{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "import numpy as np\n",
    "from conway99 import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A representative seed graph\n",
    "We start from an arbitrary vertex and its neighbours. These can necessarily be arranged as 7 blades of a fan; we fix a numbering with vertex 0 the centre, 1-14 its neighbours, and blade edges 1-2, 3-4, 5-6, 7-8, 9-10, 11-12, 13-14"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "seed15 = np.empty((15,15), dtype='int')\n",
    "for i in range(15):\n",
    "    for j in range(15):\n",
    "        seed15[i,j] = 0\n",
    "\n",
    "# 1-14 all nhbrs of 0\n",
    "for i in range(1,15):\n",
    "    seed15[0,i] = 1\n",
    "    seed15[i,0] =1\n",
    "    \n",
    "# By fixing an ordering, a single representative suffices\n",
    "for i in [1,3,5,7,9,11,13]:\n",
    "    seed15[i,i+1] = 1\n",
    "    seed15[i+1,i] = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 1 1 1 1 1 1 1 1 1 1 1 1 1 1]\n",
      " [1 0 1 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 1 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 0 0 0 1 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 0 0 1 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 0 0 0 0 0 1 0 0 0 0 0 0 0 0]\n",
      " [1 0 0 0 0 1 0 0 0 0 0 0 0 0 0]\n",
      " [1 0 0 0 0 0 0 0 1 0 0 0 0 0 0]\n",
      " [1 0 0 0 0 0 0 1 0 0 0 0 0 0 0]\n",
      " [1 0 0 0 0 0 0 0 0 0 1 0 0 0 0]\n",
      " [1 0 0 0 0 0 0 0 0 1 0 0 0 0 0]\n",
      " [1 0 0 0 0 0 0 0 0 0 0 0 1 0 0]\n",
      " [1 0 0 0 0 0 0 0 0 0 0 1 0 0 0]\n",
      " [1 0 0 0 0 0 0 0 0 0 0 0 0 0 1]\n",
      " [1 0 0 0 0 0 0 0 0 0 0 0 0 1 0]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# review\n",
    "print(seed15)\n",
    "plot_given_edges(seed15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Verify some details\n",
    "assert len(seed15)*len(seed15) == num_known_zeros(seed15) + num_known_ones(seed15) + num_unknowns(seed15)\n",
    "assert not(has_unknown_values(seed15))\n",
    "assert lambda_compatible(seed15)\n",
    "assert mu_compatible(seed15)\n",
    "assert meets_adjacency_requirements(seed15, debug=True)\n",
    "assert graph_is_valid(seed15)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Adding vertex 15\n",
    "(NB, as we started numbering at 0, this is our 16th vertex)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0]\n",
      " [1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1]\n",
      " [1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 2]\n",
      " [1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 2]\n",
      " [1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 2]\n",
      " [1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 2]\n",
      " [1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 2]\n",
      " [1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 2]\n",
      " [1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 2]\n",
      " [1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 2]\n",
      " [1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 2]\n",
      " [1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 2]\n",
      " [1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 2]\n",
      " [1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2]\n",
      " [1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 2]\n",
      " [0 1 2 2 2 2 2 2 2 2 2 2 2 2 2 0]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Generate template with an additional vertex, and review\n",
    "seed16 = get_supermatrix_template_first_unsat(seed15)\n",
    "print(seed16)\n",
    "plot_given_edges(seed16)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Currently 0 graphs, 1 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 0 graphs, 1 candidates\n",
      "Adding branch 0 candidate\n",
      "Adding branch 1 candidate\n",
      "Currently 0 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 0 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 0 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 0 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 0 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 0 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 0 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 0 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 0 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 0 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 0 graphs, 2 candidates\n",
      "Branch 0 yielded compatible graph\n",
      "Branch 1 invalid\n",
      "Currently 1 graphs, 1 candidates\n",
      "Adding branch 0 candidate\n",
      "Adding branch 1 candidate\n",
      "Currently 1 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 1 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 1 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 1 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 1 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 1 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 1 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 1 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 1 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 1 graphs, 2 candidates\n",
      "Branch 0 yielded compatible graph\n",
      "Branch 1 invalid\n",
      "Currently 2 graphs, 1 candidates\n",
      "Adding branch 0 candidate\n",
      "Adding branch 1 candidate\n",
      "Currently 2 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 2 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 2 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 2 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 2 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 2 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 2 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 2 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 2 graphs, 2 candidates\n",
      "Branch 0 yielded compatible graph\n",
      "Branch 1 invalid\n",
      "Currently 3 graphs, 1 candidates\n",
      "Adding branch 0 candidate\n",
      "Adding branch 1 candidate\n",
      "Currently 3 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 3 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 3 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 3 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 3 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 3 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 3 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 3 graphs, 2 candidates\n",
      "Branch 0 yielded compatible graph\n",
      "Branch 1 invalid\n",
      "Currently 4 graphs, 1 candidates\n",
      "Adding branch 0 candidate\n",
      "Adding branch 1 candidate\n",
      "Currently 4 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 4 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 4 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 4 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 4 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 4 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 4 graphs, 2 candidates\n",
      "Branch 0 yielded compatible graph\n",
      "Branch 1 invalid\n",
      "Currently 5 graphs, 1 candidates\n",
      "Adding branch 0 candidate\n",
      "Adding branch 1 candidate\n",
      "Currently 5 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 5 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 5 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 5 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 5 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 5 graphs, 2 candidates\n",
      "Branch 0 yielded compatible graph\n",
      "Branch 1 invalid\n",
      "Currently 6 graphs, 1 candidates\n",
      "Adding branch 0 candidate\n",
      "Adding branch 1 candidate\n",
      "Currently 6 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 6 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 6 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 6 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 6 graphs, 2 candidates\n",
      "Branch 0 yielded compatible graph\n",
      "Branch 1 invalid\n",
      "Currently 7 graphs, 1 candidates\n",
      "Adding branch 0 candidate\n",
      "Adding branch 1 candidate\n",
      "Currently 7 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 7 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 7 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 7 graphs, 2 candidates\n",
      "Branch 0 yielded compatible graph\n",
      "Branch 1 invalid\n",
      "Currently 8 graphs, 1 candidates\n",
      "Adding branch 0 candidate\n",
      "Adding branch 1 candidate\n",
      "Currently 8 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 8 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 8 graphs, 2 candidates\n",
      "Branch 0 yielded compatible graph\n",
      "Branch 1 invalid\n",
      "Currently 9 graphs, 1 candidates\n",
      "Adding branch 0 candidate\n",
      "Adding branch 1 candidate\n",
      "Currently 9 graphs, 2 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 9 graphs, 2 candidates\n",
      "Branch 0 yielded compatible graph\n",
      "Branch 1 invalid\n",
      "Currently 10 graphs, 1 candidates\n",
      "Adding branch 0 candidate\n",
      "Adding branch 1 candidate\n",
      "Currently 10 graphs, 2 candidates\n",
      "Branch 0 yielded compatible graph\n",
      "Branch 1 invalid\n",
      "Currently 11 graphs, 1 candidates\n",
      "Branch 0 yielded compatible graph\n",
      "Branch 1 yielded compatible graph\n",
      "Reduces to 12 valid graphs\n",
      "Wall time: 104 ms\n"
     ]
    }
   ],
   "source": [
    "# Fill in the template\n",
    "%time super16 = templates_to_valid_graphs([seed16], verbose=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t1 reps for 1 candidates\n"
     ]
    }
   ],
   "source": [
    "# Reduce to eliminate equivalent graphs\n",
    "rep16 = reduce_mod_equivalence(super16, verbose=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Turns out, there's only really one way to extend this! Let's take a look\n",
    "plot_given_edges(rep16[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This was expected:\n",
    "\n",
    "By mu=2 condition, as 15 is not a nhbr of 0, they have 2 mutual nhbrs\n",
    " * As the nhbrs of 0 are 1-14, 15 nhbrs two of these.\n",
    " * We assumed 1-15 already; this prevents 2-15 (else 1,2 are nhbrs with two mutual nhbrs - 0, 15 - violating lambda=1) \n",
    " * So 15 nhbrs precisely 1 of vertices 3-14, and these 12 choices are equivalent\n",
    " * So to fix notation we can force this nhbr to be vertex 14\n",
    " \n",
    "Moreover, we could have applied this at the template stage to reduce the search space."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0]\n",
      " [1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1]\n",
      " [1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 2]\n",
      " [1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 2]\n",
      " [1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 2]\n",
      " [1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 2]\n",
      " [1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 2]\n",
      " [1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 2]\n",
      " [1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 2]\n",
      " [1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 2]\n",
      " [1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 2]\n",
      " [1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 2]\n",
      " [1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 2]\n",
      " [1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2]\n",
      " [1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1]\n",
      " [0 1 2 2 2 2 2 2 2 2 2 2 2 2 1 0]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# alternative template \n",
    "seed16 = get_supermatrix_template_first_unsat(seed15, forced_edge=(15,14))\n",
    "print(seed16)\n",
    "plot_given_edges(seed16)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Currently 0 graphs, 1 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 0 graphs, 1 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 0 graphs, 1 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 0 graphs, 1 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 0 graphs, 1 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 0 graphs, 1 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 0 graphs, 1 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 0 graphs, 1 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 0 graphs, 1 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 0 graphs, 1 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 0 graphs, 1 candidates\n",
      "Adding branch 0 candidate\n",
      "Branch 1 invalid\n",
