Graphene_defects.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "8966fbd8",
   "metadata": {},
   "source": [
    "## Vacancies in graphene: an application of adiabatic quantum optimization\n",
    "\n",
    "Notebook to reproduce the <a href=\"https://arxiv.org/abs/2010.05803\">results on graphene defects</a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "6f7082ef",
   "metadata": {},
   "outputs": [],
   "source": [
    "from pymatgen.core.structure import Molecule, Structure, Lattice\n",
    "from pymatgen.symmetry.analyzer import SpacegroupAnalyzer\n",
    "from pymatgen.ext.matproj import MPRester\n",
    "from pymatgen.io.ase import AseAtomsAdaptor\n",
    "from pymatgen.analysis.graphs import StructureGraph, ConnectedSite\n",
    "from pymatgen.analysis.local_env import VoronoiNN\n",
    "\n",
    "from ase.visualize import view\n",
    "import copy\n",
    "import time\n",
    "import itertools\n",
    "\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bb86e59c",
   "metadata": {},
   "source": [
    "## Create the structure "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "id": "19fa31b4",
   "metadata": {},
   "outputs": [],
   "source": [
    "with MPRester(\"p5vAQV3F1QuxFcxVT\") as m:    \n",
    "    graphene_mp = m.get_structure_by_material_id(\"mp-48\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 343,
   "id": "3ed625fb",
   "metadata": {},
   "outputs": [],
   "source": [
    "with MPRester(\"p5vAQV3F1QuxFcxVT\") as m:    \n",
    "    graphene_mp = m.get_structure_by_material_id(\"mp-30\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 345,
   "id": "d9695da2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 0.]])"
      ]
     },
     "execution_count": 345,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "graphene_mp.frac_coords"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "1e5a01a9",
   "metadata": {},
   "outputs": [],
   "source": [
    "lattice = np.array([[ 1.233862, -2.137112,  0.      ],\n",
    "                   [ 1.233862,  2.137112,  0.      ],\n",
    "                   [ 0.      ,  0.      ,  8.685038]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "baf24d69",
   "metadata": {},
   "outputs": [],
   "source": [
    "graphene = Structure(lattice, species=['C','C'], coords=[[2/3, 1/3, 0. ],[1/3, 2/3, 0.]])\n",
    "graphene = SpacegroupAnalyzer(graphene).get_conventional_standard_structure()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "36c64f2d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Structure Summary\n",
       "Lattice\n",
       "    abc : 7.4031724240988614 7.4031724240988614 8.685038\n",
       " angles : 90.0 90.0 120.00000000000001\n",
       " volume : 412.2285660225962\n",
       "      A : 3.7015862120494307 -6.411335387866038 0.0\n",
       "      B : 3.7015862120494307 6.411335387866038 0.0\n",
       "      C : 0.0 0.0 8.685038\n",
       "PeriodicSite: C (1.2339, 0.7124, 0.0000) [0.1111, 0.2222, 0.0000]\n",
       "PeriodicSite: C (2.4677, 2.8495, 0.0000) [0.1111, 0.5556, 0.0000]\n",
       "PeriodicSite: C (3.7016, 4.9866, 0.0000) [0.1111, 0.8889, 0.0000]\n",
       "PeriodicSite: C (2.4677, -1.4247, 0.0000) [0.4444, 0.2222, 0.0000]\n",
       "PeriodicSite: C (3.7016, 0.7124, 0.0000) [0.4444, 0.5556, 0.0000]\n",
       "PeriodicSite: C (4.9354, 2.8495, 0.0000) [0.4444, 0.8889, 0.0000]\n",
       "PeriodicSite: C (3.7016, -3.5619, 0.0000) [0.7778, 0.2222, 0.0000]\n",
       "PeriodicSite: C (4.9354, -1.4247, 0.0000) [0.7778, 0.5556, 0.0000]\n",
       "PeriodicSite: C (6.1693, 0.7124, 0.0000) [0.7778, 0.8889, 0.0000]\n",
       "PeriodicSite: C (1.2339, -0.7124, 0.0000) [0.2222, 0.1111, 0.0000]\n",
       "PeriodicSite: C (2.4677, 1.4247, 0.0000) [0.2222, 0.4444, 0.0000]\n",
       "PeriodicSite: C (3.7016, 3.5619, 0.0000) [0.2222, 0.7778, 0.0000]\n",
       "PeriodicSite: C (2.4677, -2.8495, 0.0000) [0.5556, 0.1111, 0.0000]\n",
       "PeriodicSite: C (3.7016, -0.7124, 0.0000) [0.5556, 0.4444, 0.0000]\n",
       "PeriodicSite: C (4.9354, 1.4247, 0.0000) [0.5556, 0.7778, 0.0000]\n",
       "PeriodicSite: C (3.7016, -4.9866, 0.0000) [0.8889, 0.1111, 0.0000]\n",
       "PeriodicSite: C (4.9354, -2.8495, 0.0000) [0.8889, 0.4444, 0.0000]\n",
       "PeriodicSite: C (6.1693, -0.7124, 0.0000) [0.8889, 0.7778, 0.0000]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_supercell = 3\n",
    "scaling_matrix = np.identity(3)*n_supercell\n",
    "scaling_matrix[2][2] = 1\n",
    "graphene_supercell = copy.deepcopy(graphene)\n",
    "graphene_supercell.make_supercell(scaling_matrix)\n",
    "graphene_supercell"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "d6d8f0e8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Popen: returncode: None args: ['/Users/brunocamino/miniconda3/envs/qc/bin/p...>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "view(AseAtomsAdaptor().get_atoms(graphene_supercell))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d359b86f",
   "metadata": {},
   "source": [
    "## Map the structure to a graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "id": "789d861e",
   "metadata": {},
   "outputs": [],
   "source": [
    "graphene_graph = StructureGraph.with_local_env_strategy(graphene_supercell,strategy=VoronoiNN())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fcab3131",
   "metadata": {},
   "source": [
    "## Build the adjacency matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7d858f43",
   "metadata": {},
   "source": [
    "#### Periodic boundary conditions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 299,
   "id": "51032cac",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3])"
      ]
     },
     "execution_count": 299,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "distance_matrix_pbc = np.round(graphene_supercell.distance_matrix,5)\n",
    "shells = np.unique(distance_matrix_pbc[0])\n",
    "np.sum(np.round(distance_matrix_pbc,5) == np.round(shells[1],5), axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 297,
   "id": "3ced66e5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.     , 1.42474, 2.46772, 2.84948, 3.76951, 4.27422])"
      ]
     },
     "execution_count": 297,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "shells"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "2ce3dfe2",
   "metadata": {},
   "outputs": [],
   "source": [
    "adjacency_matrix = np.round(distance_matrix_pbc,5) == np.round(shells[1],5)\n",
    "num_neighbours = np.sum(adjacency_matrix, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "f6f830e2",
   "metadata": {},
   "outputs": [],
   "source": [
    "adjacency_matrix = adjacency_matrix.astype(int)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4f222ec8",
   "metadata": {},
   "source": [
    "## Define the binary variables that encode the problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "b1b4e639",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array([[1]*graphene_supercell.num_sites]*graphene_supercell.num_sites)\n",
    "np.fill_diagonal(x,0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "71947dc6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n",
       "       [1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n",
       "       [1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n",
       "       [1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n",
       "       [1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n",
       "       [1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n",
       "       [1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n",
       "       [1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n",
       "       [1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n",
       "       [1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1],\n",
       "       [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1],\n",
       "       [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1],\n",
       "       [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1],\n",
       "       [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1],\n",
       "       [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1],\n",
       "       [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1],\n",
       "       [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1],\n",
       "       [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fa968dd3",
   "metadata": {},
   "source": [
    "#### Classical"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "0a2d8960",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-48, -48, -48, -48, -48, -48, -48, -48, -48, -48, -48, -48, -48,\n",
       "       -48, -48, -48, -48, -48])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "E_tmp = -np.matmul(x,adjacency_matrix)\n",
    "np.sum(x*E_tmp,axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a9ed1c3f",
   "metadata": {},
   "source": [
    "### Classical full calculation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "id": "0e0e2bdd",
   "metadata": {},
   "outputs": [],
   "source": [
    "time_0 = time.time()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "id": "40486b05",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_classical_1 = list(itertools.product([0, 1], repeat=18))\n",
    "X_classical_2 = np.array(X_classical_1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "id": "0f4e12e7",
   "metadata": {},
   "outputs": [],
   "source": [
    "sorting = np.argsort(np.sum(X_classical_2,axis=1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "id": "6d864057",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_classical = X_classical_2[sorting]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "id": "c34f49bc",
   "metadata": {},
   "outputs": [],
   "source": [
    "E_tmp = -np.matmul(X_classical,adjacency_matrix)\n",
    "E_classical = np.sum(X_classical*E_tmp,axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "id": "aeb75e36",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-42, -40, -38, -36, -34, -32, -30, -28, -26, -24, -22, -20, -18,\n",
       "       -16, -14, -12, -10,  -8,  -6,  -4,  -2,   0])"
      ]
     },
     "execution_count": 150,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.unique(E_classical)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "id": "722c5181",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.39359593391418457\n"
     ]
    }
   ],
   "source": [
    "print(time.time()-time_0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c43b8d49",
   "metadata": {},
   "source": [
    "# Quantum Adiabatic Computing"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e7da7071",
   "metadata": {},
   "source": [
    "## Binary Quadratic Model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d0e607a",
   "metadata": {},
   "source": [
    "### Unconstrained"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 244,
   "id": "80f512fa",
   "metadata": {},
   "outputs": [],
   "source": [
    "from dimod import BinaryQuadraticModel\n",
    "from dwave.system import EmbeddingComposite, DWaveSampler\n",
    "\n",
    "X = np.arange(graphene_supercell.num_sites)\n",
    "\n",
    "Q = np.triu(-adjacency_matrix.astype(int),0)\n",
    "bqm = BinaryQuadraticModel.from_qubo(Q)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 245,
   "id": "0a33f73d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]"
      ]
     },
     "execution_count": 245,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.tolist()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 247,
   "id": "5e53e6ea",
   "metadata": {},
   "outputs": [],
   "source": [
    "sampler = EmbeddingComposite(DWaveSampler())\n",
    "sampleset_unconstrained = sampler.sample(bqm, num_reads = 100, \n",
    "                                         label='Graphene 3x3 unconstrained')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "id": "b49ff972",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_unconstrained = sampleset_unconstrained.to_pandas_dataframe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 541,
   "id": "7cffaa59",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>10</th>\n",
       "      <th>11</th>\n",
       "      <th>12</th>\n",
       "      <th>13</th>\n",
       "      <th>14</th>\n",
       "      <th>15</th>\n",
       "      <th>16</th>\n",
       "      <th>17</th>\n",
       "      <th>energy</th>\n",
       "      <th>num_occurrences</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-27.0</td>\n",
       "      <td>100</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   0  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  energy  \\\n",
       "0  1  1  1  1  1  1  1  1  1  1   1   1   1   1   1   1   1   1   -27.0   \n",
       "\n",
       "   num_occurrences  \n",
       "0              100  "
      ]
     },
     "execution_count": 541,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_unconstrained.loc[:, df_unconstrained.columns != 'chain_break_fraction']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 194,
   "id": "6689eb08",
   "metadata": {},
   "outputs": [],
   "source": [
    "df = copy.deepcopy(df_unconstrained)\n",
    "min_energy = min(df['energy' ])\n",
    "n_atoms = graphene_supercell.num_sites \n",
    "df_unconstrained_low = df[df['energy' ] == min_energy].iloc[: , :n_atoms]\n",
    "array_un = df[df['energy' ] == min_energy].iloc[: , :n_atoms].to_numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "id": "f5ecd908",
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], dtype=int8)"
      ]
     },
     "execution_count": 195,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "array_un"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "68f51bf5",
   "metadata": {},
   "source": [
    "#### Lower Q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 559,
   "id": "3eebc79e",
   "metadata": {},
   "outputs": [],
   "source": [
    "from dimod import BinaryQuadraticModel\n",
    "from dwave.system import EmbeddingComposite, DWaveSampler\n",
    "\n",
