AnchorGK.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "### Import cell"
   ],
   "metadata": {
    "collapsed": false
   },
   "id": "f58d9951e47eb37a"
  },
  {
   "cell_type": "code",
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2024-03-25 18:38:18.988634: I tensorflow/core/util/port.cc:110] oneDNN custom operations are on. You may see slightly different numerical results due to floating-point round-off errors from different computation orders. To turn them off, set the environment variable `TF_ENABLE_ONEDNN_OPTS=0`.\n",
      "2024-03-25 18:38:19.012294: I tensorflow/core/platform/cpu_feature_guard.cc:182] This TensorFlow binary is optimized to use available CPU instructions in performance-critical operations.\n",
      "To enable the following instructions: AVX2 AVX_VNNI FMA, in other operations, rebuild TensorFlow with the appropriate compiler flags.\n",
      "2024-03-25 18:38:19.393363: W tensorflow/compiler/tf2tensorrt/utils/py_utils.cc:38] TF-TRT Warning: Could not find TensorRT\n"
     ]
    }
   ],
   "source": [
    "\n",
    "import os\n",
    "import sys\n",
    "import torch\n",
    "from torch.autograd import Variable\n",
    "import numpy as np\n",
    "import torch.nn.functional as F\n",
    "import torch.optim as optim\n",
    "from torch import nn\n",
    "import matplotlib.pyplot as plt\n",
    "from utils import (load_nerl_data,\n",
    "    get_normalized_adj,\n",
    "    get_Laplace,\n",
    "    calculate_random_walk_matrix,\n",
    "    test_error_cap,\n",
    "    test_error\n",
    ")\n",
    "import random\n",
    "import copy\n",
    "import scipy\n",
    "from scipy.io import loadmat\n",
    "import math\n",
    "import pandas as pd\n",
    "from basic_structure import D_GCN, C_GCN, K_GCN,IGNNK\n",
    "from basic_process import *\n",
    "from sklearn.manifold import TSNE\n",
    "import os\n",
    "import pandas as pd\n",
    "from sklearn import linear_model\n",
    "from pandas import read_csv "
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-25T05:38:19.844510Z",
     "start_time": "2024-03-25T05:38:17.998087Z"
    }
   },
   "id": "3e74108de2f4df",
   "execution_count": 1
  },
  {
   "cell_type": "code",
   "outputs": [],
   "source": [
    "from utils import *"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-25T05:38:19.847272Z",
     "start_time": "2024-03-25T05:38:19.845432Z"
    }
   },
   "id": "1d98a6a9d305cf3d",
   "execution_count": 2
  },
  {
   "cell_type": "code",
   "outputs": [
    {
     "data": {
      "text/plain": "<All keys matched successfully>"
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_o_n_m = 20 #sampled space dimension\n",
    "\n",
    "h = 24 #sampled time dimension\n",
    "\n",
    "z = 100 #hidden dimension for graph convolution\n",
    "\n",
    "K = 1 #If using diffusion convolution, the actual diffusion convolution step is K+1\n",
    "\n",
    "n_m = 20 #number of mask node during training\n",
    "\n",
    "N_u = 50 #target locations, N_u locations will be deleted from the training data\n",
    "\n",
    "Max_episode = 750 #max training episode\n",
    "\n",
    "learning_rate = 0.0001 #the learning_rate for Adam optimizer\n",
    "\n",
    "batch_size = 8\n",
    "\n",
    "E_maxvalue=80\n",
    "\n",
    "STmodel = IGNNK(h, z, K)\n",
    "STmodel.load_state_dict(torch.load('model/IGNNK_ushcn_750iter_2023-11-26 12:25:53.pth'))"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-25T05:38:19.882795Z",
     "start_time": "2024-03-25T05:38:19.847814Z"
    }
   },
   "id": "42ac953bf03bfd51",
   "execution_count": 3
  },
  {
   "cell_type": "code",
   "outputs": [],
   "source": [
    "#Read all data\n",
    "pathroot='data/NDBC/all_stations'\n",
    "PATH_ROOT = os.getcwd()\n",
    "ROOT = os.path.join(PATH_ROOT, pathroot)\n",
    "filenames = os.listdir(ROOT)\n",
    "# Sort all files\n",
    "filenames.sort()\n",
    "data = []\n",
    "for i in filenames:\n",
    "    PATH_CSV = os.path.join(ROOT, i)\n",
    "    with open(PATH_CSV, 'r') as file:\n",
    "# Use splitlines() to divide contents in the documents into lists.\n",
    "        content_list = file.read().splitlines()\n",
    "# Transform lists into Numpy.\n",
    "    content_matrix = np.array([list(map(float, line.split())) for line in content_list])\n",
    "    data.append(content_matrix)\n",
    "data = np.array(data).transpose(1, 2, 0)\n",
    "X_raw=data"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-25T05:38:21.663081Z",
     "start_time": "2024-03-25T05:38:19.883588Z"
    }
   },
   "id": "14f5d15359ebd8d5",
   "execution_count": 4
  },
  {
   "cell_type": "code",
   "outputs": [],
   "source": [
    "Station_info=pd.read_csv('data/NDBC/Station_info.csv')"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-25T05:38:21.668631Z",
     "start_time": "2024-03-25T05:38:21.664758Z"
    }
   },
   "id": "fbf754f976258a49",
   "execution_count": 5
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Experiment 1: Raw setting on IGNNK without training"
   ],
   "metadata": {
    "collapsed": false
   },
   "id": "1eb2e73e5116069b"
  },
  {
   "cell_type": "code",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best model in the 5 -th column is 0.40352601831183693 0.5088791407814893 -2.0018908772340307\n",
      "Best model in the 6 -th column is 0.1411266781166549 0.1804560280265735 -2.0065000682516088\n",
      "Best model in the 7 -th column is 0.1080074476969392 0.1418104682791045 -1.839235293152675\n",
      "Best model in the 8 -th column is 0.07047534916285692 0.09903405982849459 -0.6631597810723096\n",
      "Best model in the 9 -th column is 0.23394033180461932 0.2910954930464806 -2.6891267739028377\n",
      "Best model in the 10 -th column is 0.12240251247475493 0.151003131106556 -2.662159706744909\n",
      "Best model in the 11 -th column is 0.42374578401253 0.5127201027197579 -2.19312763841895\n",
      "Best model in the 12 -th column is 0.03289810527367924 0.04290030633038398 -11.119319152080367\n",
      "Best model in the 13 -th column is 0.5673032852716019 0.6638559782332828 -39.51562018379573\n",
      "Best model in the 14 -th column is 0.44205008405445867 0.5270998671359972 -4.929568892482556\n",
      "Best model in the 15 -th column is 0.5960648350147367 0.6273097089296188 -15.588660447963075\n",
      "Best model in the 16 -th column is 0.8388929130770701 0.8557961282654142 -23.941683690276637\n"
     ]
    }
   ],
   "source": [
    "for j in range(5,X_raw.shape[1]-1):\n",
    "        NDBC_lat=pd.DataFrame(Station_info.iloc[:,1])\n",
    "        NDBC_long=pd.DataFrame(Station_info.iloc[:,3])\n",
    "        NDBC_ID=pd.DataFrame(Station_info.iloc[:,0])\n",
    "        Adj_dist=adj_dist(NDBC_lat,NDBC_long)\n",
    "        X_raw_0=X_raw[:,j,:]#GET the first feature\n",
    "        #print(X_raw_0.shape)\n",
    "        # Count the num of missing values in each column\n",
    "        missing_counts_per_column = np.sum(np.isnan(X_raw_0), axis=0)\n",
    "        # print results\n",
    "       # print(\"Incomplete data number in each column：\", missing_counts_per_column)\n",
    "        #Get the index if the value is not zero\n",
    "        # Find the columns where missing values exist.\n",
    "        columns_with_missing_data = np.any(np.isnan(X_raw_0), axis=0)\n",
    "\n",
    "        # Get the column numbers when missing value exist.\n",
    "        missing_columns = np.where(columns_with_missing_data)[0]\n",
    "\n",
    "        #Get new data after deletion.\n",
    "        #Delete those columns(Stations) if there is not any features.\n",
    "        result = np.delete(X_raw_0, missing_columns, axis=1)\n",
    "        result = (result - np.min(result)) / (np.max(result) - np.min(result))\n",
    "        #Mean results---for SNE\n",
    "        mean_result_axis_1=np.mean(result,axis=0)\n",
    "        mean_result_axis_1=mean_result_axis_1.reshape(-1,1)        #Get new adjacency matrix after deletion.\n",
    "        NDBC_long=NDBC_long.transpose()\n",
    "        NDBC_long_aft=NDBC_long.drop(columns=missing_columns)\n",
    "        # Reconstruct the index in the DataFrame and get the longitude after deletion.\n",
    "        NDBC_long_aft = NDBC_long_aft.reset_index(drop=True)\n",
    "        Temp_long=NDBC_long_aft.values\n",
    "\n",
    "        NDBC_lat=NDBC_lat.transpose()\n",
    "        NDBC_lat_aft=NDBC_lat.drop(columns=missing_columns)\n",
    "        # Reconstruct the index in the DataFrame and get the latitude after deletion.\n",
    "        NDBC_lat_aft = NDBC_lat_aft.reset_index(drop=True)\n",
    "        Temp_lat=NDBC_lat_aft.values\n",
    "\n",
    "        merged_array = np.concatenate([mean_result_axis_1, Temp_long.T,Temp_lat.T], axis=1)\n",
    "        tsne = TSNE(n_components=2, random_state=30,perplexity=1) #Make sure random seed to be the same for the reproducibility.\n",
    "        array_aft = tsne.fit_transform(merged_array)\n",
    "\n",
    "        #GEt the new ADJ matrix.\n",
    "        Adj_dist=adj_dist(pd.DataFrame(array_aft[:,0]),pd.DataFrame(array_aft[:,1]))\n",
    "        capacities=np.ones((Adj_dist.shape[0], 1))\n",
    "        capacities=capacities.flatten()\n",
    "        split_line1 = int(result.shape[0] * 0.7)\n",
    "        training_set = result[:split_line1, :]\n",
    "        test_set = result[split_line1:, :]\n",
    "        rand = np.random.RandomState(0) # Fixed random output, just an example when seed = 0.\n",
    "        unknow_set = rand.choice(list(range(0,result.shape[1])),N_u,replace=True)#Stations to be predicted\n",
    "        unknow_set = set(unknow_set)\n",
    "        full_set = set(range(0,result.shape[1]))\n",
    "        know_set = full_set - unknow_set\n",
    "        training_set_s = training_set[:, list(know_set)]   # get the training data in the sample time period\n",
    "        A_s = Adj_dist[:, list(know_set)][list(know_set), :]\n",
    "        MAE_t, RMSE_t, R2_t, nrel_ignnk_res  = test_error_cap(STmodel, unknow_set, full_set,test_set, Adj_dist,h,capacities)\n",
    "        print('Best model in the',j, '-th column is', MAE_t, RMSE_t, R2_t)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-25T05:38:34.938300Z",
     "start_time": "2024-03-25T05:38:21.669298Z"
    }
   },
   "id": "ff24071781b84949",
   "execution_count": 6
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Experiment 3.1: IGNNK-Training-dis-MI-based graph-3DGNN (Format:Metd-Adj-Only one defined graph-3DGNN)"
   ],
   "metadata": {
    "collapsed": false
   },
   "id": "35c08e146d826928"
  },
  {
   "cell_type": "code",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(8784, 103)\n",
      "Incomplete data number in each column： [8784    0    0    0    0    0    0    0    0    0    0    0    0    0\n",
      "    0    0    0    0    0    0    0    0    0    0    0    0    0    0\n",
      "    0    0    0    0    0    0 8784    0    0    0 8784    0    0    0\n",
      "    0    0    0    0    0    0    0 8784 8784    0    0    0    0 8784\n",
      " 8784    0    0    0    0    0    0    0    0    0    0    0    0    0\n",
      "    0    0    0 8784    0    0    0    0    0    0    0 8784    0 8784\n",
      "    0    0    0    0    0    0    0    0    0    0    0    0    0    0\n",
      "    0    0    0    0    0]\n",
      "The column numbers with missing values are： [ 0 34 38 49 50 55 56 73 81 83]\n",
      "(8784, 93)\n",
      "Row 0 - Column Numbers: [ 1  2  4 79  5 20  3 77 21 17 83 85 78 87 91 12 15 31 11 43 19 44 35 30\n",
      " 74 90 16 10 33 64 42 34 61 13 32 46 22 63 92 56 18  8 41], MI Values: [0.8272601132894586, 0.6901375697065202, 0.4673606483958732, 0.45757637448269683, 0.4363240338301644, 0.4190235175463517, 0.37428008133733837, 0.37263024544485734, 0.33215728219304985, 0.3299090634675217, 0.3150689617867082, 0.29292039446620866, 0.22793155006306698, 0.22350595260037576, 0.2084899516681764, 0.19725693559810153, 0.16436438822998234, 0.1621107642515911, 0.15513395543730368, 0.13586993979589845, 0.13409996608400565, 0.12631372813239938, 0.11361591888716127, 0.10962686909974106, 0.10670490036675684, 0.10411775455289352, 0.10173701560948789, 0.10125880394889375, 0.0966457877057838, 0.0917156023777439, 0.08872664637913985, 0.08750394746818291, 0.07987921333337233, 0.0779097501756647, 0.07772961987272176, 0.07681250087322766, 0.07596636122032496, 0.07375851842511771, 0.07334383362524477, 0.0724236272383223, 0.06937049801544504, 0.06869053966721506, 0.06665335877298872]\n",
      "Row 1 - Column Numbers: [ 0 20  2 85 21 77  4 79 17  5 91 87 83  3 11 15 12 78 31 19 10 16 43 35\n",
      " 30 33 13 90 64 74 44 22 42 61 18 34 92  8 46 56 24 28 36], MI Values: [0.8272601132894577, 0.5324618722588088, 0.52600823699178, 0.4273072620362397, 0.4023069759074378, 0.39111917114037187, 0.34043212687770286, 0.33742367205695434, 0.3283135513911546, 0.32209271522604777, 0.3192857717713018, 0.3012243820649747, 0.2950417871731199, 0.25018137359531334, 0.2344515509245717, 0.23100847367209631, 0.22954525563754213, 0.22306577157731855, 0.161217443157323, 0.16120899606897954, 0.14396039237957936, 0.13986782406464826, 0.12913107009156644, 0.11642248941903688, 0.1150059734774116, 0.10934085523256787, 0.10726653658897867, 0.10532886649482887, 0.10272291690296598, 0.10197487194243937, 0.09756958090356083, 0.0945249676245794, 0.09265639520815494, 0.09192328803022942, 0.09060525299304167, 0.09049841174829254, 0.08048114102267423, 0.08040105111154183, 0.08010342629738876, 0.07992095121214415, 0.07658487183692309, 0.07617110541908634, 0.07458627225738823]\n",
      "Row 2 - Column Numbers: [ 4 79  5  0  3  1 78 31 20 77 85 21 17 12 35 43 87 83 30 33 91 74 11 44\n",
      " 34 10 36 15 13 86 29 39 19 42 37 32 40 38 89 64 28 61 41], MI Values: [1.0421298348636876, 0.889753767585324, 0.8252189069592397, 0.6901375697065175, 0.6346295603606373, 0.52600823699178, 0.4089563958436999, 0.2885791692349038, 0.26984073230595396, 0.23544670375941035, 0.21914515387782174, 0.2125857191397058, 0.20709995929092173, 0.19750308970805186, 0.18701920286034568, 0.18681968571483498, 0.18419330652618005, 0.1805652907247035, 0.15876062884895603, 0.158099218500249, 0.15702895570463316, 0.15700514453794945, 0.15460225559136997, 0.14614605566375083, 0.11747560005255142, 0.1108491328808272, 0.1096084538611164, 0.10428901675494728, 0.10194617541772022, 0.09732347543015507, 0.09469648273846154, 0.09409837181553105, 0.09214628161064109, 0.09190658625377424, 0.0914136839587858, 0.09002264997452336, 0.08826839034197409, 0.08794009077204912, 0.08732427486062821, 0.08295219935787657, 0.08247104503342495, 0.08075786448081335, 0.07942866688885175]\n",
      "Row 3 - Column Numbers: [ 2  5 79  4  0 84  1 78 77 31 20 17 85 83 21 87 43 35 12 74 91 33 44 30\n",
      " 11 34 64 36 86 10 46 37 41 89 39 32 38 15 29 42 40 19 56], MI Values: [0.6346295603606364, 0.6014752255233811, 0.5216221690633258, 0.5005956595959162, 0.37428008133733837, 0.29367624960262795, 0.2501813735953151, 0.22968546503017784, 0.168588428573063, 0.15053120343368054, 0.14918195632018705, 0.135719601508959, 0.12331183579416383, 0.12212949345012802, 0.12006037445413753, 0.10828482718467836, 0.1038170751558507, 0.10166237481487972, 0.10067391244311352, 0.0993121350767705, 0.09857437391434942, 0.09072061229028172, 0.09034618967547559, 0.08507553529173251, 0.08430822621926293, 0.07711971317009514, 0.0732968907767324, 0.07188834325973747, 0.06840077448593984, 0.06747669748327834, 0.0662602861970365, 0.06558274587027046, 0.06306413363040075, 0.06298051391441817, 0.06157433149594205, 0.06126513617121354, 0.06113916617078008, 0.06068970280665109, 0.06048824178377199, 0.05799913453610728, 0.057212613678012225, 0.05676014452040157, 0.05643454058528263]\n",
      "Row 4 - Column Numbers: [ 2  5 79  3  0 78  1 44 31 20 77 17 85 12 87 21 83 35 43 11 64 74 30 33\n",
      " 91 10 34 63 36 32 13 19 61 86 24 23 38 46 89 29 15 88 40], MI Values: [1.0421298348636858, 0.9112659905285279, 0.893437297964442, 0.5005956595959136, 0.4673606483958741, 0.3522117773810223, 0.34043212687770286, 0.25771696574601854, 0.227791945861342, 0.17593949417667076, 0.1718626691037226, 0.15309018167041533, 0.14716514799944758, 0.1468250597240388, 0.1467876478550929, 0.14440832752750676, 0.1374753305211449, 0.13262659195667847, 0.13167838609283677, 0.1303296358704138, 0.1297991451019085, 0.1295289172486882, 0.12417935392990831, 0.12068089113273661, 0.11543451299135477, 0.09954623668022755, 0.09367692420842033, 0.09074112883170127, 0.08771441417981674, 0.08734619315226588, 0.08641934307043808, 0.08049320130510296, 0.0793639777794386, 0.07935824289618232, 0.07926789355999908, 0.07907845045093165, 0.07857614620487485, 0.07856401142111924, 0.07698715238078346, 0.07666467817423595, 0.07652558554478439, 0.07609992946234811, 0.07604174073334136]\n",
      "Row 5 - Column Numbers: [ 4 79  2  3  0 78  1 31 43 36 35  7 77 33 20 74 17 30 21 83 85 44 87 86\n",
      " 37 12 29 91 38 89 39 11 28 40 34 42 32 10 41 80 88 90 15], MI Values: [0.9112659905285261, 0.8539429780686714, 0.8252189069592406, 0.6014752255233793, 0.4363240338301635, 0.40195030351981753, 0.32209271522605043, 0.2760329582147678, 0.20819529046906293, 0.20674579006625127, 0.19563347399244257, 0.18293846291297733, 0.17144637756480563, 0.17076852453711044, 0.1697430692708517, 0.16810983519107303, 0.16129782284088812, 0.14845254677791608, 0.1420832575295341, 0.14139989403188924, 0.14129091651330405, 0.13308552892848002, 0.13204341952919751, 0.1305167490968433, 0.12301925557245497, 0.12297734107820624, 0.11470618022646395, 0.11292935145386807, 0.10350223849688867, 0.1028680671126736, 0.10050281527196514, 0.09942878741363614, 0.09875071075038111, 0.09746128685535993, 0.09670112680553178, 0.09376382987344023, 0.09331795784564356, 0.08681805312730084, 0.08605778397885011, 0.08230865790885478, 0.07740754667316363, 0.07668497735519875, 0.07561477718424658]\n",
      "Row 6 - Column Numbers: [64 14 46 63 12 23  8 57  9 62 11 61 32 45 87 13 44  4 10 54 28 47  7 84\n",
      " 27 69 52 72 36 30 35 79 65 74 41  2 56 26 66 34  1 85 92], MI Values: [0.478605916453672, 0.1659311007796953, 0.13099684473508688, 0.11759316702334122, 0.11209322621671447, 0.09453623691659319, 0.08865574838552437, 0.0859220172096915, 0.08576932695849138, 0.08134777223811529, 0.07911821580729761, 0.07748176490715508, 0.07727934830261152, 0.07607959090818373, 0.07597112239010162, 0.07148486877965077, 0.07123886187653383, 0.07119374646681464, 0.06986362657552991, 0.067773162297458, 0.06638342779498618, 0.06549702884688458, 0.0654621562897697, 0.0649124734204598, 0.06278134191716767, 0.06183066532204595, 0.0613978125590382, 0.05919388460622166, 0.05838254740344251, 0.05558434696104264, 0.055331827053077376, 0.05403814410428076, 0.053136251620639285, 0.0529400614221025, 0.05243412828986749, 0.052066717960047804, 0.0518643235699745, 0.05140858603128606, 0.05121302295318664, 0.0509936262443027, 0.05053181341582125, 0.05019818795246955, 0.04816604793903778]\n",
      "Row 7 - Column Numbers: [ 5 17 64 21 63 57 23 46 61  6 79  2  4 52 87 12 27  3 62  9  0  8  1 73\n",
      " 10 20 69 19 47 54 58 11 14 68 88 74 30 32 33 67 31 72 34], MI Values: [0.1829384629129791, 0.10524195919111623, 0.0946233457977872, 0.09121449964563944, 0.07907681278759338, 0.07616119177035774, 0.0681607842361398, 0.06676341580429312, 0.066597172827497, 0.06546215628976793, 0.059427428725374654, 0.05901064569144587, 0.05558987853756037, 0.054813377473760916, 0.05399825056106078, 0.053976980524889306, 0.05053310241240361, 0.05009254312144673, 0.0482538265970307, 0.04809050593593689, 0.047727363031476955, 0.047556140122899215, 0.0474209934989922, 0.047129770164868745, 0.04693364118155152, 0.04555598545496231, 0.04435919441098868, 0.04338328445526862, 0.0431716643311324, 0.04278103642929665, 0.041407256502377976, 0.040946924073455904, 0.04074963195215808, 0.03718480535959223, 0.03666191730525448, 0.036462534916334555, 0.03612339642617801, 0.03608454747954237, 0.03558055210133837, 0.035520966996969605, 0.035348553502023705, 0.03526695646017597, 0.035145156518217036]\n",
      "Row 8 - Column Numbers: [10  9 14 26 11 13 25 91 85 87 12 32 64 24 27 20 21 34 17  6 23 15  1 74\n",
      " 33 30 44  0 28  4  2 77 46  5 89 31 83 78 79 35 88 63 19], MI Values: [0.48698986391151955, 0.375802297419666, 0.2819697411476927, 0.2524540408417879, 0.2289457453068362, 0.21963152219072413, 0.16233774299458315, 0.12410132440415467, 0.11970109613176039, 0.11717444758841289, 0.10941441927598472, 0.10441158737263923, 0.10254326229904187, 0.10209066826928259, 0.09968544490658893, 0.09860668116430737, 0.09797349325439786, 0.09279000891834333, 0.08886645776288304, 0.08865574838552615, 0.08474539401989478, 0.08043587263141738, 0.0804010511115445, 0.07707447313008853, 0.07565747720513727, 0.07521271366405902, 0.0702725389356953, 0.06869053966721772, 0.06518271250260987, 0.06434639902210026, 0.06327216027249083, 0.062200056513681545, 0.06204077732827784, 0.060054597826602496, 0.05864248331363431, 0.05824452931784396, 0.05824405082485651, 0.0575396306220366, 0.05661802684946515, 0.055954172623136955, 0.05292091189701953, 0.052721647755728185, 0.05241070031981643]\n",
      "Row 9 - Column Numbers: [ 8 10 26 13 14 11 32  6 12 25 87 34 64 20 27 91 24 21 17 85 36  1 23  0\n",
