day_23_author_network_fragility.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "7423be59",
   "metadata": {},
   "outputs": [],
   "source": [
    "import networkx as nx\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "# for the explode statement; convert string to list\n",
    "from ast import literal_eval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "102626ff",
   "metadata": {},
   "outputs": [],
   "source": [
    "# for visualization\n",
    "from IPython.display import SVG \n",
    "from sknetwork.visualization import svg_graph \n",
    "from sknetwork.data import Bunch \n",
    "from sknetwork.ranking import PageRank \n",
    "from scipy.sparse import csr_matrix\n",
    "\n",
    "def draw_graph(G, show_names=False, node_size=1, font_size=10, edge_width=0.5):\n",
    "\n",
    "    adjacency = nx.to_scipy_sparse_array(G, nodelist=None, dtype=None, weight='weight', format='csr')\n",
    "    adjacency = csr_matrix(adjacency) # fix to weird sknetwork-csr issue; comment out to troubleshoot\n",
    "    \n",
    "    names = np.array(list(G.nodes))\n",
    "    \n",
    "    graph = Bunch()\n",
    "    graph.adjacency = adjacency\n",
    "    graph.names = np.array(names)\n",
    "    \n",
    "    pagerank = PageRank()\n",
    "    scores = pagerank.fit_transform(adjacency)\n",
    "\n",
    "    if show_names:\n",
    "        \n",
    "        image = svg_graph(graph.adjacency, font_size=font_size, node_size=node_size, names=graph.names, width=700, height=500, scores=scores, edge_width=edge_width)\n",
    "    \n",
    "    else:\n",
    "        \n",
    "        image = svg_graph(graph.adjacency, node_size=node_size, width=700, height=500, scores = scores, edge_width=edge_width)\n",
    "    \n",
    "    return SVG(image)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77a12aec",
   "metadata": {},
   "source": [
    "# Create Graph using Bipartite Projection on Arxiv Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "443c3cd4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>authors</th>\n",
       "      <th>title</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Dustin Nguyen</td>\n",
       "      <td>Neural ODEs as a discovery tool to characteriz...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Yuan-Sen Ting</td>\n",
       "      <td>Neural ODEs as a discovery tool to characteriz...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Todd A. Thompson</td>\n",
       "      <td>Neural ODEs as a discovery tool to characteriz...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Sebastian Lopez</td>\n",
       "      <td>Neural ODEs as a discovery tool to characteriz...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Laura A. Lopez</td>\n",
       "      <td>Neural ODEs as a discovery tool to characteriz...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            authors                                              title\n",
       "0     Dustin Nguyen  Neural ODEs as a discovery tool to characteriz...\n",
       "1     Yuan-Sen Ting  Neural ODEs as a discovery tool to characteriz...\n",
       "2  Todd A. Thompson  Neural ODEs as a discovery tool to characteriz...\n",
       "3   Sebastian Lopez  Neural ODEs as a discovery tool to characteriz...\n",
       "4    Laura A. Lopez  Neural ODEs as a discovery tool to characteriz..."
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = 'data/arxiv_network_science_data.csv'\n",
    "\n",
    "df = pd.read_csv(data)\n",
    "df['authors'] = df['authors'].apply(literal_eval)\n",
    "\n",
    "df = df[['authors', 'title']]\n",
    "df = df.explode('authors')\n",
    "df.reset_index(drop=True, inplace=True)\n",
    "\n",
    "# fix the & so that scikit-network stops crashing\n",
    "df['authors'] = df['authors'].str.replace('&', 'and')\n",
    "df['title'] = df['title'].str.replace('&', 'and')\n",
    "\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "e5726918",
   "metadata": {},
   "outputs": [],
   "source": [
    "from networkx.algorithms import bipartite\n",
    "\n",
    "B = nx.from_pandas_edgelist(df, source='authors', target='title')\n",
    "G = bipartite.projected_graph(B, df['authors'])\n",
    "\n",
    "G = nx.k_core(G, 2) # no isolates or two-node groups"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "fbee3229",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Graph with 59260 nodes and 302588 edges\n"
     ]
    }
   ],
   "source": [
    "print(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "3618797d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.00017233192168756068"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.density(G) # very sparse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "4ca51e2f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>node</th>\n",
       "      <th>degrees</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Dustin Nguyen</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Yuan-Sen Ting</td>\n",
       "      <td>36</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Todd A. Thompson</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Sebastian Lopez</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Laura A. Lopez</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               node  degrees\n",
       "0     Dustin Nguyen        4\n",
       "1     Yuan-Sen Ting       36\n",
       "2  Todd A. Thompson        4\n",
       "3   Sebastian Lopez        4\n",
       "4    Laura A. Lopez        4"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "degree_df = pd.DataFrame(G.degree)\n",
    "degree_df.columns = ['node', 'degrees']\n",
    "\n",
    "degree_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "30c5a20e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: ylabel='Frequency'>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "degree_df['degrees'].plot.hist(bins=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f9952d45",
   "metadata": {},
   "source": [
    "# Network Attack Simulation\n",
    "\n",
    "Today, I am trying a very aggressive attack on a large collaboration network. The goal isn't just to disrupt the network but to be able to see the network structures that can withstand such an attack. In each loop, many nodes are removed at once to cause maximum disruption WITHOUT completely destroying the network"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4970d1f5",
   "metadata": {},
   "source": [
    "# Simulation 1: Iterative Attack"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "dae86ccb",
   "metadata": {},
   "outputs": [],
   "source": [
    "# need for iteration\n",
    "\n",
    "def get_key_node_df(G):\n",
    "    \n",
    "    G = G.copy()\n",
    "    \n",
    "    cent_df = pd.DataFrame(nx.pagerank(G), index=[0]).T # cent = centrality\n",
    "\n",
    "    cent_df.columns = ['pagerank'] # betweenness centrality\n",
    "    cent_df.sort_values('pagerank', inplace=True, ascending=False)\n",
    "    \n",
    "    return cent_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "ee1c73a4",
   "metadata": {},
   "outputs": [],
   "source": [
    "G1 = G.copy() # keep G for use with simulation 2\n",
    "\n",
    "#draw_graph(nx.k_core(G1,3), show_names=False, node_size=3) # will take a long time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "fd578e0c",
   "metadata": {},
   "outputs": [],
   "source": [
    "def remove_nodes(G, iterations=50, cut_size=500):\n",
    "    \n",
    "    results = {}\n",
    "    \n",
    "    G = G.copy()\n",
    "    \n",
    "    for i in range(iterations):\n",
    "        \n",
    "        results[i] = {}\n",
    "        \n",
    "        results[i]['nodes'] = len(G.nodes)\n",
    "        results[i]['edges'] = len(G.edges)\n",