    "X = np.arange(graphene_supercell.num_sites)\n",
    "\n",
    "Q = np.triu(-0.0001*adjacency_matrix.astype(int),0)\n",
    "bqm = BinaryQuadraticModel.from_qubo(Q)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 560,
   "id": "ae8dbf51",
   "metadata": {},
   "outputs": [],
   "source": [
    "sampler = EmbeddingComposite(DWaveSampler())\n",
    "sampleset_unconstrained = sampler.sample(bqm, num_reads = 100, \n",
    "                                         label='Graphene 3x3 unconstrained')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 561,
   "id": "0291f328",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_unconstrained = sampleset_unconstrained.to_pandas_dataframe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 562,
   "id": "d2ab77c2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>10</th>\n",
       "      <th>11</th>\n",
       "      <th>12</th>\n",
       "      <th>13</th>\n",
       "      <th>14</th>\n",
       "      <th>15</th>\n",
       "      <th>16</th>\n",
       "      <th>17</th>\n",
       "      <th>energy</th>\n",
       "      <th>num_occurrences</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-0.0027</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-0.0027</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-0.0027</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-0.0027</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-0.0027</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-0.0027</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-0.0027</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-0.0027</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-0.0027</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-0.0027</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100 rows × 20 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    0  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  energy  \\\n",
       "0   1  1  1  1  1  1  1  1  1  1   1   1   1   1   1   1   1   1 -0.0027   \n",
       "1   1  1  1  1  1  1  1  1  1  1   1   1   1   1   1   1   1   1 -0.0027   \n",
       "2   1  1  1  1  1  1  1  1  1  1   1   1   1   1   1   1   1   1 -0.0027   \n",
       "3   1  1  1  1  1  1  1  1  1  1   1   1   1   1   1   1   1   1 -0.0027   \n",
       "4   1  1  1  1  1  1  1  1  1  1   1   1   1   1   1   1   1   1 -0.0027   \n",
       ".. .. .. .. .. .. .. .. .. .. ..  ..  ..  ..  ..  ..  ..  ..  ..     ...   \n",
       "95  1  1  1  1  1  1  1  1  1  1   1   1   1   1   1   1   1   1 -0.0027   \n",
       "96  1  1  1  1  1  1  1  1  1  1   1   1   1   1   1   1   1   1 -0.0027   \n",
       "97  1  1  1  1  1  1  1  1  1  1   1   1   1   1   1   1   1   1 -0.0027   \n",
       "98  1  1  1  1  1  1  1  1  1  1   1   1   1   1   1   1   1   1 -0.0027   \n",
       "99  1  1  1  1  1  1  1  1  1  1   1   1   1   1   1   1   1   1 -0.0027   \n",
       "\n",
       "    num_occurrences  \n",
       "0                 1  \n",
       "1                 1  \n",
       "2                 1  \n",
       "3                 1  \n",
       "4                 1  \n",
       "..              ...  \n",
       "95                1  \n",
       "96                1  \n",
       "97                1  \n",
       "98                1  \n",
       "99                1  \n",
       "\n",
       "[100 rows x 20 columns]"
      ]
     },
     "execution_count": 562,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_unconstrained.loc[:, df_unconstrained.columns != 'chain_break_fraction']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 563,
   "id": "1729cc67",
   "metadata": {},
   "outputs": [],
   "source": [
    "df = copy.deepcopy(df_unconstrained)\n",
    "min_energy = min(df['energy' ])\n",
    "n_atoms = graphene_supercell.num_sites \n",
    "df_unconstrained_low = df[df['energy' ] == min_energy].iloc[: , :n_atoms]\n",
    "array_un = df[df['energy' ] == min_energy].iloc[: , :n_atoms].to_numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 564,
   "id": "bfd8d910",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], dtype=int8),\n",
       " array([100]))"
      ]
     },
     "execution_count": 564,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.unique(array_un,axis=0, return_counts=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "959510f3",
   "metadata": {},
   "source": [
    "### Constrained"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "01e9eee0",
   "metadata": {},
   "source": [
    "#### 1 vacancy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 264,
   "id": "92fbde65",
   "metadata": {},
   "outputs": [],
   "source": [
    "from dimod import BinaryQuadraticModel\n",
    "from dwave.system import EmbeddingComposite, DWaveSampler\n",
    "\n",
    "X = np.arange(graphene_supercell.num_sites)\n",
    "\n",
    "Q = np.triu(-adjacency_matrix.astype(int),0)\n",
    "bqm = BinaryQuadraticModel.from_qubo(Q)\n",
    "\n",
    "c_n_vacancies = [(i,1) for i in X]\n",
    "\n",
    "num_vacancies = 1\n",
    "\n",
    "bqm.add_linear_equality_constraint(\n",
    "        c_n_vacancies,\n",
    "        constant= -(graphene_supercell.num_sites-num_vacancies),\n",
    "        lagrange_multiplier = 1000\n",
    "        )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 265,
   "id": "34f4f9be",
   "metadata": {},
   "outputs": [],
   "source": [
    "sampler = EmbeddingComposite(DWaveSampler())\n",
    "sampleset_1v = sampler.sample(bqm, num_reads = 1000, label='Graphene 3x3 1 vacancy')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 266,
   "id": "78a9d70f",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_1v = sampleset_1v.to_pandas_dataframe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 267,
   "id": "f6204932",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>...</th>\n",
       "      <th>11</th>\n",
       "      <th>12</th>\n",
       "      <th>13</th>\n",
       "      <th>14</th>\n",
       "      <th>15</th>\n",
       "      <th>16</th>\n",
       "      <th>17</th>\n",
       "      <th>chain_break_fraction</th>\n",
       "      <th>energy</th>\n",
       "      <th>num_occurrences</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-24.0</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-24.0</td>\n",
       "      <td>26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-24.0</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-24.0</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-24.0</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>285</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.055556</td>\n",
       "      <td>978.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>286</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.055556</td>\n",
       "      <td>3982.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>287</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.055556</td>\n",
       "      <td>3982.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>288</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>8985.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>289</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.055556</td>\n",
       "      <td>978.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>290 rows × 21 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     0  1  2  3  4  5  6  7  8  9  ...  11  12  13  14  15  16  17  \\\n",
       "0    1  1  1  1  1  1  1  1  1  1  ...   1   1   0   1   1   1   1   \n",
       "1    1  1  1  1  0  1  1  1  1  1  ...   1   1   1   1   1   1   1   \n",
       "2    0  1  1  1  1  1  1  1  1  1  ...   1   1   1   1   1   1   1   \n",
       "3    1  1  1  1  1  1  1  1  1  1  ...   1   1   1   1   1   0   1   \n",
       "4    1  1  1  1  1  1  0  1  1  1  ...   1   1   1   1   1   1   1   \n",
       "..  .. .. .. .. .. .. .. .. .. ..  ...  ..  ..  ..  ..  ..  ..  ..   \n",
       "285  1  1  0  1  1  1  1  1  1  0  ...   1   1   1   1   1   1   1   \n",
       "286  1  0  1  1  1  1  1  1  1  1  ...   1   0   0   1   1   1   1   \n",
       "287  1  1  1  1  1  0  1  1  1  1  ...   1   1   0   1   1   1   1   \n",
       "288  1  1  1  1  1  1  1  1  1  0  ...   0   1   1   1   1   0   1   \n",
       "289  1  0  1  1  1  1  1  1  1  1  ...   1   1   1   1   1   1   1   \n",
       "\n",
       "     chain_break_fraction  energy  num_occurrences  \n",
       "0                0.000000   -24.0                6  \n",
       "1                0.000000   -24.0               26  \n",
       "2                0.000000   -24.0                9  \n",
       "3                0.000000   -24.0                7  \n",
       "4                0.000000   -24.0                5  \n",
       "..                    ...     ...              ...  \n",
       "285              0.055556   978.0                1  \n",
       "286              0.055556  3982.0                1  \n",
       "287              0.055556  3982.0                1  \n",
       "288              0.000000  8985.0                1  \n",
       "289              0.055556   978.0                1  \n",
       "\n",
       "[290 rows x 21 columns]"
      ]
     },
     "execution_count": 267,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_1v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 515,
   "id": "e6ab842b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>10</th>\n",
       "      <th>11</th>\n",
       "      <th>12</th>\n",
       "      <th>13</th>\n",
       "      <th>14</th>\n",
       "      <th>15</th>\n",
       "      <th>16</th>\n",
       "      <th>17</th>\n",
       "      <th>energy</th>\n",
       "      <th>num_occurrences</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>75</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>978.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>360</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>979.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     0  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  energy  \\\n",
       "75   1  0  1  1  1  1  1  1  1  1   1   0   1   1   1   1   1   1   978.0   \n",
       "360  1  1  1  1  1  1  1  1  0  1   1   1   1   0   1   1   1   1   979.0   \n",
       "\n",
       "     num_occurrences  \n",
       "75                 1  \n",
       "360                1  "
      ]
     },
     "execution_count": 515,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_1v[df_1v['energy'] > -24.0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 504,
   "id": "e3be625a",
   "metadata": {},
   "outputs": [],
   "source": [
    "df = copy.deepcopy(df_1v)\n",
    "min_energy = min(df['energy' ])\n",
    "n_atoms = graphene_supercell.num_sites \n",
    "df_1v_low = df[df['energy' ] == min_energy].iloc[: , :n_atoms]\n",
    "array_1v = df[df['energy' ] == min_energy].iloc[: , :n_atoms].to_numpy()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3cd79fb0",
   "metadata": {},
   "source": [
    "#### 2 vacancies"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 223,
   "id": "6f82664b",
   "metadata": {},
   "outputs": [],
   "source": [
    "from dimod import BinaryQuadraticModel\n",
    "from dwave.system import EmbeddingComposite, DWaveSampler\n",
    "\n",
    "X = np.arange(graphene_supercell.num_sites)\n",
    "\n",
    "Q = np.triu(-adjacency_matrix.astype(int),0)\n",
    "bqm = BinaryQuadraticModel.from_qubo(Q)\n",
    "\n",
    "c_n_vacancies = [(i,1) for i in X]\n",
    "\n",
    "num_vacancies = 2\n",
    "\n",
    "bqm.add_linear_equality_constraint(\n",
    "        c_n_vacancies,\n",
    "        constant= -(graphene_supercell.num_sites-num_vacancies),\n",
    "        lagrange_multiplier = 1000\n",
    "        )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 225,
   "id": "3f0696a1",
   "metadata": {},
   "outputs": [],
   "source": [
    "sampler = EmbeddingComposite(DWaveSampler())\n",
    "#sampleset_2v = sampler.sample(bqm, num_reads = 1000, label='Example - Simple Ocean Programs: BQM')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 226,
   "id": "1a25ae6a",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_2v = sampleset_2v.to_pandas_dataframe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 539,
   "id": "26efcb93",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>...</th>\n",
       "      <th>11</th>\n",
       "      <th>12</th>\n",
       "      <th>13</th>\n",
       "      <th>14</th>\n",
       "      <th>15</th>\n",
       "      <th>16</th>\n",
       "      <th>17</th>\n",
       "      <th>chain_break_fraction</th>\n",
       "      <th>energy</th>\n",
       "      <th>num_occurrences</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-22.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-22.0</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-22.0</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-22.0</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-22.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>559</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.055556</td>\n",
       "      <td>-21.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>560</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.055556</td>\n",
       "      <td>-21.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>561</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0.055556</td>\n",
       "      <td>-21.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>562</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.055556</td>\n",
       "      <td>-21.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>564</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.055556</td>\n",
       "      <td>-21.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>166 rows × 21 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     0  1  2  3  4  5  6  7  8  9  ...  11  12  13  14  15  16  17  \\\n",
       "0    1  1  1  1  1  1  1  0  1  1  ...   1   1   1   1   1   1   0   \n",
       "1    1  1  1  1  1  1  1  0  1  1  ...   1   1   0   1   1   1   1   \n",