      "Currently 0 graphs, 1 candidates\n",
      "Branch 0 yielded compatible graph\n",
      "Branch 1 invalid\n",
      "Reduces to 1 valid graphs\n",
      "Wall time: 14 ms\n"
     ]
    }
   ],
   "source": [
    "# Fill in the template\n",
    "%time super16 = templates_to_valid_graphs([seed16], verbose=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2020-04-29 15:23:19.396633: 1 seed templates generated\n",
      "2020-04-29 15:23:19.408601: 1 valid graphs from templates\n",
      "\t1 reps for 1 candidates\n",
      "2020-04-29 15:23:19.408601: Reduced to 1 representatives\n",
      "Wall time: 12 ms\n"
     ]
    }
   ],
   "source": [
    "# For convenience, can wrap up the templating, search, and reduction steps for a list of seed graphs\n",
    "%time rep16 = find_valid_supergraphs_first_unsat([seed15], forced_edge=(15,14))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# confirm this is what we expected from the individual steps:\n",
    "plot_given_edges(rep16[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Saturating vertex 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We know one of the blades centred at vertex 1; namely 1-0-2-1.\n",
    "\n",
    "We also have part of another, containing vertex 15.\n",
    "\n",
    "wlog, let vertex 16 be the other vertex of that blade (_we already force 1-16, so suffices to set 15-16_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2020-04-29 15:23:19.498323: 1 seed templates generated\n",
      "2020-04-29 15:23:19.610058: 11 valid graphs from templates\n",
      "\t1 reps for 1 candidates\n",
      "\t2 reps for 11 candidates\n",
      "2020-04-29 15:23:19.611021: Reduced to 2 representatives\n",
      "Wall time: 114 ms\n"
     ]
    }
   ],
   "source": [
    "%time rep17 = find_valid_supergraphs_first_unsat(rep16, forced_edge=(15,16))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vertex 17 necessarily starts a new blade, so no forcing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2020-04-29 15:23:19.617042: 2 seed templates generated\n",
      "2020-04-29 15:23:19.885288: 20 valid graphs from templates\n",
      "\t1 reps for 1 candidates\n",
      "\t2 reps for 11 candidates\n",
      "\t3 reps for 12 candidates\n",
      "2020-04-29 15:23:19.887282: Reduced to 3 representatives\n",
      "Wall time: 270 ms\n"
     ]
    }
   ],
   "source": [
    "%time rep18 = find_valid_supergraphs_first_unsat(rep17)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, we can then force vertex 18 to be the other vertex of that blade"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2020-04-29 15:23:19.894263: 3 seed templates generated\n",
      "2020-04-29 15:23:20.292231: 27 valid graphs from templates\n",
      "\t1 reps for 1 candidates\n",
      "\t2 reps for 2 candidates\n",
      "\t3 reps for 3 candidates\n",
      "\t4 reps for 18 candidates\n",
      "\t5 reps for 19 candidates\n",
      "2020-04-29 15:23:20.294194: Reduced to 5 representatives\n",
      "Wall time: 402 ms\n"
     ]
    }
   ],
   "source": [
    "%time rep19 = find_valid_supergraphs_first_unsat(rep18, forced_edge=(17,18))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Continue in this fashion until we have all nhbrs of vertex 1, with forced fan pattern 0-2, 15-16, 17-18, 19-20, 21-22, 23-24, 25-26"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2020-04-29 15:23:20.301175: 5 seed templates generated\n",
      "2020-04-29 15:23:21.095083: 40 valid graphs from templates\n",
      "\t1 reps for 1 candidates\n",
      "\t2 reps for 9 candidates\n",
      "\t3 reps for 17 candidates\n",
      "\t4 reps for 20 candidates\n",
      "\t5 reps for 25 candidates\n",
      "\t6 reps for 26 candidates\n",
      "\t7 reps for 33 candidates\n",
      "\t8 reps for 34 candidates\n",
      "2020-04-29 15:23:21.100039: Reduced to 8 representatives\n",
      "Wall time: 801 ms\n"
     ]
    }
   ],
   "source": [
    "%time rep20 = find_valid_supergraphs_first_unsat(rep19)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2020-04-29 15:23:21.107055: 8 seed templates generated\n",
      "2020-04-29 15:23:22.314206: 56 valid graphs from templates\n",
      "\t1 reps for 1 candidates\n",
      "\t2 reps for 2 candidates\n",
      "\t3 reps for 3 candidates\n",
      "\t4 reps for 14 candidates\n",
      "\t5 reps for 16 candidates\n",
      "\t6 reps for 17 candidates\n",
      "\t7 reps for 28 candidates\n",
      "\t8 reps for 33 candidates\n",
      "\t9 reps for 42 candidates\n",
      "\t10 reps for 50 candidates\n",
      "2020-04-29 15:23:22.320149: Reduced to 10 representatives\n",
      "Wall time: 1.21 s\n"
     ]
    }
   ],
   "source": [
    "%time rep21 = find_valid_supergraphs_first_unsat(rep20, forced_edge=(19,20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2020-04-29 15:23:22.327166: 10 seed templates generated\n",
      "2020-04-29 15:23:24.034595: 60 valid graphs from templates\n",
      "\t1 reps for 1 candidates\n",
      "\t2 reps for 7 candidates\n",
      "\t3 reps for 9 candidates\n",
      "\t4 reps for 13 candidates\n",
      "\t5 reps for 19 candidates\n",
      "\t6 reps for 25 candidates\n",
      "\t7 reps for 28 candidates\n",
      "\t8 reps for 31 candidates\n",
      "\t9 reps for 32 candidates\n",
      "\t10 reps for 37 candidates\n",
      "\t11 reps for 43 candidates\n",
      "\t12 reps for 44 candidates\n",
      "\t13 reps for 46 candidates\n",
      "\t14 reps for 49 candidates\n",
      "\t15 reps for 50 candidates\n",
      "\t16 reps for 55 candidates\n",
      "\t17 reps for 56 candidates\n",
      "2020-04-29 15:23:24.044569: Reduced to 17 representatives\n",
      "Wall time: 1.72 s\n"
     ]
    }
   ],
   "source": [
    "%time rep22 = find_valid_supergraphs_first_unsat(rep21)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2020-04-29 15:23:24.051581: 17 seed templates generated\n",
      "2020-04-29 15:23:26.773858: 85 valid graphs from templates\n",
      "\t1 reps for 1 candidates\n",
      "\t2 reps for 2 candidates\n",
      "\t3 reps for 3 candidates\n",
      "\t4 reps for 10 candidates\n",
      "\t5 reps for 12 candidates\n",
      "\t6 reps for 13 candidates\n",
      "\t7 reps for 20 candidates\n",
      "\t8 reps for 22 candidates\n",
      "\t9 reps for 27 candidates\n",
      "\t10 reps for 35 candidates\n",
      "\t11 reps for 42 candidates\n",
      "\t12 reps for 43 candidates\n",
      "\t13 reps for 50 candidates\n",
      "\t14 reps for 60 candidates\n",
      "\t15 reps for 70 candidates\n",
      "\t16 reps for 76 candidates\n",
      "\t17 reps for 81 candidates\n",
      "2020-04-29 15:23:26.786828: Reduced to 17 representatives\n",
      "Wall time: 2.74 s\n"
     ]
    }
   ],
   "source": [
    "%time rep23 = find_valid_supergraphs_first_unsat(rep22, forced_edge=(21,22))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2020-04-29 15:23:26.793806: 17 seed templates generated\n",
      "2020-04-29 15:23:29.752891: 68 valid graphs from templates\n",
      "\t1 reps for 1 candidates\n",
      "\t2 reps for 5 candidates\n",
      "\t3 reps for 9 candidates\n",
      "\t4 reps for 13 candidates\n",
      "\t5 reps for 15 candidates\n",
      "\t6 reps for 17 candidates\n",
      "\t7 reps for 21 candidates\n",
      "\t8 reps for 25 candidates\n",
      "\t9 reps for 26 candidates\n",
      "\t10 reps for 29 candidates\n",
      "\t11 reps for 31 candidates\n",
      "\t12 reps for 33 candidates\n",
      "\t13 reps for 34 candidates\n",
      "\t14 reps for 37 candidates\n",
      "\t15 reps for 41 candidates\n",
      "\t16 reps for 45 candidates\n",
      "\t17 reps for 46 candidates\n",
      "\t18 reps for 49 candidates\n",
      "\t19 reps for 50 candidates\n",
      "\t20 reps for 53 candidates\n",
      "\t21 reps for 57 candidates\n",
      "\t22 reps for 58 candidates\n",
      "\t23 reps for 61 candidates\n",
      "\t24 reps for 62 candidates\n",
      "\t25 reps for 65 candidates\n",
      "\t26 reps for 66 candidates\n",
      "2020-04-29 15:23:29.767866: Reduced to 26 representatives\n",
      "Wall time: 2.98 s\n"
     ]
    }
   ],
   "source": [
    "%time rep24 = find_valid_supergraphs_first_unsat(rep23)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2020-04-29 15:23:29.775797: 26 seed templates generated\n",
      "2020-04-29 15:23:33.773138: 78 valid graphs from templates\n",
      "\t1 reps for 1 candidates\n",
      "\t2 reps for 2 candidates\n",
      "\t3 reps for 6 candidates\n",
      "\t4 reps for 8 candidates\n",
      "\t5 reps for 12 candidates\n",
      "\t6 reps for 14 candidates\n",
      "\t7 reps for 18 candidates\n",
      "\t8 reps for 23 candidates\n",
      "\t9 reps for 27 candidates\n",
      "\t10 reps for 29 candidates\n",
      "\t11 reps for 33 candidates\n",
      "\t12 reps for 39 candidates\n",
      "\t13 reps for 45 candidates\n",
      "\t14 reps for 53 candidates\n",
      "\t15 reps for 57 candidates\n",
      "\t16 reps for 60 candidates\n",
      "\t17 reps for 67 candidates\n",
      "\t18 reps for 70 candidates\n",
      "\t19 reps for 76 candidates\n",
      "2020-04-29 15:23:33.787099: Reduced to 19 representatives\n",
      "Wall time: 4.01 s\n"
     ]
    }
   ],
   "source": [
    "%time rep25 = find_valid_supergraphs_first_unsat(rep24, forced_edge=(23,24))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2020-04-29 15:23:33.795085: 19 seed templates generated\n",
      "2020-04-29 15:23:36.668401: 38 valid graphs from templates\n",
      "\t1 reps for 1 candidates\n",
      "\t2 reps for 3 candidates\n",
      "\t3 reps for 5 candidates\n",
      "\t4 reps for 7 candidates\n",
      "\t5 reps for 9 candidates\n",
      "\t6 reps for 11 candidates\n",
      "\t7 reps for 13 candidates\n",
      "\t8 reps for 15 candidates\n",
      "\t9 reps for 17 candidates\n",
      "\t10 reps for 19 candidates\n",
      "\t11 reps for 21 candidates\n",
      "\t12 reps for 23 candidates\n",
      "\t13 reps for 25 candidates\n",
      "\t14 reps for 27 candidates\n",
      "\t15 reps for 29 candidates\n",
      "\t16 reps for 31 candidates\n",
      "\t17 reps for 33 candidates\n",
      "\t18 reps for 35 candidates\n",
      "\t19 reps for 37 candidates\n",
      "2020-04-29 15:23:36.678373: Reduced to 19 representatives\n",
      "Wall time: 2.89 s\n"
     ]
    }
   ],
   "source": [
    "%time rep26 = find_valid_supergraphs_first_unsat(rep25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2020-04-29 15:23:36.687311: 19 seed templates generated\n",
      "2020-04-29 15:23:38.904415: 19 valid graphs from templates\n",
      "\t1 reps for 1 candidates\n",
      "\t2 reps for 2 candidates\n",
      "\t3 reps for 4 candidates\n",
      "\t4 reps for 6 candidates\n",
      "\t5 reps for 8 candidates\n",
      "\t6 reps for 10 candidates\n",
      "\t7 reps for 12 candidates\n",
      "\t8 reps for 14 candidates\n",
      "\t9 reps for 16 candidates\n",
      "\t10 reps for 18 candidates\n",
      "\t11 reps for 19 candidates\n",
      "2020-04-29 15:23:38.909406: Reduced to 11 representatives\n",
      "Wall time: 2.23 s\n"
     ]
    }
   ],
   "source": [
    "%time rep27 = find_valid_supergraphs_first_unsat(rep26, forced_edge=(25,26))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Review an example\n",
    "\n",
    "plot_given_edges(rep27[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Saturating vertex 2\n",
    "\n",
    "Although we have multiple possible 27-vertex graphs, for each of them we know that vertex 2 has degree 2: \n",
    " * As a neighbour of vertex 0, it can only have one mutual neighbour amongst vertices 1,3-14, which is vertex 1\n",
    " * As a neighbour of vertex 1, it can only have one mutual neighbour amongst vertices 0,15-26, which is vertex 0\n",
    "    \n",
    "Thus we have precisely one blade centered at vertex 2, 2-0-1-2. \n",
    "\n",
    "We require 6 more, and may arrange them to ensure blade edges 27-28, 29-30, 31-32, 33-34, 35-36, 37-38."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Confirm our claim:\n",
    "[vertex_degrees(a)[2] for a in rep27]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2020-04-29 15:23:53.125054: 11 seed templates generated\n",
      "2020-04-29 15:24:48.721349: 1546 valid graphs from templates\n",
      "\t1 reps for 1 candidates\n",
      "\t2 reps for 3 candidates\n",
      "\t3 reps for 133 candidates\n",
      "\t4 reps for 134 candidates\n",
      "\t5 reps for 135 candidates\n",
      "\t6 reps for 140 candidates\n",
      "\t7 reps for 277 candidates\n",
      "\t8 reps for 278 candidates\n",
      "\t9 reps for 279 candidates\n",
      "\t10 reps for 283 candidates\n",
      "\t11 reps for 286 candidates\n",
      "\t12 reps for 303 candidates\n",
      "\t13 reps for 304 candidates\n",
      "\t14 reps for 417 candidates\n",
      "\t15 reps for 418 candidates\n",