    "        \n",
    "        print('running loop: {}'.format(i))\n",
    "    \n",
    "        cent_df = get_key_node_df(G)\n",
    "\n",
    "        drop_nodes = sorted(cent_df[0:cut_size].index)\n",
    "        \n",
    "        #print('removing key nodes: {}'.format(drop_nodes))\n",
    "\n",
    "        G.remove_nodes_from(drop_nodes)\n",
    "\n",
    "        G = nx.k_core(G, 2) # no isolates or two-node groups\n",
    "\n",
    "        print(G)\n",
    "        \n",
    "        print()\n",
    "        print('---------------')\n",
    "        print()\n",
    "        \n",
    "    return G, results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "5836204c",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "running loop: 0\n",
      "Graph with 57667 nodes and 283092 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 1\n",
      "Graph with 56456 nodes and 270366 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 2\n",
      "Graph with 55444 nodes and 258832 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 3\n",
      "Graph with 54383 nodes and 246298 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 4\n",
      "Graph with 53549 nodes and 234207 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 5\n",
      "Graph with 52786 nodes and 224604 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 6\n",
      "Graph with 52034 nodes and 218385 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 7\n",
      "Graph with 51149 nodes and 212846 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 8\n",
      "Graph with 49829 nodes and 207389 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 9\n",
      "Graph with 48178 nodes and 202885 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 10\n",
      "Graph with 47165 nodes and 194321 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 11\n",
      "Graph with 45898 nodes and 190310 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 12\n",
      "Graph with 44932 nodes and 184470 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 13\n",
      "Graph with 43997 nodes and 180344 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 14\n",
      "Graph with 43081 nodes and 177198 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 15\n",
      "Graph with 42348 nodes and 169154 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 16\n",
      "Graph with 41818 nodes and 149056 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 17\n",
      "Graph with 41318 nodes and 135931 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 18\n",
      "Graph with 40818 nodes and 115944 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 19\n",
      "Graph with 40318 nodes and 108836 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 20\n",
      "Graph with 39817 nodes and 103214 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 21\n",
      "Graph with 39313 nodes and 96519 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 22\n",
      "Graph with 38809 nodes and 91609 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 23\n",
      "Graph with 38305 nodes and 87304 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 24\n",
      "Graph with 37798 nodes and 84664 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 25\n",
      "Graph with 37293 nodes and 82467 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 26\n",
      "Graph with 36790 nodes and 79413 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 27\n",
      "Graph with 36281 nodes and 76928 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 28\n",
      "Graph with 35753 nodes and 75048 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 29\n",
      "Graph with 35251 nodes and 72218 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 30\n",
      "Graph with 34748 nodes and 69608 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 31\n",
      "Graph with 34243 nodes and 67552 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 32\n",
      "Graph with 33724 nodes and 65134 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 33\n",
      "Graph with 33195 nodes and 63430 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 34\n",
      "Graph with 32690 nodes and 61739 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 35\n",
      "Graph with 32176 nodes and 60758 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 36\n",
      "Graph with 31639 nodes and 59892 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 37\n",
      "Graph with 31124 nodes and 58191 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 38\n",
      "Graph with 30616 nodes and 55424 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 39\n",
      "Graph with 30114 nodes and 53603 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 40\n",
      "Graph with 29598 nodes and 51152 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 41\n",
      "Graph with 29055 nodes and 50311 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 42\n",
      "Graph with 28538 nodes and 49380 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 43\n",
      "Graph with 28001 nodes and 48582 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 44\n",
      "Graph with 27489 nodes and 47279 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 45\n",
      "Graph with 26959 nodes and 46381 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 46\n",
      "Graph with 26453 nodes and 44822 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 47\n",
      "Graph with 25912 nodes and 43883 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 48\n",
      "Graph with 25402 nodes and 42474 edges\n",
      "\n",
      "---------------\n",
      "\n",
      "running loop: 49\n",
      "Graph with 24893 nodes and 41180 edges\n",
      "\n",
      "---------------\n",
      "\n"
     ]
    }
   ],
   "source": [
    "G1, results = remove_nodes(G1, iterations=50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "083f1f93",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>nodes</th>\n",
       "      <th>edges</th>\n",
       "      <th>nodes_dropped</th>\n",
       "      <th>edges_dropped</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>59260</td>\n",
       "      <td>302588</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>57667</td>\n",
       "      <td>283092</td>\n",
       "      <td>1593.0</td>\n",
       "      <td>19496.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>56456</td>\n",
       "      <td>270366</td>\n",
       "      <td>1211.0</td>\n",
       "      <td>12726.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>55444</td>\n",
       "      <td>258832</td>\n",
       "      <td>1012.0</td>\n",
       "      <td>11534.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>54383</td>\n",
       "      <td>246298</td>\n",
       "      <td>1061.0</td>\n",
       "      <td>12534.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   nodes   edges  nodes_dropped  edges_dropped\n",
       "0  59260  302588            0.0            0.0\n",
       "1  57667  283092         1593.0        19496.0\n",
       "2  56456  270366         1211.0        12726.0\n",
       "3  55444  258832         1012.0        11534.0\n",
       "4  54383  246298         1061.0        12534.0"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result_df = pd.DataFrame(results).T\n",
    "result_df['nodes_dropped'] = result_df['nodes'].diff(1).abs()\n",
    "result_df['edges_dropped'] = result_df['edges'].diff(1).abs()\n",
    "result_df.fillna(0, inplace=True)\n",
    "result_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "70bfa1d2",
   "metadata": {},
   "outputs": [
    {
     "data": {
