWlpOHLkiFyXKPBnkbq5uXEd\nQ2zS09Mxbtw4+Pr6UokKgYq0Hri5ueH48eNcxyDkq/z9/bF//34EBgZCTU2N6zicyszMRHx8vFTt\nUlQbhYWFcHR0hKenJwYOHMh1HKlGRVoPBgwYgFevXiEpSfpe+EvkR1xcHGbNmoXAwEC0atWK6zic\n8/HxgYuLi0zeTFNdXY2JEyfCzs4O8+bN4zqO1KMirQcNGjTA5MmTaVRKJFZOTg6cnZ2xd+9edO1a\ntxc8yxLGGE6cOCGz07pLly5FaWkpdu3aJffT96JARVpP3NzccPLkSVRXC/uWBUJEq6ysDCNHjsS0\nadPg4uLCdRyJcPv2bSgqKsrk42re3t4ICAiAn58flOr64g3yESrSemJsbIxWrVohIiKC6yiECDDG\n4OHhAT09PSxfvpzrOBLjr5uMZG20Fh0djcWLFyM4OJieIhAh6dvDS4r9ddPR4MGDuY5CCABg06ZN\nSExMxI0bN6CoSD9XAwCPx4Ofnx/i42ux/acUyMjIwJgxY3D8+HF07tyZ6zgyhb5z6tGECRNw6dIl\nFBQUcB2FEAQFBWHXrl24cOEC1NXVuY4jMYKCgtC1a1fo6elxHUVkiouL4eTkhMWLF8PBwYHrODKH\nirQeNWvWDP369YOfnx/XUYicS0hIwMyZM+Hv7y9ThSEKsvbsKJ/Px+TJk9G9e3csWCBdr7aTFlSk\n9YyeKSVce/fuHZycnLBjxw5YW1tzHUeivH79Grdv38bIkSO5jiIynp6eyMvLw759+2RuzVdSUJHW\ns6FDhyI5ORmpqbV5NRUholFeXo5Ro0Zh4sSJmDhxItdxJI6vry9GjhwJDQ0NrqOIxMmTJ3HmzBmc\nP38eysrKXMeRWVSk9UxJSQkTJ07EiRMnuI5C5AxjDHPmzIGOjg7WrFnDdRyJwxiTqWndmJgYLFy4\nEEFBQWjevDnXcWQaFSkH3NzccOLECfD5fK6j1Lt3795hx46dWOz5OworqvDDTz/j6NGjKCkp4Tqa\nzNu+fTsePHgAHx8fukP3Ex4+fIji4mL07t2b6yhCe/HiBUaPHo1jx47B1NSU6zgyj76bOGBhYQFt\nbW1cv36d6yj15s6dOxg9aQq+7WiAZdcf4niTTihfsB67G7TEj6cuQPfbNpj9w4949uwZ11Fl0qVL\nl7BlyxYEBQVBU1OT6zgS6fjx43B1dZX6HzJKSkrg5OSEBQsWYPjw4VzHkQv0GjWObN26FY8fP8ax\nY8e4jiJ2W7fvwPKNm1Dmtgj8EVOBRk3//UWvs9Dw3AEonz+Is97H6C8AEUpKSoK9vT0CAwPRo0cP\nruNIpIqKCujp6eH27dvo0KED13HqjM/nw8XFBRoaGvD29qabi+qJdP/oJcUmTZqEwMBAmZ/S3Lhl\nK1bsPYDSk7fBd/vp0yUKAC3boOrH/6B0z3/hMn0mLl68WL9BZdT79+/h6OiILVu2UIl+QUhICIyM\njKS6RAFg5cqVePXqFQ4ePEglWo+oSDnSokUL9OjRA/7+/lxHEZvIyEis3rYDJQfCgVZta3aQmTV4\nOwMxbuo0ZGRkiDWfrKuoqMCYMWMwZswYuLq6ch1Honl7e2Pq1KlcxxDK2bNnceLECQQEBMjkG2sk\nGRUph2T9mdKVm7agdP4aoOW3tTvQ3AYVjq7Yuc9LPMHkAGMM8+fPh5aWFtatW8d1HIn2/v17XL16\nFWPHjuU6Sp3dvXsX8+fPx4ULF/DNN99wHUfuUJFyyMnJCQ8fPsSLFy+4jiJyaWlpuHvnDjBkXJ2O\nr3SZjcPHjqGsrEzEyeTD7t27cfv2bZw6dQoNGjTgOo5EO336NIYNGwZtbW2uo9RJdnY2Ro4ciUOH\nDsHc3JzrOHKJipRDqqqqGDt2LHx8fLiOInL7Dx9BtbMboKpWtxO06Qh07iLTU9/iEh4ejvXr1yMo\nKAhaWlpcx5F40vzsaGlpKUaMGIG5c+dixIgRXMeRW1SkHPtrelfWbp5++OQpKs2Fu7ml+DsbPHn6\nVESJ5MPTp08xefJknDt3Du3bt+c6jsRLTExETk4O+vfvz3WUWmOMYfr06TA0NMSvv/7KdRy5RkXK\nMRsbGzDGEBsby3UUkSooLAQ0hBwNaWojt6BQNIHkQF5eHpycnLB+/XqZ2FSgPhw/fhyTJ0+Wyunv\ntWvX4vnz5zh8+DDdocsxKlKOKSgoyORNR1paWkBpsXAnKS1GU22amqyJyspKuLi4YPjw4ZgxYwbX\ncaRCVVUVTp48KZXTuufPn8ehQ4cQGBgINbU6Lp8QkaEilQBTpkzBuXPnZOrGGtOOHdAw6b5Q52gQ\nF42XL14gKytLRKlk14IFC6CkpITNmzdzHUVqREREQE9PT+pecv3w4UPMnj0bgYGBaNmyJddxCKhI\nJUKbNm1gaWmJ4OBgrqOIzJyZM6AUeBSorKjbCV6/QINHsSgrK0PXrl1hYmKCRYsW4cqVKygvLxdt\nWCm3b98+XL16FWfOnJHKKUquSONNRq9fv4azszO8vLzQpUsXruOQ/0dFKiHc3Nzg7e3NdQyR6dy5\nM0w6dwYiAup0fMM/DmLaVDecOXMGOTk5OHbsGLS0tODp6QldXV04OTnBy8tL7jdtuHLlClavXo3g\n4GCJ2PpSWhQUFCAkJATjx4/nOkqNlZWVYeTIkZg5cybGjBnDdRzyN7TXroQoKSmBnp4enjx5ghYt\nWnAdRySCg4Mx/vuFKD15G2hai9c4PXsM9Zn98ODmDRgZGf3rl3NzcxEeHo6QkBCEhYWhadOmGDJk\nCBwcHGBnZwdVVVURfgrJ9ezZM/Tq1QtnzpxB3759uY4jVQ4dOoTQ0FCcP3+e6yg1whjDlClTUFlZ\niTNnztDNRRKGRqQSQkNDAyNGjICvry/XUUTG0dERcyeOg/pcByDvXc0OSkuC+tyhOLhjxydLFACa\nNWuGCRMm4MSJE3j9+jVOnjyJZs2aYdWqVdDV1cXw4cOxd+9epKWlifDTSJb8/Hw4Ojpi9erVVKJ1\nIG3Tuhs3bsTTp09x7NgxKlEJRCNSCRIVFYUffvgBjx49kplvFsYYli1fgd0nfFEyewUwxAVQ+cSI\nseADFAK9oXZ0A7y2boGr65Q6XS8vLw8REREICQlBaGgotLS04ODgAAcHB/Tp00cm7nCsqqrC8OHD\nYWhoiF27dnEdR+qkpqaiZ8+eePnyJZSUlLiO81UXLlzAvHnzEBsbi9atW3Mdh3wCFakE4fP50NfX\nR0BAACwtLbmOI1JhYWFYu30n7t+7hyonV1QamgNqGkBJIZTvXYNiZCAchg7Dbz8vRNeuXUVyTT6f\nj0ePHglKNS4uDj179hQUq4GBgUiuU98WLFiApKQkXLp0CQ0bNuQ6jtRZvnw5CgsLsWPHDq6jfNWj\nR48wYMAAXLx4Ed27d+c6DvkMKlIJI03f5HWRlpaGw8e88ST9OYpKSpCemgpzI0Mc3O8FXV1dsV47\nPz//o9GqmpqaYG21b9++UFdXF+v1ReHQoUPYsmULYmJi0KRJE67jSB1p+mH17du36N69O9avX48J\nEyZwHYd8ARWphJG2aSdhbd++Henp6di9e3e9XpcxhoSEBISEhCAkJAT3799Hjx49BMVqZGTEyfQ6\nY+yz17127RpcXFxw48YNGBoa1nMy2SAtyyfl5eXo378/+vbtizVr1nAdh3wF3WwkYTp27AgDAwOE\nhIRwHaVemJiYICkpqd6vq6CgADMzMyxZsgRRUVHIzs7G7Nmz8eTJEwwcOBD6+vqYO3cugoODUVws\n5A5NX5Cfn4+dO7bD3Ewf2tqqaNCgAZo0UUevnmbw8fERbNKRnp6OcePGwdfXl0pUCH/dZCTJJcoY\nw+zZs/HNN99g1apVXMchNUAjUgkkbbfmC+Ply5ewsrJCTk4O11EEGGNITEwUTAHfuXMH1tbWgrXV\nzp07C/0XcWlpKX5ZNB+nTp+GQ19FzJ5SCnNjQEMdKCwCrscCXic08fAxMHv2fPxx/s8bTubNmyei\nTyl/pOURsy1btsDX1xc3b96EhoYG13FIDVCRSqCCggK0bdsWaWlpaNasGddxxIoxhsaNGyM9PV1i\nP2tRUREiIyMF08AABFPA/fv3r/WryvLy8jDUoQ866KVi24oyfPOFR2yfpQMT5zVAcZkeHsWnQFlZ\nWZiPItd8fHxw5swZXLx4keson3Xx4kW4u7sjJiYGbdq04ToOqSGa2pVAjRo1goODA86cOcN1FLFT\nUFCAsbExJ9O7NaWlpQVnZ2fs378fGRkZCA0NhZGREfbu3YtWrVqhX79+2LRpExISEr76OryysjKM\ncB4IG/MUnNz95RIFAAN94EZANdrrvcPcOdNl7nV79cnb2xtTp07lOsZnJSYmYtq0aTh//jyVqJSh\nIpVQsvhGmM/hap20LhQUFNC5c2f89NNPuHz5Ml6/fo2ffvoJmZmZcHZ2Rps2beDu7g5/f38UFBT8\n6/g9u3dBW+0Jtq2oQE1nh1VVgXP7SxF9IxDh4eEi/kTyISsrC3FxcXB0dOQ6yie9f/8ejo6O2Lp1\nK2xtbbmOQ2qJilRCDRw4EC9fvsSTJ0+4jiJ2xsbGSExM5DpGnWhqan60k1JERARMTExw8OBB6Onp\noU+fPtiwYQMePXqE6upqeHltw/IFPCjW8jtPUwP4eVYJ9u7ZKJ4PIuN8fHzg4uIikdtHVlRUYPTo\n0XBxccGUKXXbiIRwi9ZIJdjixYuhqKiIDRs2cB1FrMLCwrB582ZERERwHUWkSktLERUVJVhbzcvL\nQyvdYiREVtZ4NPp3JaVAm26quP/gCdq1ayfyvLKKMQYjIyOcOHECNjY2XMf5CGMMHh4eePPmDQID\nA6FY25+wiESgPzUJ5ubmBh8fH1RXV3MdRaykeUT6Jerq6hg6dCh2796N1NRU9O9ngzmudStR4M87\nescMY/D39xdtUBkXExMDBQUFWFtbcx3lX3bt2oXY2Fj4+vpSiUox+pOTYCYmJmjVqpXMjdT+SU9P\nDyUlJcjLy+M6iliVlhSirZ5w52j3bTnevn0tmkByQlKfHQ0NDcWGDRsQFBRU6zu/iWShIpVw8nDT\nkTTcuSsKlVWVEHZrXKWGQHk5TzSB5EBZWRn8/Pwkbu3x6dOncHV1hZ+fH03TywDa8VrCTZgwAZ6e\nnigoKJCatd26MDExQWJiInr16sV1FLFp0qQZcj8Id44374E9hw4gLCwShoaGMDIy+ujfzZs3l7iR\nF5eCgoJgaWmJb7/9lusoAnl5eXB0dMTGjRtl+v93eUJFKuGaNWuGfv36wc/PDzNnzuQ6jtjIw4i0\nT59hCAy7jkmjSup0PGNA0GUNXLoUgBYtWiAlJQXJycm4ceMGDh8+jOTkZDDGYGho+FG5GhoawsDA\nQC53yZG0945WVlZi7NixcHZ2xrRp07iOQ0SE7tqVAgEBAfj999/RyUgPKSlPUVxcCi0tDRgadobH\nrIXo37+/1N+oEBoaii1btsj0enBhYSHatWuBx1d4aFWHHequ3AAWrG6L+ITnnx11vn//HikpKYKS\n/evfaWlp0NHR+dcI1tDQEO3atUODBg2E/HTcKS4uhq+vLw4ePI43b3JQVVUFLa1G6NGjOwIC/PD6\n9WuJ+SFi7ty5yMzMRFBQkFT/npOPUZFKMMYY9u3dg+3b/wNFvMHiuYCVGaClCRQVA7EPgX0nNMEr\n18KiRcvh7jFLaqf1srKyYGNjg1evXnEdRazmzpmOpionsHZJ7e7EZgxwnqYOB+fNmDN3bq2vW11d\njRcvXnxUrn8V7ps3b9C+ffuPylUapooLCgqwZMky+PichIJCO5SUmAJoDKABAB4UFVOgoHAPXbt2\nxbZt69GzZ09O8+7duxf79u3D7du3oa2tzWkWIlpUpBKqqqoKM2dMRlJCMHavKUV3S3zysQnGgNv3\ngPme6rCyHg2v/cek8iddxhgaNWqEzMxMmX7PZkZGBmxtLHBkSwGG9q/5cVv3N8CxP9ogJjYempqa\nIs3E4/GQmpr6UbkmJyd/dqrYyMgIHTt25HSU9/LlS9jZDUB2tjYqKnoB+Nz3dDWARKipReLQoT2Y\nNGlSPab8n4iICEyePBnR0dHo0KEDJxmI+FCRSiDGGDzcXZGV5g//w6XQqMH7potLAKdp6jA2m4jd\new5K7CjiS6ytrbFt2zbORw7idvv2bTg7DcTe/5Rg7Fd2rGMMWLerIQ6dboIbN+/X+00ztZ0qNjIy\nQtu2bcX6w1x+fj4sLbvjxYu2qK7uCaAm/6+/hZraaZw9e7zetwlMSUlB7969cfbsWdjb29frtUn9\noCKVQP7+/ljh6YpbF0qgVYvBR0EhYO2ogS3bzmD48OHiCygm06dPh42NDTw8PLiOInZxcXEY4TwY\n7fR4mOtahBFDgL+/2KWoGDh5/s+pezWNNgi8cBmtWrXiLvA/VFdXIysr65Ml++bNG+jr639yPVYU\nU8WTJrnhjz9SUFExpJZHZkNd/Sxevaq/vwM+fPgAGxsbLFq0CO7u7vVyTVL/qEglUL++3TB7/D24\nONX+2BN+wOlLvRASekP0wcRsy5YtePnyJXbs2MF1lHpRWVmJCxcuYN/ejUhKSkRnA+U/30daDDx+\nUo5+/ewxd94v6Nu3r1TNMPxzqvjv//5rqvifJWtgYAB19a9PveTl5aF167YoK5sLoAZTNf+grn4B\n69dPxQ8//FCHT1Y7VVVVGDZsGDp16oSdO3eK/XqEO1SkEubJkyfo368rMmJ4qMurJ8vKgG+7qSIm\n9rHUrcWEhIRg27ZtuHz5MtdR6l16ejoyMjJQUlICbW1tGBoaomXLllzHEinGGHJzc/9VrikpKUhL\nS0Pz5s3/NYL951Txli1bsXz5afB4dZ2ezYSe3jVkZaWK/YeTH3/8EU+fPsXFixfRUNidOIhEoz9d\nCXPypDfcxlTWqUSBP1+5NXlUNXxPnsDyFatEG07M5OFZ0s/R19eHvr4+1zHESkFBATo6OtDR0UGP\nHj0++rW/TxX/Va4XL15EcnIy3r59C319fRgaGiIq6hZ4vGFCpGiD/Pwy3L9/H1ZWVsJ9oC84ePAg\nwsLCEBMTQyUqB+hPWMJkv0xHH4sqoc5hqF+JR8+fiyhR/WnTpg0KCwuRn5+Pxo0bcx2H1KMGDRqg\nffv2aN++PQYPHvzRr5WWliI1NRUpKSm4dOkygGZCXEkBioo6yM7OFluRXr16Fb///jtu3rxJ/x/L\nCel+il8GlZWVQthXJqqqADxe3XbP4dJfL82W11Ep+TR1dXWYmZlhzJgxUFBgEPbnf8YaoKysTDTh\n/iEtLQ3jx4+Hr68vDAwMxHINInmoSCVMo0bN8CFfuHPkFwKNGzcXTaB69teeu4R8irq6FgDhSlBR\nsVwsI8WCggI4OjpixYoVGDBggMjPTyQXFamE6d7dDmHXhHvgPjRKE1bdpPNZTHleJyVf161bNwCp\nQpyhDGVlWTA3NxdVJAB/rvFOmDABffv2xdw67DxFpBsVqYQZP2ECbt7lI/Nl3Y5/lg48fAyMHTtW\ntMHqCY1IyZf88suP0NR8BKBuDxsoKMRjwIABaNGiDpsdf8HixYtRUVEhN49ukY9RkUoYDQ0N9O8/\nALuP1u34nUeAwUOGQlXYhVaO0IiUfEmfPn3QoEEZgKw6HM2gofEIv/yyQKSZjh49iqCgIJw7dw5K\nSkoiPTeRDlSkEuTDhw9wd3fH9euxOHZWDVdquadCSCRw5oIawsOjMG/ePBQWFoonqBi1adMG+fn5\nyM8XcqGYyJzHjx/Dzs4OurpNoKoaDKB2N9QpK1+BsXF72NnZiSzTjRs3sHTpUgQHB6Np06YiOy+R\nLlSkEoAxBj8/P5iYmEBJSQnJycnwDwjB+LnqCIms2TmCwgDXH9URFByBp0+foqKiAiYmJggMDBRv\neBFTVFRE586d8eTJE66jEAlRVlYGT09P9O3bF1OnTsXTp0/w00+zoa7uC6CgBmdgUFa+glat3iA0\nNEhkGzE8f/4cLi4u8PHxQadOnURyTiKlmBzR1tZm+fn5XMf4SFZWFnN0dGTGxsbs5s2bH/1adHQ0\n+0a3EXNxVmdR58H42WDs1f/+4WeDXTkHNnq4BmvZojG7c+fOR8dHRUUxQ0NDNmrUKJadnV2fP2c3\n8QAAIABJREFUH0sobm5u7NChQ1zHIBLgc/8P8/l8tnnzFqaqqs2UlHoz4EcGrPzHP78xwJlparZj\nXbrYsNzcXJHlKiwsZKampmzHjh0iOyeRXlSkHKmqqmK7du1izZo1Y6tWrWJlZWWf/Lr8/Hy2a+dO\n1slIjxkbaTJXFw02b5oqc3XRYJ0MNJmJcVu2d88eVlBQ8MnjeTwe8/T0ZDo6OszLy4tVV1eL82OJ\nxMaNG9nChQu5jkE4lJeXx2bMmMH09PRYQEDAZ7/u2bNn7IcfFjJNzcZMS8uIqatbM1VVW6apaclU\nVbWZnd0A9t///pdVVVWJLFtVVRVzdHRk7u7ujM/ni+y8RHrRXrscSEhIgLu7O5SVlXHw4MEaTQsx\nxhAdHY3U1FQUFhYK9mO1tbWt0VTV48eP4e7ujoYNG+LgwYPo3LmzKD6KWFy8eBG7du1CWFgY11FI\nPWP/v8yxYMECjBw5EuvXr6/RS7B5PB4uX76MN2/eoLy8HE2aNIGtra1Ytl1cunQpYmJiEB4eDuW6\n7uVJZAu3PV6/uB6R8ng89ttvvzEdHR124MCBeh8dVlVVsT179jAdHR22cuXKz46CuZaens709PS4\njkHqWWZmJhs+fDgzNjZm0dHRXMf5pOPHjzN9fX327t07rqMQCUI3G9WTqKgomJmZITk5GfHx8fDw\n8ICiYv3+9jdo0ADz5s3Dw4cP8eDBA1haWiI6OrpeM9RE27Zt8eHDBxQU1ORGEiLtqqursWvXLnTp\n0gXdu3fHw4cP/7WpvSS4ffs2Fi1ahKCgIOjo6HAdh0gQ2rRezPLy8rB48WKEhYVh7969cHKqw0tG\nRUxPTw+BgYHw9/eHi4sLnJycsGHDBs6nvP+iqKiITp06ISkpCba2tlzHIWL092WOmzdvSuzdr1lZ\nWRg9ejSOHTsGExMTruMQCUMjUjFhjOHs2bMwNTWFqqoqEhMTJaJE/6KgoIDRo0cjMTERfD4fJiYm\nCAgI4DqWgImJCW3MIMN4PB6WLVuGfv36YcaMGYiKipLYEi0uLoaTkxN+/vlnDBsmzCvciKyiEakY\nZGVlYe7cucjIyMD58+clelTVuHFjHDhwANevX4eHhwdOnDiBPXv2oHXr1pzmMjY2pq0CZdTVq1fh\n4eEBCwsLxMfHS/QLzPl8PlxdXdGlSxf89NNPXMchEopGpCJUXV2NnTt3okuXLrCxscGDBw8kukT/\nzs7ODo8ePYKZmRksLCzg5eUFPp/PWR4akcqevLw8zJgxA66urti6dSv8/PwkukQBYPny5Xj79i28\nvLxEtpEDkT1UpCISHx+PHj16wN/fH9HR0fD09JS6W+NVVFSwatUqREVF4eTJk+jduzdnZUYjUtnB\nGMOZM2dgYmICdXV1iVvm+JxTp07h5MmT8Pf3h4qKCtdxiCTj+rbh+iSOx19KS0vZ0qVLWfPmzdmh\nQ4ekYsODmqiurmb79u1jOjo6bPny5fX+qEx1dTVTV1f/7EYTRDpkZmayoUOHMhMTE3br1i2u49RY\nbGws09HRYY8ePeI6CpECNCIVQmRkJMzMzJCeno74+HjMnDmz3h9pERdFRUXMmTMHcXFxiI+Ph4WF\nBW7cqOUu+kJe/687d4n0+fsyh62trVQtc7x8+RKjRo3CkSNHYGZmxnUcIgXoZqM6yM3NxS+//IKI\niAjs3bsXjo6OXEcSm9atWyMgIAD+/v6YMGEChg0bho0bN6Jx48Ziv/Zf66Q2NjZivxYRnUePHsHd\n3R3q6uqIjo6GkZER15FqrLS0FCNGjMD8+fOlYvqZSAbZGD7VE8YYTp8+DVNTU2hqaiIxMVGmS/Tv\nRo0ahcTERCgqKsLExATnz58HE/PukrROKl14PB5+/fVXDBw4EB4eHoiMjJSqEmWMYerUqejcuTOW\nLFnCdRwiRWhEWkOZmZmYM2cOXrx4gYCAALkcJTVq1AheXl6YNGkS3N3d4ePjgz179kBPT08s1zMx\nMcG+ffvEcm4iWleuXMGsWbPQtWtXxMfHo0WLFlxHqrXVq1fjxYsXuHr1Kt2hS2pFLkakfD4fubm5\n4PP5eP/+Paqqqmp8bHV1NbZv346uXbuiV69eePDggVyW6N/16tULcXFxsLS0hKWlJfbu3SuWR2Vo\nRCr5cnNzMW3aNEybNg3bt2/H2bNnpbJE/fz8cOTIEQQEBEBVVZXrOETacHyzk1hlZWWxpb95skbf\ntGAqjRozNG7GVBo3ZeqNm7A5Py5gycnJXzz+4cOHzMrKitnb23/1a+VVUlIS69mzJ7O1tWUJCQki\nPXdVVRVTU1OjO3clEJ/PZ76+vqxFixbshx9+YIWFhVxHqrN79+4xHR0d9uDBA66jECklk0VaXFzM\nRk+awlQaN2Eqk+YzBCUyJLL//RP+nCm5/8rUdHSZvcOwf73JoaSkhC1evJg1b96cHTlyhN45+BXV\n1dXMy8uL6ejoME9PT8bj8UR2bktLSxYTEyOy8xHhPX/+nA0ZMoR99913Uv9n8+rVK6anp8fOnz/P\ndRQixWRuajc/Px/WffriYokCyi9noXzZbqCD8cdf1LodKhesA+9yFm61NoWFbQ+8fPkSABAREQEz\nMzNkZmYiISEB06dPp/WSr1BUVMTs2bMRFxeHpKQkWFhY4Pr16yI5N+1wJDmqqqqwfft2WFlZoXfv\n3rh//z6sra25jlVnPB4Pzs7OmDVrFkaNGsV1HCLFZOpmo8rKSjiMHI1Uo+5/FujXClBZBRULNyBH\nuwl6DxoCWwszREdHY9++fbQ5dR20bt0a58+fR2BgICZOnAgHBwds2rQJTZo0qfM5TUxMaJ1UAsTF\nxWHmzJnQ1tbG7du3YWBgwHUkoTDGMGPGDHTo0AG//fYb13GIlJOpEenp06eRUFKJ8qU7v16if1M9\nfTEyWhvieWYWEhMTqUSFNGLECCQmJkJJSQkmJibw8/Or86MyxsbGNCLlUGlpKZYsWYJBgwZh7ty5\nuHLlitSXKACsX78ez549w9GjR2nGiQhNpop04559KHFbBDRoULsDFRSAOcvxLCuL7tgTkUaNGmHf\nvn3w8/PDypUr4ezsjBcvXtT6PDQi5U5ERAS+++47mVvmCAgIgJeXFy5cuAA1NTWu4xAZIDNFev/+\nfWS8eg3Y1XE02ckCFbp6uHjxomiDybmePXviwYMHsLKygqWlJXbv3o3q6uoaH9+uXTu8e/cORUVF\nYkxJ/u79+/dwc3PDjBkzsGvXLpw5cwbffPMN17FEIi4uDh4eHggICECrVq24jkNkhAKr65ybhFm5\nchXWvCwF/6eNdT/Jqb0Yn/0Ap48dEV0wIvD06VN4eHigoqIChw4dwnfffffVYxITE9Gv3wBYWlpB\nU1MTuro66NevD5ydnaGkpFQPqaXL+/fvceKEDx6nPEN+cTGaaGnBrJMRpkyZjKZNm37xWMYYTp06\nhZ9//hkTJkzAmjVroKmpWU/Jxe/Nmzfo3r07Nm3ahHHjxnEdh8gQmRmRvs7NBb+5kD9hNm+JN7m5\noglE/qVTp06IiorC9OnT0a9fP3h6eqKsrOxfX8cYg5+fH7p27YFu3Xrj3bsOCAsDzp/nwcsrBdOn\nL4Oubmt4ev75rkjy54zMmMmu+LajATxvPsIxHWMEGPfH0WadsSzyLlrrd8CEadMRFxf3yeOfP38u\nuDksODgY27dvl6kSLSsrw8iRIzF16lQqUSJyMlOkfFEMrGVg/UfSKSoqwsPDA/Hx8UhOToaZmRmi\noqIEv15eXo7Ro8dj2rRFePBADzzefDA2EIAVAEsAPVBUNAn5+WOxZUs4jI3NER8fz9GnkQxeBw7C\nzmEYAlqZo+xSKnhrvYGJ84ERbsDE+Shd74Oy/6bgXNNO6DlwMI4d8xYcW1VVha1bt6Jbt26wt7fH\nvXv30K1bN84+izgwxjBr1iy0atUKK1as4DoOkUEy8/hLK51mUMjOgVB1mvsGOk3E/1YTArRs2RJ+\nfn4ICgrClClTMHjwYGzYsAFTpkzHtWvPweNNAfClqVtdlJc7oLz8MXr16ovY2Jvo3LlzfcWXGF77\nD2DR+k0oPXETaNPx81/YtDn4Mxaj1N4R8+cMgYKCAszMvoO7uzsaN26MmJgYdOz4heOl2ObNm5GQ\nkIAbN27IzGsOiWSRmTXSO3fuoN/Y8Si5mArU8ZtF0cUKqs+fYMiQIXBwcMCQIUPEtiE7+Z/CwkIs\nW7YMx4/7oLKyGcrLJ6E2P+MpKMShRYv7yMhIhbKysviCSpg7d+6gr6MzSo/f+HKJ/lPaEzSc0hNa\nisC2bdvg5uYmE3fjfkpwcDBmz56N2NhY+l4mYiMzP55169YNrZs1BaLD6naCZ4+hnfcaT58+hbOz\nM65cuQJzc3N89913WLx4Ma5evYqKigrRhiYAAG1tbWzduhWMKaC8fBhqO1HCmAWKi9UQGBgonoAS\nau3W7eDN+LV2JQoAHTqjetov6DN4CKZOnSqzJZqQkIAZM2bA39+fSpSIlcyMSAHg6NGj+P6wL0oP\nXq71qFTFcyp+MWuPNSv/t4ZSXV2NO3fuICQkBKGhoUhOTkbfvn3h4OAABwcHtGnTRtQfQW6dPn0a\ns2atRlHR+DqeIRFdurzE/fu3RJpLUuXk5KB9p84oC30OaNdhOSLvHVSHGyI7Pe2rd/NKo3fv3qF7\n9+5Yu3YtJk2axHUcIuNkqkjLy8th07c/EjvbovKnTTW+eUjRdzda/7EPj2JufXE7u7dv3yI8PBwh\nISEIDw+Hrq6uYBq4d+/eUFFREdVHkTtWVj1w//63AIy/+rWfVg01tT2Ii4uBoaGhKKNJpA0bN2HV\n/WcoW3mozudQ/3UK1vXrhh9//EGEybhXUVGBAQMGoFevXli3bh3XcYgckJmpXQBQUVFBRPAFtL17\nGSpr5wLl/3604iNVVWjotRo6vttwLfTSV/eE1dXVxeTJk+Hr64ucnBwcO3YM2tra8PT0RPPmzeHk\n5AQvLy9kZGSI7kPJibS0VADCTL81gLJyazx79kxUkSRa3NNklJkKt2F8qWl3JCSniCiRZGCMYc6c\nOWjatCnWrl3LdRwiJ2RqRPqXwsJCjJs6HVHXr6N6xDRUuswG9Nr/7wve56DB+cNQ8TsAE0MDBJ05\nJfTLiN+/f4/Lly8jJCQEYWFhaNKkiWAK2M7OjrYe/ApVVQ2Ul/8AQJjfp5NQUEiTizszq9U0gJUH\nAQchnokM9MbIpEj4nzwhumAc2759O7y9vREdHS1Tz8ESySYzj7/8nba2NkL8/8CzZ8+wy2s/jk3o\nBqasggaa2uCXFKO6pAguLuOw8FIwLCwsRHJNHR0dTJgwARMmTACfz8eDBw8QGhqKVatWISEhAb17\n9xYUa4cOHURyTVmiqqqO8vIKCFOk2tqqOHEiQC5eOjBxhjv8SoTcNrGkCE20tEQTSAKEhIRg8+bN\nuH37NpUoqVcyOSL9p4qKCrx58waFhYX/v82cbr1uVp2XlycYrYaGhkJbW1vweI29vT1tnA3A0tIG\ncXHtAXSq4xmqoa6+F/fvR6NTp7qeQ3qsXbce/4nPRNny/XU+h9pvbviPnSUWLlwgwmTcSEpKgr29\nPQIDA9GjRw+u4xA5IxdFKkn4fD4ePXqEkJAQhISEIC4uDr169RIUq4GBgcw+jvAlPj4+mDdvPYqK\n6jpVmQRz8wzExcWKNJekevXqFfSNTVAengloatf+BPm5UB3aES9Sn0FHR0f0AetRbm4urK2t8fvv\nv8PNzY3rOEQOUZFyLD8/HxEREYJiVVNTE0wB29vbQ0NDg+uI9aKsrAy6uq1QVDQZQLNaH6+ldQYH\nDizHhAkTRB9OQg0b44KQTn3AJs6r9bGKx7ZgVE4C/HyOiyFZ/amsrMSgQYPQrVs3bNq0ies4RE5R\nkUoQxhji4+MRGhqKkJAQ3L9/H7a2toJiNTIykunR6m+/LceOHedQWuoCoObvlFVQSICubgwyM9Pk\n6hGkW7duYeDosSg9EQ20blfzAzOfQd2tN66HXETXrl3Flk/c/rpDNzs7G4GBgWhQ2/cQEyIiVKQS\nrKCgAFeuXBGMVpWUlATPrfbr10/mbqioqqrC4MHDcft2Dng8R9TsXrgn0NQMx+3b12FqairuiBJn\n+85d8Ny5B6UHwmtWplmpUPcYhG2ev2KWh7vY84nT7t27ceDAAdy6dQva2nWY3iZERKhIpQRjDImJ\niYJSvXv3LqytrQVrq8bGxjIxWuXxeBg7diKiouJQUmIDwBCfftw5F8rK96GhkYrLly9J9chKWNt3\n7oLn+g3gzfgVzMkV0Gr07y8q+ACFC8ehdnQDtqxehTmzZ9V/UBEKDw+Hq6srbt26BX19fa7jEDlH\nRSqlioqKEBkZKShWAILRav/+/aElxY818Pl8+Pr6YuPGHXj+PAtlZabg8xvhzxFqKTQ1M6Cg8AYe\nHjPw008L0KqVkO+hlQG3bt3Cuu07EXE5HAqDx6LM2ApQ1wJKi6AaH4Oyi2fg6OQEz0U/oXv37lzH\nFUpycjLs7Ozg5+cHOzs7ruMQQkUqCxhjePLkiWBtNSYmBlZWVoK1VVNTU6kdrT548AA+PqeQlZWN\n8vJy6Og0w4ABfTB27Fi5Wg+tqdevX+OY93E8fpaK/KIiNNHWhpmRIcJCQzBjxgyp33f2w4cPsLa2\nxpIlSzBjxgyu4xACgIpUJhUXF+Pq1auC0WplZaVgtDpgwAA0avSJqT8i086cOYOjR48iPDyc6yh1\nVllZiaFDh8LU1BTbt2/nOg4hAlSkMo4xhpSUFEGp3rp1C126dBGsrZqbm0vtaJXUHI/HQ+vWrREf\nHy+1rxT7/vvvkZqaiuDgYDRsKJObshEpRUUqZ0pLSxEVFSUo1tLS0o9Gq1/buJ9ILw8PD+jr62Pp\n0qVcR6m1/fv3Y+fOnYiJiaEZFSJxqEjl3LNnzwRrqzdu3IC5ublgbdXCwkIuNoCXF9HR0Zg5cyaS\nkpKkahYiMjISEyZMQHR0NDp2rOVLzAmpB1SkRIDH4+HatWuCYi0oKMDgwYPh4OCAQYMGyeQLoOUJ\nYwyGhobw9fWVmjt3U1NT0bNnT5w+fRr9+vXjOg4hn0RFSj4rPT1dsNH+tWvXYGpqKlhb7dq1K41W\npdCaNWuQk5ODvXv3ch3lq/Lz82Fra4sff/wRs2fP5joOIZ9FRUpqpKysDDdu3BCsrebm5n40WpX2\njc/lRUZGBqysrJCdnS3Rjw9VVVVh+PDh6NixI/bs2cN1HEK+iIqU1ElGRoZgCjgqKgqdOnUSrK1a\nWVnRvqcSrG/fvpg/fz5Gjx7NdZTPWrhwIR4/foyQkBC6Q5dIPCpSIrTy8nJER0cLRqs5OTkYNGgQ\nHBwcMHjwYOjq6nIdkfyNt7c3/P39ERQUxHWUTzp8+DA2bdqE2NhYuoucSAUqUiJyWVlZCA0NRWho\nKCIjI2FgYCBYW7W2tqbRKseKiorw7bffIiUlReJ+yLl+/TrGjh2L69evw8jIiOs4hNQIFSkRq4qK\nCty6dUswWs3OzsbAgQMFo9UWLVpwHVEuubq6okuXLliwYAHXUQSeP38OW1tb+Pj4YODAgVzHIaTG\nqEhJvcrOzhasrV65cgXt27cXrK3a2NjQelg9uXLlCn7++WfExcVxHQUAUFhYiB49emDWrFn4/vvv\nuY5DSK1QkRLOVFZWIiYmRjBazcjIwIABAwTTwPRWF/Hh8/lo164dgoODYW5uzmmW6upqODs7Q09P\nD15eXlK1WQQhABUpkSCvX79GWFgYQkJCcPnyZbRp00ZQqj169ICSkhLXEWXKb7/9Bh6Ph23btnGa\nY/Hixbh79y7Cw8Ppz5hIJSpSIpGqqqoQGxsr2BAiNTUV/fv3FxSrtG68LklSUlJgZ2eHFy9ecFZg\n3t7eWLt2LWJjY9GsWTNOMhAiLCpSIhXevHkjGK2Gh4ejVatWgrXVnj17QllZmeuIUqlHjx5YtmwZ\nhg8fXu/Xjo6OxsiRI3Ht2jV07ty53q9PiKhQkRKpU11djbt37wrWVpOTk9G3b19BsbZp04briFLj\nwIEDiIiIgJ+fX71eNzMzE7a2tjhy5AgcHBzq9dqEiBoVKZF67969Q1hYGEJDQxEWFgZdXV3Bq+F6\n9+4t0VvhcS0/Px/t2rVDenp6vb2UoLi4GD179sTUqVOxcOHCerkmIeJERUpkSnV1Ne7fvy9YW01K\nSkKfPn0Ea6vt27fnOqLEGTduHOzt7TFnzhyxX4vP52P06NFo2rQpDh8+THfoEplARUpkWm5uLsLD\nwxESEoKwsDA0adJEMAVsZ2cHVVVVriNy7tKlS1i9ejViYmLEfq1ly5bh5s2biIiIoHVtIjOoSInc\n4PP5ePjwoWBtNSEhAb179xYUa4cOHbiOyImqqip8++23iIqKEuu2fL6+vvj9998RGxuL5s2bi+06\nhNQ3KlIit/Ly8hARESGYBtbS0hJMAdvb20NNTY3riPVm0aJFUFZWxrp168Ry/tjYWDg6OiIyMhKm\npqZiuQYhXKEiJQR/jlYfPXok2L7w4cOH6NWrl6BYDQwMZHo9LyEhAUOHDkVGRobIXyrw4sUL2NjY\nYP/+/XB0dBTpuQmRBFSkhHxCfn7+R6NVVVVVwRSwvb09NDQ0uI4ocl26dMGmTZswYMAAkZ2zpKQE\nvXv3xvjx47F48WKRnZcQSUJFSshXMMaQkJAgWFu9f/8+bG1tBcVqZGQkE6PVnTt34t69e/Dx8RHJ\n+fh8PlxcXKChoQFvb2+Z+D0i5FOoSAmppcLCQly5ckVQrA0bNhQ8t9qvXz9oampyHbFO3r17BwMD\nA7x48QJaWlpCn2/FihW4fPkyIiMj6e5oItOoSAkRAmMMiYmJgrXVO3fuwNraWlCsxsbGUjUSc3Z2\nxogRIzBt2jShznP27FksXrwYd+7cwTfffCOidIRIJipSQkSoqKgIkZGRgtEqAEGp9u/fXyQjPXHy\n9/fHzp07ce3atTqf4969e3BwcMDly5dhYWEhwnSESCYqUkLEhDGGp0+fCko1JiYGVlZWgrVVU1NT\niRutlpeXQ09PD3fu3KnTLlDZ2dmwtrbG7t27MXLkSDEkJETyUJESUk9KSkpw9epVQbFWVFQIRqsD\nBgxAo0aNuI4IAJg/fz6aN2+OFStW1Oo4Ho8HOzs7jBgxAr/99puY0hEieahICeEAYwwpKSmCtdXo\n6Gh06dJF8Nyqubk5Z6PVu3fvYvz48UhNTa1xBsYYJk6cCEVFRZw8eVLiRtqEiBMVKSESoLS0FFFR\nUYJiLSkp+Wi02qRJk3rLwhiDiYkJDhw4gN69e9fomLVr1yI4OBhRUVFytSMUIQAVKSESKTU1VbAZ\nxI0bN2BmZiZYW7WwsICioqJYr79p0yakpKRg3bp1SE1NRVFRETQ0NNC+fXu0bt36o689f/48Fi5c\niNjYWLRs2VKsuQiRRFSkhEg4Ho+H69evC9ZWCwoKMHjwYDg4OGDQoEEif48oYwz+/v6YMX08FBQa\nwKijKrQ0gZJSIDm1HDY23TF33mIMGTIE8fHxGDRoEEJDQ9G1a1eR5iBEWlCREiJl0tPTBVPA165d\ng6mpqWBttWvXrkKNVl+9eoVRIwejMD8Ds6cUw20s0Ej7f7/O4wFng4B9J7SQX6SN4hI+du7cibFj\nx4rgkxEinahICZFiZWVluHnzpmC0+v79+49Gqzo6OjU+V2ZmJvrYdYPHxA/49fsqfO1+oUOngMVr\nVBB1LRbm5uZCfhJCpBcVKSEyJCMjA6GhoQgNDcXVq1fRqVMnwdqqlZXVZ9/sUlRUBBvr7zBz3Ess\n9Kiu8fXOBgGL1jTDnbsJtD5K5BYVKSEyqqKi4qPRak5ODgYNGgQHBwcMHjwYurq6gq/duWMHrkcs\nw/lDvFpf58flSlBpPA+bNm8XZXxCpAYVKSFy4sWLF4K11cjISBgYGGDIkCEYMmQIpk9zweFNr9Db\nuvbnTcsAbJw0kZX1lh59IXKJipQQOVRRUYFbt24hNDQU586dA6qeIy0GX10X/RyHyZoY77oHbm5u\nog1KiBRoyHUAQkj9U1ZWhr29Pezt7dGwoSIalK6vc4kCwOihxbga+V8qUiKXxPtUNyFE4uXl5qB5\nM+HOodMU+PDhnWgCESJlqEgJkXNKSsqoqvmNup9UWQk0bKgkmkCESBkqUkLknK6uHrKyhVvlefEK\naN689de/kBAZREVKiJwbPWYMTgUqoaKibsczBnj7acJlnKtogxEiJahICZFznTp1gomJKfwv1e34\n6LtARVUj9O3bV7TBCJESVKSEEMydtwSbvDRQVla746qrgf/sUsOcOYvoHaREbtFzpIQQ8Pl8jB/n\nDJRfge8eHpRqcN8QY8CPy5UR/8wcYeE3oKKiIv6ghEggGpESQqCoqIgTPn4oqbKG0zR1vHz15a9/\nlwtM+UEVdxIMERAYRiVK5BoVKSEEAKCqqooLQZdh2X02zAepY9RMDVy+/ud7SBn78xVqt+4CU35Q\nh2FvVWjpjEPk1Vg0adKE6+iEcIqmdgkh/1JcXAzfkydx4MBWPHmagYqKajRsqIgO+q0wc+YPmDpt\nushfKE6ItKIiJYR8VWVlJRo2bEg3FBHyCVSkhBBCiBBojZQQQggRAhUpIYQQIgQqUkIIIUQIVKSE\nEEKIEKhICSGEECFQkRJCCCFCoCIlhBBChEBFSgghhAiBipQQQggRAhUpIYQQIgQqUkIIIUQIVKSE\nEEKIEKhICSGEECFQkRJCCCFCoCIlhBBChEBFSgghhAiBipQQQggRAhUpIYQQIgQqUkIIIUQIVKSE\nEEKIEKhICSGEECFQkRJCCCFCoCIlhBBChEBFSgghhAiBipQQQggRAhUpIYQQIgQqUkIIIUQIVKSE\nEEKIEKhICSGEECFQkRJCCCFCoCIlhBBChEBFSgghhAiBipQQQggRAhUpIYQQIgQqUkIIIUQIVKSE\nEEKIEKhICSGEECFQkRJCCCFCoCIlhBBChEBFSgghhAiBipQQQggRAhUpIYQQIgQqUkJFlVoZAAAA\nyklEQVQIIUQIVKSEEEKIEKhICSGEECFQkRJCCCFCoCIlhBBChEBFSgghhAiBipQQQggRAhUpIYQQ\nIgQqUkIIIUQIVKSEEEKIEKhICSGEECFQkRJCCCFCoCIlhBBChEBFSgghhAiBipQQQggRAhUpIYQQ\nIgQqUkIIIUQIVKSEEEKIEKhICSGEECFQkRJCCCFCoCIlhBBChEBFSgghhAiBipQQQggRAhUpIYQQ\nIgQqUkIIIUQIVKSEEEKIEKhICSGEECFQkRJCCCFC+D9LTTgVanivRgAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x4ca2610>"
]
}
],
"prompt_number": 6
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A 4-colouring of a 3-regular graph is still in accordance with Theorem 1. We might, though, do better by experimenting a little with node orderings or colour choice strategies. The first thing worth trying would be a few random orderings, hoping to hit upon one that uses only 3\n",
"colours."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"random.seed(1)\n",
"\n",
"G = nx.dodecahedral_graph()\n",
"nodes = G.nodes()\n",
"random.shuffle(nodes)\n",
"vcolour(G, nodes = nodes)\n",
"nlist = [[2,3,4,5,6],[8,1,0,19,18,17,16,15,14,7],[9,10,11,12,13]]\n",
"nx.draw_shell(G, nlist = nlist , node_color = colours(G), **options)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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buXKlyo6klElJSQn74YcfmJmZGdu4cSMTCoVcR6q069evs9q1a7Nbt25xHYWo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\nuwAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x4e94390>"
]
}
],
"prompt_number": 7
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As luck would have it, we have hit upon a 3-colouring straight away, without much effort."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Improved Vertex Colourings"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In this section we do a little experiment to test the following theorem of Dominic A. Welsh and Martin B. Powell.\n",