      "\t16 reps for 419 candidates\n",
      "\t17 reps for 428 candidates\n",
      "\t18 reps for 443 candidates\n",
      "\t19 reps for 444 candidates\n",
      "\t20 reps for 553 candidates\n",
      "\t21 reps for 554 candidates\n",
      "\t22 reps for 555 candidates\n",
      "\t23 reps for 557 candidates\n",
      "\t24 reps for 561 candidates\n",
      "\t25 reps for 562 candidates\n",
      "\t26 reps for 697 candidates\n",
      "\t27 reps for 698 candidates\n",
      "\t28 reps for 699 candidates\n",
      "\t29 reps for 701 candidates\n",
      "\t30 reps for 703 candidates\n",
      "\t31 reps for 707 candidates\n",
      "\t32 reps for 708 candidates\n",
      "\t33 reps for 749 candidates\n",
      "\t34 reps for 750 candidates\n",
      "\t35 reps for 773 candidates\n",
      "\t36 reps for 774 candidates\n",
      "\t37 reps for 776 candidates\n",
      "\t38 reps for 839 candidates\n",
      "\t39 reps for 840 candidates\n",
      "\t40 reps for 841 candidates\n",
      "\t41 reps for 843 candidates\n",
      "\t42 reps for 849 candidates\n",
      "\t43 reps for 850 candidates\n",
      "\t44 reps for 891 candidates\n",
      "\t45 reps for 892 candidates\n",
      "\t46 reps for 977 candidates\n",
      "\t47 reps for 978 candidates\n",
      "\t48 reps for 979 candidates\n",
      "\t49 reps for 981 candidates\n",
      "\t50 reps for 982 candidates\n",
      "\t51 reps for 983 candidates\n",
      "\t52 reps for 988 candidates\n",
      "\t53 reps for 1055 candidates\n",
      "\t54 reps for 1056 candidates\n",
      "\t55 reps for 1058 candidates\n",
      "\t56 reps for 1121 candidates\n",
      "\t57 reps for 1122 candidates\n",
      "\t58 reps for 1123 candidates\n",
      "\t59 reps for 1125 candidates\n",
      "\t60 reps for 1126 candidates\n",
      "\t61 reps for 1127 candidates\n",
      "\t62 reps for 1132 candidates\n",
      "\t63 reps for 1199 candidates\n",
      "\t64 reps for 1200 candidates\n",
      "\t65 reps for 1261 candidates\n",
      "\t66 reps for 1262 candidates\n",
      "\t67 reps for 1263 candidates\n",
      "\t68 reps for 1265 candidates\n",
      "\t69 reps for 1266 candidates\n",
      "\t70 reps for 1267 candidates\n",
      "\t71 reps for 1268 candidates\n",
      "\t72 reps for 1269 candidates\n",
      "\t73 reps for 1272 candidates\n",
      "\t74 reps for 1365 candidates\n",
      "\t75 reps for 1403 candidates\n",
      "\t76 reps for 1404 candidates\n",
      "\t77 reps for 1405 candidates\n",
      "\t78 reps for 1407 candidates\n",
      "\t79 reps for 1408 candidates\n",
      "\t80 reps for 1409 candidates\n",
      "\t81 reps for 1410 candidates\n",
      "\t82 reps for 1411 candidates\n",
      "\t83 reps for 1414 candidates\n",
      "2020-04-29 15:24:49.082385: Reduced to 83 representatives\n",
      "Wall time: 56 s\n"
     ]
    }
   ],
   "source": [
    "# Begin to saturate\n",
    "%time rep28 = find_valid_supergraphs_first_unsat(rep27)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[14,\n",
       " 14,\n",
       " 3,\n",
       " 4,\n",
       " 3,\n",
       " 3,\n",
       " 3,\n",
       " 3,\n",
       " 3,\n",
       " 3,\n",
       " 3,\n",
       " 3,\n",
       " 3,\n",
       " 3,\n",
       " 3,\n",
       " 4,\n",
       " 3,\n",
       " 3,\n",
       " 3,\n",
       " 3,\n",
       " 3,\n",
       " 3,\n",
       " 3,\n",
       " 3,\n",
       " 3,\n",
       " 3,\n",
       " 3,\n",
       " 3]"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vertex_degrees(rep28[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2020-04-28 17:08:49.804767: 83 seed templates generated\n",
      "2020-04-28 17:15:22.354170: 9627 valid graphs from templates\n",
      "\t1 reps for 1 candidates\n",
      "\t2 reps for 2 candidates\n",
      "\t3 reps for 3 candidates\n",
      "\t4 reps for 4 candidates\n",
      "\t5 reps for 5 candidates\n",
      "\t6 reps for 6 candidates\n",
      "\t7 reps for 7 candidates\n",
      "\t8 reps for 8 candidates\n",
      "\t9 reps for 9 candidates\n",
      "\t10 reps for 10 candidates\n",
      "\t11 reps for 11 candidates\n",
      "\t12 reps for 12 candidates\n",
      "\t13 reps for 13 candidates\n",
      "\t14 reps for 14 candidates\n",
      "\t15 reps for 15 candidates\n",
      "\t16 reps for 16 candidates\n",
      "\t17 reps for 17 candidates\n",
      "\t18 reps for 18 candidates\n",
      "\t19 reps for 19 candidates\n",
      "\t20 reps for 20 candidates\n",
      "\t21 reps for 22 candidates\n",
      "\t22 reps for 23 candidates\n",
      "\t23 reps for 24 candidates\n",
      "\t24 reps for 25 candidates\n",
      "\t25 reps for 26 candidates\n",
      "\t26 reps for 27 candidates\n",
      "\t27 reps for 28 candidates\n",
      "\t28 reps for 29 candidates\n",
      "\t29 reps for 31 candidates\n",
      "\t30 reps for 33 candidates\n",
      "\t31 reps for 34 candidates\n",
      "\t32 reps for 35 candidates\n",
      "\t33 reps for 36 candidates\n",
      "\t34 reps for 37 candidates\n",
      "\t35 reps for 38 candidates\n",
      "\t36 reps for 39 candidates\n",
      "\t37 reps for 40 candidates\n",
      "\t38 reps for 44 candidates\n",
      "\t39 reps for 45 candidates\n",
      "\t40 reps for 46 candidates\n",
      "\t41 reps for 47 candidates\n",
      "\t42 reps for 48 candidates\n",
      "\t43 reps for 49 candidates\n",
      "\t44 reps for 51 candidates\n",
      "\t45 reps for 55 candidates\n",
      "\t46 reps for 56 candidates\n",
      "\t47 reps for 57 candidates\n",
      "\t48 reps for 58 candidates\n",
      "\t49 reps for 59 candidates\n",
      "\t50 reps for 60 candidates\n",
      "\t51 reps for 66 candidates\n",
      "\t52 reps for 67 candidates\n",
      "\t53 reps for 68 candidates\n",
      "\t54 reps for 69 candidates\n",
      "\t55 reps for 71 candidates\n",
      "\t56 reps for 77 candidates\n",
      "\t57 reps for 78 candidates\n",
      "\t58 reps for 79 candidates\n",
      "\t59 reps for 80 candidates\n",
      "\t60 reps for 88 candidates\n",
      "\t61 reps for 89 candidates\n",
      "\t62 reps for 91 candidates\n",
      "\t63 reps for 99 candidates\n",
      "\t64 reps for 100 candidates\n",
      "\t65 reps for 109 candidates\n",
      "\t66 reps for 120 candidates\n",
      "\t67 reps for 121 candidates\n",
      "\t68 reps for 122 candidates\n",
      "\t69 reps for 123 candidates\n",
      "\t70 reps for 125 candidates\n",
      "\t71 reps for 126 candidates\n",
      "\t72 reps for 127 candidates\n",
      "\t73 reps for 128 candidates\n",
      "\t74 reps for 129 candidates\n",
      "\t75 reps for 130 candidates\n",
      "\t76 reps for 132 candidates\n",
      "\t77 reps for 133 candidates\n",
      "\t78 reps for 134 candidates\n",
      "\t79 reps for 135 candidates\n",
      "\t80 reps for 136 candidates\n",
      "\t81 reps for 137 candidates\n",
      "\t82 reps for 139 candidates\n",
      "\t83 reps for 140 candidates\n",
      "\t84 reps for 141 candidates\n",
      "\t85 reps for 142 candidates\n",
      "\t86 reps for 143 candidates\n",
      "\t87 reps for 144 candidates\n",
      "\t88 reps for 145 candidates\n",
      "\t89 reps for 146 candidates\n",
      "\t90 reps for 150 candidates\n",
      "\t91 reps for 151 candidates\n",
      "\t92 reps for 152 candidates\n",
      "\t93 reps for 153 candidates\n",
      "\t94 reps for 155 candidates\n",
      "\t95 reps for 156 candidates\n",
      "\t96 reps for 157 candidates\n",
      "\t97 reps for 161 candidates\n",
      "\t98 reps for 162 candidates\n",
      "\t99 reps for 163 candidates\n",
      "\t100 reps for 164 candidates\n",
      "\t101 reps for 165 candidates\n",
      "\t102 reps for 166 candidates\n",
      "\t103 reps for 168 candidates\n",
      "\t104 reps for 172 candidates\n",
      "\t105 reps for 173 candidates\n",
      "\t106 reps for 174 candidates\n",
      "\t107 reps for 175 candidates\n",
      "\t108 reps for 176 candidates\n",
      "\t109 reps for 177 candidates\n",
      "\t110 reps for 183 candidates\n",
      "\t111 reps for 184 candidates\n",
      "\t112 reps for 185 candidates\n",
      "\t113 reps for 186 candidates\n",
      "\t114 reps for 188 candidates\n",
      "\t115 reps for 195 candidates\n",
      "\t116 reps for 196 candidates\n",
      "\t117 reps for 197 candidates\n",
      "\t118 reps for 204 candidates\n",
      "\t119 reps for 205 candidates\n",
      "\t120 reps for 215 candidates\n",
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      "\t124 reps for 237 candidates\n",
      "\t125 reps for 239 candidates\n",
      "\t126 reps for 240 candidates\n",
      "\t127 reps for 241 candidates\n",
      "\t128 reps for 242 candidates\n",
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      "\t154 reps for 274 candidates\n",
      "\t155 reps for 275 candidates\n",
      "\t156 reps for 276 candidates\n",
      "\t157 reps for 277 candidates\n",
      "\t158 reps for 278 candidates\n",
      "\t159 reps for 279 candidates\n",
      "\t160 reps for 280 candidates\n",
      "\t161 reps for 281 candidates\n",
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      "\t165 reps for 285 candidates\n",
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      "\t168 reps for 288 candidates\n",
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      "\t183 reps for 309 candidates\n",
      "\t184 reps for 310 candidates\n",
      "\t185 reps for 311 candidates\n",
      "\t186 reps for 313 candidates\n",
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      "\t188 reps for 315 candidates\n",
      "\t189 reps for 316 candidates\n",
      "\t190 reps for 321 candidates\n",
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      "\t250 reps for 421 candidates\n",
      "\t251 reps for 429 candidates\n",
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      "\t254 reps for 440 candidates\n",
      "\t255 reps for 441 candidates\n",
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      "\t258 reps for 451 candidates\n",
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      "\t260 reps for 453 candidates\n",
      "\t261 reps for 463 candidates\n",
      "\t262 reps for 474 candidates\n",
      "\t263 reps for 477 candidates\n",
      "\t264 reps for 478 candidates\n",
      "\t265 reps for 479 candidates\n",
      "\t266 reps for 480 candidates\n",
      "\t267 reps for 485 candidates\n",
      "\t268 reps for 486 candidates\n",
      "\t269 reps for 487 candidates\n",
      "\t270 reps for 489 candidates\n",
      "\t271 reps for 490 candidates\n",
      "\t272 reps for 491 candidates\n",
      "\t273 reps for 492 candidates\n",
      "\t274 reps for 493 candidates\n",
      "\t275 reps for 498 candidates\n",
      "\t276 reps for 499 candidates\n",
      "\t277 reps for 500 candidates\n",
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      "\t279 reps for 502 candidates\n",
      "\t280 reps for 512 candidates\n",
      "\t281 reps for 513 candidates\n",
      "\t282 reps for 514 candidates\n",
      "\t283 reps for 515 candidates\n",
      "\t284 reps for 516 candidates\n",
      "\t285 reps for 521 candidates\n",
      "\t286 reps for 522 candidates\n",
      "\t287 reps for 523 candidates\n",
      "\t288 reps for 524 candidates\n",
      "\t289 reps for 525 candidates\n",
      "\t290 reps for 526 candidates\n",
      "\t291 reps for 535 candidates\n",
      "\t292 reps for 536 candidates\n",
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      "\t294 reps for 538 candidates\n",
      "\t295 reps for 539 candidates\n",
      "\t296 reps for 540 candidates\n",
      "\t297 reps for 545 candidates\n",
      "\t298 reps for 546 candidates\n",
      "\t299 reps for 547 candidates\n",
      "\t300 reps for 548 candidates\n",
      "\t301 reps for 549 candidates\n",
      "\t302 reps for 551 candidates\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t303 reps for 553 candidates\n",
      "\t304 reps for 558 candidates\n",
      "\t305 reps for 559 candidates\n",
      "\t306 reps for 560 candidates\n",
      "\t307 reps for 561 candidates\n",
      "\t308 reps for 562 candidates\n",
      "\t309 reps for 564 candidates\n",
      "\t310 reps for 568 candidates\n",
      "\t311 reps for 569 candidates\n",
      "\t312 reps for 570 candidates\n",
      "\t313 reps for 571 candidates\n",
      "\t314 reps for 572 candidates\n",
      "\t315 reps for 573 candidates\n",
      "\t316 reps for 574 candidates\n",
      "\t317 reps for 575 candidates\n",
      "\t318 reps for 576 candidates\n",
      "\t319 reps for 583 candidates\n",
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      "\t323 reps for 587 candidates\n",
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      "\t331 reps for 604 candidates\n",
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      "\t361 reps for 749 candidates\n",