       "2    1  1  1  1  1  1  1  0  1  1  ...   1   1   1   1   1   0   1   \n",
       "3    1  1  1  1  1  1  1  1  0  1  ...   1   1   1   1   1   1   0   \n",
       "4    1  1  0  1  1  1  1  1  1  1  ...   0   1   1   1   1   1   1   \n",
       "..  .. .. .. .. .. .. .. .. .. ..  ...  ..  ..  ..  ..  ..  ..  ..   \n",
       "559  1  1  1  1  1  0  1  1  1  0  ...   1   1   1   1   1   1   1   \n",
       "560  1  1  1  1  1  1  0  1  0  1  ...   1   1   1   1   1   1   1   \n",
       "561  1  1  1  0  1  1  1  1  1  1  ...   1   1   1   1   1   1   0   \n",
       "562  1  1  1  1  1  1  1  1  1  1  ...   1   1   1   1   0   1   1   \n",
       "564  1  1  0  1  0  1  1  1  1  1  ...   1   1   1   1   1   1   1   \n",
       "\n",
       "     chain_break_fraction  energy  num_occurrences  \n",
       "0                0.000000   -22.0                1  \n",
       "1                0.000000   -22.0                4  \n",
       "2                0.000000   -22.0                4  \n",
       "3                0.000000   -22.0                7  \n",
       "4                0.000000   -22.0                1  \n",
       "..                    ...     ...              ...  \n",
       "559              0.055556   -21.0                1  \n",
       "560              0.055556   -21.0                1  \n",
       "561              0.055556   -21.0                1  \n",
       "562              0.055556   -21.0                1  \n",
       "564              0.055556   -21.0                1  \n",
       "\n",
       "[166 rows x 21 columns]"
      ]
     },
     "execution_count": 539,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_2v[df_2v['energy'] <0 ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 528,
   "id": "f2b6fbac",
   "metadata": {},
   "outputs": [],
   "source": [
    "df = copy.deepcopy(df_2v)\n",
    "min_energy = min(df['energy' ])\n",
    "energies_unique = np.unique(df['energy' ])\n",
    "n_atoms = graphene_supercell.num_sites \n",
    "df_2v_low = df[df['energy' ] == min_energy].iloc[: , :n_atoms]\n",
    "array_2v = df[df['energy' ] == min_energy].iloc[: , :n_atoms].to_numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 229,
   "id": "ab1dd614",
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>...</th>\n",
       "      <th>11</th>\n",
       "      <th>12</th>\n",
       "      <th>13</th>\n",
       "      <th>14</th>\n",
       "      <th>15</th>\n",
       "      <th>16</th>\n",
       "      <th>17</th>\n",
       "      <th>chain_break_fraction</th>\n",
       "      <th>energy</th>\n",
       "      <th>num_occurrences</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-22.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-22.0</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-22.0</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-22.0</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-22.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-22.0</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-22.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-22.0</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-22.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-22.0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-22.0</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-22.0</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-22.0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-22.0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-22.0</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-22.0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-22.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-22.0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-22.0</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-22.0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-22.0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-22.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-22.0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-22.0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-22.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-21.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-21.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-21.0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-21.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-21.0</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-21.0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-21.0</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-21.0</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-21.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-21.0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-21.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-21.0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-21.0</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-21.0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-21.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-21.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-21.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-21.0</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-21.0</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-21.0</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-21.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-21.0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-21.0</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-21.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-21.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>50 rows × 21 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    0  1  2  3  4  5  6  7  8  9  ...  11  12  13  14  15  16  17  \\\n",
       "0   1  1  1  1  1  1  1  0  1  1  ...   1   1   1   1   1   1   0   \n",
       "1   1  1  1  1  1  1  1  0  1  1  ...   1   1   0   1   1   1   1   \n",
       "2   1  1  1  1  1  1  1  0  1  1  ...   1   1   1   1   1   0   1   \n",
       "3   1  1  1  1  1  1  1  1  0  1  ...   1   1   1   1   1   1   0   \n",
       "4   1  1  0  1  1  1  1  1  1  1  ...   0   1   1   1   1   1   1   \n",
       "5   1  0  1  1  1  1  1  1  1  1  ...   1   1   1   1   1   0   1   \n",
       "6   1  0  1  1  1  1  1  1  1  1  ...   0   1   1   1   1   1   1   \n",
       "7   1  1  0  1  1  1  1  1  1  0  ...   1   1   1   1   1   1   1   \n",
       "8   1  1  1  1  1  0  1  1  1  1  ...   0   1   1   1   1   1   1   \n",
       "9   1  1  1  1  1  0  1  1  1  1  ...   1   1   1   0   1   1   1   \n",
       "10  1  1  1  1  1  0  1  1  1  1  ...   1   0   1   1   1   1   1   \n",
       "11  1  1  1  1  1  1  1  1  0  1  ...   1   1   1   1   0   1   1   \n",
       "12  1  1  1  1  0  1  1  1  1  1  ...   1   1   0   1   1   1   1   \n",
       "13  1  1  1  0  1  1  1  1  1  1  ...   1   1   0   1   1   1   1   \n",
       "14  1  1  0  1  1  1  1  1  1  1  ...   1   1   1   1   1   1   0   \n",
       "15  1  1  1  0  1  1  1  1  1  1  ...   1   0   1   1   1   1   1   \n",
       "16  0  1  1  1  1  1  1  1  1  0  ...   1   1   1   1   1   1   1   \n",
       "17  0  1  1  1  1  1  1  1  1  1  ...   1   1   1   1   1   1   1   \n",
       "18  1  1  1  1  1  1  1  1  0  1  ...   1   1   1   0   1   1   1   \n",
       "19  1  1  1  1  0  1  1  1  1  1  ...   1   1   1   0   1   1   1   \n",
       "20  1  1  1  1  1  1  0  1  1  1  ...   1   0   1   1   1   1   1   \n",
       "21  1  1  1  0  1  1  1  1  1  0  ...   1   1   1   1   1   1   1   \n",
       "22  0  1  1  1  1  1  1  1  1  1  ...   1   1   1   1   0   1   1   \n",
       "23  1  1  1  1  1  1  0  1  1  1  ...   1   1   1   1   1   0   1   \n",
       "24  1  1  1  1  1  1  0  1  1  1  ...   1   1   1   1   0   1   1   \n",
       "25  1  1  1  1  1  1  1  1  1  1  ...   1   0   1   1   1   1   0   \n",
       "26  1  1  1  1  1  1  1  1  1  1  ...   1   0   0   1   1   1   1   \n",
       "27  1  1  1  1  1  1  1  1  1  1  ...   1   1   1   1   1   0   0   \n",
       "28  1  1  1  1  1  1  1  1  0  1  ...   1   1   0   1   1   1   1   \n",
       "29  1  1  0  1  1  0  1  1  1  1  ...   1   1   1   1   1   1   1   \n",
       "30  1  1  1  1  1  1  1  0  1  1  ...   1   0   1   1   1   1   1   \n",
       "31  1  1  1  1  1  1  1  1  0  1  ...   1   0   1   1   1   1   1   \n",
       "32  1  1  1  1  1  1  1  1  1  1  ...   1   1   0   1   1   0   1   \n",
       "33  1  1  1  1  1  1  1  1  1  1  ...   1   1   0   1   1   1   0   \n",
       "34  1  0  1  1  1  1  1  1  1  1  ...   1   1   1   1   1   1   0   \n",
       "35  1  1  1  1  1  1  1  1  1  1  ...   0   1   1   1   1   1   1   \n",
       "36  1  1  1  1  1  1  1  1  1  0  ...   1   1   1   1   1   1   1   \n",
       "37  1  0  1  1  1  1  1  0  1  1  ...   1   1   1   1   1   1   1   \n",
       "38  0  1  1  1  1  1  1  1  0  1  ...   1   1   1   1   1   1   1   \n",
       "39  1  1  1  1  1  1  1  1  1  1  ...   0   1   1   0   1   1   1   \n",
       "40  1  1  1  1  1  0  1  1  1  0  ...   1   1   1   1   1   1   1   \n",
       "41  1  1  0  1  1  1  1  1  1  1  ...   1   1   1   1   1   0   1   \n",
       "42  1  0  1  1  1  1  1  1  1  0  ...   1   1   1   1   1   1   1   \n",
       "43  1  1  1  1  1  1  1  1  1  0  ...   1   1   0   1   1   1   1   \n",
       "44  1  1  0  1  0  1  1  1  1  1  ...   1   1   1   1   1   1   1   \n",
       "45  1  1  1  1  1  1  1  1  1  1  ...   0   1   0   1   1   1   1   \n",
       "46  1  1  1  1  1  0  1  1  0  1  ...   1   1   1   1   1   1   1   \n",
       "47  1  1  1  1  1  1  1  1  1  0  ...   1   0   1   1   1   1   1   \n",
       "48  1  1  1  1  1  1  1  1  1  1  ...   0   1   1   1   1   0   1   \n",
       "49  1  1  0  1  1  1  1  0  1  1  ...   1   1   1   1   1   1   1   \n",
       "\n",
       "    chain_break_fraction  energy  num_occurrences  \n",
       "0                    0.0   -22.0                1  \n",
       "1                    0.0   -22.0                4  \n",
       "2                    0.0   -22.0                4  \n",
       "3                    0.0   -22.0                7  \n",
       "4                    0.0   -22.0                1  \n",
       "5                    0.0   -22.0                4  \n",
       "6                    0.0   -22.0                1  \n",
       "7                    0.0   -22.0                3  \n",
       "8                    0.0   -22.0                1  \n",
       "9                    0.0   -22.0                2  \n",
       "10                   0.0   -22.0                4  \n",
       "11                   0.0   -22.0                3  \n",
       "12                   0.0   -22.0                2  \n",
       "13                   0.0   -22.0                2  \n",
       "14                   0.0   -22.0                6  \n",
       "15                   0.0   -22.0                2  \n",
       "16                   0.0   -22.0                1  \n",
       "17                   0.0   -22.0                2  \n",
       "18                   0.0   -22.0                5  \n",
       "19                   0.0   -22.0                2  \n",
       "20                   0.0   -22.0                2  \n",
       "21                   0.0   -22.0                1  \n",
       "22                   0.0   -22.0                2  \n",
       "23                   0.0   -22.0                2  \n",
       "24                   0.0   -22.0                1  \n",
       "25                   0.0   -21.0                1  \n",
       "26                   0.0   -21.0                1  \n",
       "27                   0.0   -21.0                2  \n",
       "28                   0.0   -21.0                1  \n",
       "29                   0.0   -21.0                3  \n",
       "30                   0.0   -21.0                2  \n",
       "31                   0.0   -21.0                4  \n",
       "32                   0.0   -21.0                4  \n",
       "33                   0.0   -21.0                1  \n",
       "34                   0.0   -21.0                2  \n",
       "35                   0.0   -21.0                1  \n",
       "36                   0.0   -21.0                2  \n",
       "37                   0.0   -21.0                3  \n",
       "38                   0.0   -21.0                2  \n",
       "39                   0.0   -21.0                1  \n",
       "40                   0.0   -21.0                1  \n",
       "41                   0.0   -21.0                1  \n",
       "42                   0.0   -21.0                3  \n",
       "43                   0.0   -21.0                4  \n",
       "44                   0.0   -21.0                9  \n",
       "45                   0.0   -21.0                1  \n",
       "46                   0.0   -21.0                2  \n",
       "47                   0.0   -21.0                3  \n",
       "48                   0.0   -21.0                1  \n",
       "49                   0.0   -21.0                1  \n",
       "\n",
       "[50 rows x 21 columns]"
      ]
     },
     "execution_count": 229,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head(50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 529,
   "id": "6b6244c2",
   "metadata": {},
   "outputs": [],
   "source": [
    "array_2v = df[df['energy' ] <0.].iloc[: , :n_atoms].to_numpy()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "25305965",
   "metadata": {},
   "source": [
    "#### 3 vacancies"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 442,
   "id": "2f9afbe4",
   "metadata": {},
   "outputs": [],
   "source": [
    "from dimod import BinaryQuadraticModel\n",
    "from dwave.system import EmbeddingComposite, DWaveSampler\n",
    "\n",
    "X = np.arange(graphene_supercell.num_sites)\n",
    "\n",
    "Q = np.triu(-adjacency_matrix.astype(int),0)\n",
    "bqm = BinaryQuadraticModel.from_qubo(Q)\n",
    "\n",
    "c_n_vacancies = [(i,1) for i in X]\n",
    "\n",
    "num_vacancies = 3\n",
    "\n",
    "bqm.add_linear_equality_constraint(\n",
    "        c_n_vacancies,\n",
