Creating dependency graph from definition file.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from lxml import etree\n",
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "from networkx.drawing.nx_agraph import graphviz_layout\n",
    "from pulp import LpProblem, LpMinimize, LpVariable, lpSum, LpStatus"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import extract as X\n",
    "import parsing_xml as px"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "#ag = etree.parse('/home/luis/planetmath_defs.xml').getroot()\n",
    "ag = etree.parse('/media/hd1/planetmath/datasets/planetmath_definitions.xml.gz').getroot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "def_dict has this many elements  3379\n"
     ]
    }
   ],
   "source": [
    "G = nx.DiGraph()\n",
    "def_dict = {} #keys: dfndum Value: list of hashes of statements where the is appears\n",
    "hash_dict = {} # keys: hashe of statements, Values: the text of the statement\n",
    "for D in ag.iter(tag = 'stmnt'):\n",
    "    hash_dict[hash(D.text)] = D.text\n",
    "    \n",
    "for d in ag.iter(tag = 'dfndum'):\n",
    "    D = d.getparent().find('stmnt').text\n",
    "    if d.text.strip() in def_dict:\n",
    "        def_dict[d.text.strip()].append(hash(D))\n",
    "    else:\n",
    "        def_dict[d.text.strip()] = [hash(D),]\n",
    "print('def_dict has this many elements ', len(def_dict.values()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "dgraph = nx.DiGraph()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "doing k= 0\n",
      "doing k= 1000\n",
      "doing k= 2000\n",
      "doing k= 3000\n"
     ]
    }
   ],
   "source": [
    "empty_str_if_none = lambda s: s if s  else ''\n",
    "for k,d_raw in enumerate(def_dict.keys()):\n",
    "    d = d_raw.strip()\n",
    "    if k%1000 == 0:\n",
    "        print('doing k=', k)\n",
    "    for Def in ag.iter(tag = 'definition'):\n",
    "        D = Def.find('.//stmnt')\n",
    "        #Check if D is not a definition for d\n",
    "        if hash(D.text) in def_dict[d]:\n",
    "            pass\n",
    "        else:\n",
    "            dfndum_lst = [c.text for c in D.getparent().findall('.//dfndum') ]\n",
    "            if d in empty_str_if_none(D.text):\n",
    "                add_edges_lst = [(d, p.strip()) for p in dfndum_lst if d != p]\n",
    "                dgraph.add_edges_from(add_edges_lst)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "456"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-10-7af4741658f0>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      5\u001b[0m }\n\u001b[1;32m      6\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfigure\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfigsize\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m100\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m30\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 7\u001b[0;31m \u001b[0mpos\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mgraphviz_layout\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdgraph\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mprog\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'dot'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      8\u001b[0m \u001b[0mnx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdraw_networkx\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdgraph\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpos\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mopts\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      9\u001b[0m \u001b[0;31m#plt.savefig('data/starts_with_p_spectral.png')\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/.local/lib/python3.8/site-packages/networkx/drawing/nx_agraph.py\u001b[0m in \u001b[0;36mgraphviz_layout\u001b[0;34m(G, prog, root, args)\u001b[0m\n\u001b[1;32m    235\u001b[0m     \u001b[0mThis\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0ma\u001b[0m \u001b[0mwrapper\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mpygraphviz_layout\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    236\u001b[0m     \"\"\"\n\u001b[0;32m--> 237\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mpygraphviz_layout\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mG\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mprog\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mprog\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mroot\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mroot\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    238\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    239\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/.local/lib/python3.8/site-packages/networkx/drawing/nx_agraph.py\u001b[0m in \u001b[0;36mpygraphviz_layout\u001b[0;34m(G, prog, root, args)\u001b[0m\n\u001b[1;32m    283\u001b[0m         \u001b[0margs\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;34mf\"-Groot={root}\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    284\u001b[0m     \u001b[0mA\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mto_agraph\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mG\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 285\u001b[0;31m     \u001b[0mA\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlayout\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mprog\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mprog\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    286\u001b[0m     \u001b[0mnode_pos\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    287\u001b[0m     \u001b[0;32mfor\u001b[0m \u001b[0mn\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mG\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/.local/lib/python3.8/site-packages/pygraphviz/agraph.py\u001b[0m in \u001b[0;36mlayout\u001b[0;34m(self, prog, args)\u001b[0m\n\u001b[1;32m   1420\u001b[0m         \"\"\"\n\u001b[1;32m   1421\u001b[0m         \u001b[0mfmt\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m\"dot\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1422\u001b[0;31m         \u001b[0mdata\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_run_prog\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mprog\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\" \"\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mjoin\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"-T\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfmt\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1423\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfrom_string\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1424\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mhas_layout\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mTrue\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/.local/lib/python3.8/site-packages/pygraphviz/agraph.py\u001b[0m in \u001b[0;36m_run_prog\u001b[0;34m(self, prog, args)\u001b[0m\n\u001b[1;32m   1381\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1382\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0mt\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mthreads\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1383\u001b[0;31m             \u001b[0mt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mjoin\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1384\u001b[0m         \u001b[0mp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mwait\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1385\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/lib/python3.8/threading.py\u001b[0m in \u001b[0;36mjoin\u001b[0;34m(self, timeout)\u001b[0m\n\u001b[1;32m   1009\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1010\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mtimeout\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1011\u001b[0;31m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_wait_for_tstate_lock\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1012\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1013\u001b[0m             \u001b[0;31m# the behavior of a negative timeout isn't documented, but\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/lib/python3.8/threading.py\u001b[0m in \u001b[0;36m_wait_for_tstate_lock\u001b[0;34m(self, block, timeout)\u001b[0m\n\u001b[1;32m   1025\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mlock\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m  \u001b[0;31m# already determined that the C code is done\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1026\u001b[0m             \u001b[0;32massert\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_is_stopped\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1027\u001b[0;31m         \u001b[0;32melif\u001b[0m \u001b[0mlock\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0macquire\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mblock\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtimeout\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1028\u001b[0m             \u001b[0mlock\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrelease\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1029\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_stop\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 7200x2160 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "opts = {\n",
    "    'node_size': 300,\n",
    "    'width': 0.5,\n",
    "    'with_labels': False,\n",
    "}\n",
    "plt.figure(1, figsize=(100,30))\n",
    "pos = graphviz_layout(dgraph, prog='dot')\n",
    "nx.draw_networkx(dgraph, pos, **opts)\n",
    "#plt.savefig('data/starts_with_p_spectral.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'15 Puzzle',\n",
       " 'Achilles number',\n",
       " 'Armstrong number',\n",
       " 'Artin symbol',\n",
       " 'BASIC',\n",
       " 'Baumslag-Solitar group',\n",
       " 'Beatty sequence',\n",
       " 'Belgian number',\n",
       " 'Bernoulli number',\n",
       " 'Blum number',\n",
       " 'Boolean filter',\n",
       " 'Boubaker Polynomials',\n",
       " 'Brown-Zeisel number',\n",
       " 'Burnside group',\n",
       " 'C',\n",
       " 'C++',\n",
       " 'Caesar shift cipher',\n",
       " 'Cantor space',\n",
       " 'Carmichael function',\n",
       " 'Cayley table',\n",
       " 'Chebyshev equation',\n",
       " 'Chebyshev functions',\n",
       " 'Church integer',\n",
       " 'Collatz sequence',\n",
       " 'Coxeter group',\n",
       " 'Cullen number',\n",
       " 'Dedekind domain',\n",
       " 'Dedekind zeta function',\n",
       " 'Diophantine equation',\n",
       " 'Diophantine function',\n",
       " 'Dirichlet L-series',\n",
       " 'Dirichlet convolution',\n",
       " 'Dynkin diagram',\n",
       " 'Egyptian fraction',\n",
       " 'Egyptian math',\n",
       " 'Eisenstein integers',\n",
       " 'Eisenstein prime',\n",
       " 'Euclidean valuation',\n",
       " 'Euler numbers',\n",
       " 'Euler product formula',\n",
       " 'Euler-Gompertz constant',\n",
       " 'FC',\n",
       " 'Fano plane',\n",
       " 'Fibonacci fraction',\n",
       " 'Fortunate number',\n",
       " 'Frattini subset',\n",
       " 'Freiman isomorphism',\n",
       " 'Friedman number',\n",
       " 'Gauss hypergeometric function',\n",
       " 'Gaussian integer',\n",
       " 'Gaussian polynomials',\n",
       " 'Gaussian prime',\n",
       " 'Gaussian sum',\n",
       " 'Grothendieck group',\n",
       " 'Gudermannian function',\n",
       " 'Hadamard matrix',\n",
       " 'Harshad number',\n",
       " 'Haskell',\n",
       " 'Hausdorff measure',\n",
       " 'Hermite equation',\n",
       " 'Hermite polynomials',\n",
       " 'Hopfian',\n",
       " 'Hurwitz equation',\n",
       " 'Jacobi symbol',\n",
       " 'Java',\n",
       " 'JavaScript',\n",
       " 'Kaprekar number',\n",
       " 'Keith number',\n",
       " 'Kenosymplirostic numbers',\n",
       " 'Kodaira dimension',\n",
       " 'Kronecker delta',\n",
       " 'Kronecker symbol',\n",
       " 'Krull dimension',\n",
       " 'Laver table',\n",
       " 'Leech lattice',\n",
       " 'Leyland number',\n",
       " 'Lucas chain',\n",
       " 'Lucas-Carmichael number',\n",
       " 'Mangoldt summatory function',\n",
       " 'Markov number',\n",
       " 'Markov-computable',\n",
       " 'MathWorld',\n",
       " 'Mellin transform',\n",
       " 'Mian-Chowla sequence',\n",
       " 'Morse homology',\n",
       " 'Motzkin number',\n",
       " 'Noetherian topological space',\n",
       " 'Noosphere Tables',\n",
       " 'On-Line Encyclopedia of Integer Sequences',\n",
       " 'Ore number',\n",
       " 'Perrin number',\n",
       " 'Petersen graph',\n",
       " 'Pi-Search Page',\n",
       " 'Pillai prime',\n",
       " 'PlanetMath',\n",
       " 'Post canonical system',\n",
       " 'Poulet number',\n",