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      "\t401 reps for 1010 candidates\n",
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      "\t406 reps for 1064 candidates\n",
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      "\t416 reps for 1161 candidates\n",
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      "\t429 reps for 1199 candidates\n",
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      "\t442 reps for 1215 candidates\n",
      "\t443 reps for 1218 candidates\n",
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    },
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     "text": [
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    },
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      "\t887 reps for 2691 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t1176 reps for 3912 candidates\n",
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     ]
    },
    {
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     "output_type": "stream",
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      "\t1443 reps for 5785 candidates\n",
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      "\t1554 reps for 6287 candidates\n",
      "\t1555 reps for 6288 candidates\n",
      "\t1556 reps for 6289 candidates\n",
      "\t1557 reps for 6290 candidates\n",
      "\t1558 reps for 6291 candidates\n",
      "\t1559 reps for 6292 candidates\n",
      "\t1560 reps for 6293 candidates\n",
      "\t1561 reps for 6302 candidates\n",
      "\t1562 reps for 6303 candidates\n",
      "\t1563 reps for 6304 candidates\n",
      "\t1564 reps for 6309 candidates\n",
      "\t1565 reps for 6310 candidates\n",
      "\t1566 reps for 6313 candidates\n",
      "\t1567 reps for 6314 candidates\n",
      "\t1568 reps for 6315 candidates\n",
      "\t1569 reps for 6320 candidates\n",
      "\t1570 reps for 6321 candidates\n",
      "\t1571 reps for 6322 candidates\n",
      "\t1572 reps for 6323 candidates\n",
      "\t1573 reps for 6324 candidates\n",
      "\t1574 reps for 6330 candidates\n",
      "\t1575 reps for 6331 candidates\n",
      "\t1576 reps for 6332 candidates\n",
      "\t1577 reps for 6333 candidates\n",
      "\t1578 reps for 6334 candidates\n",
      "\t1579 reps for 6341 candidates\n",
      "\t1580 reps for 6342 candidates\n",
      "\t1581 reps for 6387 candidates\n",
      "\t1582 reps for 6388 candidates\n",
      "\t1583 reps for 6396 candidates\n",
      "\t1584 reps for 6397 candidates\n",
      "\t1585 reps for 6398 candidates\n",
      "\t1586 reps for 6399 candidates\n",
      "\t1587 reps for 6402 candidates\n",
      "\t1588 reps for 6407 candidates\n",
      "\t1589 reps for 6408 candidates\n",
      "\t1590 reps for 6409 candidates\n",
      "\t1591 reps for 6410 candidates\n",
      "\t1592 reps for 6427 candidates\n",
      "\t1593 reps for 6428 candidates\n",
      "\t1594 reps for 6438 candidates\n",
      "\t1595 reps for 6439 candidates\n",
      "\t1596 reps for 6513 candidates\n",
      "\t1597 reps for 6514 candidates\n",
      "\t1598 reps for 6524 candidates\n",
      "\t1599 reps for 6527 candidates\n",
      "\t1600 reps for 6528 candidates\n",
      "\t1601 reps for 6538 candidates\n",
      "\t1602 reps for 6539 candidates\n",
      "\t1603 reps for 6546 candidates\n",
      "\t1604 reps for 6549 candidates\n",
      "\t1605 reps for 6557 candidates\n",
      "\t1606 reps for 6645 candidates\n",
      "\t1607 reps for 6656 candidates\n",
      "\t1608 reps for 6663 candidates\n",
      "\t1609 reps for 6665 candidates\n",
      "\t1610 reps for 6674 candidates\n",
      "\t1611 reps for 6752 candidates\n",
      "\t1612 reps for 6753 candidates\n",
      "\t1613 reps for 6754 candidates\n",
      "\t1614 reps for 6755 candidates\n",
      "\t1615 reps for 6756 candidates\n",
      "\t1616 reps for 6760 candidates\n",
      "\t1617 reps for 6763 candidates\n",
      "\t1618 reps for 6764 candidates\n",
      "\t1619 reps for 6765 candidates\n",
      "\t1620 reps for 6766 candidates\n",
      "\t1621 reps for 6767 candidates\n",
      "\t1622 reps for 6774 candidates\n",
      "\t1623 reps for 6775 candidates\n",
      "\t1624 reps for 6777 candidates\n",
      "\t1625 reps for 6778 candidates\n",
      "\t1626 reps for 6785 candidates\n",
      "\t1627 reps for 6786 candidates\n",
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      "\t1629 reps for 6790 candidates\n",
      "\t1630 reps for 6791 candidates\n",
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      "\t1632 reps for 6795 candidates\n",
      "\t1633 reps for 6851 candidates\n",
      "\t1634 reps for 6852 candidates\n",
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      "\t1636 reps for 6872 candidates\n",
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      "\t1640 reps for 6879 candidates\n",
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      "\t1644 reps for 6886 candidates\n",
      "\t1645 reps for 6894 candidates\n",
      "\t1646 reps for 6895 candidates\n",
      "\t1647 reps for 6896 candidates\n",
      "\t1648 reps for 6897 candidates\n",
      "\t1649 reps for 6905 candidates\n",
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      "\t1654 reps for 6913 candidates\n",
      "\t1655 reps for 6982 candidates\n",
      "\t1656 reps for 6991 candidates\n",
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      "\t1658 reps for 6993 candidates\n",
      "\t1659 reps for 6994 candidates\n",
      "\t1660 reps for 6995 candidates\n",
      "\t1661 reps for 6996 candidates\n",
      "\t1662 reps for 7000 candidates\n",
      "\t1663 reps for 7003 candidates\n",
      "\t1664 reps for 7004 candidates\n",
      "\t1665 reps for 7006 candidates\n",
      "\t1666 reps for 7007 candidates\n",
      "\t1667 reps for 7008 candidates\n",
      "\t1668 reps for 7009 candidates\n",
      "\t1669 reps for 7010 candidates\n",
      "\t1670 reps for 7011 candidates\n",
      "\t1671 reps for 7014 candidates\n",
      "\t1672 reps for 7015 candidates\n",
      "\t1673 reps for 7018 candidates\n",
      "\t1674 reps for 7019 candidates\n",
      "\t1675 reps for 7020 candidates\n",
      "\t1676 reps for 7022 candidates\n",
      "\t1677 reps for 7023 candidates\n",
      "\t1678 reps for 7024 candidates\n",
      "\t1679 reps for 7025 candidates\n",
      "\t1680 reps for 7027 candidates\n",
      "\t1681 reps for 7028 candidates\n",
      "\t1682 reps for 7029 candidates\n",
      "\t1683 reps for 7030 candidates\n",
      "\t1684 reps for 7033 candidates\n",
      "\t1685 reps for 7035 candidates\n",
      "\t1686 reps for 7036 candidates\n",
      "\t1687 reps for 7038 candidates\n",
      "\t1688 reps for 7039 candidates\n",
      "\t1689 reps for 7040 candidates\n",
      "\t1690 reps for 7041 candidates\n",
      "\t1691 reps for 7057 candidates\n",
      "\t1692 reps for 7062 candidates\n",
      "\t1693 reps for 7063 candidates\n",
      "\t1694 reps for 7071 candidates\n",
      "\t1695 reps for 7072 candidates\n",
      "\t1696 reps for 7073 candidates\n",
      "\t1697 reps for 7074 candidates\n",
      "\t1698 reps for 7082 candidates\n",
      "\t1699 reps for 7083 candidates\n",
      "\t1700 reps for 7084 candidates\n",
      "\t1701 reps for 7105 candidates\n",
      "\t1702 reps for 7110 candidates\n",
      "\t1703 reps for 7111 candidates\n",
      "\t1704 reps for 7126 candidates\n",
      "\t1705 reps for 7127 candidates\n",
      "\t1706 reps for 7137 candidates\n",
      "\t1707 reps for 7138 candidates\n",
      "\t1708 reps for 7144 candidates\n",
      "\t1709 reps for 7145 candidates\n",
      "\t1710 reps for 7146 candidates\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t1711 reps for 7214 candidates\n",
      "\t1712 reps for 7215 candidates\n",
      "\t1713 reps for 7225 candidates\n",
      "\t1714 reps for 7230 candidates\n",
      "\t1715 reps for 7231 candidates\n",
      "\t1716 reps for 7241 candidates\n",
      "\t1717 reps for 7242 candidates\n",
      "\t1718 reps for 7247 candidates\n",
      "\t1719 reps for 7252 candidates\n",
      "\t1720 reps for 7258 candidates\n",
      "\t1721 reps for 7265 candidates\n",
      "\t1722 reps for 7266 candidates\n",
      "\t1723 reps for 7350 candidates\n",
      "\t1724 reps for 7361 candidates\n",
      "\t1725 reps for 7366 candidates\n",
      "\t1726 reps for 7370 candidates\n",
      "\t1727 reps for 7377 candidates\n",
      "\t1728 reps for 7383 candidates\n",
      "\t1729 reps for 7385 candidates\n",
      "\t1730 reps for 7457 candidates\n",
      "\t1731 reps for 7460 candidates\n",
      "\t1732 reps for 7461 candidates\n",
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      "\t1734 reps for 7463 candidates\n",
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      "\t1830 reps for 8488 candidates\n",
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      "\t1835 reps for 8493 candidates\n",
      "\t1836 reps for 8498 candidates\n",
      "\t1837 reps for 8499 candidates\n",
      "\t1838 reps for 8500 candidates\n",
      "\t1839 reps for 8501 candidates\n",
      "\t1840 reps for 8532 candidates\n",
      "\t1841 reps for 8533 candidates\n",
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      "\t1843 reps for 8540 candidates\n",
      "\t1844 reps for 8542 candidates\n",
      "\t1845 reps for 8549 candidates\n",
      "\t1846 reps for 8550 candidates\n",
      "\t1847 reps for 8551 candidates\n",
      "\t1848 reps for 8552 candidates\n",
      "\t1849 reps for 8563 candidates\n",
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      "\t1852 reps for 8574 candidates\n",
      "\t1853 reps for 8584 candidates\n",
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      "\t1857 reps for 8599 candidates\n",
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      "\t1859 reps for 8604 candidates\n",
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      "\t1861 reps for 8608 candidates\n",
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      "\t1884 reps for 8705 candidates\n",
      "\t1885 reps for 8706 candidates\n",
      "\t1886 reps for 8711 candidates\n",
      "\t1887 reps for 8721 candidates\n",
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      "\t1890 reps for 8771 candidates\n",
      "\t1891 reps for 8816 candidates\n",
      "\t1892 reps for 8817 candidates\n",
      "\t1893 reps for 8838 candidates\n",
      "\t1894 reps for 8882 candidates\n",
      "\t1895 reps for 8885 candidates\n",
      "\t1896 reps for 8923 candidates\n",
      "\t1897 reps for 8934 candidates\n",
      "\t1898 reps for 8937 candidates\n",
      "\t1899 reps for 8938 candidates\n",
      "\t1900 reps for 8942 candidates\n",
      "\t1901 reps for 8947 candidates\n",
      "\t1902 reps for 8948 candidates\n",
      "\t1903 reps for 8949 candidates\n",
      "\t1904 reps for 8950 candidates\n",
      "\t1905 reps for 8951 candidates\n",
      "\t1906 reps for 8955 candidates\n",
      "\t1907 reps for 9035 candidates\n",
      "\t1908 reps for 9036 candidates\n",
      "\t1909 reps for 9045 candidates\n",
      "\t1910 reps for 9057 candidates\n",
      "\t1911 reps for 9058 candidates\n",
      "\t1912 reps for 9060 candidates\n",
      "\t1913 reps for 9061 candidates\n",
      "\t1914 reps for 9062 candidates\n",
      "\t1915 reps for 9063 candidates\n",
      "\t1916 reps for 9066 candidates\n",
      "\t1917 reps for 9067 candidates\n",
      "\t1918 reps for 9068 candidates\n",
      "\t1919 reps for 9071 candidates\n",
      "\t1920 reps for 9072 candidates\n",
      "\t1921 reps for 9076 candidates\n",
      "\t1922 reps for 9079 candidates\n",
      "\t1923 reps for 9081 candidates\n",
      "\t1924 reps for 9082 candidates\n",
      "\t1925 reps for 9083 candidates\n",
      "\t1926 reps for 9084 candidates\n",
      "\t1927 reps for 9095 candidates\n",
      "\t1928 reps for 9101 candidates\n",
      "\t1929 reps for 9104 candidates\n",
      "\t1930 reps for 9105 candidates\n",
      "\t1931 reps for 9106 candidates\n",
      "\t1932 reps for 9112 candidates\n",
      "\t1933 reps for 9113 candidates\n",
      "\t1934 reps for 9116 candidates\n",
      "\t1935 reps for 9117 candidates\n",
      "\t1936 reps for 9160 candidates\n",
      "\t1937 reps for 9161 candidates\n",
      "\t1938 reps for 9171 candidates\n",
      "\t1939 reps for 9180 candidates\n",
      "\t1940 reps for 9181 candidates\n",
      "\t1941 reps for 9187 candidates\n",
      "\t1942 reps for 9188 candidates\n",
      "\t1943 reps for 9279 candidates\n",
      "\t1944 reps for 9280 candidates\n",
      "\t1945 reps for 9301 candidates\n",
      "\t1946 reps for 9307 candidates\n",
      "\t1947 reps for 9312 candidates\n",
      "\t1948 reps for 9390 candidates\n",
      "\t1949 reps for 9401 candidates\n",
      "\t1950 reps for 9406 candidates\n",
      "\t1951 reps for 9408 candidates\n",