    "        constant= -(graphene_supercell.num_sites-num_vacancies),\n",
    "        lagrange_multiplier = 1000\n",
    "        )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 443,
   "id": "efa0c528",
   "metadata": {},
   "outputs": [],
   "source": [
    "sampler = EmbeddingComposite(DWaveSampler())\n",
    "#sampleset_3v = sampler.sample(bqm, num_reads = 1000, label='Example - Simple Ocean Programs: BQM')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 444,
   "id": "9db8898e",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_3v = sampleset_3v.to_pandas_dataframe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 445,
   "id": "bf369da2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>10</th>\n",
       "      <th>11</th>\n",
       "      <th>12</th>\n",
       "      <th>13</th>\n",
       "      <th>14</th>\n",
       "      <th>15</th>\n",
       "      <th>16</th>\n",
       "      <th>17</th>\n",
       "      <th>energy</th>\n",
       "      <th>num_occurrences</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-18.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-18.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-19.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-18.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-18.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>995</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-19.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>996</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-19.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>997</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-18.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>998</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-19.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>999</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-18.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1000 rows × 20 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     0  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  energy  \\\n",
       "0    1  0  0  1  1  1  1  1  1  1   1   1   1   0   1   1   1   1   -18.0   \n",
       "1    1  1  1  0  0  0  1  1  1  1   1   1   1   1   1   1   1   1   -18.0   \n",
       "2    0  1  1  1  1  0  1  1  1  1   0   1   1   1   1   1   1   1   -19.0   \n",
       "3    1  0  1  0  1  1  0  1  1  1   1   1   1   1   1   1   1   1   -18.0   \n",
       "4    0  1  1  1  1  0  1  1  0  1   1   1   1   1   1   1   1   1   -18.0   \n",
       "..  .. .. .. .. .. .. .. .. .. ..  ..  ..  ..  ..  ..  ..  ..  ..     ...   \n",
       "995  1  1  1  0  1  0  1  1  1  1   1   1   1   0   1   1   1   1   -19.0   \n",
       "996  1  1  1  1  0  1  1  1  1  1   1   1   1   0   1   0   1   1   -19.0   \n",
       "997  1  1  1  0  0  1  1  0  1  1   1   1   1   1   1   1   1   1   -18.0   \n",
       "998  0  1  1  1  1  0  1  1  1  1   1   1   1   1   1   0   1   1   -19.0   \n",
       "999  1  1  1  1  1  1  1  0  1  0   1   0   1   1   1   1   1   1   -18.0   \n",
       "\n",
       "     num_occurrences  \n",
       "0                  1  \n",
       "1                  1  \n",
       "2                  1  \n",
       "3                  1  \n",
       "4                  1  \n",
       "..               ...  \n",
       "995                1  \n",
       "996                1  \n",
       "997                1  \n",
       "998                1  \n",
       "999                1  \n",
       "\n",
       "[1000 rows x 20 columns]"
      ]
     },
     "execution_count": 445,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_3v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 452,
   "id": "fef49483",
   "metadata": {},
   "outputs": [],
   "source": [
    "df = copy.deepcopy(df_3v)\n",
    "min_energy = min(df['energy' ])\n",
    "energies_unique = np.unique(df['energy' ])\n",
    "n_atoms = graphene_supercell.num_sites \n",
    "df_3v_low = df[df['energy' ] == min_energy].iloc[: , :n_atoms]\n",
    "#array_3v = df[df['energy' ] == min_energy].iloc[: , :n_atoms].to_numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 447,
   "id": "18d3cf95",
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>10</th>\n",
       "      <th>11</th>\n",
       "      <th>12</th>\n",
       "      <th>13</th>\n",
       "      <th>14</th>\n",
       "      <th>15</th>\n",
       "      <th>16</th>\n",
       "      <th>17</th>\n",
       "      <th>energy</th>\n",
       "      <th>num_occurrences</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-18.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-18.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-19.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-18.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-18.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>-18.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>-19.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-18.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>-19.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-19.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-18.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-18.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-19.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-18.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-18.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-19.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>-18.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>-18.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-18.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-20.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-19.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-19.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-18.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>-18.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-18.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-19.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>-18.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-19.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-18.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>-19.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>-18.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-19.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-18.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-19.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>-18.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-18.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>-18.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-19.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-19.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>-18.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>-18.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-19.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-19.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-19.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-19.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-18.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-19.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>-20.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-19.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-18.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    0  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  energy  \\\n",
       "0   1  0  0  1  1  1  1  1  1  1   1   1   1   0   1   1   1   1   -18.0   \n",
       "1   1  1  1  0  0  0  1  1  1  1   1   1   1   1   1   1   1   1   -18.0   \n",
       "2   0  1  1  1  1  0  1  1  1  1   0   1   1   1   1   1   1   1   -19.0   \n",
       "3   1  0  1  0  1  1  0  1  1  1   1   1   1   1   1   1   1   1   -18.0   \n",
       "4   0  1  1  1  1  0  1  1  0  1   1   1   1   1   1   1   1   1   -18.0   \n",
       "5   1  1  1  0  0  1  1  1  1  1   1   1   1   1   1   1   0   1   -18.0   \n",
       "6   1  1  1  0  1  1  1  0  1  1   1   1   1   1   1   1   1   0   -19.0   \n",
       "7   0  1  1  1  1  1  1  1  1  1   1   0   1   1   0   1   1   1   -18.0   \n",
       "8   0  1  1  1  1  1  1  1  1  0   1   1   1   1   1   1   0   1   -19.0   \n",
       "9   1  1  1  1  1  1  1  0  1  1   0   1   1   0   1   1   1   1   -19.0   \n",
       "10  1  1  1  1  1  1  1  1  1  0   1   0   1   1   0   1   1   1   -18.0   \n",
       "11  0  1  1  0  1  1  1  0  1  1   1   1   1   1   1   1   1   1   -18.0   \n",
       "12  0  1  0  1  1  1  1  1  1  1   1   0   1   1   1   1   1   1   -19.0   \n",
       "13  1  1  1  1  1  1  1  1  1  1   1   1   0   0   1   0   1   1   -18.0   \n",
       "14  1  1  1  1  1  1  1  1  0  0   0   1   1   1   1   1   1   1   -18.0   \n",
       "15  1  1  0  1  0  1  1  1  1  1   0   1   1   1   1   1   1   1   -19.0   \n",
       "16  1  1  1  1  0  1  1  1  1  1   1   1   0   1   1   1   1   0   -18.0   \n",
       "17  0  1  1  1  1  1  1  1  1  1   1   1   1   0   1   1   0   1   -18.0   \n",
       "18  0  0  1  1  1  1  1  1  1  1   1   1   1   1   0   1   1   1   -18.0   \n",
       "19  1  1  1  1  1  1  0  1  1  1   1   1   0   1   1   0   1   1   -20.0   \n",
       "20  1  1  1  1  1  0  1  0  1  1   1   1   1   0   1   1   1   1   -19.0   \n",
       "21  1  1  1  0  1  1  1  1  0  0   1   1   1   1   1   1   1   1   -19.0   \n",
       "22  1  1  1  1  1  1  1  0  1  1   0   1   1   1   0   1   1   1   -18.0   \n",
       "23  1  1  1  1  0  1  1  1  1  1   1   1   1   1   1   0   0   1   -18.0   \n",
       "24  1  1  0  1  1  1  1  0  1  1   0   1   1   1   1   1   1   1   -18.0   \n",
       "25  1  1  0  1  1  1  1  1  0  1   1   1   1   1   1   0   1   1   -19.0   \n",
       "26  0  1  1  1  1  1  1  1  1  1   1   1   1   1   0   1   0   1   -18.0   \n",
       "27  1  0  1  1  1  1  1  1  1  1   0   1   1   1   1   0   1   1   -19.0   \n",
       "28  1  0  1  1  1  1  1  1  1  0   1   1   1   1   0   1   1   1   -18.0   \n",
       "29  1  1  1  1  1  1  1  1  0  1   1   1   1   1   1   1   0   0   -19.0   \n",
       "30  1  1  0  1  1  1  1  1  1  1   1   1   1   0   1   1   0   1   -18.0   \n",
       "31  1  1  1  1  1  1  1  0  0  1   1   1   1   1   0   1   1   1   -19.0   \n",
       "32  1  1  0  1  0  1  1  0  1  1   1   1   1   1   1   1   1   1   -18.0   \n",
       "33  1  1  1  1  1  1  1  0  1  1   1   1   0   0   1   1   1   1   -19.0   \n",
       "34  1  1  1  1  1  0  1  1  1  1   1   1   1   0   1   1   1   0   -18.0   \n",
       "35  1  0  0  0  1  1  1  1  1  1   1   1   1   1   1   1   1   1   -18.0   \n",
       "36  1  1  1  1  1  1  1  1  1  1   1   0   1   1   0   1   0   1   -18.0   \n",
       "37  1  1  1  1  1  1  0  0  1  1   1   1   0   1   1   1   1   1   -19.0   \n",
       "38  1  0  1  1  1  1  1  1  1  1   1   0   0   1   1   1   1   1   -19.0   \n",
       "39  1  1  1  1  1  0  1  1  1  0   1   1   1   1   1   1   1   0   -18.0   \n",
       "40  1  1  1  1  1  1  1  1  1  1   1   1   1   1   0   0   1   0   -18.0   \n",
       "41  0  1  1  1  1  1  1  1  1  0   1   0   1   1   1   1   1   1   -19.0   \n",
       "42  1  1  0  1  1  0  1  1  1  0   1   1   1   1   1   1   1   1   -19.0   \n",
       "43  1  1  1  1  1  0  1  1  1  1   1   1   0   1   1   0   1   1   -19.0   \n",
       "44  1  1  1  1  1  0  1  0  1  1   1   1   1   1   0   1   1   1   -19.0   \n",
       "45  1  0  1  1  1  1  1  1  1  1   1   1   0   1   1   0   1   1   -18.0   \n",
       "46  1  1  0  1  1  1  1  1  0  1   1   1   1   1   1   0   1   1   -19.0   \n",
       "47  1  1  1  1  1  1  1  0  0  1   1   1   1   1   1   1   1   0   -20.0   \n",
       "48  1  1  1  1  1  1  0  0  1  1   1   1   0   1   1   1   1   1   -19.0   \n",
       "49  1  1  1  1  1  1  0  1  1  0   0   1   1   1   1   1   1   1   -18.0   \n",
       "\n",
       "    num_occurrences  \n",
       "0                 1  \n",
       "1                 1  \n",
       "2                 1  \n",
       "3                 1  \n",
       "4                 1  \n",
       "5                 1  \n",
       "6                 1  \n",
       "7                 1  \n",
       "8                 1  \n",
       "9                 1  \n",
       "10                1  \n",
       "11                1  \n",
       "12                1  \n",
       "13                1  \n",
       "14                1  \n",
       "15                1  \n",
       "16                1  \n",
       "17                1  \n",
       "18                1  \n",
       "19                1  \n",
       "20                1  \n",
       "21                1  \n",
       "22                1  \n",
       "23                1  \n",
       "24                1  \n",
       "25                1  \n",
       "26                1  \n",
       "27                1  \n",
       "28                1  \n",
       "29                1  \n",
       "30                1  \n",
       "31                1  \n",
       "32                1  \n",
       "33                1  \n",
       "34                1  \n",
       "35                1  \n",
       "36                1  \n",
       "37                1  \n",
       "38                1  \n",
       "39                1  \n",
       "40                1  \n",
       "41                1  \n",
       "42                1  \n",
       "43                1  \n",
       "44                1  \n",
       "45                1  \n",
       "46                1  \n",
       "47                1  \n",
       "48                1  \n",
       "49                1  "
      ]
     },
     "execution_count": 447,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head(50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 461,
   "id": "03b68c61",
   "metadata": {},
   "outputs": [],
   "source": [
    "array_3v = df[df['energy' ] <0.].iloc[: , :n_atoms].to_numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 457,
   "id": "4563a841",
   "metadata": {},
   "outputs": [],