      " 28 41 74 63  7 30 62 83 15 61 54  2 72 19 57 79 40 89 78], MI Values: [0.37580229741966775, 0.2739374700127568, 0.1888349353819665, 0.18881791101212642, 0.17302647019022377, 0.14827272551388315, 0.08690570143561605, 0.08576932695849404, 0.08575515951341117, 0.07942615953296617, 0.07512326148058257, 0.06858253221368038, 0.06743046912400352, 0.0606112133373804, 0.060249930177727506, 0.05872512110265582, 0.05556219929455963, 0.05510777850993431, 0.053827948456972585, 0.05356332489102211, 0.05062803388903436, 0.05042486996980955, 0.04914461256289693, 0.04911468770996663, 0.04892501848965658, 0.04833957062141003, 0.04817579082966983, 0.04815235147500374, 0.048090505935939554, 0.047497107903827995, 0.046442659973216394, 0.04500640957005597, 0.044571645079205524, 0.04384180562593176, 0.04255922801340173, 0.04239438289088415, 0.041960240322472586, 0.04195403205745141, 0.04175321361746853, 0.041721734850988845, 0.041382496982518724, 0.039247318738780734, 0.03916411448757362]\n",
      "Row 10 - Column Numbers: [11  8 13  9 91 85 14 87 12 26  1 20 64 25 24  2 21 17 78 79  0 61  4 23\n",
      " 83 15 34  5 77 31 44 32 27 33 30 74 28 43 35  6 41 46 53], MI Values: [0.4993554128442783, 0.4869898639115231, 0.4066358068899456, 0.27393747001275504, 0.2579871837894956, 0.25686672570808167, 0.2251698714598369, 0.22104675256482142, 0.17468399623417863, 0.1595045585205188, 0.14396039237957758, 0.13028693835191518, 0.12993063246484482, 0.1129190817547916, 0.11268616419256361, 0.1108491328808281, 0.10815686636048127, 0.10750415858836693, 0.10461732375843713, 0.10144296896099103, 0.10125880394889109, 0.10067720955484294, 0.09954623668022666, 0.09526800567615812, 0.09120163011638649, 0.09068210425726964, 0.08709868991881109, 0.08681805312730351, 0.08644635750351704, 0.08544174110632596, 0.08386645043593433, 0.08091774681887642, 0.07918640410680755, 0.077949740915769, 0.07776056152449495, 0.07645994681407409, 0.07299784236684648, 0.07182439963604015, 0.07091448732899508, 0.06986362657553258, 0.06936075480536807, 0.06801559120089085, 0.06799093673704792]\n",
      "Row 11 - Column Numbers: [10 85 61 12 13 91 87  1  8 20 21 17 77  0  2 83  9  4 78 14 79 31 24 15\n",
      " 64  5 35 43 44 74  3 33  6 42 30 28 90 34 19 89 22 23 80], MI Values: [0.499355412844281, 0.447794898444446, 0.4211796194747075, 0.4197051791498847, 0.40682029470780456, 0.3865429355312857, 0.296573849422912, 0.23445155092457082, 0.22894574530684064, 0.21618413086183974, 0.17612200358653762, 0.1627161637347161, 0.15529190588759256, 0.15513395543730546, 0.15460225559137086, 0.14976259321938645, 0.1482727255138805, 0.13032963587041646, 0.12508164598781324, 0.12287505739090143, 0.12041417972820945, 0.11341149652601601, 0.10784355126935719, 0.10663625668288024, 0.10500346113093073, 0.09942878741363259, 0.096740469127222, 0.09481730555193213, 0.08789263097170963, 0.08465931443259134, 0.08430822621926115, 0.0819176206772605, 0.0791182158072985, 0.07587529502254231, 0.0758563574615021, 0.07518085992455958, 0.07463339072882835, 0.0729801592932775, 0.06976258783125644, 0.0691934966107981, 0.06893504056359223, 0.06614162517794231, 0.06530714718931119]\n",
      "Row 12 - Column Numbers: [11 13  1  2  0 20 10 85 79 77 21  4 31 74 43 30 87 33 91 35 17 78  5 83\n",
      "  6 61  8 64 86  3 34 36 14 37 28 40 39 29 42 89 44 38  9], MI Values: [0.41970517914988204, 0.2820044236370247, 0.22954525563754302, 0.19750308970805097, 0.19725693559809976, 0.19049650601974388, 0.17468399623417863, 0.16892847033331915, 0.15745268691877712, 0.15476368455904232, 0.1470253698180608, 0.1468250597240388, 0.14662969753092625, 0.14286051344793105, 0.14156956810136734, 0.13732974337876414, 0.13558171850873002, 0.13072864694938868, 0.12921883418740698, 0.12855491233259286, 0.12797358847181428, 0.1251376255189447, 0.12297734107820624, 0.12178764257401742, 0.11209322621671713, 0.11175003676089723, 0.10941441927598472, 0.10535355610052655, 0.10135095971922237, 0.10067391244311619, 0.09993696526051199, 0.09709484343702979, 0.09629848458173385, 0.09592473158963521, 0.09501229751970186, 0.09185969685608963, 0.09122469199042715, 0.08955815291430014, 0.08912140713055461, 0.08890082125607712, 0.08654874505815524, 0.08621577314512052, 0.08575515951341028]\n",
      "Row 13 - Column Numbers: [11 10 12  8  9 85 91 87 78  1 20  2 31 14 35 30 43 33 44  4 79 21 28 74\n",
      " 25  0 34 17 26  6 64 83  5 15 77 36 42 32 80 89 61 54 70], MI Values: [0.406820294707801, 0.40663580688994827, 0.28200442363702294, 0.21963152219071969, 0.18881791101212642, 0.15241639531040452, 0.15188179879224428, 0.11270707168405014, 0.10855159929809766, 0.10726653658897689, 0.10347968403017482, 0.10194617541771755, 0.10045734833963227, 0.09715275871665696, 0.095142371568528, 0.09258617061155316, 0.09195467760153075, 0.08878636983820609, 0.08824878688846738, 0.08641934307043897, 0.08620980383680887, 0.08274041805652033, 0.08202421217934308, 0.08012866253161732, 0.07985596483401824, 0.07790975017566382, 0.07495306478076014, 0.07488041542475532, 0.07181363072769464, 0.07148486877965166, 0.07002602341222808, 0.06900697369544506, 0.06846734306451818, 0.0666776158158564, 0.0664440140391962, 0.06379802149536751, 0.062408309849672605, 0.062004348452000535, 0.05890185010481819, 0.057406820089648924, 0.05485204269998434, 0.05430024107788256, 0.054016668508986676]\n",
      "Row 14 - Column Numbers: [ 8 10  9 26  6 27 64 11 87 25 63 85 13 12 46 91 47 24 20 77 34 17 37 61\n",
      " 36 86 56 29 23 55 79  0 48 83  4 74  2  5 57 32 72 51 30], MI Values: [0.2819697411476918, 0.22516987145983425, 0.17302647019022466, 0.17093143981882442, 0.16593110077969708, 0.1515567092969663, 0.12701720438150055, 0.12287505739089966, 0.12022624072505117, 0.10808026792929493, 0.09840075284083127, 0.09779637211347314, 0.0971527587166543, 0.09629848458173651, 0.09266115822732779, 0.09231436655408931, 0.09074348902636675, 0.07873666169272209, 0.07681486761087797, 0.07067488479129924, 0.06725286085851412, 0.06554506282266725, 0.0641664994737523, 0.06170135977184188, 0.061668865682766416, 0.06094423783477776, 0.05952118983744992, 0.0587014765905316, 0.0585240406935128, 0.05661782886078903, 0.056059091866146105, 0.05562693284596332, 0.05528245353972583, 0.05451886276258566, 0.05432706381529773, 0.05401613896216251, 0.05270106891950288, 0.05173567448447702, 0.05167205271928932, 0.05104880529890021, 0.050294567082459274, 0.05026820068852178, 0.04979484407518253]\n",
      "Row 15 - Column Numbers: [21 16 22 20 17 19 18 85 83  1 91 87 77 73  0 11  2 10  8 12 79  4  5 56\n",
      " 90 23 42 78 61 13 24 35 43 31  3 80 68 32 46 92 57 33 53], MI Values: [0.48722604389986746, 0.47765933545984574, 0.42274734051130114, 0.3684773490976543, 0.3095265239658307, 0.30125231966110366, 0.27326227718117746, 0.2607931482272843, 0.23569399663760038, 0.23100847367209187, 0.226286992520925, 0.22368717713125363, 0.2109149525053864, 0.17737229996765436, 0.16436438822998056, 0.10663625668287935, 0.10428901675494551, 0.09068210425726964, 0.08043587263142005, 0.07994733324017389, 0.07750166086596355, 0.07652558554478794, 0.07561477718424747, 0.07262961413739166, 0.07254756653808414, 0.07129603115169658, 0.06699419564638731, 0.06674255678354601, 0.06669711932901201, 0.0666776158158564, 0.06508609948717492, 0.06380756444094082, 0.06258859383481585, 0.06209333159081609, 0.06068970280665109, 0.06004207076621171, 0.05863023036643167, 0.05587065130398727, 0.05560717684994554, 0.055416447648041434, 0.054577733516099514, 0.051477381196054495, 0.05145699897161915]\n",
      "Row 16 - Column Numbers: [15 18 22 19 21 85 73 17 20 83  1 91 87  0 77 68  2 42 10 23 56 61  5 11\n",
      "  4 90 13 78 57 63 79  3 64 46 92 52 84 80 24 53  8 47 32], MI Values: [0.47765933545984485, 0.39646468501385357, 0.3870402149910266, 0.3091588054074448, 0.28541688685649813, 0.2495265251234624, 0.23365823269839403, 0.19302253406145908, 0.17044387506372072, 0.16718927849869658, 0.13986782406464915, 0.13528675087576136, 0.12870418125103722, 0.101737015609487, 0.09654894383117263, 0.08013941132973557, 0.07497954269839457, 0.0675083713658422, 0.06746525386392133, 0.06694340591739856, 0.06331255297438165, 0.06108123440198021, 0.059929091775576815, 0.05975370525344825, 0.05524048992921937, 0.052897766030480575, 0.051451103064484194, 0.050915937056171146, 0.049854047095866605, 0.049689454222085594, 0.04856746770346909, 0.04659548808807035, 0.046006140165719245, 0.04556275492620987, 0.04529324898574405, 0.04328046495819304, 0.04310793055946416, 0.04279362459041813, 0.04234654693679207, 0.04223363657743562, 0.04159168613493058, 0.040768941888324584, 0.04067108310344292]\n",
      "Row 17 - Column Numbers: [83 21 20  0  1 15 77 19 85  2 91 87 16 92 11  5 22 79  4 18  3 12 73 46\n",
      " 90 10  7 78 64 57 31  8 42 61 56 43 13 62 68 74 35 53 52], MI Values: [1.0668147455974486, 1.021617623019086, 0.4934266968283074, 0.3299090634675217, 0.3283135513911546, 0.30952652396583336, 0.299093897359759, 0.2719089149660965, 0.24799566598007683, 0.20709995929092084, 0.2001069525344823, 0.19689724643638318, 0.1930225340614582, 0.16969542448540675, 0.16271616373471876, 0.16129782284088456, 0.15874125412953077, 0.15630527248319748, 0.153090181670418, 0.13764098894343224, 0.13571960150895812, 0.1279735884718134, 0.11461081534221496, 0.11280369881762375, 0.11040902183482348, 0.1075041585883687, 0.10524195919111712, 0.1047767078550299, 0.10037328777475985, 0.0992868325667029, 0.09616040667204562, 0.0888664577628866, 0.0846645868325373, 0.08457972685715465, 0.07971577342061753, 0.07861749607301505, 0.07488041542475354, 0.07054503826931136, 0.06961403770779029, 0.06954563307844097, 0.06903264964802336, 0.06894645621138906, 0.06703671873903527]\n",
      "Row 18 - Column Numbers: [73 19 16 22 15 21 17 83 20  1 91 85 87 77 63 88  0 57 46 72 32 64 90 92\n",
      " 56 78  2 68 42 61 11 70 82  4 62 10 52  5 48 36 75 53 55], MI Values: [0.7893958078076464, 0.5505196890502351, 0.39646468501385357, 0.32015585431856763, 0.27326227718117746, 0.1986950339873701, 0.1376409889434349, 0.1300561044353925, 0.1028199239054004, 0.09060525299304434, 0.08043542246333768, 0.07840025513521187, 0.07415089398027508, 0.073829802711872, 0.0698631855232481, 0.06947413178679618, 0.06937049801544681, 0.0555089312872461, 0.05501723067444342, 0.05297227066477728, 0.05286118816878638, 0.05264544534878457, 0.052266576769972595, 0.050573593189831456, 0.05004107750332221, 0.04951922140218912, 0.04704017567014063, 0.04656039319276406, 0.04583471052896382, 0.04531110745527123, 0.0452698374916638, 0.044711784493036255, 0.04452332972605788, 0.04430454607192402, 0.04406838905054933, 0.04345714793886302, 0.04316032552696658, 0.04294014239589039, 0.04283733769362108, 0.042177627147790275, 0.04216690271784085, 0.04179825178695218, 0.041337731296333224]\n",
      "Row 19 - Column Numbers: [18 73 21 16 15 83 17 22 20  1 77  0 85 87 91  2 90 64 12  4 46 79 92  5\n",
      " 11 68 78 42 10 57 72 75 62  3 31 52 70 56 32  8 30 35 43], MI Values: [0.5505196890502289, 0.4449658563187162, 0.3588428833857771, 0.3091588054074439, 0.301252319661101, 0.28206410473166965, 0.2719089149661009, 0.23610468619476066, 0.2076473979554514, 0.16120899606897776, 0.1483996768217315, 0.13409996608400476, 0.12862613575316484, 0.11907016274300641, 0.10649322098528025, 0.09214628161063843, 0.08561032186586814, 0.08194120218001011, 0.0811618444653357, 0.08049320130510296, 0.07977684117637374, 0.07277800134663526, 0.0708353227962224, 0.07067602202174772, 0.06976258783125466, 0.06634530228217983, 0.06322232364202662, 0.06322090154945581, 0.06289596277964993, 0.06149090076405361, 0.06050821759755998, 0.058831519684985345, 0.05762318703291758, 0.05676014452040601, 0.055853509021861925, 0.05518017282950449, 0.0544766833802548, 0.05387141021679831, 0.05309676005317332, 0.05241070031981998, 0.052023287162046294, 0.05003592431078108, 0.04839550757959277]\n",
      "Row 20 - Column Numbers: [77 21  1 17 83 85  0 15 91 87  2 11 19 12 79  4 16  5 22  3 10 64 78 13\n",
      " 18 61  8 90 31 56 24 46 14 30 92 74 68 34 73 33 42 44 43], MI Values: [0.6456828762580988, 0.5615054795942642, 0.5324618722588088, 0.49342669682830653, 0.4589017533899522, 0.42552426145736355, 0.4190235175463517, 0.3684773490976534, 0.3510509439994527, 0.3260490569519252, 0.26984073230595484, 0.21618413086183885, 0.20764739795544962, 0.190496506019743, 0.18041597931931808, 0.17593949417666988, 0.1704438750637216, 0.16974306927085436, 0.1497647957772532, 0.14918195632018527, 0.13028693835191607, 0.11253209164347666, 0.11158401518017502, 0.10347968403017305, 0.10281992390539951, 0.10190813419336298, 0.09860668116430649, 0.08732179357987757, 0.0842263209541052, 0.0828616535343425, 0.08129397459731802, 0.07862828607228867, 0.0768148676108753, 0.07673835654706895, 0.07064869314149558, 0.06733550911625219, 0.0667893192001614, 0.06677633392818816, 0.06621492860686207, 0.06372475882601236, 0.06355486571293412, 0.061150149623385275, 0.060827899523522966]\n",
      "Row 21 - Column Numbers: [17 83 20 15  1 19  0 16 77 85 22  2 91 18 87 11 12 73  4  5 79 90  3 92\n",
      " 10 78  8 42 61 64 56  7 46 31 68 13 57 43 62 44 35 52 26], MI Values: [1.0216176230190834, 0.7488876659638635, 0.5615054795942669, 0.48722604389986657, 0.4023069759074396, 0.3588428833857771, 0.33215728219305163, 0.2854168868564999, 0.28331594629221524, 0.2688208314872229, 0.22456476967975902, 0.2125857191397058, 0.2086854981064592, 0.19869503398736654, 0.18708052814614362, 0.1761220035865394, 0.14702536981806258, 0.14619238110757227, 0.144408327527505, 0.142083257529535, 0.13959981733842852, 0.12517520234618917, 0.12006037445413664, 0.1117978672601394, 0.10815686636048305, 0.10268663613005469, 0.09797349325439786, 0.09722563185672684, 0.09520585153422978, 0.09236995631917555, 0.09187841023316423, 0.09121449964563855, 0.08964547025689651, 0.08819779567887132, 0.08274897552593963, 0.08274041805651944, 0.08110178494543518, 0.07911198418960996, 0.07348744391152273, 0.06846944162919932, 0.06815788789081711, 0.06802973139084845, 0.06522771175571496]\n",
      "Row 22 - Column Numbers: [15 16 18 19 21 73 17 20 83 85 91 77  1 87 23  0 11  2 56 10 79 13 57  5\n",
      " 42 32 61  8  3 74 64 34 70 24 78 63 68 90 43 72 35 53 62], MI Values: [0.4227473405113029, 0.3870402149910266, 0.32015585431856763, 0.23610468619476155, 0.22456476967976258, 0.19668419399470238, 0.15874125412953077, 0.14976479577725232, 0.14502492612060003, 0.11578837068495584, 0.1063924866874304, 0.10378871318925587, 0.09452496762458118, 0.08969080820395181, 0.07632786384865842, 0.07596636122032496, 0.06893504056359401, 0.06328881794610464, 0.06098127462148906, 0.05727822396969895, 0.054970003136741497, 0.051323177882335536, 0.05062976172811151, 0.050465669694910176, 0.05027063548670352, 0.049760788383411025, 0.047233204160109565, 0.04542566347070398, 0.04382301867003058, 0.04368901502755573, 0.04358675196225281, 0.042850022291132994, 0.04278545874037132, 0.04263132941212078, 0.04245227781570726, 0.04240480524732426, 0.04177115423568889, 0.04146334279107311, 0.041258234396297944, 0.04113645596182369, 0.040745425400359636, 0.040726001607573004, 0.040577710389676724]\n",
      "Row 23 - Column Numbers: [64 57 87 44 10  6 24 91 85 61  8  4 22 63 15  7 16  0 11 17 92  2 12 21\n",
      " 14 55 47  1 74 56  5 13 79 62  9 31 25 77 26 83 32 20 46], MI Values: [0.1238287448328963, 0.11007546217848985, 0.10279703918589878, 0.09985139888774786, 0.09526800567615457, 0.09453623691659319, 0.09442643580457855, 0.092779592553069, 0.08797109748794085, 0.08578580449603201, 0.08474539401989523, 0.07907845045093076, 0.07632786384865975, 0.07257144170704688, 0.07129603115169214, 0.06816078423614158, 0.06694340591739678, 0.06631267495817283, 0.06614162517793609, 0.06462454817737662, 0.06377017167667276, 0.06238952944812581, 0.06198182224754323, 0.06102500139047695, 0.05852404069351369, 0.058494817456543835, 0.057048950299178, 0.056427588090688374, 0.05575798124214959, 0.05424612918912608, 0.053944258296575676, 0.053394179519995255, 0.05090816537458753, 0.049627949735287835, 0.04914461256289693, 0.04830377167633948, 0.0479154062061089, 0.047404493128977876, 0.04534942266509967, 0.044620281399040174, 0.04423650621570019, 0.04399862638296703, 0.04319511791377284]\n",
      "Row 24 - Column Numbers: [87 25 85 10 11  8 26 91 23 77 64 12 20  4 14 63 61  1 56  0 15 46  2 44\n",
      "  9 27 21 30 75 32 79 62  5 31  3 78 68 60 22 34 16 17  6], MI Values: [0.12664131656206834, 0.12184764568086237, 0.11662871191984614, 0.1126861641925645, 0.10784355126935541, 0.10209066826928304, 0.09988104072929094, 0.09541744286183551, 0.09442643580457988, 0.08554737930800638, 0.08433207450633073, 0.08382766133586106, 0.08129397459731003, 0.07926789356000175, 0.07873666169272342, 0.07871775795832381, 0.07660849160601568, 0.07658487183691687, 0.06753872107738834, 0.06575943129935258, 0.06508609948716693, 0.06378754370319006, 0.06196951220919278, 0.05575375327102261, 0.055562199294558745, 0.05318120567191542, 0.05262117138877809, 0.05116230585414172, 0.05083179402329918, 0.049254453905052564, 0.04814401145309244, 0.04665448807793737, 0.04619072869628571, 0.0458151748730149, 0.044434685459121326, 0.043901624829374875, 0.04323480914173228, 0.04291271895550075, 0.04263132941212122, 0.04238722505216597, 0.042346546936791185, 0.041908005215020694, 0.04135516870134959]\n",
      "Row 25 - Column Numbers: [26  8 24 10 14 13  9 27 64 20 32 30 63 11 21 12 74 33 17 56 23 85 91 15\n",
      " 87 28 61 89 34 38  1 40 43 52 36 80 35 37 41 83 86 88 16], MI Values: [0.22448983276060552, 0.16233774299458315, 0.12184764568086015, 0.11291908175479026, 0.10808026792929493, 0.07985596483401203, 0.07942615953296661, 0.06742082698712792, 0.057769002718598195, 0.05586583465511197, 0.054965263207836124, 0.05443370142787174, 0.053776458305056174, 0.05343401191718833, 0.05308655380792704, 0.05045720325549752, 0.05034647749383048, 0.04992384501594582, 0.0492451891629031, 0.04834454363245477, 0.0479154062061089, 0.047684160601328074, 0.047297099255485975, 0.04577736523629383, 0.0457726787254078, 0.045771120375120766, 0.04566515411493954, 0.043420484714855156, 0.043385152301504526, 0.04150956737140632, 0.04116356278905453, 0.040902739036422275, 0.039271536657020434, 0.03872861083601631, 0.03870735899101785, 0.03823640170302056, 0.03689051731253823, 0.03648924728638114, 0.03594012672179936, 0.03543675472183061, 0.0353375347334941, 0.033978841582392505, 0.033213377245050246]\n",
      "Row 26 - Column Numbers: [ 8 25  9 14 10 27 24 64 13 30 32 21 11 17 20 91 74 85 87 33 34 46  6 43\n",
      " 15 36 35  1 12 63 23 83 41 80 31 72 56 86 84 52 37 28 61], MI Values: [0.25245404084178746, 0.22448983276060552, 0.1888349353819665, 0.1709314398188191, 0.15950455852051704, 0.10013893815186226, 0.09988104072928916, 0.08361194904788949, 0.07181363072768843, 0.06658416020495395, 0.06642109881221003, 0.06522771175571318, 0.06133706698861552, 0.060864275396509626, 0.06030983748989538, 0.05855558719449405, 0.058118774994220246, 0.05502112683089955, 0.054955567957541085, 0.0548802691847472, 0.05446576296866468, 0.05385131209205429, 0.05140858603128562, 0.04892271442605356, 0.048556550337056414, 0.047843331021867996, 0.04718698058252446, 0.04666834102500239, 0.04641197580127887, 0.04620099613250428, 0.045349422665099226, 0.045142856596432246, 0.04487870650962478, 0.04102053350114243, 0.03975973670425059, 0.039456412404046404, 0.03926146380477791, 0.03883323698171193, 0.038101405951134204, 0.03717014915810957, 0.03702701389699303, 0.03678714727422072, 0.036512909297854]\n",
      "Row 27 - Column Numbers: [65 64 14 46 45 26  8 10 25  6 84  9 12 38 11 13 24 53 74  7 44 21 63 85\n",
      " 47 91 62  0 86  4  3  5 31 43 61 87 76 20 80  1 77 37 29], MI Values: [0.6065603894953897, 0.18682361749818366, 0.1515567092969663, 0.13632308186498676, 0.10364354834176126, 0.10013893815186492, 0.09968544490658893, 0.07918640410680577, 0.06742082698712792, 0.06278134191716767, 0.06038028586904787, 0.06024993017772662, 0.05954908040441431, 0.05566701959818321, 0.05365543785469562, 0.05349787902327563, 0.053181205671913645, 0.05121607804495909, 0.05107317746817763, 0.050533102412405384, 0.05024731173365815, 0.04849977979742892, 0.04791989593709012, 0.04765153600392935, 0.04741748068507423, 0.04718827956837135, 0.04704704797821968, 0.046555580550760034, 0.045963625687851284, 0.0458714770575126, 0.04550892471748291, 0.04427143864075678, 0.044267360807431544, 0.04422157037556218, 0.044030392965271226, 0.043659800788907965, 0.04331808077932564, 0.04308091954790427, 0.04297197397555763, 0.042923144439217076, 0.04277349385328666, 0.04153155742864545, 0.040719138411590805]\n",
      "Row 28 - Column Numbers: [89 38 88 37 40 86 29 41 39 36 33 74 30 34 35 43 32 31 56 78  5 44 12 80\n",
      " 79  2 13 42  1 11 10  4 62  6  8 68 90 64 52 17  0 54 61], MI Values: [1.0046755344608442, 0.8668221841314496, 0.7614158768816583, 0.7435037784407115, 0.7401508914135695, 0.7092838503040948, 0.6969500914396249, 0.6683242642188869, 0.6188553437563042, 0.5887599355969604, 0.573378254007582, 0.4637692211865332, 0.44110042693832696, 0.43990166348400894, 0.3542576214733666, 0.3130926126664333, 0.3038339983430083, 0.1631475034181804, 0.14153000235829616, 0.10874080446091217, 0.09875071075037845, 0.0973992316948431, 0.09501229751970275, 0.09424947908653536, 0.09026690572979579, 0.08247104503342673, 0.08202421217934486, 0.08020834452426495, 0.07617110541908723, 0.0751808599245587, 0.07299784236684648, 0.07194026557628508, 0.07174551471409618, 0.06638342779498885, 0.06518271250260632, 0.06489586595952179, 0.0643523399002186, 0.06270446068020075, 0.05772311949448383, 0.056954572674678516, 0.05644466945878257, 0.05541299819598944, 0.05407556787339285]\n",
      "Row 29 - Column Numbers: [37 86 38 89 39 28 40 36 88 74 33 41 43 35 30 34 31 56 32  5 78 79 44 80\n",