      "\t1952 reps for 9417 candidates\n",
      "\t1953 reps for 9420 candidates\n",
      "\t1954 reps for 9517 candidates\n",
      "\t1955 reps for 9519 candidates\n",
      "\t1956 reps for 9528 candidates\n",
      "\t1957 reps for 9529 candidates\n",
      "\t1958 reps for 9531 candidates\n",
      "\t1959 reps for 9608 candidates\n",
      "\t1960 reps for 9609 candidates\n",
      "\t1961 reps for 9618 candidates\n",
      "2020-04-28 17:16:01.868490: Reduced to 1961 representatives\n",
      "Wall time: 7min 12s\n"
     ]
    }
   ],
   "source": [
    "%time rep29 = find_valid_supergraphs(rep28, forced_edge=(27,28))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2020-04-28 17:20:47.337324: 1961 seed templates generated\n",
      "2020-04-28 20:30:44.488288: 193030 valid graphs from templates\n",
      "\t1 reps for 1 candidates\n",
      "\t2 reps for 2 candidates\n",
      "\t3 reps for 3 candidates\n",
      "\t4 reps for 13 candidates\n",
      "\t5 reps for 14 candidates\n",
      "\t6 reps for 93 candidates\n",
      "\t7 reps for 94 candidates\n",
      "\t8 reps for 104 candidates\n",
      "\t9 reps for 105 candidates\n",
      "\t10 reps for 183 candidates\n",
      "\t11 reps for 184 candidates\n",
      "\t12 reps for 185 candidates\n",
      "\t13 reps for 193 candidates\n",
      "\t14 reps for 195 candidates\n",
      "\t15 reps for 196 candidates\n",
      "\t16 reps for 274 candidates\n",
      "\t17 reps for 275 candidates\n",
      "\t18 reps for 276 candidates\n",
      "\t19 reps for 277 candidates\n",
      "\t20 reps for 278 candidates\n",
      "\t21 reps for 279 candidates\n",
      "\t22 reps for 293 candidates\n",
      "\t23 reps for 294 candidates\n",
      "\t24 reps for 295 candidates\n",
      "\t25 reps for 296 candidates\n",
      "\t26 reps for 297 candidates\n",
      "\t27 reps for 303 candidates\n",
      "\t28 reps for 305 candidates\n",
      "\t29 reps for 307 candidates\n",
      "\t30 reps for 317 candidates\n",
      "\t31 reps for 318 candidates\n",
      "\t32 reps for 366 candidates\n",
      "\t33 reps for 367 candidates\n",
      "\t34 reps for 368 candidates\n",
      "\t35 reps for 369 candidates\n",
      "\t36 reps for 375 candidates\n",
      "\t37 reps for 377 candidates\n",
      "\t38 reps for 378 candidates\n",
      "\t39 reps for 386 candidates\n",
      "\t40 reps for 387 candidates\n",
      "\t41 reps for 388 candidates\n",
      "\t42 reps for 389 candidates\n",
      "\t43 reps for 440 candidates\n",
      "\t44 reps for 441 candidates\n",
      "\t45 reps for 449 candidates\n",
      "\t46 reps for 457 candidates\n",
      "\t47 reps for 458 candidates\n",
      "\t48 reps for 459 candidates\n",
      "\t49 reps for 460 candidates\n",
      "\t50 reps for 461 candidates\n",
      "\t51 reps for 467 candidates\n",
      "\t52 reps for 469 candidates\n",
      "\t53 reps for 470 candidates\n",
      "\t54 reps for 478 candidates\n",
      "\t55 reps for 479 candidates\n",
      "\t56 reps for 480 candidates\n",
      "\t57 reps for 481 candidates\n",
      "\t58 reps for 532 candidates\n",
      "\t59 reps for 533 candidates\n",
      "\t60 reps for 541 candidates\n",
      "\t61 reps for 549 candidates\n",
      "\t62 reps for 550 candidates\n",
      "\t63 reps for 551 candidates\n",
      "\t64 reps for 552 candidates\n",
      "\t65 reps for 558 candidates\n",
      "\t66 reps for 559 candidates\n",
      "\t67 reps for 560 candidates\n",
      "\t68 reps for 561 candidates\n",
      "\t69 reps for 562 candidates\n",
      "\t70 reps for 568 candidates\n",
      "\t71 reps for 569 candidates\n",
      "\t72 reps for 572 candidates\n",
      "\t73 reps for 573 candidates\n",
      "\t74 reps for 641 candidates\n",
      "\t75 reps for 643 candidates\n",
      "\t76 reps for 644 candidates\n",
      "\t77 reps for 713 candidates\n",
      "\t78 reps for 714 candidates\n",
      "\t79 reps for 733 candidates\n",
      "\t80 reps for 735 candidates\n",
      "\t81 reps for 736 candidates\n",
      "\t82 reps for 753 candidates\n",
      "\t83 reps for 757 candidates\n",
      "\t84 reps for 825 candidates\n",
      "\t85 reps for 826 candidates\n",
      "\t86 reps for 827 candidates\n",
      "\t87 reps for 828 candidates\n",
      "\t88 reps for 829 candidates\n",
      "\t89 reps for 835 candidates\n",
      "\t90 reps for 837 candidates\n",
      "\t91 reps for 838 candidates\n",
      "\t92 reps for 846 candidates\n",
      "\t93 reps for 847 candidates\n",
      "\t94 reps for 848 candidates\n",
      "\t95 reps for 849 candidates\n",
      "\t96 reps for 900 candidates\n",
      "\t97 reps for 901 candidates\n",
      "\t98 reps for 909 candidates\n",
      "\t99 reps for 917 candidates\n",
      "\t100 reps for 919 candidates\n",
      "\t101 reps for 1007 candidates\n",
      "\t102 reps for 1008 candidates\n",
      "\t103 reps for 1009 candidates\n",
      "\t104 reps for 1010 candidates\n",
      "\t105 reps for 1079 candidates\n",
      "\t106 reps for 1080 candidates\n",
      "\t107 reps for 1081 candidates\n",
      "\t108 reps for 1089 candidates\n",
      "\t109 reps for 1090 candidates\n",
      "\t110 reps for 1098 candidates\n",
      "\t111 reps for 1099 candidates\n",
      "\t112 reps for 1103 candidates\n",
      "\t113 reps for 1108 candidates\n",
      "\t114 reps for 1109 candidates\n",
      "\t115 reps for 1110 candidates\n",
      "\t116 reps for 1111 candidates\n",
      "\t117 reps for 1115 candidates\n",
      "\t118 reps for 1188 candidates\n",
      "\t119 reps for 1198 candidates\n",
      "\t120 reps for 1199 candidates\n",
      "\t121 reps for 1203 candidates\n",
      "\t122 reps for 1208 candidates\n",
      "\t123 reps for 1209 candidates\n",
      "\t124 reps for 1210 candidates\n",
      "\t125 reps for 1211 candidates\n",
      "\t126 reps for 1214 candidates\n",
      "\t127 reps for 1215 candidates\n",
      "\t128 reps for 1298 candidates\n",
      "\t129 reps for 1299 candidates\n",
      "\t130 reps for 1300 candidates\n",
      "\t131 reps for 1301 candidates\n",
      "\t132 reps for 1303 candidates\n",
      "\t133 reps for 1304 candidates\n",
      "\t134 reps for 1305 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t292 reps for 2078 candidates\n",
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     ]
    },
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     "text": [
      "\t601 reps for 2834 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t888 reps for 3443 candidates\n",
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
      "\t1160 reps for 3935 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t1425 reps for 4678 candidates\n",
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
      "\t1693 reps for 5551 candidates\n",
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     ]
    },
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     "text": [
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t2502 reps for 8278 candidates\n",
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    },
    {
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     "output_type": "stream",
     "text": [
      "\t2767 reps for 8629 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t3046 reps for 9322 candidates\n",
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    {
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      "\t3314 reps for 10103 candidates\n",
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    },
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      "\t3580 reps for 10969 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t4102 reps for 12077 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t4363 reps for 12391 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t4630 reps for 12989 candidates\n",
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      "\t4895 reps for 13755 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t5154 reps for 14321 candidates\n",
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
      "\t5416 reps for 15227 candidates\n",
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     ]
    },
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     "output_type": "stream",
     "text": [
      "\t5673 reps for 16203 candidates\n",
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      "\t5934 reps for 17505 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t6191 reps for 18430 candidates\n",
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     ]
    },
    {
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     "text": [
      "\t6450 reps for 19743 candidates\n",
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    },
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     "text": [
      "\t6707 reps for 21063 candidates\n",
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      "\t6968 reps for 21938 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t7233 reps for 22527 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t7493 reps for 23319 candidates\n",
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    },
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     "output_type": "stream",
     "text": [
      "\t7750 reps for 24398 candidates\n",
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      "\t8008 reps for 24985 candidates\n",
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    {
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     "output_type": "stream",
     "text": [
      "\t8268 reps for 25555 candidates\n",
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     ]
    },
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     "text": [
      "\t8528 reps for 25930 candidates\n",
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
      "\t8785 reps for 26347 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t9046 reps for 26608 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t9303 reps for 26916 candidates\n",
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    },
    {
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     "output_type": "stream",
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      "\t9565 reps for 27312 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t10581 reps for 28608 candidates\n",
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     "text": [
      "\t10831 reps for 28903 candidates\n",
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     ]
    },
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      "\t11082 reps for 29204 candidates\n",
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     ]
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    {
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      "\t11334 reps for 29576 candidates\n",
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      "\t11585 reps for 29914 candidates\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t11586 reps for 29915 candidates\n",
      "\t11587 reps for 29919 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t11839 reps for 30328 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t12089 reps for 30578 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t12339 reps for 31190 candidates\n",
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      "\t12589 reps for 31909 candidates\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t12590 reps for 31910 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t12842 reps for 32468 candidates\n",
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    },
    {
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      "\t13342 reps for 33246 candidates\n",
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      "\t13844 reps for 34730 candidates\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t13845 reps for 34731 candidates\n",
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
      "\t14094 reps for 35595 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t14346 reps for 36377 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t14598 reps for 36902 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t14847 reps for 37491 candidates\n",
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
      "\t15099 reps for 38233 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t15349 reps for 38756 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t15601 reps for 39245 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t15852 reps for 39726 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t16102 reps for 40164 candidates\n",
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      "\t16351 reps for 40450 candidates\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t16352 reps for 40451 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t16601 reps for 40733 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t16850 reps for 41125 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t17100 reps for 41512 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t17351 reps for 41815 candidates\n",