   "source": [
    "array_3v = df.to_numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 460,
   "id": "7f961da0",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([-20., -19., -18., 984.]),\n",
       " array([ 19,   2,   0, 599]),\n",
       " array([ 54, 392, 553,   1]))"
      ]
     },
     "execution_count": 460,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.unique(array_3v[:,18],return_counts=True,return_index=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "609247f8",
   "metadata": {},
   "source": [
    "### Add num of bonds constraint"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "36d7b0f0",
   "metadata": {},
   "outputs": [],
   "source": [
    "from dimod import BinaryQuadraticModel\n",
    "from dwave.system import EmbeddingComposite, DWaveSampler\n",
    "\n",
    "X = np.arange(graphene_supercell.num_sites)\n",
    "\n",
    "Q = np.triu(-adjacency_matrix.astype(int),0)\n",
    "bqm = BinaryQuadraticModel.from_qubo(Q)\n",
    "\n",
    "c_n_vacancies = [(i,1) for i in X]\n",
    "\n",
    "num_vacancies = 2\n",
    "\n",
    "#print(bqm.to_numpy_matrix())\n",
    "bqm.add_linear_equality_constraint(\n",
    "        c_n_vacancies,\n",
    "        constant= -(graphene_supercell.num_sites-num_vacancies),\n",
    "        lagrange_multiplier = 10\n",
    "        )\n",
    "\n",
    "for i in range(graphene_supercell.num_sites):\n",
    "    c_n_bonds = [(i,adjacency_matrix.astype(int)[j,i]) for j in X]\n",
    "    #print(c_n_bonds)\n",
    "    bqm.add_linear_inequality_constraint(\n",
    "        c_n_bonds,\n",
    "        lb= -2, \n",
    "        lagrange_multiplier=1,\n",
    "        label = 'Min bonds_'+str(i)\n",
    "    )\n",
    "\n",
    "#bqm.to_numpy_vectors()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "id": "23f2a9f5",
   "metadata": {},
   "outputs": [],
   "source": [
    "sampler = EmbeddingComposite(DWaveSampler())\n",
    "sampleset_2v_b = sampler.sample(bqm, num_reads = 100,  label='2 vacancies, min bonds')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "id": "b428927b",
   "metadata": {},
   "outputs": [],
   "source": [
    "sampleset_2v_b_df = sampleset_2v_b.to_pandas_dataframe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "id": "a099dae2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>...</th>\n",
       "      <th>11</th>\n",
       "      <th>12</th>\n",
       "      <th>13</th>\n",
       "      <th>14</th>\n",
       "      <th>15</th>\n",
       "      <th>16</th>\n",
       "      <th>17</th>\n",
       "      <th>chain_break_fraction</th>\n",
       "      <th>energy</th>\n",
       "      <th>num_occurrences</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>122.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>123.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>123.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>123.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>123.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>88</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.055556</td>\n",
       "      <td>123.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>89</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>151.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>90</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>151.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>91</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>151.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>92</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>151.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>93 rows × 21 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    0  1  2  3  4  5  6  7  8  9  ...  11  12  13  14  15  16  17  \\\n",
       "0   1  1  1  1  1  0  1  1  1  1  ...   1   1   1   0   1   1   1   \n",
       "1   1  1  1  1  1  1  0  1  1  1  ...   1   1   1   1   1   1   0   \n",
       "2   1  1  1  1  1  1  1  1  1  0  ...   1   1   0   1   1   1   1   \n",
       "3   0  1  1  1  1  1  0  1  1  1  ...   1   1   1   1   1   1   1   \n",
       "4   1  1  1  1  1  1  1  1  1  1  ...   1   0   1   1   1   1   0   \n",
       ".. .. .. .. .. .. .. .. .. .. ..  ...  ..  ..  ..  ..  ..  ..  ..   \n",
       "88  1  0  1  0  1  1  1  1  1  1  ...   1   1   1   1   1   1   1   \n",
       "89  1  1  1  1  1  1  1  1  1  1  ...   1   0   1   0   0   0   1   \n",
       "90  1  1  1  0  1  1  1  1  1  1  ...   0   1   1   0   0   1   1   \n",
       "91  1  1  1  1  0  1  0  1  0  0  ...   1   1   1   1   1   1   1   \n",
       "92  1  1  1  0  1  1  1  1  1  1  ...   0   1   1   1   0   0   1   \n",
       "\n",
       "    chain_break_fraction  energy  num_occurrences  \n",
       "0               0.000000   122.0                1  \n",
       "1               0.000000   123.0                1  \n",
       "2               0.000000   123.0                1  \n",
       "3               0.000000   123.0                1  \n",
       "4               0.000000   123.0                1  \n",
       "..                   ...     ...              ...  \n",
       "88              0.055556   123.0                1  \n",
       "89              0.000000   151.0                1  \n",
       "90              0.000000   151.0                1  \n",
       "91              0.000000   151.0                1  \n",
       "92              0.000000   151.0                1  \n",
       "\n",
       "[93 rows x 21 columns]"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sampleset_2v_b_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "id": "456a197b",
   "metadata": {},
   "outputs": [],
   "source": [
    "config_vector = sampleset_2v_b_df[sampleset_2v_b_df['chain_break_fraction'] == 0.].iloc[:,0:18].to_numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "id": "f08dff30",
   "metadata": {},
   "outputs": [],
   "source": [
    "E_vector = sampleset_2v_b_df[sampleset_2v_b_df['chain_break_fraction'] == 0.]['energy'].to_numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "id": "1266c1a5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([16, 16, 16, 16, 16, 16, 16, 16, 16, 15, 15, 15, 15, 15, 15, 15, 15,\n",
       "       15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,\n",
       "       15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,\n",
       "       15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,\n",
       "       15, 15, 17, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14])"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(config_vector,axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "id": "2032fbee",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([122., 123., 125., 126., 127., 139., 148., 149., 150., 151.]),\n",
       " array([ 0,  1,  9, 17, 35, 70, 71, 72, 74, 77]),\n",
       " array([ 1,  8,  8, 18, 35,  1,  1,  2,  3,  4]))"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.unique(E_vector,return_index=True,return_counts=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "id": "4ebbf22d",
   "metadata": {},
   "outputs": [],
   "source": [
    "c = copy.deepcopy(graphene_supercell)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "id": "7afc2aa4",
   "metadata": {},
   "outputs": [],
   "source": [
    "d = np.where(config_vector[17] == 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "id": "068e9a13",
   "metadata": {},
   "outputs": [],
   "source": [
    "c.replace(d[0][0],1)\n",
    "c.replace(d[0][1],1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "id": "1abbb3d6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Popen: returncode: None args: ['/Users/brunocamino/miniconda3/envs/qc/bin/p...>"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "view(AseAtomsAdaptor().get_atoms(c))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e4ed2bb9",
   "metadata": {},
   "source": [
    "### Add num of bonds as an objective\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 337,
   "id": "300b5aac",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Unonstrained quadratic model + contraints used\n"
     ]
    }
   ],
   "source": [
    "bqm = build_quadratic_model(graphene_supercell,num_vacancies=2)\n",
    "dataframe, config, energy = run_anneal(bqm,num_reads=100, return_config_E=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 257,
   "id": "31d3a61f",
   "metadata": {},
   "outputs": [],
   "source": [
    "from dimod import BinaryQuadraticModel\n",
    "from dwave.system import EmbeddingComposite, DWaveSampler\n",
    "\n",
    "X = np.arange(graphene_supercell.num_sites)\n",
    "\n",
    "Q = np.triu(-10*adjacency_matrix.astype(int),0)\n",
    "bqm = BinaryQuadraticModel.from_qubo(Q)\n",
    "\n",
    "'''for i in range(graphene_supercell.num_sites):    \n",
    "    for j in range(graphene_supercell.num_sites):\n",
    "        bqm.add_variable(X[i],-0.1*adjacency_matrix[i,j])'''\n",
    "\n",
    "for i in range(graphene_supercell.num_sites):  \n",
    "    #print(i)\n",
    "    neighbours = np.where(adjacency_matrix[i,:] == 1)[0]\n",
    "    for j in range(len(neighbours)):\n",
    "        for k in range(len(neighbours)):\n",
    "            if k > j:\n",
    "                #print(neighbours[j],neighbours[k])\n",
    "                bqm.add_interaction(X[neighbours[j]],X[neighbours[k]],1)\n",
    "        \n",
    "c_n_vacancies = [(i,1) for i in X]\n",
    "\n",
    "num_vacancies = 3\n",
    "\n",
    "#print(bqm.to_numpy_matrix())\n",
    "bqm.add_linear_equality_constraint(\n",
    "        c_n_vacancies,\n",
    "        constant= -(graphene_supercell.num_sites-num_vacancies),\n",
    "        lagrange_multiplier = 1000\n",
    "        )\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 258,
   "id": "2e4a256c",
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/f2/8kc7y9697m59bwltxjd42y300000gn/T/ipykernel_3075/185314096.py:1: DeprecationWarning: bqm.to_numpy_matrix() is deprecated since dimod 0.10.0 and will be removed in 0.12.0\n",
      "  bqm.to_numpy_matrix()\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[-29000.,   2001.,   2001.,   2001.,   2001.,   2000.,   2001.,\n",
       "          2000.,   2001.,   1990.,   1990.,   2000.,   2000.,   2000.,\n",
       "          2000.,   1990.,   2000.,   2000.],\n",
       "       [     0., -29000.,   2001.,   2000.,   2001.,   2001.,   2001.,\n",
       "          2001.,   2000.,   2000.,   1990.,   1990.,   2000.,   2000.,\n",
       "          2000.,   2000.,   1990.,   2000.],\n",
       "       [     0.,      0., -29000.,   2001.,   2000.,   2001.,   2000.,\n",
       "          2001.,   2001.,   1990.,   2000.,   1990.,   2000.,   2000.,\n",
       "          2000.,   2000.,   2000.,   1990.],\n",
       "       [     0.,      0.,      0., -29000.,   2001.,   2001.,   2001.,\n",
       "          2001.,   2000.,   1990.,   2000.,   2000.,   1990.,   1990.,\n",
       "          2000.,   2000.,   2000.,   2000.],\n",
       "       [     0.,      0.,      0.,      0., -29000.,   2001.,   2000.,\n",
       "          2001.,   2001.,   2000.,   1990.,   2000.,   2000.,   1990.,\n",
       "          1990.,   2000.,   2000.,   2000.],\n",
       "       [     0.,      0.,      0.,      0.,      0., -29000.,   2001.,\n",
       "          2000.,   2001.,   2000.,   2000.,   1990.,   1990.,   2000.,\n",
       "          1990.,   2000.,   2000.,   2000.],\n",
       "       [     0.,      0.,      0.,      0.,      0.,      0., -29000.,\n",
       "          2001.,   2001.,   2000.,   2000.,   2000.,   1990.,   2000.,\n",
       "          2000.,   1990.,   1990.,   2000.],\n",
       "       [     0.,      0.,      0.,      0.,      0.,      0.,      0.,\n",
       "        -29000.,   2001.,   2000.,   2000.,   2000.,   2000.,   1990.,\n",
       "          2000.,   2000.,   1990.,   1990.],\n",
       "       [     0.,      0.,      0.,      0.,      0.,      0.,      0.,\n",
       "             0., -29000.,   2000.,   2000.,   2000.,   2000.,   2000.,\n",
       "          1990.,   1990.,   2000.,   1990.],\n",
       "       [     0.,      0.,      0.,      0.,      0.,      0.,      0.,\n",
       "             0.,      0., -29000.,   2001.,   2001.,   2001.,   2001.,\n",
       "          2000.,   2001.,   2000.,   2001.],\n",
       "       [     0.,      0.,      0.,      0.,      0.,      0.,      0.,\n",
       "             0.,      0.,      0., -29000.,   2001.,   2000.,   2001.,\n",
       "          2001.,   2001.,   2001.,   2000.],\n",
       "       [     0.,      0.,      0.,      0.,      0.,      0.,      0.,\n",
       "             0.,      0.,      0.,      0., -29000.,   2001.,   2000.,\n",
       "          2001.,   2000.,   2001.,   2001.],\n",
       "       [     0.,      0.,      0.,      0.,      0.,      0.,      0.,\n",
       "             0.,      0.,      0.,      0.,      0., -29000.,   2001.,\n",
       "          2001.,   2001.,   2001.,   2000.],\n",
       "       [     0.,      0.,      0.,      0.,      0.,      0.,      0.,\n",
       "             0.,      0.,      0.,      0.,      0.,      0., -29000.,\n",
       "          2001.,   2000.,   2001.,   2001.],\n",
       "       [     0.,      0.,      0.,      0.,      0.,      0.,      0.,\n",
       "             0.,      0.,      0.,      0.,      0.,      0.,      0.,\n",
       "        -29000.,   2001.,   2000.,   2001.],\n",
       "       [     0.,      0.,      0.,      0.,      0.,      0.,      0.,\n",
       "             0.,      0.,      0.,      0.,      0.,      0.,      0.,\n",
       "             0., -29000.,   2001.,   2001.],\n",
       "       [     0.,      0.,      0.,      0.,      0.,      0.,      0.,\n",
       "             0.,      0.,      0.,      0.,      0.,      0.,      0.,\n",
       "             0.,      0., -29000.,   2001.],\n",
       "       [     0.,      0.,      0.,      0.,      0.,      0.,      0.,\n",
       "             0.,      0.,      0.,      0.,      0.,      0.,      0.,\n",
       "             0.,      0.,      0., -29000.]])"