      "  2 12  4 90  1  0 87 42 46 77  3 14 64 11 85 62 63 57 13], MI Values: [1.124331483930141, 0.9904397714916939, 0.8561076404645682, 0.7571541803206943, 0.7394482075767632, 0.6969500914396267, 0.6243050233062002, 0.6127287729060686, 0.5162986988948424, 0.5004203013385551, 0.4839723248105665, 0.44277394507430223, 0.3862199704096003, 0.3611089233159852, 0.3044944524915385, 0.30210464330076015, 0.20191448281292157, 0.171307375513706, 0.1557361930389609, 0.11470618022646129, 0.1142833513780932, 0.10420208049496082, 0.10392751587923588, 0.09785175941231206, 0.09469648273846332, 0.08955815291429925, 0.07666467817423417, 0.07002944857802351, 0.06654779481397011, 0.06576826886766884, 0.06531253837083639, 0.06416664878429135, 0.06302637459570448, 0.06065012243418977, 0.06048824178377199, 0.058701476590528046, 0.05802769428221577, 0.049098105017652216, 0.04872740090602523, 0.04751490159093841, 0.04718646229756551, 0.047177310303764486, 0.04510718141365366]\n",
      "Row 30 - Column Numbers: [33 35 74 32 34 43 28 31 36 86 89 40 37 38 41 88 29 39 78 79  2 44  5 12\n",
      " 80  4 42  1  0 52 13  3 64 90 10 20 11  8 87 56 85 26 77], MI Values: [0.8392067051587295, 0.6637829223064537, 0.6484729630309518, 0.5649484715892896, 0.5416346036080313, 0.4933942675879779, 0.4411004269383261, 0.4130016958463507, 0.38187736651662174, 0.3742297238726069, 0.3717084490392537, 0.3527990507831582, 0.33036985608766933, 0.32508215731131695, 0.315969342937767, 0.3120618690279784, 0.3044944524915376, 0.2926134592339231, 0.245510624027526, 0.1906085060616709, 0.15876062884895248, 0.15101976681000995, 0.14845254677791608, 0.1373297433787659, 0.13577620649841027, 0.1241793539299092, 0.11531395362702757, 0.1150059734774116, 0.10962686909974106, 0.10641737910058513, 0.09258617061154961, 0.08507553529173606, 0.08219023403697623, 0.07857807032348152, 0.07776056152449762, 0.0767383565470654, 0.0758563574615021, 0.07521271366405902, 0.07367325277221859, 0.06707550157230102, 0.06691537715915796, 0.06658416020495572, 0.06275013897899484]\n",
      "Row 31 - Column Numbers: [43 78 35 30 33 44 74 79  2  5 36 42 86  4 37 29 34 80 32 38 28  0  1 89\n",
      " 39  3 12 40 41 88 11 87 85 13 17 21 10 91 20 83 77 64 90], MI Values: [0.8121927311946013, 0.7638100129208842, 0.7457506706593477, 0.41300169584634716, 0.40367630493282647, 0.3834036968008201, 0.36859551535020874, 0.3469763013969196, 0.288579169234902, 0.2760329582147696, 0.2539363056818278, 0.2480981515670253, 0.22807412650458492, 0.22779194586134022, 0.21452991980362057, 0.20191448281292157, 0.1870476252617994, 0.18479080672561743, 0.17115190570613592, 0.167611070828948, 0.16314750341817774, 0.16211076425159288, 0.16121744315732478, 0.15421271891570942, 0.1526762354992739, 0.15053120343368143, 0.14662969753092536, 0.1369994315782277, 0.12987048179875593, 0.1178467066606661, 0.11341149652601867, 0.10896037047705764, 0.1060824704994614, 0.10045734833963404, 0.09616040667204917, 0.08819779567887043, 0.08544174110632508, 0.08539580505605926, 0.0842263209541061, 0.08252825085347038, 0.07208828414576374, 0.06851019554836757, 0.06594386443863964]\n",
      "Row 32 - Column Numbers: [34 30 52 33 28 88 40 74 35 89 41 86 38 43 39 37 36 31 29 44 54 78  8 79\n",
      "  5  2  4  9 62 10 12 42  0  6 80 64  1 26 87 61 90 13  3], MI Values: [0.6589132113122833, 0.5649484715892905, 0.5366720434860506, 0.31429643099880256, 0.3038339983430083, 0.2746754336314945, 0.264343537327707, 0.254749734631722, 0.24376381697460836, 0.23990089864081465, 0.2315338746347546, 0.2027410833178278, 0.197909157760205, 0.19253106758836758, 0.1831205200479813, 0.17952444982802795, 0.17752977924984759, 0.1711519057061368, 0.15573619303895825, 0.12104168683611505, 0.11793416791373534, 0.1155347151347117, 0.10441158737263923, 0.09567236193821138, 0.09331795784564623, 0.09002264997452247, 0.087346193152265, 0.08690570143561605, 0.08212300251017712, 0.08091774681887465, 0.07909381487392952, 0.07802938607998389, 0.07772961987272353, 0.0772793483026124, 0.07650826602535332, 0.07345476684191166, 0.07062525451403978, 0.06642109881221536, 0.06429935007831045, 0.06347776301673225, 0.06345428849975132, 0.06200434845199787, 0.061265136171211765]\n",
      "Row 33 - Column Numbers: [74 30 36 35 43 86 28 37 89 38 29 40 34 39 41 88 31 32 78  5 79  2 44 80\n",
      " 12  4 42  1 56  0  3 13 85 64 87 11 90 10  8 52 77 61 91], MI Values: [1.1137204124807507, 0.8392067051587295, 0.7259968303690219, 0.676225408758059, 0.6277452858407466, 0.6078933190308362, 0.5733782540075802, 0.5576286905708168, 0.5364183007679388, 0.49716674763380553, 0.4839723248105665, 0.4791060933274043, 0.45408232882174193, 0.4358859922207907, 0.4346502711337248, 0.4047557520194287, 0.40367630493282647, 0.31429643099880256, 0.21439117181920508, 0.1707685245371131, 0.1675397929716098, 0.1580992185002481, 0.1558944425895863, 0.1513697471049289, 0.13072864694939046, 0.12068089113273839, 0.11403454812488523, 0.10934085523256698, 0.10568767232683207, 0.09664578770578203, 0.09072061229028083, 0.08878636983820609, 0.0853957938074732, 0.08444826940177563, 0.0822160314308702, 0.08191762067726316, 0.07829650162065782, 0.07794974091576812, 0.07565747720513549, 0.0721596876850441, 0.06870563600714075, 0.06766819910745436, 0.06454231972101443]\n",
      "Row 34 - Column Numbers: [32 41 40 89 30 88 33 28 38 39 74 86 37 36 29 35 43 31 78 52 79  2 12 80\n",
      "  5  4  8 44  1 56  0 10 42  3 13 11  9 85 90 14 20 87 91], MI Values: [0.6589132113122842, 0.6479726613644816, 0.6043685240765004, 0.5628237492307457, 0.5416346036080313, 0.521645640678436, 0.45408232882174193, 0.43990166348400983, 0.4368469340751924, 0.39158474017250366, 0.3551015296305442, 0.3436127338197732, 0.3342616147154853, 0.30793458819287167, 0.30210464330076015, 0.2547895016786663, 0.25147509845387006, 0.18704762526179852, 0.1318444892478734, 0.12773246250446846, 0.12182153097619519, 0.11747560005254787, 0.09993696526051377, 0.09689650292456253, 0.09670112680552911, 0.09367692420841855, 0.09279000891834333, 0.09093985620778966, 0.09049841174829432, 0.08918579292805706, 0.08750394746818113, 0.08709868991881464, 0.08002420593659476, 0.07711971317009425, 0.07495306478075747, 0.07298015929327839, 0.0685825322136786, 0.06771394965493194, 0.06748508102814021, 0.06725286085851323, 0.06677633392818727, 0.06352632300524341, 0.05979450877373882]\n",
      "Row 35 - Column Numbers: [43 31 33 30 74 36 86 37 29 78 28 38 89 44 39 34 40 32 88 79 80 41  5  2\n",
      " 42  4 12  1  0  3 11 13 56 85 87 90 10 64 17 21 83 15 91], MI Values: [1.3860244468954068, 0.7457506706593469, 0.676225408758059, 0.6637829223064564, 0.6417520640136267, 0.41003162791165604, 0.39846097278793113, 0.37245697314779047, 0.36110892331598254, 0.36035661286731724, 0.3542576214733648, 0.28812166153925034, 0.28455742734958633, 0.2744838416218025, 0.25908379307944696, 0.2547895016786681, 0.2444710266515937, 0.24376381697461103, 0.2113827569500044, 0.20596754398312012, 0.2032245059398745, 0.20034425775401932, 0.1956334739924417, 0.1870192028603448, 0.18522516757732976, 0.13262659195667936, 0.1285549123325911, 0.11642248941903688, 0.11361591888716038, 0.1016623748148815, 0.09674046912721845, 0.095142371568528, 0.0801836035458896, 0.07727436282669675, 0.07446311599579492, 0.07216427126333969, 0.07091448732899774, 0.06950218448865986, 0.06903264964802514, 0.06815788789081711, 0.06455351051612634, 0.06380756444093993, 0.05848415311997446]\n",
      "Row 36 - Column Numbers: [86 37 33 29 74 28 89 41 38 40 39 43 35 88 30 34 31  5 32 56 78 79 80 44\n",
      "  2 12  4 42  1  3 90 10  0 13 72 14 77 64 87 57 70 46  6], MI Values: [1.0233770024292177, 0.8615166885581989, 0.7259968303690219, 0.6127287729060713, 0.6090092895887054, 0.5887599355969613, 0.5752000583378694, 0.5713794920745894, 0.5355098016260644, 0.47454758830574484, 0.4665352887983394, 0.4335648849167999, 0.41003162791165515, 0.39112029603754017, 0.38187736651661996, 0.30793458819287167, 0.2539363056818287, 0.20674579006625216, 0.1775297792498458, 0.15081603715863867, 0.14656523125808896, 0.11619314258747515, 0.11571876599131148, 0.1145234869763252, 0.10960845386111995, 0.0970948434370289, 0.0877144141798194, 0.07775809933113642, 0.07458627225738823, 0.07188834325973659, 0.06954945457795603, 0.06702934232361812, 0.06656537960473763, 0.0637980214953684, 0.06265064870037129, 0.06166886568276819, 0.06121318706422585, 0.06076563582838368, 0.0603698282500984, 0.0600022474540296, 0.05999309743629677, 0.059587362304820424, 0.05838254740343718]\n",
      "Row 37 - Column Numbers: [86 29 36 38 89 28 39 40 33 74 88 41 43 35 56 34 30 31 32  5 78 79 44 80\n",
      " 12  2  4 90  1 42 87 46  3  0 14 77 57 64 75 10 81 85 72], MI Values: [1.45827221487633, 1.1243314839301428, 0.8615166885582006, 0.8339552318828192, 0.75725247965641, 0.7435037784407115, 0.6894104126018572, 0.6269405732545383, 0.557628690570815, 0.5514988683591895, 0.5065004040074994, 0.4944806219210722, 0.4048082990644746, 0.37245697314779047, 0.35940226604219117, 0.3342616147154871, 0.3303698560876711, 0.21452991980362324, 0.17952444982802884, 0.12301925557245674, 0.1229936336440689, 0.11167013683338922, 0.10660787110909098, 0.09822950179437395, 0.09592473158963699, 0.09141368395878491, 0.07514331037207178, 0.07091755529673804, 0.06883285800983607, 0.06871969299735081, 0.066765545099301, 0.06572403954205441, 0.06558274587026869, 0.06455866987752579, 0.06416649947375319, 0.06138718973277957, 0.05958381308008942, 0.0586839187321484, 0.05770927457102015, 0.05541200876063623, 0.0543002203644134, 0.053567885640179114, 0.053098326138301566]\n",
      "Row 38 - Column Numbers: [89 39 40 28 29 37 88 86 41 36 33 74 34 30 43 35 32 31 56 78  5 79 44  2\n",
      " 80 12  4 90 42 87 64 10  3  0 46 54 27 63  1 55 61 52 81], MI Values: [1.2419280927673926, 0.9495031915623935, 0.9353087992452069, 0.8668221841314478, 0.8561076404645709, 0.8339552318828174, 0.7568375359220987, 0.7540596341394155, 0.6590139783160547, 0.5355098016260609, 0.49716674763380464, 0.4638361476100483, 0.4368469340751897, 0.32508215731131607, 0.2970750486302043, 0.28812166153925034, 0.19790915776020768, 0.16761107082894533, 0.14324753303636406, 0.10392867184476451, 0.10350223849689133, 0.09301615106454886, 0.08916423701914233, 0.08794009077204823, 0.08653427377214928, 0.08621577314512141, 0.07857614620487752, 0.07291292443408093, 0.06775644455948626, 0.06587368807998661, 0.06444153292271437, 0.06239411896947633, 0.0611391661707783, 0.05890813572238418, 0.05743119615494585, 0.05657172017433254, 0.0556670195981841, 0.052999594620209756, 0.05251122766241956, 0.05144646558632271, 0.050525831605085614, 0.05046119874021926, 0.050427398365081366]\n",
      "Row 39 - Column Numbers: [89 40 38 88 29 37 86 28 41 36 33 74 34 30 43 35 32 31 56 78 79  5  2 44\n",
      " 12  4 80 90 46 64 42  0  3  1 87 54 57 10 85 81 11 75 13], MI Values: [1.0535035116401659, 0.980751027799518, 0.9495031915623944, 0.7414381495833338, 0.7394482075767623, 0.6894104126018581, 0.6322229406595952, 0.6188553437562998, 0.597892725921354, 0.46653528879833495, 0.4358859922207863, 0.41880685619855296, 0.3915847401725019, 0.29261345923392224, 0.2629228824826715, 0.2590837930794496, 0.18312052004798485, 0.15267623549927567, 0.11061737849190223, 0.10303541936903038, 0.10121071598448683, 0.10050281527196514, 0.09409837181553016, 0.09268755609898616, 0.09122469199042627, 0.07574221883219856, 0.07038469791400459, 0.06777425757345945, 0.06718928231977817, 0.06637371235615408, 0.06470157204124849, 0.06376207874312012, 0.06157433149594027, 0.059317843630458, 0.056927475789509074, 0.0553570174716711, 0.050475458950668184, 0.049665682066896366, 0.048873507505192926, 0.048724267224924844, 0.048532049612547645, 0.045653657389332025, 0.045387402202069715]\n",
      "Row 40 - Column Numbers: [88 89 39 38 41 28 37 29 34 86 33 36 74 30 32 35 43 31 56 79 78  5 12  2\n",
      " 90 80 44  4 64 46 10 42 11  0 54  3 87 62 52  8  1 61 13], MI Values: [1.358468758232667, 1.2392621662048944, 0.9807510277995188, 0.935308799245206, 0.926520358369948, 0.7401508914135668, 0.6269405732545383, 0.624305023306202, 0.6043685240764987, 0.5904546129889008, 0.4791060933274034, 0.47454758830574484, 0.42293019416571376, 0.3527990507831582, 0.2643435373277079, 0.24447102665159282, 0.24139738990497683, 0.13699943157822414, 0.10838563263965639, 0.1029822194696477, 0.09964875862896427, 0.09746128685535993, 0.09185969685609141, 0.08826839034197231, 0.08755455049272953, 0.08752252944643946, 0.08181196297427373, 0.07604174073333958, 0.072912801172893, 0.07131829013591684, 0.06301067329213339, 0.06159199509503921, 0.0600744169282601, 0.05966325856990995, 0.05887006365191372, 0.05721261367801134, 0.05676698284365411, 0.05477366448826615, 0.054719591158505665, 0.0521148561565834, 0.05184786967249444, 0.05173422697187924, 0.050382935130099504]\n",
      "Row 41 - Column Numbers: [40 89 88 28 38 34 39 36 37 86 29 33 74 30 32 43 35 31 56 78 79  5 44  2\n",
      " 80 12 90 62 10  0  1  3 42  4 61 64 92 11 70  6  8 52 13], MI Values: [0.9265203583699506, 0.9100181021852727, 0.8687228214668874, 0.6683242642188896, 0.6590139783160538, 0.6479726613644816, 0.5978927259213549, 0.5713794920745912, 0.4944806219210731, 0.47456031717445235, 0.44277394507429957, 0.4346502711337239, 0.33199699186004406, 0.3159693429377697, 0.23153387463475372, 0.21422375662965543, 0.20034425775401843, 0.1298704817987586, 0.11875744932887322, 0.0926509060956926, 0.08676758111423233, 0.086057783978851, 0.08262255635642912, 0.07942866688885086, 0.0785488622631787, 0.0742530711565692, 0.07307672025710232, 0.06941263844280599, 0.06936075480536719, 0.06665335877299139, 0.06410363270210784, 0.06306413363039987, 0.06207958706935557, 0.05954608451087129, 0.0593461118278249, 0.057899646129423665, 0.05389698575662916, 0.053384856694632, 0.05325141402769873, 0.05243412828986749, 0.052078907698307475, 0.05177082062384475, 0.050887404336976694]\n",
      "Row 42 - Column Numbers: [90 31 44 43 35 78 80 30 92 33 21  5  1 74  2 79 12  0 17 83 28 34 85 32\n",
      " 36 11 86 91 37 38 16  4 15 10 39 29 20 19 87 89 13 41 40], MI Values: [0.5736361560630607, 0.24809815156702442, 0.237501584176659, 0.2123646632862819, 0.18522516757733065, 0.17401757617932745, 0.14508216519352857, 0.11531395362702668, 0.11438741669921182, 0.11403454812488256, 0.09722563185672684, 0.09376382987344112, 0.09265639520815316, 0.09219897198964677, 0.09190658625377246, 0.09102336506577036, 0.08912140713055283, 0.08872664637914252, 0.08466458683253641, 0.08290682477634803, 0.08020834452426406, 0.08002420593659121, 0.07969793759561306, 0.07802938607998477, 0.07775809933113642, 0.07587529502253965, 0.0754741707644273, 0.06881214952706838, 0.06871969299735348, 0.06775644455948715, 0.06750837136584042, 0.06712048581871777, 0.06699419564638998, 0.06547249101527441, 0.06470157204125115, 0.06416664878429224, 0.06355486571293678, 0.0632209015494567, 0.0630884431737817, 0.06261691628512, 0.06240830984967349, 0.06207958706935468, 0.0615919950950401]\n",
      "Row 43 - Column Numbers: [35 31 33 74 30 36 86 37 29 78 28 44 38 89 39 34 40 80 41 42  5 79 88 32\n",
      "  2 12  0  4  1  3 11 13 87 85 56 83 21 17 90 10 91 77 64], MI Values: [1.386024446895405, 0.8121927311945987, 0.6277452858407475, 0.6243039700489881, 0.4933942675879788, 0.433564884916799, 0.4240950333084843, 0.4048082990644737, 0.38621997040959855, 0.370397111365631, 0.3130926126664342, 0.30395671539799096, 0.2970750486302043, 0.28802774608809134, 0.2629228824826706, 0.25147509845387095, 0.24139738990497772, 0.2276321837680122, 0.21422375662965365, 0.21236466328628278, 0.20819529046906204, 0.20739130754119195, 0.20626412498042956, 0.1925310675883667, 0.18681968571483676, 0.14156956810137, 0.1358699397958949, 0.1316783860928359, 0.12913107009156466, 0.1038170751558507, 0.09481730555192946, 0.09195467760152898, 0.08755593140089069, 0.08744850763647793, 0.08170555433368687, 0.081560766459293, 0.07911198418961085, 0.07861749607301682, 0.07721049556759585, 0.07182439963604015, 0.07147186167010044, 0.06546454180161465, 0.06421723199729623]\n",
      "Row 44 - Column Numbers: [31 43 78 35  4 42 33 79 30  2 74  5 54  0 64 32 36 80 86 37 29 87 23 88\n",
      "  1 28 39 89 34  3 38 13 11 12 10 85 46 41 40 63 91 62  6], MI Values: [0.38340369680082365, 0.3039567153979892, 0.2940959242977499, 0.27448384162180073, 0.2577169657460203, 0.23750158417665634, 0.15589444258958807, 0.1535208253346898, 0.15101976681000817, 0.14614605566374905, 0.13751208245379942, 0.1330855289284827, 0.13216267787018499, 0.12631372813240205, 0.12575424005177993, 0.12104168683611682, 0.11452348697632786, 0.11196280971917094, 0.10936129874317668, 0.10660787110909098, 0.10392751587923676, 0.10044717697415884, 0.09985139888775052, 0.09784483548609302, 0.09756958090355994, 0.0973992316948431, 0.09268755609898616, 0.09241113709100457, 0.09093985620779232, 0.0903461896754747, 0.08916423701913878, 0.0882487868884656, 0.08789263097170785, 0.0865487450581588, 0.08386645043593699, 0.08318123056251459, 0.08302480760550157, 0.08262255635642735, 0.08181196297427551, 0.08074364625578223, 0.07356394424112711, 0.07306242342033098, 0.07123886187653294]\n",
      "Row 45 - Column Numbers: [65 60 66 76 64 63 69 27 84 53 54  6 75 62 57 70 81 12 46 61 11 50 72 87\n",
      "  1 10 85 52 49 68 13 77  3 48 21 24 32 90 91  8 30 79 15], MI Values: [0.3355390992669385, 0.24105785735212137, 0.16669975622521527, 0.14089157380955708, 0.13477024068243892, 0.11692650889904499, 0.10868038934784607, 0.10364354834175771, 0.10150362847124583, 0.09056761307301286, 0.0798331274015025, 0.07607959090818639, 0.07550304956704501, 0.07129070394238113, 0.06353587781859105, 0.06252081423776445, 0.05993439653997168, 0.05696539251436761, 0.05614165957912931, 0.05305353245500477, 0.05289097853795344, 0.05163697152796942, 0.05126811930396258, 0.049018668863451076, 0.048759179040770206, 0.04826951163990145, 0.04548841097074785, 0.045170627201460256, 0.04515557347533239, 0.04505498244851758, 0.04468423892141704, 0.04437075080106645, 0.04344271363863772, 0.042062378026346714, 0.041189709960936405, 0.04052516260945005, 0.04034464006210747, 0.04008368476259694, 0.039929482136464856, 0.039675854506701747, 0.039107723692991314, 0.038854237195490526, 0.038161379909507964]\n",
      "Row 46 - Column Numbers: [64 51 55 59 48 68 47 58 61 87 75 49 72 56 54 84 27 70 67  6 74 57 17 69\n",
      " 81 14 21 50 77 63 44 52 85  1 19 76 20  4  0 79 62  2 40], MI Values: [1.1094691017199603, 0.36567183873432274, 0.3141727399115952, 0.23992709365254683, 0.2171439106790931, 0.19852690016740127, 0.18923509125775695, 0.1858984961031256, 0.17267857439960022, 0.16549438774061187, 0.15983167864594883, 0.15828858721216044, 0.15559450174685807, 0.1460850846009656, 0.14012136027135202, 0.13751725928655478, 0.13632308186498943, 0.1328114960531792, 0.13279522094755158, 0.13099684473508688, 0.11736212179504424, 0.11368720902898488, 0.11280369881762642, 0.105422623025202, 0.10140282553967683, 0.09266115822732957, 0.08964547025689651, 0.08911598382671393, 0.08487347419103042, 0.08355750196952805, 0.08302480760550068, 0.08232030940720492, 0.08171791357507097, 0.08010342629738698, 0.07977684117637374, 0.07963991449703212, 0.07862828607228867, 0.07856401142112102, 0.07681250087322677, 0.07650530330583649, 0.07403272493206359, 0.07325788085011453, 0.07131829013591773]\n",
      "Row 47 - Column Numbers: [48 55 82 49 51 64 46 61 56 50 14 57 87 54 63 75 67 70 69  6 72 74 68 23\n",
      "  4 52 20 59 38 27 85 84 11 81 33 92 89 60 41  7 36 77 19], MI Values: [0.4249124097885648, 0.4187425231559816, 0.3602265067790995, 0.2776897644328633, 0.24912743330867393, 0.1987447932521178, 0.18923509125775695, 0.15384874665912562, 0.10368137158256019, 0.09785925823341302, 0.09074348902636764, 0.08687796447828866, 0.08569788060934425, 0.08001798979213337, 0.07907233827318905, 0.07403127407645904, 0.07249971148987289, 0.07068379697727956, 0.06874455994522588, 0.06549702884688635, 0.06175094572082518, 0.06009771362514993, 0.05906462224581688, 0.05704895029918333, 0.056865014508378664, 0.05682164950861601, 0.05161482461035316, 0.05139487626535377, 0.050000458629791744, 0.047417480685076896, 0.04726109720318572, 0.04708602460329292, 0.0467491462024574, 0.04656568399330041, 0.045808067196454694, 0.04460527570146677, 0.04416183571061527, 0.043961928173374076, 0.04334931626754024, 0.043171664331128845, 0.04285749863832411, 0.041651660789991496, 0.040805913716284614]\n",
      "Row 48 - Column Numbers: [49 55 47 51 46 50 64 75 68 67 69 87 61 54 58 81 59 70 56 57 63 14 52 84\n",
      "  6 73 72 91 60 66 18 45 85 11 74 21 17  4 76 38 19 32 44], MI Values: [0.553678897514204, 0.5019751647569173, 0.4249124097885639, 0.2875171464071613, 0.2171439106790931, 0.1743136297813912, 0.11110937927605313, 0.10037244122026134, 0.08934545133594263, 0.08190429469032878, 0.0736143304488408, 0.07327006385127088, 0.0721867594925314, 0.07042527416616018, 0.0687315220763578, 0.06681937537003169, 0.06642447830364517, 0.06437836072642522, 0.0635873831512015, 0.060791248768552464, 0.057609186216970976, 0.05528245353972938, 0.05372925078899371, 0.04909830573294105, 0.04808633609087387, 0.045306406824380474, 0.04489736208567496, 0.044709846969715805, 0.04357966587574236, 0.04284931649405177, 0.04283733769362197, 0.0420623780263476, 0.040772805188195704, 0.04013167977317522, 0.03986903738847314, 0.03954931815568408, 0.03897874301162396, 0.03884934604555568, 0.0387817158798871, 0.03828887823525573, 0.03729803186228775, 0.03670448581979002, 0.03666047870806732]\n",
      "Row 49 - Column Numbers: [48 55 47 50 51 75 46 69 54 64 68 81 52 61 57 67 87 63 70 56 60 84 11 14\n",
