{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "source": [ "%pylab inline\n", "import numpy as np\n", "from conway99 import *\n", "import pickle" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# A representative seed graph\n", "We start from an arbitrary vertex and its neighbours. These can necessarily be arranged as 7 blades of a fan; we fix a numbering with vertex 0 the centre, 1-14 its neighbours, and blade edges 1-2, 3-4, 5-6, 7-8, 9-10, 11-12, 13-14" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "seed15 = np.empty((15,15), dtype='int')\n", "for i in range(15):\n", " for j in range(15):\n", " seed15[i,j] = 0\n", "\n", "# 1-14 all nhbrs of 0\n", "for i in range(1,15):\n", " seed15[0,i] = 1\n", " seed15[i,0] =1\n", " \n", "# By fixing an ordering, a single representative suffices\n", "for i in [1,3,5,7,9,11,13]:\n", " seed15[i,i+1] = 1\n", " seed15[i+1,i] = 1" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[0 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n", " [1 0 1 0 0 0 0 0 0 0 0 0 0 0 0]\n", " [1 1 0 0 0 0 0 0 0 0 0 0 0 0 0]\n", " [1 0 0 0 1 0 0 0 0 0 0 0 0 0 0]\n", " [1 0 0 1 0 0 0 0 0 0 0 0 0 0 0]\n", " [1 0 0 0 0 0 1 0 0 0 0 0 0 0 0]\n", " [1 0 0 0 0 1 0 0 0 0 0 0 0 0 0]\n", " [1 0 0 0 0 0 0 0 1 0 0 0 0 0 0]\n", " [1 0 0 0 0 0 0 1 0 0 0 0 0 0 0]\n", " [1 0 0 0 0 0 0 0 0 0 1 0 0 0 0]\n", " [1 0 0 0 0 0 0 0 0 1 0 0 0 0 0]\n", " [1 0 0 0 0 0 0 0 0 0 0 0 1 0 0]\n", " [1 0 0 0 0 0 0 0 0 0 0 1 0 0 0]\n", " [1 0 0 0 0 0 0 0 0 0 0 0 0 0 1]\n", " [1 0 0 0 0 0 0 0 0 0 0 0 0 1 0]]\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "C:\\Users\\Graeme\\Anaconda3\\lib\\site-packages\\networkx\\drawing\\nx_pylab.py:611: MatplotlibDeprecationWarning: isinstance(..., numbers.Number)\n", " if cb.is_numlike(alpha):\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# review\n", "print(seed15)\n", "plot_given_edges(seed15)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# Verify some details\n", "assert len(seed15)*len(seed15) == num_known_zeros(seed15) + num_known_ones(seed15) + num_unknowns(seed15)\n", "assert not(has_unknown_values(seed15))\n", "assert lambda_compatible(seed15)\n", "assert mu_compatible(seed15)\n", "assert meets_adjacency_requirements(seed15, debug=True)\n", "assert graph_is_valid(seed15)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Adding vertex 15\n", "(NB, as we started numbering at 0, this is our 16th vertex)\n", "\n", "wlog, we let this be a neighbour of vertex 1" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0]\n", " [1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1]\n", " [1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 2]\n", " [1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 2]\n", " [1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 2]\n", " [1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 2]\n", " [1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 2]\n", " [1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 2]\n", " [1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 2]\n", " [1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 2]\n", " [1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 2]\n", " [1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 2]\n", " [1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 2]\n", " [1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2]\n", " [1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 2]\n", " [0 1 2 2 2 2 2 2 2 2 2 2 2 2 2 0]]\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Generate template with an additional vertex, and review\n", "seed16 = get_supermatrix_template(seed15, forced_edges=[(1,15)])\n", "print(seed16)\n", "plot_given_edges(seed16)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Wall time: 32.9 ms\n" ] } ], "source": [ "# Fill in the template\n", "%time super16 = templates_to_valid_graphs([seed16], verbose=0)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\t1 reps from 1 candidates\n" ] } ], "source": [ "# Reduce to eliminate equivalent graphs\n", "rep16 = reduce_mod_equivalence(super16, verbose=True)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Turns out, there's only really one way to extend this! Let's take a look\n", "plot_given_edges(rep16[0])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This was expected:\n", "\n", "By mu=2 condition, as 15 is not a nhbr of 0, they have 2 mutual nhbrs\n", " * As the nhbrs of 0 are 1-14, 15 nhbrs two of these.\n", " * We assumed 1-15 already; this prevents 2-15 (else 1,2 are nhbrs with two mutual nhbrs - 0, 15 - violating lambda=1) \n", " * So 15 nhbrs precisely 1 of vertices 3-14, and these 12 choices are equivalent\n", " * So to fix notation we can force this nhbr to be vertex 14\n", " \n", "Moreover, we could have applied this at the template stage to reduce the search space." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0]\n", " [1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1]\n", " [1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 2]\n", " [1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 2]\n", " [1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 2]\n", " [1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 2]\n", " [1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 2]\n", " [1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 2]\n", " [1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 2]\n", " [1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 2]\n", " [1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 2]\n", " [1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 2]\n", " [1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 2]\n", " [1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2]\n", " [1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1]\n", " [0 1 2 2 2 2 2 2 2 2 2 2 2 2 1 0]]\n" ] }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAd0AAAE/CAYAAAADsRnnAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4zLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvnQurowAAIABJREFUeJzs3XdYFFcXB+DfWoEgRWkCxt4Vu7EgsUZBumAHS2KMxtg1mqjRxIREMZqY2KIRQRQFBZGiQVTsnygholHsUVBAikgXds/3x0YDSllgd2cXzvs8PMrszL1nh5k9O/feuSMiIgJjjDHGFK6O0AEwxhhjtQUnXcYYY0xJOOkyxhhjSsJJlzHGGFMSTrqMMcaYknDSZYwxxpSEky5jjDGmJJx0GWOMMSXhpMsYY4wpCSddxhhjTEk46TLGGGNKwkmXMcYYUxJOuowxxpiScNJljDHGlISTLmOMMaYknHQZY4wxJakndACMMQGlpABeXsC1a0BmJqCrC1hYANOmAYaGQkenHngfskoQEREJHQRjTMmiowEPDyA8XPp7fv5/r2lqAkSAtTWwfDnQp48wMao63oesCjjpMlbbbN0KLF4M5OVJE0NZRCJp8vD0BGbNUl586oD3IasiTrqM1SavkkVuruzbaGlx0iiO9yGrBk66jNUW0dHA4MFvJYvBAC7hvwEeZgDi39xWSwuIigJ691ZwkCqulH2o/cYqeQBmA9j85ra8Dxl49DJjtYeHh7Q5tBS/AMj+9+ethAtIt/PwUFxs6qKUfZhd7CcZgCYA19K25X3IwEmXsdohJUU64KeqDVtEQFgY8OyZfONSJzLswwAARgAGlfYi70MGTrqM1Q5eXuW+vByAAYCBAE6XtZJIVGE5NZoM730PAHcAorJWqO37kHHSZaxWuHat5C0txfwA4D6ARAAfA7ADcK+0FfPygLg4RUWo+srZhwDwCEAUgCnllVHb9yHjpMtYrZCZWeZL7wFoBKAhpAljIICwslbOyJB3ZOqjnH0IAN4ALAG0rKic2rwPGSddxmoFXV2ZVxUBKLPXUl9fHtGopwr2oTcquMp9pTbvQ8ZJl7HaoLBjRxTVr//W8ucAjgPIB1