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1/s//+T/pq1/9aiouLk6lpaXpuOOOy1+1e43TTjstNW7cOL300kupe/fuqVGjRql58+bpBz/4QX6fPtvfueeem37zm9+kPffcMzVo0CDtvffe6Z577lnnsWvzXKWU0vz589O3vvWttPPOO6cmTZqkb33rW2natGmbdTX1xx57LA0cODDtsssu+avIv/nmm+vdZu7cuSki0ve///2N1v6sW265JZ144onpS1/6Utppp51ScXFx2nPPPdP3v//9NG/evBpjZ82alQ499NC00047pYhIRxxxxGY9J2uupn7ttdemK6+8Mu2xxx6puLg4HXjggenRRx+tdc8AbJ9yKW3gcq0AwA7l9NNPj9///ve1uihYLpeLc889N8aMGZNBZ1vH6NGj44ILLojZs2fX+DRFXTF37txo3759XH/99XHRRRdt63YAyJiPqQMAO5S///3vMWfOnLjqqqviuOOOq5NBHACEcQBgh3LCCSdEZWVlfP3rX4+bb755W7cDAOvlY+oAAACQMT9tBgAAABkTxgEAACBjwjgAAABkbIe9gNvq1atjwYIF0aRJk8jlctu6HQAAAHZwKaX48MMPo6KiIurV2/i57x02jC9YsCBat269rdsAAADgC2bevHmxxx57bHTMDhvGmzRpEhGfPglNmzbdxt0AAACwo1uyZEm0bt06n0c3ZocN42s+mt60aVNhHAAAgMzU5qvSLuAGAAAAGRPGAQAAIGPCOAAAAGRMGAcAAICMCeMAAACQMWEcAAAAMiaMAwAAQMaEcQAAAMiYMA4AAAAZE8YBAAAgY8I4AAAAZEwYBwAAgIwJ4wAAAJAxYRwAAAAyJowDAABAxoRxAAAAyJgwDgAAABkTxgEAACBjwjgAAABkTBgHAACAjAnjAAAAkDFhHAAAADImjAMAAEDGhHEAAADImDAOAAAAGRPGAQAAIGNF27oBoPDaXfrwJsfMveaYDDoBAADWx5lxAAAAyJgwDgAAABkTxgEAACBjwjgAAABkTBgHAACAjAnjAAAAkDFhHAAAADImjAMAAEDGhHEAAADImDAOAAAAGRPGAQAAIGPCOAAAAGRMGAcAAICMbXYYf/rpp+PYY4+NioqKyOVyMWnSpHXGvPrqq9GvX78oLS2NJk2axCGHHBLvvvtufn11dXWcf/750bJly2jcuHH069cv5s+fX6PG4sWLY+DAgVFaWhqlpaUxcODA+M9//rPZOwgAAAB1zWaH8WXLlsX+++8fY8aMWe/6f/zjH3HYYYfF3nvvHU8++WS8+OKL8dOf/jQaNmyYHzNkyJCYOHFiTJgwIaZOnRpLly6Nvn37xqpVq/JjBgwYELNmzYrJkyfH5MmTY9asWTFw4MAt2EUAAACoW3IppbTFG+dyMXHixDj++OPzy0455ZRo0KBB3H333evdpqqqKnbddde4++674+STT46IiAULFkTr1q3jz3/+c/Tu3TteffXV2HfffeOZZ56JLl26RETEM888E127do3XXnst9tprr032tmTJkigtLY2qqqpo2rTplu4ibJfaXfrwJsfMveaYDDoBAIAvjs3JoQX9zvjq1avj4Ycfjq985SvRu3fvaNWqVXTp0qXGR9lnzpwZK1eujKOOOiq/rKKiIjp27BjTpk2LiIjp06dHaWlpPohHRBxyyCFRWlqaH7O26urqWLJkSY0bAAAA1EUFDeOLFi2KpUuXxjXXXBNHH310PPbYY3HCCSfEiSeeGE899VRERFRWVkZxcXE0a9asxrZlZWVRWVmZH9OqVat16rdq1So/Zm0jR47Mf7+8tLQ0WrduXchdAwAAgIIp+JnxiIjjjjsufvSjH8UBBxwQl156afTt2zduvvnmjW6bUopcLpe//9n/3tCYzxo2bFhUVVXlb/PmzfscewIAAABbT1Ehi7Vs2TKKiopi3333rbF8n332ialTp0ZERHl5eaxYsSIWL15c4+z4okWLolu3bvkx77333jr133///SgrK1vvY5eUlERJSUmhdmWTavOd3AjfywUAAGBdBT0zXlxcHAcffHC8/vrrNZa/8cYb0bZt24iI6Ny5czRo0CCmTJmSX79w4cKYPXt2Pox37do1qqqq4rnnnsuPefbZZ6Oqqio/BgAAALZXm31mfOnSpfHWW2/l78+ZMydmzZoVzZs3jzZt2sSPf/zjOPnkk+Pwww+PI488MiZPnhwPPfRQPPnkkxERUVpaGoMHD46hQ4dGixYtonnz5nHRRRdFp06domfPnhHx6Zn0o48+Os4888y45ZZbIiLirLPOir59+9bqSuoAAABQl212GJ8xY0YceeSR+fsXXnhhREScdtppMW7cuDjhhBPi5ptvjpEjR8YFF1wQe+21V/zhD3+Iww47LL/NjTfeGEVFRdG/f/9Yvnx59OjRI8aNGxf169fPj7nnnnviggsuyF91vV+/fhv8bXMAAADYnnyu3xmvy7b274z7zjh1md8ZBwCA7G2z3xkHAAAANk0YBwAAgIwJ4wAAAJAxYRwAAAAyJowDAABAxoRxAAAAyJgwDgAAABkTxgEAACBjwjgAAABkTBgHAACAjAnjAAAAkDFhHAAAADImjAMAAEDGhHEAAADImDAOAAAAGRPGAQAAIGPCOAAAAGRMGAcAAICMCeMAAACQMWEcAAAAMiaMAwAAQMaEcQAAAMiYMA4AAAAZE8YBAAAgY8I4AAAAZEwYBwAAgIwJ4wAAAJAxYRwAAAAyJowDAABAxoRxAAAAyJgwDgAAABkTxgEAACBjwjgAAABkTBgHAACAjAnjAAAAkDFhHAAAADImjAMAAEDGhHEAAADImDAOAAAAGRPGAQAAIGPCOAAAAGRMGAcAAICMCeMAAACQMWEcAAAAMiaMAwAAQMaEcQAAAMiYMA4AAAAZE8YBAAAgY8I4AAAAZEwYBwAAgIwJ4wAAAJAxYRwAAAAyJowDAABAxoRxAAAAyJgwDgAAABkTxgEAACBjwjgAAABkTBgHAACAjAnjAAAAkDFhHAAAADK22WH86aefjmOPPTYqKioil8vFpEmTNjj27LPPjlwuF6NGjaqxvLq6Os4///xo2bJlNG7cOPr16xfz58+vMWbx4sUxcODAKC0tjdLS0hg4cGD85z//2dx2AQAAoM7Z7DC+bNmy2H///WPMmDEbHTdp0qR49tlno6KiYp11Q4YMiYkTJ8aECRNi6tSpsXTp0ujbt2+sWrUqP2bAgAExa9asmDx5ckyePDlmzZoVAwcO3Nx2AQAAoM4p2twN+vTpE3369NnomH/+859x3nnnxaOPPhrHHHNMjXVVVVVx++23x9133x09e/aMiIjx48dH69at4/HHH4/evXvHq6++GpMnT45nnnkmunTpEhERt912W3Tt2jVef/312GuvvTa3bQAAAKgzCv6d8dWrV8fAgQPjxz/+cey3337rrJ85c2asXLkyjjrqqPyyioqK6NixY0ybNi0iIqZPnx6lpaX5IB4Rccghh0RpaWl+zNqqq6tjyZIlNW4AAABQFxU8jF977bVRVFQUF1xwwXrXV1ZWRnFxcTRr1qzG8rKysqisrMyPadWq1TrbtmrVKj9mbSNHjsx/v7y0tDRat279OfcEAAAAto6ChvGZM2fGTTfdFOPGjYtcLrdZ26aUamyzvu3XHvNZw4YNi6qqqvxt3rx5m9c8AAAAZKSgYfxvf/tbLFq0KNq0aRNFRUVRVFQU77zzTgwdOjTatWsXERHl5eWxYsWKWLx4cY1tFy1aFGVlZfkx77333jr133///fyYtZWUlETTpk1r3AAAAKAuKmgYHzhwYLz00ksxa9as/K2ioiJ+/OMfx6OPPhoREZ07d44GDRrElClT8tstXLgwZs+eHd26dYuIiK5du0ZVVVU899xz+THPPvtsVFVV5ccAAADA9mqzr6a+dOnSeOutt/L358yZE7NmzYrmzZtHmzZtokWLFjXGN2jQIMrLy/NXQC8tLY3BgwfH0KFDo0WLFtG8efO46KKLolOnTvmrq++zzz5x9NFHx5lnnhm33HJLREScddZZ0bdvX1dSBwAAYLu32WF8xowZceSRR+bvX3jhhRERcdppp8W4ceNqVePGG2+MoqKi6N+/fyxfvjx69OgR48aNi/r16+fH3HPPPXHBBRfkr7rer1+/Tf62OQAAAGwPcimltK2b2BqWLFkSpaWlUVVVtVW+P97u0odrNW7uNcdsehAUWG1en16bAABQWJuTQwv+02YAAADAxgnjAAAAkDFhHAAAADImjAMAAEDGhHEAAADImDAOAAAAGRPGAQAAIGPCOAAAAGRMGAcAAICMCeMAAACQMWEcAAAAMiaMAwAAQMaEcQAAAMiYMA4AAAAZE8YBAAAgY8I4AAAAZEwYBwAAgIwJ4wAAAJAxYRwAAAAyJowDAABAxoRxAAAAyFjRtm4A+FS7Sx+u1bi51xyzlTsBAAC2NmfGAQAAIGPCOAAAAGRMGAcAAICMCeMAAACQMWEcAAAAMiaMAwAAQMaEcQAAAMiYMA4AAAAZE8YBAAAgY8I4AAAAZEwYBwAAgIwJ4wAAAJAxYRwAAAAyJowDAABAxoRxAAAAyJgwDgAAABkTxgEAACBjwjgAAABkrGhbNwB8MbS79OFNjpl7zTEZdAIAANueM+MAAACQMWEcAAAAMiaMAwAAQMaEcQAAAMiYMA4AAAAZE8YBAAAgY8I4AAAAZEwYBwAAgIwJ4wAAAJAxYRwAAAAyJowDAABAxoRxAAAAyJgwDgAAABkTxgEAACBjwjgAAABkTBgHAACAjAnjAAAAkDFhHAAAADImjAMAAEDGNjuMP/3003HsscdGRUVF5HK5mDRpUn7dypUr45JLLolOnTpF48aNo6KiIgYNGhQLFiyoUaO6ujrOP//8aNmyZTRu3Dj69esX8+fPrzFm8eLFMXDgwCgtLY3S0tIYOHBg/Oc//9minazr2l368CZvAAAA7Dg2O4wvW7Ys9t9//xgzZsw66z766KN44YUX4qc//Wm88MIL8cADD8Qbb7wR/fr1qzFuyJAhMXHixJgwYUJMnTo1li5dGn379o1Vq1blxwwYMCBmzZoVkydPjsmTJ8esWbNi4MCBW7CLAAAAULcUbe4Gffr0iT59+qx3XWlpaUyZMqXGstGjR8fXvva1ePfdd6NNmzZRVVUVt99+e9x9993Rs2fPiIgYP358tG7dOh5//PHo3bt3vPrqqzF58uR45plnokuXLhERcdttt0XXrl3j9ddfj7322mtz2wYAAIA6Y6t/Z7yqqipyuVzssssuERExc+bMWLlyZRx11FH5MRUVFdGxY8eYNm1aRERMnz49SktL80E8IuKQQw6J0tLS/Ji1VVdXx5IlS2rcAAAAoC7aqmH8448/jksvvTQGDBgQTZs2jYiIysrKKC4ujmbNmtUYW1ZWFpWVlfkxrVq1Wqdeq1at8mPWNnLkyPz3y0tLS6N169YF3hsAAAAojK0WxleuXBmnnHJKrF69On7zm99scnxKKXK5XP7+Z/97Q2M+a9iwYVFVVZW/zZs3b8ubBwAAgK1oq4TxlStXRv/+/WPOnDkxZcqU/FnxiIjy8vJYsWJFLF68uMY2ixYtirKysvyY9957b52677//fn7M2kpKSqJp06Y1bgAAAFAXFTyMrwnib775Zjz++OPRokWLGus7d+4cDRo0qHGht4ULF8bs2bOjW7duERHRtWvXqKqqiueeey4/5tlnn42qqqr8GAAAANhebfbV1JcuXRpvvfVW/v6cOXNi1qxZ0bx586ioqIhvf/vb8cILL8Sf/vSnWLVqVf473s2bN4/i4uIoLS2NwYMHx9ChQ6NFixbRvHnzuOiii6JTp075q6vvs88+cfTRR8eZZ54Zt9xyS0REnHXWWdG3b19XUgcAAGC7t9lhfMaMGXHkkUfm71944YUREXHaaafF8OHD48EHH4yIiAMOOKDGdn/961+je/fuERFx4403RlFRUfTv3z+WL18ePXr0iHHjxkX9+vXz4++555644IIL8ldd79ev33p/2xwAAAC2N5sdxrt37x4ppQ2u39i6NRo2bBijR4+O0aNHb3BM8+bNY/z48ZvbHgAAANR5W/13xgEAAICahHEAAADImDAOAAAAGRPGAQAAIGPCOAAAAGRMGAcAAICMCeMAAACQMWEcAAAAMiaMAwAAQMaEcQAAAMiYMA4AAAAZE8YBAAAgY8I4AAAAZEwYBwAAgIwJ4wAAAJAxYRwAAAAyJowDAABAxoRxAAAAyJgwDgAAABkTxgEAACBjwjgAAABkTBgHAACAjAnjAAAAkDFhHAAAADImjAMAAEDGhHEAAADImDAOAAAAGRPGAQAAIGPCOAAAAGRMGAcAAICMCeMAAACQMWEcAAAAMiaMAwAAQMaEcQAAAMiYMA4AAAAZE8YBAAAgY8I4AAAAZEwYBwAAgIwJ4wAAAJAxYRwAAAAyJowDAABAxoRxAAAAyJgwDgAAABkr2tYNUDe1u/ThWo2be80xW7kTAACAHY8z4wAAAJAxYRwAAAAyJowDAABAxoRxAAAAyJgwDgAAABkTxgEAACBjwjgAAABkTBgHAACAjAnjAAAAkDFhHAAAADImjAMAAEDGhHEAAADImDAOAAAAGRPGAQAAIGPCOAAAAGRMGAcAAICMFW3uBk8//XRcf/31MXPmzFi4cGFMnDgxjj/++Pz6lFJceeWVceutt8bixYujS5cu8etf/zr222+//Jjq6uq46KKL4r777ovly5dHjx494je/+U3sscce+TGLFy+OCy64IB588MGIiOjXr1+MHj06dtllly3f2y+Adpc+vMkxc685JoNO2BHU5vUU4TUFAACba7PPjC9btiz233//GDNmzHrXX3fddXHDDTfEmDFj4vnnn4/y8vLo1atXfPjhh/kxQ4YMiYkTJ8aECRNi6tSpsXTp0ujbt2+sWrUqP2bAgAExa9asmDx5ckyePDlmzZoVAwcO3IJdBAAAgLpls8+M9+nTJ/r06bPedSmlGDVqVFx++eVx4oknRkTEXXfdFWVlZXHvvffG2WefHVVVVXH77bfH3XffHT179oyIiPHjx0fr1q3j8ccfj969e8err74akydPjmeeeSa6dOkSERG33XZbdO3aNV5//fXYa6+9tnR/AQAAYJsr6HfG58yZE5WVlXHUUUfll5WUlMQRRxwR06ZNi4iImTNnxsqVK2uMqaioiI4dO+bHTJ8+PUpLS/NBPCLikEMOidLS0vyYtVVXV8eSJUtq3AAAAKAuKmgYr6ysjIiIsrKyGsvLysry6yorK6O4uDiaNWu20TGtWrVap36rVq3yY9Y2cuTIKC0tzd9at279ufcHAAAAtoatcjX1XC5X435KaZ1la1t7zPrGb6zOsGHDoqqqKn+bN2/eFnQOAAAAW19Bw3h5eXlExDpnrxctWpQ/W15eXh4rVqyIxYsXb3TMe++9t079999/f52z7muUlJRE06ZNa9wAAACgLipoGG/fvn2Ul5fHlClT8stWrFgRTz31VHTr1i0iIjp37hwNGjSoMWbhwoUxe/bs/JiuXbtGVVVVPPfcc/kxzz77bFRVVeXHAAAAwPZqs6+mvnTp0njrrbfy9+fMmROzZs2K5s2bR5s2bWLIkCExYsSI6NChQ3To0CFGjBgRO+20UwwYMCAiIkpLS2Pw4MExdOjQaNGiRTRv3jwuuuii6NSpU/7q6vvss08cffTRceaZZ8Ytt9wSERFnnXVW9O3b15XUAQAA2O5tdhifMWNGHHnkkfn7F154YUREnHbaaTFu3Li4+OKLY/ny5XHOOefE4sWLo0uXLvHYY49FkyZN8tvceOONUVRUFP3794/ly5dHjx49Yty4cVG/fv38mHvuuScuuOCC/FXX+/Xrt8HfNgcAAIDtyWaH8e7du0dKaYPrc7lcDB8+PIYPH77BMQ0bNozRo0fH6NGjNzimefPmMX78+M1tDwAAAOq8rXI1dQAAAGDDhHEAAADImDAOAAAAGRPGAQAAIGPCOAAAAGRss6+mDrCttbv04U2OmXvNMRl0AgAAW8aZcQAAAMiYMA4AAAAZE8YBAAAgY8I4AAAAZEwYBwAAgIwJ4wAAAJAxYRwAAAAyJowDAABAxoRxAAAAyJgwDgAAABkr2tYNAGwr7S59uFbj5l5zzFbuBACALxpnxgEAACBjwjgAAABkTBgHAACAjAnjAAAAkDFhHAAAADImjAMAAEDG/LQZQAHU5mfS/EQaAABrODMOAAAAGRPGAQAAIGPCOAAAAGRMGAcAAICMCeMAAACQMWEcAAAAMiaMAwAAQMaEcQAAAMiYMA4AAAAZE8YBAAAgY0XbugHY3rW79OFNjpl7zTEZdAIAAGwvnBkHAACAjAnjAAAAkDFhHAAAADImjAMAAEDGhHEAAADImDAOAAAAGRPGAQAAIGPCOAAAAGRMGAcAAICMCeMAAACQMWEcAAAAMiaMAwAAQMaEcQAAAMiYMA4AAAAZE8YBAAAgY8I4AAAAZEwYBwAAgIwVbesG2PG1u/ThTY6Ze80xGXQCAABQNzgzDgAAABkTxgEAACBjwjgAAABkTBgHAACAjAnjAAAAkDFhHAAAADImjAMAAEDGhHEAAADIWMHD+CeffBI/+clPon379tGoUaP40pe+FFdddVWsXr06PyalFMOHD4+Kiopo1KhRdO/ePV555ZUadaqrq+P888+Pli1bRuPGjaNfv34xf/78QrcLAAAAmSt4GL/22mvj5ptvjjFjxsSrr74a1113XVx//fUxevTo/JjrrrsubrjhhhgzZkw8//zzUV5eHr169YoPP/wwP2bIkCExceLEmDBhQkydOjWWLl0affv2jVWrVhW6ZQAAAMhUUaELTp8+PY477rg45phjIiKiXbt2cd9998WMGTMi4tOz4qNGjYrLL788TjzxxIiIuOuuu6KsrCzuvffeOPvss6Oqqipuv/32uPvuu6Nnz54RETF+/Pho3bp1PP7449G7d+91Hre6ujqqq6vz95csWVLoXQMAAICCKPiZ8cMOOyz+8pe/xBtvvBERES+++GJMnTo1vvnNb0ZExJw5c6KysjKOOuqo/DYlJSVxxBFHxLRp0yIiYubMmbFy5coaYyoqKqJjx475MWsbOXJklJaW5m+tW7cu9K4BAABAQRT8zPgll1wSVVVVsffee0f9+vVj1apVcfXVV8d3vvOdiIiorKyMiIiysrIa25WVlcU777yTH1NcXBzNmjVbZ8ya7dc2bNiwuPDCC/P3lyxZIpADAABQJxU8jN9///0xfvz4uPfee2O//faLWbNmxZAhQ6KioiJOO+20/LhcLldju5TSOsvWtrExJSUlUVJS8vl3AAAAALaygofxH//4x3HppZfGKaecEhERnTp1infeeSdGjhwZp512WpSXl0fEp2e/d9ttt/x2ixYtyp8tLy8vjxUrVsTixYtrnB1ftGhRdOvWrdAtAwAAQKYK/p3xjz76KOrVq1m2fv36+Z82a9++fZSXl8eUKVPy61esWBFPPfVUPmh37tw5GjRoUGPMwoULY/bs2cI4AAAA272Cnxk/9thj4+qrr442bdrEfvvtF3//+9/jhhtuiP/6r/+KiE8/nj5kyJAYMWJEdOjQITp06BAjRoyInXbaKQYMGBAREaWlpTF48OAYOnRotGjRIpo3bx4XXXRRdOrUKX91dQAAANheFTyMjx49On7605/GOeecE4sWLYqKioo4++yz42c/+1l+zMUXXxzLly+Pc845JxYvXhxdunSJxx57LJo0aZIfc+ONN0ZRUVH0798/li9fHj169Ihx48ZF/fr1C90yAAAAZKrgYbxJkyYxatSoGDVq1AbH5HK5GD58eAwfPnyDYxo2bBijR4+O0aNHF7pFAAAA2KYK/p1xAAAAYOOEcQAAAMiYMA4AAAAZE8YBAAAgY8I4AAAAZKzgV1OHraXdpQ/Xatzca47Zyp0AAAB8Ps6MAwAAQMaEcQAAAMiYMA4AAAAZ851xvpBq8/1z3z0HAAC2FmfGAQAAIGPCOAAAAGRMGAcAAICMCeMAAACQMWEcAAAAMiaMAwAAQMb8tBlAHVKbn92L8NN7AADbO2fGAQAAIGPCOAAAAGRMGAcAAICMCeMAAACQMWEcAAAAMiaMAwAAQMaEcQAAAMiYMA4AAAAZE8YBAAAgY8I4AAAAZEwYBwAAgIwJ4wAAAJAxYRwAAAAyJowDAABAxoRxAAAAyJgwDgAAABkTxgEAACBjwjgAAABkTBgHAACAjAnjAAAAkDFhHAAAADImjAMAAEDGhHEAAADImDAOAAAAGRPGAQAAIGPCOAAAAGRMGAcAAICMCeMAAACQMWEcAAAAMiaMAwAAQMaEcQAAAMiYMA4AAAAZE8YBAAAgY8I4AAAAZEwYBwAAgIwJ4wAAAJAxYRwAAAAyJowDAABAxoRxAAAAyJgwDgAAABkTxgEAACBjwjgAAABkTBgHAACAjG2VMP7Pf/4zTj311GjRokXstNNOccABB8TMmTPz61NKMXz48KioqIhGjRpF9+7d45VXXqlRo7q6Os4///xo2bJlNG7cOPr16xfz58/fGu0CAABApgoexhcvXhyHHnpoNGjQIB555JH43//93/jlL38Zu+yyS37MddddFzfccEOMGTMmnn/++SgvL49evXrFhx9+mB8zZMiQmDhxYkyYMCGmTp0aS5cujb59+8aqVasK3TIAAABkqqjQBa+99tpo3bp13Hnnnfll7dq1y/93SilGjRoVl19+eZx44okREXHXXXdFWVlZ3HvvvXH22WdHVVVV3H777XH33XdHz549IyJi/Pjx0bp163j88cejd+/e6zxudXV1VFdX5+8vWbKk0LsGAAAABVHwM+MPPvhgHHTQQXHSSSdFq1at4sADD4zbbrstv37OnDlRWVkZRx11VH5ZSUlJHHHEETFt2rSIiJg5c2asXLmyxpiKioro2LFjfszaRo4cGaWlpflb69atC71rAAAAUBAFD+Nvv/12jB07Njp06BCPPvpofP/7348LLrgg/ud//iciIiorKyMioqysrMZ2ZWVl+XWVlZVRXFwczZo12+CYtQ0bNiyqqqryt3nz5hV61wAAAKAgCv4x9dWrV8dBBx0UI0aMiIiIAw88MF555ZUYO3ZsDBo0KD8ul8vV2C6ltM6ytW1sTElJSZSUlHzO7gEAAGDrK/iZ8d122y323XffGsv22WefePfddyMiory8PCJinTPcixYtyp8tLy8vjxUrVsTixYs3OAYAAAC2VwUP44ceemi8/vrrNZa98cYb0bZt24iIaN++fZSXl8eUKVPy61esWBFPPfVUdOvWLSIiOnfuHA0aNKgxZuHChTF79uz8GAAAANheFfxj6j/60Y+iW7duMWLEiOjfv38899xzceutt8att94aEZ9+PH3IkCExYsSI6NChQ3To0CFGjBgRO+20UwwYMCAiIkpLS2Pw4MExdOjQaNGiRTRv3jwuuuii6NSpU/7q6gAAALC9KngYP/jgg2PixIkxbNiwuOqqq6J9+/YxatSo+O53v5sfc/HFF8fy5cvjnHPOicWLF0eXLl3iscceiyZNmuTH3HjjjVFUVBT9+/eP5cuXR48ePWLcuHFRv379QrcMAAAAmSp4GI+I6Nu3b/Tt23eD63O5XAwfPjyGDx++wTENGzaM0aNHx+jRo7dChwAAALDtFPw74wAAAMDGCeMAAACQMWEcAAAAMiaMAwAAQMaEcQAAAMiYMA4AAAAZE8YBAAAgY8I4AAAAZEwYBwAAgIwJ4wAAAJAxYRwAAAAyJowDAABAxoRxAAAAyFjRtm4AAACgLml36cObHDP3mmMy6IQtsb38/3NmHAAAADLmzDgAANRh28tZPrau2rwOIrwWtifOjAMAAEDGnBkH2EE5kwIAbE3O1n8+wjgAQAH5x2n2POfA9sjH1AEAACBjwjgAAABkzMfUAQDYJlzbAvgiE8YBAIDtXl29doCDTmyIMA4AAAUmGAKbIowDAAB8gTgoUztb+6CaMA4A1MqO/o+3HX3/oJDq6pl/2J4I4wBQIIUMc4WqVRf/wVwXe6L2dvSDFjv6/kFd9UX82xPGAYDt1o7+j7cd+aAMrLGj/x3DhgjjAGxSXQwEdbEnAIDaqretGwAAAIAvGmEcAAAAMiaMAwAAQMaEcQAAAMiYMA4AAAAZE8YBAAAgY8I4AAAAZEwYBwAAgIwJ4wAAAJAxYRwAAAAyJowDAABAxoRxAAAAyJgwDgAAABkTxgEAACBjwjgAAABkTBgHAACAjAnjAAAAkDFhHAAAADImjAMAAEDGhHEAAADImDAOAAAAGRPGAQAAIGPCOAAAAGRMGAcAAICMCeMAAACQMWEcAAAAMiaMAwAAQMaEcQAAAMiYMA4AAAAZE8YBAAAgY8I4AAAAZGyrh/GRI0dGLpeLIUOG5JellGL48OFRUVERjRo1iu7du8crr7xSY7vq6uo4//zzo2XLltG4cePo169fzJ8/f2u3CwAAAFvdVg3jzz//fNx6663x1a9+tcby6667Lm644YYYM2ZMPP/881FeXh69evWKDz/8MD9myJAhMXHixJgwYUJMnTo1li5dGn379o1Vq1ZtzZYBAABgq9tqYXzp0qXx3e9+N2677bZo1qxZfnlKKUaNGhWXX355nHjiidGxY8e466674qOPPop77703IiKqqqri9ttvj1/+8pfRs2fPOPDAA2P8+PHx8ssvx+OPP77ex6uuro4lS5bUuAEAAEBdtNXC+LnnnhvHHHNM9OzZs8byOXPmRGVlZRx11FH5ZSUlJXHEEUfEtGnTIiJi5syZsXLlyhpjKioqomPHjvkxaxs5cmSUlpbmb61bt94KewUAAACf31YJ4xMmTIgXXnghRo4cuc66ysrKiIgoKyursbysrCy/rrKyMoqLi2ucUV97zNqGDRsWVVVV+du8efMKsSsAAABQcEWFLjhv3rz44Q9/GI899lg0bNhwg+NyuVyN+ymldZatbWNjSkpKoqSkZPMbBgAAgIwV/Mz4zJkzY9GiRdG5c+coKiqKoqKieOqpp+JXv/pVFBUV5c+Ir32Ge9GiRfl15eXlsWLFili8ePEGxwAAAMD2quBhvEePHvHyyy/HrFmz8reDDjoovvvd78asWbPiS1/6UpSXl8eUKVPy26xYsSKeeuqp6NatW0REdO7cORo0aFBjzMKFC2P27Nn5MQAAALC9KvjH1Js0aRIdO3assaxx48bRokWL/PIhQ4bEiBEjokOHDtGhQ4cYMWJE7LTTTjFgwICIiCgtLY3BgwfH0KFDo0WLFtG8efO46KKLolOnTutcEA4AAAC2NwUP47Vx8cUXx/Lly+Occ86JxYsXR5cuXeKxxx6LJk2a5MfceOONUVRUFP3794/ly5dHjx49Yty4cVG/fv1t0TIAAAAUTCZh/Mknn6xxP5fLxfDhw2P48OEb3KZhw4YxevToGD169NZtDgAAADK21X5nHAAAAFg/YRwAAAAyJowDAABAxoRxAAAAyJgwDgAAABkTxgEAACBjwjgAAABkTBgHAACAjAnjAAAAkDFhHAAAADImjAMAAEDGhHEAAADImDAOAAAAGRPGAQAAIGPCOAAAAGRMGAcAAICMCeMAAACQMWEcAAAAMiaMAwAAQMaEcQAAAMiYMA4AAAAZE8YBAAAgY8I4AAAAZEwYBwAAgIwJ4wAAAJAxYRwAAAAyJowDAABAxoRxAAAAyJgwDgAAABkTxgEAACBjwjgAAABkTBgHAACAjAnjAAAAkDFhHAAAADImjAMAAEDGhHEAAADImDAOAAAAGRPGAQAAIGPCOAAAAGRMGAcAAICMCeMAAACQMWEcAAAAMiaMAwAAQMaEcQAAAMiYMA4AAAAZE8YBAAAgY8I4AAAAZEwYBwAAgIwJ4wAAAJAxYRwAAAAyJowDAABAxoRxAAAAyJgwDgAAABkTxgEAACBjwjgAAABkTBgHAACAjAnjAAAAkDFhHAAAADImjAMAAEDGhHEAAADIWMHD+MiRI+Pggw+OJk2aRKtWreL444+P119/vcaYlFIMHz48KioqolGjRtG9e/d45ZVXaoyprq6O888/P1q2bBmNGzeOfv36xfz58wvdLgAAAGSu4GH8qaeeinPPPTeeeeaZmDJlSnzyySdx1FFHxbJly/JjrrvuurjhhhtizJgx8fzzz0d5eXn06tUrPvzww/yYIUOGxMSJE2PChAkxderUWLp0afTt2zdWrVpV6JYBAAAgU0WFLjh58uQa9++8885o1apVzJw5Mw4//PBIKcWoUaPi8ssvjxNPPDEiIu66664oKyuLe++9N84+++yoqqqK22+/Pe6+++7o2bNnRESMHz8+WrduHY8//nj07t17ncetrq6O6urq/P0lS5YUetcAAACgILb6d8arqqoiIqJ58+YRETFnzpyorKyMo446Kj+mpKQkjjjiiJg2bVpERMycOTNWrlxZY0xFRUV07NgxP2ZtI0eOjNLS0vytdevWW2uXAAAA4HPZqmE8pRQXXnhhHHbYYdGxY8eIiKisrIyIiLKyshpjy8rK8usqKyujuLg4mjVrtsExaxs2bFhUVVXlb/PmzSv07gAAAEBBFPxj6p913nnnxUsvvRRTp05dZ10ul6txP6W0zrK1bWxMSUlJlJSUbHmzAAAAkJGtdmb8/PPPjwcffDD++te/xh577JFfXl5eHhGxzhnuRYsW5c+Wl5eXx4oVK2Lx4sUbHAMAAADbq4KH8ZRSnHfeefHAAw/EE088Ee3bt6+xvn379lFeXh5TpkzJL1uxYkU89dRT0a1bt4iI6Ny5czRo0KDGmIULF8bs2bPzYwAAAGB7VfCPqZ977rlx7733xh//+Mdo0qRJ/gx4aWlpNGrUKHK5XAwZMiRGjBgRHTp0iA4dOsSIESNip512igEDBuTHDh48OIYOHRotWrSI5s2bx0UXXRSdOnXKX10dAAAAtlcFD+Njx46NiIju3bvXWH7nnXfG6aefHhERF198cSxfvjzOOeecWLx4cXTp0iUee+yxaNKkSX78jTfeGEVFRdG/f/9Yvnx59OjRI8aNGxf169cvdMsAAACQqYKH8ZTSJsfkcrkYPnx4DB8+fINjGjZsGKNHj47Ro0cXsDsAAADY9rb674wDAAAANQnjAAAAkDFhHAAAADImjAMAAEDGhHEAAADImDAOAAAAGRPGAQAAIGPCOAAAAGRMGAcAAICMCeMAAACQMWEcAAAAMiaMAwAAQMaEcQAAAMiYMA4AAAAZE8YBAAAgY8I4AAAAZEwYBwAAgIwJ4wAAAJAxYRwAAAAyJowDAABAxoRxAAAAyJgwDgAAABkTxgEAACBjwjgAAABkTBgHAACAjAnjAAAAkDFhHAAAADImjAMAAEDGhHEAAADImDAOAAAAGRPGAQAAIGPCOAAAAGRMGAcAAICMCeMAAACQMWEcAAAAMiaMAwAAQMaEcQAAAMiYMA4AAAAZE8YBAAAgY8I4AAAAZEwYBwAAgIwJ4wAAAJAxYRwAAAAyJowDAABAxoRxAAAAyJgwDgAAABkTxgEAACBjwjgAAABkTBgHAACAjAnjAAAAkDFhHAAAADImjAMAAEDGhHEAAADImDAOAAAAGRPGAQAAIGPCOAAAAGRMGAcAAICMCeMAAACQMWEcAAAAMiaMAwAAQMbqfBj/zW9+E+3bt4+GDRtG586d429/+9u2bgkAAAA+lzodxu+///4YMmRIXH755fH3v/89vv71r0efPn3i3Xff3datAQAAwBar02H8hhtuiMGDB8cZZ5wR++yzT4waNSpat24dY8eO3datAQAAwBYr2tYNbMiKFSti5syZcemll9ZYftRRR8W0adPWGV9dXR3V1dX5+1VVVRERsWTJkq3S3+rqj2o1rjaPX5tatd2PQtWqi/tXF3sqZK26uH91sadC1qqL+1cXeypkrbq4f3Wxp0LWqov7Vxd7KmSturh/dbGnQtaqi/tXF3sqZK26uH91sadC1qqL+1cXeypkrS3ZvzX/nVLa5Ha5VJtR28CCBQti9913j//7f/9vdOvWLb98xIgRcdddd8Xrr79eY/zw4cPjyiuvzLpNAAAAqGHevHmxxx57bHRMnT0zvkYul6txP6W0zrKIiGHDhsWFF16Yv7969er497//HS1atFjv+DWWLFkSrVu3jnnz5kXTpk23uM9C1dnReypkLT1lX0tP2dfSU/a19JR9LT1lX0tP2dfSU/a19JR9LT19mlc//PDDqKio2GS9OhvGW7ZsGfXr14/KysoayxctWhRlZWXrjC8pKYmSkpIay3bZZZdaP17Tpk0/9/+cQtYpZK262FMha+kp+1p6yr6WnrKvpafsa+kp+1p6yr6WnrKvpafsa33ReyotLa1VnTp7Abfi4uLo3LlzTJkypcbyKVOm1PjYOgAAAGxv6uyZ8YiICy+8MAYOHBgHHXRQdO3aNW699dZ499134/vf//62bg0AAAC2WJ0O4yeffHJ88MEHcdVVV8XChQujY8eO8ec//znatm1bsMcoKSmJK664Yp2PuG+rOjt6T4Wspafsa+kp+1p6yr6WnrKvpafsa+kp+1p6yr6WnrKvpafNU2evpg4AAAA7qjr7nXEAAADYUQnjAAAAkDFhHAAAADImjAMAAEDGhHFqzbX+AAAACqNO/7RZoc2fPz/Gjh0b06ZNi8rKysjlclFWVhbdunWL73//+9G6dett3WKdVlJSEi+++GLss88+27qVHdLChQtj7NixMXXq1Fi4cGHUr18/2rdvH8cff3ycfvrpUb9+/W3dIgAAUCBfmJ82mzp1avTp0ydat24dRx11VJSVlUVKKRYtWhRTpkyJefPmxSOPPBKHHnpoQR5v3rx5ccUVV8Qdd9yxybHLly+PmTNnRvPmzWPfffetse7jjz+O3/72tzFo0KBN1nn11VfjmWeeia5du8bee+8dr732Wtx0001RXV0dp556anzjG9+oVe8XXnjhepffdNNNceqpp0aLFi0iIuKGG26oVb3PWrx4cdx1113x5ptvxm677RannXZarQ6C/P3vf49ddtkl2rdvHxER48ePj7Fjx8a7774bbdu2jfPOOy9OOeWUWvVw/vnnR//+/ePrX//6Zve/ttGjR8eMGTPimGOOif79+8fdd98dI0eOjNWrV8eJJ54YV111VRQVbfqY14wZM6Jnz57Rvn37aNSoUTz77LPx3e9+N1asWBGPPvpo7LPPPvHoo49GkyZNPnfPsKNYtmxZ3HvvvescYD300EPjO9/5TjRu3PhzP8Z7770Xt9xyS/zsZz+r9Tbz58+PXXbZJXbeeecay1euXBnTp0+Pww8/fJM1Pvjgg3jppZdi//33j+bNm8e//vWvuP3226O6ujpOOumkz31Q9Etf+lI8+uij0aFDhy2usXLlynj44Yfz8/kJJ5xQq+d8/vz50bBhw2jZsmVERPztb3+Lm2++OT+fn3vuudG1a9da9fDLX/4yvv3tb0fbtm23eD/WeOihh2LGjBlx9NFHR9euXeOJJ56IX/ziF/n5/Kyzzqp1reXLl8d999233oOrPXr0+Ny9wo4ki7k8YvPn80LM5RF1fz7f0rk8onDzeSHn8ojtbD5PXxAHHXRQGjJkyAbXDxkyJB100EEFe7xZs2alevXqbXLc66+/ntq2bZtyuVyqV69eOuKII9KCBQvy6ysrK2tV55FHHknFxcWpefPmqWHDhumRRx5Ju+66a+rZs2fq0aNHKioqSn/5y19q1Xsul0sHHHBA6t69e41bLpdLBx98cOrevXs68sgja1Vrt912S//6179SSim9/fbbqby8PJWXl6devXqlPfbYI5WWlqZXX311k3UOPPDA9MQTT6SUUrrttttSo0aN0gUXXJDGjh2bhgwZknbeeed0++2313r/6tWrlzp06JCuueaatHDhwlptt7arrroqNWnSJH3rW99K5eXl6ZprrkktWrRIP//5z9OIESPSrrvumn72s5/Vqtahhx6ahg8fnr9/9913py5duqSUUvr3v/+dDjjggHTBBRfUurelS5emW2+9NZ1++unp6KOPTn369Emnn356uu2229LSpUs3b0c3orKyMl155ZW1Hj9v3rz04YcfrrN8xYoV6amnnqp1nX/961/piSeeSB988EFKKaX3338/XXPNNenKK69M//u//1vrOuvTvn379MYbb3yuGitWrEgTJ05M1113Xbr77rs36zmfN29eev/99/P3n3766TRgwIB02GGHpe9+97tp2rRptarzi1/8Is2dO3eze9+QBx98MP3sZz/LP/5f/vKX1KdPn9S7d+90yy231LrORx99lG6//fb0ve99Lx199NHpmGOOSeedd156/PHHN6ufV155JVVUVKRddtklHXfccemss85KZ555ZjruuOPSLrvsknbffff0yiuvbFbN9antXJ5SSgsWLEgHH3xwqlevXqpfv34aNGhQjdd7befzZ599NpWWlqZcLpeaNWuWZsyYkdq3b586dOiQvvzlL6dGjRqlmTNn1qqnm266ab23+vXrp2HDhuXv10bXrl3T4sWLU0opLVq0KHXq1CkVFxenDh06pIYNG6Y2bdqk+fPn16rOn//855RSSpMmTUr16tVL/fr1S5dcckk64YQTUoMGDdJDDz1Uq55yuVyqX79+6tmzZ5owYUKqrq6u1XZrGzt2bCoqKkqdO3dOTZs2TePHj09NmjRJZ5xxRjr77LNTo0aN0qhRo2pV680330xt27ZNLVq0SLvttlvK5XLpmGOOSV26dEn169dPJ510Ulq5cmWte8tiPt/cuTylwsznW3MuT2nbzueFmstTKux8Xqi5PKXCzOdZzeUp1X4+L9RcnlLdnM8LNZevqVWI+bxQc3lKdXs+X58vTBhv2LBheu211za4/tVXX00NGzasdb0//vGPG73deOONtfpDPf7441Pfvn3T+++/n95888107LHHpvbt26d33nknpVT7P/iuXbumyy+/PKWU0n333ZeaNWuWLrvssvz6yy67LPXq1atW+zZixIjUvn37dcJ7UVHRZk+IuVwuvffeeymllE455ZTUvXv3tGzZspRSSh9//HHq27dv+va3v73JOjvttFP+OTnwwAPXecO455570r777lvrnh5//PH0wx/+MLVs2TI1aNAg9evXLz300ENp1apVtd63L33pS+kPf/hDSunTCb5+/fpp/Pjx+fUPPPBA+vKXv1yrWo0aNUr/+Mc/8vdXrVqVGjRokCorK1NKKT322GOpoqKiVrW8sdXuja0uhpQ1tXbUN7ZCvql17949nXLKKevdr+rq6vSd73wnde/efZN1XnzxxY3e7r///lq/NgcNGpQOOeSQ9Pzzz6cpU6akgw46KHXu3Dn9+9//Til9+jrP5XKbrNOzZ890xhlnpCVLlqTrr78+7bHHHumMM87Irx88eHA6/vjja9VTLpdLe+yxR2rXrl2NWy6XS7vvvntq165dat++fa1rrZnPzzzzzHTAAQfkD2b+61//St26dUv/9V//tck6TZo0SXPmzEkppdSlS5d0zTXX1Fg/evTodOCBB9a6pzvvvDMdd9xxqUGDBqlFixbphz/8YXr55Zdrtf0a++yzT7r11ltTSik98cQTqWHDhunXv/51fv2dd96Z9tlnn1rV6tOnTzr77LPz7ycjR45Mffr0SSml9MYbb6R27dqlK664ola1HHRy0CmlHfugU6Hm8pQKN58Xai5PqW7O54Way1Mq3HxeqLk8pbo7n2/IFyaMt2/fPt1xxx0bXH/HHXfU+h8kKf2/s6u5XG6Dt9r8wbdq1Sq99NJLNZadc845qU2bNukf//hHrd/UmjZtmt58882U0qdBrqioqMab2Msvv5zKyspqvX/PPfdc+spXvpKGDh2aVqxYkVL6/GF8fQH/mWeeSXvssccm67Ro0SLNmDEjpfTpczZr1qwa6996663UqFGjze5pxYoV6f7770+9e/dO9evXTxUVFemyyy7LP5cb06hRo/wBgpRSatCgQZo9e3b+/ty5c9NOO+1Uq57atm2bpk6dmr+/YMGClMvl0kcffZRSSmnOnDm1Pljkja12b2x1MaSktGO/sRXyTa1Ro0YbnY9efvnlWs0JG5vL1yyvbUipqKhIzz77bP7+xx9/nI477rh0wAEHpA8++KDW83mzZs3yZwVXrFiR6tWrV6PuCy+8kHbfffda9XTWWWelAw44YJ2zjJ93Pv/KV76S/vSnP9VY/9e//jW1a9duk3VKS0vTiy++mFL6dD5f899rvPXWW7WeOz/b03vvvZeuvfbatPfee6d69eqlgw8+ON16661pyZIlm6yzvvn8s38rc+bMqXVPO+20U42zsdXV1alBgwb5T4lNmjSpVs9TSg46Oej0/3raUQ86FWouT6lw83mh5vKU6uZ8Xqi5PKXCzeeFmstTqrvz+YZ8YcL4r3/961RcXJzOPffcNGnSpDR9+vT0zDPPpEmTJqVzzz03lZSUpLFjx9a6XkVFRZo4ceIG1//973+v1R9qkyZN1vtRrPPOOy/tscce6emnn97sMJ5SSjvvvHONM61z587drDP/KaX04YcfpkGDBqWvfvWr6aWXXkoNGjTYon+8LVq0KKX06XP22bCa0qd/ECUlJZusc+qpp6bBgwenlFI66aST0k9+8pMa60eMGJE6depU657W/MF/1jvvvJOuuOKK1LZt21o95+3bt0+PPPJISunTN5569eql3/72t/n1Dz/8cK3/QH/4wx+mjh07pkceeSQ98cQT6cgjj6zxD6zJkyenPffcs1a1vLHV7o2tLoaUlHbsN7ZCvqlVVFSkSZMmbXD9xIkTa/VpkpYtW6bbb789zZ07d723hx9+uNavzcaNG6/zkdiVK1em448/Pj+P1qZW48aN8/+IT2nd+fydd97ZrPl84sSJqXXr1mn06NH5ZVv6Ol8zn7dq1Wqd7efOnVur+bxfv37p0ksvTSml1Lt373XOWN52222pQ4cOte5pffP5008/nU477bTUuHHj1Lhx403WWfN+m1JK//znP1Mul0sPP/xwfv2TTz5ZqwPHKX362vzswfDFixenXC6X/3t7++23a/U8peSgk4NO6/a0ox10KtRcnlLh5vNCzeVratW1+bxQc3lKhZvPCzWXp1R35/MN+cKE8ZRSmjBhQurSpUsqKirKvwkVFRWlLl26pPvvv3+zah177LHppz/96QbXz5o1q1ZHhg8++OD0P//zP+tdd+6556ZddtmlVn/wX/3qV/PBMKVP36A/+/Ggv/3tb5t15v+z7rvvvlRWVpbq1au3RW9qnTp1SgceeGDaeeed0wMPPFBj/VNPPVWrN9t//vOfqV27dunwww9PF154YWrUqFE67LDD0plnnpkOP/zwVFxcXOMPbVM9re8Pfo3Vq1enxx57bJN1Lr/88rTrrrumM844I7Vv3z4NGzYstWnTJo0dOzbdfPPNqXXr1ulHP/pRrXr68MMPU//+/fOvzW7duqW33347v/7RRx+tEfQ3xhtb7d/Y6lpISWnHfmMr5JvaFVdckUpLS9P111+fZs2alRYuXJgqKyvTrFmz0vXXX5+aNWtWq+/A9u7dO/33f//3BtfXdi5PKaVOnTql3//+9+ssX/Nab9OmTa1e53vvvXeNTxH96U9/yn9KJqXaf6Los+bPn5++8Y1vpKOPPjotXLhwi1/n3/zmN9MJJ5yQmjVrlv8I7hrTp0+v1Sew/vd//ze1aNEiDRo0KP33f/932nnnndOpp56arr766jRo0KBUUlKS7rzzzlr1VK9evY3O51VVVfkzgRtz7rnnpg4dOqSf//zn6Wtf+1o67bTT0t57750eeeSRNHny5NSpU6daf7rltNNOS0cccUR69dVX09tvv51OPvnkGmdAn3zyydS6deta1XLQyUGnNT3tqAedCjWXp1S4+bxQc3lKdXM+L9RcnlLh5vNCzeUp1d35fEO+UGF8jRUrVqQFCxakBQsW5D+CvbmefvrpGuF3bUuXLk1PPvnkJuuMGDEi/7Ge9fnBD35Qq4lj7Nix6xy9/azLLrssf2Z5S8ybNy9NmjRpsy8WM3z48Bq3yZMn11h/0UUXpVNOOaVWtRYvXpwuueSStO+++6aGDRum4uLi1LZt2zRgwID0/PPP17qndu3a5Y/cfh6ffPJJ+vnPf5769u2b//jZfffdl1q3bp1atGiRTj/99M1+vpYvX77eC+JsDm9sm/fGVpdCSko79htbod/Urrnmmvx3FevVq5c/w7fbbrula6+9tlY1HnjggXT33XdvcP2///3vNG7cuFrVuvjii9NRRx213nUrV65M/fr1q9XrfPjw4em+++7b4PrLLrssnXjiibXq6bNWr16dRowYkcrLy1P9+vU3+3V++umn17itfYDwoosuSr17965VrbfeeiudcsopqUmTJvmD4w0aNEjdunXb6KfO1rapg6u1tXTp0nTGGWekjh07pu9///tpxYoV6frrr0/FxcUpl8ul7t271/px3nvvvXTIIYfkX5ft2rVLL7zwQn797373u/SrX/2qVrUcdHLQKaUd/6BTIebylAo3nxdqLk+pbs7nhZzLUyrMfF6ouTylujufb8gXMozDjm57fGOr7T8Et8YbW10KKSntuG9sW+tN7e23307Tpk1L06ZNq/GJkqytXLkyVVVVbXD9J598UpArIi9btix9/PHHW7z9jBkz0qhRo/Lf8S2UpUuXpuXLl2/WNqtXr06VlZWf6+D41rR8+fJaf51jbW+88cY6n1LbEg46bZ66NJ+/9dZb6eSTT3bQqZY+O5d/9lMSn9fq1as3a/yG5vI1dQoxl6+pVYj5/IYbbijIfL6mpy2Zy9dsv2Y+/zwXjV1fT4WwbNmygs3nhezrC/M74/BFNGfOnKisrIyIiPLy8vzvtGftk08+iY8++iiaNm263vWrVq2K+fPnF+T3JT/66KOoX79+lJSUbPa2M2fOjKlTp8agQYOiWbNmn7uXNZYtWxb169ePhg0bbtZ2KaVYtGhRrF69Olq2bBkNGjQoWE+F8PHHH8fKlSujSZMmm7Xdm2++GdXV1bH33ntHUVHRVuoOdixftPn888zlEXVrPt9R5/KIrTefFxcXx4svvvi5f4O7kLXqYk+FrKWnbVPLv4JgB9a+fft1/sE2b968uOKKK+KOO+743PVrW6uoqGiD/3CLiFiwYEFceeWVBenpgw8+2OL969y5c3Tu3DkiCvs8/fvf/96iWrlcLsrKymosK1RfhajTsGHDaNiw4WbX6tChQ0F6Wr58ecycOTOaN28e++67b411H3/8cfz2t7+NQYMGZVZnR++pkLX0VPtar776ajzzzDPRrVu36Nq1a7z22mtx3XXXRXV1dZx66qnxjW98Y7PqdO3aNfbee+947bXX4qabbtrsOkVFRfHPf/4z/vCHP3zuWoXqaX21GjduHK+99loMHTp0i2t169Yt9tprr8+9f5+tc9VVVxVk/wrZ0+d9zrt16xZFRUVbVOvCCy9c7/JVq1bFNddcEy1atIiIiBtuuCGzWnWxp0LW0tO2qbVBBTvHDmwXNuf3ZLOqpafsa23vPb3++uupbdu2+Y9IHnHEEWnBggX59bW9onOh6uzoPe3o+1cXe0oppUceeSQVFxen5s2bp4YNG6ZHHnkk7brrrqlnz56pR48eqaioaJ2fDN2adXb0nnb0/auLPeVyuXTAAQek7t2717jlcrl08MEHp+7du6cjjzyyVj0VqlZd7GlH37+62FOha22IMA47mD/+8Y8bvd144421/odgoWrpyf4Vuqfjjz8+9e3bN73//vvpzTffTMcee2xq3759/md7aht4ClVnR+9pR9+/uthTSil17do1XX755SmlTy8Q2qxZs3TZZZfl11922WWpV69emdXZ0XsqZC091a7WiBEjUvv27dcJ7lty8b1C1aqLPRWylp62Ta0NEcZhB7Ox35P97O/KZllLT/av0D21atUqvfTSSzWWnXPOOalNmzbpH//4R60DT6Hq7Og9FbKWnmpfq2nTpunNN99MKaW0atWqVFRUVOPnpF5++eVaXdm7UHV29J4KWUtPta/13HPPpa985Stp6NCh+Qs5bmnYKVStuthTIWvpadvUWp96W/4Bd6Au2m233eIPf/hDrF69er23F154IfNaerJ/he5p+fLl61ws6Ne//nX069cvjjjiiHjjjTcyrbOj91TIWnqqfa3PqlevXjRs2DB22WWX/LImTZpEVVXVNqmzo/dUyFp62riDDz44Zs6cGe+//34cdNBB8fLLL0cul9vsPgpZqy72VMhaeto2tdZHGIcdTOfOnTcaanK5XKRa/ohCoWrpyf4Vuqe99947ZsyYsc7y0aNHx3HHHRf9+vXLtM6O3lMha+mp9rXatWsXb731Vv7+9OnTo02bNvn78+bNi9122y2zOjt6T4Wspafa14qI2HnnneOuu+6KYcOGRa9evWLVqlW13nZr1aqLPRWylp62Ta11FOT8OlBnPP300+mRRx7Z4PqlS5emJ598MtNaerJ/he5pxIgRqU+fPhtc/4Mf/KBWv11fqDo7ek+FrKWn2tcaO3Zs+tOf/rTB9ZdddlkaPHhwZnV29J4KWUtPta+1tnnz5qVJkyalpUuXbtH2W6NWXeypkLX0tG1qpeR3xgEAACBzPqYOAAAAGRPGAQAAIGPCOAAAAGRMGAcAAICMCeMAAACQMWEcAAAAMiaMAwAAQMb+fwEKzk6ZQo8QAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 1200x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_= result_df['nodes_dropped'].plot.bar(figsize=(12,8), title='Nodes Dropped by Step')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "e34a305c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1200x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_= result_df['edges_dropped'].plot.bar(figsize=(12,8), title='Edges Dropped by Step')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "03990fb1",
   "metadata": {},
   "outputs": [],
   "source": [
    "# learning at each iteration\n",
    "# speeding up at each step, because smaller networks\n",
    "# betweenness centrality and shortest path related things are very slow on larger networks\n",
    "# pagerank can be used instead\n",
    "# use a centrality that can determine importance beyond number of edges; goal is to cut bridge nodes\n",
    "# attack options are only limited by creativity\n",
    "\n",
    "# on complex network, might need larger cut sizes to be effective\n",
    "# goal was to shatter the network as quickly as possible\n",
    "\n",
    "# collaborative networks seem to be more resilient in nature; considering that some papers have dozens of authors"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91cb4da8",
   "metadata": {},
   "source": [
    "# Investigate Surviving Structures"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "92599bd0",
   "metadata": {},
   "outputs": [],
   "source": [
    "def show_component_count(components, cutoff=4):\n",
    "\n",
    "    i = 0\n",
    "    \n",
    "    for c in components:\n",
    "        \n",
    "        if len(c) > cutoff:\n",
    "\n",
    "            print('c: {} - len: {}'.format(i, len(c)))\n",
    "\n",
    "        i += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "ef944798",
   "metadata": {},
   "outputs": [],
   "source": [
    "def draw_component(G, component, show_names=False):\n",
    "    \n",
    "    G = G.copy()\n",
    "\n",
    "    G_check = G.subgraph(component)\n",
    "\n",
    "    return draw_graph(G_check, show_names=show_names, node_size=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "e264166d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4848"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "components = list(nx.connected_components(G))\n",
    "len(components)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "1c25f690",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "c: 0 - len: 76\n",
      "c: 1 - len: 32185\n",
      "c: 189 - len: 49\n",
      "c: 309 - len: 44\n",
      "c: 463 - len: 50\n",
      "c: 607 - len: 86\n",
      "c: 649 - len: 62\n",
      "c: 653 - len: 120\n",
      "c: 810 - len: 42\n",
      "c: 1012 - len: 73\n",
      "c: 1061 - len: 57\n",
      "c: 1073 - len: 47\n"
     ]
    }
   ],
   "source": [
    "show_component_count(components, 40)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "9e2f4484",
   "metadata": {},
   "outputs": [
    {
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       "<circle cx=\"697\" cy=\"221\" r=\"3.0\" style=\"fill:rgb(205, 217, 236);stroke:black;stroke-width:1.0\"/>\n",
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      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "component = components[816]\n",
    "\n",
    "draw_component(G, component)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "3aa00d3b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6363"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "components = list(nx.connected_components(G1))\n",
    "len(components)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "6fe27bd6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "c: 50 - len: 10\n",
      "c: 53 - len: 10\n",
      "c: 89 - len: 10\n",
      "c: 673 - len: 10\n",
      "c: 891 - len: 10\n",
      "c: 928 - len: 10\n",
      "c: 949 - len: 10\n",
      "c: 1025 - len: 10\n",
      "c: 1358 - len: 10\n",
      "c: 1386 - len: 10\n",
      "c: 1462 - len: 10\n",
      "c: 1816 - len: 10\n",
      "c: 2395 - len: 10\n",
      "c: 2407 - len: 10\n",
      "c: 2629 - len: 10\n",
      "c: 2686 - len: 10\n",
      "c: 2859 - len: 10\n",
      "c: 3004 - len: 10\n",
      "c: 3084 - len: 10\n",
      "c: 3119 - len: 10\n",
      "c: 3146 - len: 10\n",
      "c: 3502 - len: 10\n",
      "c: 4968 - len: 10\n",
      "c: 5266 - len: 10\n",
      "c: 5298 - len: 10\n"
     ]
    }
   ],
   "source": [
    "show_component_count(components, 9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "62c8680c",
   "metadata": {},
   "outputs": [
    {
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       "<circle cx=\"448\" cy=\"520\" r=\"3.0\" style=\"fill:rgb(219, 220, 222);stroke:black;stroke-width:1.0\"/>\n",
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       "<circle cx=\"258\" cy=\"223\" r=\"3.0\" style=\"fill:rgb(219, 220, 222);stroke:black;stroke-width:1.0\"/>\n",
       "<text text-anchor=\"start\" x=\"726\" y=\"196\" font-size=\"10\">Eduardo Brandao</text><text text-anchor=\"start\" x=\"701\" y=\"404\" font-size=\"10\">Florent Pigeon</text><text text-anchor=\"start\" x=\"476\" y=\"310\" font-size=\"10\">Amaury Habrard</text><text text-anchor=\"start\" x=\"58\" y=\"137\" font-size=\"10\">François Jacquenet</text><text text-anchor=\"start\" x=\"299\" y=\"20\" font-size=\"10\">Jean-Philippe Colombier</text><text text-anchor=\"start\" x=\"454\" y=\"520\" font-size=\"10\">Stefan Duffner</text><text text-anchor=\"start\" x=\"200\" y=\"484\" font-size=\"10\">Anthony Nakhoul</text><text text-anchor=\"start\" x=\"26\" y=\"346\" font-size=\"10\">Florence Garrelie</text><text text-anchor=\"start\" x=\"551\" y=\"56\" font-size=\"10\">Marc Sebban</text><text text-anchor=\"start\" x=\"264\" y=\"223\" font-size=\"10\">Rémi Emonet</text></svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "component = components[53]\n",
    "\n",
    "draw_component(G1, component, show_names=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "6409c13b",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<text text-anchor=\"start\" x=\"488\" y=\"20\" font-size=\"10\">Gokhan Secinti</text><text text-anchor=\"start\" x=\"52\" y=\"99\" font-size=\"10\">Emre Horsanali</text><text text-anchor=\"start\" x=\"444\" y=\"520\" font-size=\"10\">Berk Canberk</text><text text-anchor=\"start\" x=\"26\" y=\"404\" font-size=\"10\">Aytac Karameseoglu</text><text text-anchor=\"start\" x=\"726\" y=\"280\" font-size=\"10\">Yagmur Yigit</text></svg>"