      "  6 45 13 66 58 12 59 72 10  1 79  4 77 85 32  0 74 40 36], MI Values: [0.5536788975142031, 0.30360053691119226, 0.27768976443285975, 0.2735029225169381, 0.1755926065938338, 0.16380558437787318, 0.15828858721215955, 0.09982396156077034, 0.0899951771509615, 0.08729689308508082, 0.0805251845303161, 0.07578213385519295, 0.0734512632183959, 0.07118839940287724, 0.06818162225492586, 0.06462675171117471, 0.05826597066506878, 0.05474056322253951, 0.05205162711625633, 0.04949584081348313, 0.04890714820172626, 0.047598231033918914, 0.0471786080006531, 0.04697649944513582, 0.04612338247236547, 0.04515557347533328, 0.04394002279515519, 0.0427889260255494, 0.04277730549634029, 0.041579343265056856, 0.03968935771140636, 0.03878327857790431, 0.03721262391298552, 0.03708316769882014, 0.03707875631470614, 0.03437124492900345, 0.03420072144079178, 0.03393860185339559, 0.03373647790879719, 0.03296788902954706, 0.032940030634634354, 0.03271399526283414, 0.03233124919474406]\n",
      "Row 50 - Column Numbers: [75 49 48 69 81 57 54 47 55 68 52 46 64 84 87 51 76 45 67 10 12 14 66 63\n",
      " 60  4 74 85 17 11  6 70 33 79 83  8 36 24 21  0 88 89 40], MI Values: [0.38569583316040035, 0.273502922516939, 0.1743136297813921, 0.13649561521326792, 0.13615369070630745, 0.12386611734750641, 0.11005231669100635, 0.0978592582334139, 0.09343475605257989, 0.09313301709157429, 0.08963552340153047, 0.0891159838267166, 0.08223331555010471, 0.06909627215253966, 0.0664099664637332, 0.05717803565613533, 0.05211485875131405, 0.051636971527967646, 0.049028136696537494, 0.04645372478558407, 0.046362851486650314, 0.04624367400979423, 0.04570965837784602, 0.04395880445259959, 0.04352223482917594, 0.04297224529545307, 0.04249884332512721, 0.04210332584072418, 0.041711486256092556, 0.041695189003549515, 0.04113881744298897, 0.04104741966052927, 0.04091402778420328, 0.04064421390754891, 0.04045686991204356, 0.03995848045904005, 0.03949861996272741, 0.039383429640937884, 0.038877820203155444, 0.03883494246593333, 0.038717645473936635, 0.038634738171873906, 0.03778877017396365]\n",
      "Row 51 - Column Numbers: [55 46 48 47 49 59 64 61 56 58 68 67 50 54 84 14 87  6 44 52 75 69 63 70\n",
      " 21 76 66 60 57 89  4 32 41 40 81 38 11 23 62 74 72  0 88], MI Values: [0.4918905885238507, 0.36567183873432274, 0.2875171464071622, 0.24912743330867393, 0.1755926065938347, 0.15335403151725657, 0.14408460937434686, 0.1323322880421669, 0.09492283806278046, 0.08131092018359531, 0.06392417227606728, 0.06049342127079882, 0.05717803565613444, 0.05383149700687451, 0.050444118959005024, 0.05026820068852356, 0.04809307532768603, 0.04800319914719342, 0.0474286517687057, 0.046076652615822944, 0.04517706634337504, 0.043804660168771825, 0.042590107680609, 0.03955596847245513, 0.0389668719566183, 0.03840491710777805, 0.03826743593598536, 0.03684825881094511, 0.03623578817846784, 0.0361041768011896, 0.03552228501544441, 0.034884214114486056, 0.03474350659770309, 0.034398958953260284, 0.03368774459666746, 0.03349076627149561, 0.03327235828735464, 0.03304187113566659, 0.03265504215054538, 0.03189647338370527, 0.03187888017866847, 0.03186557598989026, 0.031744992944004125]\n",
      "Row 52 - Column Numbers: [69 32 57 54 81 75 68 34 30 64 50 46 49 33 21 17 63 88  6 61 55 35 86 28\n",
      " 47 19 66  7  4 40 48 74 41 10 72 37 84 58 38 83 70 20  1], MI Values: [0.5772799725175162, 0.5366720434860497, 0.5130885687568068, 0.3225256074571332, 0.29251898737336113, 0.193542163657888, 0.12789690664174191, 0.1277324625044658, 0.10641737910058513, 0.0948475569445888, 0.0896355234015278, 0.0823203094072067, 0.07345126321839857, 0.072159687685045, 0.06802973139084934, 0.06703671873903261, 0.06405860187379542, 0.06273572137952055, 0.06139781255903909, 0.06122875212893497, 0.06013022861701689, 0.05843192812514708, 0.057757311630738606, 0.05772311949448383, 0.05682164950861601, 0.05518017282950538, 0.05499973892547416, 0.05481337747376269, 0.054736479053383746, 0.054719591158505665, 0.05372925078899371, 0.05209049250429132, 0.05177082062384297, 0.05139303267069195, 0.05111353303252564, 0.05089562323484653, 0.05067571023863948, 0.050481480883075136, 0.05046119874022281, 0.05022240658314203, 0.05011325603669903, 0.04998115622272348, 0.04960552836869159]\n",
      "Row 53 - Column Numbers: [62 63 64 45 70 85 17 10 91 72 60  4 69 87 12 46 21 11 15 27 20 19 65  1\n",
      "  5  8  0 84 83 14 16 30 18 79 22 28 73 36 66 33 44  2  9], MI Values: [0.40877114705633577, 0.10768325129662326, 0.09142254528217908, 0.09056761307301286, 0.07763014753084896, 0.07291262831419587, 0.06894645621138817, 0.06799093673704526, 0.06654270992309375, 0.06557217989953035, 0.06551159416228547, 0.06101431583981842, 0.05994221903533248, 0.05849475346295652, 0.05643638304159726, 0.05373645940673466, 0.05359496095281546, 0.05257556822858955, 0.05145699897162004, 0.0512160780449582, 0.04985185416914284, 0.047971786345549106, 0.047543267529873035, 0.04687607939115512, 0.046211483174281476, 0.045677188956067205, 0.04379488308218882, 0.04284987062613599, 0.04248356027197353, 0.042449553699675846, 0.04223363657743473, 0.04200308548928522, 0.04179825178695129, 0.04128772798638014, 0.04072600160757123, 0.04068711874009434, 0.03933717348757071, 0.03925453370539245, 0.03848324031768957, 0.03752841617132585, 0.03638983181890776, 0.03585269752426079, 0.03562342742166713]\n",
      "Row 54 - Column Numbers: [81 69 52 75 57 68 64 46 44 32 50 62 63 84 49 47 45 66 76 70 74 55 61 87\n",
      " 48 58 72  6 60 83 30 40 21 35 17 38 36 56 28 39 88 13 51], MI Values: [0.7379530571253516, 0.6991638866458327, 0.3225256074571341, 0.28357752574033057, 0.2796508865934202, 0.2576301492482225, 0.15163383746901538, 0.14012136027135202, 0.1321626778701832, 0.11793416791373446, 0.11005231669100635, 0.09996017287947367, 0.09375651906359739, 0.09285394516933021, 0.0899951771509615, 0.08001798979213337, 0.0798331274015025, 0.07892182637938827, 0.07324275519206846, 0.07247468124904266, 0.07245070956178878, 0.07176330422608057, 0.07112370577561311, 0.07067226287875972, 0.07042527416615751, 0.06899903291146714, 0.06863149347900066, 0.06777316229745178, 0.06704206660250378, 0.06494064826102708, 0.060874758017741115, 0.05887006365191105, 0.05810380963000572, 0.05748468340966095, 0.05669604970686226, 0.05657172017433165, 0.05650255737683452, 0.0557378324255442, 0.05541299819598766, 0.055357017471672876, 0.05436024408042606, 0.05430024107788167, 0.05383149700687362]\n",
      "Row 55 - Column Numbers: [48 51 47 46 49 64 59 61 50 58 68 75 67 69 56 54 81 84 63 52 57 23 87 14\n",
      " 70  0 38 73 41  1 44 37  4  6 88 72 11 86 36 89 76 62 74], MI Values: [0.5019751647569191, 0.4918905885238507, 0.4187425231559816, 0.3141727399115961, 0.30360053691119226, 0.1455355267788132, 0.10391523768986577, 0.10320434092076614, 0.09343475605257989, 0.09039691815655626, 0.08433296148313651, 0.07894014514832115, 0.07810178261121159, 0.07626677924718717, 0.07457832871124648, 0.07176330422608146, 0.0666084572296537, 0.0649658298184459, 0.06183261687680819, 0.06013022861701511, 0.05926409456159032, 0.05849481745654206, 0.05810381930205111, 0.05661782886079081, 0.05210958027079382, 0.05151582272524369, 0.05144646558632182, 0.0513717845320274, 0.04985324468381247, 0.04872468386788853, 0.04840563532307751, 0.047905222457149677, 0.047753548931313006, 0.04774985453638614, 0.046832066350649626, 0.046337404344297006, 0.04532790922027541, 0.04508240476302117, 0.04498650870497656, 0.04457765391180146, 0.044450219960144643, 0.04410009039404095, 0.04400663644262881]\n",
      "Row 56 - Column Numbers: [61 37 64 86 29 36 46 38 28 67 74 89 41 59 39 40 33 87 47 51 21 34 88 20\n",
      " 43 35  1 17 63 55  2 68 15  0  4 85 91 24 30 77 58 48 16], MI Values: [0.43147747233694655, 0.3594022660421903, 0.22066317128273738, 0.19813479850705384, 0.1713073755137069, 0.1508160371586369, 0.14608508460096736, 0.14324753303636495, 0.14153000235829616, 0.1390223315396053, 0.12763532576626613, 0.12759658270105412, 0.11875744932887322, 0.1140267649058524, 0.11061737849190578, 0.10838563263965728, 0.10568767232682852, 0.10439486730787184, 0.10368137158256019, 0.09492283806277957, 0.09187841023316512, 0.08918579292805973, 0.08812813925290719, 0.08286165353433983, 0.08170555433368776, 0.08018360354588872, 0.07992095121214593, 0.07971577342061753, 0.07711766737948622, 0.07457832871124559, 0.07436029178819847, 0.07341505483174426, 0.07262961413738722, 0.07242362723832141, 0.0720538145634535, 0.07002602366231869, 0.06996541088145225, 0.06753872107738657, 0.06707550157230013, 0.0658465345860213, 0.06480713020071249, 0.06358738315120327, 0.06331255297437988]\n",
      "Row 57 - Column Numbers: [52 69 75 54 81 63 64 68 50 46 23 72 87 17 74 61 47  6 70 21  7 84 62 49\n",
      " 73 82 92 58 45  0 19 66 56 48 36 37 55  5 44 83 60 79 77], MI Values: [0.5130885687568085, 0.4492286562322283, 0.3175403262160419, 0.2796508865934202, 0.2386747781742029, 0.19893022670047156, 0.1706591351738478, 0.12717047965108375, 0.12386611734750552, 0.113687209028984, 0.11007546217848985, 0.1056703039813307, 0.09943857195888661, 0.09928683256670379, 0.09565681017050132, 0.09358492153412179, 0.08687796447829044, 0.08592201720969239, 0.08195684550894988, 0.08110178494543341, 0.07616119177035774, 0.07392888704485934, 0.07251648801624277, 0.06818162225492586, 0.0667097043144338, 0.06659031769662516, 0.06608857489515785, 0.06605291746158404, 0.06353587781859193, 0.061740263953568686, 0.061490900764048284, 0.06146140592633831, 0.06124498359253927, 0.060791248768552464, 0.06000224745403049, 0.0595838130800912, 0.059264094561592096, 0.058399152771426266, 0.05763128744059465, 0.05711690835432748, 0.056631880706102145, 0.05618380082027041, 0.05594599871005901]\n",
      "Row 58 - Column Numbers: [46 59 67 61 64 55 75 51 81 54 48 68 57 56 44 69  0 52 88 79  5 84 73  4\n",
      " 74 40 17 87 49 70 72  7 89 47 62 38  2 43 37 50 60 77 86], MI Values: [0.1858984961031256, 0.17684958964553754, 0.1376164223851939, 0.10259159901626358, 0.09323139589981633, 0.09039691815655537, 0.08672016085400625, 0.0813109201835962, 0.07170077496787108, 0.06899903291146536, 0.06873152207635869, 0.06709058591021666, 0.06605291746158226, 0.0648071302007116, 0.06182062594159721, 0.053739795644960786, 0.05071325731351273, 0.05048148088307869, 0.04789057473566327, 0.047499732845677656, 0.04605361797762875, 0.045749765509683904, 0.04511521302719235, 0.0451146228488728, 0.04429686953990242, 0.0436866294276701, 0.042952045110664194, 0.04293717981312373, 0.04277730549634118, 0.04249097503546562, 0.041569158118069716, 0.0414072565023762, 0.04087411787997919, 0.04008012588680554, 0.03946179272307493, 0.039370558103208886, 0.03780798205952163, 0.03731442430222387, 0.03713892176412692, 0.036719401321429146, 0.03638037155973528, 0.03628517346620885, 0.03595011355909605]\n",
      "Row 59 - Column Numbers: [80 46 61 58 51 56 55 64 67 48 75 47 44 74 68 81 73 41 33 90 43 54 40 49\n",
      " 62 84 88 57 89 38 45 21 79 70 37 50 31  3 87 52 86  5 69], MI Values: [0.2465372262762342, 0.23992709365254772, 0.18600181466110133, 0.1768495896455411, 0.1533540315172539, 0.11402676490585151, 0.10391523768986577, 0.10143685103057543, 0.07292707939904464, 0.0664244783036434, 0.05458094170480976, 0.051394876265351996, 0.048036989305325406, 0.046929431867398286, 0.0468761986306756, 0.04281709288360336, 0.041442701275810734, 0.04123745905248555, 0.04109308677692969, 0.04080241822363018, 0.0405708194427179, 0.04002737117363697, 0.039970526744237844, 0.039689357711408135, 0.03937800895674659, 0.03858909846737113, 0.038104381220402495, 0.03733929606864361, 0.037336166429184026, 0.03621910618345936, 0.036194932260467994, 0.03564645785808285, 0.03530947035182841, 0.034605332803858246, 0.034270780090086106, 0.03385625356854849, 0.033688224144492906, 0.03365099687676132, 0.03359866945243972, 0.03358824636426494, 0.033156708793527834, 0.032867078986785536, 0.03252523413328934]\n",
      "Row 60 - Column Numbers: [45 66 64 75 69 76 46 54 53 84 81 57 65 63 56 70 49 61 52  6 47 62 48 50\n",
      " 24 55 10 87  1  4 68 72 51 58  8 17 85 21 11 44  0  9  2], MI Values: [0.24105785735212315, 0.14313213465555208, 0.13185070300011947, 0.08789136339985504, 0.08538631330874047, 0.07359513171289755, 0.06886160619467585, 0.067042066602502, 0.06551159416228902, 0.062130659320295045, 0.06016542150362536, 0.056631880706101256, 0.05516399778635517, 0.05208181872897821, 0.04990175130811547, 0.04924267114111114, 0.048907148201728035, 0.04565762279498298, 0.04550928202171889, 0.04432955091321311, 0.0439619281733723, 0.043609459383989524, 0.04357966587574058, 0.04352223482917683, 0.042912718955503415, 0.04289723654803357, 0.04246041760917052, 0.041422133425950136, 0.039365018633776394, 0.03811521797273176, 0.03776259020466188, 0.03735714461537043, 0.03684825881094511, 0.0363803715597415, 0.03495408974131564, 0.034779085744490956, 0.034559288190181725, 0.03360900022740143, 0.033444948836911514, 0.032907121469348155, 0.032668405905845965, 0.0324609794611499, 0.03181022364805397]\n",
      "Row 61 - Column Numbers: [56 11 64 59 46 47 51 87 12 85 55 58 20 10 21 57  1 91 63 23 17 69  2 68\n",
      "  0  4  6 24 79 77 83 48 49 54 74 67 33 15  7 84 32 14 52], MI Values: [0.43147747233694567, 0.42117961947471017, 0.30274924109928225, 0.186001814661104, 0.17267857439960288, 0.1538487466591274, 0.1323322880421669, 0.11609849133691696, 0.11175003676089812, 0.10334008173381015, 0.10320434092076347, 0.10259159901626269, 0.10190813419336209, 0.10067720955483761, 0.09520585153423244, 0.09358492153412534, 0.0919232880302312, 0.0871403303663465, 0.08651352031480286, 0.08578580449603024, 0.0845797268571502, 0.08175995345877496, 0.0807578644808169, 0.0801785495224161, 0.07987921333337233, 0.0793639777794386, 0.07748176490715064, 0.0766084916060148, 0.07561052109916311, 0.07553429240407095, 0.07310938021788527, 0.07218675949252873, 0.07118839940287724, 0.07112370577561222, 0.07004761148596383, 0.06954426713919748, 0.06766819910745347, 0.06669711932901201, 0.06659717282749611, 0.06553165111754122, 0.06347776301673225, 0.061701359771839215, 0.06122875212893497]\n",
      "Row 62 - Column Numbers: [53 63 64 54 72 32  6 70 46 21 44 57 28 45 17 41 69 85  0 87 34 30 84 33\n",
      " 74 19 40 88 12  2 37 20  4 75 11 10  1 31 89 43 36 61 23], MI Values: [0.40877114705633755, 0.1279415691665342, 0.11842971465453456, 0.09996017287947367, 0.08923240114087871, 0.08212300251017979, 0.08134777223811351, 0.07551883001699622, 0.07403272493206625, 0.07348744391152451, 0.0730624234203292, 0.07251648801624189, 0.07174551471409796, 0.07129070394237846, 0.07054503826931224, 0.0694126384428051, 0.06494490899076766, 0.06122602061900739, 0.060570066674142886, 0.06022931405757159, 0.05971560831514555, 0.058950094823821075, 0.05873104823880926, 0.05850112049998302, 0.05785656052338606, 0.057623187032919354, 0.05477366448826526, 0.05440889071046939, 0.05387677226496379, 0.05315849709315046, 0.052254464230390596, 0.05209308293447634, 0.051951533735175026, 0.05132260781067011, 0.05125901030097513, 0.05100764313742001, 0.050656346920683326, 0.05058193701037439, 0.05028273620915957, 0.05013562158198859, 0.0501292056996574, 0.05003847734903477, 0.04962794973529405]\n",
      "Row 63 - Column Numbers: [57 64 72 87 70 62  6 45 65 53 14 54  4 61 92 46 44 84  7 47 24 56 91 74\n",
      " 66  0 85 23 18 76 69 52 82 73 68 55 11 10  1 81 48 43 17], MI Values: [0.19893022670047422, 0.16474578635889525, 0.14441268837025323, 0.14223108828764808, 0.1360734064984701, 0.12794156916653598, 0.11759316702333766, 0.1169265088990441, 0.10914449076512156, 0.10768325129662504, 0.09840075284083394, 0.09375651906359561, 0.09074112883170304, 0.08651352031480108, 0.08472994154227464, 0.08355750196953071, 0.08074364625578578, 0.07977254852835358, 0.07907681278759515, 0.0790723382731855, 0.07871775795832114, 0.07711766737948711, 0.07678764806995986, 0.0765734948289225, 0.07406004109092024, 0.07375851842512127, 0.07313981190535657, 0.07257144170705043, 0.06986318552324633, 0.06663758575631373, 0.0653233908008124, 0.06405860187379808, 0.06403591879491888, 0.06298018698645702, 0.0628392353335725, 0.0618326168768073, 0.06124640975608653, 0.05988190445075414, 0.0589489276098476, 0.057634411390770524, 0.05760918621697009, 0.05744789795037342, 0.056767715502631155]\n",
      "Row 64 - Column Numbers: [46  6 61 56 87 47 27 68 57 63 54 55 51 75 74 84 69 45 60 10  4 14 44 23\n",
      " 62 72 20 66 48 76 65 85 12 11 81 70  1  8 59 17 52  7 77], MI Values: [1.1094691017199603, 0.4786059164536729, 0.30274924109928225, 0.22066317128273738, 0.22048913023609096, 0.1987447932521187, 0.18682361749818366, 0.17760682722466647, 0.17065913517384423, 0.1647457863588926, 0.1516338374690145, 0.1455355267788141, 0.14408460937434509, 0.14236178948324518, 0.14209884783445936, 0.13984183102276582, 0.13741479855139893, 0.13477024068243804, 0.13185070300012303, 0.1299306324648466, 0.12979914510191115, 0.12701720438149788, 0.12575424005177815, 0.12382874483289896, 0.11842971465453278, 0.11641659888849265, 0.11253209164348021, 0.11225512605831867, 0.11110937927605224, 0.10732056478952767, 0.10654049307470448, 0.10591493223352533, 0.10535355610052566, 0.10500346113093073, 0.1037050834642379, 0.10306102384276805, 0.10272291690296331, 0.10254326229903832, 0.10143685103057631, 0.1003732877747634, 0.09484755694459235, 0.09462334579778542, 0.09447565520740842]\n",
      "Row 65 - Column Numbers: [27 45 63 64 66 76 60  6 84 53 62 13 46 31 74 23 57 79 15  1 61 28 90 87\n",
      " 25 18 47 35  4 10 19 22  2 16 54 17 38  5 70 43 11 71 55], MI Values: [0.6065603894953897, 0.3355390992669385, 0.10914449076511978, 0.10654049307470537, 0.07400054698096614, 0.06574940460414158, 0.05516399778635073, 0.05313625162063573, 0.05200772742261606, 0.04754326752987392, 0.04210859287540458, 0.04141383027204526, 0.04065382889106317, 0.04016739913483747, 0.03927197805547333, 0.03543013877976531, 0.03532486757824671, 0.03390511473012481, 0.03356935029377528, 0.0334370867070275, 0.03268513124965988, 0.032538341997700115, 0.03243135734308211, 0.03240600070639843, 0.03173822340394317, 0.03125147202710554, 0.030917863808890722, 0.030897225961695085, 0.03052268994560059, 0.030516181395221054, 0.030348441731518072, 0.030328529199157295, 0.030171195067245193, 0.030140476904725766, 0.029872492359135805, 0.029334903001505097, 0.029234888513575363, 0.02891810299955555, 0.02890138730320313, 0.02881055664071308, 0.028497828396734093, 0.02842485280534124, 0.028331991996227934]\n",
      "Row 66 - Column Numbers: [76 84 45 60 64 69 54 63 65 44 75 46 81 57 87 52 10  6 68 32  3 50 70 62\n",
      "  8 48 11 49 55 88 12 53 27 51 21 41 30 34 89 56 61 85 35], MI Values: [0.3276867048743224, 0.19621110110385498, 0.16669975622521527, 0.14313213465555208, 0.11225512605832044, 0.08774329941118442, 0.07892182637938827, 0.07406004109092112, 0.07400054698096792, 0.0657832364108204, 0.06574781745996905, 0.06557772498449133, 0.06464382902376808, 0.061461405926340085, 0.057380307752954884, 0.05499973892547505, 0.052649459598339554, 0.05121302295319019, 0.049935593149331936, 0.046364996147670645, 0.04601614539536314, 0.04570965837784691, 0.045050505206226, 0.044186414063735135, 0.042936712655239795, 0.042849316494054435, 0.04280397591400931, 0.0427889260255494, 0.042241733113475455, 0.039561716831260973, 0.0386714507746424, 0.038483240317686906, 0.03842749677431723, 0.03826743593598536, 0.0377725314890629, 0.03736335808473523, 0.03715626177182507, 0.03696164121794787, 0.03657013877780546, 0.03621018306623114, 0.036192436537979766, 0.03603333099672312, 0.03582784273636985]\n",
      "Row 67 - Column Numbers: [56 58 46 48 55 59 47 61 64 49 51 68 70 75 50 54 63 69 72 81 73 57 87 41\n",
      " 79  7 52 92 71  3 34 33 36 45 18 22 74  2 21 39 77 40 89], MI Values: [0.1390223315396062, 0.13761642238519123, 0.1327952209475507, 0.0819042946903279, 0.07810178261121248, 0.07292707939904286, 0.07249971148987466, 0.06954426713920014, 0.067158129948651, 0.06462675171117294, 0.06049342127079882, 0.05573066244705327, 0.05131323241564267, 0.050048166172831365, 0.04902813669653483, 0.04789187006885953, 0.04359634849634464, 0.04356102015565355, 0.042934138904747066, 0.041962299374367795, 0.03947764246554897, 0.03874132263576069, 0.0375586609402454, 0.03748203714709142, 0.03612567970739633, 0.03552096699697227, 0.03431893068828895, 0.03385542532989394, 0.03284593157964766, 0.03260253611544073, 0.03230214768395179, 0.032080902109909104, 0.032068284532125624, 0.031703696876647314, 0.03167709034729871, 0.03152308217100508, 0.0313239473107263, 0.030862122044114315, 0.030431654414645237, 0.030192101527670268, 0.03015615956557216, 0.03014741947648325, 0.030105513462540756]\n",
      "Row 68 - Column Numbers: [81 54 69 46 64 75 52 57 50 48 55 87 21 49 61 16 84 56 17 83 44 58 20 19\n",
      " 28 74 51 70  1 63 72  4  0 47 76 15 79  2 67 85 73 88 40], MI Values: [0.273919599429445, 0.25763014924822425, 0.21452460580928268, 0.19852690016740215, 0.17760682722466647, 0.13909061707178783, 0.1278969066417437, 0.12717047965108375, 0.0931330170915734, 0.0893454513359444, 0.0843329614831374, 0.08279666247431816, 0.08274897552594052, 0.08052518453031432, 0.08017854952241699, 0.08013941132973379, 0.07495229498264155, 0.07341505483174426, 0.06961403770779029, 0.06805662497684573, 0.06773250218080751, 0.06709058591021577, 0.06678931920015962, 0.06634530228217894, 0.0648958659595209, 0.06481434993591328, 0.06392417227606728, 0.06381372155874665, 0.06377396532315771, 0.06283923533357072, 0.061596290425321776, 0.06062743353392808, 0.05987241738861382, 0.05906462224581688, 0.05900909169327839, 0.05863023036643522, 0.056674954088558493, 0.05663641300834321, 0.05573066244705327, 0.05285999918476847, 0.05115265774466682, 0.05105981583143748, 0.050255155238578375]\n",
      "Row 69 - Column Numbers: [54 52 81 57 75 68 64 50 45 46 49 84 66 60 76 61 55 48 70 47 72 63 62 21\n",