      ]
     },
     "execution_count": 258,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bqm.to_numpy_matrix()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 271,
   "id": "9193b6c1",
   "metadata": {},
   "outputs": [],
   "source": [
    "sampler = EmbeddingComposite(DWaveSampler())\n",
    "sampleset_2v_b = sampler.sample(bqm, num_reads = 1000,  label='2 vacancies, min bonds')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 272,
   "id": "01fb53d4",
   "metadata": {},
   "outputs": [],
   "source": [
    "sampleset_2v_b_df = sampleset_2v_b.to_pandas_dataframe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 273,
   "id": "b7c1e4bc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>...</th>\n",
       "      <th>11</th>\n",
       "      <th>12</th>\n",
       "      <th>13</th>\n",
       "      <th>14</th>\n",
       "      <th>15</th>\n",
       "      <th>16</th>\n",
       "      <th>17</th>\n",
       "      <th>chain_break_fraction</th>\n",
       "      <th>energy</th>\n",
       "      <th>num_occurrences</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0.055556</td>\n",
       "      <td>-154.0</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0.055556</td>\n",
       "      <td>-154.0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0.055556</td>\n",
       "      <td>-153.0</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0.055556</td>\n",
       "      <td>-153.0</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0.055556</td>\n",
       "      <td>-153.0</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>807</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.055556</td>\n",
       "      <td>870.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>808</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0.055556</td>\n",
       "      <td>885.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>809</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.055556</td>\n",
       "      <td>862.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>810</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0.055556</td>\n",
       "      <td>871.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>811</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0.166667</td>\n",
       "      <td>-143.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>812 rows × 21 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     0  1  2  3  4  5  6  7  8  9  ...  11  12  13  14  15  16  17  \\\n",
       "0    1  1  0  1  0  1  1  1  1  1  ...   1   1   1   1   1   1   0   \n",
       "1    1  0  1  0  1  1  1  1  1  1  ...   1   1   1   1   1   0   1   \n",
       "2    1  0  0  1  1  1  1  1  1  1  ...   1   1   1   1   1   1   0   \n",
       "3    1  0  0  1  1  1  1  1  1  1  ...   1   1   1   1   1   0   1   \n",
       "4    1  0  1  1  0  1  1  1  1  1  ...   1   1   1   1   1   0   1   \n",
       "..  .. .. .. .. .. .. .. .. .. ..  ...  ..  ..  ..  ..  ..  ..  ..   \n",
       "807  1  1  0  1  0  1  0  1  1  1  ...   1   0   1   1   1   1   1   \n",
       "808  1  1  1  1  1  1  1  1  1  1  ...   0   0   1   0   1   0   1   \n",
       "809  1  1  0  0  1  1  1  1  1  0  ...   1   1   1   1   0   1   1   \n",
       "810  1  0  1  1  1  1  1  1  0  1  ...   1   0   1   1   1   0   1   \n",
       "811  1  0  1  1  1  1  1  1  1  1  ...   1   1   1   0   1   1   0   \n",
       "\n",
       "     chain_break_fraction  energy  num_occurrences  \n",
       "0                0.055556  -154.0                5  \n",
       "1                0.055556  -154.0                2  \n",
       "2                0.055556  -153.0                5  \n",
       "3                0.055556  -153.0                6  \n",
       "4                0.055556  -153.0                4  \n",
       "..                    ...     ...              ...  \n",
       "807              0.055556   870.0                1  \n",
       "808              0.055556   885.0                1  \n",
       "809              0.055556   862.0                1  \n",
       "810              0.055556   871.0                1  \n",
       "811              0.166667  -143.0                1  \n",
       "\n",
       "[812 rows x 21 columns]"
      ]
     },
     "execution_count": 273,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sampleset_2v_b_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 274,
   "id": "b04e2ad6",
   "metadata": {},
   "outputs": [],
   "source": [
    "config_vector = sampleset_2v_b_df[sampleset_2v_b_df['chain_break_fraction'] == 0.].iloc[:,0:18].to_numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 275,
   "id": "de7c99ea",
   "metadata": {},
   "outputs": [],
   "source": [
    "E_vector = sampleset_2v_b_df[sampleset_2v_b_df['chain_break_fraction'] == 0.]['energy'].to_numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 276,
   "id": "ad98b327",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,\n",
       "       15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,\n",
       "       15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,\n",
       "       15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,\n",
       "       15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,\n",
       "       15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,\n",
       "       15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,\n",
       "       15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,\n",
       "       15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,\n",
       "       15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,\n",
       "       15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,\n",
       "       15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,\n",
       "       15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,\n",
       "       15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,\n",
       "       15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,\n",
       "       15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,\n",
       "       15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16,\n",
       "       16, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,\n",
       "       14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,\n",
       "       14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,\n",
       "       14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,\n",
       "       14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,\n",
       "       14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,\n",
       "       14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,\n",
       "       14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,\n",
       "       14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,\n",
       "       14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,\n",
       "       14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,\n",
       "       14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,\n",
       "       14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,\n",
       "       14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,\n",
       "       14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,\n",
       "       14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,\n",
       "       14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,\n",
       "       14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,\n",
       "       14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,\n",
       "       14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,\n",
       "       14, 14, 14, 14, 14, 14, 14, 14, 14, 13, 13, 13, 13, 13, 13, 13, 13,\n",
       "       13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13,\n",
       "       13, 13, 13, 13, 13, 13])"
      ]
     },
     "execution_count": 276,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(config_vector,axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 277,
   "id": "1177c712",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([-163., -154., -153., -144., -143., -142., -141.,  822.,  832.,\n",
       "         833.,  852.,  853.,  860.,  861.,  862.,  863.,  870.,  871.,\n",
       "         872.,  873.,  881.,  882.,  883.,  884.,  885., 3867., 3868.,\n",
       "        3877., 3878., 3884., 3885., 3886., 3887., 3888., 3896., 3897.,\n",
       "        3899., 3907., 3908., 3912.]),\n",
       " array([  0,  22,  48, 135, 153, 229, 259, 277, 278, 286, 290, 302, 304,\n",
       "        306, 344, 388, 404, 413, 434, 530, 558, 560, 587, 607, 614, 638,\n",
       "        639, 640, 644, 645, 646, 647, 648, 651, 652, 653, 661, 665, 666,\n",
       "        667]),\n",
       " array([22, 26, 87, 18, 76, 30, 18,  1,  8,  4, 12,  2,  2, 38, 44, 16,  9,\n",
       "        21, 96, 28,  2, 27, 20,  7, 24,  1,  1,  4,  1,  1,  1,  1,  3,  1,\n",
       "         1,  8,  4,  1,  1,  2]))"
      ]
     },
     "execution_count": 277,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.unique(E_vector,return_index=True,return_counts=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 279,
   "id": "337ce5d8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Popen: returncode: None args: ['/Users/brunocamino/miniconda3/envs/qc/bin/p...>"
      ]
     },
     "execution_count": 279,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = 259\n",
    "c = copy.deepcopy(graphene_supercell)\n",
    "\n",
    "d = np.where(config_vector[a] == 0)\n",
    "\n",
    "c.replace(d[0][0],1)\n",
    "c.replace(d[0][1],1)\n",
    "c.replace(d[0][2],1)\n",
    "\n",
    "view(AseAtomsAdaptor().get_atoms(c))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "id": "4b4781b1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Popen: returncode: None args: ['/Users/brunocamino/miniconda3/envs/qc/bin/p...>"
      ]
     },
     "execution_count": 176,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "view(AseAtomsAdaptor().get_atoms(c))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "id": "378fc984",
   "metadata": {},
   "outputs": [],
   "source": [
    "from dimod import BinaryQuadraticModel\n",
    "from dwave.system import EmbeddingComposite, DWaveSampler\n",
    "\n",
    "X = np.arange(graphene_supercell.num_sites)\n",
    "\n",
    "Q = np.triu(-adjacency_matrix.astype(int),0)\n",
    "bqm = BinaryQuadraticModel.from_qubo(Q)\n",
    "\n",
    "for i in range(graphene_supercell.num_sites):    \n",
    "    for j in range(graphene_supercell.num_sites):\n",
    "        bqm.add_variable(X[i],-adjacency_matrix[i,j])\n",
    "\n",
    "\n",
    "c_n_vacancies = [(i,1) for i in X]\n",
    "\n",
    "num_vacancies = 2\n",
    "\n",
    "#print(bqm.to_numpy_matrix())\n",
    "bqm.add_linear_equality_constraint(\n",
    "        c_n_vacancies,\n",
    "        constant= -(graphene_supercell.num_sites-num_vacancies),\n",
    "        lagrange_multiplier = 1000\n",
    "        )\n",
    "sampler = EmbeddingComposite(DWaveSampler())\n",
    "sampleset_2v_b = sampler.sample(bqm, num_reads = 100,  label='2 vacancies, min bonds')\n",
    "\n",
    "sampleset_2v_b_df = sampleset_2v_b.to_pandas_dataframe()\n",
    "\n",
    "sampleset_2v_b_df\n",
    "\n",
    "config_vector = sampleset_2v_b_df[sampleset_2v_b_df['chain_break_fraction'] == 0.].iloc[:,0:18].to_numpy()\n",
    "\n",
    "E_vector = sampleset_2v_b_df[sampleset_2v_b_df['chain_break_fraction'] == 0.]['energy'].to_numpy()\n",
    "\n",
    "np.sum(config_vector,axis=1)\n",
    "\n",
    "np.unique(E_vector,return_index=True,return_counts=True)\n",
    "\n",
    "c = copy.deepcopy(graphene_supercell)\n",
    "\n",
    "d = np.where(config_vector[17] == 0)\n",
    "\n",
    "c.replace(d[0][0],1)\n",
    "c.replace(d[0][1],1)\n",
    "\n",
    "view(AseAtomsAdaptor().get_atoms(c))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "31e72835",
   "metadata": {},
   "source": [
    "## Constrained Quadratic Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 300,
   "id": "e20621b8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Num vacancies'"
      ]
     },
     "execution_count": 300,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from dimod import ConstrainedQuadraticModel, Binary, quicksum\n",
    "from dwave.system import LeapHybridCQMSampler\n",
    "\n",
    "cqm = ConstrainedQuadraticModel()\n",
    "\n",
    "atoms = [Binary(i) for i in range(graphene_supercell.num_sites)]\n",
    "\n",
    "atoms = np.array(atoms)\n",
    "\n",
    "Q = np.triu(-adjacency_matrix.astype(int),0)\n",
    "bqm = BinaryQuadraticModel.from_qubo(Q)\n",
    "\n",
    "#set the objective (minimise the energy of the adjacency matrix)\n",
    "\n",
    "cqm.set_objective(bqm)\n",
    "\n",
    "num_vacancies = 3\n",
    "\n",
    "#set the constraint: number of vacancies\n",
    "cqm.add_constraint(quicksum(atoms[i] for i in range(graphene_supercell.num_sites)) \\\n",
    "                   == (graphene_supercell.num_sites - num_vacancies), label='Num vacancies')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e9c67ea0",
   "metadata": {},
   "source": [
    "### Constaint min n bonds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 301,
   "id": "4d87b7a7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "BinaryQuadraticModel({0: 3.0}, {}, 0.0, 'BINARY')\n",
      "BinaryQuadraticModel({1: 3.0}, {}, 0.0, 'BINARY')\n",
      "BinaryQuadraticModel({2: 3.0}, {}, 0.0, 'BINARY')\n",
      "BinaryQuadraticModel({3: 3.0}, {}, 0.0, 'BINARY')\n",
      "BinaryQuadraticModel({4: 3.0}, {}, 0.0, 'BINARY')\n",
      "BinaryQuadraticModel({5: 3.0}, {}, 0.0, 'BINARY')\n",
      "BinaryQuadraticModel({6: 3.0}, {}, 0.0, 'BINARY')\n",
      "BinaryQuadraticModel({7: 3.0}, {}, 0.0, 'BINARY')\n",
      "BinaryQuadraticModel({8: 3.0}, {}, 0.0, 'BINARY')\n",
      "BinaryQuadraticModel({9: 3.0}, {}, 0.0, 'BINARY')\n",
      "BinaryQuadraticModel({10: 3.0}, {}, 0.0, 'BINARY')\n",
      "BinaryQuadraticModel({11: 3.0}, {}, 0.0, 'BINARY')\n",
      "BinaryQuadraticModel({12: 3.0}, {}, 0.0, 'BINARY')\n",
      "BinaryQuadraticModel({13: 3.0}, {}, 0.0, 'BINARY')\n",
      "BinaryQuadraticModel({14: 3.0}, {}, 0.0, 'BINARY')\n",
      "BinaryQuadraticModel({15: 3.0}, {}, 0.0, 'BINARY')\n",
      "BinaryQuadraticModel({16: 3.0}, {}, 0.0, 'BINARY')\n",
      "BinaryQuadraticModel({17: 3.0}, {}, 0.0, 'BINARY')\n"
     ]
    }
   ],
   "source": [
    "for i in range(graphene_supercell.num_sites):\n",
    "    print(quicksum(atoms[i]*adjacency_matrix[i]))\n",
    "    cqm.add_constraint(quicksum(atoms[i]*adjacency_matrix[i]) \\\n",
    "                   >= 2, label='Min_coord_'+str(i))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 302,
   "id": "55e6c31b",
   "metadata": {},
   "outputs": [],