       " 'Pratt certificate',\n",
       " 'Prime Pages',\n",
       " 'Proth number',\n",
       " 'Proth prime',\n",
       " 'Puiseux series',\n",
       " 'Pythagorean prime',\n",
       " 'Ramanujan trigonometric sum',\n",
       " 'Ramsey numbers',\n",
       " 'Rayleigh-Ritz method',\n",
       " 'Reisner Papyrus',\n",
       " 'Riesel number',\n",
       " 'Riesz decomposition property',\n",
       " 'Ruth-Aaron number',\n",
       " 'Salem number',\n",
       " 'Schur function',\n",
       " 'Smarandache function',\n",
       " 'Smarandache geometries',\n",
       " 'Smarandache-Wellin number',\n",
       " 'Sobolev space',\n",
       " 'Steinberg group',\n",
       " 'Stern prime',\n",
       " 'Stirling numbers of the first kind',\n",
       " 'Sylow p-subgroup',\n",
       " 'Thabit number',\n",
       " 'Tutte polynomial',\n",
       " 'URM computable',\n",
       " 'Ulam spiral',\n",
       " 'Wagstaff prime',\n",
       " 'Wieferich prime',\n",
       " 'Wilson quotient',\n",
       " 'Windows Calculator',\n",
       " 'Wirsing condition',\n",
       " 'Witt polynomials',\n",
       " 'Woodall number',\n",
       " 'Zuckerman number',\n",
       " 'abundance',\n",
       " 'abundant number',\n",
       " 'addition chain',\n",
       " 'additive',\n",
       " 'additive persistence',\n",
       " 'adjacent fraction',\n",
       " 'affine space',\n",
       " 'algebraic integer',\n",
       " 'algebraic unit',\n",
       " 'almost perfect number',\n",
       " 'almost prime',\n",
       " 'alternating factorial',\n",
       " 'amenable number',\n",
       " 'anthyphairetic ratio',\n",
       " 'antiharmonic number',\n",
       " 'antiprism',\n",
       " 'apothem',\n",
       " 'arithmetic',\n",
       " 'arithmetic derivative',\n",
       " 'aspect ratio',\n",
       " 'associate',\n",
       " 'associate class',\n",
       " 'automorphic number',\n",
       " 'base',\n",
       " 'base of the power',\n",
       " 'basis of a module',\n",
       " 'behavior',\n",
       " 'beprisque number',\n",
       " 'bilinear extension',\n",
       " 'binomial coefficient',\n",
       " 'biquadratic field',\n",
       " 'bitwise XOR',\n",
       " 'bounded maximization',\n",
       " 'branch point',\n",
       " 'cabtaxi number',\n",
       " 'cancellative',\n",
       " 'ceiling',\n",
       " 'center',\n",
       " 'central binomial coefficient',\n",
       " 'centralizer',\n",
       " 'characteristic',\n",
       " 'characteristic polynomial',\n",
       " 'chi-squared random variable',\n",
       " 'class number',\n",
       " 'colossally abundant number',\n",
       " 'commensurable',\n",
       " 'comparable',\n",
       " 'complete matching',\n",
       " 'complete residue system',\n",
       " 'complete weight enumerator',\n",
       " 'complex analytic submanifold',\n",
       " 'complex logarithm',\n",
       " 'composite number',\n",
       " 'composition series',\n",
       " 'computable function',\n",
       " 'configuration',\n",
       " 'confluent',\n",
       " 'contact structure',\n",
       " 'contains',\n",
       " 'context-free',\n",
       " 'continuous from the left',\n",
       " 'contrageometric mean',\n",
       " 'contraharmonic mean',\n",
       " 'converges almost everywhere',\n",
       " 'converges uniformly',\n",
       " 'convex subset',\n",
       " 'coprime',\n",
       " 'course-of-values recursion',\n",
       " 'covering system',\n",
       " 'crazy dice',\n",
       " 'critical strip',\n",
       " 'cusp form',\n",
       " 'cycle of generalized eigenvectors',\n",
       " 'cyclic Gray code',\n",
       " 'cyclic number',\n",
       " 'cyclic ring',\n",
       " 'cyclotomic equation',\n",
       " 'cyclotomic field',\n",
       " 'cyclotomic polynomial',\n",
       " 'cyclotomic units',\n",
       " 'decimal number',\n",
       " 'decimal point',\n",
       " 'decomposable',\n",
       " 'deficiency',\n",
       " 'deficient number',\n",
       " 'definite language',\n",
       " 'degree',\n",
       " 'delta functor',\n",
       " 'dense',\n",
       " 'derivative function',\n",
       " 'digamma function',\n",
       " 'digit sum',\n",
       " 'digitaddition generator',\n",
       " 'discrete valuation',\n",
       " 'discriminant',\n",
       " 'discriminant ideal',\n",
       " 'divided difference table',\n",
       " 'divisibility',\n",
       " 'divisibility test',\n",
       " 'divisible',\n",
       " 'division idempotent',\n",
       " 'double factorial',\n",
       " 'doubly even number',\n",
       " 'dual closure',\n",
       " 'elementary operation',\n",
       " 'elementary recursive',\n",
       " 'elliptic curve cryptography',\n",
       " 'elliptic curve discrete logarithm problem',\n",
       " 'empty word',\n",
       " 'equidigital number',\n",
       " 'equipotence',\n",
       " 'equivalent',\n",
       " 'essential component',\n",
       " 'even lattice',\n",
       " 'even-even-odd rule',\n",
       " 'eventually coincide',\n",
       " 'exactly divides',\n",
       " 'expansivity',\n",
       " 'exponent',\n",
       " 'exponential factorial',\n",
       " 'extraordinary number',\n",
       " 'extravagant number',\n",
       " 'factor',\n",
       " 'factorial',\n",
       " 'factorial base',\n",
       " 'factorial prime',\n",
       " 'factorion',\n",
       " 'filter',\n",
       " 'finitary consequence operator',\n",
       " 'finite chain',\n",
       " 'finite dimensional distributions',\n",
       " 'finite field',\n",
       " 'finite group',\n",
       " 'first order',\n",
       " 'first order language',\n",
       " 'fixed-point arithmetic',\n",
       " 'flag f-vector',\n",
       " 'floor',\n",
       " 'formally congruent',\n",
       " 'forward difference',\n",
       " 'fourth power',\n",
       " 'fractal',\n",
       " 'fraction power',\n",
       " 'fractional derivative',\n",
       " 'fractional integration',\n",
       " 'fractional number',\n",
       " 'fractional part',\n",
       " 'free category',\n",
       " 'freely generates',\n",
       " 'frugal number',\n",
       " 'function series',\n",
       " 'fundamental units',\n",
       " 'gamma function',\n",
       " 'gcd',\n",
       " 'general linear group',\n",
       " 'generalized Smarandache palindrome',\n",
       " 'generator',\n",
       " 'graded module homomorphism',\n",
       " 'graph labeling',\n",
       " 'greatest common divisor',\n",
       " 'greatest element',\n",
       " 'group algebra',\n",
       " 'group system',\n",
       " 'half plane',\n",
       " 'happy ending problem',\n",
       " 'happy number',\n",
       " 'has a rank',\n",
       " 'height function',\n",
       " 'hexagonal number',\n",
       " 'highly abundant number',\n",
       " 'homotopy groups',\n",
       " 'hyperperfect number',\n",
       " 'impolite number',\n",
       " 'in-place sorting algorithm',\n",
       " 'incident',\n",
       " 'ind-variety',\n",
       " 'indefinite sum',\n",
       " 'index',\n",
       " 'induce',\n",
       " 'inductive closure',\n",
       " 'inert',\n",
       " 'infinite prime',\n",
       " 'injective dimension',\n",
       " 'insertion',\n",
       " 'integer factorization',\n",
       " 'integer part',\n",
       " 'integrable',\n",
       " 'integral current',\n",
       " 'integral element',\n",
       " 'intercession',\n",
       " 'inverse limit',\n",
       " 'irrational',\n",
       " 'irreducible continuous geometry',\n",
       " 'iterated totient function',\n",
       " 'iteration',\n",
       " 'iterator',\n",
       " 'jet',\n",
       " 'knot sequence',\n",
       " 'lattice of subgroups',\n",
       " 'least common multiple',\n",
       " 'least prime factor',\n",
       " 'least significant bit',\n",
       " 'left noetherian',\n",
       " 'left power',\n",
       " 'length',\n",
       " 'linear congruence',\n",
       " 'linear erasing',\n",
       " 'linear recurrence',\n",
       " 'logical connective',\n",
       " 'logical equivalence',\n",
       " 'look and say sequence',\n",
       " 'lucky number',\n",
       " 'magic constant',\n",
       " 'mantissa',\n",
       " 'mathematical definition',\n",
       " 'matrix group',\n",
       " 'meet-infinite distributive',\n",
       " 'minimal model',\n",
       " 'minimal negation operator',\n",
       " 'minimal sufficient statistic',\n",
       " 'mixed fraction',\n",
       " 'mode',\n",
       " 'modular group',\n",
       " 'modular theory',\n",
       " 'modulus',\n",
       " 'monomial',\n",
       " 'morphic number',\n",
       " 'most significant digit',\n",
       " 'multi-index',\n",
       " 'multigrade operator',\n",
       " 'multigraph',\n",
       " 'multinomial distribution',\n",
       " 'multiplication',\n",
       " 'multiplicative',\n",
       " 'multiplicative congruence',\n",
       " 'multiplicative encoding',\n",
       " 'multiplicative persistence',\n",
       " 'multiply perfect number',\n",
       " 'natural power function',\n",
       " 'near-pencil',\n",
       " 'near-square prime',\n",
       " 'nearly decomposable',\n",
       " 'needle-in-the-haystack',\n",
       " 'negative',\n",
       " 'negative number',\n",
       " 'neutrosophic logic',\n",
       " 'neutrosophic set',\n",
       " 'nil',\n",
       " 'nilpotent',\n",
       " 'nilpotent ideal',\n",
       " 'nilpotent matrix',\n",
       " 'non-associative',\n",
       " 'non-associative ring',\n",
       " 'non-centrality parameter',\n",
       " 'non-commutative',\n",
       " 'non-standard analysis',\n",
       " 'noncototient',\n",
       " 'nonprincipal ultrafilter',\n",
       " 'nontotient',\n",
       " 'normal form',\n",
       " 'number congruence',\n",
       " 'number of distinct prime factors function',\n",
       " 'odd number',\n",
       " 'omnific integers',\n",
       " 'operator',\n",
       " 'order',\n",
       " 'order of an elliptic function',\n",
       " 'order of contact',\n",
       " 'ordered field',\n",
       " 'ordered tree',\n",
       " 'orderly number',\n",
       " 'orientable',\n",
       " 'overring',\n",
       " 'pairing function',\n",
       " 'palindromic number',\n",
       " 'parasitic number',\n",
       " 'partial operation',\n",
       " 'partition',\n",
       " 'pentagonal number',\n",
       " 'perfect number',\n",
       " 'perfect power',\n",
       " 'perfect ruler',\n",
       " 'perfect square',\n",
       " 'perfect totient number',\n",
       " 'periodic extension',\n",
       " 'permutation matrix',\n",
       " 'pi',\n",
       " 'plane graph',\n",
       " 'polite number',\n",
       " 'polydivisible number',\n",
       " 'polynomial',\n",
       " 'power',\n",
       " 'power of an integer',\n",
       " 'practical number',\n",
       " 'primality',\n",
       " 'primality certificate',\n",
       " 'primality testing',\n",
       " 'primary pseudoperfect number',\n",
       " 'prime',\n",
       " 'prime constant',\n",
       " 'prime counting function',\n",
       " 'prime difference function',\n",
       " 'prime divisor',\n",
       " 'prime gap',\n",
       " 'prime integer topology',\n",
       " 'prime partition',\n",
       " 'prime pyramid',\n",
       " 'prime signature',\n",
       " 'prime subfield',\n",
       " 'primitive recursion',\n",
       " 'primitive recursive number',\n",
       " 'primitive root',\n",
       " 'principal ideal ring',\n",
       " 'probable prime',\n",
       " 'procyclic group',\n",
       " 'proof',\n",
       " 'proper divisor',\n",
       " 'proportional',\n",
       " 'pseudorandom numbers',\n",
       " 'pure lambda calculus',\n",
       " 'pure submodule',\n",
       " 'quadratic covariation',\n",
       " 'quadratic number field',\n",
       " 'quandles',\n",
       " 'quasi-invariant',\n",
       " 'quasicyclic',\n",
       " 'quotient category',\n",
       " 'radian',\n",
       " 'radical',\n",
       " 'radicand',\n",
       " 'rate of return',\n",
       " 'rational',\n",
       " 'rational numbers',\n",
       " 'ray class group',\n",
       " 'real embedding',\n",
       " 'real number',\n",
       " 'real quadratic field',\n",
       " 'real submanifold',\n",
       " 'recurrent state',\n",
       " 'recursively enumerable set',\n",
       " 'redundant',\n",
       " 'refactorable number',\n",
       " 'regular ideal',\n",
       " 'residue at infinity',\n",
       " 'residue class group',\n",
       " 'restriction',\n",
       " 'rig',\n",
       " 'ring adjunction',\n",
       " 'ring of algebraic integers',\n",
       " 'ring of integers',\n",
       " 'root-discriminant',\n",
       " 'rough number',\n",
       " 'rounding up',\n",
       " 'ruler function',\n",
       " 'saturated multiplicatively closed',\n",
       " 'scientific calculator',\n",
       " 'scientific notation',\n",
       " 'seed number',\n",
       " 'self number',\n",
       " 'self-descriptive number',\n",