      "  6 53 74 87 12 17 56 58 88 83 33 10 13 44 41 43 35 31 15], MI Values: [0.6991638866458345, 0.5772799725175153, 0.5173059047442399, 0.4492286562322283, 0.3365455824566368, 0.2145246058092809, 0.13741479855139715, 0.1364956152132697, 0.10868038934784607, 0.105422623025202, 0.09982396156077122, 0.09384699164640953, 0.08774329941118264, 0.08538631330874047, 0.08467890285416413, 0.0817599534587723, 0.07626677924718717, 0.07361433044884258, 0.06977140079906086, 0.06874455994522854, 0.06641906563649336, 0.06532339080081417, 0.06494490899076943, 0.06484185380561414, 0.06183066532204684, 0.05994221903533159, 0.05666686695618495, 0.05545803544337424, 0.05531483615886046, 0.05499612699967926, 0.05440393974544655, 0.053739795644960786, 0.0536959399704946, 0.053145985839573306, 0.05089832960081431, 0.050097225136772394, 0.04984063431350716, 0.04878869749796966, 0.04863991014106883, 0.04807444378004, 0.04771493976945074, 0.04694746829499152, 0.04658331443336472]\n",
      "Row 70 - Column Numbers: [72 71 63 46 64 57 53 62 54 47 69 87 48 68 45 36 82 56 17 61 21  4 19 13\n",
      " 74 41 55 49 67 52 60 11 15 75 28 84 32 85 66 18 44 35 31], MI Values: [0.5037025298153655, 0.1468401051584065, 0.13607340649846478, 0.13281149605317744, 0.10306102384276628, 0.08195684550894988, 0.07763014753084718, 0.07551883001699711, 0.07247468124904355, 0.07068379697728044, 0.06977140079905908, 0.0660251334839197, 0.06437836072642344, 0.06381372155874754, 0.06252081423776268, 0.05999309743629233, 0.05982269100457582, 0.057890813506117134, 0.056376474765788664, 0.055299683066056815, 0.05505815458498908, 0.05456383162511802, 0.05447668338025302, 0.05401666850898579, 0.05386607986701808, 0.053251414027695176, 0.05210958027079293, 0.05205162711625011, 0.05131323241564267, 0.050113256036700804, 0.049242671141108474, 0.049105160517478375, 0.04807318298614227, 0.047127393802390394, 0.04650128507184803, 0.046494250587683084, 0.04569125616274494, 0.04506890618240256, 0.04505050520622156, 0.04471178449303981, 0.04423971269111515, 0.044000657807371724, 0.043861067541813625]\n",
      "Row 71 - Column Numbers: [70 72 57 46 63 52 64 69 62 40 88 45 19 54 89 73 53 41 18 20 36 74 28 48\n",
      " 38 68 67 55 16 21 15 32 35 85 39 49  1 33 92 86 66 29 34], MI Values: [0.14684010515840784, 0.10642931109237441, 0.052528980782009516, 0.05241768981868278, 0.050201259190097325, 0.04467108973151124, 0.04327708127836605, 0.040533665195546575, 0.03859241843659156, 0.038561516805054374, 0.03818678028153677, 0.03813838976859696, 0.03800425250052175, 0.03790080375870186, 0.03715871144142646, 0.03588263349891774, 0.03548282442189432, 0.035353727634690024, 0.0352925510429718, 0.03441557456072353, 0.03423058910657151, 0.03397324312542693, 0.03394914598687837, 0.033806395276054335, 0.033705883841912865, 0.03342612831626557, 0.03284593157964988, 0.032719080030302106, 0.032663553226116804, 0.031987069591433936, 0.03175109221050576, 0.03144013441961224, 0.031402843954976944, 0.030959505480408822, 0.03087881443926932, 0.030695717699147362, 0.030567471549774794, 0.030379323571904315, 0.03005020752412957, 0.03002178949951162, 0.029856386276476243, 0.029726472501970136, 0.029722945487696606]\n",
      "Row 72 - Column Numbers: [70 46 63 64 71 57 62 54 87 69 53 74 36 17 47 68 19 56  6  4 21 37 18 12\n",
      " 13 79 45 52 61 14 15 85 84 11  8 83 38 55 31 10 41 48 40], MI Values: [0.5037025298153646, 0.1555945017468563, 0.14441268837025323, 0.11641659888849354, 0.10642931109237264, 0.10567030398132982, 0.08923240114088049, 0.06863149347899888, 0.06757571466233703, 0.06641906563649602, 0.06557217989953035, 0.06265296415556598, 0.06265064870036952, 0.06242048665925726, 0.06175094572082429, 0.06159629042532533, 0.06050821759756175, 0.060467185737427265, 0.059193884606223435, 0.05724329216191926, 0.054151749566812235, 0.053098326138301566, 0.05297227066477639, 0.05260851139547462, 0.052594084364699256, 0.05231208801533249, 0.05126811930396524, 0.051113533032526526, 0.050320783879531206, 0.050294567082459274, 0.049828300730804465, 0.04936721830032109, 0.04876829570450525, 0.048098306904397425, 0.04777061216579881, 0.04705935242895354, 0.04699176949630246, 0.04633740434429967, 0.04575550443701104, 0.04517050064331052, 0.04508851409560233, 0.0448973620856723, 0.04481721096307467]\n",
      "Row 73 - Column Numbers: [18 19 16 22 15 21 83 17 46 57 20 64 92  0 85 63 87  1 90 91 75 32 61 78\n",
      " 55 68 81 80  4 77 42 56  5 62  7  2 44 48 79 58 30 52 82], MI Values: [0.7893958078076446, 0.44496585631871355, 0.23365823269839314, 0.1966841939947015, 0.17737229996765524, 0.14619238110757227, 0.13046110819555246, 0.11461081534221584, 0.0669864466316632, 0.0667097043144338, 0.06621492860686029, 0.06604549816659055, 0.06534747712790967, 0.0649060502864538, 0.06342521947019009, 0.06298018698645524, 0.0611623897499598, 0.05958199657264185, 0.05918069294481576, 0.05854277511136363, 0.053336867008316524, 0.052349661683105175, 0.052132518258837024, 0.051741026293754544, 0.05137178453202651, 0.05115265774467037, 0.050731494761138585, 0.05035070457441204, 0.04944023723216873, 0.04929230770196469, 0.04884463429679364, 0.04879117015815915, 0.04871526329810205, 0.047892505862648704, 0.04712977016487141, 0.046741524692998304, 0.045420776171674504, 0.04530640682438136, 0.04518328366119828, 0.0451152130271959, 0.04476241509419232, 0.04425296906975085, 0.04269677500715918]\n",
      "Row 74 - Column Numbers: [33 30 35 43 36 86 37 29 89 38 28 40 39 31 34 88 41 32 78  5 79  2 12 64\n",
      " 44 80  4 56 46 87  0  1  3 57 42 11 13 85  8 63 10 54 90], MI Values: [1.1137204124807516, 0.6484729630309527, 0.6417520640136294, 0.624303970048989, 0.609009289588708, 0.5888147458720638, 0.5514988683591922, 0.5004203013385569, 0.4790798574401238, 0.463836147610051, 0.4637692211865332, 0.42293019416571376, 0.4188068561985556, 0.3685955153502105, 0.3551015296305451, 0.3455870286773939, 0.33199699186004406, 0.2547497346317229, 0.20415303191621437, 0.1681098351910748, 0.1650927025452713, 0.15700514453794945, 0.14286051344793105, 0.14209884783445847, 0.13751208245379942, 0.13689592489073021, 0.12952891724869087, 0.12763532576626435, 0.11736212179504246, 0.1087269697985187, 0.10670490036675684, 0.10197487194244381, 0.09931213507677228, 0.09565681017049954, 0.09219897198964855, 0.08465931443258867, 0.08012866253161377, 0.07970796683611514, 0.07707447313009208, 0.07657349482892162, 0.07645994681407764, 0.0724507095617879, 0.07133347033568604]\n",
      "Row 75 - Column Numbers: [50 69 57 81 54 52 49 46 64 68 84 48 60 58 87 55 45 47 66 74 77 79 44  0\n",
      " 19 76 37 63 86 59  2 73 13  4 36 61 17  1 62 24 88 67 10], MI Values: [0.38569583316039946, 0.3365455824566368, 0.31754032621604367, 0.299464626985233, 0.2835775257403297, 0.1935421636578889, 0.16380558437787318, 0.1598316786459506, 0.1423617894832443, 0.1390906170717887, 0.10426683306186213, 0.1003724412202649, 0.0878913633998506, 0.08672016085400713, 0.08358299144459647, 0.07894014514831671, 0.07550304956704768, 0.07403127407645904, 0.06574781745996994, 0.0641015831058036, 0.06280999904077333, 0.06198112586282889, 0.05994952546050758, 0.058932901704030094, 0.05883151968498446, 0.05840596267275, 0.05770927457101749, 0.05585066540116479, 0.05527900384734252, 0.05458094170481065, 0.054081184944083205, 0.05333686700831475, 0.053243057542840866, 0.05294436526442681, 0.05286496782731209, 0.052800446177284854, 0.052136357413616885, 0.051665821434266235, 0.05132260781066744, 0.05083179402329918, 0.05043949403648362, 0.05004816617282959, 0.049905532084435045]\n",
      "Row 76 - Column Numbers: [66 84 45 64 69 46 60 54 63 65 68 81 75 87 50 61 56 55 27 52  3 48 51 57\n",
      " 44 88 62  6 85 40  1 74 41  0 58 49 15 39  4 89 14 53 47], MI Values: [0.3276867048743197, 0.24938687538324178, 0.14089157380955797, 0.10732056478952945, 0.08467890285416502, 0.07963991449703123, 0.07359513171289844, 0.07324275519206669, 0.06663758575631462, 0.06574940460414425, 0.05900909169328106, 0.05870728910141754, 0.05840596267275089, 0.05227845227554617, 0.052114858751312276, 0.0475376914479817, 0.045768277880542385, 0.044450219960143755, 0.04331808077932564, 0.0397320107747241, 0.039450383303536896, 0.038781715879885326, 0.03840491710777716, 0.03729854865264848, 0.03695081877679929, 0.03575037533056857, 0.03553028432121241, 0.035006496062266024, 0.03479280267248619, 0.03355427583083603, 0.03330372063304132, 0.03324378852283871, 0.03314054463399074, 0.0329832469916953, 0.03260929208367003, 0.03200075462167984, 0.03142627895452854, 0.031226808565940622, 0.030530087758511293, 0.030180324229658773, 0.03013702346379077, 0.029953159421307163, 0.029614370974226034]\n",
      "Row 77 - Column Numbers: [20  1  0 17 85 21 83 87 91  2 15 79  4  5  3 11 12 19 22 16 64 78 90 10\n",
      " 24 46 61 18 31 14 33 80 74 13 56 43 75 30  8 86 37 36 29], MI Values: [0.6456828762580971, 0.3911191711403701, 0.37263024544485734, 0.2990938973597581, 0.2972324555956005, 0.2833159462922179, 0.2721591618925645, 0.2624972226636384, 0.2612330298469274, 0.23544670375940946, 0.2109149525053855, 0.19755911895090694, 0.1718626691037235, 0.17144637756480563, 0.16858842857306655, 0.15529190588759256, 0.15476368455904055, 0.14839967682173594, 0.10378871318925587, 0.09654894383117352, 0.09447565520740842, 0.0909806859788258, 0.08763090580224553, 0.0864463575035197, 0.08554737930801348, 0.0848734741910322, 0.07553429240407361, 0.07382980271187378, 0.07208828414576551, 0.07067488479129658, 0.06870563600713986, 0.06782462499272324, 0.06750317812053108, 0.06644401403919531, 0.06584653458601863, 0.06546454180161732, 0.06280999904077245, 0.06275013897899573, 0.06220005651368066, 0.061947295051053786, 0.061387189732781344, 0.061213187064223185, 0.06065012243418888]\n",
      "Row 78 - Column Numbers: [31 79  2  5 43 35  4 44 30  3  0  1 33 74 42 36 85 86 34 12 11 37 87 32\n",
      " 29 91 20 80 28 13 89 17 10 38 39 21 40 83 41 88 77 90 15], MI Values: [0.7638100129208834, 0.5291499102562947, 0.40895639584369636, 0.40195030351981753, 0.3703971113656319, 0.36035661286731635, 0.3522117773810214, 0.2940959242977499, 0.24551062402752422, 0.22968546503017695, 0.2279315500630652, 0.22306577157731855, 0.21439117181920508, 0.20415303191621348, 0.17401757617932834, 0.14656523125808896, 0.13481869307475858, 0.1340783425963794, 0.13184448924787695, 0.1251376255189447, 0.12508164598781324, 0.12299363364406979, 0.12204190372473, 0.11553471513471436, 0.11428335137809142, 0.11180728144593566, 0.11158401518017325, 0.11158379763401793, 0.10874080446091128, 0.10855159929809233, 0.10703752567566749, 0.10477670785503168, 0.10461732375843713, 0.1039286718447654, 0.1030354193690286, 0.10268663613005558, 0.09964875862896339, 0.09402627710304756, 0.09265090609569437, 0.09216904048066343, 0.09098068597882403, 0.07220152388185497, 0.06674255678354513]\n",
      "Row 79 - Column Numbers: [ 4  2  5 78  3  0 31  1 43 35 77 85 30 20 87 33 74 12 17 44 91 21 83 34\n",
      " 11 36 86 37 29 40 10 39 32 38 89 42 28 64 41 13 80 88 15], MI Values: [0.893437297964442, 0.8897537675853213, 0.8539429780686696, 0.5291499102562955, 0.5216221690633249, 0.45757637448269506, 0.3469763013969196, 0.3374236720569561, 0.2073913075411946, 0.20596754398312012, 0.19755911895090428, 0.1962347079230513, 0.1906085060616718, 0.1804159793193154, 0.17746826908973823, 0.1675397929716107, 0.1650927025452722, 0.15745268691877623, 0.15630527248319837, 0.15352082533469336, 0.14530314536725086, 0.13959981733842763, 0.13601963987999888, 0.1218215309761943, 0.12041417972820856, 0.11619314258747693, 0.11181972450478295, 0.111670136833391, 0.10420208049496171, 0.10298221946964947, 0.10144296896099547, 0.10121071598448594, 0.09567236193821316, 0.09301615106454975, 0.09254555638649187, 0.09102336506577213, 0.09026690572979756, 0.08736827809746561, 0.08676758111423233, 0.08620980383680976, 0.08466381307331439, 0.0785679892861264, 0.07750166086596]\n",
      "Row 80 - Column Numbers: [59 43 35 90 31 33 42 74 30 36 44 78 92 86 89 37 29 34 28 40 38 79  5 41\n",
      " 32 12 82 88 39  2 77 11 21  0  4 15 13  3  1 83 10 73 20], MI Values: [0.24653722627623686, 0.2276321837680122, 0.20322450593987362, 0.19218618079188143, 0.18479080672562098, 0.15136974710492979, 0.1450821651935268, 0.13689592489073021, 0.1357762064984085, 0.11571876599131237, 0.11196280971917005, 0.11158379763401705, 0.11010018137622524, 0.10493827763350172, 0.1044402309887209, 0.09822950179437395, 0.09785175941231472, 0.09689650292456431, 0.09424947908653714, 0.08752252944644034, 0.08653427377215017, 0.08466381307331616, 0.08230865790885655, 0.07854886226317959, 0.07650826602535155, 0.07494487051346166, 0.07370725535800648, 0.07253038686003155, 0.07038469791400903, 0.06970774963285731, 0.06782462499272057, 0.06530714718931119, 0.0638719053811343, 0.06157503922592156, 0.06148036084266284, 0.06004207076621082, 0.058901850104819964, 0.05522028921117084, 0.05429317094593511, 0.05309818158656032, 0.05282851504111541, 0.050350704574411154, 0.04844480590909317]\n",
      "Row 81 - Column Numbers: [54 69 75 52 68 57 50 64 46 49 58 84 74 48 55 66 87 60 45 76 77 44 36 79\n",
      " 63 86  0 61 83 37 17 33 73 38 43 39 31  4 89 47  1  2 88], MI Values: [0.7379530571253508, 0.5173059047442399, 0.29946462698523035, 0.2925189873733629, 0.27391959942944677, 0.2386747781742029, 0.136153690706311, 0.10370508346423613, 0.10140282553967683, 0.07578213385519295, 0.07170077496787108, 0.07127138714810943, 0.06860495539301592, 0.06681937537003346, 0.06660845722965725, 0.06464382902377075, 0.0635620255990954, 0.06016542150362536, 0.05993439653997257, 0.05870728910141665, 0.05853791406893283, 0.05807485470139717, 0.057863475935761244, 0.057830546664649596, 0.05763441139077141, 0.05615165444273362, 0.05562579056591499, 0.05549932064581764, 0.05488123319225746, 0.05430022036441429, 0.05358151425610025, 0.052620584599597287, 0.05073149476113681, 0.0504273983650787, 0.050018232148672404, 0.048724267224924844, 0.04741589778476474, 0.04724272848531896, 0.047045769301623075, 0.046565683993298634, 0.045974451396885385, 0.04564404577717607, 0.0445681886862177]\n",
      "Row 82 - Column Numbers: [47 92 90 80 57 63 70 64 36 41 87 74 18 42 19 85 73 86 56 43 72 78 35  6\n",
      " 31 33 29 27 44  2 21 69 34  0  5 79 15 62 30 40 23 17 46], MI Values: [0.36022650677909773, 0.20000700401697546, 0.12362127498379927, 0.07370725535800737, 0.06659031769662516, 0.06403591879492154, 0.05982269100458204, 0.048128802238390556, 0.04758120157348866, 0.04550467421470117, 0.0453016185285815, 0.04463464698039843, 0.04452332972605699, 0.043705855049582354, 0.0432350339578198, 0.042804256191230294, 0.04269677500715918, 0.042518243369825015, 0.04216181372132244, 0.041122564560073904, 0.04035249569417232, 0.040056300664696565, 0.03993065515482197, 0.039067233966030734, 0.0389505477899581, 0.038744171751281975, 0.03800177521638748, 0.037944489427784056, 0.03731345765145644, 0.03724063933802757, 0.03716957593935177, 0.037114565896340324, 0.03697025658167963, 0.03665464470504798, 0.036577827982953615, 0.035438406074370654, 0.03489171478971809, 0.03464472319516876, 0.034410902358763096, 0.034146025613621234, 0.03378679926427086, 0.033662159409545644, 0.033650920178660115]\n",
      "Row 83 - Column Numbers: [17 21 20  0  1 19 77 15 85  2 16 91 87 11 22  5  4 79 73 18  3 12 90 92\n",
      " 78 10 42 31 43 64 61 13 68 54 35 33 46 44 74  8 57 81 14], MI Values: [1.066814745597446, 0.7488876659638617, 0.4589017533899531, 0.31506896178670907, 0.29504178717312346, 0.28206410473167054, 0.2721591618925654, 0.23569399663760304, 0.19808986460266986, 0.18056529072470173, 0.16718927849869747, 0.1656431210139937, 0.15326102264911245, 0.14976259321938912, 0.1450249261206027, 0.14139989403189102, 0.1374753305211458, 0.13601963988000332, 0.13046110819555246, 0.13005610443538984, 0.12212949345012714, 0.12178764257401475, 0.09999792818939479, 0.09786512673510916, 0.09402627710304579, 0.09120163011639004, 0.08290682477634537, 0.08252825085346682, 0.08156076645929478, 0.07860224780761271, 0.07310938021788527, 0.06900697369544506, 0.06805662497684573, 0.06494064826102797, 0.06455351051612457, 0.06416764584976953, 0.06223055486476259, 0.06102533227363338, 0.05968287991838661, 0.05824405082485473, 0.05711690835432748, 0.05488123319225924, 0.05451886276258566]\n",
      "Row 84 - Column Numbers: [ 3 76 66 64 46 75 45 69 54 63 68 57 81 50 87 61 55  6 60 44 27 62 56 74\n",
      "  0 65 52  1 51 20 17 48 72 21 49 85 47 70 58 41 40 88  2], MI Values: [0.29367624960262795, 0.24938687538324178, 0.19621110110385587, 0.13984183102276848, 0.1375172592865539, 0.1042668330618639, 0.10150362847124583, 0.09384699164641042, 0.09285394516933199, 0.07977254852835536, 0.07495229498264333, 0.07392888704485934, 0.07127138714810854, 0.06909627215253789, 0.06894787220913212, 0.06553165111754211, 0.06496582981844412, 0.06491247342046069, 0.062130659320295045, 0.06139751027721019, 0.0603802858690452, 0.058731048238805705, 0.05731245332677215, 0.05441190520910766, 0.052023584398917855, 0.05200772742261517, 0.050675710238638594, 0.050658360235747324, 0.050444118959005024, 0.04966907275681187, 0.04912116274816558, 0.049098305732939274, 0.0487682957045088, 0.047929493455121985, 0.047598231033918026, 0.04751424056243447, 0.047086024603290255, 0.046494250587683084, 0.045749765509683904, 0.04533916101688806, 0.04511370164638606, 0.04442062560320448, 0.04432867747156788]\n",
      "Row 85 - Column Numbers: [91 87 11  1 20 77  0 21 15 10 16 17  2 83 79 12 13  4  5 78 19  3  8 24\n",
      " 22 31 64 61 14 23 43 33 44 46 74 42 18 35 90 92 63 53 56], MI Values: [1.0397326027081109, 0.7808738531896484, 0.4477948984444424, 0.4273072620362388, 0.42552426145736, 0.2972324555956032, 0.29292039446620866, 0.2688208314872229, 0.2607931482272816, 0.25686672570808433, 0.24952652512346507, 0.24799566598007594, 0.2191451538778244, 0.19808986460266986, 0.1962347079230522, 0.16892847033332092, 0.15241639531040452, 0.14716514799944846, 0.14129091651330672, 0.13481869307476035, 0.12862613575316306, 0.12331183579416649, 0.1197010961317595, 0.11662871191985147, 0.11578837068495584, 0.10608247049946584, 0.10591493223352089, 0.10334008173380838, 0.0977963721134758, 0.08797109748794707, 0.08744850763647705, 0.08539579380747231, 0.08318123056251547, 0.08171791357506919, 0.0797079668361178, 0.07969793759561306, 0.07840025513521187, 0.0772743628266932, 0.07673080277470046, 0.07434137186871315, 0.07313981190535657, 0.07291262831419587, 0.0700260236623178]\n",
      "Row 86 - Column Numbers: [37 36 29 38 89 28 39 33 40 74 88 41 43 35 30 34 31 32 56 78  5 79 44 80\n",
      " 12  2  4 42 90  3 87  1  0 77 14 52 64 46 81 75 85 11 63], MI Values: [1.4582722148763292, 1.0233770024292141, 0.9904397714916922, 0.7540596341394137, 0.733195425690325, 0.7092838503040939, 0.6322229406595898, 0.6078933190308362, 0.5904546129888963, 0.5888147458720656, 0.4974361490677621, 0.47456031717445146, 0.4240950333084834, 0.398460972787932, 0.37422972387261133, 0.3436127338197741, 0.22807412650458492, 0.2027410833178278, 0.1981347985070574, 0.1340783425963794, 0.1305167490968442, 0.11181972450478028, 0.10936129874318112, 0.10493827763349994, 0.10135095971922325, 0.09732347543015418, 0.0793582428961841, 0.07547417076442908, 0.07370447561000759, 0.06840077448593984, 0.06585251441988405, 0.0648701268193781, 0.06364451470636467, 0.0619472950510529, 0.06094423783477332, 0.05775731163073594, 0.057120350210864146, 0.05635429843615114, 0.0561516544427354, 0.05527900384733986, 0.053398504926430945, 0.05262110212995097, 0.05220962062188317]\n",
      "Row 87 - Column Numbers: [91 85 20  1 11 77 15  0 10 64 17 21  2 79 46 83  4 63 12  5 16 24 78 14\n",
      " 19  8 61 13 31 74  3 56 23 44 57 22 43 47 75 68 33  6  9], MI Values: [0.8254953838532577, 0.7808738531896502, 0.32604905695192254, 0.3012243820649747, 0.2965738494229102, 0.2624972226636402, 0.2236871771312554, 0.22350595260037398, 0.2210467525648223, 0.22048913023609007, 0.19689724643638407, 0.18708052814614184, 0.18419330652618005, 0.17746826908973734, 0.16549438774061542, 0.15326102264911423, 0.1467876478550867, 0.14223108828764808, 0.13558171850872913, 0.13204341952919485, 0.12870418125103367, 0.126641316562071, 0.12204190372472912, 0.12022624072505206, 0.11907016274300819, 0.11717444758841289, 0.11609849133691608, 0.11270707168404748, 0.10896037047705942, 0.10872696979851781, 0.10828482718467924, 0.10439486730786829, 0.1027970391859041, 0.10044717697416417, 0.09943857195888395, 0.08969080820395003, 0.08755593140089335, 0.08569788060934336, 0.08358299144459647, 0.0827966624743155, 0.08221603143086931, 0.07597112239010073, 0.0751232614805879]\n",
      "Row 88 - Column Numbers: [40 89 41 28 38 39 34 29 37 86 33 36 74 30 32 35 43 31 44 78 56 79  5  4\n",
      " 64 80 12 90 18  2 46 52 42  0 10  3  1 62 54 69  8 63 17], MI Values: [1.3584687582326698, 1.1135577021657408, 0.8687228214668892, 0.7614158768816592, 0.7568375359221005, 0.7414381495833346, 0.521645640678436, 0.5162986988948415, 0.5065004040074976, 0.4974361490677621, 0.4047557520194278, 0.39112029603754017, 0.3455870286773921, 0.3120618690279793, 0.27467543363149716, 0.2113827569500053, 0.2062641249804278, 0.1178467066606661, 0.0978448354860939, 0.09216904048066343, 0.0881281392529063, 0.07856798928612552, 0.07740754667316185, 0.07609992946234723, 0.07448577255951516, 0.07253038686002977, 0.07191036153530916, 0.07018600624848581, 0.06947413178679351, 0.06925480718800436, 0.0665871977414545, 0.06273572137952144, 0.06114199250922159, 0.06063371495187919, 0.06012914210785869, 0.05512401310494486, 0.05476304444835467, 0.05440889071046939, 0.05436024408042606, 0.053695939970491935, 0.05292091189701864, 0.05201826811016552, 0.05132084037915341]\n",
      "Row 89 - Column Numbers: [38 40 88 39 28 41 37 29 86 36 34 33 74 30 43 35 32 31 56 78 80  5 79 44\n",