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      "\t17599 reps for 42206 candidates\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t17600 reps for 42207 candidates\n",
      "\t17601 reps for 42208 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t17849 reps for 42573 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t18101 reps for 42825 candidates\n",
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    {
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     "output_type": "stream",
     "text": [
      "\t18351 reps for 43076 candidates\n",
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      "\t18599 reps for 43482 candidates\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t18600 reps for 43484 candidates\n",
      "\t18601 reps for 43485 candidates\n",
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      "\t18850 reps for 43809 candidates\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t18851 reps for 43810 candidates\n",
      "\t18852 reps for 43811 candidates\n",
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
      "\t19102 reps for 44113 candidates\n",
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    },
    {
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     "text": [
      "\t19354 reps for 44402 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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     ]
    },
    {
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     "text": [
      "\t20353 reps for 45884 candidates\n",
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     ]
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     "output_type": "stream",
     "text": [
      "\t20602 reps for 46402 candidates\n",
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
      "\t20853 reps for 46994 candidates\n",
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    },
    {
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     "output_type": "stream",
     "text": [
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
      "\t22604 reps for 50870 candidates\n",
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
      "\t22855 reps for 51343 candidates\n",
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     "text": [
      "\t23105 reps for 51989 candidates\n",
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      "\t23353 reps for 52237 candidates\n"
     ]
    },
    {
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     "output_type": "stream",
     "text": [
      "\t23354 reps for 52238 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t23603 reps for 52487 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t23852 reps for 52736 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t24101 reps for 52985 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t24351 reps for 53588 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t24600 reps for 54082 candidates\n",
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     ]
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    {
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     "output_type": "stream",
     "text": [
      "\t24850 reps for 54396 candidates\n",
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     ]
    },
    {
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      "\t25100 reps for 54969 candidates\n",
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      "\t25351 reps for 55628 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t25600 reps for 56102 candidates\n",
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     "output_type": "stream",
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      "\t25851 reps for 56405 candidates\n",
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t26600 reps for 58048 candidates\n",
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
      "\t26851 reps for 58350 candidates\n",
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     ]
    },
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     "output_type": "stream",
     "text": [
      "\t27102 reps for 58723 candidates\n",
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     ]
    },
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     "output_type": "stream",
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      "\t27351 reps for 59939 candidates\n",
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
      "\t27600 reps for 60920 candidates\n",
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
      "\t27850 reps for 61474 candidates\n",
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    },
    {
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     "text": [
      "\t28348 reps for 62544 candidates\n",
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     "text": [
      "\t28598 reps for 63222 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t28849 reps for 63777 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t29099 reps for 64219 candidates\n",
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
      "\t29349 reps for 64748 candidates\n",
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    },
    {
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     "text": [
      "\t29598 reps for 65476 candidates\n",
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    },
    {
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     "text": [
      "\t30345 reps for 67999 candidates\n",
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      "\t30595 reps for 68703 candidates\n",
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    },
    {
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     "output_type": "stream",
     "text": [
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    },
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      "\t31593 reps for 71315 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t31842 reps for 71946 candidates\n",
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
      "\t32092 reps for 72524 candidates\n",
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      "\t32340 reps for 73146 candidates\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t32341 reps for 73150 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t32591 reps for 73634 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t32840 reps for 74331 candidates\n",
      "\t32841 reps for 74332 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t33090 reps for 74967 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t33340 reps for 75564 candidates\n",
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    },
    {
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     "text": [
      "\t33590 reps for 76142 candidates\n",
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      "\t33840 reps for 76626 candidates\n",
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    },
    {
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     "output_type": "stream",
     "text": [
      "\t34089 reps for 77112 candidates\n",
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    },
    {
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      "\t34338 reps for 77662 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t34588 reps for 78270 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t34837 reps for 78756 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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    },
    {
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     "output_type": "stream",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t35586 reps for 80076 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t35836 reps for 80326 candidates\n",
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      "\t36085 reps for 80575 candidates\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t36086 reps for 80576 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t36336 reps for 80826 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t36586 reps for 81076 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t36835 reps for 81370 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t37084 reps for 81754 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t37334 reps for 82004 candidates\n",
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      "\t37583 reps for 82253 candidates\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t37584 reps for 82254 candidates\n",
      "\t37585 reps for 82255 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t37834 reps for 82504 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t38083 reps for 82798 candidates\n",
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
      "\t38332 reps for 83182 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t38582 reps for 83432 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t38832 reps for 83832 candidates\n",
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    },
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     "output_type": "stream",
     "text": [
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t39582 reps for 84732 candidates\n",
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    },
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      "\t39832 reps for 84982 candidates\n",
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
      "\t40082 reps for 85232 candidates\n",
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    },
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      "\t40332 reps for 85632 candidates\n",
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    },
    {
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     "output_type": "stream",
     "text": [
      "\t40582 reps for 85882 candidates\n",
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    },
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     "output_type": "stream",
     "text": [
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t42330 reps for 87780 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t42580 reps for 88030 candidates\n",
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    },
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     "output_type": "stream",
     "text": [
      "\t42829 reps for 88467 candidates\n",
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     ]
    },
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      "\t43079 reps for 88717 candidates\n",
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    },
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     "output_type": "stream",
     "text": [
      "\t43329 reps for 89169 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t43827 reps for 90143 candidates\n",
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
      "\t44077 reps for 90571 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t44327 reps for 91066 candidates\n",
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     ]
    },
    {
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     "text": [
      "\t44577 reps for 91738 candidates\n",
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    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t44826 reps for 92032 candidates\n",
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    },
    {
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     "output_type": "stream",
     "text": [
      "\t45075 reps for 92326 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t45325 reps for 92838 candidates\n",
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     ]
    },
    {
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     "text": [
      "\t45574 reps for 93348 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t45824 reps for 93598 candidates\n",
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     ]
    },
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     "text": [
      "\t46074 reps for 93848 candidates\n",
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     ]
    },
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     "text": [
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
      "\t46823 reps for 95083 candidates\n",
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     ]
    },
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     "text": [
      "\t47073 reps for 95333 candidates\n",
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     "text": [
      "\t47323 reps for 95697 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t47573 reps for 96316 candidates\n",
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      "\t47822 reps for 96988 candidates\n",