       " 'semi-standard tableau',\n",
       " 'semiperfect number',\n",
       " 'set of homogeneity',\n",
       " 'shuffle',\n",
       " 'sieve of Eratosthenes',\n",
       " 'silent step',\n",
       " 'singly even number',\n",
       " 'smooth number',\n",
       " 'spark of a matrix',\n",
       " 'sparsely totient number',\n",
       " 'sphenic number',\n",
       " 'square root',\n",
       " 'square root of 3',\n",
       " 'square-free sequence',\n",
       " 'stable distribution function',\n",
       " 'stably isomorphic',\n",
       " 'star height',\n",
       " 'star-free',\n",
       " 'strictly non-palindromic number',\n",
       " 'strictly stationary process',\n",
       " 'string',\n",
       " 'sturdy number',\n",
       " 'subalgebra',\n",
       " 'submodular inequality',\n",
       " 'successor ordinal',\n",
       " 'sum-product number',\n",
       " 'superincreasing sequence',\n",
       " 'superior highly composite number',\n",
       " 'superperfect number',\n",
       " 'supplementary',\n",
       " 'symmetrizable',\n",
       " 'symmetrizer',\n",
       " 'symmetry about',\n",
       " 'systematic sampling',\n",
       " 'terminating',\n",
       " 'tetrahedral number',\n",
       " 'topologically mixing',\n",
       " 'totally finite measure',\n",
       " 'totally ramified',\n",
       " 'totative',\n",
       " 'traveling hump sequence',\n",
       " 'trimorphic number',\n",
       " 'trivial subgroup',\n",
       " 'truth-value semantics for intuitionistic propositional logic is sound',\n",
       " 'unary relation',\n",
       " 'uniform dimension',\n",
       " 'uniformizer',\n",
       " 'unitary divisor',\n",
       " 'unitary perfect number',\n",
       " 'untouchable number',\n",
       " 'unusual number',\n",
       " 'upcrossing',\n",
       " 'upper triangular',\n",
       " 'vampire number',\n",
       " 'vertex',\n",
       " 'von Neumann integer',\n",
       " 'wandering point',\n",
       " 'weak Mordell-Weil theorem',\n",
       " 'weak subalgebra',\n",
       " 'well-ordering',\n",
       " 'winding number',\n",
       " 'zero',\n",
       " 'zero ring',\n",
       " 'zero set',\n",
       " 'zeroless pandigital number'}"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.descendants_at_distance(dgraph, 'integer', 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'D',\n",
       " 'T',\n",
       " 'ample',\n",
       " 'biquadratic field',\n",
       " 'domain',\n",
       " 'field',\n",
       " 'ideal',\n",
       " 'integral',\n",
       " 'integral domain',\n",
       " 'irreducible',\n",
       " 'maximal',\n",
       " 'prime',\n",
       " 'principal ideal',\n",
       " 'reducible'}"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.descendants_at_distance(dgraph.reverse(), 'PID', 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Done!! Reversed 40 cycles\n"
     ]
    }
   ],
   "source": [
    "cycle_cnt = 0\n",
    "while True:\n",
    "    try:\n",
    "        #cycle_edge = nx.find_cycle(dgraph)[0]\n",
    "        #dgraph.remove_edge(*cycle_edge)\n",
    "        cycle_edges = nx.find_cycle(dgraph)\n",
    "        for c in cycle_edges:\n",
    "            dgraph.remove_edge(*c)\n",
    "        #dgraph.add_edge(cycle_edge[1], cycle_edge[0])\n",
    "        cycle_cnt += 1\n",
    "    except nx.NetworkXNoCycle:\n",
    "        print(f'Done!! Reversed {cycle_cnt} cycles')\n",
    "        break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[l_Achilles_number,\n",
       " l_Apéry’s_constant,\n",
       " l_Armstrong_number,\n",
       " l_Artin_map,\n",
       " l_Basel_problem,\n",
       " l_Beatty_sequence,\n",
       " l_Bernoulli_number,\n",
       " l_Bernoulli_periodic_function,\n",
       " l_Bernoulli_polynomial,\n",
       " l_Bernoulli_polynomials_and_numbers,\n",
       " l_Blum_number,\n",
       " l_Brocard’s_problem,\n",
       " l_Brun’s_constant,\n",
       " l_Brun’s_constant_for_prime_quadruplets,\n",
       " l_Cahen’s_constant,\n",
       " l_Carmichael_function,\n",
       " l_Carol_number,\n",
       " l_Champernowne’s_constant,\n",
       " l_Chebyshev_functions,\n",
       " l_Chen_prime,\n",
       " l_Chinese_hypothesis,\n",
       " l_Collatz_sequence,\n",
       " l_Compositorial,\n",
       " l_Conway’s_constant,\n",
       " l_Copeland_Erdős_constant,\n",
       " l_Cullen_number,\n",
       " l_Cullen_prime,\n",
       " l_Cunningham_chain,\n",
       " l_Dedekind_domain,\n",
       " l_Dedekind_zeta_function,\n",
       " l_Demlo_number,\n",
       " l_Diophantine_equation,\n",
       " l_Dirichlet_L_series,\n",
       " l_Dirichlet_character,\n",
       " l_Dirichlet_eta_function,\n",
       " l_Dirichlet_hyperbola_method,\n",
       " l_Eisenstein_integers,\n",
       " l_Eisenstein_prime,\n",
       " l_Erdős_Selfridge_classification_of_primes,\n",
       " l_Erdős_Woods_number,\n",
       " l_Euclid_Mullin_sequence,\n",
       " l_Euler_Gompertz_constant,\n",
       " l_Euler_numbers,\n",
       " l_Euler_phi_function,\n",
       " l_Euler_polynomial,\n",
       " l_Euler_product,\n",
       " l_Euler_pseudoprime,\n",
       " l_Euler’s_lucky_number,\n",
       " l_Farey_pair,\n",
       " l_Farey_sequence,\n",
       " l_Fermat_quotient,\n",
       " l_Fibonacci_fraction,\n",
       " l_Fibonacci_sequence,\n",
       " l_Fortunate_number,\n",
       " l_Fortunate_prime,\n",
       " l_Fourier_coefficients,\n",
       " l_Freiman_isomorphism,\n",
       " l_Friedman_number,\n",
       " l_Galois_representation,\n",
       " l_Gauss_sum,\n",
       " l_Gaussian_integer,\n",
       " l_Gaussian_prime,\n",
       " l_Gaussian_sum,\n",
       " l_Gelfond_Schneider_constant,\n",
       " l_Gelfond’s_constant,\n",
       " l_Giuga_number,\n",
       " l_Gregory_series,\n",
       " l_Harshad_number,\n",
       " l_Hecke_algebra,\n",
       " l_Hensel’s_lemma_for_integers,\n",
       " l_Hermite_numbers,\n",
       " l_Hermitian_dot_product_(finite_fields),\n",
       " l_Higgs_prime,\n",
       " l_Hilbert_symbol,\n",
       " l_Hurwitz_equation,\n",
       " l_Jacobi_symbol,\n",
       " l_Jacobsthal_sequence,\n",
       " l_Jordan’s_totient_function,\n",
       " l_Kaprekar_constant,\n",
       " l_Kaprekar_number,\n",
       " l_Keith_number,\n",
       " l_Kloosterman_sum,\n",
       " l_Knödel_number,\n",
       " l_Kronecker_symbol,\n",
       " l_Kronecker’s_Jugendtraum,\n",
       " l_Kynea_number,\n",
       " l_Legendre_symbol,\n",
       " l_Leyland_number,\n",
       " l_Liouville_number,\n",
       " l_Lucas_Carmichael_number,\n",
       " l_Lucas_chain,\n",
       " l_Lychrel_number,\n",
       " l_Mangoldt_function,\n",
       " l_Mangoldt_summatory_function,\n",
       " l_Markov_number,\n",
       " l_Mersenne_numbers,\n",
       " l_Mertens_function,\n",
       " l_Mian_Chowla_sequence,\n",
       " l_Mills’_constant,\n",
       " l_Möbius_function,\n",
       " l_Ore_number,\n",
       " l_Padovan_sequence,\n",
       " l_Pell_number,\n",
       " l_Perrin_pseudoprime,\n",
       " l_Perrin_sequence,\n",
       " l_Pierpont_prime,\n",
       " l_Pillai_prime,\n",
       " l_Poulet_number,\n",
       " l_Pratt_certificate,\n",
       " l_Proth_number,\n",
       " l_Proth_prime,\n",
       " l_Prouhet_Thue_Morse_constant,\n",
       " l_Prouhet_Thue_Morse_sequence,\n",
       " l_Pythagorean_n_tuple,\n",
       " l_Pythagorean_prime,\n",
       " l_Pythagorean_triplet,\n",
       " l_Ramanujan_prime,\n",
       " l_Ramanujan_sum,\n",
       " l_Ramanujan_tau_function,\n",
       " l_Rare_numbers,\n",
       " l_Riemann,\n",
       " l_Riemann_zeta_function,\n",
       " l_Ruth_Aaron_pair,\n",
       " l_Salem_number,\n",
       " l_Schnirelmann_density,\n",
       " l_Shantha_prime,\n",
       " l_Sierpinski_number,\n",
       " l_Skewes’_number,\n",
       " l_Smarandache_Wellin_number,\n",
       " l_Smarandache_Wellin_prime,\n",
       " l_Smarandache_function,\n",
       " l_Smith_number,\n",
       " l_Sophie_Germain_prime,\n",
       " l_Stern_Brocot_tree,\n",
       " l_Stern_prime,\n",
       " l_Størmer_number,\n",
       " l_Sylvester’s_sequence,\n",
       " l_Thabit_number,\n",
       " l_Ulam_spiral,\n",
       " l_Viswanath’s_constant,\n",
       " l_Wagstaff_prime,\n",
       " l_Wall_Sun_Sun_prime,\n",
       " l_Weierstrass_equation_of_an_elliptic_curve,\n",
       " l_Wieferich_prime,\n",
       " l_Wilson_prime,\n",
       " l_Wilson_quotient,\n",
       " l_Wilson’s_primeth_recurrence,\n",
       " l_Wirsing_condition,\n",
       " l_Woodall_number,\n",
       " l_Zeisel_number,\n",
       " l_Znám’s_problem,\n",
       " l_Zuckerman_number,\n",
       " l_a_formula_for_amicable_pairs,\n",
       " l_abelian_number_field,\n",
       " l_abundance,\n",
       " l_abundant_number,\n",
       " l_addition,\n",
       " l_addition_chain,\n",
       " l_additive_basis,\n",
       " l_additive_function,\n",
       " l_adjacent_fraction,\n",
       " l_adèle,\n",
       " l_algebraic_conjugates,\n",
       " l_algebraic_integer,\n",
       " l_algebraic_number,\n",
       " l_aliquot_sequence,\n",
       " l_almost_perfect_number,\n",
       " l_alternating_sum,\n",
       " l_amenable_number,\n",
       " l_amicable_numbers,\n",
       " l_antiharmonic_number,\n",
       " l_approximating_algebraic_numbers_with_linear_recurrences,\n",
       " l_arithmetic_derivative,\n",
       " l_arithmetic_function,\n",
       " l_asymptotic_basis,\n",
       " l_asymptotic_density,\n",
       " l_asymptotic_estimate,\n",
       " l_automorphic_number,\n",
       " l_balanced_prime,\n",
       " l_beprisque_number,\n",
       " l_binary_Golay_code,\n",
       " l_binomial_coefficient,\n",
       " l_binomial_equation,\n",
       " l_biquadratic_extension,\n",
       " l_biquadratic_field,\n",
       " l_bitwise_XOR,\n",
       " l_canonical_height_on_an_elliptic_curve,\n",
       " l_centered_hexagonal_number,\n",
       " l_character_of_a_finite_group,\n",
       " l_classical_groups,\n",
       " l_closed_form,\n",
       " l_colossally_abundant_number,\n",
       " l_complex_multiplication,\n",
       " l_composite_number,\n",
       " l_content_of_a_polynomial,\n",
       " l_content_of_polynomial,\n",
       " l_continued_fraction,\n",
       " l_convergence_of_Riemann_zeta_series,\n",
       " l_convolution_method,\n",
       " l_coprime,\n",
       " l_covering_system,\n",
       " l_critical_strip,\n",
       " l_cuban_prime,\n",
       " l_cube_root,\n",
       " l_cusp_form,\n",
       " l_cyclic_number,\n",
       " l_cyclotomic_extension,\n",
       " l_cyclotomic_field,\n",
       " l_cyclotomic_polynomial,\n",
       " l_cyclotomic_units,\n",
       " l_de_Polignac’s_formula,\n",
       " l_decimal_fraction,\n",
       " l_deficiency,\n",
       " l_deficient_number,\n",
       " l_determination_of_even_abundant_numbers_with_one_odd_prime_factor,\n",
       " l_diagonal_quadratic_form,\n",
       " l_digit_sum,\n",
       " l_digitaddition_generator,\n",
       " l_digital_number_system,\n",
       " l_digital_root,\n",
       " l_dihedral_prime,\n",
       " l_discrete_logarithm,\n",
       " l_discriminant,\n",
       " l_discriminant_in_algebraic_number_field,\n",
       " l_divisibility,\n",
       " l_divisibility_test,\n",
       " l_divisor_theory,\n",
       " l_double_Mersenne_number,\n",
       " l_doubly_even_number,\n",
       " l_duodecimal,\n",
       " l_elliptic_curve,\n",
       " l_emirp,\n",
       " l_equidigital_number,\n",
       " l_essential_component,\n",
       " l_even_lattice,\n",
       " l_even_number,\n",
       " l_eventually_coincide,\n",
       " l_exactly_divides,\n",
       " l_extraordinary_number,\n",
       " l_extravagant_number,\n",
       " l_factorial_base,\n",
       " l_factorial_base_representation_of_fractions,\n",
       " l_factorial_prime,\n",
       " l_factorion,\n",
       " l_field_of_algebraic_numbers,\n",
       " l_fixed_point_arithmetic,\n",
       " l_formal_congruence,\n",
       " l_fraction,\n",
       " l_fractional_part,\n",
       " l_frugal_number,\n",
       " l_full_reptend_prime,\n",
       " l_function_field,\n",
       " l_functional_equation_of_the_Riemann_zeta_function,\n",
       " l_fundamental_character_of_level,\n",
       " l_fundamental_units,\n",
       " l_generalized_Bernoulli_number,\n",
       " l_generalized_Riemann_hypothesis,\n",
       " l_generalized_Smarandache_palindrome,\n",
       " l_generalized_binomial_coefficients,\n",
       " l_generalized_zeta_function,\n",
       " l_googol,\n",
       " l_googolplex,\n",
       " l_greatest_common_divisor,\n",
       " l_grössencharacter,\n",
       " l_happy_number,\n",
       " l_harmonic_mean,\n",
       " l_hexadecimal,\n",
       " l_hexagonal_number,\n",
       " l_highly_abundant_number,\n",
       " l_highly_composite_number,\n",