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     },
     "execution_count": 31,
     "metadata": {},
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   ],
   "source": [
    "component = components[56]\n",
    "\n",
    "draw_component(G1, component, show_names=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "98454455",
   "metadata": {},
   "outputs": [
    {
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       "<text text-anchor=\"start\" x=\"101\" y=\"520\" font-size=\"10\">Tomáš Čejka</text><text text-anchor=\"start\" x=\"726\" y=\"464\" font-size=\"10\">Karel Hynek</text><text text-anchor=\"start\" x=\"26\" y=\"75\" font-size=\"10\">Jaroslav Pešek</text><text text-anchor=\"start\" x=\"650\" y=\"20\" font-size=\"10\">Josef Koumar</text></svg>"
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     "execution_count": 32,
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   "source": [
    "component = components[92]\n",
    "\n",
    "draw_component(G1, component, show_names=True)"
   ]
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  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "01daea57",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Graph with 59260 nodes and 302588 edges\n"
     ]
    }
   ],
   "source": [
    "print(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "a39fd9b1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Graph with 24893 nodes and 41180 edges\n"
     ]
    }
   ],
   "source": [
    "print(G1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "91e5f845",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.00017233192168756068"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.density(G) # very sparse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "32bc4a2d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.00013291662540323073"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.density(G1) # very sparse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "41402435",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>node</th>\n",
       "      <th>degrees</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Dustin Nguyen</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Yuan-Sen Ting</td>\n",
       "      <td>36</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Todd A. Thompson</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Sebastian Lopez</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Laura A. Lopez</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               node  degrees\n",
       "0     Dustin Nguyen        4\n",
       "1     Yuan-Sen Ting       36\n",
       "2  Todd A. Thompson        4\n",
       "3   Sebastian Lopez        4\n",
       "4    Laura A. Lopez        4"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "degree_df = pd.DataFrame(G.degree)\n",
    "degree_df.columns = ['node', 'degrees']\n",
    "\n",
    "degree_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "44c3dda6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: ylabel='Frequency'>"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "degree_df['degrees'].plot.hist()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "5bb6c446",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>node</th>\n",
       "      <th>degrees</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Purvik Patel</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Franc O</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Jonathan Blazek</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Lorenz Kummer</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Samir Moustafa</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              node  degrees\n",
       "0     Purvik Patel        2\n",
       "1          Franc O        2\n",
       "2  Jonathan Blazek        2\n",
       "3    Lorenz Kummer        3\n",
       "4   Samir Moustafa        3"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "degree_df = pd.DataFrame(G1.degree)\n",
    "degree_df.columns = ['node', 'degrees']\n",
    "\n",
    "degree_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "e1d117f0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: ylabel='Frequency'>"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "degree_df['degrees'].plot.hist()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "78f1f913",
   "metadata": {},
   "outputs": [],
   "source": [
    "nodes = [len(G.nodes), len(G1.nodes)]\n",
    "edges = [len(G.edges), len(G1.edges)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "7a494a14",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "final_df = pd.DataFrame({'nodes':nodes, 'edges':edges})\n",
    "final_df.sort_index(ascending=True, inplace=True)\n",
    "\n",
    "final_df['nodes'].plot.bar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "33620645",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ihAAAgLEIIQAAYCxCCAAAGIsQAgAAxiKEAACAsQghAABgrAmFUF1dnR5//HElJCQoJSVFa9as0blz56JmIpGItmzZIo/Ho7i4OC1btkwffvhh1Ew4HNbmzZuVnJys+Ph4FRUVqbe3N2omEAjI6/XKsixZliWv16urV69GzVy8eFGFhYWKj49XcnKyysvLNTw8HDVz5swZ5eTkKC4uTrNmzdLWrVsViUQmstsAAGCKmlAIHTt2TJs2bZLP51Nra6v++Mc/Ki8vT4ODg/bMK6+8ovr6eu3evVvt7e1yu93Kzc3VtWvX7JmKigo1NjaqoaFBbW1tun79ugoKCjQ6OmrPFBcXq6urS83NzWpublZXV5e8Xq+9fXR0VKtXr9bg4KDa2trU0NCggwcPqqqqyp4JhULKzc2Vx+NRe3u7du3ape3bt6u+vv6O3iwAADC1OCJf4/DI5cuXlZKSomPHjul73/ueIpGIPB6PKioq9Pzzz0v64uiPy+XSyy+/rKefflrBYFAzZ87Uvn37tG7dOknSpUuXlJaWpkOHDik/P19nz57VggUL5PP5lJWVJUny+XzKzs7Wxx9/rPT0dB0+fFgFBQXq6emRx+ORJDU0NKikpEQDAwNKTEzUnj17VFNTo/7+fjmdTknStm3btGvXLvX29srhcHzpPoZCIVmWpWAwqMTExDt9qx5Ic15omuwl4D66sG31ZC8BAO6ar/r7+2tdIxQMBiVJDz30kCTp/Pnz8vv9ysvLs2ecTqdycnJ04sQJSVJHR4dGRkaiZjwejzIyMuyZkydPyrIsO4IkafHixbIsK2omIyPDjiBJys/PVzgcVkdHhz2Tk5NjR9DYzKVLl3ThwoWvs+sAAGAKuOMQikQiqqys1BNPPKGMjAxJkt/vlyS5XK6oWZfLZW/z+/2KjY1VUlLSuDMpKSk3vWZKSkrUzI2vk5SUpNjY2HFnxn4em7lROBxWKBSKugEAgKnpjkPo2Wef1W9/+1v913/9103bbjzlFIlEvvQ01I0zt5q/GzNjZwJvt566ujr7Am3LspSWljbuugEAwIPrjkJo8+bNevvtt/Wb3/xGjzzyiH2/2+2WdPPRloGBAftIjNvt1vDwsAKBwLgz/f39N73u5cuXo2ZufJ1AIKCRkZFxZwYGBiTdfNRqTE1NjYLBoH3r6ekZ550AAAAPsgmFUCQS0bPPPqtf/epXeu+99zR37tyo7XPnzpXb7VZra6t93/DwsI4dO6YlS5ZIkjIzMzV9+vSomb6+PnV3d9sz2dnZCgaDOn36tD1z6tQpBYPBqJnu7m719fXZMy0tLXI6ncrMzLRnjh8/HvWR+paWFnk8Hs2ZM+eW++h0OpWYmBh1AwAAU9OEQmjTpk3av3+/3nzzTSUkJMjv98vv92toaEjSF6ebKioqVFtbq8bGRnV3d6ukpEQzZsxQcXGxJMmyLG3cuFFVVVU6cuSIOjs7tX79ei1cuFArVqyQJM2fP18rV65UaWmpfD6ffD6fSktLVVBQoPT0dElSXl6eFixYIK/Xq87OTh05ckTV1dUqLS2146W4uFhOp1MlJSXq7u5WY2OjamtrVVlZ+ZU+MQYAAKa2aRMZ3rNnjyRp2bJlUff/4he/UElJiSTpueee09DQkMrKyhQIBJSVlaWWlhYlJCTY8zt37tS0adO0du1aDQ0Nafny5dq7d69iYmLsmQMHDqi8vNz+dFlRUZF2795tb4+JiVFTU5PKysq0dOlSxcXFqbi4WNu3b7dnLMtSa2urNm3apEWLFikpKUmVlZWqrKycyG4DAIAp6mt9j5AJ+B4hmILvEQIwldyX7xECAAB4kBFCAADAWIQQAAAwFiEEAACMRQgBAABjEUIAAMBYhBAAADAWIQQAAIxFCAEAAGMRQgAAwFiEEAAAMBYhBAAAjEUIAQAAYxFCAADAWIQQAAAwFiEEAACMRQgBAABjEUIAAMBYhBAAADAWIQQAAIxFCAEAAGMRQgAAwFiEEAAAMBYhBAAAjEUIAQAAYxFCAADAWIQQAAAwFiEEAACMRQgBAABjEUIAAMBYhBAAADAWIQQAAIxFCAEAAGMRQgAAwFiEEAAAMBYhBAAAjEUIAQAAYxFCAADAWIQQAAAwFiEEAACMRQgBAABjEUIAAMBYhBAAADAWIQQAAIxFCAEAAGMRQgAAwFiEEAAAMBYhBAAAjDXhEDp+/LgKCwvl8XjkcDj061//Omp7SUmJHA5H1G3x4sVRM+FwWJs3b1ZycrLi4+NVVFSk3t7eqJlAICCv1yvLsmRZlrxer65evRo1c/HiRRUWFio+Pl7JyckqLy/X8PBw1MyZM2eUk5OjuLg4zZo1S1u3blUkEpnobgMAgClowiE0ODioxx57TLt3777tzMqVK9XX12ffDh06FLW9oqJCjY2NamhoUFtbm65fv66CggKNjo7aM8XFxerq6lJzc7Oam5vV1dUlr9drbx8dHdXq1as1ODiotrY2NTQ06ODBg6qqqrJnQqGQcnNz5fF41N7erl27dmn79u2qr6+f6G4DAIApaNpEH7Bq1SqtWrVq3Bmn0ym3233LbcFgUK+//rr27dunFStWSJL279+vtLQ0vfvuu8rPz9fZs2fV3Nwsn8+nrKwsSdJrr72m7OxsnTt3Tunp6WppadFHH32knp4eeTweSdKOHTtUUlKil156SYmJiTpw4ID+8Ic/aO/evXI6ncrIyNAnn3yi+vp6VVZWyuFwTHT3AQDAFHJPrhE6evSoUlJSNG/ePJWWlmpgYMDe1tHRoZGREeXl5dn3eTweZWRk6MSJE5KkkydPyrIsO4IkafHixbIsK2omIyPDjiBJys/PVzgcVkdHhz2Tk5Mjp9MZNXPp0iVduHDhlmsPh8MKhUJRNwAAMDXd9RBatWqVDhw4oPfee087duxQe3u7vv/97yscDkuS/H6/YmNjlZSUFPU4l8slv99vz6SkpNz03CkpKVEzLpcrantSUpJiY2PHnRn7eWzmRnV1dfZ1SZZlKS0tbaJvAQAAeEBM+NTYl1m3bp39nzMyMrRo0SLNnj1bTU1Neuqpp277uEgkEnWq6lanre7GzNiF0rc7LVZTU6PKykr751AoRAwBADBF3fOPz6empmr27Nn69NNPJUlut1vDw8MKBAJRcwMDA/bRGrfbrf7+/pue6/Lly1EzNx7VCQQCGhkZGXdm7DTdjUeKxjidTiUmJkbdAADA1HTPQ+jKlSvq6elRamqqJCkzM1PTp09Xa2urPdPX16fu7m4tWbJEkpSdna1gMKjTp0/bM6dOnVIwGIya6e7uVl9fnz3T0tIip9OpzMxMe+b48eNRH6lvaWmRx+PRnDlz7tk+AwCAB8OEQ+j69evq6upSV1eXJOn8+fPq6urSxYsXdf36dVVXV+vkyZO6cOGCjh49qsLCQiUnJ+uHP/yhJMmyLG3cuFFVVVU6cuSIOjs7tX79ei1cuND+FNn8+fO1cuVKlZaWyufzyefzqbS0VAUFBUpPT5ck5eXlacGCBfJ6vers7NSRI0dUXV2t0tJS+yhOcXGxnE6nSkpK1N3drcbGRtXW1vKJMQAAIOkOrhH64IMP9OSTT9o/j11Ps2HDBu3Zs0dnzpzRG2+8oatXryo1NVVPPvmk3nrrLSUkJNiP2blzp6ZNm6a1a9dqaGhIy5cv1969exUTE2PPHDhwQOXl5fany4qKiqK+uygmJkZNTU0qKyvT0qVLFRcXp+LiYm3fvt2esSxLra2t2rRpkxYtWqSkpCRVVlZGXQMEAADM5YjwNcvjCoVCsixLwWDQuOuF5rzQNNlLwH10YdvqyV4CANw1X/X3N39rDAAAGIsQAgAAxiKEAACAsQghAABgLEIIAAAYixACAADGIoQAAICxCCEAAGAsQggAABiLEAIAAMYihAAAgLEIIQAAYCxCCAAAGIsQAgAAxiKEAACAsQghAABgLEIIAAAYixACAADGIoQAAICxCCEAAGAsQggAABiLEAIAAMYihAAAgLEIIQAAYCxCCAAAGIsQAgAAxiKEAACAsQghAABgLEIIAAAYixACAADGIoQAAICxCCEAAGAsQggAABiLEAIAAMYihAAAgLEIIQAAYCxCCAAAGIsQAgAAxiKEAACAsQghAABgLEIIAAAYixACAADGIoQAAICxCCEAAGAsQggAABiLEAIAAMYihAAAgLEmHELHjx9XYWGhPB6PHA6Hfv3rX0dtj0Qi2rJlizwej+Li4rRs2TJ9+OGHUTPhcFibN29WcnKy4uPjVVRUpN7e3qiZQCAgr9cry7JkWZa8Xq+uXr0aNXPx4kUVFhYqPj5eycnJKi8v1/DwcNTMmTNnlJOTo7i4OM2aNUtbt25VJBKZ6G4DAIApaMIhNDg4qMcee0y7d+++5fZXXnlF9fX12r17t9rb2+V2u5Wbm6tr167ZMxUVFWpsbFRDQ4Pa2tp0/fp1FRQUaHR01J4pLi5WV1eXmpub1dzcrK6uLnm9Xnv76OioVq9ercHBQbW1tamhoUEHDx5UVVWVPRMKhZSbmyuPx6P29nbt2rVL27dvV319/UR3GwAATEGOyNc4POJwONTY2Kg1a9ZI+uJokMfjUUVFhZ5//nlJXxz9cblcevnll/X0008rGAxq5syZ2rdvn9atWydJunTpktLS0nTo0CHl5+fr7NmzWrBggXw+n7KysiRJPp9P2dnZ+vjjj5Wenq7Dhw+roKBAPT098ng8kqSGhgaVlJRoYGBAiYmJ2rNnj2pqatTf3y+n0ylJ2rZtm3bt2qXe3l45HI4v3cdQKCTLshQMBpWYmHinb9UDac4LTZO9BNxHF7atnuwlAMBd81V/f9/Va4TOnz8vv9+vvLw8+z6n06mcnBydOHFCktTR0aGRkZGoGY/Ho4yMDHvm5MmTsizLjiBJWrx4sSzLiprJyMiwI0iS8vPzFQ6H1dHRYc/k5OTYETQ2c+nSJV24cOGW+xAOhxUKhaJuAABgarqrIeT3+yVJLpcr6n6Xy2Vv8/v9io2NVVJS0rgzKSkpNz1/SkpK1MyNr5OUlKTY2NhxZ8Z+Hpu5UV1dnX1dkmVZSktL+/IdBwAAD6R78qmxG085RSKRLz0NdePMrebvxszYmcDbraempkbBYNC+9fT0jLtuAADw4LqrIeR2uyXdfLRlYGDAPhLjdrs1PDysQCAw7kx/f/9Nz3/58uWomRtfJxAIaGRkZNyZgYEBSTcftRrjdDqVmJgYdQMAAFPTXQ2huXPnyu12q7W11b5veHhYx44d05IlSyRJmZmZmj59etRMX1+furu77Zns7GwFg0GdPn3anjl16pSCwWDUTHd3t/r6+uyZlpYWOZ1OZWZm2jPHjx+P+kh9S0uLPB6P5syZczd3HQAAPIAmHELXr19XV1eXurq6JH1xgXRXV5cuXrwoh8OhiooK1dbWqrGxUd3d3SopKdGMGTNUXFwsSbIsSxs3blRVVZWOHDmizs5OrV+/XgsXLtSKFSskSfPnz9fKlStVWloqn88nn8+n0tJSFRQUKD09XZKUl5enBQsWyOv1qrOzU0eOHFF1dbVKS0vtozjFxcVyOp0qKSlRd3e3GhsbVVtbq8rKyq/0iTEAADC1TZvoAz744AM9+eST9s+VlZWSpA0bNmjv3r167rnnNDQ0pLKyMgUCAWVlZamlpUUJCQn2Y3bu3Klp06Zp7dq1Ghoa0vLly7V3717FxMTYMwcOHFB5ebn96bKioqKo7y6KiYlRU1OTysrKtHTpUsXFxam4uFjbt2+3ZyzLUmtrqzZt2qRFixYpKSlJlZWV9poBAIDZvtb3CJmA7xGCKfgeIQBTyaR8jxAAAMCDhBACAADGIoQAAICxCCEAAGAsQggAABiLEAIAAMYihAAAgLEIIQAAYCxCCAAAGIsQAgAAxiKEAACAsQghAABgLEIIAAAYixACAADGIoQAAICxCCEAAGAsQggAABiLEAIAAMYihAAAgLEIIQAAYCxCCAAAGIsQAgAAxiKEAACAsQghAABgLEIIAAAYixACAADGIoQAAICxCCEAAGAsQggAABiLEAIAAMYihAAAgLEIIQAAYCxCCAAAGIsQAgAAxiKEAACAsQghAABgLEIIAAAYixACAADGIoQAAICxCCEAAGAsQggAABiLEAIAAMYihAAAgLEIIQAAYCxCCAAAGIsQAgAAxiKEAACAse56CG3ZskUOhyPq5na77e2RSERbtmyRx+NRXFycli1bpg8//DDqOcLhsDZv3qzk5GTFx8erqKhIvb29UTOBQEBer1eWZcmyLHm9Xl29ejVq5uLFiyosLFR8fLySk5NVXl6u4eHhu73LAADgAXVPjgh997vfVV9fn307c+aMve2VV15RfX29du/erfb2drndbuXm5uratWv2TEVFhRobG9XQ0KC2tjZdv35dBQUFGh0dtWeKi4vV1dWl5uZmNTc3q6urS16v194+Ojqq1atXa3BwUG1tbWpoaNDBgwdVVVV1L3YZAAA8gKbdkyedNi3qKNCYSCSiV199VS+++KKeeuopSdIvf/lLuVwuvfnmm3r66acVDAb1+uuva9++fVqxYoUkaf/+/UpLS9O7776r/Px8nT17Vs3NzfL5fMrKypIkvfbaa8rOzta5c+eUnp6ulpYWffTRR+rp6ZHH45Ek7dixQyUlJXrppZeUmJh4L3YdAAA8QO7JEaFPP/1UHo9Hc+fO1d/8zd/od7/7nSTp/Pnz8vv9ysvLs2edTqdycnJ04sQJSVJHR4dGRkaiZjwejzIyMuyZkydPyrIsO4IkafHixbIsK2omIyPDjiBJys/PVzgcVkdHx23XHg6HFQqFom4AAGBquushlJWVpTfeeEP//d//rddee01+v19LlizRlStX5Pf7JUkulyvqMS6Xy97m9/sVGxurpKSkcWdSUlJueu2UlJSomRtfJykpSbGxsfbMrdTV1dnXHVmWpbS0tAm+AwAA4EFx10No1apV+uu//mstXLhQK1asUFNTk6QvToGNcTgcUY+JRCI33XejG2duNX8nMzeqqalRMBi0bz09PeOuCwAAPLju+cfn4+PjtXDhQn366af2dUM3HpEZGBiwj9643W4NDw8rEAiMO9Pf33/Ta12+fDlq5sbXCQQCGhkZuelI0f/ldDqVmJgYdQMAAFPTPQ+hcDiss2fPKjU1VXPnzpXb7VZra6u9fXh4WMeOHdOSJUskSZmZmZo+fXrUTF9fn7q7u+2Z7OxsBYNBnT592p45deqUgsFg1Ex3d7f6+vrsmZaWFjmdTmVmZt7TfQYAAA+Gu/6pserqahUWFurP//zPNTAwoJ/+9KcKhULasGGDHA6HKioqVFtbq+985zv6zne+o9raWs2YMUPFxcWSJMuytHHjRlVVVenhhx/WQw89pOrqavtUmyTNnz9fK1euVGlpqX7+859Lkn70ox+poKBA6enpkqS8vDwtWLBAXq9XP/vZz/T73/9e1dXVKi0t5SgPAACQdA9CqLe3V3/7t3+rzz77TDNnztTixYvl8/k0e/ZsSdJzzz2noaEhlZWVKRAIKCsrSy0tLUpISLCfY+fOnZo2bZrWrl2roaEhLV++XHv37lVMTIw9c+DAAZWXl9ufLisqKtLu3bvt7TExMWpqalJZWZmWLl2quLg4FRcXa/v27Xd7lwEAwAPKEYlEIpO9iG+yUCgky7IUDAaNO5I054WmyV4C7qML21ZP9hIA4K75qr+/+VtjAADAWIQQAAAwFiEEAACMdU/+1hgA4JuNawDNwjWAt8cRIQAAYCxCCAAAGIsQAgAAxiKEAACAsQghAABgLEIIAAAYixACAADGIoQAAICxCCEAAGAsQggAABiLEAIAAMYihAAAgLEIIQAAYCxCCAAAGIsQAgAAxiKEAACAsQghAABgLEIIAAAYixACAADGIoQAAICxCCEAAGAsQggAABiLEAIAAMYihAAAgLEIIQAAYCxCCAAAGIsQAgAAxiKEAACAsQghAABgLEIIAAAYixACAADGIoQAAICxCCEAAGAsQggAABiLEAIAAMYihAAAgLEIIQAAYCxCCAAAGIsQAgAAxiKEAACAsQghAABgLEIIAAAYixACAADGMiKE/u3f/k1z587Vt771LWVmZur999+f7CUBAIBvgCkfQm+99ZYqKir04osvqrOzU3/1V3+lVatW6eLFi5O9NAAAMMmmfAjV19dr48aN+od/+AfNnz9fr776qtLS0rRnz57JXhoAAJhk0yZ7AffS8PCwOjo69MILL0Tdn5eXpxMnTtzyMeFwWOFw2P45GAxKkkKh0L1b6DfU5+H/N9lLwH1k4n/HTca/b7OY+O97bJ8jkci4c1M6hD777DONjo7K5XJF3e9yueT3+2/5mLq6Ov3kJz+56f60tLR7skbgm8J6dbJXAOBeMfnf97Vr12RZ1m23T+kQGuNwOKJ+jkQiN903pqamRpWVlfbPn3/+uX7/+9/r4Ycfvu1jMHWEQiGlpaWpp6dHiYmJk70cAHcR/77NEolEdO3aNXk8nnHnpnQIJScnKyYm5qajPwMDAzcdJRrjdDrldDqj7vuzP/uze7VEfEMlJibyP5TAFMW/b3OMdyRozJS+WDo2NlaZmZlqbW2Nur+1tVVLliyZpFUBAIBviil9REiSKisr5fV6tWjRImVnZ+vf//3fdfHiRT3zzDOTvTQAADDJpnwIrVu3TleuXNHWrVvV19enjIwMHTp0SLNnz57speEbyOl06sc//vFNp0cBPPj4941bcUS+7HNlAAAAU9SUvkYIAABgPIQQAAAwFiEEAACMRQgBAABjEUIAAMBYU/7j88B4ent7tWfPHp04cUJ+v18Oh0Mul0tLlizRM888w9+YA4Apjo/Pw1htbW1atWqV0tLSlJeXJ5fLpUgkooGBAbW2tqqnp0eHDx/W0qVLJ3upAO6Bnp4e/fjHP9Z//ud/TvZSMIkIIRjr8ccf1xNPPKGdO3fecvs//dM/qa2tTe3t7fd5ZQDuh//93//VX/7lX2p0dHSyl4JJRAjBWHFxcerq6lJ6evott3/88cf6i7/4Cw0NDd3nlQG4G95+++1xt//ud79TVVUVIWQ4rhGCsVJTU3XixInbhtDJkyeVmpp6n1cF4G5Zs2aNHA6Hxvv/+w6H4z6uCN9EhBCMVV1drWeeeUYdHR3Kzc2Vy+WSw+GQ3+9Xa2ur/uM//kOvvvrqZC8TwB1KTU3Vv/7rv2rNmjW33N7V1aXMzMz7uyh84xBCMFZZWZkefvhh7dy5Uz//+c/tw+MxMTHKzMzUG2+8obVr107yKgHcqczMTP3P//zPbUPoy44WwQxcIwRIGhkZ0WeffSZJSk5O1vTp0yd5RQC+rvfff1+Dg4NauXLlLbcPDg7qgw8+UE5Ozn1eGb5JCCEAAGAsvlkaAAAYixACAADGIoQAAICxCCEAAGAsQggAABiLEAIAAMYihAAAgLEIIQAAYKz/D8oqmWxpIenoAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "final_df['edges'].plot.bar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "bf74a321",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>nodes</th>\n",
       "      <th>edges</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>59260</td>\n",
       "      <td>302588</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>24893</td>\n",
       "      <td>41180</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   nodes   edges\n",
       "0  59260  302588\n",
       "1  24893   41180"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "final_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "289e7cae",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3a6d012b",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f14a4ce0",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.11.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}