   "source": [
    "cqm_sampler = LeapHybridCQMSampler()\n",
    "sampleset = cqm_sampler.sample_cqm(cqm,time_limit=5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 304,
   "id": "557f7682",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Sample(sample={0: 1.0, 1: 1.0, 2: 1.0, 3: 0.0, 4: 1.0, 5: 1.0, 6: 1.0, 7: 1.0, 8: 1.0, 9: 1.0, 10: 1.0, 11: 1.0, 12: 0.0, 13: 1.0, 14: 1.0, 15: 1.0, 16: 1.0, 17: 1.0}, energy=-22.0, num_occurrences=1, is_feasible=False, is_satisfied=array([ True,  True,  True,  True,  True,  True,  True,  True, False,\n",
       "       False, False,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True]))"
      ]
     },
     "execution_count": 304,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sampleset.first"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 216,
   "id": "ddb260c1",
   "metadata": {},
   "outputs": [],
   "source": [
    "cqm_sampler = LeapHybridCQMSampler()\n",
    "sampleset_bonds = cqm_sampler.sample_cqm(cqm,time_limit=5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 224,
   "id": "328e7351",
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SampleSet(rec.array([([1., 1., 1., 1., 1., 1., 1., 0., 1., 1., 1., 1., 1., 1., 1., 1., 0., 0.], -20., 6,  True, [ True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True]),\n",
       "           ([1., 1., 1., 1., 1., 1., 0., 1., 1., 1., 1., 1., 0., 1., 1., 1., 0., 1.], -20., 1,  True, [ True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True]),\n",
       "           ([1., 1., 0., 1., 1., 1., 1., 0., 1., 1., 1., 1., 1., 1., 1., 1., 1., 0.], -20., 2,  True, [ True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True]),\n",
       "           ([0., 1., 1., 1., 1., 1., 1., 1., 1., 0., 0., 1., 1., 1., 1., 1., 1., 1.], -20., 2, False, [False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False,  True, False, False]),\n",
       "           ([1., 1., 0., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 0.], -22., 1, False, [ True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True, False,  True,  True]),\n",
       "           ([1., 1., 1., 1., 1., 1., 0., 1., 1., 1., 1., 1., 0., 1., 1., 0., 1., 1.], -20., 1,  True, [ True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True]),\n",
       "           ([1., 0., 1., 1., 1., 0., 1., 1., 1., 1., 1., 0., 1., 1., 1., 1., 1., 1.], -20., 5,  True, [ True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True]),\n",
       "           ([1., 1., 0., 1., 1., 1., 1., 1., 1., 1., 1., 0., 1., 1., 1., 1., 1., 0.], -20., 1,  True, [ True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True]),\n",
       "           ([1., 0., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 0., 1., 1., 0., 1.], -19., 1,  True, [ True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True]),\n",
       "           ([1., 0., 1., 1., 1., 1., 1., 1., 1., 1., 0., 1., 1., 1., 1., 1., 0., 1.], -20., 1,  True, [ True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True]),\n",
       "           ([1., 1., 1., 0., 1., 1., 1., 1., 1., 0., 1., 1., 0., 1., 1., 1., 1., 1.], -20., 3,  True, [ True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True]),\n",
       "           ([1., 1., 1., 1., 1., 1., 0., 1., 0., 1., 1., 1., 1., 1., 1., 0., 1., 1.], -20., 2,  True, [ True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True]),\n",
       "           ([1., 1., 1., 0., 1., 0., 1., 1., 1., 1., 1., 1., 0., 1., 1., 1., 1., 1.], -20., 2,  True, [ True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True]),\n",
       "           ([1., 1., 1., 1., 1., 1., 0., 1., 1., 1., 1., 1., 1., 1., 1., 0., 0., 1.], -20., 1,  True, [ True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True]),\n",
       "           ([1., 1., 1., 1., 1., 0., 1., 1., 1., 1., 1., 1., 0., 1., 0., 1., 1., 1.], -20., 1,  True, [ True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True]),\n",
       "           ([1., 0., 0., 1., 1., 1., 1., 1., 1., 1., 1., 0., 1., 1., 1., 1., 1., 1.], -20., 1,  True, [ True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True]),\n",
       "           ([1., 1., 0., 1., 1., 1., 1., 1., 1., 0., 1., 1., 1., 1., 1., 1., 1., 0.], -20., 2,  True, [ True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True]),\n",
       "           ([1., 1., 1., 0., 1., 1., 1., 1., 1., 0., 1., 1., 1., 0., 1., 1., 1., 1.], -20., 2,  True, [ True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True]),\n",
       "           ([1., 1., 0., 0., 1., 1., 1., 1., 1., 0., 1., 1., 1., 1., 1., 1., 1., 1.], -20., 1,  True, [ True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True]),\n",
       "           ([1., 1., 1., 1., 1., 1., 1., 1., 0., 1., 1., 1., 1., 1., 0., 1., 1., 0.], -20., 1,  True, [ True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True]),\n",
       "           ([1., 1., 1., 1., 1., 0., 1., 1., 0., 1., 1., 1., 1., 1., 0., 1., 1., 1.], -20., 5,  True, [ True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True]),\n",
       "           ([1., 1., 1., 1., 0., 1., 1., 1., 1., 1., 1., 1., 1., 0., 0., 1., 1., 1.], -20., 1,  True, [ True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True]),\n",
       "           ([1., 1., 1., 1., 0., 1., 1., 0., 1., 1., 1., 1., 1., 0., 1., 1., 1., 1.], -20., 3,  True, [ True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True]),\n",
       "           ([1., 0., 1., 1., 1., 1., 1., 0., 1., 1., 1., 1., 1., 1., 1., 1., 0., 1.], -20., 2,  True, [ True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True]),\n",
       "           ([1., 1., 1., 1., 1., 1., 1., 0., 1., 1., 1., 1., 1., 0., 1., 1., 0., 1.], -20., 2,  True, [ True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True]),\n",
       "           ([1., 1., 1., 1., 1., 1., 0., 0., 1., 1., 1., 1., 1., 1., 1., 1., 0., 1.], -20., 1,  True, [ True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True]),\n",
       "           ([1., 0., 1., 1., 1., 1., 1., 1., 1., 1., 1., 0., 1., 1., 1., 1., 0., 1.], -20., 1,  True, [ True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True]),\n",
       "           ([1., 1., 1., 1., 0., 1., 1., 1., 1., 1., 0., 1., 1., 1., 0., 1., 1., 1.], -20., 1,  True, [ True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True,  True])],\n",
       "          dtype=[('sample', '<f8', (18,)), ('energy', '<f8'), ('num_occurrences', '<i4'), ('is_feasible', '?'), ('is_satisfied', '?', (19,))]), Variables(range(0, 18)), {'constraint_labels': ['Min_coord_8', 'Min_coord_16', 'Min_coord_11', 'Min_coord_14', 'Min_coord_0', 'Min_coord_2', 'Min_coord_3', 'Min_coord_17', 'Min_coord_12', 'Min_coord_13', 'Min_coord_10', 'Min_coord_5', 'Min_coord_7', 'Min_coord_15', 'Min_coord_9', 'Min_coord_4', 'Num vacancies', 'Min_coord_6', 'Min_coord_1'], 'qpu_access_time': 15152, 'charge_time': 5000000, 'run_time': 5002722, 'problem_id': 'f7bcf2c4-e480-4aec-8ccd-8ee4da054814'}, 'INTEGER')"
      ]
     },
     "execution_count": 224,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sampleset_bonds.aggregate()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "21382b7c",
   "metadata": {},
   "source": [
    "### Analyse structures"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 248,
   "id": "90921987",
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([  0,   0,   1,   1,   2,   2,   3,   3,   4,   4,   5,   5,   6,\n",
       "          6,   7,   7,   8,   8,   9,   9,  10,  10,  11,  11,  12,  12,\n",
       "         13,  13,  14,  14,  15,  15,  16,  16,  17,  17,  18,  18,  19,\n",
       "         19,  20,  20,  21,  21,  22,  22,  23,  23,  24,  24,  25,  25,\n",
       "         26,  26,  27,  27,  28,  28,  29,  29,  30,  30,  31,  31,  32,\n",
       "         32,  33,  33,  34,  34,  35,  35,  36,  36,  37,  37,  38,  38,\n",
       "         39,  39,  40,  40,  41,  41,  42,  42,  43,  43,  44,  44,  45,\n",
       "         45,  46,  46,  47,  47,  48,  48,  49,  49,  50,  50,  51,  51,\n",
       "         52,  52,  53,  53,  54,  54,  55,  55,  56,  56,  57,  57,  58,\n",
       "         58,  59,  59,  60,  60,  61,  61,  62,  62,  63,  63,  64,  64,\n",
       "         65,  65,  66,  66,  67,  67,  68,  68,  69,  69,  70,  70,  71,\n",
       "         71,  72,  72,  73,  73,  74,  74,  75,  75,  76,  76,  77,  77,\n",
       "         78,  78,  79,  79,  80,  80,  81,  81,  82,  82,  83,  83,  84,\n",
       "         84,  85,  85,  86,  86,  87,  87,  88,  88,  89,  89,  90,  90,\n",
       "         91,  91,  92,  92,  93,  93,  94,  94,  95,  95,  96,  96,  97,\n",
       "         97,  98,  98,  99,  99, 100, 100, 101, 101, 102, 102, 103, 103,\n",
       "        104, 104, 105, 105, 106, 106, 107, 107, 108, 108, 109, 109, 110,\n",
       "        110, 111, 111, 112, 112, 113, 113, 114, 114, 115, 115, 116, 116,\n",
       "        117, 117, 118, 118, 119, 119, 120, 120, 121, 121, 122, 122, 123,\n",
       "        123, 124, 124, 125, 125, 126, 126, 127, 127, 128, 128, 129, 129,\n",
       "        130, 130, 131, 131, 132, 132, 133, 133, 134, 134, 135, 135, 136,\n",
       "        136, 137, 137, 138, 138, 139, 139, 140, 140, 141, 141, 142, 142,\n",
       "        143, 143, 144, 144, 145, 145, 146, 146, 147, 147, 148, 148, 149,\n",
       "        149, 150, 150, 151, 151, 152, 152, 153, 153, 154, 154, 155, 155,\n",
       "        156, 156, 157, 157, 158, 158, 159, 159, 160, 160, 161, 161, 162,\n",
       "        162, 163, 163, 164, 164, 165, 165]),\n",
       " array([ 7, 17,  7, 13,  7, 16,  8, 17,  2, 11,  1, 16,  1, 11,  2,  9,  5,\n",
       "        11,  5, 14,  5, 12,  8, 15,  4, 13,  3, 13,  2, 17,  3, 12,  0,  9,\n",
       "         0, 10,  8, 14,  4, 14,  6, 12,  3,  9,  0, 15,  6, 16,  6, 15, 12,\n",
       "        17, 12, 13, 16, 17,  8, 13,  2,  5,  7, 12,  8, 12, 13, 16, 13, 17,\n",
       "         1, 17, 10, 11,  9, 10,  1,  7,  0,  8, 11, 14,  5,  9,  2, 16,  1,\n",
       "         9,  9, 13,  2,  4, 11, 13,  5,  8,  9, 12, 11, 16,  2,  7, 13, 14,\n",
       "         1, 14,  6, 13,  0, 12,  7, 10, 11, 17,  1, 12,  7,  9,  5,  7,  7,\n",
       "         8,  2, 14,  2, 10,  9, 14,  2, 13,  7, 14, 14, 17,  0,  7,  0,  4,\n",
       "         2,  8, 13, 15, 10, 14,  8, 16, 10, 17,  0,  1,  1, 13,  7, 15,  2,\n",
       "        12, 12, 15,  1,  2,  0, 17,  8, 10, 10, 13,  1,  8, 11, 12, 10, 16,\n",
       "         8, 11,  0,  2,  2,  3,  5, 17,  5, 10, 12, 16,  5, 16,  0, 16,  2,\n",
       "         6,  9, 16,  0,  3,  6,  9,  5,  6,  4, 17,  3,  4, 14, 16, 15, 16,\n",
       "         4,  8,  0, 14,  4, 12,  3, 10,  5, 13,  9, 15,  3, 14, 10, 15,  6,\n",
       "         8,  3,  7,  3, 16,  2, 15,  4, 16,  0,  6,  5, 15,  6, 17,  3, 17,\n",
       "         6, 11,  6, 14, 12, 14,  4,  7,  4,  6,  6, 10,  3,  6,  1,  3,  4,\n",
       "         5,  1,  6,  0, 13,  0,  5,  1,  4,  3,  8,  3,  5,  4,  9,  6,  7,\n",
       "         4, 15, 14, 15,  0,  9,  3,  9,  3, 10,  9, 10,  6,  9,  0,  6,  4,\n",
       "         6,  0,  3,  3,  6,  3,  4,  0,  4,  2,  6,  2, 17,  7, 16,  7,  8,\n",
       "         0,  4,  0,  8,  0, 16,  8, 17, 16, 17,  9, 14,  2, 14,  3,  6,  5,\n",
       "         9,  6,  8,  3, 17, 10, 15,  2,  4]))"
      ]
     },
     "execution_count": 248,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vacancy_pos = np.where(array_2v == 0)\n",
    "vacancy_pos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 578,
   "id": "75799534",
   "metadata": {},
   "outputs": [],
   "source": [
    "structures = []\n",
    "for i,pos in enumerate(array_3v):\n",
    "    structure = copy.deepcopy(graphene_supercell)\n",
    "    #print(structure.sites[np.where(pos == 0)[0][0]].distance(structure.sites[np.where(pos == 0)[0][1]]))\n",
    "    #structure.remove_sites(np.where(pos == 0)[0])\n",
    "    structure.replace(np.where(pos == 0)[0][0],1)\n",
    "    structure.replace(np.where(pos == 0)[0][1],1)\n",
    "    structure.replace(np.where(pos == 0)[0][2],1)\n",
    "    structures.append(structure)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 579,
   "id": "e270c0e4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Popen: returncode: None args: ['/Users/brunocamino/miniconda3/envs/qc/bin/p...>"
      ]
     },
     "execution_count": 579,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#a = SpacegroupAnalyzer(structures[0]).get_conventional_standard_structure()\n",
    "view(AseAtomsAdaptor().get_atoms(structures[-3]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 465,
   "id": "9b217de3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1], dtype=int8)"
      ]
     },
     "execution_count": 465,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "array_3v[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91e7e130",
   "metadata": {},
   "source": [
    "# Structural analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 280,
   "id": "e91bf4ec",
   "metadata": {},
   "outputs": [],
   "source": [
    "def cart2sph(x, y, z):\n",
    "    hxy = np.hypot(x, y)\n",
    "    r = np.hypot(hxy, z)\n",
    "    el = np.arctan2(z, hxy)\n",
    "    az = np.arctan2(y, x)\n",
    "    if np.around(az,6) ==  np.around(2*np.pi,6) \\\n",
    "    or np.around(az,6) ==  -np.around(2*np.pi,6):\n",
    "        az = 0.\n",
    "    if np.around(az,6) < 0.:\n",
    "        az = np.round(2*np.pi+az,6)\n",
    "    return [round(az,6), round(el,6), round(r,6)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 281,
   "id": "0c9a2421",
   "metadata": {},
   "outputs": [],
   "source": [
    "max_shell = 2\n",
    "centered_sph_coords = []\n",
    "centered_sph_coords_structure = []\n",
    "neighbours_spatial_dist = []\n",
    "neighbours_spatial_dist_all = []\n",
    "import time\n",
    "#time0 = time.time()\n",
    "#for k,structure in enumerate(structures[0:100]): #TMP only calculate 100 structures\n",
    "for k,structure in enumerate(structures): \n",
    "    time0 = time.time()\n",
    "    neighbours_spatial_dist = []\n",
    "    \n",
    "    for j in range(structure.num_sites):\n",
    "        centered_sph_coords = []\n",
    "        neighbours_spatial_dist_atom = []\n",
    "        \n",
    "        for n in range(max_shell+1):\n",
    "            atom_indices = np.where(np.round(structure.distance_matrix[j],5) == np.round(shells[n],5))[0].tolist()\n",
    "            centered_sph_coords = []\n",
    "            for i in atom_indices:\n",
    "\n",
    "                translation_vector = structure.sites[j].distance_and_image(structure.sites[i])[1]\n",
    "                new_cart_coords = structure.cart_coords[i]+(translation_vector*structure.lattice.abc)\n",
    "                centered_cart_coords = new_cart_coords-structure.cart_coords[j] \n",
    "\n",
    "                centered_sph_coords.append(cart2sph(centered_cart_coords[0],centered_cart_coords[1],centered_cart_coords[2]))        \n",