       " l_hyperbolic_plane_in_quadratic_spaces,\n",
       " l_hyperperfect_number,\n",
       " l_ideal_class,\n",
       " l_ideal_norm,\n",
       " l_idèle,\n",
       " l_imaginary_quadratic_field,\n",
       " l_impractical_number,\n",
       " l_index_of_an_integer_with_respect_to_a_primitive_root,\n",
       " l_inner_product,\n",
       " l_integer,\n",
       " l_integer_factorization,\n",
       " l_integer_part,\n",
       " l_integral_basis,\n",
       " l_interprime,\n",
       " l_irrational,\n",
       " l_irrationality_measure,\n",
       " l_iterated_sum_of_divisors_function,\n",
       " l_iterated_totient_function,\n",
       " l_lattice_in,\n",
       " l_least_common_multiple,\n",
       " l_least_prime_factor,\n",
       " l_least_significant_digit,\n",
       " l_linear_congruence,\n",
       " l_linear_recurrence,\n",
       " l_look_and_say_sequence,\n",
       " l_lucky_number,\n",
       " l_lucky_prime,\n",
       " l_mantissa_function,\n",
       " l_mean,\n",
       " l_minimal_polynomial,\n",
       " l_minimal_prime,\n",
       " l_mixed_fraction,\n",
       " l_modular_form,\n",
       " l_modulus,\n",
       " l_morphic_number,\n",
       " l_most_significant_digit,\n",
       " l_multiplicative_congruence,\n",
       " l_multiplicative_digital_root,\n",
       " l_multiplicative_function,\n",
       " l_multiplicatively_independent,\n",
       " l_multiply_perfect_number,\n",
       " l_mutually_coprime,\n",
       " l_near_square_prime,\n",
       " l_noncototient,\n",
       " l_nontotient,\n",
       " l_normal_order,\n",
       " l_number_field,\n",
       " l_number_of_(nondistinct)_prime_factors_function,\n",
       " l_number_of_distinct_prime_factors_function,\n",
       " l_number_of_the_beast,\n",
       " l_numeration_system,\n",
       " l_oblong_number,\n",
       " l_odd_number,\n",
       " l_opposite_polynomial,\n",
       " l_orderly_number,\n",
       " l_palindrome,\n",
       " l_palindromic_number,\n",
       " l_palindromic_prime,\n",
       " l_pandigital_number,\n",
       " l_parasitic_number,\n",
       " l_part_of_a_partition,\n",
       " l_partial_fractions,\n",
       " l_perfect_number,\n",
       " l_perfect_power,\n",
       " l_perfect_totient_number,\n",
       " l_period,\n",
       " l_permutable_prime,\n",
       " l_polite_number,\n",
       " l_polydivisible_number,\n",
       " l_polygonal_number,\n",
       " l_polynomial_ring,\n",
       " l_positive_definite_form,\n",
       " l_power_basis_over,\n",
       " l_power_of_an_integer,\n",
       " l_power_of_two,\n",
       " l_practical_number,\n",
       " l_primality,\n",
       " l_primality_certificate,\n",
       " l_primality_testing,\n",
       " l_primary_pseudoperfect_number,\n",
       " l_prime,\n",
       " l_prime_constant,\n",
       " l_prime_counting_function,\n",
       " l_prime_difference_function,\n",
       " l_prime_gap,\n",
       " l_prime_magic_square,\n",
       " l_prime_pyramid,\n",
       " l_prime_quadruplet,\n",
       " l_prime_signature,\n",
       " l_primefree_sequence,\n",
       " l_primitive_root,\n",
       " l_primitive_semiperfect_number,\n",
       " l_primorial,\n",
       " l_primorial_prime,\n",
       " l_probable_prime,\n",
       " l_product_of_divisors_function,\n",
       " l_proper_divisor,\n",
       " l_pseudoprime,\n",
       " l_pseudorandom_numbers,\n",
       " l_pure_cubic_field,\n",
       " l_quadratic_form,\n",
       " l_quadratic_function_associated_with_a_linear_functional,\n",
       " l_quadratic_residue,\n",
       " l_quasiperfect_number,\n",
       " l_quaternion_algebra,\n",
       " l_ramification_index,\n",
       " l_random_Fibonacci_sequence,\n",
       " l_rational_points_on_one_dimensional_sphere,\n",
       " l_ray_class_field,\n",
       " l_ray_class_group,\n",
       " l_reduced_integral_binary_quadratic_forms,\n",
       " l_refactorable_number,\n",
       " l_regular_prime,\n",
       " l_regulator,\n",
       " l_regulator_of_an_elliptic_curve,\n",
       " l_repdigit,\n",
       " l_repunit,\n",
       " l_residue_systems,\n",
       " l_restricted_direct_product,\n",
       " l_root_discriminant,\n",
       " l_root_of_unity,\n",
       " l_rough_number,\n",
       " l_safe_prime,\n",
       " l_scientific_notation,\n",
       " l_self_descriptive_number,\n",
       " l_self_number,\n",
       " l_semi_inner_product,\n",
       " l_semiperfect_number,\n",
       " l_semiprime,\n",
       " l_short_Taylor_theorem,\n",
       " l_sieve_of_Eratosthenes,\n",
       " l_singly_even_number,\n",
       " l_smooth_number,\n",
       " l_sparsely_totient_number,\n",
       " l_sphenic_number,\n",
       " l_square,\n",
       " l_square_free_number,\n",
       " l_square_free_sequence,\n",
       " l_square_root,\n",
       " l_square_root_of_2,\n",
       " l_square_root_of_3,\n",
       " l_square_root_of_5,\n",
       " l_squarefull_number,\n",
       " l_strictly_non_palindromic_number,\n",
       " l_strobogrammatic_number,\n",
       " l_strobogrammatic_prime,\n",
       " l_strong_prime,\n",
       " l_sturdy_number,\n",
       " l_sum_free,\n",
       " l_sum_product_number,\n",
       " l_sumset,\n",
       " l_super_Poulet_number,\n",
       " l_superincreasing_sequence,\n",
       " l_superperfect_number,\n",
       " l_surd,\n",
       " l_symmetric_bilinear_form,\n",
       " l_table_of_factors_of_small_Mersenne_numbers,\n",
       " l_tacit_multiplication_operator,\n",
       " l_tetrahedral_number,\n",
       " l_the_Grössencharacter_associated_to_a_CM_elliptic_curve,\n",
       " l_totative,\n",
       " l_totient,\n",
       " l_totient_valence_function,\n",
       " l_transcendental_number,\n",
       " l_triangular_number_counting_function,\n",
       " l_triangular_numbers,\n",
       " l_trimorphic_number,\n",
       " l_unambiguity_of_factorial_base_representation,\n",
       " l_uniformly_distributed,\n",
       " l_uniqueness_of_Moebius_function,\n",
       " l_unit_fraction,\n",
       " l_unitary_divisor,\n",
       " l_unitary_perfect_number,\n",
       " l_unramified_action,\n",
       " l_untouchable_number,\n",
       " l_unusual_number,\n",
       " l_vampire_number,\n",
       " l_weak_prime,\n",
       " l_weird_number,\n",
       " l_wheel_factorization,\n",
       " l_zero]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Toy Example\n",
    "#dgraph = nx.DiGraph()                \n",
    "#dgraph.add_nodes_from([repr(i) for i in range(5)])\n",
    "#dgraph.add_edges_from([('0','1'),('1','2'),('1','3'),('3','4')])\n",
    "\n",
    "ranking = LpProblem('NodeRankingProblem', LpMinimize)\n",
    "l = LpVariable.dict('l', list(dgraph.nodes()), 0)\n",
    "# Add the objective first\n",
    "ranking += lpSum([l[w] - l[v] for v,w in dgraph.edges()])\n",
    "# the constraints\n",
    "for v,w in dgraph.edges():\n",
    "    ranking += l[w] - l[v] >= 1\n",
    "ranking.solve()\n",
    "ranking.variables()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 1, 2, 3, 4]"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(dgraph.nodes())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('integer', 236),\n",
       " ('prime', 223),\n",
       " ('square', 55),\n",
       " ('zero', 54),\n",
       " ('mean', 47),\n",
       " ('fraction', 38),\n",
       " ('addition', 23),\n",
       " ('number field', 21),\n",
       " ('Riemann', 18),\n",
       " ('perfect number', 18),\n",
       " ('least significant digit', 16),\n",
       " ('coprime', 16),\n",
       " ('irrational', 13),\n",
       " ('totient', 11),\n",
       " ('period', 11),\n",
       " ('algebraic number', 11),\n",
       " ('composite number', 10),\n",
       " ('even number', 8),\n",
       " ('prime counting function', 8),\n",
       " ('elliptic curve', 7),\n",
       " ('palindromic number', 7),\n",
       " ('algebraic integer', 7),\n",
       " ('odd number', 6),\n",
       " ('multiplicative function', 6),\n",
       " ('abundant number', 6),\n",
       " ('digital root', 6),\n",
       " ('Fibonacci sequence', 6),\n",
       " ('minimal polynomial', 6),\n",
       " ('continued fraction', 5),\n",
       " ('proper divisor', 5),\n",
       " ('primality', 5),\n",
       " ('divisibility', 5),\n",
       " ('greatest common divisor', 5),\n",
       " ('Bernoulli number', 4),\n",
       " ('palindrome', 4),\n",
       " ('number of distinct prime factors function', 4),\n",
       " ('semiprime', 4),\n",
       " ('repunit', 4),\n",
       " ('inner product', 4),\n",
       " ('Mersenne numbers', 4),\n",
       " ('Diophantine equation', 4),\n",
       " ('transcendental number', 4),\n",
       " ('cyclotomic extension', 3),\n",
       " ('Bernoulli polynomial', 3),\n",
       " ('quadratic form', 3),\n",
       " ('amicable numbers', 3),\n",
       " ('harmonic mean', 3),\n",
       " ('polynomial ring', 3),\n",
       " ('probable prime', 3),\n",
       " ('integer part', 3),\n",
       " ('sumset', 3),\n",
       " ('restricted direct product', 3),\n",
       " ('Proth number', 3),\n",
       " ('arithmetic function', 3),\n",
       " ('closed form', 3),\n",
       " ('asymptotic density', 3),\n",
       " ('oblong number', 2),\n",
       " ('Möbius function', 2),\n",
       " ('triangular numbers', 2),\n",
       " ('primorial', 2),\n",
       " ('most significant digit', 2),\n",
       " ('Legendre symbol', 2),\n",
       " ('lattice in', 1),\n",
       " ('algebraic conjugates', 1),\n",
       " ('Gregory series', 1),\n",
       " ('Mangoldt function', 1),\n",
       " ('iterated sum of divisors function', 1),\n",
       " ('Riemann zeta function', 1),\n",
       " ('cusp form', 1),\n",
       " ('Schnirelmann density', 1),\n",
       " ('least prime factor', 1),\n",
       " ('Prouhet-Thue-Morse sequence', 1),\n",
       " ('Sophie Germain prime', 1),\n",
       " ('Brun’s constant', 1),\n",
       " ('quadratic residue', 1),\n",
       " ('highly composite number', 1),\n",
       " ('plastic constant', 0),\n",
       " ('Padovan sequence', 0),\n",
       " ('multiplication operator', 0),\n",
       " ('Gaussian integer', 0),\n",
       " ('Apéry’s constant', 0),\n",
       " ('square root', 0),\n",
       " ('discriminant', 0),\n",
       " ('Fourier coefficients', 0),\n",
       " ('short Taylor theorem', 0),\n",
       " ('Dirichlet hyperbola method', 0),\n",
       " ('prime quadruplet', 0),\n",
       " ('lucky number', 0),\n",
       " ('deficient number', 0),\n",
       " ('random numbers', 0),\n",
       " ('root of unity', 0),\n",
       " ('multiplicative digital root', 0),\n",
       " ('digit sum', 0),\n",
       " ('Mian-Chowla sequence', 0),\n",
       " ('morphic number', 0),\n",
       " ('integer factorization', 0),\n",
       " ('additive basis', 0),\n",
       " ('bitwise NOT', 0),\n",
       " ('generalized Bernoulli number', 0),\n",
       " ('biquadratic extension', 0),\n",
       " ('complex multiplication', 0),\n",
       " ('convolution method', 0),\n",
       " ('sieve of Eratosthenes', 0),\n",
       " ('geometric mean', 0),\n",
       " ('symmetric bilinear form', 0),\n",
       " ('Wilson quotient', 0),\n",
       " ('tacit multiplication operator', -1),\n",
       " ('Gaussian prime', -1),\n",
       " ('surd', -1),\n",
       " ('irrationality measure', -1),\n",
       " ('sphenic number', -1),\n",
       " ('regulator', -1),\n",
       " ('modulus', -1),\n",
       " ('binomial coefficient', -1),\n",
       " ('super-Poulet number', -1),\n",
       " ('Lychrel number', -1),\n",
       " ('palindromic prime', -1),\n",
       " ('diagonal quadratic form', -1),\n",
       " ('Harshad number', -1),\n",
       " ('hyperperfect number', -1),\n",
       " ('adjacent fraction', -1),\n",
       " ('fractional part', -1),\n",
       " ('uniformly distributed', -1),\n",
       " ('Farey pair', -1),\n",
       " ('Sylvester’s sequence', -1),\n",
       " ('random Fibonacci sequence', -1),\n",
       " ('content of a polynomial', -1),\n",
       " ('hexagonal number', -1),\n",
       " ('primorial prime', -1),\n",
       " ('googolplex', -1),\n",
       " ('totient valence function', -1),\n",
       " ('primality certificate', -1),\n",
       " ('pseudoprime', -1),\n",
       " ('bitwise XOR', -1),\n",
       " ('Basel problem', -1),\n",
       " ('convergence of Riemann zeta series', -1),\n",
       " ('Collatz sequence', -1),\n",
       " ('sum-free', -1),\n",
       " ('Brocard’s problem', -1),\n",
       " ('imaginary quadratic field', -1),\n",
       " ('squarefull number', -1),\n",
       " ('cube root', -1),\n",
       " ('Friedman number', -1),\n",
       " ('self-descriptive number', -1),\n",
       " ('Cullen number', -1),\n",
       " ('quasiperfect number', -1),\n",
       " ('look and say sequence', -1),\n",
       " ('Gauss sum', -1),\n",
       " ('Prouhet-Thue-Morse constant', -1),\n",