AEwBfAGQAjSytEUxPo2lWBUao4CwtAQ6PUly5A2jxf6qjlYqi270PGSZexmuzJkydYsWIFum3cCIlY/NbrhQBWADCEdCDVZgBBANqXVhgRMHWq4oJVdeW89z0AnCFtpi9PQX4+fOrWRX45fcOsZuOky1gNFBMTAzc3N3Tp0gXPnz/HkYsX0cDBQTp6thhDANEAsiC96r0EYERpBYpEgI1N7Z7A38hIOpey6O2xydsB+FSwOYlEyLK0hF9kJFq2bIlvv/0W6enpCgmVqS5OuozVEGKxGIGBgXj//ffh6OgICwsL3Lt3D7/88gvatm0rnXhfU7NqhWtqSrev7aqxD0WamjD88UeEhoYiIiICd+7cQZs2bTBv3jw8fPhQvnEylcVJlzE19+LFC/z0009o164dfvjhB8yePRv37t3DkiVLoF980E6fPtL5f7W0KlfBq3mDefpCue3DLl26wMvLC3FxcWjYsCF69eqFiRMn4s8//1RA0EylEGNMLT148IAWLFhAjRs3prFjx9LFixdl23DLFiItLSKRiEjaU1v6j0gkXW/LFsW+EXX07z6UyGkfZmZm0vr168nc3JyGDRtGx44dI4lEoqQ3w5SJH3jAmBohIpw/fx6bNm3C6dOnMX36dMyZMwfvvvtu5Qq6ckU6D3BYmLSPsth8wkUNGkBcVISGjo7S5lS+wi3dlStIX7IE70RFoaGGRsk5mV89T9fGplL78OXLl/Dz84OnpydEIhEWL16M8ePHo34pI8+ZeuKky5gaKCwshL+/PzZu3Ijnz59j3rx5mDp1KrS133zGTSU9eyadljAuTjppg74+Cjt0QIfvv8fFu3dhZGQkl/hrqmXLlqFRfj6+NDMrsQ/Rtat0tHMVB54REY4fP47169fj9u3bmD9/PmbMmAEdHR35vgGmdJx0GVNh6enp2L59O3799Ve0a9cOCxYswOjRo1GnjmKHY0yYMAFDhgzBxx9/rNB61F2HDh2wd+9e9FZga0BMTAzWr1+PiIgIfPjhh5g3bx5MTU0VVh9TLB5IxZgKunXrFmbNmoU2bdrg9u3bCAkJwcmTJ2FnZ6fwhAsALi4u8Pf3V3g96uzmzZvIyclBr169FFpPz549sX//fly5cgX5+fno0qULpk2bhhs3bii0XqYYnHQZUxFEhIiICNjY2OD999+HkZER/v77b+zevRvdu3dXaizW1ta4fPkyUlNTlVqvOgkMDISjoyNEpdy3qwgtWrTATz/9hLt376JNmzYYPnw4Ro8ejdOnT4MbLNUHNy8zVhUpKdK+0GvXpBPh6+pKpwmcNq3S/Xh5eXnw9fXFpk2bIBKJsGDBAkycOBEaZUw5qCxjx47FyJEj8eGHHwoah6rq27cvvv/+ewwdOlSQ+vPz8+Hj4wNPT0/o6OhgyZIlcHZ2Rr169SpXkByPZSYDYQZNM6amLl8mcnIi0tCQ/hS/PURTU7rMyUm6XgWePn1KK1euJCMjI7KxsaGIiAiVuk3kwIEDNHLkSKHDUEmPHz+mxo0b08uXL4UOhcRiMQUGBtKAAQOoZcuWtHnzZsrOzq54Qzkey0x2nHQZk5Wc7m/9888/acqUKaSvr0+zZs2iW7duKfmNyCYrK4t0dHQoLS1N6FBUzi+//ELu7u5Ch/GW8+fPk6OjIxkaGtLKlSspOTm59BX5Xm3BcJ8uY7LYuhVYvBjIzZV+HJWHSLre4sXS7SCdojE4OBhDhgyBnZ0dOnbsiLt372LLli1o377UxwsITltbG8OHD0dwcLDQoaicV/25qmbAgAEIDAzEuXPnkJycjPbt2+OTTz7BnTt3/lupmscyqyahsz5jKu/yZem3/VKuBPYD1AEgLYBaAXTmjdclmprkt3gxtW7dmvr06UP79u1TiSZJWe3bt49Gjx4tdBgqJS0tjXR0dCgnJ0foUCqUlJREK1asIAMDA3JycqK/du4s9Vh+AJA1QHoAGQP0KUCFbx7vWlpE0dFCvyW1xwOpGKuIszMQFPTWVUEEgI8AHADQF8DTf5ebFVtHDCDa1BTigwcxYMAApY10lZcXL17A3Nwcjx49gp6entDhqAQfHx8cPnwYgYGBQocis5ycHPz+++9ot2wZhufmou4br9sAMAKwDdKnTY0AMAPA3OIriUSAkxNw6JBSYq6puHmZsfKkpADh4aU2w30FYBWAfpCeSGYomXABoC6AfunpGNiundolXADQ0dHBkCFDcPToUaFDURmq2rRcnnfeeQefjRuHDySStxIuADwAMBaABgATAKMAvHUXMJF02tBnzxQbbA3HSZex8nh5lbpYDOAKgGcA2gAwBzAHQF5pK4tEZZajDlxdXREQECB0GCohNzcXkZGRsLW1FTqUyvPyQllf++YB8AOQCyARQDikifctan4sqwJOuoyV59o1ID//rcXJAAoBBAA4CyAWwJ8A1pZWRl6edF5eNWVnZ4dTp07hxYsXQociuIiICPTq1QtNmjQROpTKK+NYBoD3Ib2y1YH0C2RvAKVey6v5sawKOOkyVp7MzFIXv3qM+WcAmgIwALAQQFhZ5WRkyDsypdHV1YWVlRVCQkKEDkVwQUFBcHJyEjqMqinjWJYAGAnAGUAOgFQAGQA+L6scNT6WVQEnXcbKo6tb6mJ9SK8IZO6lLf4weTXETcxAUVERjh49CgcHB6FDqZoyjuV0AI8h7R5pCKAJgGko5wukmh/LQuOky1h5LCyAMqZjnAZgM4AUSK8MNgEotadPU1P6qDc1Zm9vj8jISGRnZwsdimDOnj2LFi1aVP7ZxaqijGPZAEBLAFsBFEE6enkPgG6llVEDjmWhcdJlrDxTp5b50koAfQC0A9ARQA8AX5a2IlG55agDfX19DBgwAKGhoUKHIhi1bloGyj0GDwM4BsAQ0oGB9QBsLG3FGnAsC42TLmPlMTICrK2lozbfUB/AFkivDJIA/AzpLRcliESAjU2NmDjexcWl1jYxExGCgoLU7lahEso5lrsDOA1pi00qAH9I79stoQYdy0LiyTEYq0h0NDB4sHQ6vMrS0gKiogAFPuRcWdLS0tCqVSs8efIE77zzjtDhKFVMTAzGjx+P+Ph4tbzf+jU+lgXHV7qMVaRPH8DTU/qhUwl5deqg0MOjxnxINWnSBO+99x7Cw8OFDkXplP3sXIXp0wf/zJ2LSqdcLS3pOVBDjmUhcdJlTBazZv2XeCv64BWJQFpa2Nu9OyafPw+JRKKcGJWgtjYxBwYGqnd/7r8SExNhuXcvbn30kczH8uuEO2uWcoKs4TjpMiarWbOkzWtOTtJRoJqaJV/X1JQud3KCKCoKbufPIykpCUuWLBEmXgVwcnLCsWPHkJdX6txbNdKdO3eQlpaG9957T+hQqiUnJwd2dnaYPXs2ev72m8zHMqKiOOHKEffpMlYVz55Jp8OLi5NOFqCvL72VYurUEgNNMjIyYGlpiRkzZmD+/PmChStPw4YNw2effabeg4oqYf369bh37x62bdsmdChVJpFIMGbMGOjq6mL37t0lm8llPJaZfHDSZUzBHj16hAEDBmDjxo1wdXUVOpxq27p1K86dOwdfX1+hQ1GKgQMHYtWqVRg5cqTQoVTZ0qVL8b///Q8RERFo0KCB0OHUapx0GVOCv/76CyNGjEBAQACsrKyEDqdakpKS0LFjRzx9+hQaZUwcUlO8eq/Jyclqm6x27tyJH374AZcuXVLPOaNrGO7TZUwJunXrhn379sHV1RV///230OFUi4mJCbp164aIiAihQ1G4I0eOwNraWm0T7smTJ/Hll18iJCSEE66K4KTLmJIMHz4cnp6esLGxwZMnT4QOp1pcXFzg7+8vdBgKp86zUMXHx2PChAnw8/ND+/bthQ6H/YublxlTMg8PDxw4cABnzpyBjo6O0OFUyZMnT9ClSxc8ffoUDRs2FDochcjMzESzZs2QmJiIRo0aCR1OpaSlpaFfv35YtmwZPvzwQ6HDYcXwlS5jSrZs2TL0798fY8aMwcuXL4UOp0pMTU3RuXNnREZGCh2KwoSHh8PKykrtEm5BQQGcnZ3h7OzMCVcFcdJlTMlEIhF++eUXaGlpYcaMGVDXxqaaPlHGq1mo1AkRYebMmWjSpAk8PDyEDoeVgpuXGRNIbm4uhg4diuHDh2Pt2rVCh1Npjx8/Rvfu3ZGUlIT69esLHY5cFRQUwNjYGLdv34aR0VtT/6ssDw8PBAQE4MyZM7Vufmx1wVe6jAlES0sLR48exYEDB7B9+3ahw6m0Zs2aoV27djh58qTQochdZGQkunbtqlYJNyAgAFu3bsXRo0c54aowTrqMCcjQ0BDHjh3DmjVrcPToUaHDqTRXV9ca2cSsbnMtR0dHY9asWThy5AhMTU2FDoeVg5uXGVMB0dHRGD16NI4ePapWc/z+888/6N27N548eVJjmpjFYjFMTU1x8eJFtGrVSuhwKvTo0SP0798fW7duhb29vdDhsArwlS5jKqBPnz7YvXs3HB0dcefOHaHDkVnz5s3RsmVLREVFCR2K3Fy8eBEmJiZqkXCzsrJgZ2eHhQsXcsJVE5x0GVMRo0ePxtdffw1ra2ukpKQIHY7MatooZnWZEEMsFmPChAl47733sHDhQqHDYTLi5mXGVMyqVatw7NgxnDp1Si0GxNy/fx/9+/fHkydPULduXaHDqRYiQps2bXDo0CF0795d6HDKtWDBAsTFxSE8PLzGNO3XBnyly5iKWbNmDTp37ozx48ejqKhI6HAq1KpVK5ibm+PMmTNCh1JtcXFxkEgk6Natm9ChlGvr1q0IDw+Hv78/J1w1w0mXMRUjEomwY8cOvHz5Ep9++qlaTJ5RU5qYXzUtl3jerIo5fvw41qxZg9DQUOjr6wsdDqskTrqMqaD69esjICAA0dHR+O6774QOp0IuLi44fPgwxGKx0KFUi6rPQnXjxg24ubnB398frVu3FjocVgWcdBlTUY0aNUJoaCh27tyJPXv2CB1Oudq2bQtjY2OcP39e6FCq7OHDh0hMTMTAgQOFDqVUKSkpsLOzg6enJwYNGiR0OKyKOOkypsKaNm2KsLAwLF26FH/88YfQ4ZRL3ZuYg4KCYGdnp5KDwfLz8+Ho6IiJEyfC3d1d6HBYNfDoZcbUwLlz5+Ds7Izjx4+jR48eQodTqlu3bmHYsGF4/Pgx6tRRv+/zgwcPxuLFi2Frayt0KCUQESZNmoSioiL4+fmp5b5l/+G/HmNqwNLSElu3boWdnR3++ecfocMpVYcOHdC4cWNcunRJ6FAq7dmzZ4iNjcXw4cOFDuUtX3/9Ne7du4c9e/Zwwq0B+C/ImJoYM2YMli5dilGjRiE9PV3ocErl4uICf39/ocOotKNHj2LEiBHQ0NAQOpQS9u/fj927d+PIkSPQ1NQUOhwmB5x0GVMjc+fOha2tLRwcHJCfny90OG951a8rkUiEDqVSVHEWqgsXLmDu3LkIDg6GiYmJ0OEwOeE+XcbUjEQiwaRJk1BYWIiDBw+qXJNjp06dsHv3brV5cEN2djZMTU3x6NEj6OnpCR0OAODBgwcYMGAAdu3aBRsbG6HDYXKkWmcrY6xCderUgZeXF1JTU7Fw4UKVmzxD3ZqYjx8/jv79+6tMws3MzIStrS2++OILTrg1ECddxtRQw4YNERQUhBMnTmDjxo1Ch1PCqyZmVfsyUBZVmhCjqKgIY8eOxZAhQ/DZZ58JHQ5TAE66jKkpPT09hIeHY+PGjThw4IDQ4bzWtWtXNGjQAFevXhU6lAq9fPkSYWFhcHBwEDoUEBHmzZuHOnXqYNOmTUKHwxSEky5jaqxZs2YIDQ3FZ599pjLPtBWJRHB1dVWLiTKioqLQvn17mJqaCh0KNm/ejKioKPj5+aFevXpCh8MUhJMuY2rOwsICfn5+GDt2LG7cuCF0OAD+69dV9SZmVWlaDg0Nxffff4+QkBDo6uoKHQ5TIE66jNUAQ4cOxY8//ggbGxskJiYKHc7rZ9HGxsYKHEnZJBIJjhw5IvitQteuXcO0adNw6NAhtGjRQtBYmOJx0mWshpg0aRJmz54NGxsbZGZmChqLOjQxR0dHQ1dXF+3atRMshqSkJNjZ2eHnn39G//79BYuDKQ/fp8tYDUJEmDNnDuLj4xEWFoYGDRoIFsuVK1cwceJExMfHq+TzaZctW4a6devi22+/FaT+vLw8DB48GKNHj8aqVasEiaFWSUkBvLyAa9eAzExAVxewsACmTQMMDZUWBiddxmoYsVgMFxcXaGtrw9vbW7CER0Ro2bIlgoODYWFhIUgM5enQoQN8fHzQp08fpdctkUgwfvx4NGjQAD4+Pir5paTGiI4GPDyA8HDp78VnctPUBIgAa2tg+XJACccCNy8zVsPUrVsX+/btw7179/DFF18IFodIJFLZx/3dvHkTOTk56N27tyD1r1q1ComJidi5cycnXEXauhUYPBgICpIm2zenTs3Lky4LCpKut3WrwkPipMtYDaSpqYng4GAcPnwYW7ZsESwOVe3XDQoKgqOjoyAJz9vbG/v27UNQUJDKPWChRtm6FVi8GMjNlV7NlodIut7ixQpPvJx0GauhDAwMEB4ejrVr1+LIkSOCxNC3b19kZ2erzK1Mrwh1q9DZs2exePFihISEwFCJ/Yi1TnT0fwm3mJsAhgLQBdAGQOCb271KvFeuKCw0TrqM1WCtWrVCcHAwPvroI1y8eFHp9YtEIowZM0alrnYTEhJw7949WFlZKbXeu3fvwtXVFb6+vujUqZNS6651PDykTcfFFAFwAGALIB3ADgCTAdx+c9u8POn2CsJJl7Earnfv3tizZw+cnJxw+/ZbHzEKp2pNzEeOHMHo0aNRv359pdWZkZEBW1tbrF69GiNGjFBavbVSSop00NQbTcq3ADwBsABAXUiveAcC8HlzeyIgLAx49kwh4XHSZawWsLGxwbfffgtra2skJycrte5+/fohPT0dt27dUmq9ZQkMDFTqhBiFhYVwcXGBtbU1PvnkE6XVW2t5eZW6uLReXQJwvbSVRaIyy6kuTrqM1RIffvgh3NzcYGtri+zsbKXVW6dOHZVpYs7IyMDly5cxcuRIpdRHRJg9eza0tLTg6emplDprvWvX3h6lDKADACMA6wEUAvgDQBSA3LfWhLSJOS5OIeFx0mWsFvnqq69gYWGBcePGoaioSGn1qsqtQyEhIRg6dCi0tLSUUt+GDRtw+fJl7Nu3D3Xr1lVKnbVeGbOx1QcQBCAUgAmADQDGAjAvq5yMDAUEx0mXsVpFJBJh27ZtkEgkmDVrltIeSDBw4EAkJyfjzp07SqmvLEFBQUprWg4KCsLGjRsREhKCRo0aKaVOBulMU2WwgPTqNg3AcQD3AfQta2V9fXlHBoCTLmO1Tv369eHv74+YmBisXbtWKXXWrVsXzs7Ogl7t5uXl4cSJE7C1tVV4XTExMZgxYwaCgoLQrFkzhdfHpIqKinCzQQMUlNGqcA1APqRNyp4AngKYWtqKmppA164KiZGTLmO1kLa2NkJDQ7F7927s3r1bKXUK3cT8xx9/oFevXmjSpIlC60lMTISDgwO2bdsmyBSTtQ0RISYmBvPnz4e5uTkWXbuGumVMeuIDoCmkfbuRACIANCy9UGDqVIXEy0mXsVrKxMQE4eHhWL58OY4dO6bw+qysrJCQkID79+8rvK7SvJqFSpFycnJgZ2eHTz/9FGPGjFFoXbXd48eP8f3336NLly5wcXGBjo4Ozpw5g7ArV1DPzk46AvkN6wFkAMgGEA7pBBlvEYkAGxuFPQSBH3jAWC134cIFODo64tixY+jZs6dC6/rkk0/QunVrLFmyRKH1vKmoqAgmJiaIiYnBu+++q5A6JBIJxowZA319fezatYvnVFaArKwsHDp0CN7e3oiNjYWLiwvc3d0xcODAkvs7Olo6l3JuqWOTy6elBURFAQqal5uvdBmr5QYMGIDt27fDzs4ODx48UGhdLi4u8Pf3V2gdpTl37hxatGihsIQLSB8VmJGRgW3btnHClaOioiKEh4dj4sSJaNasGQIDAzF79mw8efIEO3bsgKWl5dv7u08fwNNTmkArQ0tLup0CH4RRT2ElM8bUhpOTExITE2FtbY3z588rrN9z8ODBePDgAf755x80b95cIXWURtFzLe/cuRNBQUG4ePGioM8wrimICLGxsfDx8cH+/fvx7rvvws3NDT/99JPsc1bPmgUAkCxaBMrLQ7k3bIlE0sFTnp6vt1MUbl5mjL32+eef49y5czhx4gQ0NTUVUseMGTPQsWNHLFy4UCHlv4mI0KJFC4SFhaFz585yL//kyZOYMGECzp49i3bt2sm9/NokISEBvr6+8PHxQXZ2Ntzc3DB58mS0b9++ymV+N2YM7K5fR9dHj6TJtficzK+ep2tjI32erhIe9chJlzH2mkQiweTJk5Gfnw9/f3+FTOhw/PhxrF69WmkPYIiJicG4ceNw+/ZtuTf7xsfHw8rKCn5+fhgyZIhcy64tsrKycPjwYfj4+CAmJgZjxoyBm5sbLC0tUadO9XpA79+/j759+yI+Ph5NJBLp1I5xcdKJL/T1pbcFTZ2qsEFTpeGkyxgroaCgANbW1ujSpQt++uknuSeqwsJCmJiYIDY2Vin3sK5cuRIFBQVYt26dXMtNS0tDv379sHz5ckyfPl2uZdd0RUVFiIyMhI+PD0JCQjBo0CC4u7vDzs5Ors8Ynjp1Klq0aIHVq1fLrczq4qTLGHvL8+fPMWjQIEyZMgWLFy+We/nTp09Ht27dMG/ePLmX/aauXbtix44d6N+/v9zKLCgowAcffIB+/frhhx9+kFu5Nd1ff/0Fb29v7N+/H+bm5nBzc8P48eMV8mzhW7duwcrKCnfu3IFuObNUKRsnXcZYqRISEjBgwAD88MMPmDBhglzLDgsLg4eHB86ePSvXct909+5dDBo0CImJidVuqnyFiDBt2jS8ePECAQEBciu3pkpMTMS+ffvg4+ODzMxMTJ48GW5ubujQoYNC6x0/fjx69OiBzz//XKH1VBYnXcZYmeLi4jBs2DAcOHBArn2WBQUFaNq0Ka5fvw5TU1O5lfsmT09P3L17F9u2bZNbmR4eHggICMCZM2fwzjvvyK3cmiQ7OxuBgYHw8fFBdHQ0nJ2d4e7ujkGDBinlS8q1a9cwcuRI3L17V+X+RvwVjTFWpq5du+LAgQMYN24c4uT4qLOGDRvC1tYWhw8flluZpZH3rUIBAQHYunUrjh49qnIf5kITi8WIiIiAm5sbzM3N4efnhw8//BBPnjzBrl278P777yutVWDVqlVYtmyZSv6N+EqXMVah/fv34/PPP8eFCxdgbl7mw9Aq5ejRo9iwYQNOnz4tl/LelJSUhI4dOyI5OVku985GR0fDxsYGf/zxB3r06CGHCGuGa9euwcfHB/v27UPTpk1f99MaGxsLEs/ly5cxZswY3LlzR66DsuSFJ8dgjFVowoQJSEhIgLW1Nc6dOyeXgSkjRoyAu7s7kpKSYGJiIocoSwoODsaoUaPkknAfPXoER0dH7Nq1ixMugKdPn77up01PT8ekSZMQERGBTp06CR0aVq5ciRUrVqhkwgW4eZkxJqPFixdjyJAhcHJyQkFBQbXL09DQgI2NDQIDA+UQ3dsCAwPl8uzcrKws2NnZYeHChbC3t5dDZOopJycHe/fuxciRI9GpUyfcuHEDGzduxMOHD+Hh4aESCffMmTO4c+cOpk2bJnQoZeLmZcaYzMRiMVxdXaGhoYG9e/dWu48uKCgImzdvRmRkpJwilHrx4gXMzc2RmJhYrQfIi8ViODg4wNTUFNu3b691cyqLxWKcOnUKPj4+CA4ORv/+/eHm5gYHBwdoVXZeYwUjIrz//vv48MMPMWXKFKHDKRMnXcZYpeTl5WH48OGwtLSs9j2qeXl5aNq0Ke7cuSPXezX9/Pzg4+OD0NDQapWzYMECxMXFITw8HPXr15dTdKrv+vXr8PHxga+vL4yMjODu7o4JEyYI1k8ri4iICHz22We4fv066tVT3Z5T1Y1yGsUOAAAgAElEQVSMMaaSNDU1ERwcjIEDB6JZs2aYM2dOtcoaNWoUAgMD8fHHH8stRnk0LW/duhXh4eG4ePFirUi4SUlJr/tpU1NTMWnSJBw/flwh81XLGxFhxYoV+Prrr1U64QIAiDHGquD+/ftkampKhw8frlY5/v7+NGLECDlFRZSfn0+6urqUlJRU5TKOHTtGxsbGdPfuXbnFpYpycnLI19eXRo0aRXp6ejRlyhQ6ceIEFRUVCR1apQQHB5OFhQWJxWKhQ6kQJ13GWJVduXKFDA0N6fz581UuIycnh3R0dCg1NVUuMYWGhpKlpWWVt79+/ToZGhrSmTNn5BKPqhGLxRQZGUlTpkwhPT09GjVqFPn6+lJ2drbQoVWJWCwmCwsLOnLkiNChyIRHLzPGqqxXr17w9vaGs7Mz4uPjq1SGlpYWPvjgAwQFBcklpqCgoCo3LaekpMDOzg4//vgjBg0aJJd4VMWNGzewbNkyNG/eHIsWLYKFhQX+/vvv1w+IV8WJJGQREBCAhg0bws7OTuhQZMIDqRhj1bZ792588803uHDhQpXuuT1w4AC8vLwQHh5erTjEYjFMTU1x8eJFtGrVqlLb5ufnY+jQoRg2bBi++eabasWhKpKTk7F//354e3sjOTkZkyZNgpubG7p27Sp0aHJRVFSELl264Oeff8YHH3wgdDgy4aTLGJOLr7/+GkeOHEFUVBS0tbUrtW12djbMzMzw8OFD6OvrVzmG8+fPY/bs2fjrr78qtR0RYdKkSRCLxdi/f79aP8QgNzcXR44cgY+PDy5cuAB7e3u4u7tjyJAhCnk+spC8vb2xc+dOREVFqc3tXOp7ZDHGVMrKlSvRs2dPuLq6orCwsFLbamtrY9iwYQgODq5WDFWda/nrr7/G/fv34eXlpZYJVyKR4NSpU5g+fTrMzMzg5eWFiRMnIjExEd7e3hg+fHiNS7iFhYVYvXo11q5dqzYJF+CkyxiTE5FIhK1bt6JOnTr45JNPUNlGNBcXF/j7+1e5fiKq0q1C+/fvx+7du3HkyBFoampWuX4h3Lx5E1988QVatGiB+fPnv54p6vjx45g8ebLa9tPKYvfu3WjTpg2srKyEDqVSuHmZMSZX2dnZGDJkCEaPHo3Vq1fLvN2rWaQeP35cpbmd4+LiYGdnhwcPHsh85XPhwgU4OjoiMjJSbfo5U1JS4OfnB29vbzx58uR1P62FhYXQoSlNfn4+2rZti0OHDqFv375Ch1MpfKXLGJMrbW1thISEwMfHB7t27ZJ5Ox0dHQwZMgRHjx6tUr2vrnJlTbgPHjyAi4sL9uzZo/IJNy8vDwcOHICtrS3atWuH6OhofPfdd3j8+DHWr19fqxIuAGzfvh09e/ZUu4QLgCfHYIwpRnx8PBkbG1NoaKjM23h7e5O9vX2V6uvRowdFRUXJtO7z58+pU6dO9PPPP1epLmUQi8V0+vRp+vDDD0lfX5+GDx9O3t7elJWVJXRogsrOziYTExOKjY0VOpQq4eZlxpjCXLx4Efb29ggPD0fv3r0rXP/58+d49913kZCQAB0dHZnrefjwIfr27YunT59WOGCoqKgIo0ePRtu2bfHLL7/IXIey3Lp16/W8x40aNYK7uzsmTpwIMzMzoUNTCT/88ANiYmJw4MABoUOpEm5eZowpTP/+/bFz507Y29vj/v37Fa6vp6eHQYMGVfpBBUFBQbCzs6sw4RIR5s2bhzp16mDTpk2VqkORnj17hs2bN6Nv374YMmQI8vPzERQUhGvXrmHJkiWccP+VmZmJDRs2VGqsgKpR8ZmhGRNQSgrg5QVcuwZkZgK6uoCFBTBtGiDHJ+LUdA4ODkhMTIS1tTXOnz8PAwODctd3dXVFQEAAJkyYIHMdQUFBWLRoUYXrbd68GVFRUTh//rzgE+Pn5+fj6NGj8Pb2xtmzZ2Fra4tvvvkGw4YNEzw2wZVx7u1ITYW1tTU6duwodIRVJ3DzNmOq5/JlIicnIg0N6Q/w34+mpnSZk5N0PSazZcuWUf/+/SknJ6fc9dLS0khHR0fmvsuUlBTS1dWlvLy8ctcLCQmhpk2b0oMHD2QNWe7EYjFFRUXRRx99RPr6+jRs2DDy8vKiFy9eCBaTSinn3JNoaFAeQFkjRqj1ucdJl7Hitmwh0tIiEolKJts3f0Qi6XpbtggdsdoQi8U0adIkcnR0rPApNiNHjqQDBw7IVO7vv/9OLi4u5a7z119/kaGhIV24cEHmeOUpPj6eVqxYQS1atKDOnTvT999/T48fPxYkFpVVS849TrqMvfLqpC/vhH/zR41PfiEUFBTQsGHDaPbs2SSRSMpcb+fOneTq6ipTmXZ2drR3794yX3/69Cm9++67tH///krHWx3Pnj2jzZs3U9++fcnY2Jjmz59PMTEx5b7vWqsWnXucdBkjkjZXaWnRZoB6AdQAoCnFTvAb/y7X+/dn2L/LXp/80dFCvwO18fz5c7KwsKDvv/++zHWePXtGOjo6FTZFZ2VlUaNGjSgjI6PU13Nzc6lv3760Zs2aasUsq7y8PPL39yd7e3vS0dGhCRMmUFhYGBUWFiqlfrVUwblHAJ0AqD1AmgANBuihGp97PHqZMQDw8ADy8mAKYAWA6W+8bAogAEA6gFQA9gDGv3oxL0+6PZOJrq4uwsLCsGXLFvj6+pa6joGBAfr27VvhU4eOHz+Ofv36QU9P763XJBIJpkyZgrZt22LlypVyib00RIRz585h5syZMDMzw5YtW+Do6IjHjx9j3759sLa25oFR5ang3EsF4AzgG0jPv94Axr16UQ3PPT4SGEtJAcLDASI4/7voCoCEYqvo/fsDAASgLoC7r14kAsLCgGfPeFSzjMzMzBAWFoahQ4fCxMQEw4YNe2sdFxcXBAQEYMyYMWWWU95cy6tWrUJiYiIiIyMVMiH+nTt34OPjg71790JDQwPu7u6IjY1Fs2bN5F5XjSXDuXcYQGcArv/+vhqAAYBbADqo4bnHV7qMeXnJvKoeAA0AnwH4ovgLIlGlymFA586dcfDgQUyYMAHXrl1763UnJyeEh4cjLy+v1O0LCwsRFhYGe3v7t17z9vbGvn37EBQUBA0NDbnFnJaWhi1btqB///6wtLTEixcv4O/v//oB8ZxwK0mGc+YGgG7Ffn8HQOt/lwNQu3OPky5j164B+fkyrfocQCaAXwD0KP5CXh4QFyf/2Gq4999/H5s3b8bo0aPx+PHjEq8ZGRmhZ8+eOH78eKnbnj59Gu3atXtr4oizZ89iyZIlCAkJgaEcrn4KCgpw+PBhODk5oVWrVjhz5gxWrFiBhIQEbNq0Cb169VKrR8upCiLCyytXKjz3sgG8+fgLXQBZr35Rs3OPm5cZy8ys1OrvAPgEgCGAmwCM/l1ekJyMBkT8AVxJ48aNQ0JCAqytrXHu3LkS/bOvmphLe0ZuUFDQW03Ld+/ehaurK3x9fdGpU6cqx0REuHjxIry9veHv7w8LCwu4ubnBy8urSk9Aqi2ICNnZ2UhKSkJycnKp/776f3JyMgLFYlhXUKY2gBdvLHsBoFHxBRkZ8nwbCsVJl7EqfIhKAOQCSMR/STfo9GlM0dSEmZkZzM3NYW5uXuL/r36MjY1r3APFq2vhwoV4/PgxHB0dcfz4cTRs2BAA4OzsjC+//BIFBQWvlwHSQVJBQUE4efLk62UZGRmwtbXFmjVrMHz48CrFce/evdf9tPXr14ebmxtiYmLQvHnz6r1BNZebm1tuIi2eUOvUqQMTExOYmJjA2Nj49b+9e/cu8buxsTE0Z8wAyhhM90pnAHuK/Z4D4N6/y1/T15f7e1YUTrqMWVgAhw4B+fkoAlAEQPzvTz6kJ8kpSAdvWEB60q8AoA/g9WR0mpoYt2YN7D79FImJiUhISEBCQgISExNx+/ZtnDx58vWy9PR0GBsbl0jEbyZnU1NTNGjQQNl7QjAikQgbNmzAuHHjMHXqVPj6+r7+8LawsMDpgwcx8unT19MCphcWYkFhIdo3bgxA2r/r4uICGxsbzJw5s1J1p6en4+DBg/D29sbdu3cxfvx4+Pn51fhm4/z8/NdXnBUl0qKiohJJ9NX/LSwsMGLEiBKJVFtbW/YgZDj3nAAsAXAIwGgAX0N6HnZ4VYamJqDij2Ysjp8yxORHXecqTkkBmjcH8vOxGsCaN17+CtJv1SshHVWpCaAPgO8hPfkBABoawKNHMr3Ply9f4unTp6+TcPEE/er/SUlJ0NfXf+sq+c2r6HfeeUdOO0E15OfnY8SIEejXrx/Wr18PREfj3kcfodn169IvIcX6/17Wq4cG9eqBrK3xnUSC/0kkCAwMlKkVoaCgAGFhYfDx8UFkZCRGjRoFNzc3jBw5EvXr11fkW1Soly9fIiUlRaZEmpeX9zpRvnlV+uaVaqNGjRTzBUSGc281gBMA5gD4B8B7ALwAtHi1UiXOPVXASZdVX3S09F65V/dUFh8YoakpvaXG2hpYvhzo00eYGCvi7AwEBUljrSyRCHBykn5jlxOxWIzk5OQSibi05KylpVVqE3bxZbq6ump1xZaeno6BAwfi165dMTQ0FJSXB1E5fxeJSIQCAKIff4TG/PllrkdEuHTpEnx8fHDw4EF07twZbm5ucHFxKfU+X1VRVFSE1NTUEv2hZf374sULGBoalplIiydUPT091TguVOzcUzROuqx6tm4FFi+WjiAs71ASiaQJ2NMTmDVLefHJKjoaNHgwRLm5ld9WSwuIigJkeF6sPBER0tLSSk3GxX+IqNw+ZjMzMxgYGKBOHdW5mSF17VporVoFrcp8PGlplXp83b9//3U/bZ06deDm5obJkyejRYsW8g26EiQSCdLS0mRKpOnp6WjcuHGZV6HF/23SpIlK/R1lEh0NDB4MqNG5Vx2cdFnVvUq4lTlZyvhgFBoR4cCQIXA4exaaEonsG6ro+ynuxYsXZV4pv/rJzs6ucACYiYmJcgaAlfEhnA7gQwB/QNq/7gFg4pvb/vshnNG6NQ4ePAgfHx/Ex8dj/PjxcHNzQ58+fRR2dUdEyMjIKHWk7pv/Pnv2DLq6uhU26xobG8PAwKDmz2hVgz5LKsJJl1VNKR+MBQBmQ9r/kg6gDYDvgLdvCVCxb6dEhMWLF+Ps2bM4PX48tFauVP8r90rKy8t7Kxm/+XtqaupbA8DeTNCmpqYlRhlXSRnNjRMgHTW+C0AspINqLqDkKFaJSITLTZtiZHY2PvjgA7i5uWHUqFFVHpRGRHjx4oVMiTQlJQVaWloVNusaGxvDyMhIrfuOFaKmtJpVgJMuq5pSPhhzAKwHMBXAuwDCIP2gjEOxQQ+ASvXDEBG++OILHDt2DCdPnoS+vj5w5Yq0jzosTBpr8RmRXvVR29hI+6hV5IuDMhQWFlY4AOzp06fQ19evsJ+5zAFgxQbWFJcD6Wjx6wDa/bvMDYAZpAPaiiuqVw85N29Ct02bMt/Lm/eSltfE26BBgwqbdU1MTGBkZCTX2a9qpVpw7nHSZZVXxgdjaSwgHYH41uy5KjLicPXq1Th06BBOnToFAwODki8+eyYdjR0XJ735Xl9femvC1KmCx62qxGIxUlJSyuxffrVcQ0Oj1GZsy4sX0c7XF3UKCkqU+yeAAQCKTwjpCSAKwNE3Y2jYEDfHjcP5AQPKTKhE9FYSLSuhamlpKXSfsVLU4HOPky6rvHXrgK++qjDpJgNoDmlTYIc3X9TUBNasAZYsUUyMMvDw8IC3tzeioqJgZGRU8QYyIOnjMkFEkEgkJX7n16Q/YrEYWVlZSEtLQ2pqKtLT05Geno60tDQs/usv2JUyQ9hZSCe8Tyq27DcAvgBOl/J3OGluDj9r6zITqra2tmqM3GW1Tg3vnWcKIcNcxYUAJgGYglISLgDk5eHY+vX4OjBQkGSQnZ2NvLw86OrqonPnzuVuJ2tdxdWpUwcikajUH37t7eWvr3zv3St1Wk6ZpgIsZmj37hi6Y0e5xyhjQuCkyyqvgrmKJZD2tzWA9MEAZenTti3Wr1un9A/83bt3Y+fOnTh06BDMzc3L3a4qdbGqk0ycCOzf/9bydpDOVnQHQNt/l/2FN6YCLE6NpgVktQsnXVZ55cxVTJDe1pEM6UCq8sZnNmndGgMHDpRvbBXYsWMHdu7cidOnTwt6nyb7T2ZmJo4dO4bg4GC0CQzEcpEIGm+0HLwD6YPMVwHYCWmXxRFIRy+/SaKhgTpqNC0gq13U7C5qphIsLKQDoUoxC9In7xyFdLrEMgkwX+ru3bvxzTffIDIykhOuwP755x/88ssv+OCDD9CsWTN4e3vDysoKn1y6hIZl3N6zBdKBVEaQjorfitKvdF/m52PM0aPYu3cvcnJyFPYeGKsKHkjFKq+M0cv/QHprUEOUbELZDmn/bglKHr3s6+uLpUuX4uTJk2jfvr1S6mT/ISJcvXoVwcHBCA4ORmJiIkaPHg17e3t88MEH0NbWBhHh999/h8ns2bB++bJqVwQiEcT29jg0cSK8vLxw8eJFODs7Y+rUqbC0tOTmfyY4TrqsatRovlR/f3/MnTsXJ06cQOfOZfYCMjnLz8/HqVOnXidabW1tODg4wN7eHv379y8xu1V8fDxmzpyJnJwc7J0/H+0//rhK0wKSpiZEZ868vofzyZMn8PX1hZeXF/Lz8zFlyhS4u7tzSwcTDjFWFZcvE2lpEUnTbuV+tLSIoqOVEmZQUBAZGxtTbGysUuqr7Z49e0ZeXl7k7OxMOjo6ZGlpSevWraNbt26Vun5+fj6tXr2amjRpQj/99BMVFRVJX9iypdLHV369evSVsTHdvXv3rXokEglFR0fTp59+Sk2aNKHBgweTl5cXZWVlKXJ3MPYWTrqs6qrwwUhaWtLtlCA0NJSMjIzoypUrSqmvtoqPj6d169aRpaUl6ejokLOzM3l5eVFKSkq52505c4Y6dOhA9vb29OjRo7dXeHV8iUTlH1Mi0evj6tdffyVjY2OKiooqs978/HwKCAggW1tb0tXVpSlTptCpU6dILBZXd1cwViFOuqx6qvDBqAzHjx8nQ0NDunTpklLqq02Kioro7NmztGTJEmrfvj2ZmprSzJkzKSwsjPLy8ircPj09nT766CMyMzOjQ4cOkUQiKXvl6GgiZ2eSNGxIuW9e2datS6ShQeTsXKLl5I8//iBDQ0PavXt3hbEkJSXRhg0bqGvXrtSiRQtatWpVqVfKjMkLJ11Wff9+MJKGBpGmZokPxpf16pX6wahIp06dIkNDQzp79qxS6qsNsrKy6PDhwzRlyhQyMDCgbt260cqVKyk6OlrmK0SJREL79++npk2b0uzZs+n58+cy138uMJB+ad6cyM2NyNaWcsaMoZUaGvQyMbHU9f/++29q1aoVLVu2TKb4JBIJxcTE0Ny5c8nAwIAGDRpEu3btohcvXsgcI2Oy4KTL5CclhWjdutcfjA/ff592deggXa4kZ8+eJQMDAzp58qTS6qypEhMTadu2bWRjY0ONGjWi4cOH0+bNm+nhw4eVLuv+/fs0atQo6tKlC124cKHS2+/YsYOmTp1aYlnv3r3L/Ts/e/aMBg0aRE5OTpSdnS1zXQUFBRQYGEgODg6kq6tLkydPphMnTnDzM5MLTrpMYe7fv0+mpqZKq+/SpUtkaGhIx48fV1qdNYlEIqHY2Fj6+uuvqXfv3qSvr08TJ04kPz+/Sl2VFldYWEjr16+nJk2akIeHB718+bJK5SxZsoS+/fbbEsvWrFlDCxcuLHe7/Px8mjJlCvXo0YMSEhIqXW9ycjJt2rSJunfvTs2aNaMvv/ySbt++XelyGHuFky5TGIlEQnp6epSUlKTwuq5cuUJGRkYUGhqq8LpqkoKCAoqIiKDPPvuMmjdvTi1btqT58+fTyZMnq5wgX7l8+TJ1796dhg8fXu1+UkdHRzp48GCJZVevXqW2bdtWuK1EIqHvv/+ezMzMKLoaXRyxsbG0YMECMjIyooEDB9KOHTuq/GWE1V6cdJlCDRkyhMLDwxVaR2xsLBkbG1NgYKBC66kp0tPTydfXl8aNG0d6enr03nvv0bfffkvXr18vf1CTjF68eEFz584lY2Nj8vHxkUuZXbp0oZiYmBLLJBIJmZmZlXk70psOHz5MBgYGFBAQUK1YXr58ScHBweTs7Ey6uro0ceJEOn78+H+3OzFWDk66TKEWLlxI3333ncLKv379OpmYmLx1FcRKunfvHm3atImGDh1KjRo1Ijs7O/rtt9/o6dOncq3nyJEj1KxZM5o6dSqlpqbKpUyxWEyampqlDmqaOXMmrV+/Xuayrl69Subm5vTdd9/J5cvAs2fPaPPmzdSrVy8yMzOj5cuXy/wlgNVOnHSZQu3du5dcXFwUUvatW7fI1NSUfH19FVK+OhOLxXTp0iX64osvqEuXLmRkZETTp0+nI0eOUE5OjtzrS0hIIGdnZ2rbti1FRkbKtexHjx6RiYlJqa+FhISQlZVVpcpLSEignj17kru7O+Xn58sjRCIiiouLo8WLF5OJiQn169ePtm7dSunp6XIrn9UMnHSZQt24cYNat24t93Lv3LlD5ubm9Pvvv8u9bHWVm5tLwcHB9NFHH5GJiQl16tSJli1bRhcuXFBY06dYLKZff/2VDAwMaMWKFTLdp1tZJ0+eJEtLy1Jfy83NJR0dHUpLS6tUmdnZ2eTs7EyWlpYVTuJRWYWFhRQSEkKurq6ko6ND48aNo7CwMCosLJRrPUw9cdJlClVUVERaWlpyHXDy4MEDevfdd2n79u1yK1NdJSUl0a5du8jBwYEaNWpEgwcPph9//JHu3Lmj8LqvXbtG/fr1o4EDB9KNGzcUVs/27dtp2rRpZb5ub29Pe/furXS5YrGYli9fTq1atVJY/GlpafTrr79S3759qWnTprR06VKF7ium+jjpMoXr168fnT59Wi5lPXr0iFq2bEmbN2+WS3nqRiKR0I0bN8jDw4P69+9Purq65OrqSj4+PnLrQ61Ibm4uLV++nAwMDGjbtm0Kv3918eLF5Y4L+O2332jcuHFVLn/Pnj1kaGhIx44dq3IZsvj777/p888/J1NTU+rTpw/9+uuvlb5CZ+qPky5TuFmzZtHGjRurXU5iYiK1bduWPD095RCV+igsLKTTp0/TwoULqXXr1tSsWTP69NNP6fjx43Ltk5RFREQEtW7dmsaOHUtPnjxRSp0ODg7k7+9f5utPnjwhPT29at3idPbsWTIxMaFffvmlymXIqrCwkMLDw2n8+PGko6NDLi4uFBISws3PtQQnXaZwv/32G7m7u1erjKSkJOrQoYNCR0KrkszMTDp48CBNnjyZGjduTD179qTVq1fTn3/+KZdRt5WVkpJCbm5u1Lx5cwoJCVFq3Z07d6Y///yz3HX69OlT7QFc9+7do44dO9KcOXOUlgAzMjJo27Zt1L9/fzI2NqZFixbRtWvXlFI3E0aVnhPNWGX06NEDMTExVd4+NTUVw4cPx7hx47B8+XI5RqZaHj9+jC1btmDkyJEwMzPD77//jgEDBiA2NhZXr17FV199he7duyv1QexEBC8vL3Tp0gWGhoa4fv06Ro8erbT6JRIJ7t27hzZt2pS7np2dHY4ePVqtulq1aoWLFy/i9u3bsLW1RWZmZrXKk4Wenh5mzpyJCxcuICoqCg0aNIC1tTV69eqFzZs3IzU1VeExMCUTOuuzmi8/P580NDQoNze30tump6dT9+7dadmyZYJc4SmSRCKhq1ev0ldffUU9evSgJk2akJubGwUEBKjERPvx8fE0ZMgQ6tmzp2CPR/znn3+oadOmFa4XExNDrVu3lssxUlhYSJ9++il16tSJ7t27V+3yKquoqIj++OMPmjhxIunq6pKTkxMdOXKk2jOEMdXASZcpRbdu3eh///tfpbZ5/vw59enThxYsWFBjEm5+fj6Fh4fTrFmzyNzcnNq0aUOLFi2iqKgolenTKygooG+++YaaNGlCP/74o6BxRUZGynQfrkQiIXNzc7p586bc6t68eTOZmJgI+rSq58+f02+//UaWlpZkZGRE8+fPp9jYWMHiYdXHzctMKXr06IE///xT5vWzsrJgbW2Nvn37YsOGDUptUpW3tLQ0+Pj4wNXVFcbGxli7di1atGiBiIgI3L59G56enrCyskK9evWEDhXnz59Hjx49cOnSJVy9ehULFiwQNK47d+5U2LQMACKRCLa2ttVuYi5uzpw52L17N5ydneHt7S23citDV1cXH330Ec6ePYtz585BW1sbdnZ26N69OzZt2oSUlBRB4mLVIHTWZ7XDzz//TDNnzpRp3ezsbLKysqIZM2ao7ePUbt++TZ6enmRlZUWNGjUiR0dH+v333yk5OVno0EqVkZFBM2fOJFNTUzp48KDKtCwsWrSIPDw8ZFo3NDSUBg0aJPcYbty4QS1btqQvvvhCJY5HsVhMkZGR5ObmRrq6umRvb0+HDx+mgoICoUNjMuArXaYUsg6mysvLg4ODA1q2bIlt27ahTh31OETFYjEuXLiAZcuWoVOnTrCyssLt27exdOlSJCcnIzAwENOmTYORkZHQoZZARPD390fnzp0BADdu3ICrq6vKtCzcvXsXbdu2lWndoUOH4q+//kJaWppcY+jUqRP+97//ISoqCmPHjkVubq5cy6+sOnXqYOjQofD29sbjx4/h6OiITZs2wczMDHPnzkVMTAyISNAYWdlExH8dpgRZWVkwMTFBZmZmmc2VBQUFcHR0ROPGjeHt7Y26desqOcrKycnJQUREBIKDgxESEgITExPY29vD3t4evXv3VvkvDP/88w8+/fRTPHjwADt27MDAgQOFDuktnTt3xr59+9CtWzeZ1nd0dISLiwsmT54s91gKCgowY8YM/P333wgODoapqanc66iO+/fvw9vbG3v27IG2tjamTp2KSZMmwcTEROjQWHHCXmiz2qRdu3YUFxdX6msFBQVkZ2dHLi4uKjOgqDRPnjyh7du30zV4ZgUAACAASURBVOjRo6lRo0Y0bNgw+umnn+j+/ftChyazwsJC2rBhAzVp0oTWrl2rss2SYrGYNDQ0KDs7W+Ztdu7cSWPHjlVYTBKJhL799lsyNzenq1evKqye6hCLxXTq1CmaOnUq6erq0ujRo8nf31/pE6mw0nHSZUozbtw42rNnz1vLX758Sc7OzmRvb69yt0VIJBK6du0arV27lvr27Ut6eno0YcIE2r9/P2VkZAgdXqVdvXqVevbsSUOGDKH4+HihwynXw4cPydTUtFLbPH36lPT09BT+RcLf358MDAzo8OHDCq2nurKysmjPnj00ZMgQatKkCc2ePZsuX76sMn32tZFqt3+xGqW0EcxisRju7u7Iy8vDwYMHUb9+fYGi+09hYSEiIyMxb948tGrVCvb29khJScF3332H5ORk7Nu3D+PHj4eenp7QocosOzsbixYtgrW1NebOnYvIyEi0a9dO6LDKVZn+3FdMTEzQrl07nD17VkFRSbm4uCA8PByfffYZfvjhB5XtQ9XW1oa7uztOnjyJK1euwMTEBOPHj0eXLl2wbt06PHnyROgQax1OukxpevbsWSLpSiQSTJ8+HampqTh8+DAaNmwoWGzPnz+Hn58fJk6cCGNjYyxfvhxGRkYIDg7G/fv38dNPP2HYsGFo0KCBYDFWVWhoKLp06YJnz57h+vXrmDJlisoMlCqPrLcLvUkes1PJonfv3rh06RIOHDiA6dOn4+XLlwqvszpatGiBlStX4u7du9i2bRtu376Nzp07w8bGBgcOHEB+fr7QIdYKPJCKKU1qaipat26NjIwMAMDMmTNx584dhIWFQUtLS+nxPHz4EMHBwQgODsbly5dhZWUFe3t72Nraqtwgmap4+vQp5s2bh5iYGGzbtg3Dhw8XOqRKWbRoEYyMjPD5559XarvY2FiMGTMGd+/eVcqXi5ycHEyePBnp6ek4dOgQDAwMFF6nvOTk5CAwMBB79uxBTEwMXF1dMXXqVLz33ntq8cVMHfGVLlMaAwMD6Orq4v79+5gzZw5u3ryJkJAQpSVciUSC6OhorFy5EhYWFujbty9iY2MxZ84cPH36FCEhIfj444/VPuFKJBJs374dFhYWaNu2LeLi4tQu4QJVa14GgG7duqGwsBA3b95UQFRve+edd3Do0CH0798f/fr1U1q98vDOO+9g8uTJiIiIwJ9//olmzZrB3d0dHTt2hIeHBxISEoQOscbhK12mVPb29hCLxUhNTUVERAR0dHQUWl9eXh5OnjyJ4OBgHD16FLq6urC3t4eDgwPee+89lb8tqbJu3LiBmTNnQiwWY8eOHejatavQIVVZp06d4OfnBwsLi0pvO3v2bLRo0QJLly5VQGRl8/LywtKlS+Hr64sRI0YotW55ISJcvHgRe/bsgb+/P/r06YMpU6bA0dFRkBapGkfIUVysdpFIJDRgwAAyNjam9PR0hdWTkpJCv//+Ozk6OpKOjg5ZWVmRp6enyo/WrY68vDxasWIFGRgY0K+//qoSMydVR1FREWloaFBOTk6Vtg8LCyNLS0s5RyWbqKgoMjY2pi1btghSvzzl5ubSvn37aOTIkaSvr08zZsygc+fO8ejnauArXaY0q1atgre3N1q3bo3IyEi5lUtEiI+Pf90/GxcXhxEjRsDBwQE2NjZo0qSJ3OpSRadOncLMmTNhYWGBn3/+We2bxwFpf7ulpWWVmzfz8/NhbGyM+/fvC/L3v3fvHmxtbTFixAj8+OOPKjGvdnUlJCRg79692LNnz+u7Dtzd3fHuu+8KHZp6ETjps1pi7dq11KlTJ4qJiSEjI6Nqf1MuLCykqKgoWrRoEbVt25bMzMxo1qxZFB4eTnl5eXKKWrWlpqbS1KlTqVmzZnTkyBGhw5GriIgIGjx4cLXKcHR0JG9vbzlFVHkZGRk0YsQIsra2pszMTMHikDeJREKXLl2iTz75hBo3bkzDhg0jb2/vSk1iUpvxQCpWdSkpwLp1wOTJgJ2d9N9164Bnz0qs5unpiT179uDEiRPo3r07JBIJnj59WunqsrKycOjQIUyZMgUmJiaYP38+tLW14efn9/oB8KNGjYKGhoa83qFKIiL4+Pigc+fO0NXVxY0bN2Bvby90WHJV1duFilPWrUNl0dPTQ2hoKFq0aIEBAwbg/+3dd1RU5/Y38O+oVBViAdGoiMZo0LGiIjaMCoKMEaLRqLl2jSX+oi+JMXpt8V5LwMQbgi1Gk4tGo16RYqWIsVCMBrCDBlCUEhuIDHW/fxwgI9KZmTNlf9aa5TDnzDl7XMDm7LOf5/nzzz9Fi0WZJBIJBgwYgG3btiE1NRVz587FgQMH0LZtW8yaNQvnzp3T2HHLGkHsrM+0UHQ0kbs7kbGx8AD+fpiYCK+5uxNFR9PWrVupY8eOdP/+/bK3jxo1ioKCgmp0qvv375Ovry+NHj2amjZtSk5OTuTj40PJycmq+nQaLTExkUaOHEm9evWi6OhoscNRmSVLltCmTZvqdYy0tDS1zE5VneLiYvrPf/5DVlZWdOHCBVFjUaWHDx/S5s2bydbWljp27Ehr166lP//8U+ywNA4nXVY7vr5EpqZEEsmrybb8QyKhfEND+rJ5c0pKSnrlEJ9//jmtW7euwsMXFxfT1atXae3atdSnTx9q3rw5TZ06lX799VedKtHVVn5+Pv373/+mFi1a0Ndff63R81Mrg0wmU8oUiwMGDKAzZ84oIaL6O378OFlYWJCfn5/YoahUcXExxcTE0MKFC6lFixbk6OhIe/fupezsbLFD0wicdFnNlSbcqpJtuUeRiYnwPgUHDhwgd3f3sq/z8vLo1KlTtHDhQmrXrh116tSJli5dSmfPntX55FITly5dIqlUSqNHj9aqhRXqo2vXrhQXF1fv46xfv54WL16shIiUIz4+njp06EArV67U+g7zmpDL5XT48GFyc3Mjc3NzmjZtGoWFhenFZ68MJ11WM9HR9J2BAfUFyBCgaZUk2TUAAaAziq+bmhLFxJQd6vbt29SuXTvy8/OjCRMmkLm5OQ0cOJA2bNhA169f5+EIJZ49e0YLFiyg1q1b0y+//KI3/y+FhYVkZGRU5+FCimJjY8nGxkaj/u/S09PJwcGBxo8fr5TPqC3S0tLI29ubpFIpWVtb06pVqygxMVHssNSOG6lYzWzYgDYFBVgJYGYlu9wFcBhA6/IbcnOBDRtw9+5dfPPNN5g7dy7u378PPz8/jB49Grdv335lAXh9n36OiPC///0P3bp1Q0FBAa5fv45Jkybpzf/L/fv3YWFhoZSJGKRSKQoLC3Hjxg0lRKYclpaWCA0NhZGREYYNG1anpkJt1KpVKyxduhSxsbE4evQonj17hoEDB2Lo0KH48ccfkZ2dLXaI6iF21mdaID39lYapFZVc6Y4GKBgg6/JXugDJJRKytbCg2bNnU0BAADk4OFBoaKjYn0zjpKSk0NixY6lr16507tw5scMRxenTp2n48OFKO96CBQtow4YNSjueshQXF9NXX31F7dq1o6tXr4odjijy8vLo6NGj9N5775G5uTlNnTqVQkJCdLr8zFe6rHp791a7yyEAhgBcK9neyNAQ8Z6e2LVrF2QyGfr27YsrV64oMUjtVlRUhK1bt6J3797o27cv/vjjDwwZMkTssEShjOFCisQeOlQZiUSClStXwtvbG6NGjcKxY8fEDkntDA0NMW7cOPj7+yMhIQF2dnbw9PREhw4dsHLlSiQkJNT/JDUc2qg2Ymd9pgWmTHnlqrX8lW42QG8BdK/k64qudAkg+uijskPu2bOHJk+eLOKH0hxXr16lfv360bBhw+jWrVtihyO6Tz/9lDZv3qy04+Xm5pKZmRllZmYq7ZjKFhUVRW3atKHNmzdr1P1nsfzxxx+0ZMkSsrS0JAcHB9q5cyc9e/asdgepxdBGdeIrXVa958+r3LwawEcAbKo7TsmSfkDFC9rrm5ycHHz22WdwcnLCxx9/jPDwcHTp0kXssERX19WFKmNsbIwRI0bg+PHjSjumsvXv3x+RkZHYt28fZs+erfFr86paz549sWXLFjx48ABffPEFTp48ifbt22Py5Mk4ffo0ioqKqj7Atm2AoyPg7w/I5cJDUW6u8Jq/v7Dftm2q+iiv4aTLqmduXuXmUAD/AWBV8rgP4AMAm8rv2KxZ2VNbW1skJSUhJydHmZFqjZMnT6J79+54+PAhrl27hpkzZ+pNo1R1lF1eBjS3xKyoXbt2OH/+PP766y84OTnh8ePHYockOgMDA8hkMhw5cgR3796Fg4MDvvzyS1hbW2P58uW4devW62/atg3w9ARevhSua6tCJOzn6am+xKvW62qmnTZtIjI2pgKAcgH6AqCpJc8LAPoLoEcKj7YA/VpSdn6lnFOuZNi3b1+6ePGiSB9KHGlpaTRp0iSysbGhkydPih2OxikoKCAjIyN6+fKlUo+bnp5O5ubmos9OVROFhYX02Wef0VtvvcW3GyoRHx9Pnp6eZGVlRfb29rRt2zZh5bLo6ArnEpgCkBVATQHqDNCuim5/lRvaqCqcdFn1SrqXV5eMwVV8rK7gm7fCe7rGxkQZGa8cdvbs2eTj4yPSh1KvoqIi2rVrF1lYWNDnn3+uV+Mza+PevXvUrl07lRzb3t6eTp8+rZJjq8Lu3bvJ0tKSQkJCxA5FYxUUFFBwcDBNmDCBzMzMKOrNN6mogtnyrgEkL3l+E6BWAF2uYBY98vBQecxcXmbVs7QEXFywSiJ5LeuuqWD3JAAjFV+QSABXV8DC4pX9+vTpoxf3dW/evAlHR0fs2rULZ86cwaZNm3gx8EokJCQo9X6uIm0oMSuaOXMmDh48iMmTJ2PHjh1ih6ORGjVqBFdXV/z6669Iio5Gn/R0NKigpNwNgFHJc0nJ4275nYiA48dV3tXMSZfVyOHOnSGv68ohJibA8uWvvazrzVR5eXlYs2YNhgwZggkTJuDixYvo2bOn2GFpNFXczy1VmnRJi1bAcXR0xPnz57FlyxYsWbKk+gYiPdbs2LEq1y1eAMAUQFcIE/hUOLxRIqnREMn64KTLqlRQUIAFCxZgVWAgXqxdC9T2Cs3UFPDyAuzsXtvUo0cP3Lx5Uyc7NSMiItCzZ0/Exsbijz/+wCeffIKGDRuKHZbGU+WVbvfu3VFcXIzr16+r5Piq0rlzZ0RGRiIuLg7vvfcesrKyxA5JM8XFvd6lrMAXQDaA3wB44O8r31fk5gLx8SoJrxQnXVapx48fw9nZGSkpKYiMjITlqlVCAjU1Ff4irIpE8nfCnT+/wl1MTU1hY2OjUVP01deTJ08wa9YsTJkyBRs2bMDRo0fRtm1bscPSGsoeLqRIIpFoXYm5VLNmzXDy5Em8+eabGDRoEJKTk8UOSfNUM7QRABoCGAzgAYBKe5UVhjaqAiddVqHr16+jf//+6NevH44dOwYzMzNhw/z5QEQE4O4OGBsLpWNFJibC6+7uwn6VJNxSulJiJiLs378f3bp1g6mpKW7cuAF3d3exw9I6qiwvA9p3X1eRgYEBtm/fjlmzZmHgwIGIjIwUOyTNUs3QRkWFqOCebimFoY0qofJWLaZ1AgMDycLCgn7++eeqd8zIEIYBffQRkZub8O/mza91KVfF29ubFi1aVM+IxXXv3j1ydnYmqVRKkZGRYoejtUqHC+Xm5qrsHHK5nMzMzCg9PV1l51CHoKAgsrCwoP3794sdiuYoGdpYvnM5HaBfSoYwFgJ0EiBTgPwrGjZUwdBGZeOky8oUFxfTxo0bqU2bNmpLHmFhYTRo0CC1nEvZ8vPzadOmTdSiRQvauHEj5efnix2SVrt79y61b99e5efx8PCgPXv2qPw8qhYXF1e2RB5PHUmvLcxS+sgAaChA5iXjdLsDtLOihFvJ0EZl4/IyAwDI5XL84x//wKFDhxAVFYUBAwao5by9evVCbGys1nVlRkdHw87ODiEhIYiKisKyZctgYGAgdlhaTZVNVIpkMhmCgoJUfh5Vk0qliIqKwunTp/Hhhx8iNzdX7JDEVTK0kcr1m1gAiADwDEAWgHgAcyp6fyVDG5WNky7Do0ePMGzYMBQUFODcuXNqbfxp1qwZLCwskJiYqLZz1kd2djYWL16M9957D59//jlOnTqFTp06iR2WTlD1/dxSrq6uCAkJQV5ensrPpWqtWrVCeHg4GjRoAEdHR6SlpYkdkqjSZsxA5f3L1ahkaKOycdLVc5cvX0b//v0xduxY/PLLL6JM2qAtzVT+/v6wtbVFTk4Orl27hilTpvB8yUqkritdS0tL2NraIiIiQuXnUgdjY2Ps27cPY8aMwYABAxAbGyt2SKJITEyE/Sef4OL77yt1aKOycdLVYwcOHICrqyu+++47rFixQrQE0rt3b41eWzc1NRUeHh5YtmwZ/vvf/2L37t1o0aKF2GHpHFUOFypPm7uYKyKRSLBq1Sps3rwZI0eO1KnPVhPXr1+Ho6MjVqxYgRGHDil1aKPSqfSOMdNIRUVF9OWXX1KHDh0oNjZW7HAoODiYRo4cKXYYryksLCQfHx9q2bIlrVq1SqVdtYyoc+fOdP36dbWcKz4+nqytrXWyASkyMpLatGlD3t7eOvn5yvv999/JysqK/Pz8Xt0QEyPMpWxsLHQlV7SeroeHWhY5UCQh0qI50Vi9ZWdn46OPPsKTJ09w5MgRWKi4aaAmHj16BKlUiszMTI0p18bFxWHu3LkwMDDAjh07YGtrK3ZIOq2wsBBNmjTBs2fPYGxsrPLzERFsbGwQGBgIqVSq8vOpW0pKCmQyGfr374/vv/8ehoaGYoekEhcvXoS7uzu2b99e+bj4zExhasf4eGHii2bNAKkUmD5d5U1TFVJrimeiunfvHkmlUpo9e7bGLXFmZWVFycnJYodBOTk5tGzZMrKwsKCdO3dSUVGR2CHphcTERLK2tlbrORctWkT/+te/1HpOdcrKyiI3NzcaPnw4PX78WOxwlC40NJRatmxJJ06cEDuUWuF7unri3LlzcHBwwJw5c7Bz506N+8tXE5qpzpw5A6lUiqSkJMTFxWHOnDlo0IB/RNRBXU1UinTtvm55TZs2hb+/P/r06QN7e3vcuXNH7JCUJjg4GJMmTcLhw4cxevRoscOpFf6Nogd27dqFCRMm4Oeff8Ynn3yiMSVcRWI2U2VkZGDq1KmYO3cufHx8cODAAVhZWYkSi75S13AhRcOGDcPNmzeRkZGh1vOqU8OGDeHl5YXPPvsMQ4YMQXh4uNgh1dvhw4cxc+ZMBAQEYNiwYWKHU2ucdHVYYWEhFi9eDG9vb/z2228YNWqU2CFVSoy1dYkIe/bsQffu3WFlZYVr167BxcVFrTEwgTo7l0sZGRlh5MiRCA4OVut5xTBnzhwcOHAAkyZNwg8//CB2OHVWeuFw6tQp2Nvbix1OnXDS1VFPnjyBi4sLEhISEBkZibffflvskKqk7vLynTt38O677+L777/HqVOn4OXlhcaNG6vt/OxVYpSXAd0vMSsaPnw4fvvtN2zevBmenp5aNwvc9u3bsWLFCoSFhaFXr15ih1NnnHR10K1btzBgwAD06NEDQUFBeOONN8QOqVo2NjbIzs5GZmamSs+Tl5eHdevWwcHBAePGjUNUVBR69+6t0nOy6olRXgaE2alCQ0N1Ynaqmnj77bcRGRmJK1euYNy4ccjOzhY7pBrZsmULNm/ejIiICLzzzjtih1MvnHR1zIkTJzB06FCsWLEC3t7eWrNwukQiUfnV7vnz59G7d2/ExMTgypUr+L//+z+t+f/RZQUFBUhJSUHHjh3Vfm4LCwt0794dZ8+eVfu5xdK8eXOcPHkSVlZWGDx4MFJSUsQOqVJEhHXr1mHHjh2IiIgQ5XtE2Tjp6ggigre3N2bNmgV/f39Mnz5d7JBqTVVJ9+nTp5g3bx4mTpyIdevWISAgAO3bt1f6eVjdJCcno02bNjAyMhLl/PpUYi5laGiInTt3Ytq0abC3t0dUVJTYIb2GiLBs2TIcOnQI586dQ7t27cQOSSk46eqAvLw8zJgxA35+foiMjISDg4PYIdVJnz59lNrBTEQ4ePAgunXrhoYNG+LGjRsYP368RnZv6zOx7ueWKk26pGfzBEkkEixduhQ7duyAm5sbDh48KHZIZYqLi7Fo0SKEh4fj7NmzaNWqldghKU0jsQNg9ZOWlgYPDw+8+eabOH/+vFY3A/Xu3Rvr1q1TyrGSkpKwcOFCJCcn4/Dhw1r7h4g+EOt+bilbW1s0bNgQ8fHx6NGjh2hxiEUmkyEkJARjx47F7du38c9//lPUP0wLCwsxe/Zs3L17FyEhITA3NxctFlXgK10tdvXqVQwYMADOzs44ePCgVidcAOjSpQtSU1ORlZVV52MUFhbC29sbdnZ2GDRoEK5cucIJV8OJMVxIkUQigZubm96VmBX17NkTUVFRCA4OxpQpUyCX13mBvHrJz8/H5MmTkZqaipMnT+pcwgU46WqtQ4cOwcnJCVu2bMHq1at1YuakRo0aQSqV1nlpst9//x39+/fHiRMnEBkZiS+//FLjZt5irxO7vAzo533d8qysrHD27FkUFRVh+PDhSE9PV+v55XI53n//fcjlcgQGBmr9RURltP83tZ4pLi7G6tWr4enpiTNnzuD9998XOyTlycjA5wAsli4FZDJg6lRg82ZhwvIqvHjxAkuWLMGYMWPw6aef4syZM6KWK1ntiF1eBoTZqW7duqX2RKNpTExM8Msvv8DJyQkDBgxAfHy8Ws6bk5MDNzc3NG7cGEeOHFHLoheiEXPiZ1Y7L168oPfff58cHBwoLS1N7HCUJzqayN2dyNiYCgwMKl6Cy91d2K+cgIAAat++PU2bNo0yMzNFCJ7VR35+PhkaGmrEAhzjx4+n3bt3ix2Gxti3bx+1bNmSgoKCVHqeZ8+e0aBBg2j69OlUWFio0nNpAk66WiIpKYl69uxJM2bMILlcLnY4yuPrS2RqSiSRvJpsyz8kEmE/X18iInr48CGNHz+e3nrrLQoJCRH5Q7C6unPnDtnY2IgdBhER/fTTTzRu3Dixw9AoFy9epNatW9M333yjkrV5MzMzqW/fvrRw4UK9WdGLy8ta4MKFCxg4cCCmTZuG3bt3izaeUem2bQM8PYGXL4XUWhUi4OVLkKcnIj78ED169ECXLl0QFxeHESNGqCdepnSacD+3lKurK8LCwkRrItJEAwcOxKVLl7B7927Mnz8fBQUFSjt2WloaHB0dMWLECHz33Xc60ZdSE/rxKbXYjz/+CHd3d/z4449YsmSJ7owxjYn5O+Eq8AFgB8AIwPQK3iZ5+RL9f/0Vl3x8sH79epiYmKg+VqYymnA/t1TLli0hlUp1YiUeZbK2tsaFCxdw//59uLi44OnTp5XvnJEh9GFMnVplX0ZKSgqGDh2KiRMnYuPGjbrze60GOOlqqMLCQixduhQbN27Eb7/9pnVrRlZrwwYgN/e1l9sAWAlgZhVvNSbCW7/+qqrImBqJPVyoPJlMhqCgILHD0DhmZmYICAiAVCqFvb09EhISXt0hJgbw8ACsrYHVq4F9+4CgIOHfNWuA9u2F7TExSExMxNChQ/Hxxx+LPiZYFGLXt9nrnj59Ss7OzjRq1Ch68uSJ2OEoX3q60BxVxT3cFQBNq+oer7ExUUaG2J+E1ZOzs7PKG3Vq4/r169SuXTuV3L/UFdu3bydLS0sKDw8XXqhFX0aRsTEtMzenHTt2iPoZxMRXuhrmzp07sLe3R9euXXH8+HE0a9ZM7JCUb+/e+h9DIlHOcZioNKm8DADvvPMODAwMEBcXJ3YoGmvevHnYt28fPvjgA1yYOrVWfRkN5HKsz83FXC1bVlCZOOlqkNOnT2PIkCHw9PTEt99+i0aNdHSWzrg4oL7NKrm5gJrGEDLVyM/Px4MHD2BjYyN2KGV4dqqaGTlyJGJ8fdFn//7X+jIAIAGAMYCpFby3UX6+kKgvX1Z1mBqJk64GICJs3boV06ZNw+HDhzF79myxQ1Kt58+Vc5yqGjqYxktKSkLbtm01btYwnp2qZqz370dlU1gsBNCvqjfn5gp9HXpIRy+ltEd+fj4WLFiAmJgYXLp0CR06dBA7JJUqLi7G44ICWCjjYLpYetcjmjRcSNHQoUNx+/ZtpKWlwcrKSuxwNFNGBnDiBCQVlJQPAHgDgAOAxMreTwQcPy50NVso5beB1uArXRFlZGRgxIgRePLkCS5cuKCzCffFixc4evQoZs6cidatW+Pnq1dRUEnpvBCAHEBRyUNe8tprTEwAqVRVITM10LT7uaUMDQ3h5OSE4OBgsUPRXJX0U2QBWAXAuybH0NO+DE66IomNjUX//v0xfPhwHD58GE2aNBE7JKVKSUmBr68vXFxc0KZNG/j6+qJXr164dOkS/l98PAwqSbrrAZgA2AjAr+T5+op2JAKmT1dR9EwdNG24kCIuMVejkr6MfwKYBaBGy83raV8Gl5dFcPToUcybNw/fffcdJk6cKHY4SlFcXIzLly8jMDAQgYGBePDgAVxdXTFz5kwcPHgQZmZmr77BxQXw93+t43FNyaNKEgng6qp3ZSldk5CQAFdXV7HDqJCrqysWLlwIuVyu25Pv11UFfRl/AAgBcLU2x9HDvgxOumpERFi/fj127dqFEydOoG/fvmKHVC85OTkICQlBYGAggoOD0axZM8hkMvj4+GDgwIFo2LBh5W9evhw4darCzsdqmZgI72daTVPLywDQokUL9OzZE2FhYRr7h4GoKljn9iyAJADtS75+AeEW0Q0AVyo7jh72ZXDSVZOXL19ixowZSE5ORlRUFFq3bi12SHXy4MGDsqvZ8+fPo1+/fpDJZFi+fDk6depU8wP16wd4eVU4FWSVTE2F99nZ1T54pjHy8/ORmpqqUcOFyistMXPSrUCPHsCRI6+UmOcCmKSwixeEJLytsmPoaV+GhKi6Ec2svu7fv49x48ahW7du2LlzK63bjQAADQ1JREFUp1aVq4qLi/H777+XJdqUlBS4uLhAJpNh9OjRMK/gL95aKV30IDe36sH1EonwQ+rlBcyfX79zMtHdvn0bY8aMQWJipf2tort58yacnJyQkpKif1MVVicjQ5jysYrx9msgdC/7VbaDsTGQkqJ3t4m4kUrFIiMjYW9vj0mTJuGnn37SioT78uVLBAQEYM6cOWjbti3+8Y9/QC6XY+vWrUhPT4efnx8mTpxY/4QLCAk0IgJwdxd+CMsvYGBiIrzu7i7sxwlXJ2jqcCFFXbt2hZGREWJjY8UORfNYWgp9GVX8MbIGVSRcPe7L4PKyCv3888/w9PTEnj17MGbMGLHDqVJqaiqCgoIQGBiIc+fOwc7ODjKZDMuWLVP9fTc7O6FUlZkpDCGIjxcaLJo1E8pP06fr5Q+nLtPk+7mlFGen6tWrl9jhaB7uy6gTLi+rQFFREb744gscPXoUAQEBsLW1FTuk1xARrly5UlY2TkpKwujRo8vKxm+88YbYITIdtnDhQnTp0gWLFy8WO5QqhYaGYvny5YiOjhY7FM2kuCZ2TZX2Zehp1YqvdJXs+fPnmDx5MuRyOaKiotCiRQuxQyqTm5uL0NBQBAYGIigoCE2aNIFMJsOWLVswaNAg3Z3rmWmchIQEuLm5iR1GtYYMGYKEhAQ8evRIa5sfVao0cXJfRo3xPV0lSkxMxMCBA2FjY4OTJ09qRMJ99OgRdu3ahbFjx6JVq1bw8vLC22+/jfDwcNy+fRteXl4YNmwYJ1ymVtpQXgZ4dqoa4b6MWuHyspKEhoZiypQpWLt2LebNmydaHESEq1evll3N3r17F87OzmVl4+bNm4sWG2MAkJeXB3Nzc2RnZ8PAwEDscKrl5+eHQ4cO4dixY2KHovm4L6NanHTriYjg6+uLr776CgcOHICjo6PaY8jNzUVYWFhZojUxMYFMJoNMJsPgwYO14hcb0x+3bt2CTCZDQkKC2KHUyOPHj2FjY4P09HSYlL+KY6yWuKZYD/n5+Vi8eDEuXLiAixcvomPHjmo7d1paWlm38dmzZ9GrVy+4ubkhJCQEXbp04XGFTGNpw3AhRS1atECvXr0QFham8aMQmObjpFtHf/31F8aPHw8zMzNcvHgRTZs2Ven5iAixsbFl3cYJCQlwdnbGBx98gD179nDZmGkNbbmfq6h0dipOuqy+OOnWwbVr1zB27FhMmjQJ69evR4MGqulHk8vlCA8PLysbGxoaQiaTYePGjRgyZAiXjZlWSkxMxDvvvCN2GLUik8kwcuRIEBFXkVi9cNKtpYCAAMyePRvffvstJk+erPTjp6enIzg4GIGBgQgLC0OPHj0gk8lw6tQpdO3alX/gmdZLSEjA2LFjxQ6jVrp06QITExNcvXoVffr0ETscpsU46dYQEWHjxo3w9fVFcHAw+vXrp7TjxsfHl5WNb926BScnJ3h4eGDXrl1o2bKlUs7DmKbQxvKyRCKBTCZDUFAQJ11WL9y9XAO5ubmYPXs2EhIS4O/vjzZt2tTreHl5eQgPDy9rhGrYsGFZt/HQoUNhaGiopMgZ0yylw4VevHihdWPDw8LCsGzZMsTExIgdCtNi2vVdL4LU1FS4u7ujc+fOiIiIqPOQgYyMjLKycWhoKKRSKdzc3HD8+HHY2tpy2ZjphXv37qF9+/Zal3ABYXaqxMREPHz4sN5/eDP9pX3f+fWVkSEM3o6LA54/FxZj7tEDmDHjtcHb0dHR8PDwwKJFi7Bs2bJaJUYiwrVr18rKxjdv3sSoUaMwbtw47Ny5k8vGTC9p23AhRQYGBnB2dkZwcDDmzJkjdjhMS+lPeTkmBtiwAThxQvhacR1IExNhzlAXF2Hli379sH//fnz66af44Ycfatz0kZeXh4iIiLJuYwCvlI2NjIyU/akY0ypbtmxBcnIytm7dKnYodbJv3z4cPHgQAQEBYofCtJR+JN1aLJROJiY4NngwliYkICAgAN27d6/y0JmZmTh+/DgCAwMREhICW1vbskTbrVs3LhszpmD+/Pno1q0bFi1aJHYodfLkyRN06NCBZ6didab75eXaLD1FBMnLl3AOCUHsxo1oWkHCJSLcuHGjrGx87do1jBw5EjKZDL6+vrC0tFTBh2BMNyQkJGDcuHFih1FnzZs3R+/evREaGqoVqyQxzaPbV7oxMfAZNAh7CwoQD+BDAHtLNiUBsAHQWGH3ZQD+WfqFqamwIoadHfLz8xEREVHWbVxUVFR2Nevo6MhlY8ZqyNraGmFhYejUqZPYodSZl5cXEhISsGPHDrFDYVpIt5Ouhwf+d/QoGgA4BSAXryfdAlR8uU8SCVL69IGnjQ3OnDmDrl27liVaqVTKZWPGakkul+ONN97QyuFCim7fvo13330XDx484N8DrNa09zu/OhkZwIkT8Cj58jKAB7V4u4QIra9ehftHH8HHxwetWrVSQZCM6TiF0QIFDx7goKEhGm3ZUuFoAW3RpUsXNG7cGFeuXEHfvn3FDodpGd1dxH7v3hrtZg2gLYAZAP4qt83QyAiT8/M54TJWWzExgIcHYG0NrF4N7NuHphEReC87G1izBmjfXtiupRNNlC6AwFht6W7SjYt7dVhQOS0BxABIBvA7gGwAU8rvlJsrLMbMGKu5bdsAR0fA31/4GSz/c5ibK7zm7y/st22bGFHWi5ubGyddVie6W15+/rzKzU0A2JU8bwXAB0BrAFkAzBR3fPpUBcExpqNqOVoAL18K+wPA/PmqjU2JBg8ejOy7d/F8xQqYJydXO9EOY6V090rX3LxWu5e2Q7zWVdasmTKiYUz3xcQAnp7wefkSdgCMAExX2BwJYBSA5gAsAEwA8Aj4O/FevqzmgOsoJgYGEyfiWnY2Gn/9NbBvHxAUJPyrA6Vzplq6m3R79ACMjVEIQA6gqOQhB1AIIArAbQDFAB4DWAzAEcArqdrEBJBK1Rg0Y1pswwYgNxdtAKwEMLPc5qcA5kIYOZAMoCmEXgoAQsl5wwY1BVoPCqVzw+JiNCooeHW7DpTOmWrp7pChjAzA2hpr5HKsLbdpNYAuAL4EkAGhnDwKwGYAVoo7GhsDKSlcKmKsOiU/b4r3b1dCGDGwt5K3XAEwDEI/BQDN/3mrTem8lKkp4OWlVaVzplq6e6VraQm4uGCNRAICXnmsgTBRxp8AciCUuH5GuYQrkQCurpr7C4AxTVLD0QKKzgHopviCRFKn46hFNaXzfADjAXSAcKvqbOkGbSudM5XT3aQLCIsX1HV+VBMT4f2MsepVM1rgtd0BrAPwteKLubmguDglB6Yk1ZTOAWAwAD+U++Md0J7SOVML3e1eBoB+/YTSTl1LQnZ21e/LGKt2tICiRAAuALYCGFJuW5CfH6YcO4amTZvCzMzslX9r+1qTJk3QoIESritKJtoBUaWT7RgC+LTkecPy7ycCjh8HMjO5csZ0POkCf99LqeEqQzAx4XswjNVWDUcLJAMYCWGO848q2D5myhQ88PVFVlYWsrOzy/5VfJ6VlYWsrCykpqZWuV9OTg5MTU3rlbibNm2Klnv2wBh/j3Cok9LS+Wef1ecoTAfoftIFhATar59Q4jl+XPgByM39e3vperqurkJJma9wGaudHj2AI0cAuRyFEEYIKI4YaAQgHcC7ABYC+LiiY5iYoEHPnjAzM4OZmVlFe9RKcXExcnJyXkvYFSXxtLS0CvfLysqCV3o6JhUW1i8YnmiHldDd7uXKZGYKf3HGxwsTXzRrJgwLmj6dSz+M1ZVC9/IaoMIRAxIITYyNy217UfpEU7uXZTJhHK6Cqjqz20K4t+tYfoObG8CzWOk9/bjSVWRhwSUexpStZLQA/P2xhghrKtltdWXv1+TRArWcaKdSPNEOg653LzPG1EdXRwuUTLQDoNLJdgAgr+RrQBhCJIfCDHc80Q4rwUmXMaYcpaMFTE1r9z5NHy0wfXrZ0/UATABshFBCNil5DRAm3DEBkArAueR5cukbiV45DtNf+ndPlzGmWqUzN+nSaAEPD2Fqx7r8upRIAHd3odGM6T1Ouowx5bt8WbdGC8TECHMp12a8fylTUyAiQjs+J1M5TrqMMdXRpdECPPcyUwJOuowxVlO6WDpnasVJlzHGakPXSudMrTjpMsZYXehS6ZypDSddxhhjTE14nC5jjDGmJpx0GWOMMTXhpMsYY4ypCSddxhhjTE046TLGGGNqwkmXMcYYUxNOuowxxpiacNJljDHG1ISTLmOMMaYmnHQZY4wxNeGkyxhjjKkJJ13GGGNMTTjpMsYYY2rCSZcxxhhTE066jDHGmJpw0mWMMcbUhJMuY4wxpiacdBljjDE14aTLGGOMqQknXcYYY0xNOOkyxhhjasJJlzHGGFMTTrqMMcaYmnDSZYwxxtSEky5jjDGmJpx0GWOMMTXhpMsYY4ypCSddxhhjTE046TLGGGNqwkmXMcYYUxNOuowxxpiacNJljDHG1OT/A4RoAbqLMB9TAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# alternative template \n", "seed16 = get_supermatrix_template(seed15, forced_edges=[(1,15), (15,14)])\n", "print(seed16)\n", "plot_given_edges(seed16)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Wall time: 5.02 ms\n" ] } ], "source": [ "# Fill in the template\n", "%time super16 = templates_to_valid_graphs([seed16], verbose=0)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2020-07-08 16:46:25.728381: Starting with 1 seeds\n", "Currently 0 graphs, 1 candidates\n", "Currently 0 graphs, 1 candidates\n", "Currently 0 graphs, 1 candidates\n", "Currently 0 graphs, 1 candidates\n", "Currently 0 graphs, 1 candidates\n", "Currently 0 graphs, 1 candidates\n", "Currently 0 graphs, 1 candidates\n", "Currently 0 graphs, 1 candidates\n", "Currently 0 graphs, 1 candidates\n", "Currently 0 graphs, 1 candidates\n", "Currently 0 graphs, 1 candidates\n", "Currently 0 graphs, 1 candidates\n", "2020-07-08 16:46:25.733368: 1 valid graphs from templates\n", "\t1 reps from 1 candidates\n", "2020-07-08 16:46:25.733368: Reduced to 1 representatives\n", "Wall time: 4.99 ms\n" ] } ], "source": [ "# For convenience, can wrap up the templating, search, and reduction steps for a list of seed graphs\n", "%time rep16 = find_valid_supergraphs([seed15], forced_edges=[(1,15), (15,14)])" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# confirm this is what we expected from the individual steps:\n", "plot_given_edges(rep16[0])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Saturating vertex 1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We know one of the blades centred at vertex 1; namely 1-0-2-1.\n", "\n", "We also have part of another, containing vertex 15.\n", "\n", "wlog, let vertex 16 be the other vertex of that blade (_so we force 1-16, and 15-16_)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2020-07-08 16:46:25.825090: Starting with 1 seeds\n", "2020-07-08 16:46:25.864019: 11 valid graphs from templates\n", "2020-07-08 16:46:25.866010: Reduced to 2 representatives\n", "Wall time: 40.9 ms\n" ] } ], "source": [ "%time rep17 = find_valid_supergraphs(rep16, forced_edges=[(1,16),(15,16)], verbose=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Vertex 17 necessarily starts a new blade, so only forcing 1-17" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2020-07-08 16:46:25.871963: Starting with 2 seeds\n", "2020-07-08 16:46:25.973691: 20 valid graphs from templates\n", "2020-07-08 16:46:25.975686: Reduced to 3 representatives\n", "Wall time: 104 ms\n" ] } ], "source": [ "%time rep18 = find_valid_supergraphs(rep17, forced_edges=[(1,17)], verbose=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "However, we can then force vertex 18 to be the other vertex of that blade" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2020-07-08 16:46:25.980673: Starting with 3 seeds\n", "2020-07-08 16:46:26.133264: 27 valid graphs from templates\n", "2020-07-08 16:46:26.137253: Reduced to 5 representatives\n", "Wall time: 158 ms\n" ] } ], "source": [ "%time rep19 = find_valid_supergraphs(rep18, forced_edges=[(1,18),(17,18)], verbose=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Continue in this fashion until we have all nhbrs of vertex 1, with forced fan pattern 0-2, 15-16, 17-18, 19-20, 21-22, 23-24, 25-26" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2020-07-08 16:46:26.144234: Starting with 5 seeds\n", "2020-07-08 16:46:26.432496: 40 valid graphs from templates\n", "2020-07-08 16:46:26.437481: Reduced to 8 representatives\n", "Wall time: 293 ms\n" ] } ], "source": [ "%time rep20 = find_valid_supergraphs(rep19, forced_edges=[(1,19)], verbose=False)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2020-07-08 16:46:26.444433: Starting with 8 seeds\n", "2020-07-08 16:46:26.874315: 56 valid graphs from templates\n", "2020-07-08 16:46:26.882261: Reduced to 10 representatives\n", "Wall time: 438 ms\n" ] } ], "source": [ "%time rep21 = find_valid_supergraphs(rep20, forced_edges=[(1,20), (19,20)], verbose=False)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2020-07-08 16:46:26.887248: Starting with 10 seeds\n", "2020-07-08 16:46:27.510578: 60 valid graphs from templates\n", "2020-07-08 16:46:27.518557: Reduced to 17 representatives\n", "Wall time: 632 ms\n" ] } ], "source": [ "%time rep22 = find_valid_supergraphs(rep21, forced_edges=[(1,21)], verbose=False)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2020-07-08 16:46:27.525540: Starting with 17 seeds\n", "2020-07-08 16:46:28.506946: 85 valid graphs from templates\n", "2020-07-08 16:46:28.519913: Reduced to 17 representatives\n", "Wall time: 994 ms\n" ] } ], "source": [ "%time rep23 = find_valid_supergraphs(rep22, forced_edges=[(1,22), (21,22)], verbose=False)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2020-07-08 16:46:28.523869: Starting with 17 seeds\n", "2020-07-08 16:46:29.543090: 68 valid graphs from templates\n", "2020-07-08 16:46:29.553066: Reduced to 26 representatives\n", "Wall time: 1.03 s\n" ] } ], "source": [ "%time rep24 = find_valid_supergraphs(rep23, forced_edges=[(1,23)], verbose=False)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2020-07-08 16:46:29.558021: Starting with 26 seeds\n", "2020-07-08 16:46:30.889488: 78 valid graphs from templates\n", "2020-07-08 16:46:30.901459: Reduced to 19 representatives\n", "Wall time: 1.34 s\n" ] } ], "source": [ "%time rep25 = find_valid_supergraphs(rep24, forced_edges=[(1,24), (23,24)], verbose=False)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2020-07-08 16:46:30.907411: Starting with 19 seeds\n", "2020-07-08 16:46:31.851913: 38 valid graphs from templates\n", "2020-07-08 16:46:31.857908: Reduced to 19 representatives\n", "Wall time: 950 ms\n" ] } ], "source": [ "%time rep26 = find_valid_supergraphs(rep25, forced_edges=[(1,25)], verbose=False)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2020-07-08 16:46:31.865847: Starting with 19 seeds\n", "2020-07-08 16:46:32.581961: 19 valid graphs from templates\n", "2020-07-08 16:46:32.585951: Reduced to 11 representatives\n", "Wall time: 720 ms\n" ] } ], "source": [ "%time rep27 = find_valid_supergraphs(rep26, forced_edges=[(1,26),(25,26)], verbose=False)" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Review an example\n", "\n", "plot_given_edges(rep27[0])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Saturating vertex 2\n", "\n", "Although we have multiple possible 27-vertex graphs, for each of them we know that vertex 2 has degree 2: \n", " * As a neighbour of vertex 0, it can only have one mutual neighbour amongst vertices 1,3-14, which is vertex 1\n", " * As a neighbour of vertex 1, it can only have one mutual neighbour amongst vertices 0,15-26, which is vertex 0\n", " \n", "Thus we have precisely one blade centered at vertex 2, 2-0-1-2. " ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Confirm our claim:\n", "[vertex_degrees(a)[2] for a in rep27]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We note that vertices 2 and 3 are non-adjacent. Thus, they will have two mutual neighbours. \n", "\n", "Vertex 0 is one of these, but they cannot currently have another:\n", " * Vertex 1 neighbours 2 but not 3\n", " * Vertex 4 neighbours 3 but not 2\n", " * Vertices 5-14 neighbour neither 2 nor 3\n", " * Vertices v=15-26 neighbour vertex 1. Thus if v neighboured vertex 2, we'd have two mutual neighbours 0,v of 1,2. As 1 already neighbours 2, this is forbidden by the lambda condition." ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[[0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0]]" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Confirm our claim:\n", "[mutual_neighbours(2,3,a) for a in rep27]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "wlog, we may arrange for vertex 27 to be the second mutual neighbour of vertices 2 and 3. \n", "As a non-nhbr of 0, these are their two mutual neighbours, so by mu condition 27 is not a neighbour of any of 4 through 14." ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[(4, 27),\n", " (5, 27),\n", " (6, 27),\n", " (7, 27),\n", " (8, 27),\n", " (9, 27),\n", " (10, 27),\n", " (11, 27),\n", " (12, 27),\n", " (13, 27),\n", " (14, 27)]" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "non_edges27 = [(k,27) for k in range(4,15)]\n", "non_edges27" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2020-07-08 16:46:32.720561: Starting with 11 seeds\n", "2020-07-08 16:46:33.753826: 131 valid graphs from templates\n", "2020-07-08 16:46:33.777762: Reduced to 66 representatives\n", "Wall time: 1.06 s\n" ] } ], "source": [ "%time rep28 = find_valid_supergraphs(rep27, forced_edges=[(2,27),(3,27)], forced_non_edges=non_edges27, verbose=False)" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[15]" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "min([[k for k in range(27) if r[27][k] and k not in [2,3]] for r in rep28])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Similarly, vertices 2 and 4 are non-adajcent, with at least 1 mutual neighbour 0. Do they have any more?" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "max([len(mutual_neighbours(2,4,a)) for a in rep28])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "No, so we introduce their second mutual neighbour now. \n", "\n", "Again, it cannot have any additional mutual neighbours with vertex 0, so is not adjacent to 3 or 5 through 14." ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [], "source": [ "non_edges28 = [(k,28) for k in range(15) if k not in [2,4]]" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2020-07-08 16:46:33.800670: Starting with 66 seeds\n", "2020-07-08 16:46:41.777754: 1396 valid graphs from templates\n", "2020-07-08 16:46:42.045040: Reduced to 630 representatives\n", "Wall time: 8.24 s\n" ] } ], "source": [ "%time rep29 = find_valid_supergraphs(rep28, forced_edges=[(2,28),(4,28)], forced_non_edges=non_edges28, verbose=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Similarly for vertex 5, there is only vertex 0 as a mutual neighbour with vertex 2:" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "max([len(mutual_neighbours(2,5,a)) for a in rep29])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So we add their second mutual neighbour next:" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [], "source": [ "non_edges29 = [(k,29) for k in range(15) if k not in [2,5]]" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2020-07-08 16:46:42.069026: Starting with 630 seeds\n", "2020-07-08 16:48:10.368789: 12878 valid graphs from templates\n", "2020-07-08 16:48:12.792308: Reduced to 9932 representatives\n", "Wall time: 1min 30s\n" ] } ], "source": [ "%time rep30 = find_valid_supergraphs(rep29, forced_edges=[(2,29),(5,29)], forced_non_edges=non_edges29, verbose=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Again for vertex 6, there is only vertex 0 as a mutual neighbour with vertex 2:" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "max([len(mutual_neighbours(2,6,a)) for a in rep30])" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [], "source": [ "non_edges30 = [(k,30) for k in range(15) if k not in [2,6]]" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2020-07-08 16:48:12.893004: Starting with 9932 seeds\n", "2020-07-08 17:17:17.958235: 217303 valid graphs from templates\n", "2020-07-08 17:18:01.256380: Reduced to 135195 representatives\n", "Wall time: 29min 48s\n" ] } ], "source": [ "%time rep31 = find_valid_supergraphs(rep30, forced_edges=[(2,30),(6,30)], forced_non_edges=non_edges30, verbose=False)" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [], "source": [ "pickle.dump( rep31, open( \"fullsearch-31.p\", \"wb\" ) )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "_next stage errors out due to insufficient memory_" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Again for vertex 7, there is only vertex 0 as a mutual neighbour with vertex 2:" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "max([len(mutual_neighbours(2,7,a)) for a in rep31])" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [], "source": [ "non_edges31 = [(k,31) for k in range(15) if k not in [2,7]]" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [], "source": [ "#%time rep32 = find_valid_supergraphs(rep31, forced_edges=[(2,31),(7,31)], forced_non_edges=non_edges31, verbose=False)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 2 }