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    },
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     "output_type": "stream",
     "text": [
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      "\t48320 reps for 98170 candidates\n",
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     "text": [
      "\t48569 reps for 98704 candidates\n",
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      "\t48818 reps for 99356 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t49067 reps for 100026 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t49308 reps for 100557 candidates\n",
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     "output_type": "stream",
     "text": [
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    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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    },
    {
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     "text": [
      "\t50274 reps for 102640 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t50515 reps for 103196 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t50757 reps for 103640 candidates\n",
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    },
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     "output_type": "stream",
     "text": [
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      "\t51239 reps for 104531 candidates\n",
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      "\t51480 reps for 104896 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t51721 reps for 105188 candidates\n",
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
      "\t51962 reps for 105480 candidates\n",
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      "\t52202 reps for 105771 candidates\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t52203 reps for 105772 candidates\n",
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
      "\t52445 reps for 106106 candidates\n",
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    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t52926 reps for 106915 candidates\n",
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    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t53167 reps for 107294 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t53648 reps for 108053 candidates\n",
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    },
    {
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     "output_type": "stream",
     "text": [
      "\t53890 reps for 108346 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t54132 reps for 108640 candidates\n",
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    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t54614 reps for 109312 candidates\n",
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
      "\t54855 reps for 109684 candidates\n",
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     "text": [
      "\t55097 reps for 109977 candidates\n",
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    },
    {
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     "output_type": "stream",
     "text": [
      "\t55338 reps for 110269 candidates\n",
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    },
    {
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     "text": [
      "\t55822 reps for 110836 candidates\n",
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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    },
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     "output_type": "stream",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t58477 reps for 115574 candidates\n",
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    {
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     "output_type": "stream",
     "text": [
      "\t58718 reps for 115962 candidates\n",
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    },
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     "output_type": "stream",
     "text": [
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     "text": [
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    },
    {
     "name": "stdout",
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     "text": [
      "\t61610 reps for 120827 candidates\n",
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     ]
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     "text": [
      "\t61851 reps for 121119 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t62092 reps for 121459 candidates\n",
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     ]
    },
    {
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     "text": [
      "\t62333 reps for 121945 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t62574 reps for 122285 candidates\n",
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    },
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      "\t62815 reps for 122576 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t63056 reps for 122912 candidates\n",
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
      "\t63297 reps for 123380 candidates\n",
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    },
    {
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     "output_type": "stream",
     "text": [
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     ]
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      "\t63779 reps for 124008 candidates\n",
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    {
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     "text": [
      "\t64020 reps for 124393 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t64261 reps for 124692 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t64502 reps for 125016 candidates\n",
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
      "\t64743 reps for 125316 candidates\n",
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     "text": [
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
      "\t65225 reps for 125984 candidates\n",
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      "\t65466 reps for 126324 candidates\n",
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
      "\t65707 reps for 126616 candidates\n",
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      "\t65948 reps for 126952 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t66671 reps for 127920 candidates\n",
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      "\t66912 reps for 128211 candidates\n",
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     "output_type": "stream",
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      "\t67153 reps for 128596 candidates\n",
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    },
    {
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     "text": [
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    {
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    {
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    },
    {
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     "output_type": "stream",
     "text": [
      "\t68840 reps for 130999 candidates\n",
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    {
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     "text": [
      "\t69081 reps for 131371 candidates\n",
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    },
    {
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     "text": [
      "\t69322 reps for 131662 candidates\n",
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     ]
    },
    {
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     "text": [
      "\t69563 reps for 132024 candidates\n",
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     "output_type": "stream",
     "text": [
      "\t70286 reps for 133032 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t70527 reps for 133324 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t70768 reps for 133686 candidates\n",
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     "text": [
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    },
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     "text": [
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    },
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     "text": [
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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    },
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     "text": [
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    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t74142 reps for 137700 candidates\n",
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     "text": [
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t74624 reps for 138320 candidates\n",
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     "text": [
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    },
    {
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     "output_type": "stream",
     "text": [
      "\t75588 reps for 139686 candidates\n",
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     "text": [
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t76070 reps for 140218 candidates\n",
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    },
    {
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     "output_type": "stream",
     "text": [
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     "output_type": "stream",
     "text": [
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    },
    {
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     "output_type": "stream",
     "text": [
      "\t76793 reps for 140941 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t77275 reps for 141423 candidates\n",
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
      "\t77516 reps for 141714 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t77757 reps for 141955 candidates\n",
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    },
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     "text": [
      "\t77998 reps for 142196 candidates\n",
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    },
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     "text": [
      "\t78239 reps for 142437 candidates\n",
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    },
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      "\t78480 reps for 142678 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t78721 reps for 142919 candidates\n",
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    },
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      "\t78962 reps for 143160 candidates\n",
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
      "\t79203 reps for 143401 candidates\n",
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     ]
    },
    {
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     "text": [
      "\t79444 reps for 143692 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t80167 reps for 144415 candidates\n",
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    },
    {
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     "text": [
      "\t80408 reps for 144656 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t81372 reps for 145670 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t81613 reps for 145911 candidates\n",
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    },
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     "text": [
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    },
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t82818 reps for 147439 candidates\n",
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    },
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      "\t83059 reps for 147712 candidates\n",
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    },
    {
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     "text": [
      "\t83300 reps for 148043 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t83782 reps for 148696 candidates\n",
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      "\t84023 reps for 148970 candidates\n",
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    },
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     "text": [
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      "\t84505 reps for 149614 candidates\n",
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    {
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     ]
    },
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     "output_type": "stream",
     "text": [
      "\t85228 reps for 150559 candidates\n",
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    },
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      "\t85469 reps for 150872 candidates\n",
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     ]