       " ('quadratic function associated with a linear functional', -1),\n",
       " ('Erdős-Selfridge classification of primes', -1),\n",
       " ('Leyland number', -1),\n",
       " ('Compositorial', -1),\n",
       " ('Pierpont prime', -1),\n",
       " ('Jordan’s totient function', -1),\n",
       " ('Dirichlet character', -1),\n",
       " ('uniqueness of Moebius function', -1),\n",
       " ('Smarandache-Wellin prime', -1),\n",
       " ('function field', -1),\n",
       " ('Chinese hypothesis', -1),\n",
       " ('Kynea number', -1),\n",
       " ('a formula for amicable pairs', -1),\n",
       " ('Jacobi symbol', -1),\n",
       " ('Kaprekar constant', -1),\n",
       " ('classical groups', -1),\n",
       " ('Hermite numbers', -1),\n",
       " ('character of a finite group', -1),\n",
       " ('pure cubic field', -1),\n",
       " ('perfect power', -1),\n",
       " ('even lattice', -1),\n",
       " ('numeration system', -1),\n",
       " ('superincreasing sequence', -1),\n",
       " ('Gaussian sum', -1),\n",
       " ('refactorable number', -1),\n",
       " ('eventually coincide', -1),\n",
       " ('Beatty sequence', -1),\n",
       " ('exactly divides', -1),\n",
       " ('Freiman isomorphism', -1),\n",
       " ('positive definite form', -1),\n",
       " ('Hilbert symbol', -1),\n",
       " ('normal order', -1),\n",
       " ('Perrin sequence', -2),\n",
       " ('Euler numbers', -2),\n",
       " ('Euler polynomial', -2),\n",
       " ('square root of 2', -2),\n",
       " ('abelian number field', -2),\n",
       " ('canonical height on an elliptic curve', -2),\n",
       " ('quaternion algebra', -2),\n",
       " ('integral basis', -2),\n",
       " ('Pythagorean n-tuple', -2),\n",
       " ('Salem number', -2),\n",
       " ('polygonal number', -2),\n",
       " ('Bernoulli periodic function', -2),\n",
       " ('Brun’s constant for prime quadruplets', -2),\n",
       " ('lucky prime', -2),\n",
       " ('almost perfect number', -2),\n",
       " ('Mertens function', -2),\n",
       " ('unitary divisor', -2),\n",
       " ('approximating algebraic numbers with linear recurrences', -2),\n",
       " ('factorial base representation of fractions', -2),\n",
       " ('Euler product', -2),\n",
       " ('Wilson prime', -2),\n",
       " ('polite number', -2),\n",
       " ('content of polynomial', -2),\n",
       " ('Fortunate prime', -2),\n",
       " ('automorphic number', -2),\n",
       " ('opposite polynomial', -2),\n",
       " ('linear recurrence', -2),\n",
       " ('googol', -2),\n",
       " ('Perrin pseudoprime', -2),\n",
       " ('impractical number', -2),\n",
       " ('weird number', -2),\n",
       " ('generalized zeta function', -2),\n",
       " ('primitive root', -2),\n",
       " ('generalized Riemann hypothesis', -2),\n",
       " ('critical strip', -2),\n",
       " ('part of a partition', -2),\n",
       " ('asymptotic basis', -2),\n",
       " ('repdigit', -2),\n",
       " ('Smith number', -2),\n",
       " ('Hermitian dot product (finite fields)', -2),\n",
       " ('square-free sequence', -2),\n",
       " ('product of divisors function', -2),\n",
       " ('Eisenstein integers', -2),\n",
       " ('self number', -2),\n",
       " ('digitaddition generator', -2),\n",
       " ('dihedral prime', -2),\n",
       " ('Cullen prime', -2),\n",
       " ('essential component', -2),\n",
       " ('Conway’s constant', -2),\n",
       " ('cyclotomic polynomial', -2),\n",
       " ('Wilson’s primeth recurrence', -2),\n",
       " ('smooth number', -2),\n",
       " ('Kronecker’s Jugendtraum', -2),\n",
       " ('Weierstrass equation of an elliptic curve', -2),\n",
       " ('fundamental character of level', -2),\n",
       " ('Kaprekar number', -2),\n",
       " ('parasitic number', -2),\n",
       " ('polydivisible number', -2),\n",
       " ('happy number', -2),\n",
       " ('Keith number', -2),\n",
       " ('semi-inner product', -2),\n",
       " ('mutually coprime', -2),\n",
       " ('discrete logarithm', -2),\n",
       " ('equidigital number', -2),\n",
       " ('emirp', -2),\n",
       " ('Sierpinski number', -2),\n",
       " ('Wieferich prime', -2),\n",
       " ('Shantha prime', -2),\n",
       " ('weak prime', -2),\n",
       " ('orderly number', -2),\n",
       " ('Eisenstein prime', -2),\n",
       " ('frugal number', -2),\n",
       " ('extravagant number', -2),\n",
       " ('balanced prime', -2),\n",
       " ('Ulam spiral', -2),\n",
       " ('prime pyramid', -2),\n",
       " ('factorial prime', -2),\n",
       " ('Euler phi function', -2),\n",
       " ('Størmer number', -2),\n",
       " ('Kronecker symbol', -2),\n",
       " ('Chebyshev functions', -2),\n",
       " ('multiplicatively independent', -2),\n",
       " ('primefree sequence', -2),\n",
       " ('Pillai prime', -2),\n",
       " ('sturdy number', -2),\n",
       " ('binomial equation', -2),\n",
       " ('linear congruence', -2),\n",
       " ('Hurwitz equation', -2),\n",
       " ('Champernowne’s constant', -2),\n",
       " ('unambiguity of factorial base representation', -2),\n",
       " ('covering system', -2),\n",
       " ('binary Golay code', -2),\n",
       " ('Farey sequence', -3),\n",
       " ('Smarandache function', -3),\n",
       " ('Liouville number', -3),\n",
       " ('cyclotomic units', -3),\n",
       " ('adèle', -3),\n",
       " ('unramified action', -3),\n",
       " ('rational points on one dimensional sphere', -3),\n",
       " ('tetrahedral number', -3),\n",
       " ('Kloosterman sum', -3),\n",
       " ('Poulet number', -3),\n",
       " ('generalized Smarandache palindrome', -3),\n",
       " ('hyperbolic plane in quadratic spaces', -3),\n",
       " ('table of factors of small Mersenne numbers', -3),\n",
       " ('pseudorandom numbers', -3),\n",
       " ('sum-product number', -3),\n",
       " ('formal congruence', -3),\n",
       " ('practical number', -3),\n",
       " ('Znám’s problem', -3),\n",
       " ('strobogrammatic number', -3),\n",
       " ('strobogrammatic prime', -3),\n",
       " ('unit fraction', -3),\n",
       " ('Euler-Gompertz constant', -3),\n",
       " ('partial fractions', -3),\n",
       " ('Gelfond’s constant', -3),\n",
       " ('Fibonacci fraction', -3),\n",
       " ('Cahen’s constant', -3),\n",
       " ('digital number system', -3),\n",
       " ('Copeland-Erdős constant', -3),\n",
       " ('interprime', -3),\n",
       " ('Ramanujan prime', -3),\n",
       " ('Jacobsthal sequence', -3),\n",
       " ('Lucas chain', -3),\n",
       " ('Hecke algebra', -3),\n",
       " ('Zuckerman number', -3),\n",
       " ('hexadecimal', -3),\n",
       " ('totative', -3),\n",
       " ('Rare numbers', -3),\n",
       " ('primary pseudoperfect number', -3),\n",
       " ('rough number', -3),\n",
       " ('Skewes’ number', -3),\n",
       " ('Dirichlet eta function', -3),\n",
       " ('extraordinary number', -3),\n",
       " ('functional equation of the Riemann zeta function', -3),\n",
       " ('centered hexagonal number', -3),\n",
       " ('strictly non-palindromic number', -3),\n",
       " ('Wall-Sun-Sun prime', -3),\n",
       " ('Carol number', -3),\n",
       " ('Woodall number', -3),\n",
       " ('additive function', -3),\n",
       " ('permutable prime', -3),\n",
       " ('strong prime', -3),\n",
       " ('Markov number', -3),\n",
       " ('Cunningham chain', -3),\n",
       " ('cuban prime', -3),\n",
       " ('Lucas-Carmichael number', -3),\n",
       " ('scientific notation', -3),\n",
       " ('factorion', -3),\n",
       " ('Armstrong number', -3),\n",
       " ('highly abundant number', -3),\n",
       " ('colossally abundant number', -3),\n",
       " ('Stern prime', -3),\n",
       " ('aliquot sequence', -3),\n",
       " ('index of an integer with respect to a primitive root', -3),\n",
       " ('Thabit number', -3),\n",
       " ('prime difference function', -3),\n",
       " ('Knödel number', -3),\n",
       " ('Zeisel number', -3),\n",
       " ('Euclid-Mullin sequence', -3),\n",
       " ('minimal prime', -3),\n",
       " ('cyclic number', -3),\n",
       " ('power of an integer', -3),\n",
       " ('vampire number', -3),\n",
       " ('least common multiple', -3),\n",
       " ('full reptend prime', -3),\n",
       " ('multiply perfect number', -3),\n",
       " ('mantissa function', -3),\n",
       " ('Ramanujan sum', -3),\n",
       " ('Stern-Brocot tree', -4),\n",
       " ('square root of 5', -4),\n",
       " ('prime constant', -4),\n",
       " ('cyclotomic field', -4),\n",
       " ('ray class group', -4),\n",
       " ('regulator of an elliptic curve', -4),\n",
       " ('root-discriminant', -4),\n",
       " ('Dedekind domain', -4),\n",
       " ('idèle', -4),\n",
       " ('the Grössencharacter associated to a CM elliptic curve', -4),\n",
       " ('Artin map', -4),\n",
       " ('multiplicative congruence', -4),\n",
       " ('generalized binomial coefficients', -4),\n",
       " ('alternating sum', -4),\n",
       " ('Hensel’s lemma for integers', -4),\n",
       " ('Bernoulli polynomials and numbers', -4),\n",
       " ('Euler’s lucky number', -4),\n",
       " ('abundance', -4),\n",
       " ('Ruth-Aaron pair', -4),\n",
       " ('regular prime', -4),\n",
       " ('iterated totient function', -4),\n",
       " ('untouchable number', -4),\n",
       " ('fixed-point arithmetic', -4),\n",
       " ('mixed fraction', -4),\n",
       " ('addition chain', -4),\n",
       " ('duodecimal', -4),\n",
       " ('Fortunate number', -4),\n",
       " ('trimorphic number', -4),\n",
       " ('pandigital number', -4),\n",
       " ('beprisque number', -4),\n",
       " ('noncototient', -4),\n",
       " ('perfect totient number', -4),\n",
       " ('sparsely totient number', -4),\n",
       " ('Higgs prime', -4),\n",
       " ('primitive semiperfect number', -4),\n",
       " ('square-free number', -4),\n",
       " ('Mills’ constant', -4),\n",
       " ('Giuga number', -4),\n",
       " ('Pythagorean prime', -4),\n",
       " ('arithmetic derivative', -4),\n",
       " ('prime magic square', -4),\n",
       " ('Chen prime', -4),\n",
       " ('prime gap', -4),\n",
       " ('Euler pseudoprime', -4),\n",
       " ('divisor theory', -4),\n",
       " ('Smarandache-Wellin number', -4),\n",
       " ('determination of even abundant numbers with one odd prime factor', -4),\n",
       " ('amenable number', -4),\n",
       " ('double Mersenne number', -4),\n",
       " ('doubly even number', -4),\n",
       " ('square root of 3', -5),\n",
       " ('Erdős-Woods number', -5),\n",
       " ('fundamental units', -5),\n",
       " ('ideal class', -5),\n",
       " ('power basis over', -5),\n",
       " ('asymptotic estimate', -5),\n",
       " ('reduced integral binary quadratic forms', -5),\n",
       " ('power of two', -5),\n",
       " ('deficiency', -5),\n",
       " ('superperfect number', -5),\n",
       " ('Ore number', -5),\n",
       " ('unusual number', -5),\n",
       " ('triangular number counting function', -5),\n",
       " ('Viswanath’s constant', -5),\n",
       " ('modular form', -5),\n",
       " ('Fermat quotient', -5),\n",
       " ('residue systems', -5),\n",
       " ('Proth prime', -5),\n",
       " ('Pratt certificate', -5),\n",
       " ('safe prime', -5),\n",
       " ('Wirsing condition', -5),\n",
       " ('Demlo number', -5),\n",
       " ('number of (nondistinct) prime factors function', -5),\n",
       " ('near-square prime', -5),\n",
       " ('field of algebraic numbers', -5),\n",
       " ('Ramanujan tau function', -5),\n",
       " ('Pythagorean triplet', -6),\n",
       " ('ray class field', -6),\n",
       " ('Galois representation', -6),\n",
       " ('Dedekind zeta function', -6),\n",
       " ('discriminant in algebraic number field', -6),\n",
       " ('Mangoldt summatory function', -6),\n",
       " ('semiperfect number', -6),\n",
       " ('factorial base', -6),\n",
       " ('Achilles number', -6),\n",
       " ('antiharmonic number', -6),\n",
       " ('Gelfond-Schneider constant', -6),\n",
       " ('decimal fraction', -6),\n",
       " ('number of the beast', -6),\n",
       " ('Wagstaff prime', -6),\n",
       " ('unitary perfect number', -6),\n",
       " ('nontotient', -6),\n",
       " ('de Polignac’s formula', -6),\n",
       " ('wheel factorization', -6),\n",
       " ('Blum number', -7),\n",
       " ('biquadratic field', -7),\n",
       " ('grössencharacter', -7),\n",
       " ('Pell number', -7),\n",
       " ('singly even number', -7),\n",
       " ('divisibility test', -7),\n",
       " ('ideal norm', -8),\n",
       " ('Dirichlet L-series', -8),\n",
       " ('Carmichael function', -8),\n",
       " ('ramification index', -9),\n",
       " ('primality testing', -9),\n",
       " ('prime signature', -11)]"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Least specific term (terms with the most out_degree - in_degree)\n",