      " 12  2 90  4 11 64  0 10  3 42 46  1  8 13 61 87 17 54 62], MI Values: [1.2419280927673935, 1.2392621662048944, 1.113557702165739, 1.0535035116401668, 1.0046755344608442, 0.9100181021852709, 0.7572524796564108, 0.7571541803206934, 0.7331954256903233, 0.5752000583378676, 0.5628237492307493, 0.5364183007679406, 0.4790798574401274, 0.37170844903925726, 0.28802774608808956, 0.2845574273495872, 0.23990089864081376, 0.15421271891570854, 0.12759658270105323, 0.1070375256756666, 0.1044402309887218, 0.1028680671126736, 0.09254555638649009, 0.09241113709100546, 0.08890082125607357, 0.08732427486063177, 0.08143911948999971, 0.07698715238078524, 0.06919349661079899, 0.06672066841319335, 0.06566309202536758, 0.0637520285116242, 0.06298051391441373, 0.06261691628512, 0.0624690478839538, 0.06095847702589374, 0.05864248331363253, 0.05740682008964981, 0.057232186056704215, 0.0568278203392758, 0.05080254511998916, 0.05074669197352755, 0.0502827362091578]\n",
      "Row 90 - Column Numbers: [42 92 80 21 82 17  1  0 83 77 40 20 19 89 30 33 43 85  5  2 79 11 86 41\n",
      " 38 12 15 78 35 74 37 88 29 36 39 34 31 91 87 28  4 32 73], MI Values: [0.5736361560630625, 0.4459659605734716, 0.19218618079188232, 0.12517520234619095, 0.1236212749837966, 0.11040902183482082, 0.10532886649482442, 0.10411775455289263, 0.09999792818939834, 0.08763090580224375, 0.08755455049272687, 0.08732179357987846, 0.08561032186586459, 0.08143911949000593, 0.07857807032348152, 0.07829650162065516, 0.07721049556759763, 0.07673080277470312, 0.07668497735520141, 0.07646301353284013, 0.07612583152068808, 0.0746333907288248, 0.07370447561000759, 0.07307672025710321, 0.07291292443408093, 0.07254758451655796, 0.0725475665380868, 0.07220152388185319, 0.07216427126334413, 0.07133347033568604, 0.07091755529673982, 0.07018600624848581, 0.07002944857802262, 0.06954945457795869, 0.06777425757346034, 0.06748508102814021, 0.06594386443864142, 0.06571885927828625, 0.06528340240650543, 0.06435233990021594, 0.06363225684698115, 0.0634542884997531, 0.059180692944813984]\n",
      "Row 91 - Column Numbers: [85 87 11 20  1 77 10 15 21  0 17 83  2 13 79 16 12  8  4  5 78 19 22  3\n",
      " 24 23 14 61 64 31 18 63 44 43 56 42 74 92 53 90 33 46 34], MI Values: [1.0397326027081135, 0.8254953838532595, 0.3865429355312866, 0.35105094399945447, 0.3192857717713009, 0.261233029846931, 0.2579871837894956, 0.2262869925209232, 0.2086854981064592, 0.20848995166817463, 0.20010695253448052, 0.1656431210139928, 0.15702895570463316, 0.15188179879224428, 0.14530314536724998, 0.13528675087576225, 0.1292188341874061, 0.12410132440415556, 0.11543451299135388, 0.11292935145386718, 0.1118072814459321, 0.10649322098528113, 0.1063924866874304, 0.09857437391434942, 0.09541744286183729, 0.09277959255307167, 0.09231436655409198, 0.08714033036634472, 0.08652458136703967, 0.08539580505606104, 0.08043542246333857, 0.07678764806996075, 0.07356394424112533, 0.07147186167010044, 0.06996541088144959, 0.06881214952706838, 0.06784461788607654, 0.06764075156292826, 0.06654270992309197, 0.06571885927828625, 0.06454231972101443, 0.060894556193985316, 0.05979450877373971]\n",
      "Row 92 - Column Numbers: [90 82 17 42 21 80 83 63  1 85  0 19 20 91 87 57 73 23  2 30 79 77  5 78\n",
      " 15 41 74 33 11 18 36  6 32  4 12 40 34 64 86 16 28 47 10], MI Values: [0.4459659605734716, 0.20000700401697458, 0.16969542448540587, 0.11438741669920915, 0.1117978672601403, 0.11010018137622612, 0.0978651267351065, 0.08472994154227287, 0.08048114102267068, 0.07434137186871048, 0.07334383362524477, 0.07083532279622062, 0.07064869314149647, 0.06764075156292648, 0.06744167818817282, 0.06608857489515962, 0.06534747712790523, 0.06377017167667542, 0.06303769631886258, 0.06244423103829355, 0.06139810833956538, 0.06009214577031052, 0.05620640348058448, 0.05570265349391068, 0.05541644764804232, 0.05389698575662827, 0.052348572626745415, 0.051905744566475676, 0.051690795509167664, 0.05057359318983057, 0.04931200112378864, 0.048166047939036005, 0.047644557437777735, 0.04702041409510738, 0.046717369248161056, 0.04610406107367648, 0.045989563524378774, 0.0458993014321587, 0.04549260487965512, 0.04529324898574405, 0.04491292878293418, 0.044605275701465885, 0.043729188914697126]\n"
     ]
    }
   ],
   "source": [
    "#Subgraph generation module 1 --->Giving raw series, and generate a series of subgraph based on MI.\n",
    "NDBC_lat=pd.DataFrame(Station_info.iloc[:,1])\n",
    "NDBC_long=pd.DataFrame(Station_info.iloc[:,3])\n",
    "NDBC_ID=pd.DataFrame(Station_info.iloc[:,0])\n",
    "Adj_dist=adj_dist(NDBC_lat,NDBC_long)\n",
    "j=5#J-th colum, start from 5 as the first feature.\n",
    "X_raw_0=X_raw[:,j,:]#GET the first feature\n",
    "print(X_raw_0.shape)\n",
    "# Count the num of missing values in each column\n",
    "missing_counts_per_column = np.sum(np.isnan(X_raw_0), axis=0)\n",
    "# print results\n",
    "print(\"Incomplete data number in each column：\", missing_counts_per_column)\n",
    "\n",
    "#Get the index if the value is not zero\n",
    "# Find the columns where missing values exist.\n",
    "columns_with_missing_data = np.any(np.isnan(X_raw_0), axis=0)\n",
    "\n",
    "# Get the column numbers when missing value exist.\n",
    "missing_columns = np.where(columns_with_missing_data)[0]\n",
    "\n",
    "# Print results\n",
    "print(\"The column numbers with missing values are：\", missing_columns)\n",
    "\n",
    "# Get new data after deletion.\n",
    "# Delete those columns (Stations) if there is not any features.\n",
    "result = np.delete(X_raw_0, missing_columns, axis=1)\n",
    "result = (result - np.min(result)) / (np.max(result) - np.min(result))\n",
    "print(result.shape)#(8784, 93)\n",
    "\n",
    "#Determine group num here\n",
    "group_num=result.shape[1]-N_u\n",
    "\n",
    "# Initialize MI_store\n",
    "MI_store = np.zeros((result.shape[1], result.shape[1]))\n",
    "\n",
    "# Calculate mutual information\n",
    "for i in range(result.shape[1]):\n",
    "    for j in range(result.shape[1]):\n",
    "        MI_store[i, j] = calc_MI(result[:, i], result[:, j], 10)\n",
    "\n",
    "# Return column numbers and corresponding mutual information\n",
    "column_numbers = []\n",
    "MI_values = []\n",
    "\n",
    "for i in range(MI_store.shape[0]):\n",
    "    row = MI_store[i, :]\n",
    "    row_index = np.arange(MI_store.shape[0])\n",
    "    row_index = np.delete(row_index, i)  # Exclude the current row's index\n",
    "    sorted_indices = np.argsort(row[row_index])\n",
    "    max_indices = row_index[sorted_indices[-group_num:][::-1]]  # Get largest column_num\n",
    "    column_numbers.append(max_indices)\n",
    "    MI_values.append([row[j] for j in max_indices])\n",
    "\n",
    "# Output results\n",
    "for i, (columns, values) in enumerate(zip(column_numbers, MI_values)):\n",
    "    print(f\"Row {i} - Column Numbers: {columns}, MI Values: {values}\")"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-25T05:38:39.331713Z",
     "start_time": "2024-03-25T05:38:34.939145Z"
    }
   },
   "id": "8c8808ff766dd4cc",
   "execution_count": 7
  },
  {
   "cell_type": "code",
   "outputs": [],
   "source": [],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-25T05:38:39.335057Z",
     "start_time": "2024-03-25T05:38:39.333011Z"
    }
   },
   "id": "9f02d9a4ba4ad276",
   "execution_count": 7
  },
  {
   "cell_type": "code",
   "outputs": [],
   "source": [
    "\n",
    "from utils import load_data_MI\n",
    "\n",
    "import torch\n",
    "import numpy as np\n",
    "import torch.optim as optim\n",
    "from torch import nn\n",
    "import matplotlib.pyplot as plt\n",
    "from utils import *\n",
    "import random\n",
    "import pandas as pd\n",
    "from basic_structure import IGNNK\n",
    "from basic_process import *\n",
    "import argparse\n",
    "import sys\n",
    "import os\n",
    "import time\n",
    "if __name__ == \"__main__\":\n",
    "    \"\"\"\n",
    "    Model training\n",
    "    \"\"\"\n",
    "    flags = parse_args(sys.argv[1:])\n",
    "    dataset=flags.dataset\n",
    "    n_o_n_m = flags.n_o\n",
    "    h = flags.h\n",
    "    z = flags.z\n",
    "    K = flags.K\n",
    "    n_m = flags.n_m\n",
    "    n_u = flags.n_u\n",
    "    max_iter = flags.max_iter\n",
    "    learning_rate = flags.learning_rate\n",
    "    E_maxvalue = flags.E_maxvalue\n",
    "    batch_size = flags.batch_size\n",
    "    to_plot = flags.to_plot"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-25T05:38:39.342629Z",
     "start_time": "2024-03-25T05:38:39.336377Z"
    }
   },
   "id": "bd03e20a4949abb7",
   "execution_count": 8
  },
  {
   "cell_type": "code",
   "outputs": [],
   "source": [
    "def test_error_new(STmodel, unknow_set, test_data, A_s, Missing0):\n",
    "    \"\"\"\n",
    "    :param STmodel: The graph neural networks\n",
    "    :unknow_set: The unknow locations for spatial prediction\n",
    "    :test_data: The true value test_data of shape (test_num_timesteps, num_nodes)\n",
    "    :A_s: The full adjacent matrix\n",
    "    :Missing0: True: 0 in original datasets means missing data\n",
    "    :return: NAE, MAPE and RMSE\n",
    "    \"\"\"\n",
    "    unknow_set = set(unknow_set)\n",
    "    time_dim = STmodel.time_dimension\n",
    "    test_omask = np.ones(test_data.shape)\n",
    "    if Missing0 == True:\n",
    "        test_omask[test_data == 0] = 0\n",
    "    test_inputs = (test_data * test_omask).astype('float32')\n",
    "    test_inputs_s = test_inputs\n",
    "    missing_index = np.ones(np.shape(test_data))\n",
    "    missing_index[:, list(unknow_set)] = 0\n",
    "    missing_index_s = missing_index\n",
    "    o = np.zeros([test_data.shape[0]//time_dim*time_dim, test_inputs_s.shape[1]]) #Separate the test data into several h period\n",
    "    for i in range(0, test_data.shape[0]//time_dim*time_dim, time_dim):\n",
    "        inputs = test_inputs_s[i:i+time_dim, :]\n",
    "        missing_inputs = missing_index_s[i:i+time_dim, :]\n",
    "        T_inputs = inputs*missing_inputs\n",
    "        flags = parse_args(sys.argv[1:])\n",
    "        E_maxvalue = flags.E_maxvalue\n",
    "        T_inputs = T_inputs/E_maxvalue\n",
    "        T_inputs = np.expand_dims(T_inputs, axis = 0)\n",
    "        T_inputs = torch.from_numpy(T_inputs.astype('float32'))\n",
    "        A_q = torch.from_numpy((calculate_random_walk_matrix(A_s).T).astype('float32'))\n",
    "        A_h = torch.from_numpy((calculate_random_walk_matrix(A_s.T).T).astype('float32'))\n",
    "        imputation = STmodel(T_inputs, A_q, A_h)\n",
    "        imputation = imputation.data.numpy()\n",
    "        o[i:i+time_dim, :] = imputation[0, :, :]\n",
    "    flags = parse_args(sys.argv[1:])\n",
    "    dataset=flags.dataset\n",
    "    if dataset == 'NREL':\n",
    "        dataset=dataset\n",
    "    else:\n",
    "        o = o*E_maxvalue\n",
    "    truth = test_inputs_s[0:test_set.shape[0]//time_dim*time_dim]\n",
    "    o[missing_index_s[0:test_set.shape[0]//time_dim*time_dim] == 1] = truth[missing_index_s[0:test_set.shape[0]//time_dim*time_dim] == 1]\n",
    "    test_mask =  1 - missing_index_s[0:test_set.shape[0]//time_dim*time_dim]\n",
    "    if Missing0 == True:\n",
    "        test_mask[truth == 0] = 0\n",
    "        o[truth == 0] = 0\n",
    "    MAE = np.sum(np.abs(o - truth))/np.sum( test_mask)\n",
    "    RMSE = np.sqrt(np.sum((o - truth)*(o - truth))/np.sum( test_mask) )\n",
    "    MAPE = np.sum(np.abs(o - truth)/(truth + 1e-5))/np.sum( test_mask)\n",
    "    return MAE, RMSE, MAPE"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-25T05:38:39.361563Z",
     "start_time": "2024-03-25T05:38:39.343422Z"
    }
   },
   "id": "2bb7d7f43dc84be8",
   "execution_count": 9
  },
  {
   "cell_type": "code",
   "outputs": [],
   "source": [],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-25T05:38:39.364195Z",
     "start_time": "2024-03-25T05:38:39.362487Z"
    }
   },
   "id": "a7414f2143b53b8a",
   "execution_count": 9
  },
  {
   "cell_type": "code",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1, 93)\n",
      "A's shape is: (93, 93)\n",
      "X's shape is: (93, 8784)\n",
      "(8784, 103)\n",
      "Incomplete data number in each column： [8784    0    0    0    0    0    0    0    0    0    0    0    0    0\n",
      "    0    0    0    0    0    0    0    0    0    0    0    0    0    0\n",
      "    0    0    0    0    0    0 8784    0    0    0 8784    0    0    0\n",
      "    0    0    0    0    0    0    0 8784 8784    0    0    0    0 8784\n",
      " 8784    0    0    0    0    0    0    0    0    0    0    0    0    0\n",
      "    0    0    0 8784    0    0    0    0    0    0    0 8784    0 8784\n",
      "    0    0    0    0    0    0    0    0    0    0    0    0    0    0\n",
      "    0    0    0    0    0]\n",
      "The column numbers with missing values are： [ 0 34 38 49 50 55 56 73 81 83]\n",
      "(8784, 93)\n",
      "Row 0 - Column Numbers: [ 1  2  4 79  5 20  3 77 21 17 83 85 78 87 91 12 15 31 11 43 19 44 35 30\n",
      " 74 90 16 10 33 64 42 34 61 13 32 46 22 63 92 56 18  8 41], MI Values: [0.8272601132894586, 0.6901375697065202, 0.4673606483958732, 0.45757637448269683, 0.4363240338301644, 0.4190235175463517, 0.37428008133733837, 0.37263024544485734, 0.33215728219304985, 0.3299090634675217, 0.3150689617867082, 0.29292039446620866, 0.22793155006306698, 0.22350595260037576, 0.2084899516681764, 0.19725693559810153, 0.16436438822998234, 0.1621107642515911, 0.15513395543730368, 0.13586993979589845, 0.13409996608400565, 0.12631372813239938, 0.11361591888716127, 0.10962686909974106, 0.10670490036675684, 0.10411775455289352, 0.10173701560948789, 0.10125880394889375, 0.0966457877057838, 0.0917156023777439, 0.08872664637913985, 0.08750394746818291, 0.07987921333337233, 0.0779097501756647, 0.07772961987272176, 0.07681250087322766, 0.07596636122032496, 0.07375851842511771, 0.07334383362524477, 0.0724236272383223, 0.06937049801544504, 0.06869053966721506, 0.06665335877298872]\n",
      "Row 1 - Column Numbers: [ 0 20  2 85 21 77  4 79 17  5 91 87 83  3 11 15 12 78 31 19 10 16 43 35\n",
      " 30 33 13 90 64 74 44 22 42 61 18 34 92  8 46 56 24 28 36], MI Values: [0.8272601132894577, 0.5324618722588088, 0.52600823699178, 0.4273072620362397, 0.4023069759074378, 0.39111917114037187, 0.34043212687770286, 0.33742367205695434, 0.3283135513911546, 0.32209271522604777, 0.3192857717713018, 0.3012243820649747, 0.2950417871731199, 0.25018137359531334, 0.2344515509245717, 0.23100847367209631, 0.22954525563754213, 0.22306577157731855, 0.161217443157323, 0.16120899606897954, 0.14396039237957936, 0.13986782406464826, 0.12913107009156644, 0.11642248941903688, 0.1150059734774116, 0.10934085523256787, 0.10726653658897867, 0.10532886649482887, 0.10272291690296598, 0.10197487194243937, 0.09756958090356083, 0.0945249676245794, 0.09265639520815494, 0.09192328803022942, 0.09060525299304167, 0.09049841174829254, 0.08048114102267423, 0.08040105111154183, 0.08010342629738876, 0.07992095121214415, 0.07658487183692309, 0.07617110541908634, 0.07458627225738823]\n",
      "Row 2 - Column Numbers: [ 4 79  5  0  3  1 78 31 20 77 85 21 17 12 35 43 87 83 30 33 91 74 11 44\n",
      " 34 10 36 15 13 86 29 39 19 42 37 32 40 38 89 64 28 61 41], MI Values: [1.0421298348636876, 0.889753767585324, 0.8252189069592397, 0.6901375697065175, 0.6346295603606373, 0.52600823699178, 0.4089563958436999, 0.2885791692349038, 0.26984073230595396, 0.23544670375941035, 0.21914515387782174, 0.2125857191397058, 0.20709995929092173, 0.19750308970805186, 0.18701920286034568, 0.18681968571483498, 0.18419330652618005, 0.1805652907247035, 0.15876062884895603, 0.158099218500249, 0.15702895570463316, 0.15700514453794945, 0.15460225559136997, 0.14614605566375083, 0.11747560005255142, 0.1108491328808272, 0.1096084538611164, 0.10428901675494728, 0.10194617541772022, 0.09732347543015507, 0.09469648273846154, 0.09409837181553105, 0.09214628161064109, 0.09190658625377424, 0.0914136839587858, 0.09002264997452336, 0.08826839034197409, 0.08794009077204912, 0.08732427486062821, 0.08295219935787657, 0.08247104503342495, 0.08075786448081335, 0.07942866688885175]\n",
      "Row 3 - Column Numbers: [ 2  5 79  4  0 84  1 78 77 31 20 17 85 83 21 87 43 35 12 74 91 33 44 30\n",
      " 11 34 64 36 86 10 46 37 41 89 39 32 38 15 29 42 40 19 56], MI Values: [0.6346295603606364, 0.6014752255233811, 0.5216221690633258, 0.5005956595959162, 0.37428008133733837, 0.29367624960262795, 0.2501813735953151, 0.22968546503017784, 0.168588428573063, 0.15053120343368054, 0.14918195632018705, 0.135719601508959, 0.12331183579416383, 0.12212949345012802, 0.12006037445413753, 0.10828482718467836, 0.1038170751558507, 0.10166237481487972, 0.10067391244311352, 0.0993121350767705, 0.09857437391434942, 0.09072061229028172, 0.09034618967547559, 0.08507553529173251, 0.08430822621926293, 0.07711971317009514, 0.0732968907767324, 0.07188834325973747, 0.06840077448593984, 0.06747669748327834, 0.0662602861970365, 0.06558274587027046, 0.06306413363040075, 0.06298051391441817, 0.06157433149594205, 0.06126513617121354, 0.06113916617078008, 0.06068970280665109, 0.06048824178377199, 0.05799913453610728, 0.057212613678012225, 0.05676014452040157, 0.05643454058528263]\n",
      "Row 4 - Column Numbers: [ 2  5 79  3  0 78  1 44 31 20 77 17 85 12 87 21 83 35 43 11 64 74 30 33\n",
      " 91 10 34 63 36 32 13 19 61 86 24 23 38 46 89 29 15 88 40], MI Values: [1.0421298348636858, 0.9112659905285279, 0.893437297964442, 0.5005956595959136, 0.4673606483958741, 0.3522117773810223, 0.34043212687770286, 0.25771696574601854, 0.227791945861342, 0.17593949417667076, 0.1718626691037226, 0.15309018167041533, 0.14716514799944758, 0.1468250597240388, 0.1467876478550929, 0.14440832752750676, 0.1374753305211449, 0.13262659195667847, 0.13167838609283677, 0.1303296358704138, 0.1297991451019085, 0.1295289172486882, 0.12417935392990831, 0.12068089113273661, 0.11543451299135477, 0.09954623668022755, 0.09367692420842033, 0.09074112883170127, 0.08771441417981674, 0.08734619315226588, 0.08641934307043808, 0.08049320130510296, 0.0793639777794386, 0.07935824289618232, 0.07926789355999908, 0.07907845045093165, 0.07857614620487485, 0.07856401142111924, 0.07698715238078346, 0.07666467817423595, 0.07652558554478439, 0.07609992946234811, 0.07604174073334136]\n",
      "Row 5 - Column Numbers: [ 4 79  2  3  0 78  1 31 43 36 35  7 77 33 20 74 17 30 21 83 85 44 87 86\n",
      " 37 12 29 91 38 89 39 11 28 40 34 42 32 10 41 80 88 90 15], MI Values: [0.9112659905285261, 0.8539429780686714, 0.8252189069592406, 0.6014752255233793, 0.4363240338301635, 0.40195030351981753, 0.32209271522605043, 0.2760329582147678, 0.20819529046906293, 0.20674579006625127, 0.19563347399244257, 0.18293846291297733, 0.17144637756480563, 0.17076852453711044, 0.1697430692708517, 0.16810983519107303, 0.16129782284088812, 0.14845254677791608, 0.1420832575295341, 0.14139989403188924, 0.14129091651330405, 0.13308552892848002, 0.13204341952919751, 0.1305167490968433, 0.12301925557245497, 0.12297734107820624, 0.11470618022646395, 0.11292935145386807, 0.10350223849688867, 0.1028680671126736, 0.10050281527196514, 0.09942878741363614, 0.09875071075038111, 0.09746128685535993, 0.09670112680553178, 0.09376382987344023, 0.09331795784564356, 0.08681805312730084, 0.08605778397885011, 0.08230865790885478, 0.07740754667316363, 0.07668497735519875, 0.07561477718424658]\n",
      "Row 6 - Column Numbers: [64 14 46 63 12 23  8 57  9 62 11 61 32 45 87 13 44  4 10 54 28 47  7 84\n",
      " 27 69 52 72 36 30 35 79 65 74 41  2 56 26 66 34  1 85 92], MI Values: [0.478605916453672, 0.1659311007796953, 0.13099684473508688, 0.11759316702334122, 0.11209322621671447, 0.09453623691659319, 0.08865574838552437, 0.0859220172096915, 0.08576932695849138, 0.08134777223811529, 0.07911821580729761, 0.07748176490715508, 0.07727934830261152, 0.07607959090818373, 0.07597112239010162, 0.07148486877965077, 0.07123886187653383, 0.07119374646681464, 0.06986362657552991, 0.067773162297458, 0.06638342779498618, 0.06549702884688458, 0.0654621562897697, 0.0649124734204598, 0.06278134191716767, 0.06183066532204595, 0.0613978125590382, 0.05919388460622166, 0.05838254740344251, 0.05558434696104264, 0.055331827053077376, 0.05403814410428076, 0.053136251620639285, 0.0529400614221025, 0.05243412828986749, 0.052066717960047804, 0.0518643235699745, 0.05140858603128606, 0.05121302295318664, 0.0509936262443027, 0.05053181341582125, 0.05019818795246955, 0.04816604793903778]\n",
      "Row 7 - Column Numbers: [ 5 17 64 21 63 57 23 46 61  6 79  2  4 52 87 12 27  3 62  9  0  8  1 73\n",
      " 10 20 69 19 47 54 58 11 14 68 88 74 30 32 33 67 31 72 34], MI Values: [0.1829384629129791, 0.10524195919111623, 0.0946233457977872, 0.09121449964563944, 0.07907681278759338, 0.07616119177035774, 0.0681607842361398, 0.06676341580429312, 0.066597172827497, 0.06546215628976793, 0.059427428725374654, 0.05901064569144587, 0.05558987853756037, 0.054813377473760916, 0.05399825056106078, 0.053976980524889306, 0.05053310241240361, 0.05009254312144673, 0.0482538265970307, 0.04809050593593689, 0.047727363031476955, 0.047556140122899215, 0.0474209934989922, 0.047129770164868745, 0.04693364118155152, 0.04555598545496231, 0.04435919441098868, 0.04338328445526862, 0.0431716643311324, 0.04278103642929665, 0.041407256502377976, 0.040946924073455904, 0.04074963195215808, 0.03718480535959223, 0.03666191730525448, 0.036462534916334555, 0.03612339642617801, 0.03608454747954237, 0.03558055210133837, 0.035520966996969605, 0.035348553502023705, 0.03526695646017597, 0.035145156518217036]\n",
      "Row 8 - Column Numbers: [10  9 14 26 11 13 25 91 85 87 12 32 64 24 27 20 21 34 17  6 23 15  1 74\n",