"\n",
"**Theorem**\n",
"\n",
"Let $G$ be a graph of order $n$ whose vertices are listed in the order $v_{1}, v_{2}, ... v_{n}$. Then\n",
"$$\\chi(G) \\leq 1 + \\min_{1 \\leq i \\leq n}\\{\\max{\\{i - 1, deg v_{i}\\}\\}} = \\min_{1\\leq i\\leq n}{\\max{\\{i, 1 + deg v_{i}\\}}} $$\n",
"\n",
"This gist here being that we should do better if vertices are listed in order of their degree going from largest to smallest."
]
},
{
"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.\n",
"\n",
"For each ordering we calculate a total discrepancy over all graphs. That means that for each graph we calculate the difference between $\\Delta + 1$ and the number of colours used by the greedy algorithm. For each ordering we total these discrepancies over all graphs and then look at that total as a proportion of the number of graphs.\n",
"\n",
"We expect a total discrepancy between 1 and 2, with lower values representing better colourings."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import random\n",
"\n",
"disc_inorder = 0\n",
"disc_random = 0\n",
"disc_decdeg = 0\n",
"disc_incdeg = 0\n",
"\n",
"graphs = nx.graph_atlas_g()\n",
"\n",
"def ncolours(G):\n",
" \"\"\"Counts the number of different colours used on vertices in G.\"\"\"\n",
" return len(set(colours(G))) \n",
"\n",
"def clear_colouring(G):\n",
" for v in G.node:\n",
" if G.node[v].get('colour')!=None:\n",
" del G.node[v]['colour']\n",
"\n",
"for G in graphs:\n",
" nodes = G.nodes()\n",
" inorder_nodes = nodes\n",
" random_nodes = random.shuffle(nodes)\n",
" inc_deg_node = sorted(G.nodes(), key = G.degree, reverse = True)\n",
" dec_deg_node = sorted(G.nodes(), key = G.degree, reverse = False)\n",
" degseq = G.degree().values()\n",
" vcolour(G, nodes=inorder_nodes)\n",
" if degseq != []: disc_inorder += max(degseq) + 1 - ncolours(G)\n",
" clear_colouring(G)\n",
" vcolour(G, nodes=random_nodes)\n",
" if degseq != []: disc_random += max(degseq) + 1 - ncolours(G)\n",
" clear_colouring(G)\n",
" vcolour(G, nodes=dec_deg_node)\n",
" if degseq != []: disc_decdeg += max(degseq) + 1 - ncolours(G)\n",
" clear_colouring(G)\n",
" vcolour(G, nodes=inc_deg_node)\n",
" if degseq != []: disc_incdeg += max(degseq) + 1 - ncolours(G)\n",
" \n",
"print \"Total discrepancy for in order: {}\".format(1.0*disc_inorder/len(graphs))\n",
"print \"Total discrepancy for random order: {}\".format(1.0*disc_random/len(graphs))\n",
"print \"Total discrepancy for increasing degree order: {}\".format(1.0*disc_incdeg/len(graphs))\n",
"print \"Total discrepancy for decreasing degree order: {}\".format(1.0*disc_decdeg/len(graphs))\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Total discrepancy for in order: 1.86671987231\n",
"Total discrepancy for random order: 1.89944134078\n",
"Total discrepancy for increasing degree order: 2.00478850758\n",
"Total discrepancy for decreasing degree order: 1.72705506784\n"
]
}
],
"prompt_number": 8
},
{
"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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