    "node_lst = []\n",
    "for node in dgraph.nodes():\n",
    "    deg = dgraph.out_degree(node) - dgraph.in_degree(node)\n",
    "    node_lst.append((node, deg))\n",
    "sorted(node_lst, key=lambda d: -d[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Blum number\n",
      "surd\n",
      "Smarandache function\n",
      "square root of 5\n",
      "irrationality measure\n",
      "square root of 3\n",
      "Liouville number\n",
      "cyclotomic units\n",
      "ray class field\n",
      "Erdős-Woods number\n",
      "prime signature\n",
      "ray class group\n",
      "regulator of an elliptic curve\n",
      "fundamental units\n",
      "abelian number field\n",
      "grössencharacter\n",
      "canonical height on an elliptic curve\n",
      "unramified action\n",
      "root-discriminant\n",
      "idèle\n",
      "ideal norm\n",
      "ideal class\n",
      "the Grössencharacter associated to a CM elliptic curve\n",
      "discriminant in algebraic number field\n",
      "quaternion algebra\n",
      "power basis over\n",
      "multiplicative congruence\n",
      "Pythagorean n-tuple\n",
      "rational points on one dimensional sphere\n",
      "tetrahedral number\n",
      "generalized binomial coefficients\n",
      "Salem number\n",
      "Kloosterman sum\n",
      "super-Poulet number\n",
      "Hensel’s lemma for integers\n",
      "asymptotic estimate\n",
      "Bernoulli polynomials and numbers\n",
      "Bernoulli periodic function\n",
      "lucky prime\n",
      "Euler’s lucky number\n",
      "Mangoldt summatory function\n",
      "Lychrel number\n",
      "generalized Smarandache palindrome\n",
      "hyperbolic plane in quadratic spaces\n",
      "diagonal quadratic form\n",
      "reduced integral binary quadratic forms\n",
      "deficiency\n",
      "Ruth-Aaron pair\n",
      "Mertens function\n",
      "table of factors of small Mersenne numbers\n",
      "sum-product number\n",
      "superperfect number\n",
      "regular prime\n",
      "formal congruence\n",
      "untouchable number\n",
      "Ore number\n",
      "antiharmonic number\n",
      "approximating algebraic numbers with linear recurrences\n",
      "unusual number\n",
      "Gelfond-Schneider constant\n",
      "strobogrammatic prime\n",
      "triangular number counting function\n",
      "Euler-Gompertz constant\n",
      "fixed-point arithmetic\n",
      "partial fractions\n",
      "Gelfond’s constant\n",
      "Fibonacci fraction\n",
      "decimal fraction\n",
      "digital number system\n",
      "Farey pair\n",
      "singly even number\n",
      "mixed fraction\n",
      "Copeland-Erdős constant\n",
      "Dirichlet L-series\n",
      "interprime\n",
      "Ramanujan prime\n",
      "Jacobsthal sequence\n",
      "Fermat quotient\n",
      "content of polynomial\n",
      "Hecke algebra\n",
      "Zuckerman number\n",
      "duodecimal\n",
      "Fortunate prime\n",
      "trimorphic number\n",
      "opposite polynomial\n",
      "linear recurrence\n",
      "number of the beast\n",
      "Rare numbers\n",
      "beprisque number\n",
      "Wagstaff prime\n",
      "unitary perfect number\n",
      "noncototient\n",
      "Carmichael function\n",
      "perfect totient number\n",
      "nontotient\n",
      "sparsely totient number\n",
      "residue systems\n",
      "Higgs prime\n",
      "primality testing\n",
      "Proth prime\n",
      "Pratt certificate\n",
      "impractical number\n",
      "primitive semiperfect number\n",
      "Basel problem\n",
      "Wirsing condition\n",
      "Skewes’ number\n",
      "convergence of Riemann zeta series\n",
      "Dirichlet eta function\n",
      "square-free number\n",
      "Mills’ constant\n",
      "extraordinary number\n",
      "functional equation of the Riemann zeta function\n",
      "generalized zeta function\n",
      "part of a partition\n",
      "de Polignac’s formula\n",
      "asymptotic basis\n",
      "sum-free\n",
      "Demlo number\n",
      "strictly non-palindromic number\n",
      "Giuga number\n",
      "Hermitian dot product (finite fields)\n",
      "Pythagorean prime\n",
      "Brocard’s problem\n",
      "number of (nondistinct) prime factors function\n",
      "arithmetic derivative\n",
      "prime magic square\n",
      "square-free sequence\n",
      "product of divisors function\n",
      "Wall-Sun-Sun prime\n",
      "Eisenstein integers\n",
      "near-square prime\n",
      "cube root\n",
      "Carol number\n",
      "field of algebraic numbers\n",
      "Woodall number\n",
      "Cullen prime\n",
      "essential component\n",
      "Ramanujan tau function\n",
      "Conway’s constant\n",
      "Prouhet-Thue-Morse constant\n",
      "wheel factorization\n",
      "prime gap\n",
      "Wilson’s primeth recurrence\n",
      "strong prime\n",
      "Kronecker’s Jugendtraum\n",
      "Weierstrass equation of an elliptic curve\n",
      "cuban prime\n",
      "Euler pseudoprime\n",
      "Lucas-Carmichael number\n",
      "fundamental character of level\n",
      "divisor theory\n",
      "scientific notation\n",
      "Kaprekar number\n",
      "factorion\n",
      "Smarandache-Wellin number\n",
      "parasitic number\n",
      "polydivisible number\n",
      "happy number\n",
      "Armstrong number\n",
      "Keith number\n",
      "semi-inner product\n",
      "quadratic function associated with a linear functional\n",
      "highly abundant number\n",
      "colossally abundant number\n",
      "determination of even abundant numbers with one odd prime factor\n",
      "Stern prime\n",
      "aliquot sequence\n",
      "mutually coprime\n",
      "index of an integer with respect to a primitive root\n",
      "discrete logarithm\n",
      "Thabit number\n",
      "equidigital number\n",
      "emirp\n",
      "prime difference function\n",
      "Erdős-Selfridge classification of primes\n",
      "Sierpinski number\n",
      "Wieferich prime\n",
      "Leyland number\n",
      "Shantha prime\n",
      "weak prime\n",
      "amenable number\n",
      "orderly number\n",
      "Compositorial\n",
      "Eisenstein prime\n",
      "Knödel number\n",
      "frugal number\n",
      "Pierpont prime\n",
      "Zeisel number\n",
      "double Mersenne number\n",
      "doubly even number\n",
      "extravagant number\n",
      "Jordan’s totient function\n",
      "balanced prime\n",
      "Ulam spiral\n",
      "Euclid-Mullin sequence\n",
      "minimal prime\n",
      "prime pyramid\n",
      "power of an integer\n",
      "uniqueness of Moebius function\n",
      "Smarandache-Wellin prime\n",
      "factorial prime\n",
      "Størmer number\n",
      "Kynea number\n",
      "vampire number\n",
      "Chebyshev functions\n",
      "multiplicatively independent\n",
      "primefree sequence\n",
      "multiply perfect number\n",
      "Pillai prime\n",
      "Kaprekar constant\n",
      "sturdy number\n",
      "binomial equation\n",
      "mantissa function\n",
      "Ramanujan sum\n",
      "classical groups\n",
      "Hermite numbers\n",
      "character of a finite group\n",
      "pure cubic field\n",
      "even lattice\n",
      "Hurwitz equation\n",
      "numeration system\n",
      "superincreasing sequence\n",
      "Gaussian sum\n",
      "Champernowne’s constant\n",
      "unambiguity of factorial base representation\n",
      "refactorable number\n",
      "eventually coincide\n",
      "Beatty sequence\n",
      "exactly divides\n",
      "covering system\n",
      "Freiman isomorphism\n",
      "positive definite form\n",
      "binary Golay code\n",
      "Hilbert symbol\n",
      "normal order\n"
     ]
    }
   ],
   "source": [
    "#Most specific terms (terms with no descendents)\n",
    "for node in dgraph.nodes():\n",
    "    if nx.descendants(dgraph, node) == set():\n",
    "        print(node)\n",
    "        #print(node.split()[0].lower())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "lattice in\n",
      "Bernoulli polynomial\n",
      "Mangoldt function\n",
      "palindrome\n",
      "iterated sum of divisors function\n",
      "sumset\n",
      "Prouhet-Thue-Morse sequence\n",
      "restricted direct product\n",
      "divisibility\n",
      "inner product\n",
      "minimal polynomial\n",
      "closed form\n",
      "asymptotic density\n",
      "Term0\n"
     ]
    }
   ],
   "source": [
    "#dgraph.add_node('Term0')\n",
    "for node in dgraph.nodes():\n",
    "    if dgraph.in_degree(node) == 0:\n",
    "        print(node)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'Salem number',\n",
       " 'algebraic conjugates',\n",
       " 'biquadratic field',\n",
       " 'cyclotomic field',\n",
       " 'cyclotomic polynomial',\n",
       " 'discriminant in algebraic number field',\n",
       " 'field of algebraic numbers',\n",
       " 'power basis over',\n",
       " 'pure cubic field',\n",
       " 'regular prime'}"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.descendants(dgraph, 'minimal polynomial')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.006187285040598518"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.clustering(dgraph, 'integer')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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TprFgwQISEhIKXlxMMWmne/fuXe7du0fDhg3zXWesvK6Kbm+5kvpnKE0rOGAjtcBWqv6y2kglKGVZtKpclvVDGhvd4QJ5Ugsq/Pz8zJGugTlx4gQffvghDRo0wNbWlosXL+amFYoLCoWCf/75h2bNmhVpnwoVKtC3b1/CwsIEssz0MGmnu2PHDtq3b19gzaEx87oAS5cupXn18vz6RRuOfvU2o9v5wo0TNHnTgW51vBjTrhqtnu6hyoP9JlHzqsrntm7dOs9z/v7+5kjXAMjlcrZs2UKLFi3o1asXzZo148aNG8yaNQsvLy9jm6c3V65cwdnZWeu9F30IDg7ml19+eX3vLShNmPfff1/5yy+/FLiuT58+Oq0Tg4yMDKWXl5fy1KlTao97eXkp79y5k/v9uXPnlF5eXsqsrCxDm5iHmJgYZfny5ZUKhSLPc/fu3VO6uroawaqSQVpamnLBggXKqlWrKhs2bKhcv369Mjs729hmFZlFixYp+/fvL9h+QUFBykGDBgm2nylhsiVjWVlZHDhwgCVLlhS41piR7i+//ELNmjWpV6+e2uPZ2dlqzRy1a9emUqVKbNmyhZ49exraTDVUUa6mPKGHhweZmZkkJSWZ5B1yQyH0rLv4+HgiIiJYvHgxTZs2ZcWKFTRr1qxY5Gp1ITIyUuMnp8Iybtw4fH19GT9+PNWqVSv4gGKEyTrdyMhI/Pz8cHV1LXCtp6cnd+7cMYBV6shkMmbNmsXKlSs1Pmdlpd7iGxgYyPz5803C6b79dl6NX8hpy1TldYuanyuO5D/r7iFz9sboNevu8uXL/PDDD2zevJnevXsTGRmJr6+vaPYbi8jISCZPnizYfmXLlmXMmDFMmzaN3377TbB9TQGTzelu376dTp066bTWWJHuhg0b8PDwoEWLFnmek8lkedqW33//fa5fv8758+cNZWIelPnkc1WU1LzumuM36b30OHuuxJMpU+RRkcv477Hdl+PpvfQ4a47f1LiPUqlk//79vPPOO7z99ttUqFCBmJgYFixY8Fo63Lt375Kamir4zzZy5EgOHTrEuXPnBN3X2Ji0082vVOxljFG9oFAoCAsLIzg4WOPzmpyulZUVn3/+OfPnzzeEiRq5du0aFhYW+ar6l8QKhhez7goYH476rLuXHW92djZr164lICCAESNG0K1bN27evMmUKVNwcXER9wcwIv/880+BouWFwd7enqCgIK1/Y8UVk3S6N2/eJDExMU+eVBvGiHS3bduGlZWVWhvty7ya01UxZMgQNm3axOPHj8U2USOqUrH8/kBKWqSradadLqhm3R2Nvsv3339PpUqVWL58OaGhoURFRfHZZ59ha2srktWmgxD1udoYMmQIly5dIjIyUpT9jYFJ5nR37NhBp06ddO7/f7krzRA3JpRKJaGhoQQFBWk9n6acLoCbmxtdunRh+fLljB8/XmxT81BQagFKXqSradZd0o55ZN69gizlERJLK6w9fSnbZiDWrhXU1j3Pyqbn9GW0kcbx559/EhAQYEjTTYLIyEj69esnyt42NjZMnz6doKAgDh069FrceDTJSFeffC7kaAZYWFjw7JlhpjDs37+flJQUunfvrvF5hSInYtJ20QgMDGTBggUGV8tXKpW5nWj5UalSJe7du0dGRoZhDDMi2mbdpZ7fjcSmFPbVWyKxKUXG9dMk/D4VpSxLfaHEAvsqDflx0fIS6XCTk5OJi4ujbt26op2jX79+PHr0iN27d4t2DkNick43IyODQ4cO0b59e72OU0W7hiAsLIyJEydqdaqa8rkv06BBA9zc3Ni2bZtYJmrk+vXrKBQKKleunO86KysrKlWqREyM5tlurxPaZt259/sej0/Cce40knIf5XRHyZ8lkZWYt2DfQiIx6Kw7U+L48ePUr19fVPHxl4dYKo00+VtITM7pHjp0iFq1avHGG2/odZynp6dB8rrHjx/n2rVr9OnTR+sabfnclwkMDCQiIkJo8/Ilv/rcVykpwjfaZt3Zevvn/l+p+G80k8QCS4e8v5eGnnVnSoiZz30Z1afKzZs3i34usTE5p1uQwI02DBXphoWFMWHCBI35WhXa8rkv07NnTy5evGjQG1a6pBZUlBThG22z7lQosp6T9PccAJwavo9Ug9PN2cews+5MBUM53ZeHWMpk+b9npo7JOV1987kqDBHpXrhwgZMnTzJgwIB81xWUXoCcGwRDhgwxWLSrS33uy5SUSFfTrDsV8vRk4tcFkXkvGofaHSjTWvv7boxZd8YmKyuLU6dOaZxdKAYdOnTAzc2NNWvWGOR8YmFSTjc2NpbU1NRCqSsZItL95ptvGDNmDHZ2dvmu08XpAgwdOpRff/2V5ORkoUzUyo0bN5DJZFSpoptwekmJdHNm3eX9M5AlJ/BwzQSyHsTi1LgHzp0CtaZljDnrzpicPXuWKlWq4OTkZJDzSSQSQkNDmT59OpmZmQY5pxiYlNNVlYoVpixE7Eg3NjaWvXv38vnnnxe4VpecLoCXlxft27dn1apVQpiYL/rkcwGqVauWO7rndUbTrDuAh7+MQ/b4HpZOrihlWTzeu4THe5eQef9qnrXGnnVnKBJTM1l06Bqj1p9l4KqTTNlxjXJt+pGUajgH2Lx5c2rUqMHSpUsNdk6hMak63R07dvDZZ58V6lixI93vvvuOYcOG4ehYcESjS05XRWBgIAMHDmTEiBGiziXTJ58LOWV4zs7O3Lp1i4oVK4pml7HRNOsOQJ6a07wiT3nEs1N/5T5u7VYJG88XAiymMOtObLTrUZRGautE02/366VHUVRCQkLo3LkzAwYMwN7eXvTzCY3JON309HQiIyMLLW4hZqR7584dNm3aRGxsrE7rdU0vADRr1gx7e3t2795Nx44di2KmVlT53KCgIL2OUzVJvM5OF3Jm3R2JTeR59ou66QoTdSvnM/asO7HJaY+OJkOmuT1appQg+0+P4nBMIsGd/UQX6a9bty4tW7Zk/vz5TJw4UdRziYHJpBcOHDhAvXr1KF0676hyXRAz0g0PD2fgwIE6Sx3q43QlEkmu+phY3Lx5k6ysLL0FSUpKO3BhZ91ZKuUEdTLurDsxEUKPQixmzpxJeHg4T548Ef1cQmMyTlcfgRtNqD72C92VlpCQwOrVqxk7dqzOx+ia01Xx0Ucf8e+//xIXF1cYEwtE2zy0gihJ7cCqWXd2VpYU9DJJJDk3z6wvbyNqy8LXomD/VfLTo0i/epQHP4/m9uzu3J7zIQ/XTECekQq80KO4cFfcib7VqlWja9euzJ49W9TziIFJOF2lUllkpyuRSESJdn/88Ud69eqFh4eHzsfok9MFsLOzY+DAgSxYsKAwJhaItnloBVFSIl0V/Rr7sH5IYzpUd9c4685WaoGN1IIO1d35fWgTIld+w65du16bTqmX0aRHAZB2+RCP/ggj69FN7Ko2wr5acxSZ6SizX7SMZ8jkLDgoTgDxMlOnTmXRokXEx8eLfi4hMYmc7tWrV5HJZNSoUaNI+6jyukIpzScnJ7N48WJOnjyp13H6pBdUDBs2jICAAGbOnImDg4NexxbEwYMHC5X7KkmRropa3mVY1K8+SamZbDxzl+gHz1i7YTN9e3bHz8ORHgHqkyP27t1L27ZtsbCwICQk5LUQZNGmR6FUKnly8GcA3D+cgW2FWhqPVyrhwNVHJKVminqD8c033+Tjjz8mLCyMH3/8UbTzCI1JRLqqKLeov7BCR7o//fQTnTt31vtGUmGcboUKFWjZsqXghd83b94kIyOjUBeicuXKkZ2dTWJioqA2FQecHWwY2rIyc3rV4dGmr5nTqw5DW1bO40RcXFzYt28fW7duZerUqa9FxKtNj0L25D7ylEdIpDYkn9jE7fAe3Fs0mGen8950lIBB9CgmTZrEmjVruHXrlujnEgqTcrpFRcgKhvT0dH788cdCRYj65nRVjBgxgoiICEH/cAubzwX10T1mtKNyvFu2bGH69OnGNqfIaNOjkKenAKCUZSJ7Gk8pv+bIU5N4vGcR6THH1NYaSo/C3d2dL774gpkzZ4p+LqEwutNNTU3lxIkTtG3btsh7CRnpLlu2jGbNmlG9enW9j9U3p6vi7bffzi3vEorC5nNVlLS8bmFxdXVl3759bNy4kRkzZhjbnCKhTY/CstSLzjOXLmNweWcU9rXaAZAee0LDPobRoxg3bhx//fVXsQkOjO509+3bR6NGjQTJYwoV6WZlZfH999/rXdeqojDpBciJLEeMGCFo+Zg+eguaMEe6uuPm5sb+/ftZv359sYq8XkWbHoW0tBsSm1LqD/73qczCOm9rvKH0KMqUKcO4ceOYOnWqQc5XVIzudIVKLYBwke4vv/xC9erVqV+/fqGOL6zTBfj44485dOiQIDmqW7dukZ6ejp+fX6H3KCnCN0Lh7u7O/v37WbduHSEhIcY2p1Bo06OQWFrhVL8rAInbfiDx77mkXdybI+Reo7XaWkPrUYwYMYLIyEjOnDljsHMWFqM6XSFKxV5GiEhXNVa9KMPwCpvTBXBwcODjjz9m4cKFhT6/ikOHDhU4D60gSorwjZCUK1eO/fv3s2bNGsLCwoxtjt5o06MAKN2sN06Ne6DMSCM9+ghWLhVw6zFFrTUaDK9HYW9vT3BwsKBj4MXCqE730qVLWFlZCVbiJUSku3HjRtzd3TWOVdeVwuZ0VQwfPpzly5fz/PnzQu8BRU8tQM7ongcPHhTZlpKGh4cHBw4cYPXq1cyaNcvY5uiFSo9C07VaYmFJ2db98Q78hTfHbsKj/xzsKjdQX2MkPYrBgwdz5coVjhw5YtDz6otRna5KO1eo2kYnJycUCkWhu9KUSiVhYWH5DpzUhaKkFwCqVq1KgwYNCq1DoUJfkRtNSKXSEjO6R2g8PDzYv38/K1eu5LvvvjO2OXoxvHUVbKWWhTrWWHoU1tbWuUMsTbl0z+hOV6jUArzoSitsimHbtm1YWloWSkT9ZYrqdIFcPYbC/vLcvn2bZ8+e4e/vX/DiAjDndQuPp6cn+/fvZ+nSpXz//ffGNkdnCqtHYWdlQXBn4+lR9OvXj6SkJHbt2mWU8+uC0ZxucnIyp0+fpk2bNoLuW9i8ri5j1XWlKDldFR06dODZs2ccPXq0UMcLkc9VYc7rFg0vLy8OHDjA4sWLCQ8PN7Y5OqPSo7BEDsr8dZUlErCzsiS4s7/oKmP5YWlpSUhICEFBQSarBW00p7t3716aN29OqVKlCl6sB4XN6x44cICnT59qHauuD0JEuhYWFgwfPrzQ5WNCpBZUmMvGio63tzcHDhxg4cKFzJkzx9jm6Mz/fGxJ2TyTlpXLFKhHsX5IY6M6XBXdunXDwsKCTZs2GdsUjRhNe0Ho1IKKwka6qrHqlpaFy2O9TFFvpKkYMGAAM2bM4P79+3h6eup17MGDBxk1alSRbYCc9EJx+mhsqpQvX579+/fTpk0bLCws+PLLL9WeT0zNZOPpu0Q/TCElQ4aTrRS/ck70rOdtNJH00NBQPn6nJT8MbqGzHoWxkUgkhIWFMXLkSLp161bkAEhoJEojZJyVSiWenp4cOXJE55lduvLdd9+RkJCgl+TbiRMn+PDDD4mLixPEWUZERBAdHS3I0Mlhw4bh6uqqV5fTnTt3CAgIID4+XpBpFKmpqbi5ufHs2TNBLkrFDYlEIuiNmVu3btGmTRtGjx5NYGBgPpMZciJJJRh0MoOKmzdvUq9ePaKjo3F1dVV7TujXRGiUSiVt2rTh008/LXCQrKExyiXg3LlzODo6Cu5wISfSPX/+vF7H6DJWXR+EyOmqGDFiBG3btiU4OBhra2udjlHlc4Ua/+Pg4ICLiwu3bt2iUqVKguxZkqlQoQIHDhygdevWXEh3IjLNXetkhoz/HLAhJzOomDFjBsOHD8/jcIsDqmj3o48+ok+fPtjYmE4kbpSc7o4dO0RJLYD+Od2LFy/y77//MnDgQMFsECKnq6J69epUr16dDRs26HyMkPlcFea8rrBUqFCBLyM2sSfR0SQnM1y+fJm///5bL/F+U6Np06bUqlWLJUuWGNsUNYzidMXK54L+Od1Zs2YxatSoAseq64NQOV0VgYGBeqUqiipyowmz8I2wnL/zlMUnEkCaE4Fl3LrArT4UsIgAACAASURBVFnvavxKvbA39zhDTWaYOnUq48ePL/T4LFMhJCSEsLAwUlNTjW1KLgZ3uo8fP+bChQu0bNlSlP31iXTj4uLYvXs3X3zxhaA2CBnpAnTp0oUHDx5w6tSpAtfeu3ePJ0+eFFkQ/lXMka6wvDqZwdLJBcf67+V+OdRqn/uctKz61BKxJzOcOnWKY8eOMXz4cNHOYShq165N69atmTdvnrFNycXgTnf37t20atUKW1tbUfYvXbo0MplMpyvbd999xxdffIGTk1OBa/VByJwu5NQeDhs2TKfyMaHzuSrMka5waJrMYFXWkzf+NyT3y8otRzjf2r0ytuXVL6AvT2YQg8mTJzN58mTByzmNxYwZM5gzZ47JDLE0uNMVM58Lunel3b17l40bN+Yp2xECoSNdgEGDBvHXX3+RkJCQ7zoxUgtgjnSFRNtkBhVKpZJnp7cC4Nigq8Y1Yk1mOHToEDExMQwaNEjwvY2Fr68v77//vsmUPRrU6SoUCnbs2FHkNtuC0CWvGx4ezoABA3Qeq64PQud0AZydnenevTvLli3Ld50QIjeacHd3Ry6Xl8jRPUKjbTKDiudx/yJ7ch9L+7LY+2sWXhJjMoNSqSQ4OJgZM2boXClTXJg6dSqLFy/m4cOHxjbFsE739OnTuLi44OPjI+p5CsrrPnr0iFWrVol2Z1aMSBdybqgtXLgQmUyzsv/9+/dJSkqiZs2agp9bNbrHnGIoOtomM6h4dupPABwCOiOx1H7xFnoyw/bt23n69Cl9+vQRdF9ToHz58nz66acmIbVpUKcrZtXCyxQU6f744498+OGHend56YrQOV0VderUwcfHhy1btmh8/tChQ7Rs2VLwfK4Ks/CNMGibzACQlXCTjFsXkEitcayb/9+KkJMZFAoFwcHBhISEvLYNMJMmTWLt2rXcvHnTqHYY1OmKnc9VkV+km5yczKJFi5gwYYJo5xcr0gXyHecjVmpBhTnSFQZtkxkAUv6Lcu2rt8aylPZyLaEnM2zYsAFra2u6dtWcQ34dcHV1Zfjw4UafYWcwp/vo0SOio6Np3ry56OfKL9JdsGABnTp1ErWzSoycroru3bsTFxfH4X/PsujQNUatP8vAVScZtf4se+9JqNu48OLrBWGOdIVB22QGeXoy6ZcPAeDY4L1893iekcHdwxt5/Phxke2RyWRMmTKFsLAwwbStTZWxY8fy999/GzV4MFgb8K5du2jTpo1BEvTaIl3VWPV9+/aJen4xI93LD9Oo0v9b+m++g5WVldoNGaV/ewZvi6d17ClR+vTNka4wqCYz7LkSr1Y2ZlmqNG+O21zg8RIJNPEpzZ2TV6hcuTJ9+/Zl9OjRVK5cuVD2rFq1Cm9vb0Emcps6pUuXzh1iqU+Xp5AYLNI1VD4X0Foytnz5cpo0aSJ448CriJXTXXP8Jr2XHue2oiwKiWWeO+ASqQ2ZMgW7L8fTe+lxwdtFK1asyMOHD0lPTxd035JIUSczTOoawM8//8ylS5dwcnKiUaNGfPDBB3rrL2dkZDBjxowSEeWqGDFiBEePHuX06dNGOb9BnK5cLmf37t2il4qp8PT0zBPpFnWsuj6IEemuOX6T0O1Xcvr0C1grVp++VCqlcuXK5tE9AiDUZAZPT0/CwsK4efMmrVu3pl+/fjRt2pRNmzYhl8sL2A0WL15M3bp1ady4caF+juJIqVKlchtAjIFBnO6///6Ll5cX3t7iTwdNTM1k/YUkbNsM5dMVxxi1Pif3ufjntfj5+dGgQYOCNykiQud0z995Suj2aJ5n66eEL0afvrlJQjhUkxnsrCw1DoFUQ6nIdzKDg4MDgYGBxMbGMmbMGGbPno2vry8RERGkpaVp3PLZs2d88803fP3110X/YYoZgwYN4urVqxw+fNjg5zZITlc1gFJMXtUktfNvxaHYnJsMttKHZGSWJaDTGM7feSq6JqnQke6rffoqsuKv8+TgSrIexKGUZSEt7YZjvXdxDHgnd42qT39Rv/qC2GJuBxaWfo19qOVdhgUH4zhw9RESXsg5Qk6VgkKpJC3uNMsm9OF/AT757mdpaUmPHj3o0aMHR48eJTw8nBkzZjB48GACAwPx8Hih4/Djjz/Stm1batWqJdJPZ7pYW1szY8YMgoKCOHLkiEFTKwaJdMXO56pynXuuxJMpU+TJdWbIFGBpxdlHclFyna8iZE5XU5++ioRNIWTcOIulozN2leuRnXSXx7sXknHrQu4aofv0zZGu8NTyLsOifvU5+tXbjG7nS7c6XrT1c6NbHS9Gt/Pl2MS2fOyTwYbF+s1XU6UZjh07RkpKCjVq1GDAgAFERUXx+PFj5s6da/TyKWPSp08fnjx5wo4dOwx6XtGd7sOHD7l+/TpNmjQRZX+1XKeJaJIKGelq69NXymXIn+W05Lq8Nw7XbkFYl8u5ey1LjldbK2SfvjnSFQ9nBxuGtqzMnF51WP5pA+b0qsPQlpVxdrBhwoQJbN68mdjYWL33rVKlChEREcTFxVG1alXatWtH/fr1adSoUaErHl4HVEMsg4ODDTrEUnSnu3PnTtq1aydK3aqmXKcuuqRia5IKmdPV1qcvsZTiWL8LAIl/zebRH2FkPbyGlVtFSvmqX+CE7NOvVq0asbGxOt2kMSMcb7zxBqNGjWLatGlF2iMoKIhjx46RkJBAXFwcderUYdWqVWRlZQlobfHh/fffx8rKio0bNxrsnKI7XTHzuZpynbrqkoqpSSpkpJtfn36pqk2wLO1O9qObpF89ChaWlKraGIl1XkF2ofr07e3tcXNzM3orZUnkyy+/ZP/+/XqPo3qV2bNnM3ToUKKjo/n2229Zs2YNFStWZNasWSYjf2goVGN9pkyZolXTRGhEdboymYw9e/bQsWNHwffWluvUVZdUTE1SIXO62vr05c9TSNgwDXlyPO59v8V71G9Yu1ck+Z91pJ7bqWEf4T5pmPO6xsHBwYFJkyYxZcqUQu9x48YNfvvtNyZNmoREIqFjx47s2bOH7du3c/nyZSpXrsyXX37JjRs3BLTctGnbti1eXl6sWrXKIOcT1ekeO3aMSpUqqd0xFYqCNEmhYF1SsTRJhYx0tfXpy57Go8zOBAspNh6+WNo6YOVcHoDsxDtqa4Xu0zfndY3H0KFDOXfuHMeOHSvU8dOnT2fEiBG4uLioPV67dm1Wr17NxYsXsbOzo0GDBvTs2ZMTJ04IYbZJI5FICA0NZcaMGWRkZIh+PlGdrphVCwVpkkLBuqRiaJKCsDldbX36Vs7lsbB1BIWM+N+CSdz2A2mXc2oObcpXV1urBHoECFcjbY50jYetrS3Tpk0jKChI7xHoly5dYseOHYwZM0brGi8vL2bNmsWNGzdo3rw5vXv3pnnz5vzxxx+vdR6/SZMm1KlTh8WLF4t+LtGdrlj53II0SUE3XVKhNUlB2EhX1af/ahmhhbUtbh9Ox9anDtmJd0iP/gersh6UbTsYe/8X8+ckEmhTzRVnB+FGUJuFb4zLp59+yv3799m7d2/Bi19i6tSpTJgwQafxVI6Ojnz55ZfExsby5ZdfMmvWLPz8/FiwYMFr2wYeEhLCN998I/oQS9Gc7t27d7l79y6NGjUSZf/8NElBd11SIXOdKoRujtDWp2/jWQ333iGUH7WON8dtwnPwQpxeSaPYSi0Z1rqKYLbAC+EbfSMtM8IglUr5+uuv9Yp2T548yfHjx/UeNimVSunZsyfHjx9n5cqV7N69O3cIQXx8fP4HFzNq1apF27Zt+fHHH0U9j2hOd+fOnXTo0EE0QeT8NElBN11SoXOdKoQWvBGqT18o3NzcUCqV5tE9RqRHjx7IZDKtgvavMnnyZKZMmYKdXd7KFl2QSCQ0b96cLVu2EBkZCeR84hk0aBCXLl0q1J6myIwZM5g7d64gkpnaEM3pit2Fpi3XCbrrkgqd61Qhhp6uqk/fxlKCsoBCbomEfPv0i4p5dI/xsbCwIDQ0lMmTJxeYaz148CDXrl0TbNikr68vADExMfj4+NC2bVs6d+7Mvn37iv2nnypVqtC9e3dRh1hKlCK8SllZWbi6uhIXF4erq6vQ2+cy5JdTeTRJdUUigQ7V3QXTJHiZ8uXLc/ToUcqXLy/43m17DkTp3457yjIa+/SV5ORwh7WuIniE+zKDBg2iUaNGDBkyRLRzmAoSicQknYlSqaRFixYMHTqUjz/+WOuaZs2aMXz4cPr27SvYuV9+TTIyMli7di3h4eHY2NgwduxYevXqVajAIzE1k42n7xL9MIWUDBlOtlL8yjnRs563oPcl8uPu3bvUrl2bqKgorBzfENweUZzu/v37mTRpkujlJufvPKX30uM8z9b/rqqdlSXrhzQWxTF5eHhw5swZwUvl9uzZwxdffMGlS5dIzc4pd4t+8IyUjGycbK3w83CkR4Bhfjm///577t+/z5w5c0Q/l7ExVacLcPjwYfr37090dLTGAQHbtm1j0qRJnDt3TtBUn6bXRKFQsHPnTsLDw4mJiWHkyJEMHjyYMmUK/ht7VbAqU0Mw0bqaqyji/JoYMG46VyjPEztPwe0RxemOHz8eBweHIrUs6soL7QXde6dzcp3ifPQGcHFx4cqVK4JG+TKZjLp16zJz5ky6desm2L6FZevWrSxYsMDgYiHGwJSdLkDHjh3p2rUrX3zxhdrjCoUi93dG6NlnBb0mZ8+eJTw8nO3bt/Ppp5/y5Zdfap0CnvM3HE2GLH/9FIkk58ZwcGc/0f52VfaE/H2F51kyJPkMeS2sPaLkdA05JUIfTVIJSlFznSrEyOkuX74cFxcX3n//fUH3LSzmBgnTITQ0lJCQkDylXL///ju2tra8917+89bEoG7duqxZs4bz589jZWVFvXr16N27NydPnlRbZ2qCVSp7MmSKfB1uUewRPNK9efMmDRs25OHDh6KNAtfEhbtP89Uklcnl2CTFsW5Kf1FznZDTrvnw4UMcHBwE2S85OZlq1aqxc+dO6tSpI8ieRUUmk+Ho6EhSUhKlSpUytjmiYuqRLkDPnj1p0KBB7pTr7OxsqlevzqJFi0SZfabva5KSksLy5cuZO3cuPj4+jB07lvJ1mtNn2b950oMP104k806U2mNWLm/i+dmC3O/FSA9qSlcqZVk82b+CtOgjKLOeY+1embJtP8PGs5rasfrYI7jTXbhwIceOHWP16tVCbqszSamZGnOdXd9yp271quzdu1f0GWm2trY8ffoUW1tbQfabMGECSUlJLF++XJD9hOKtt95i9erV1K1b19imiEpxcLpXrlyhVatWxMbGUrp0aZYtW8a6detEG8Ja2NdEJpOxceNGwsPDSfLvjsLrLXIa8l+gcrqO9V9E6JYOb1C6cY+Xzi/8jXBNN+aTdkaQem4nVq4VsHKpQPqVI0isbfH6fJlaKao+9gg+OWLHjh306dNH6G11RqVJqonPP/+ciIgIFi5cKKoNQtbpXrt2jRUrVnDx4kVB9hMSVTvw6+50iwP+/v688847hIeHExQUxIwZMwwqV6grUqmU3r170/ad92k6ax/5VT++8T/tlTEvC1YJceNYk4CWPO1pjhysxAL33qFY2pch0cKStEsHeHZ6G2VavKgG0cceQT//Z2RkcPDgQdq3b1/wYiMwdOhQfvvtN1Hl6xQKBQqFQrA7xRMmTGDMmDGiiAYVFXNe17SYNm0aP/30E9999x316tUTrRtUCDaduVdg+vHOnF7cmdOL+HVBZD7IOwxVSMEqTQJa2Ym3QSHD0skVS/uctIF1uZzuzqyEvCpsutpTpHDs1Zq6tCeP8On0GUpr+6JsKxrlypXj3XffZcWKFYwdO1aUc8jlcqRSqSAzlw4dOsTp06dZs2aNAJYJj5+fn84dUWbEx8fHhx49ejBr1iyTVwfLT7DKwtoOu8oNsHR0JvNeNBm3LpCwfiqeny3E0qFs7johBas02SNPe/KfPS/ShJL//q967mV0tadQTje/mjrLSm1o+u1+g9bU6UNgYCC9evVi1KhRorQoC6W7IJfLGT16NN9++22hWzfFxt/fn2+++cbYZph5idKlSyOXy3WqjTUm+QlWufaYmhu0KOXZ3Fs8FHlKAhm3L2BfvZXa2rUbNjO3d9HTW64fTKFUVfVPBpb2OQ5ekfVC7lH53/9Vz72KLgJaeqcXChoCKceCTJmC3ZfjDTIEUl8aNmyIu7s727ZtE2V/ofK5q1evxs7Ojg8//FAAq8TB19eXuLi411ryrziRlJTEihUrGDhwIDNnzjS2OfmiTbBKkZ2BPFWL7oEkr7vq27M7SqWyyF99euatfbdyKQ8WUuQpj3IjW1Waw/q/4Qh5f66CS0X1crqmVlNXWEaOHMm8efNE2VuIGt3U1FQmT57MnDlzDDoaWl/s7e1xd3c3j+4xEb777jt69OhBWFgYW7ZsISYmbx7UVPAr54S1Zd7fbUVaMvcWDSL+92kk7Yzgwc+jkackYGFfBtsK6qPihRSs0iSgZWlfFoe32oJSQfy6YB79+S3plw8jsbbDsd67efbQ1R6dna6mIZAq0i4fyh3++HjvErXnxB4CWRh69OjBlStXiIqKKnixngiRXpg1axZvv/02DRs2FMgq8TAL35gG9+/fZ9myZUyZMoWyZcsyevRog3SEFoZz585xYMU3ZGbmHZVlYeeIQ823kT2+R1rUfuTpT7Gr2jineuAVtUAhBau0CWiV/d8QHALeQZ72lPSY49h4VcO910yNyoW62qOzd9A0BBJAlpLI410LwMISFJo/ZqqGQIohLlMYrK2tc8vHFi1aJOjeRXW6t27dYuHChUUePmgoVILm776b98pvxnCEhIQwcOBAvLy8gJxPc1WrVuX8+fPUrl3byNblCO+odBmio6MZOXIkpVzKcTDusdqnZgubUjh3GlngfkKL86uGBbxap2thZYNz+y9wbv+F9oP1tEenSFfbEEilUknS3z9g6ehMqWpNtR4v5hDIwjJ06FDWr18vePlYUXO6EydOJDAwEG9v4SUnxcAc6Rqf69ev8/vvv/PVV1/lPqYaYjl58mQjWpZTRrp8+XJq1qzJpEmT+PTTT7l+/ToTJkxgVDt/jeL8uiCGOL+2YQFC26OT09U2BPLZyT/JuHsZly7jkFjmVTh6GbGGQBYWd3d3unTpIliXV2JqJosOXWPmnttYtBnOqPVnWXToml4XmmPHjnHkyBHGjx8viE2GwDy6x/hMnz6dwMDAPMMmhw4dyoULF/jnn38MblNSUhIhISFUrFiRjRs3Mm/ePM6ePcvHH3+cq4ZmauL8hrJHp5BMUw1b1qObPDm0ijIt+mHtXqnAPcQaAlkUAgMD6dmzJ6NHjy50+ZjG8jnPmmw5dx9b6UPm7I3RqXxOoVAwevRowsLCsLc3zTpnTbw8useUb/q9rly6dIldu3YRGxub5zkbGxumT59OUFAQBw8eNMj7ExcXx5w5c1i3bh3dunUrsO1eJTxlKipjqn2n/3kRmRKNFRNFtUcn7YWBq06yPzpB7bGnkb+SHLkO20oBSCQWZCXcQP4sEWlpd0r5t6Bs6/559rFKiKZ64mHKly+Pt7c35cuXz/2/l5cXNjaGESl+mSZNmvDVV18VSr1LSEm6tWvXMnfuXE6cOGFQoaCiolQqcXZ2Jjo6Gjc3N2ObIwqmrL3QvXt3mjVrprXZRyaTUbNmTebNmydop+jLr4lSqeTo0aPMnj2byMhIhg4dyogRIyhXrpzO+xUkWGUocX6Ap0+f4te0PW0Dv+PU/eeC26NTpKuxpk6pBJRkXD+t9rAsOZ7Me5o/bjapV4duHpW4c+cOd+/e5fz587n/v3//PmXLltXokF92zJqEmouCqnxMX6erj47vy+VzQB7Hm56ezqRJk/j111+LlcOFnD8+VTvw6+p0TZV///2XkydPsnbtWq1rXh5i2a5dO0GjXZlMxh9//EF4eDiJiYmMHj2aNWvWFOqTWi3vMizqV1+rYJWhxPkBZs+ezTtN3mL5F61FsUenSHfRoWvM2RujtW0PIHHbHNKi9uFY/z2NQhW2UgtGt/PVKkYjl8tJSEjgzp07uY741X8fPHjAG2+8odEhv+yY9amTzcrKwsfHh127dvHWW2/pdIy2iRW6yMBpkoD7+uuviYqKYv369TrbbUoMGjSIhg0bMnToUGObIgqmGum2a9eOnj17FjgySaFQUL9+fSZPnkz37t2LfN7U1FQcHR2pWLEiHh4ejBs3jvfee0+0IbSGJD4+nurVq3PmzBkqVKggyjl0inR71PNmzt6iFVoXVMNmaWmJh4cHHh4eWutT5XI5Dx8+zOOQT506leus4+PjcXFx0eiQVf96enrmOmZra2u++OILIiIiWLx4sU4/i7byucd7l7yQgatQm/QrR4j/bbKaDNyr5XP37t1j7ty5nD59Os9+xQWz8I3h2b9/Pzdu3GDAgAEFrlUNsRw7dixdu3YttHO8d+8e8+fPZ9myZQD8+uuvNG7cuFB7mSrffPMN/fr1E83hgo5OV1sNm9qad0fj8u5ojc8JVVNnaWmJl5cXXl5eWhWUZDKZmmNWOecTJ07kPpaQkICrq2uuIy5btixr166lYcOG+Pv7U758eTw8PDSWfmkrn9NVBu5VCbjg4GCGDBmidZRJccDPz4+9e/ca24wSg1KpJDg4mJkzZ+r8qa5jx46EhYWxdu1aPvnkE73Od+HCBcLDw9m6dSv9+vXj33//pXLlyq+dw719+za//PILly9fFvU8OheUDm9dhSOxiYUaAilGTZ02pFIp3t7eeHt7a/2lkMlkPHjwQC1a9vHxYe7cuZQqVYq7d+/y6NEj3Nzc8kTKcVYVUSjy5pVzZeBKu6vJwKVdOpBHBk5VPlev1BN2795d7EuuzJGuYdm2bRtpaWn07t1b52MkEglhYWF88skn9O7du8B7I0qlkt27dxMeHk5UVBSBgYHMmTOHN954o6jmmywzZ87kiy++wN3dXdTz6Ox0VTVshRsCKXxNXVGQSqW5eWEVrVu35oMPPuDs2bNIpVKys7PzOOZbt25xXGZJtlPeC4g+MnA55XMprIkYzcyZM3FychLjxzQYPj4+JCQkkJaWVqzK3YojCoWC4OBgQkJC9L7p2qJFC/z9/Vm6dCnDhw/XuCYzM5N169YRHh6ORCJh7Nix9O7d2yiVRYbk6tWr/PnnnxpL74RGr9YpfWrqUCqws7YSfXKnUNSrVw9PT0+2bt1Kt27dsLKy4s033+TNN99UW6epfA70l4G7euMOz5490yknZ+pYWlpStWpVrl69SkBAgLHNea1Zv3499vb2dOnSpVDHh4SE8O6779K/f3+1C+Tjx49ZtGgRERERvPXWW4SHhwte7WDKTJ06lbFjxxpEElPv+qR+jX1YP6QxHaq7YyO1wPYVZR5bqQU2UguUd84T3MS+WDhcFbqoj2mTpNNXBu7cyWP07duX5OTkIlptGqhG95gRj+zsbKZMmUJYWFihnWFAQADNmzcnIiICyBkHFRgYSJUqVYiJiWHnzp3s2rWL9u3blxiHe/bsWY4cOUJgYKBBzlekwZT51bD9+ftaVq1aZbBOGCHIzs7Gx8eHHTt2UKtWLY1r8iufS9oxn9Tzu7ByeRMr1wqkX4nUPMROIYOL26iQHsuZM2dwdXWlfv361K9fnwYNGhAQEFDsUg7Tpk1DqVSavI5rYTCVkrElS5awYcMG9uzZU6R9oqOjadKkCc2bN+fYsWMMHjyYwMBAPD09dd7DVF4TIXjnnXfo1KkTI0aMMMj5BJ8GrEImk1GrVi1mz55N586dxTiFKISEhHD79m2WLFmi8fnE1Eyafbtfo9NVZGfy5MAK0q8cQZH1HJtylSn79iBsvPzV1illWWz82I8GtfyRy+XExMRw6tSp3K/z58/j7e2t5ojr1Klj0vnSdevWsXnzZjZs2GBsUwTHFBzM8+fPqVq1Kps3by605KdcLufPP/9k9uzZXLx4kWbNmrFx40YcHBz03ssUXhMhiIyM5OOPPyY6OtpgeWvRnC7Ali1bmDZtGmfPni02nVYJCQlUq1aNuLg4nJ2dNa7RNKpZZ5QKPBWJHP1Oey5XJpNx+fJlNUccFRVF5cqV1RxxrVq1BBvzXlQOHj/NkG9W0LnPZ6RkyHCyleJXzome9QzXSSQWpuBgfvjhB44cOcIff/yh97FpaWmsXLmSuXPn4urqytixYwkICKBBgwZcvny5UHfrTeE1KSpKpZJWrVoxaNAgPv30U4OdV1Snq1QqadasGcOGDaNfv35inUZw+vfvT/Xq1ZkwYYLG57V1pOmCMjuTXwc1oJl/+YIXv0RmZiZRUVFqjvjq1av4+fnlOuL69etTs2