      " 33 30 44  0 28  4  2 77 46  5 89 31 83 78 79 35 88 63 19], MI Values: [0.48698986391151955, 0.375802297419666, 0.2819697411476927, 0.2524540408417879, 0.2289457453068362, 0.21963152219072413, 0.16233774299458315, 0.12410132440415467, 0.11970109613176039, 0.11717444758841289, 0.10941441927598472, 0.10441158737263923, 0.10254326229904187, 0.10209066826928259, 0.09968544490658893, 0.09860668116430737, 0.09797349325439786, 0.09279000891834333, 0.08886645776288304, 0.08865574838552615, 0.08474539401989478, 0.08043587263141738, 0.0804010511115445, 0.07707447313008853, 0.07565747720513727, 0.07521271366405902, 0.0702725389356953, 0.06869053966721772, 0.06518271250260987, 0.06434639902210026, 0.06327216027249083, 0.062200056513681545, 0.06204077732827784, 0.060054597826602496, 0.05864248331363431, 0.05824452931784396, 0.05824405082485651, 0.0575396306220366, 0.05661802684946515, 0.055954172623136955, 0.05292091189701953, 0.052721647755728185, 0.05241070031981643]\n",
      "Row 9 - Column Numbers: [ 8 10 26 13 14 11 32  6 12 25 87 34 64 20 27 91 24 21 17 85 36  1 23  0\n",
      " 28 41 74 63  7 30 62 83 15 61 54  2 72 19 57 79 40 89 78], MI Values: [0.37580229741966775, 0.2739374700127568, 0.1888349353819665, 0.18881791101212642, 0.17302647019022377, 0.14827272551388315, 0.08690570143561605, 0.08576932695849404, 0.08575515951341117, 0.07942615953296617, 0.07512326148058257, 0.06858253221368038, 0.06743046912400352, 0.0606112133373804, 0.060249930177727506, 0.05872512110265582, 0.05556219929455963, 0.05510777850993431, 0.053827948456972585, 0.05356332489102211, 0.05062803388903436, 0.05042486996980955, 0.04914461256289693, 0.04911468770996663, 0.04892501848965658, 0.04833957062141003, 0.04817579082966983, 0.04815235147500374, 0.048090505935939554, 0.047497107903827995, 0.046442659973216394, 0.04500640957005597, 0.044571645079205524, 0.04384180562593176, 0.04255922801340173, 0.04239438289088415, 0.041960240322472586, 0.04195403205745141, 0.04175321361746853, 0.041721734850988845, 0.041382496982518724, 0.039247318738780734, 0.03916411448757362]\n",
      "Row 10 - Column Numbers: [11  8 13  9 91 85 14 87 12 26  1 20 64 25 24  2 21 17 78 79  0 61  4 23\n",
      " 83 15 34  5 77 31 44 32 27 33 30 74 28 43 35  6 41 46 53], MI Values: [0.4993554128442783, 0.4869898639115231, 0.4066358068899456, 0.27393747001275504, 0.2579871837894956, 0.25686672570808167, 0.2251698714598369, 0.22104675256482142, 0.17468399623417863, 0.1595045585205188, 0.14396039237957758, 0.13028693835191518, 0.12993063246484482, 0.1129190817547916, 0.11268616419256361, 0.1108491328808281, 0.10815686636048127, 0.10750415858836693, 0.10461732375843713, 0.10144296896099103, 0.10125880394889109, 0.10067720955484294, 0.09954623668022666, 0.09526800567615812, 0.09120163011638649, 0.09068210425726964, 0.08709868991881109, 0.08681805312730351, 0.08644635750351704, 0.08544174110632596, 0.08386645043593433, 0.08091774681887642, 0.07918640410680755, 0.077949740915769, 0.07776056152449495, 0.07645994681407409, 0.07299784236684648, 0.07182439963604015, 0.07091448732899508, 0.06986362657553258, 0.06936075480536807, 0.06801559120089085, 0.06799093673704792]\n",
      "Row 11 - Column Numbers: [10 85 61 12 13 91 87  1  8 20 21 17 77  0  2 83  9  4 78 14 79 31 24 15\n",
      " 64  5 35 43 44 74  3 33  6 42 30 28 90 34 19 89 22 23 80], MI Values: [0.499355412844281, 0.447794898444446, 0.4211796194747075, 0.4197051791498847, 0.40682029470780456, 0.3865429355312857, 0.296573849422912, 0.23445155092457082, 0.22894574530684064, 0.21618413086183974, 0.17612200358653762, 0.1627161637347161, 0.15529190588759256, 0.15513395543730546, 0.15460225559137086, 0.14976259321938645, 0.1482727255138805, 0.13032963587041646, 0.12508164598781324, 0.12287505739090143, 0.12041417972820945, 0.11341149652601601, 0.10784355126935719, 0.10663625668288024, 0.10500346113093073, 0.09942878741363259, 0.096740469127222, 0.09481730555193213, 0.08789263097170963, 0.08465931443259134, 0.08430822621926115, 0.0819176206772605, 0.0791182158072985, 0.07587529502254231, 0.0758563574615021, 0.07518085992455958, 0.07463339072882835, 0.0729801592932775, 0.06976258783125644, 0.0691934966107981, 0.06893504056359223, 0.06614162517794231, 0.06530714718931119]\n",
      "Row 12 - Column Numbers: [11 13  1  2  0 20 10 85 79 77 21  4 31 74 43 30 87 33 91 35 17 78  5 83\n",
      "  6 61  8 64 86  3 34 36 14 37 28 40 39 29 42 89 44 38  9], MI Values: [0.41970517914988204, 0.2820044236370247, 0.22954525563754302, 0.19750308970805097, 0.19725693559809976, 0.19049650601974388, 0.17468399623417863, 0.16892847033331915, 0.15745268691877712, 0.15476368455904232, 0.1470253698180608, 0.1468250597240388, 0.14662969753092625, 0.14286051344793105, 0.14156956810136734, 0.13732974337876414, 0.13558171850873002, 0.13072864694938868, 0.12921883418740698, 0.12855491233259286, 0.12797358847181428, 0.1251376255189447, 0.12297734107820624, 0.12178764257401742, 0.11209322621671713, 0.11175003676089723, 0.10941441927598472, 0.10535355610052655, 0.10135095971922237, 0.10067391244311619, 0.09993696526051199, 0.09709484343702979, 0.09629848458173385, 0.09592473158963521, 0.09501229751970186, 0.09185969685608963, 0.09122469199042715, 0.08955815291430014, 0.08912140713055461, 0.08890082125607712, 0.08654874505815524, 0.08621577314512052, 0.08575515951341028]\n",
      "Row 13 - Column Numbers: [11 10 12  8  9 85 91 87 78  1 20  2 31 14 35 30 43 33 44  4 79 21 28 74\n",
      " 25  0 34 17 26  6 64 83  5 15 77 36 42 32 80 89 61 54 70], MI Values: [0.406820294707801, 0.40663580688994827, 0.28200442363702294, 0.21963152219071969, 0.18881791101212642, 0.15241639531040452, 0.15188179879224428, 0.11270707168405014, 0.10855159929809766, 0.10726653658897689, 0.10347968403017482, 0.10194617541771755, 0.10045734833963227, 0.09715275871665696, 0.095142371568528, 0.09258617061155316, 0.09195467760153075, 0.08878636983820609, 0.08824878688846738, 0.08641934307043897, 0.08620980383680887, 0.08274041805652033, 0.08202421217934308, 0.08012866253161732, 0.07985596483401824, 0.07790975017566382, 0.07495306478076014, 0.07488041542475532, 0.07181363072769464, 0.07148486877965166, 0.07002602341222808, 0.06900697369544506, 0.06846734306451818, 0.0666776158158564, 0.0664440140391962, 0.06379802149536751, 0.062408309849672605, 0.062004348452000535, 0.05890185010481819, 0.057406820089648924, 0.05485204269998434, 0.05430024107788256, 0.054016668508986676]\n",
      "Row 14 - Column Numbers: [ 8 10  9 26  6 27 64 11 87 25 63 85 13 12 46 91 47 24 20 77 34 17 37 61\n",
      " 36 86 56 29 23 55 79  0 48 83  4 74  2  5 57 32 72 51 30], MI Values: [0.2819697411476918, 0.22516987145983425, 0.17302647019022466, 0.17093143981882442, 0.16593110077969708, 0.1515567092969663, 0.12701720438150055, 0.12287505739089966, 0.12022624072505117, 0.10808026792929493, 0.09840075284083127, 0.09779637211347314, 0.0971527587166543, 0.09629848458173651, 0.09266115822732779, 0.09231436655408931, 0.09074348902636675, 0.07873666169272209, 0.07681486761087797, 0.07067488479129924, 0.06725286085851412, 0.06554506282266725, 0.0641664994737523, 0.06170135977184188, 0.061668865682766416, 0.06094423783477776, 0.05952118983744992, 0.0587014765905316, 0.0585240406935128, 0.05661782886078903, 0.056059091866146105, 0.05562693284596332, 0.05528245353972583, 0.05451886276258566, 0.05432706381529773, 0.05401613896216251, 0.05270106891950288, 0.05173567448447702, 0.05167205271928932, 0.05104880529890021, 0.050294567082459274, 0.05026820068852178, 0.04979484407518253]\n",
      "Row 15 - Column Numbers: [21 16 22 20 17 19 18 85 83  1 91 87 77 73  0 11  2 10  8 12 79  4  5 56\n",
      " 90 23 42 78 61 13 24 35 43 31  3 80 68 32 46 92 57 33 53], MI Values: [0.48722604389986746, 0.47765933545984574, 0.42274734051130114, 0.3684773490976543, 0.3095265239658307, 0.30125231966110366, 0.27326227718117746, 0.2607931482272843, 0.23569399663760038, 0.23100847367209187, 0.226286992520925, 0.22368717713125363, 0.2109149525053864, 0.17737229996765436, 0.16436438822998056, 0.10663625668287935, 0.10428901675494551, 0.09068210425726964, 0.08043587263142005, 0.07994733324017389, 0.07750166086596355, 0.07652558554478794, 0.07561477718424747, 0.07262961413739166, 0.07254756653808414, 0.07129603115169658, 0.06699419564638731, 0.06674255678354601, 0.06669711932901201, 0.0666776158158564, 0.06508609948717492, 0.06380756444094082, 0.06258859383481585, 0.06209333159081609, 0.06068970280665109, 0.06004207076621171, 0.05863023036643167, 0.05587065130398727, 0.05560717684994554, 0.055416447648041434, 0.054577733516099514, 0.051477381196054495, 0.05145699897161915]\n",
      "Row 16 - Column Numbers: [15 18 22 19 21 85 73 17 20 83  1 91 87  0 77 68  2 42 10 23 56 61  5 11\n",
      "  4 90 13 78 57 63 79  3 64 46 92 52 84 80 24 53  8 47 32], MI Values: [0.47765933545984485, 0.39646468501385357, 0.3870402149910266, 0.3091588054074448, 0.28541688685649813, 0.2495265251234624, 0.23365823269839403, 0.19302253406145908, 0.17044387506372072, 0.16718927849869658, 0.13986782406464915, 0.13528675087576136, 0.12870418125103722, 0.101737015609487, 0.09654894383117263, 0.08013941132973557, 0.07497954269839457, 0.0675083713658422, 0.06746525386392133, 0.06694340591739856, 0.06331255297438165, 0.06108123440198021, 0.059929091775576815, 0.05975370525344825, 0.05524048992921937, 0.052897766030480575, 0.051451103064484194, 0.050915937056171146, 0.049854047095866605, 0.049689454222085594, 0.04856746770346909, 0.04659548808807035, 0.046006140165719245, 0.04556275492620987, 0.04529324898574405, 0.04328046495819304, 0.04310793055946416, 0.04279362459041813, 0.04234654693679207, 0.04223363657743562, 0.04159168613493058, 0.040768941888324584, 0.04067108310344292]\n",
      "Row 17 - Column Numbers: [83 21 20  0  1 15 77 19 85  2 91 87 16 92 11  5 22 79  4 18  3 12 73 46\n",
      " 90 10  7 78 64 57 31  8 42 61 56 43 13 62 68 74 35 53 52], MI Values: [1.0668147455974486, 1.021617623019086, 0.4934266968283074, 0.3299090634675217, 0.3283135513911546, 0.30952652396583336, 0.299093897359759, 0.2719089149660965, 0.24799566598007683, 0.20709995929092084, 0.2001069525344823, 0.19689724643638318, 0.1930225340614582, 0.16969542448540675, 0.16271616373471876, 0.16129782284088456, 0.15874125412953077, 0.15630527248319748, 0.153090181670418, 0.13764098894343224, 0.13571960150895812, 0.1279735884718134, 0.11461081534221496, 0.11280369881762375, 0.11040902183482348, 0.1075041585883687, 0.10524195919111712, 0.1047767078550299, 0.10037328777475985, 0.0992868325667029, 0.09616040667204562, 0.0888664577628866, 0.0846645868325373, 0.08457972685715465, 0.07971577342061753, 0.07861749607301505, 0.07488041542475354, 0.07054503826931136, 0.06961403770779029, 0.06954563307844097, 0.06903264964802336, 0.06894645621138906, 0.06703671873903527]\n",
      "Row 18 - Column Numbers: [73 19 16 22 15 21 17 83 20  1 91 85 87 77 63 88  0 57 46 72 32 64 90 92\n",
      " 56 78  2 68 42 61 11 70 82  4 62 10 52  5 48 36 75 53 55], MI Values: [0.7893958078076464, 0.5505196890502351, 0.39646468501385357, 0.32015585431856763, 0.27326227718117746, 0.1986950339873701, 0.1376409889434349, 0.1300561044353925, 0.1028199239054004, 0.09060525299304434, 0.08043542246333768, 0.07840025513521187, 0.07415089398027508, 0.073829802711872, 0.0698631855232481, 0.06947413178679618, 0.06937049801544681, 0.0555089312872461, 0.05501723067444342, 0.05297227066477728, 0.05286118816878638, 0.05264544534878457, 0.052266576769972595, 0.050573593189831456, 0.05004107750332221, 0.04951922140218912, 0.04704017567014063, 0.04656039319276406, 0.04583471052896382, 0.04531110745527123, 0.0452698374916638, 0.044711784493036255, 0.04452332972605788, 0.04430454607192402, 0.04406838905054933, 0.04345714793886302, 0.04316032552696658, 0.04294014239589039, 0.04283733769362108, 0.042177627147790275, 0.04216690271784085, 0.04179825178695218, 0.041337731296333224]\n",
      "Row 19 - Column Numbers: [18 73 21 16 15 83 17 22 20  1 77  0 85 87 91  2 90 64 12  4 46 79 92  5\n",
      " 11 68 78 42 10 57 72 75 62  3 31 52 70 56 32  8 30 35 43], MI Values: [0.5505196890502289, 0.4449658563187162, 0.3588428833857771, 0.3091588054074439, 0.301252319661101, 0.28206410473166965, 0.2719089149661009, 0.23610468619476066, 0.2076473979554514, 0.16120899606897776, 0.1483996768217315, 0.13409996608400476, 0.12862613575316484, 0.11907016274300641, 0.10649322098528025, 0.09214628161063843, 0.08561032186586814, 0.08194120218001011, 0.0811618444653357, 0.08049320130510296, 0.07977684117637374, 0.07277800134663526, 0.0708353227962224, 0.07067602202174772, 0.06976258783125466, 0.06634530228217983, 0.06322232364202662, 0.06322090154945581, 0.06289596277964993, 0.06149090076405361, 0.06050821759755998, 0.058831519684985345, 0.05762318703291758, 0.05676014452040601, 0.055853509021861925, 0.05518017282950449, 0.0544766833802548, 0.05387141021679831, 0.05309676005317332, 0.05241070031981998, 0.052023287162046294, 0.05003592431078108, 0.04839550757959277]\n",
      "Row 20 - Column Numbers: [77 21  1 17 83 85  0 15 91 87  2 11 19 12 79  4 16  5 22  3 10 64 78 13\n",
      " 18 61  8 90 31 56 24 46 14 30 92 74 68 34 73 33 42 44 43], MI Values: [0.6456828762580988, 0.5615054795942642, 0.5324618722588088, 0.49342669682830653, 0.4589017533899522, 0.42552426145736355, 0.4190235175463517, 0.3684773490976534, 0.3510509439994527, 0.3260490569519252, 0.26984073230595484, 0.21618413086183885, 0.20764739795544962, 0.190496506019743, 0.18041597931931808, 0.17593949417666988, 0.1704438750637216, 0.16974306927085436, 0.1497647957772532, 0.14918195632018527, 0.13028693835191607, 0.11253209164347666, 0.11158401518017502, 0.10347968403017305, 0.10281992390539951, 0.10190813419336298, 0.09860668116430649, 0.08732179357987757, 0.0842263209541052, 0.0828616535343425, 0.08129397459731802, 0.07862828607228867, 0.0768148676108753, 0.07673835654706895, 0.07064869314149558, 0.06733550911625219, 0.0667893192001614, 0.06677633392818816, 0.06621492860686207, 0.06372475882601236, 0.06355486571293412, 0.061150149623385275, 0.060827899523522966]\n",
      "Row 21 - Column Numbers: [17 83 20 15  1 19  0 16 77 85 22  2 91 18 87 11 12 73  4  5 79 90  3 92\n",
      " 10 78  8 42 61 64 56  7 46 31 68 13 57 43 62 44 35 52 26], MI Values: [1.0216176230190834, 0.7488876659638635, 0.5615054795942669, 0.48722604389986657, 0.4023069759074396, 0.3588428833857771, 0.33215728219305163, 0.2854168868564999, 0.28331594629221524, 0.2688208314872229, 0.22456476967975902, 0.2125857191397058, 0.2086854981064592, 0.19869503398736654, 0.18708052814614362, 0.1761220035865394, 0.14702536981806258, 0.14619238110757227, 0.144408327527505, 0.142083257529535, 0.13959981733842852, 0.12517520234618917, 0.12006037445413664, 0.1117978672601394, 0.10815686636048305, 0.10268663613005469, 0.09797349325439786, 0.09722563185672684, 0.09520585153422978, 0.09236995631917555, 0.09187841023316423, 0.09121449964563855, 0.08964547025689651, 0.08819779567887132, 0.08274897552593963, 0.08274041805651944, 0.08110178494543518, 0.07911198418960996, 0.07348744391152273, 0.06846944162919932, 0.06815788789081711, 0.06802973139084845, 0.06522771175571496]\n",
      "Row 22 - Column Numbers: [15 16 18 19 21 73 17 20 83 85 91 77  1 87 23  0 11  2 56 10 79 13 57  5\n",
      " 42 32 61  8  3 74 64 34 70 24 78 63 68 90 43 72 35 53 62], MI Values: [0.4227473405113029, 0.3870402149910266, 0.32015585431856763, 0.23610468619476155, 0.22456476967976258, 0.19668419399470238, 0.15874125412953077, 0.14976479577725232, 0.14502492612060003, 0.11578837068495584, 0.1063924866874304, 0.10378871318925587, 0.09452496762458118, 0.08969080820395181, 0.07632786384865842, 0.07596636122032496, 0.06893504056359401, 0.06328881794610464, 0.06098127462148906, 0.05727822396969895, 0.054970003136741497, 0.051323177882335536, 0.05062976172811151, 0.050465669694910176, 0.05027063548670352, 0.049760788383411025, 0.047233204160109565, 0.04542566347070398, 0.04382301867003058, 0.04368901502755573, 0.04358675196225281, 0.042850022291132994, 0.04278545874037132, 0.04263132941212078, 0.04245227781570726, 0.04240480524732426, 0.04177115423568889, 0.04146334279107311, 0.041258234396297944, 0.04113645596182369, 0.040745425400359636, 0.040726001607573004, 0.040577710389676724]\n",
      "Row 23 - Column Numbers: [64 57 87 44 10  6 24 91 85 61  8  4 22 63 15  7 16  0 11 17 92  2 12 21\n",
      " 14 55 47  1 74 56  5 13 79 62  9 31 25 77 26 83 32 20 46], MI Values: [0.1238287448328963, 0.11007546217848985, 0.10279703918589878, 0.09985139888774786, 0.09526800567615457, 0.09453623691659319, 0.09442643580457855, 0.092779592553069, 0.08797109748794085, 0.08578580449603201, 0.08474539401989523, 0.07907845045093076, 0.07632786384865975, 0.07257144170704688, 0.07129603115169214, 0.06816078423614158, 0.06694340591739678, 0.06631267495817283, 0.06614162517793609, 0.06462454817737662, 0.06377017167667276, 0.06238952944812581, 0.06198182224754323, 0.06102500139047695, 0.05852404069351369, 0.058494817456543835, 0.057048950299178, 0.056427588090688374, 0.05575798124214959, 0.05424612918912608, 0.053944258296575676, 0.053394179519995255, 0.05090816537458753, 0.049627949735287835, 0.04914461256289693, 0.04830377167633948, 0.0479154062061089, 0.047404493128977876, 0.04534942266509967, 0.044620281399040174, 0.04423650621570019, 0.04399862638296703, 0.04319511791377284]\n",
      "Row 24 - Column Numbers: [87 25 85 10 11  8 26 91 23 77 64 12 20  4 14 63 61  1 56  0 15 46  2 44\n",
      "  9 27 21 30 75 32 79 62  5 31  3 78 68 60 22 34 16 17  6], MI Values: [0.12664131656206834, 0.12184764568086237, 0.11662871191984614, 0.1126861641925645, 0.10784355126935541, 0.10209066826928304, 0.09988104072929094, 0.09541744286183551, 0.09442643580457988, 0.08554737930800638, 0.08433207450633073, 0.08382766133586106, 0.08129397459731003, 0.07926789356000175, 0.07873666169272342, 0.07871775795832381, 0.07660849160601568, 0.07658487183691687, 0.06753872107738834, 0.06575943129935258, 0.06508609948716693, 0.06378754370319006, 0.06196951220919278, 0.05575375327102261, 0.055562199294558745, 0.05318120567191542, 0.05262117138877809, 0.05116230585414172, 0.05083179402329918, 0.049254453905052564, 0.04814401145309244, 0.04665448807793737, 0.04619072869628571, 0.0458151748730149, 0.044434685459121326, 0.043901624829374875, 0.04323480914173228, 0.04291271895550075, 0.04263132941212122, 0.04238722505216597, 0.042346546936791185, 0.041908005215020694, 0.04135516870134959]\n",
      "Row 25 - Column Numbers: [26  8 24 10 14 13  9 27 64 20 32 30 63 11 21 12 74 33 17 56 23 85 91 15\n",
      " 87 28 61 89 34 38  1 40 43 52 36 80 35 37 41 83 86 88 16], MI Values: [0.22448983276060552, 0.16233774299458315, 0.12184764568086015, 0.11291908175479026, 0.10808026792929493, 0.07985596483401203, 0.07942615953296661, 0.06742082698712792, 0.057769002718598195, 0.05586583465511197, 0.054965263207836124, 0.05443370142787174, 0.053776458305056174, 0.05343401191718833, 0.05308655380792704, 0.05045720325549752, 0.05034647749383048, 0.04992384501594582, 0.0492451891629031, 0.04834454363245477, 0.0479154062061089, 0.047684160601328074, 0.047297099255485975, 0.04577736523629383, 0.0457726787254078, 0.045771120375120766, 0.04566515411493954, 0.043420484714855156, 0.043385152301504526, 0.04150956737140632, 0.04116356278905453, 0.040902739036422275, 0.039271536657020434, 0.03872861083601631, 0.03870735899101785, 0.03823640170302056, 0.03689051731253823, 0.03648924728638114, 0.03594012672179936, 0.03543675472183061, 0.0353375347334941, 0.033978841582392505, 0.033213377245050246]\n",
      "Row 26 - Column Numbers: [ 8 25  9 14 10 27 24 64 13 30 32 21 11 17 20 91 74 85 87 33 34 46  6 43\n",
      " 15 36 35  1 12 63 23 83 41 80 31 72 56 86 84 52 37 28 61], MI Values: [0.25245404084178746, 0.22448983276060552, 0.1888349353819665, 0.1709314398188191, 0.15950455852051704, 0.10013893815186226, 0.09988104072928916, 0.08361194904788949, 0.07181363072768843, 0.06658416020495395, 0.06642109881221003, 0.06522771175571318, 0.06133706698861552, 0.060864275396509626, 0.06030983748989538, 0.05855558719449405, 0.058118774994220246, 0.05502112683089955, 0.054955567957541085, 0.0548802691847472, 0.05446576296866468, 0.05385131209205429, 0.05140858603128562, 0.04892271442605356, 0.048556550337056414, 0.047843331021867996, 0.04718698058252446, 0.04666834102500239, 0.04641197580127887, 0.04620099613250428, 0.045349422665099226, 0.045142856596432246, 0.04487870650962478, 0.04102053350114243, 0.03975973670425059, 0.039456412404046404, 0.03926146380477791, 0.03883323698171193, 0.038101405951134204, 0.03717014915810957, 0.03702701389699303, 0.03678714727422072, 0.036512909297854]\n",
      "Row 27 - Column Numbers: [65 64 14 46 45 26  8 10 25  6 84  9 12 38 11 13 24 53 74  7 44 21 63 85\n",
      " 47 91 62  0 86  4  3  5 31 43 61 87 76 20 80  1 77 37 29], MI Values: [0.6065603894953897, 0.18682361749818366, 0.1515567092969663, 0.13632308186498676, 0.10364354834176126, 0.10013893815186492, 0.09968544490658893, 0.07918640410680577, 0.06742082698712792, 0.06278134191716767, 0.06038028586904787, 0.06024993017772662, 0.05954908040441431, 0.05566701959818321, 0.05365543785469562, 0.05349787902327563, 0.053181205671913645, 0.05121607804495909, 0.05107317746817763, 0.050533102412405384, 0.05024731173365815, 0.04849977979742892, 0.04791989593709012, 0.04765153600392935, 0.04741748068507423, 0.04718827956837135, 0.04704704797821968, 0.046555580550760034, 0.045963625687851284, 0.0458714770575126, 0.04550892471748291, 0.04427143864075678, 0.044267360807431544, 0.04422157037556218, 0.044030392965271226, 0.043659800788907965, 0.04331808077932564, 0.04308091954790427, 0.04297197397555763, 0.042923144439217076, 0.04277349385328666, 0.04153155742864545, 0.040719138411590805]\n",
      "Row 28 - Column Numbers: [89 38 88 37 40 86 29 41 39 36 33 74 30 34 35 43 32 31 56 78  5 44 12 80\n",