    "\n",
    "            spatial_distribution = np.argsort(np.array(centered_sph_coords)[:,1]*10 +\\\n",
    "                                              np.array(centered_sph_coords)[:,0])\n",
    "\n",
    "\n",
    "            neighbours_spatial_dist_atom.extend((np.array(structure.atomic_numbers)[np.array(atom_indices)[spatial_distribution]]).tolist())\n",
    "        neighbours_spatial_dist.append(neighbours_spatial_dist_atom)\n",
    "    #print(time.time()-time0)\n",
    "    neighbours_spatial_dist_all.append(neighbours_spatial_dist) \n",
    "#neighbours_spatial_dist_all = np.array(neighbours_spatial_dist_all) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 282,
   "id": "b30221e1",
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [1, 6, 6, 1, 6, 6, 1]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [1, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [1, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 1, 6, 6, 1, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [1, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [1, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [1, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [1, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [1, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [1, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [1, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 1, 6, 6, 1, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[1, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[1, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [1, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [1, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [1, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [1, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[1, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [1, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 1, 1, 6, 1],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 1, 6, 1, 1, 6, 1],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 1, 1, 6, 1],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 1, 6, 1, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 1, 6, 1, 1, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 1, 6, 1, 1, 6, 1],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 1, 6, 1, 1, 6, 1],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 1, 6, 1, 1, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1]],\n",
       " [[1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 1, 6, 1, 1, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 1, 6, 1, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6]],\n",
       " [[6, 6, 6, 1, 6, 6, 1],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 1, 1, 6, 1, 1, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 1, 1, 6, 1],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6]],\n",
       " [[6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 1, 6, 1, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 1, 6, 1, 1, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 1, 6, 1, 1, 6, 1]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 1, 6, 1, 1, 6, 1],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 1, 6, 1, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 1, 1, 6, 1, 1]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6]],\n",
       " [[6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6]],\n",
       " [[6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 1, 6, 1, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6]],\n",
       " [[1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1]],\n",
       " [[1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 1, 6, 1, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 1, 6, 1, 1, 6]],\n",
       " [[6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 1, 6, 1, 1, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6]],\n",
       " [[6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6]],\n",
       " [[1, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 1, 1, 6, 1, 1, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6]],\n",
       " [[6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 1, 6, 1, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 1, 1, 6, 1, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6]],\n",
       " [[1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6]],\n",
       " [[6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 1, 6, 1, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 1, 6, 1, 1, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 1, 6, 1, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6]],\n",
       " [[1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 1, 6, 1, 1, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 1, 6, 1, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 1, 1, 6, 1, 1, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 1, 6, 6, 1, 6, 6]],\n",
       " [[6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 1, 1, 6, 1],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 1, 1, 6, 1, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 1, 1, 6, 1, 1, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 1, 1, 6, 1],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 1, 6, 1, 1],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6]],\n",
       " [[1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 1, 1, 6, 1, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 1, 1, 6, 1, 1, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 1, 1, 6, 1, 1],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 1, 6, 6, 1, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 1, 6, 1, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 1, 6, 1, 1, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [1, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 1, 6, 1, 1, 6, 1],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 1, 1, 6, 1],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 1, 1, 6, 1],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 1, 1, 6, 1, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 1, 6, 1, 1, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 1, 1, 6, 1],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 1, 1, 6, 1, 1, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 1, 1, 6, 1, 1],\n",
       "  [6, 6, 6, 1, 6, 6, 1]],\n",
       " [[6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 1, 6, 1, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[1, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [1, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 1, 6, 1, 1, 6, 1],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 1, 6, 1, 1, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 1, 1, 6, 1],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 1, 1, 6, 1],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 1, 1, 6, 1, 1, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 1, 6, 1, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 1, 6, 6, 1, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 1, 6, 6, 1, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [1, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 1, 1, 6, 1, 1]],\n",
       " [[1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 1, 6, 1, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 1, 6, 1, 1, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6]],\n",
       " [[1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [1, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 1, 6, 6, 1, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 1, 6, 1, 1, 6, 1],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 1, 1, 6, 1],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 1, 1, 6, 1, 1],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 1, 6, 6, 1, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 1, 1, 6, 1, 1, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6]],\n",
       " [[6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [1, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 1, 6, 6, 1],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6],\n",
       "  [6, 6, 1, 6, 6, 1, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 6, 6, 6, 6, 6, 6],\n",
       "  [6, 1, 6, 6, 1, 6, 6]]]"
      ]
     },
     "execution_count": 282,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "neighbours_spatial_dist_all"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 283,
   "id": "8ee95170",
   "metadata": {},
   "outputs": [],
   "source": [
    "neighbours_spatial_dist_all_sorted = []\n",
    "sorting = []\n",
    "\n",
    "for k,structure in enumerate(structures):\n",
    "    sorted_atoms = []\n",
    "    for i in range(len(neighbours_spatial_dist_all[0])):\n",
    "        sorted_atoms.append(int(''.join([str(x) for x in neighbours_spatial_dist_all[k][i]])))\n",
    "    sorting.append(np.argsort(np.array(sorted_atoms)))    \n",
    "    neighbours_spatial_dist_all_sorted.append((np.array(neighbours_spatial_dist_all)[k][np.argsort(np.array(sorted_atoms))]).tolist())\n",
    "neighbours_spatial_dist_all_sorted = np.array(neighbours_spatial_dist_all_sorted)    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 285,
   "id": "17119a8e",
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 1, 6, 6, 1, 6, 6],\n",
       "       [1, 6, 6, 1, 6, 6, 1],\n",
       "       [6, 6, 1, 6, 6, 1, 6],\n",
       "       [6, 6, 1, 6, 6, 1, 6],\n",
       "       [6, 6, 6, 1, 6, 6, 1],\n",
       "       [6, 6, 6, 1, 6, 6, 1],\n",
       "       [6, 6, 6, 6, 6, 6, 6],\n",
       "       [6, 6, 6, 6, 6, 6, 6],\n",
       "       [6, 6, 6, 6, 6, 6, 6],\n",
       "       [6, 6, 6, 6, 6, 6, 6],\n",
       "       [6, 6, 6, 6, 6, 6, 6],\n",
       "       [6, 6, 6, 6, 6, 6, 6],\n",
       "       [6, 6, 6, 6, 6, 6, 6],\n",
       "       [6, 6, 6, 6, 6, 6, 6],\n",
       "       [6, 6, 6, 6, 6, 6, 6],\n",
       "       [6, 6, 6, 6, 6, 6, 6],\n",
       "       [6, 6, 6, 6, 6, 6, 6],\n",
       "       [6, 6, 6, 6, 6, 6, 6]])"
      ]
     },
     "execution_count": 285,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "neighbours_spatial_dist_all_sorted[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 286,
   "id": "435e0bd6",
   "metadata": {},
   "outputs": [],
   "source": [
    "neighbours_spatial_dist_all_sorted_sliced = neighbours_spatial_dist_all_sorted[:,:,1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 287,
   "id": "7a2d52c2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 6, 6, 1, 6, 6],\n",
       "       [6, 6, 1, 6, 6, 1],\n",
       "       [6, 1, 6, 6, 1, 6],\n",
       "       [6, 1, 6, 6, 1, 6],\n",
       "       [6, 6, 1, 6, 6, 1],\n",
       "       [6, 6, 1, 6, 6, 1],\n",
       "       [6, 6, 6, 6, 6, 6],\n",
       "       [6, 6, 6, 6, 6, 6],\n",
       "       [6, 6, 6, 6, 6, 6],\n",
       "       [6, 6, 6, 6, 6, 6],\n",
       "       [6, 6, 6, 6, 6, 6],\n",
       "       [6, 6, 6, 6, 6, 6],\n",
       "       [6, 6, 6, 6, 6, 6],\n",
       "       [6, 6, 6, 6, 6, 6],\n",
       "       [6, 6, 6, 6, 6, 6],\n",
       "       [6, 6, 6, 6, 6, 6],\n",
       "       [6, 6, 6, 6, 6, 6],\n",
       "       [6, 6, 6, 6, 6, 6]])"
      ]
     },
     "execution_count": 287,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "neighbours_spatial_dist_all_sorted_sliced[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 293,
   "id": "acf53c77",
   "metadata": {},
   "outputs": [],
   "source": [
    "n_structures = neighbours_spatial_dist_all_sorted_sliced.shape[0]\n",
    "vector_len = neighbours_spatial_dist_all_sorted_sliced.shape[1] * neighbours_spatial_dist_all_sorted_sliced.shape[2]\n",
    "neighbours_spatial_dist_all_sorted_sliced_flat = \\\n",
    "np.reshape(neighbours_spatial_dist_all_sorted_sliced, [n_structures,vector_len])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 301,
   "id": "57b1290b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 6, 6, 1, 6, 6, 6, 6, 1, 6, 6, 1, 6, 1, 6, 6, 1, 6, 6, 1, 6, 6,\n",
       "       1, 6, 6, 6, 1, 6, 6, 1, 6, 6, 1, 6, 6, 1, 6, 6, 6, 6, 6, 6, 6, 6,\n",
       "       6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,\n",
       "       6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,\n",
       "       6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6])"
      ]
     },
     "execution_count": 301,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "neighbours_spatial_dist_all_sorted_sliced_flat[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 314,
   "id": "21519057",
   "metadata": {},
   "outputs": [],
   "source": [
    "a,b,c = np.unique(neighbours_spatial_dist_all_sorted_sliced_flat,axis=0,return_index=True,return_counts=True,)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 315,
   "id": "4632f72d",
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in b:\n",
    "    view(AseAtomsAdaptor().get_atoms(structures[i]))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c49cf581",
   "metadata": {},
   "source": [
    "# Simulated annealing\n",
    "Only lowest energy solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 377,
   "id": "becbcdc5",
   "metadata": {},
   "outputs": [],
   "source": [
    "import neal\n",
    "\n",
    "sampler = neal.SimulatedAnnealingSampler()\n",
    "\n",
    "X = np.arange(graphene_supercell.num_sites)\n",
    "\n",
    "Q = np.triu(-adjacency_matrix.astype(int),0)\n",
    "bqm = BinaryQuadraticModel.from_qubo(Q)\n",
    "\n",
    "c_n_vacancies = [(i,1) for i in X]\n",
    "\n",
    "num_vacancies = 4\n",
    "\n",
    "bqm.add_linear_equality_constraint(\n",
    "        c_n_vacancies,\n",
    "        constant= -(graphene_supercell.num_sites-num_vacancies),\n",
    "        lagrange_multiplier = 1000\n",
    "        )\n",
    "sampleset = sampler.sample(bqm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 378,
   "id": "be68e4ea",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>10</th>\n",
       "      <th>11</th>\n",
       "      <th>12</th>\n",
       "      <th>13</th>\n",
       "      <th>14</th>\n",
       "      <th>15</th>\n",
       "      <th>16</th>\n",
       "      <th>17</th>\n",
       "      <th>energy</th>\n",
       "      <th>num_occurrences</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>-16.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   0  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  energy  \\\n",
       "0  1  1  1  0  0  1  1  1  1  0   1   1   1   1   1   1   0   1   -16.0   \n",
       "\n",
       "   num_occurrences  \n",
       "0                1  "
      ]
     },
     "execution_count": 378,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sampleset.to_pandas_dataframe()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}