ZNwVul80Ml+HPw6iMyMp5jYfXCwap61E11Xp6uGMrBvDroVXXh6litNI1q12Dfvn3UrFlT5/0ePHhAREQES5YsoUWLFowbN46mTV9IsH755ZdIJBLmzp2rt62vg9PduXMnY8aM4eLFiwbtphPV6QIcPnyYTz/91KDhe1E5ffo03bt359q1a1q1cfXRXlAhkWfzP+cUln6lX3G6Np4/f8758+fVHPGNGzeoWbOmWkTs5+cnyNy2VxFS8MeUEdvB5Dfo1VZqQbZMRpnn91gxtrdOF66oqCjCw8PZsmULffv2ZdSoUVSpkrfMUdXyevbs2TxVOgVR3J2uqjU6ODiYDz74wKDnFt3pQk6iukOHDowcWbAivKmgUm7Kr1ddH6cjlSiRnP2Dy38tFsUBqkhNTeXs2bNqjvjevXvUqVNHLSL29fUtUsqnMBednJpt/2LneMV0MDr/DgG2VtovXEqlkr179xIeHs758+cZMWIEn3/+udYUmYrg4GDi4+NzW3t1pbg73Y0bNzJr1ixOnjxp8Bv9BnG6Fy5coH379sTGxuLoKMwgObFZv349Cxcu5ODBg/mu00WSrlVVF/ZHTCRi5ng6duwoqt2aSE5O5vTp02qOOCkp/xZT/gAAIABJREFUiYCAALWIuGLFijr9AmpKr6Sc/JPUC3tyOvOUCko3+yi39fllNAn+mDpiORghLlxZWVn89ttvhIeHI5PJGDt2LH379tX5U+WTJ0/w9fUlMjKSatWqFXzAfxRnpyuTyXjrrbeYO3cuHTp0MPj5DeJ0AT7++GMqV67M9OnTDXG6IpOdnU3FihX5+++/dZoxlV/53OqlC9izZw/bt283gOW6kZSUpOaET506RVpamlo0XL9+fcqXL5/HEWu6kZi4NRxZyiNkyQnIUxK0Ol2JBDpUdzeZeXm6IIaDKcp9ATsrS5b2rkHkX2uZP38+/v7+jBs3jg4dOhQqavvmm284f/48v/32m87HFGen+/PPP7Ny5UqjlbMazOneuHGD+vXrFyvd1dDQUG7cuKH3R6+XSUpKws/Pj8OHD+Pv71/wAUbk4cOHnD59mpMnT3Lq1ClOnjwJoOaEK9eoQ7eVUVplPhM2hfA89rhWpwtgI7Xg6FdvF5uqBjEcjKYLV1b8dZ4cXEnWgziUsiykpd1wrPcujgHvqB+sVJB94zRtba4zZswY6tSpUyRb0tLSqFq1Ktu3b9d5r+LqdDMzM6lWrRpr166lWbNmRrHBYE4Xcu6WKpXKAru+TIVHjx7h6+ubb/lYQQQGBqJUKnM7gIoTSqWSe/fu5TrhU6dOcT7LDZv63ZFINVdI6OJ0C9JWNjWEdjDaar3vLhiIPCUBK1cfrN7wJP3qMUCJ+0dh2FZQb9axtpRwbGJbwS5cERER7Nixg7///lun9cXV6c6fP59du3axbds2o9lg0OLZ4OBg1q5dy/Xr1w152kLj6urK+++/X+hI9/Lly/z222/FJqXyKhKJBG9vb7p160ZoaCi7du2i9+djtDpcXTHFeXmGRNOgV6VchvxZIgAu743DtVsQ1uVyLkqy5Pg86y0kEkEHvQ4ePJhLly4RGRkp2J6mRlpaGmFhYYSEhBjVDoM6XTc3N0aOHMnUqVMNedoiERgYyE8//YRMJtP72HHjxhEUFJRnSmtxJiVD/9dB8z7ZguxTHNE06FViKcWxfo6ITeJfs3n0RxhZD69h5VaRUr5N8uwh9IXr5SGWxTGC1YV58+bRqlWrIqdjiorB28TGjBnD3r17OXfunKFPXSgCAgJ48803+fPPP/U6bufOncTFxWmV0CuuaBP80X8f3UcqvW5ou3CVqtoEy9LuZD+6SfrVo2BhSamqjZFY22nZR9gLV79+/Xj06BG7d+8WdF9T4MmTJ/zwww8moQ1icKfr6OhIcHAwkyZNMvSpC40u6mMvoyrdmT17tkG7wwyBXzknbKR5f22end9F4rY5ZMVfAyA99jiJ2+aQHnMsz1pbqQV+HsWjdFAMNF245M9TSNgwDXlyPO59v8V71G9Yu1ck+Z91pJ7bqWUfYS9cLw+xfN2i3dmzZ9O1a1d8fX2NbYrhnS7A0KFDuXr1aoE1sKZCt27duHbtms7R+ZIlSyhXrlyhNU9NmR71NM+5y7xzmbSofchTcrqqshNukBa1j6z4vPn7gublve5ounDJnsajzM4ECyk2Hr5Y2jpg5ZzTKp6deCfPHmJduFTNQJs3bxZ8b2MRHx/PokWLmDZtmrFNAQxcvfAya9euZd68eRw/frxYSD+GhYVx7do1li9fnu+6J0+e4Ofnx549e7TKQxZ3iiL4Y67T1Vy9oMjK4N6CASgynmHjXR1pmXKkXT4MChkuXSdg799SbQ8xy+527drFqFGjuHjxotbuyeJUvTBy5EgsLS2ZM2eOsU0BjBTpAnz00UdkZmYWSjXJGAwePJjNmzeTmJiY77qQkBC6du362jpcyJmXZystnECIIeflmSqqQa8vxxoW1ra4fTgdW586ZCfeIT36H6zKelC27eA8DleoQa/aaN++PW5ubqxZs0aU/Q3JrVu3WLt2rUmlM40W6QLs2LGD0aNHExUVJaoegVAMHDgQX19fJk6cqPH52NhYmjRpwqVLl0Qfbmds1hy/yfQ/LyBDd+dr1l54wfk7T+m15Jha27iuGKKVOjIykn79+nH16lWNLcXFJdIdOHAgXl5efP3118Y2JRejitx27NiRcuXK8fPPPxvTDJ0pqHxs/PjxjB8//rV3uADVLB+R/s9abKQSCsoOSSQ5jqI4Olyx8HGSYHVpK5ZK/dqADTXotXnz5tSoUYOlS5eKeh4xiY6OZuvWrYwdO9bYpqhh1EgX4MSJE/To0YOYmBjs7DSXxpgSLVu2ZOTIkfTo0UPt8f379/PZZ59x+fJlkxEWF4vU1FQCAgIICQnBr2n7AgV/2lRzZVjrKsVK5OZlhI7qUlJS6NChAwEBATTuN56wHaYpj3n27Fk6d+5MXFxcnqklxSHS/fDDD6lXrx5fffWVsU1Rw+hOF+CDDz6gUaNGWkXDTYkNGzYwf/58Dh8+nPuYXC4nICCAKVOm5HHGryNDhgwhMzOTVatW5T6Wn+BPcdFY0IaQDubZs2d06NCBOnXq8NNPPyGRSHRSqjPWhatXr17UrVs3T0rN1J3umTNn6NKlC7GxsZQqVcrY5qhhEk43OjqaFi1aEBMTQ9myeceVmxLZ2dlUqlSJv/76i7p16wKwbNkyVq9ezaFDh4pFJUZR2LJlC2PGjOHcuXPFbnhmYRHKwTx79oxOnTpRs2ZNFixYkEfP2BQvXDExMTRr1izP36apO91OnTrRpUsXhg0bZmxT8mASThdyqgOcnZ2ZNWuWsU0pkG+++YbY2FhWrFhBSkoK1apVY+vWrdSvX3zKoArDgwcPqFu3Lps2bTKaQpMxEMLBpKam0qlTJ/z9/Vm0aFGxmRkI8Nlnn+Hu7s7oSVNzxwn9uuEP+vTsZpJz8FTTaq5evWqSzUkm43Tv3btHrVq1uHDhAl5eXsY2J18SExOpWrUqsbGxhIeH8+DBg2JzM7CwKBQKOnfuTKNGjZgxY4axzTEoRXW6qampdO7cmWrVqrF48eJi5XABdp2KZuDs9dhXaYBEIskzTsiU5uAplUpatmzJ4MGD+eQTYcZiCY3JOF2Ar776iidPnmgdf25KDBo0CGdnZ5YvX87Fixfx9PQ0tkmiMm/ePH799VciIyOLRXmfkBTF6aalpdG5c2eqVKnC0qVLi53DVY0Tep6VDRLttpvKHLwdO3YwduxYgw+b1AeTcrqFHR1iDM6dO0fTpk0ZP378ax/5RUVF0aZNG44dO6ZxwOHrTmGdblpaGu+++y4+Pj4sX768mDrc4jMHTzVscvLkyfnONjQ2JhWylC1blnHjxhEcHMzGjRuNbU6+pKamolAoqFq1qrFNEZWMjAz69OnDt99+WyIdbmFJT0+nS5cuVKhQgWXLlhU7h3v+ztOcCPcVh5uVeJunB1aSef8qSnk2thVq88b/hiAtnTMN5nm2gtDt0dTyLmPwSouNGzdiaWlJt27dDHpefTGpSBdyfll9fX3ZvHkzDRs2NLY5GlEoFDRq1IimTZty5swZjhw5YmyTRGPMmDHcunWLjRs3vvaVGdrQN9JVOVwvLy9Wrlxpsh9z80OTvoYiI5X7y4YhT32MXeUGSCytSI85ipXLm3gMikDyX/rBGPoaMpmMGjVqEBERQbt27Qx23sJgcpffUqVKMW3aNCZOnGiyJSlr1qzBwsKC77//nlu3bnHmzBljmyQKe/bs4ffff2fJkiUl1uHqy/Pnz+natSuenp7F1uEmpmZyKOZRnmaNjLtXkKc+xrK0O249p+HaPQgrt4pkJ97+b7RQDkolHLj6iKTUTIPZvHr1ajw9Pfnf//5nsHMWFpNzugADBgzg/v37JimmnJaWRlBQEHPnzsXa2pphw4Yxf/58Y5slOElJSQwYMICff/650PPhShoqh+vm5sbPP/9cLB0uaB4nBCCR5uj3Kp6nkP30IbKUROSpj4EcKU+1tSDoOKH8yMzMZMaMGYSGhhaL4MAkna5UKiU0NJSJEyeiUOgvCCIm33//PS1atKBJk5wRKp999hlbtmzh0aNHRrZMOJRKJUOGDKFXr17FInIwBTIyMujWrRsuLi6sWrWq2Dpc0DxOCMD2zbew8a6OMus59xd9xr0F/VGkJwMgT3uittaQc/AWL15MrVq1aNq0qUHOV1RM0ulCjpiytbU169evN7Ypudy9e5f58+erNXC4/L+9M4+K6srW+FdVDMUgAREB5wg8EUSiNHacUEzTKP2iGBSJGhk06SghgqBGAYOz+EBAg8F2uRwIRBYqRgQhxCkGQ3BEBBQIg0oUoQpFIlXUcN8fNESsYq66NXB+a2Vlhbp3n53F4eNwztn7GzIEHh4eKt0Y5G2OHj2K8vJy7Nq1S9GpqARtgmtoaIgTJ06o/JW6zuyEGEwWTD/eBeMPg2Ew1RODXf2hazMLAMDUfUdKHPn74DU1NSmF2WRvUFrRZTAY2LNnD8LCwtDS0qLodAAAmzZtwurVqzF69OgOXw8ICMDBgwchEKi+2WJZWRk2btyI5ORkqS39CB3h8/n46KOPMGjQIHz33XcqL7hAdz54FPRtnWE0awV0x00Dr/IOAEBnjKTZIx0+eHFxcXB2doa9vb3cx5IVSj1DnJ2dYWVlhcOHDyvc4DE/Px+XLl3Cw4cPJT6zt7eHpaUl0tLS4OnpqYDsZINAIMDy5csRHh4OW1tbRaejUOqb+O0lryYe4QhMuSNR8srn8+Hh4QE9PT0kJSWpheACbXZCz6RuMdSeDAdL1wAMbT3wKm5B3NwIHQtHsEd3bNpPhw8el8tFTEwMfv1V0odPmVG6K2Nv09ZerqysDPr6+grJgaIozJgxA6tWrYKvr6/UZ06fPo2YmBj88ssvNGcnO7Zs2YL8/HxcuHBBJQ4k5EHB4xeIv1KOq6Wte/SdlbyumjYK29auhLa2Nr7//ntoaqqPu7E0O6E2uDmH8GfJNYh5r8DSHww9m1kwnLEUDI2OPQ7kaSfUxqZNm8DhcFSigvVNlF50AWDp0qUYP348wsPDFTJ+SkoKIiMjcfPmzU4vuQuFQowdOxZpaWlwcHCgOcP+k5ubCw8PD9y5cwfm5uaKTkchtJW89qS3LUQCjHiej0v/2apWgtuGsvvgPXv2DLa2trh79y5Gjhwpt3HkgdLu6b7J9u3bERcXp5AbAs3Nzdi4cSNiYmK6rCrS0NCAv7+/Sl4fa2xsxCeffIJDhw4NcMEtQbOga8EFWu+hUkxN1I2ciZRbNfQkSDPK7oO3c+dOeHt7q5zgAiqy0gWAL774ApqamrQ7eu7atQu3bt3C6dOnu32Ww+HA0tISDx8+xNChQ2nITjZ4e3uDzWbj0KFDik5FIRQ8fgGvw3loFvxlnVN/fh94VXcham4EU0sXWmaWMJrlDS0ziw7v0uFXpiiUtfdCVVUVHBwc8ODBA5iYmMhtHHmhEitdAAgPD8eJEydQXV1N25hPnz7Fvn37sHfv3h49b2xsjEWLFqnU9bGUlBTk5eVh3759ik5FYcRfKQdP2NGrTPjyObRH2UF/oguYOoPAq7yN52ckryXxhCIcvFJOV6q0svz9MQh1Gw8dTZZS+eBFRETA399fJQUXUKGVLtB60FNdXd3BJkaetLVv7KnoAsC9e/fg5uaGyspKpd/re/z4MRwcHJCZman2Ddg7o6tDozb4z8rx7FggwGBiVMgZMFgdbynQcWikSLqyE4JIAG1tbdrshIqLizF79myUlZXhnXck7warAip1xyUkJARWVlYoLCyEnZ2dXMe6c+cOMjIypF4R64qJEyfCysoKZ86cwZIlS+SUXf8RiURYsWIFAgMDB6zgAp2XvAJA4610COofg1ddAAAwmOIuIbjAXyWv/3aykPhMHZg4whAJy/8mYSekq8HA9wlRyE07hOFD6BHALVu2YP369SoruICKia6BgQE2bdqEzZs3Iz09XW7jUBSFoKAgRERE9OmbGxAQgOjoaKUW3ejoaIhEIqVzSqWbzkpeAeD1g1zwH98HALAGDYH2cBupz9FZ8qpIjPW1JX6x5O+vxO/FBRju5CT38W/evIlff/0VJ06ckPtY8kRl9nTbWL16NQoLC+V6H/bs2bPgcDhYtWpVn96fP38+njx5gps3b8o4M9lw+/ZtREVFITExUaV7BMiCzkpeAcBs2R6MCjkDk4/CIGriou7sbghf1HYSR/WrEfvCjBkzaLubHhYWhrCwMKVz9+0tKie62tra2LZtGzZu3CiX1o98Ph/r16/Hvn37+lxhpMzXx16/fo1ly5YhNjZWopx5ICKt5FUs4IMStx6sMTS0oDPWAQwtNiAWQfhSuujSUfKqjNAlulevXkVpaSlWrlwp97HkjcqJLgAsW7YMjY2NctliOHDgAKytrfvdCHnVqlU4d+4cnj9/LqPMZMP69esxefJkLF26VNGpKAWtJa8dfwxa/niImoO+qPshEpzseDw9thYU/zWYuu9Ay1Ry35aOkldlZfr06bh+/TpEIlH3D/cRiqKwefNmbN26VSndfXuLSooui8XC7t27sXnzZpl+s+vq6hAZGYmoqKh+xxo8eDAWL16sVCWK58+fR0ZGBuLj4xWditKwyGGExNdYg4yhYTQMvMq7aCrIgZjXBF3rGTD9eCeYbD2J55t5PDy6mgoOh0NHykrF0KFDYWpqiqKiIrmNkZmZiZcvX6rNQkGlroy9SZvV8sqVK+Hj4yOTmGvWrIGmpibi4uJkEq+wsBBz585FVVWVwq+P1dbW4r333kNKSgqcaDj0UCX6W/I6dYQudG59h7S0NHh5eSEoKEjtvfPeZOXKlXBwcMCaNWtkHlssFmPy5MmIiIiAu7u7zOMrApVc6QKtrR8jIyOxZcsW8Hi8fse7f/8+Tp06ha+//loG2bViZ2eHcePG9aiaTZ5QFAU/Pz/4+voSwZVCf0tev5o/CUeOHEFxcTGMjY0xbdo0LFy4ELm5uUprOSVL5Lmvm5qaCi0tLSxYsEAu8RWByoouAEybNg2TJk3q95/LFEUhODgYYWFhGDx4sIyya+XLL7/E/v37ZRqzt3z77beora1FRESEQvNQVuxHGiLUzRo6mr37cWgtebVuLwgwMzPD9u3bUVVVBRcXF/j4+GDq1KlITU2FUNj5LQlVR16iKxQKER4ejl27dqlV1zuV3V5oo6ioCM7Ozv2qUMnMzMS6detQWFgo820AkUgECwsLpKamwtHRUaaxe0JJSQmcnJzwyy+/YNy4cbSPr0r0pssYW4OFUDfrLkteRSIR0tPTERUVhZqaGgQFBcHPz09hLUrlBUVRMDMzw40bNzBq1CiZxT1y5AiSkpJw8eJFtRJdVoSKL3+GDh2K4uJi3Lt3Dx988EGv3xcIBHB3d0d0dDSsra1lnh+TyYRAIEB6ejoWLlwo8/hdwefzMW/ePGzcuBGurq60jq2KTBxhCCerIWj4swWPG5qhyWRAKP5LfdkaTLCYDPxj/FDs9ZgIFxuzLuMxmUxYW1vDz88P77//Pk6ePInAwEBwuVyMHz8eBgYG8v5fogUGg4G8vDzo6+vLrFKUx+Nh0aJFSEhIUMlOYl2h8itdAHj06BEmTZqE+/fv97o14YEDB5Ceno7s7Gy5/TblcrmwsLDAgwcPYGpqKpcxpLFhwwaUlpYiLS1NrVYKdPB2yasBWxPW5oOwaPKIfvVYqKioQFxcHBITE/Hhhx8iODgYEydO7P5FJScmJgZlZWU4ePCgTOLFxsbi8uXL+OGHH2QST6mg1IR169ZRn3/+ea/e4XA4lImJCVVYWCinrP7is88+o7Zt2yb3cdq4dOkSNWzYMOr58+e0jUnoOVwul9q9ezc1bNgwysXFhcrKyqLEYrGi0+oz+fn5lJ2dnUxiNTY2UqamplRBQYFM4ikbaiO69fX1lLGxMVVaWtrjd9auXdtroe4rhYWFlLm5OcXn8+U+FpfLpUaOHElduHBB7mMR+gefz6eOHz9O2dnZURMmTKCOHj1K8Xg8RafVa1paWih9fX2Ky+X2O9b27duppUuXyiAr5URtRJeiKGrHjh2Up6dnj5598OABNWTIEFpXgnPmzKGSk5PlOoZYLKY8PT2pgIAAuY5DkC1isZj68ccfKVdXV8rc3JzauXMnxeFwFJ1Wr5gzZw6VkZHRrxgcDocyNjamysrKZJSV8qHSV8beJjAwENeuXcOtW7e6fTYkJAQbNmygtREyHdfHEhMTUVRUhMjISLmOQ5AtDAYDLi4uyMrKQnZ2NsrKymBpaYmAgAD8/vvvik6vR8ji6tjevXvh4eEBS0v52v0oErU4SHuThIQEnD59Gjk5OR1stBt5QhiwNWBtZgDTPysQEvA5iouLoa1NX+NpkUgES0tLpKSkYMqUKTKPX1lZiSlTpuDixYtqcTgz0Pnjjz/wzTff4PDhw3ByckJISAimTp2q6LQ6JScnB9u3b8fPP//cp/efPn2KCRMmoKCgACNGSJZnqwtqJ7oCgQDjZ8yF3ZIQFDe0fu1tG20enw87YyZ2LHWC/Uh6va2ioqJQUFCAxMREmcYVCoWYNWsWPDw8sG7dOpnGJiiWpqYmHDt2DDExMTA1NUVwcDDc3d2Vri3nq1evYG5uDg6H06fFjL+/P3R0dGTS+0SZUTvR/S6vClvP3YdARAFduPf29IK7rGloaMDYsWNRUlICM7Ou73n2hm3btuHatWvIzs7u0rWYoLqIRCKcPXsW0dHRqK2tRVBQEHx9faGnJ9mER1E4ODjgwIEDmDZtWq/eq6iogKOjIx4+fIghQ4bIKTvlQK1+OtvcSwUUo0vBBVpttJsFIuzMLMF3eVX0JAjAyMgIS5Yskanzbl5eHuLj43Hs2DEiuGoMi8WCh4cHrl+/jsTERFy+fBljxoxBaGgonj59quj0APR9X3fr1q0ICAhQe8EF1Gilq0o22kVFRXBxcUFVVVW/+4O+evUKkyZNQmRkJDw8PGSUIUFVKC8vR2xsLJKTk7FgwQIEBwdjwoQJCssnNTUViYmJOHfuXI/faSvlLy8vV5sqva5Qm2WRKtlo29rawsbGBqdOnep3rMDAwPa9XMLAw9LSEt988w3Ky8thZWWFf/7zn5g7dy5ycnIU0uFs+vTpyM3NhVjcubvy24SHh2PDhg0DQnABNVnpqqKN9rlz57Br1y7k5eX1OcaZM2ewYcMG3L17V+2aqBD6Bp/PR3JyMqKjo8FisRAcHAwvLy9aHRcsLCyQnp4OGxvpRp5vcuPGDbi7u6O8vBw6Ojo0ZKd41GKl252NNif7IOrP/R+A7m206eJf//oXamtr8dtvv/Xp/ZqaGqxevRpJSUlEcAntaGtrw9fXF4WFhdi7dy8SExPx7rvvYs+ePWhoaKAlh97s64aGhiI8PHzACC6gJqLbnY12051MCLk1SmWjzWKx8MUXX/TJvFIsFsPb2xv+/v74+9//LofsCKoOg8GAq6srcnJykJmZiZKSElhYWGDt2rWorKyU69g9Fd3Lly+joqJCLcwme4NaiK6q2mj7+fkhIyOj1yfPsbGxaG5uxubNm+WUGUGdsLe3x/Hjx1FYWAgdHR04OjrC09Ozz39ldUdPRJeiKISGhmLr1q0Kt7KiG7UQXdnZaPfNcr2vGBkZwcvLq1fXxwoKCrB7924kJib22SKeMDAZPnw49uzZg8rKSkyfPh1eXl6YMWMG0tLSZGrwam1tjcbGRtTU1HT6TEZGBl69egUvLy+ZjasqqMVBWsLV3xHzU2mHLQZe9T3Up0dBe6QtmGx98B8XQVD/CEzddzD8s/9IuLpSwhYwCs/Dbaw23Nzc4OzsTMul8+LiYnzwwQeorq7u9rCjubkZjo6OWL9+Pby9veWeG0G9EQqFSEtLQ1RUFLhcLoKCguDj4wNdXd1+x16wYAGWLVsGT09Pic/EYjEmTZqEbdu2qZX3WU9Ri5WuLGy02Ww2kneuxdixY7Fv3z6YmZnB1dUVcXFxKCsrk1vuNjY2mDBhAlJTU7t99quvvoKtrS1WrFght3wIAwcNDQ0sXrwYeXl5OHr0KHJycjBmzBiEh4ejtlb6X4M9pasthpSUFLDZbMyfP79fY6gqarHSBfpvo+1qY4qE5X9r/1pjYyN++uknZGZmIjMzE3p6enBzc8O8efMwa9YsmZ62pqenY8eOHci4+LPUBj2LHUbgZu4VfPrppygoKICRkZHMxiYQ3qSsrAwxMTE4efIkFi5ciHXr1sHW1rbXcbKu5CJofwpcl/h2mMvu9maY6fgeEhIS+mSvpQ6ojehKq0jrKd1VpFEUhXv37rULcEFBAZycnNpF+N133+1X7nequVgYlgDNUfZgMpkSDXrEFAVexS187TkVK93/0a+xCISeUF9fj2+//Rbx8fGYPHkygoODMWfOnG5tnwoev0D8lXJcKa0Dv7kZDM2/7r2zNZgQiERgc8qRHOZDe7MpZUFtRBf4q/dCs6Dn1TCtNtrje9X0pqGhAT/++CMyMzORlZUFY2NjzJs3D25ubpg5c2avLqK3OdA2C4RovS3cCRQFHS0N2hv0EAY2PB4PSUlJiI6Ohra2NoKDg7FkyRKpNw567KYMgK1Jf7MpZUGtRBeQvY12d4jFYty+fbt9FVxSUoI5c+a0r4K76gtK1y8JAqG/iMViZGVlITo6GqWlpfjyyy/x6aefwtCwdbVK5nLPUTvRBYB7T17g4JVyXH5YBwZaCx/aYGswQQFwHmeCNbMtZd7kpq6uDtnZ2bhw4QKys7MxbNgwuLm5wc3NDVOnTm1fIby9HcK5sB/8JyUQNtaBwdKE1rD/gZGzH7RMRkuMQXeDHgLhTe7cuYPo6GhkZmbC29sbrh9/hqDz1Z1u7f1ZfLW9InTQ3+Zj8D8+a/9sIM5ltRTdNuRlo91TRCIR8vPz21fBFRUVcHFxgZubGy4LrfBzxYv21Xj1nv+F1rBx0DIZjeaqAohe1oI1yBjD/30YDI2O2xXSDv4IBLp58uQJ9u/fj6RHetAcMxlgSF6GEjbW4+kRf4gFPEAskhDdgTjEAonRAAACl0lEQVSX1Vp0lY1nz54hKysLP2Rfwu0RCzuIKe9JCdgjxgMAhC9qUZPQWhpp5hMLbTNJvyi6G/QQCNKob+Jj2p6LaBFJyghFUXh+MhSiP19A02Q0XpdckxBdYODNZbW4p6sqmJmZwcfHB66ffw02m93hszbBBQBK/N+yZgYTLP3BUmPR3aCHQJDGqVtPOr3R8OrGD+A9KcaQD0PAYHV+uDzQ5jIRXQXQVYMecUszOBkxAFo7oml0Irp0N+ghEKTR2VxuqatCw9XjMJy5HFqmY7uMMdDmMineVwCdNegRvX6J56kRaHlaBn17VxjO9u0mDr0NegiEt+lsLr9+eB0QCcF7VAj+4yK0PG/tbNZc9hsaNLRgNNvnrTgDZy4T0VUA0hrrCF8+R21KOITcGhi8v0hiUkqPM7C6MxGUj06bRFEUgNainjcRvqwFv+aBlDgDZy4T0VUA1mYG0NZ41uHPsmeJIRA1ccEyMAElbAH3p/8AAPRsZkF72DiJGGwNJqzNB9GWM4EgDWlzGQAMZy6D4cxl7f9dfz4Gf96/KPUgbaDNZbKnqwCkNegRNXFb/91Yh1c3z7X/I6h/LDUGBWDR5M4LLwgEOpA2l3vLQJvL5MqYgpB1gx4CQVGQudw7yEpXQfjPtgRbg9Wnd9kaLKyZLXl3l0BQBGQu9w4iugrCfqQhQt2soaPZu29Ba7269YAqmyQoN2Qu9w5ykKZA2hp90Nmgh0CQB2Qu9xyyp6sEKLJBD4EgS8hc7h4iukqEohv0EAiygszlziGiSyAQCDRCDtIIBAKBRojoEggEAo0Q0SUQCAQaIaJLIBAINEJEl0AgEGiEiC6BQCDQCBFdAoFAoBEiugQCgUAjRHQJBAKBRojoEggEAo38P2KMAP1NGEK8AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G = nx.petersen_graph()\n",
    "plt.subplot(121)\n",
    "nx.draw(G, with_labels=True, font_weight='bold')\n",
    "plt.subplot(122)\n",
    "nx.draw_shell(G, nlist=[range(5, 10), range(5)], with_labels=True, font_weight='bold')"
   ]
  }
 ],
 "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": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}