    },
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     "output_type": "stream",
     "text": [
      "\t85710 reps for 151216 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t85951 reps for 151621 candidates\n",
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     ]
    },
    {
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     "text": [
      "\t86192 reps for 151961 candidates\n",
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      "\t86432 reps for 152336 candidates\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t86433 reps for 152337 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t86674 reps for 152683 candidates\n",
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    },
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     "text": [
      "\t86915 reps for 153157 candidates\n",
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    },
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     "text": [
      "\t87156 reps for 153440 candidates\n",
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
      "\t87397 reps for 153776 candidates\n",
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    },
    {
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     "text": [
      "\t87638 reps for 154137 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t87879 reps for 154428 candidates\n",
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
      "\t88120 reps for 154679 candidates\n",
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    },
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     "text": [
      "\t88361 reps for 155005 candidates\n",
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    },
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    },
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    },
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    },
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t91494 reps for 158843 candidates\n",
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     ]
    },
    {
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      "\t91735 reps for 159084 candidates\n",
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
      "\t91976 reps for 159370 candidates\n",
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      "\t92217 reps for 159751 candidates\n",
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    },
    {
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     "output_type": "stream",
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    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t93422 reps for 161146 candidates\n",
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      "\t93663 reps for 161387 candidates\n",
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    },
    {
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     "text": [
      "\t93904 reps for 161628 candidates\n",
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      "\t94145 reps for 161869 candidates\n",
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    },
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      "\t94386 reps for 162164 candidates\n",
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    },
    {
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     "output_type": "stream",
     "text": [
      "\t95591 reps for 163505 candidates\n",
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    },
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      "\t95832 reps for 163796 candidates\n",
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    },
    {
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     "text": [
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t96555 reps for 164584 candidates\n",
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    {
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     "output_type": "stream",
     "text": [
      "\t96796 reps for 164855 candidates\n",
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
      "\t97037 reps for 165096 candidates\n",
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
      "\t97519 reps for 165673 candidates\n",
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     ]
    },
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     "text": [
      "\t97760 reps for 165914 candidates\n",
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    },
    {
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     "text": [
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     "text": [
      "\t98724 reps for 167018 candidates\n",
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      "\t101341 reps for 170090 candidates\n",
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    },
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     "text": [
      "\t102046 reps for 170875 candidates\n",
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      "\t102281 reps for 171110 candidates\n",
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     ]
    },
    {
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     "text": [
      "\t102751 reps for 171580 candidates\n",
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      "\t102986 reps for 171910 candidates\n",
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     ]
    },
    {
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     "text": [
      "\t103221 reps for 172145 candidates\n",
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      "\t103456 reps for 172380 candidates\n",
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     ]
    },
    {
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     "text": [
      "\t103691 reps for 172615 candidates\n",
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      "\t103926 reps for 172850 candidates\n",
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     ]
    },
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     "text": [
      "\t104631 reps for 173650 candidates\n",
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    },
    {
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     "text": [
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      "\t105336 reps for 174355 candidates\n",
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     ]
    },
    {
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     "text": [
      "\t105571 reps for 174590 candidates\n",
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    },
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      "\t105806 reps for 174825 candidates\n",
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     ]
    },
    {
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     "text": [
      "\t106511 reps for 175625 candidates\n",
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    },
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    },
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     "text": [
      "\t108156 reps for 177415 candidates\n",
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      "\t108391 reps for 177650 candidates\n",
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     ]
    },
    {
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     "text": [
      "\t108626 reps for 177935 candidates\n",
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      "\t108861 reps for 178215 candidates\n",
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    },
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     "text": [
      "\t109096 reps for 178450 candidates\n",
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      "\t109331 reps for 178685 candidates\n",
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     ]
    },
    {
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     "text": [
      "\t111211 reps for 180663 candidates\n",
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     ]
    },
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      "\t111446 reps for 180985 candidates\n",
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     ]
    },
    {
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     "text": [
      "\t111681 reps for 181220 candidates\n",
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     ]
    },
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     "text": [
      "\t111916 reps for 181500 candidates\n",
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    },
    {
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     "text": [
      "\t112151 reps for 181780 candidates\n",
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     ]
    },
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     "text": [
      "\t113561 reps for 183405 candidates\n",
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     ]
    },
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      "\t114501 reps for 184435 candidates\n",
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      "\t114736 reps for 184670 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t115676 reps for 185700 candidates\n",
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
      "\t115911 reps for 185980 candidates\n",
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      "\t116145 reps for 186264 candidates\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t116146 reps for 186265 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t116381 reps for 186500 candidates\n",
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    },
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     "text": [
      "\t116616 reps for 186825 candidates\n",
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      "\t116851 reps for 187155 candidates\n",
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     ]
    },
    {
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     "text": [
      "\t117086 reps for 187435 candidates\n",
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      "\t117321 reps for 187715 candidates\n",
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    },
    {
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     "text": [
      "\t117556 reps for 187950 candidates\n",
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     "text": [
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    },
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     "text": [
      "\t118026 reps for 188490 candidates\n",
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     "text": [
      "\t118261 reps for 188770 candidates\n",
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
      "\t118731 reps for 189240 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t119201 reps for 189755 candidates\n",
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    {
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     "text": [
      "\t119436 reps for 190035 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t119671 reps for 190365 candidates\n",
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      "\t120140 reps for 190834 candidates\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t120141 reps for 190835 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t120376 reps for 191070 candidates\n",
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    },
    {
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     "output_type": "stream",
     "text": [
      "\t120611 reps for 191350 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t120846 reps for 191585 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t121316 reps for 192145 candidates\n",
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    },
    {
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     "output_type": "stream",
     "text": [
      "\t121551 reps for 192380 candidates\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t121786 reps for 192665 candidates\n",
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      "\t122020 reps for 192899 candidates\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t122021 reps for 192900 candidates\n",
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      "\t122150 reps for 193029 candidates\n",
      "\t122151 reps for 193030 candidates\n",
      "2020-04-29 06:25:53.159272: Reduced to 122151 representatives\n",
      "Wall time: 13h 5min 6s\n"
     ]
    }
   ],
   "source": [
    "%time rep30 = find_valid_supergraphs(rep29)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pickle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "pickle.dump( rep30, open( \"rep30.p\", \"wb\" ) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "62.290158082610915"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(rep30)/len(rep29)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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