      " 79  2 13 42  1 11 10  4 62  6  8 68 90 64 52 17  0 54 61], MI Values: [1.0046755344608442, 0.8668221841314496, 0.7614158768816583, 0.7435037784407115, 0.7401508914135695, 0.7092838503040948, 0.6969500914396249, 0.6683242642188869, 0.6188553437563042, 0.5887599355969604, 0.573378254007582, 0.4637692211865332, 0.44110042693832696, 0.43990166348400894, 0.3542576214733666, 0.3130926126664333, 0.3038339983430083, 0.1631475034181804, 0.14153000235829616, 0.10874080446091217, 0.09875071075037845, 0.0973992316948431, 0.09501229751970275, 0.09424947908653536, 0.09026690572979579, 0.08247104503342673, 0.08202421217934486, 0.08020834452426495, 0.07617110541908723, 0.0751808599245587, 0.07299784236684648, 0.07194026557628508, 0.07174551471409618, 0.06638342779498885, 0.06518271250260632, 0.06489586595952179, 0.0643523399002186, 0.06270446068020075, 0.05772311949448383, 0.056954572674678516, 0.05644466945878257, 0.05541299819598944, 0.05407556787339285]\n",
      "Row 29 - Column Numbers: [37 86 38 89 39 28 40 36 88 74 33 41 43 35 30 34 31 56 32  5 78 79 44 80\n",
      "  2 12  4 90  1  0 87 42 46 77  3 14 64 11 85 62 63 57 13], MI Values: [1.124331483930141, 0.9904397714916939, 0.8561076404645682, 0.7571541803206943, 0.7394482075767632, 0.6969500914396267, 0.6243050233062002, 0.6127287729060686, 0.5162986988948424, 0.5004203013385551, 0.4839723248105665, 0.44277394507430223, 0.3862199704096003, 0.3611089233159852, 0.3044944524915385, 0.30210464330076015, 0.20191448281292157, 0.171307375513706, 0.1557361930389609, 0.11470618022646129, 0.1142833513780932, 0.10420208049496082, 0.10392751587923588, 0.09785175941231206, 0.09469648273846332, 0.08955815291429925, 0.07666467817423417, 0.07002944857802351, 0.06654779481397011, 0.06576826886766884, 0.06531253837083639, 0.06416664878429135, 0.06302637459570448, 0.06065012243418977, 0.06048824178377199, 0.058701476590528046, 0.05802769428221577, 0.049098105017652216, 0.04872740090602523, 0.04751490159093841, 0.04718646229756551, 0.047177310303764486, 0.04510718141365366]\n",
      "Row 30 - Column Numbers: [33 35 74 32 34 43 28 31 36 86 89 40 37 38 41 88 29 39 78 79  2 44  5 12\n",
      " 80  4 42  1  0 52 13  3 64 90 10 20 11  8 87 56 85 26 77], MI Values: [0.8392067051587295, 0.6637829223064537, 0.6484729630309518, 0.5649484715892896, 0.5416346036080313, 0.4933942675879779, 0.4411004269383261, 0.4130016958463507, 0.38187736651662174, 0.3742297238726069, 0.3717084490392537, 0.3527990507831582, 0.33036985608766933, 0.32508215731131695, 0.315969342937767, 0.3120618690279784, 0.3044944524915376, 0.2926134592339231, 0.245510624027526, 0.1906085060616709, 0.15876062884895248, 0.15101976681000995, 0.14845254677791608, 0.1373297433787659, 0.13577620649841027, 0.1241793539299092, 0.11531395362702757, 0.1150059734774116, 0.10962686909974106, 0.10641737910058513, 0.09258617061154961, 0.08507553529173606, 0.08219023403697623, 0.07857807032348152, 0.07776056152449762, 0.0767383565470654, 0.0758563574615021, 0.07521271366405902, 0.07367325277221859, 0.06707550157230102, 0.06691537715915796, 0.06658416020495572, 0.06275013897899484]\n",
      "Row 31 - Column Numbers: [43 78 35 30 33 44 74 79  2  5 36 42 86  4 37 29 34 80 32 38 28  0  1 89\n",
      " 39  3 12 40 41 88 11 87 85 13 17 21 10 91 20 83 77 64 90], MI Values: [0.8121927311946013, 0.7638100129208842, 0.7457506706593477, 0.41300169584634716, 0.40367630493282647, 0.3834036968008201, 0.36859551535020874, 0.3469763013969196, 0.288579169234902, 0.2760329582147696, 0.2539363056818278, 0.2480981515670253, 0.22807412650458492, 0.22779194586134022, 0.21452991980362057, 0.20191448281292157, 0.1870476252617994, 0.18479080672561743, 0.17115190570613592, 0.167611070828948, 0.16314750341817774, 0.16211076425159288, 0.16121744315732478, 0.15421271891570942, 0.1526762354992739, 0.15053120343368143, 0.14662969753092536, 0.1369994315782277, 0.12987048179875593, 0.1178467066606661, 0.11341149652601867, 0.10896037047705764, 0.1060824704994614, 0.10045734833963404, 0.09616040667204917, 0.08819779567887043, 0.08544174110632508, 0.08539580505605926, 0.0842263209541061, 0.08252825085347038, 0.07208828414576374, 0.06851019554836757, 0.06594386443863964]\n",
      "Row 32 - Column Numbers: [34 30 52 33 28 88 40 74 35 89 41 86 38 43 39 37 36 31 29 44 54 78  8 79\n",
      "  5  2  4  9 62 10 12 42  0  6 80 64  1 26 87 61 90 13  3], MI Values: [0.6589132113122833, 0.5649484715892905, 0.5366720434860506, 0.31429643099880256, 0.3038339983430083, 0.2746754336314945, 0.264343537327707, 0.254749734631722, 0.24376381697460836, 0.23990089864081465, 0.2315338746347546, 0.2027410833178278, 0.197909157760205, 0.19253106758836758, 0.1831205200479813, 0.17952444982802795, 0.17752977924984759, 0.1711519057061368, 0.15573619303895825, 0.12104168683611505, 0.11793416791373534, 0.1155347151347117, 0.10441158737263923, 0.09567236193821138, 0.09331795784564623, 0.09002264997452247, 0.087346193152265, 0.08690570143561605, 0.08212300251017712, 0.08091774681887465, 0.07909381487392952, 0.07802938607998389, 0.07772961987272353, 0.0772793483026124, 0.07650826602535332, 0.07345476684191166, 0.07062525451403978, 0.06642109881221536, 0.06429935007831045, 0.06347776301673225, 0.06345428849975132, 0.06200434845199787, 0.061265136171211765]\n",
      "Row 33 - Column Numbers: [74 30 36 35 43 86 28 37 89 38 29 40 34 39 41 88 31 32 78  5 79  2 44 80\n",
      " 12  4 42  1 56  0  3 13 85 64 87 11 90 10  8 52 77 61 91], MI Values: [1.1137204124807507, 0.8392067051587295, 0.7259968303690219, 0.676225408758059, 0.6277452858407466, 0.6078933190308362, 0.5733782540075802, 0.5576286905708168, 0.5364183007679388, 0.49716674763380553, 0.4839723248105665, 0.4791060933274043, 0.45408232882174193, 0.4358859922207907, 0.4346502711337248, 0.4047557520194287, 0.40367630493282647, 0.31429643099880256, 0.21439117181920508, 0.1707685245371131, 0.1675397929716098, 0.1580992185002481, 0.1558944425895863, 0.1513697471049289, 0.13072864694939046, 0.12068089113273839, 0.11403454812488523, 0.10934085523256698, 0.10568767232683207, 0.09664578770578203, 0.09072061229028083, 0.08878636983820609, 0.0853957938074732, 0.08444826940177563, 0.0822160314308702, 0.08191762067726316, 0.07829650162065782, 0.07794974091576812, 0.07565747720513549, 0.0721596876850441, 0.06870563600714075, 0.06766819910745436, 0.06454231972101443]\n",
      "Row 34 - Column Numbers: [32 41 40 89 30 88 33 28 38 39 74 86 37 36 29 35 43 31 78 52 79  2 12 80\n",
      "  5  4  8 44  1 56  0 10 42  3 13 11  9 85 90 14 20 87 91], MI Values: [0.6589132113122842, 0.6479726613644816, 0.6043685240765004, 0.5628237492307457, 0.5416346036080313, 0.521645640678436, 0.45408232882174193, 0.43990166348400983, 0.4368469340751924, 0.39158474017250366, 0.3551015296305442, 0.3436127338197732, 0.3342616147154853, 0.30793458819287167, 0.30210464330076015, 0.2547895016786663, 0.25147509845387006, 0.18704762526179852, 0.1318444892478734, 0.12773246250446846, 0.12182153097619519, 0.11747560005254787, 0.09993696526051377, 0.09689650292456253, 0.09670112680552911, 0.09367692420841855, 0.09279000891834333, 0.09093985620778966, 0.09049841174829432, 0.08918579292805706, 0.08750394746818113, 0.08709868991881464, 0.08002420593659476, 0.07711971317009425, 0.07495306478075747, 0.07298015929327839, 0.0685825322136786, 0.06771394965493194, 0.06748508102814021, 0.06725286085851323, 0.06677633392818727, 0.06352632300524341, 0.05979450877373882]\n",
      "Row 35 - Column Numbers: [43 31 33 30 74 36 86 37 29 78 28 38 89 44 39 34 40 32 88 79 80 41  5  2\n",
      " 42  4 12  1  0  3 11 13 56 85 87 90 10 64 17 21 83 15 91], MI Values: [1.3860244468954068, 0.7457506706593469, 0.676225408758059, 0.6637829223064564, 0.6417520640136267, 0.41003162791165604, 0.39846097278793113, 0.37245697314779047, 0.36110892331598254, 0.36035661286731724, 0.3542576214733648, 0.28812166153925034, 0.28455742734958633, 0.2744838416218025, 0.25908379307944696, 0.2547895016786681, 0.2444710266515937, 0.24376381697461103, 0.2113827569500044, 0.20596754398312012, 0.2032245059398745, 0.20034425775401932, 0.1956334739924417, 0.1870192028603448, 0.18522516757732976, 0.13262659195667936, 0.1285549123325911, 0.11642248941903688, 0.11361591888716038, 0.1016623748148815, 0.09674046912721845, 0.095142371568528, 0.0801836035458896, 0.07727436282669675, 0.07446311599579492, 0.07216427126333969, 0.07091448732899774, 0.06950218448865986, 0.06903264964802514, 0.06815788789081711, 0.06455351051612634, 0.06380756444093993, 0.05848415311997446]\n",
      "Row 36 - Column Numbers: [86 37 33 29 74 28 89 41 38 40 39 43 35 88 30 34 31  5 32 56 78 79 80 44\n",
      "  2 12  4 42  1  3 90 10  0 13 72 14 77 64 87 57 70 46  6], MI Values: [1.0233770024292177, 0.8615166885581989, 0.7259968303690219, 0.6127287729060713, 0.6090092895887054, 0.5887599355969613, 0.5752000583378694, 0.5713794920745894, 0.5355098016260644, 0.47454758830574484, 0.4665352887983394, 0.4335648849167999, 0.41003162791165515, 0.39112029603754017, 0.38187736651661996, 0.30793458819287167, 0.2539363056818287, 0.20674579006625216, 0.1775297792498458, 0.15081603715863867, 0.14656523125808896, 0.11619314258747515, 0.11571876599131148, 0.1145234869763252, 0.10960845386111995, 0.0970948434370289, 0.0877144141798194, 0.07775809933113642, 0.07458627225738823, 0.07188834325973659, 0.06954945457795603, 0.06702934232361812, 0.06656537960473763, 0.0637980214953684, 0.06265064870037129, 0.06166886568276819, 0.06121318706422585, 0.06076563582838368, 0.0603698282500984, 0.0600022474540296, 0.05999309743629677, 0.059587362304820424, 0.05838254740343718]\n",
      "Row 37 - Column Numbers: [86 29 36 38 89 28 39 40 33 74 88 41 43 35 56 34 30 31 32  5 78 79 44 80\n",
      " 12  2  4 90  1 42 87 46  3  0 14 77 57 64 75 10 81 85 72], MI Values: [1.45827221487633, 1.1243314839301428, 0.8615166885582006, 0.8339552318828192, 0.75725247965641, 0.7435037784407115, 0.6894104126018572, 0.6269405732545383, 0.557628690570815, 0.5514988683591895, 0.5065004040074994, 0.4944806219210722, 0.4048082990644746, 0.37245697314779047, 0.35940226604219117, 0.3342616147154871, 0.3303698560876711, 0.21452991980362324, 0.17952444982802884, 0.12301925557245674, 0.1229936336440689, 0.11167013683338922, 0.10660787110909098, 0.09822950179437395, 0.09592473158963699, 0.09141368395878491, 0.07514331037207178, 0.07091755529673804, 0.06883285800983607, 0.06871969299735081, 0.066765545099301, 0.06572403954205441, 0.06558274587026869, 0.06455866987752579, 0.06416649947375319, 0.06138718973277957, 0.05958381308008942, 0.0586839187321484, 0.05770927457102015, 0.05541200876063623, 0.0543002203644134, 0.053567885640179114, 0.053098326138301566]\n",
      "Row 38 - Column Numbers: [89 39 40 28 29 37 88 86 41 36 33 74 34 30 43 35 32 31 56 78  5 79 44  2\n",
      " 80 12  4 90 42 87 64 10  3  0 46 54 27 63  1 55 61 52 81], MI Values: [1.2419280927673926, 0.9495031915623935, 0.9353087992452069, 0.8668221841314478, 0.8561076404645709, 0.8339552318828174, 0.7568375359220987, 0.7540596341394155, 0.6590139783160547, 0.5355098016260609, 0.49716674763380464, 0.4638361476100483, 0.4368469340751897, 0.32508215731131607, 0.2970750486302043, 0.28812166153925034, 0.19790915776020768, 0.16761107082894533, 0.14324753303636406, 0.10392867184476451, 0.10350223849689133, 0.09301615106454886, 0.08916423701914233, 0.08794009077204823, 0.08653427377214928, 0.08621577314512141, 0.07857614620487752, 0.07291292443408093, 0.06775644455948626, 0.06587368807998661, 0.06444153292271437, 0.06239411896947633, 0.0611391661707783, 0.05890813572238418, 0.05743119615494585, 0.05657172017433254, 0.0556670195981841, 0.052999594620209756, 0.05251122766241956, 0.05144646558632271, 0.050525831605085614, 0.05046119874021926, 0.050427398365081366]\n",
      "Row 39 - Column Numbers: [89 40 38 88 29 37 86 28 41 36 33 74 34 30 43 35 32 31 56 78 79  5  2 44\n",
      " 12  4 80 90 46 64 42  0  3  1 87 54 57 10 85 81 11 75 13], MI Values: [1.0535035116401659, 0.980751027799518, 0.9495031915623944, 0.7414381495833338, 0.7394482075767623, 0.6894104126018581, 0.6322229406595952, 0.6188553437562998, 0.597892725921354, 0.46653528879833495, 0.4358859922207863, 0.41880685619855296, 0.3915847401725019, 0.29261345923392224, 0.2629228824826715, 0.2590837930794496, 0.18312052004798485, 0.15267623549927567, 0.11061737849190223, 0.10303541936903038, 0.10121071598448683, 0.10050281527196514, 0.09409837181553016, 0.09268755609898616, 0.09122469199042627, 0.07574221883219856, 0.07038469791400459, 0.06777425757345945, 0.06718928231977817, 0.06637371235615408, 0.06470157204124849, 0.06376207874312012, 0.06157433149594027, 0.059317843630458, 0.056927475789509074, 0.0553570174716711, 0.050475458950668184, 0.049665682066896366, 0.048873507505192926, 0.048724267224924844, 0.048532049612547645, 0.045653657389332025, 0.045387402202069715]\n",
      "Row 40 - Column Numbers: [88 89 39 38 41 28 37 29 34 86 33 36 74 30 32 35 43 31 56 79 78  5 12  2\n",
      " 90 80 44  4 64 46 10 42 11  0 54  3 87 62 52  8  1 61 13], MI Values: [1.358468758232667, 1.2392621662048944, 0.9807510277995188, 0.935308799245206, 0.926520358369948, 0.7401508914135668, 0.6269405732545383, 0.624305023306202, 0.6043685240764987, 0.5904546129889008, 0.4791060933274034, 0.47454758830574484, 0.42293019416571376, 0.3527990507831582, 0.2643435373277079, 0.24447102665159282, 0.24139738990497683, 0.13699943157822414, 0.10838563263965639, 0.1029822194696477, 0.09964875862896427, 0.09746128685535993, 0.09185969685609141, 0.08826839034197231, 0.08755455049272953, 0.08752252944643946, 0.08181196297427373, 0.07604174073333958, 0.072912801172893, 0.07131829013591684, 0.06301067329213339, 0.06159199509503921, 0.0600744169282601, 0.05966325856990995, 0.05887006365191372, 0.05721261367801134, 0.05676698284365411, 0.05477366448826615, 0.054719591158505665, 0.0521148561565834, 0.05184786967249444, 0.05173422697187924, 0.050382935130099504]\n",
      "Row 41 - Column Numbers: [40 89 88 28 38 34 39 36 37 86 29 33 74 30 32 43 35 31 56 78 79  5 44  2\n",
      " 80 12 90 62 10  0  1  3 42  4 61 64 92 11 70  6  8 52 13], MI Values: [0.9265203583699506, 0.9100181021852727, 0.8687228214668874, 0.6683242642188896, 0.6590139783160538, 0.6479726613644816, 0.5978927259213549, 0.5713794920745912, 0.4944806219210731, 0.47456031717445235, 0.44277394507429957, 0.4346502711337239, 0.33199699186004406, 0.3159693429377697, 0.23153387463475372, 0.21422375662965543, 0.20034425775401843, 0.1298704817987586, 0.11875744932887322, 0.0926509060956926, 0.08676758111423233, 0.086057783978851, 0.08262255635642912, 0.07942866688885086, 0.0785488622631787, 0.0742530711565692, 0.07307672025710232, 0.06941263844280599, 0.06936075480536719, 0.06665335877299139, 0.06410363270210784, 0.06306413363039987, 0.06207958706935557, 0.05954608451087129, 0.0593461118278249, 0.057899646129423665, 0.05389698575662916, 0.053384856694632, 0.05325141402769873, 0.05243412828986749, 0.052078907698307475, 0.05177082062384475, 0.050887404336976694]\n",
      "Row 42 - Column Numbers: [90 31 44 43 35 78 80 30 92 33 21  5  1 74  2 79 12  0 17 83 28 34 85 32\n",
      " 36 11 86 91 37 38 16  4 15 10 39 29 20 19 87 89 13 41 40], MI Values: [0.5736361560630607, 0.24809815156702442, 0.237501584176659, 0.2123646632862819, 0.18522516757733065, 0.17401757617932745, 0.14508216519352857, 0.11531395362702668, 0.11438741669921182, 0.11403454812488256, 0.09722563185672684, 0.09376382987344112, 0.09265639520815316, 0.09219897198964677, 0.09190658625377246, 0.09102336506577036, 0.08912140713055283, 0.08872664637914252, 0.08466458683253641, 0.08290682477634803, 0.08020834452426406, 0.08002420593659121, 0.07969793759561306, 0.07802938607998477, 0.07775809933113642, 0.07587529502253965, 0.0754741707644273, 0.06881214952706838, 0.06871969299735348, 0.06775644455948715, 0.06750837136584042, 0.06712048581871777, 0.06699419564638998, 0.06547249101527441, 0.06470157204125115, 0.06416664878429224, 0.06355486571293678, 0.0632209015494567, 0.0630884431737817, 0.06261691628512, 0.06240830984967349, 0.06207958706935468, 0.0615919950950401]\n",
      "Row 43 - Column Numbers: [35 31 33 74 30 36 86 37 29 78 28 44 38 89 39 34 40 80 41 42  5 79 88 32\n",
      "  2 12  0  4  1  3 11 13 87 85 56 83 21 17 90 10 91 77 64], MI Values: [1.386024446895405, 0.8121927311945987, 0.6277452858407475, 0.6243039700489881, 0.4933942675879788, 0.433564884916799, 0.4240950333084843, 0.4048082990644737, 0.38621997040959855, 0.370397111365631, 0.3130926126664342, 0.30395671539799096, 0.2970750486302043, 0.28802774608809134, 0.2629228824826706, 0.25147509845387095, 0.24139738990497772, 0.2276321837680122, 0.21422375662965365, 0.21236466328628278, 0.20819529046906204, 0.20739130754119195, 0.20626412498042956, 0.1925310675883667, 0.18681968571483676, 0.14156956810137, 0.1358699397958949, 0.1316783860928359, 0.12913107009156466, 0.1038170751558507, 0.09481730555192946, 0.09195467760152898, 0.08755593140089069, 0.08744850763647793, 0.08170555433368687, 0.081560766459293, 0.07911198418961085, 0.07861749607301682, 0.07721049556759585, 0.07182439963604015, 0.07147186167010044, 0.06546454180161465, 0.06421723199729623]\n",
      "Row 44 - Column Numbers: [31 43 78 35  4 42 33 79 30  2 74  5 54  0 64 32 36 80 86 37 29 87 23 88\n",
      "  1 28 39 89 34  3 38 13 11 12 10 85 46 41 40 63 91 62  6], MI Values: [0.38340369680082365, 0.3039567153979892, 0.2940959242977499, 0.27448384162180073, 0.2577169657460203, 0.23750158417665634, 0.15589444258958807, 0.1535208253346898, 0.15101976681000817, 0.14614605566374905, 0.13751208245379942, 0.1330855289284827, 0.13216267787018499, 0.12631372813240205, 0.12575424005177993, 0.12104168683611682, 0.11452348697632786, 0.11196280971917094, 0.10936129874317668, 0.10660787110909098, 0.10392751587923676, 0.10044717697415884, 0.09985139888775052, 0.09784483548609302, 0.09756958090355994, 0.0973992316948431, 0.09268755609898616, 0.09241113709100457, 0.09093985620779232, 0.0903461896754747, 0.08916423701913878, 0.0882487868884656, 0.08789263097170785, 0.0865487450581588, 0.08386645043593699, 0.08318123056251459, 0.08302480760550157, 0.08262255635642735, 0.08181196297427551, 0.08074364625578223, 0.07356394424112711, 0.07306242342033098, 0.07123886187653294]\n",
      "Row 45 - Column Numbers: [65 60 66 76 64 63 69 27 84 53 54  6 75 62 57 70 81 12 46 61 11 50 72 87\n",
      "  1 10 85 52 49 68 13 77  3 48 21 24 32 90 91  8 30 79 15], MI Values: [0.3355390992669385, 0.24105785735212137, 0.16669975622521527, 0.14089157380955708, 0.13477024068243892, 0.11692650889904499, 0.10868038934784607, 0.10364354834175771, 0.10150362847124583, 0.09056761307301286, 0.0798331274015025, 0.07607959090818639, 0.07550304956704501, 0.07129070394238113, 0.06353587781859105, 0.06252081423776445, 0.05993439653997168, 0.05696539251436761, 0.05614165957912931, 0.05305353245500477, 0.05289097853795344, 0.05163697152796942, 0.05126811930396258, 0.049018668863451076, 0.048759179040770206, 0.04826951163990145, 0.04548841097074785, 0.045170627201460256, 0.04515557347533239, 0.04505498244851758, 0.04468423892141704, 0.04437075080106645, 0.04344271363863772, 0.042062378026346714, 0.041189709960936405, 0.04052516260945005, 0.04034464006210747, 0.04008368476259694, 0.039929482136464856, 0.039675854506701747, 0.039107723692991314, 0.038854237195490526, 0.038161379909507964]\n",
      "Row 46 - Column Numbers: [64 51 55 59 48 68 47 58 61 87 75 49 72 56 54 84 27 70 67  6 74 57 17 69\n",
      " 81 14 21 50 77 63 44 52 85  1 19 76 20  4  0 79 62  2 40], MI Values: [1.1094691017199603, 0.36567183873432274, 0.3141727399115952, 0.23992709365254683, 0.2171439106790931, 0.19852690016740127, 0.18923509125775695, 0.1858984961031256, 0.17267857439960022, 0.16549438774061187, 0.15983167864594883, 0.15828858721216044, 0.15559450174685807, 0.1460850846009656, 0.14012136027135202, 0.13751725928655478, 0.13632308186498943, 0.1328114960531792, 0.13279522094755158, 0.13099684473508688, 0.11736212179504424, 0.11368720902898488, 0.11280369881762642, 0.105422623025202, 0.10140282553967683, 0.09266115822732957, 0.08964547025689651, 0.08911598382671393, 0.08487347419103042, 0.08355750196952805, 0.08302480760550068, 0.08232030940720492, 0.08171791357507097, 0.08010342629738698, 0.07977684117637374, 0.07963991449703212, 0.07862828607228867, 0.07856401142112102, 0.07681250087322677, 0.07650530330583649, 0.07403272493206359, 0.07325788085011453, 0.07131829013591773]\n",
      "Row 47 - Column Numbers: [48 55 82 49 51 64 46 61 56 50 14 57 87 54 63 75 67 70 69  6 72 74 68 23\n",
      "  4 52 20 59 38 27 85 84 11 81 33 92 89 60 41  7 36 77 19], MI Values: [0.4249124097885648, 0.4187425231559816, 0.3602265067790995, 0.2776897644328633, 0.24912743330867393, 0.1987447932521178, 0.18923509125775695, 0.15384874665912562, 0.10368137158256019, 0.09785925823341302, 0.09074348902636764, 0.08687796447828866, 0.08569788060934425, 0.08001798979213337, 0.07907233827318905, 0.07403127407645904, 0.07249971148987289, 0.07068379697727956, 0.06874455994522588, 0.06549702884688635, 0.06175094572082518, 0.06009771362514993, 0.05906462224581688, 0.05704895029918333, 0.056865014508378664, 0.05682164950861601, 0.05161482461035316, 0.05139487626535377, 0.050000458629791744, 0.047417480685076896, 0.04726109720318572, 0.04708602460329292, 0.0467491462024574, 0.04656568399330041, 0.045808067196454694, 0.04460527570146677, 0.04416183571061527, 0.043961928173374076, 0.04334931626754024, 0.043171664331128845, 0.04285749863832411, 0.041651660789991496, 0.040805913716284614]\n",
      "Row 48 - Column Numbers: [49 55 47 51 46 50 64 75 68 67 69 87 61 54 58 81 59 70 56 57 63 14 52 84\n",
      "  6 73 72 91 60 66 18 45 85 11 74 21 17  4 76 38 19 32 44], MI Values: [0.553678897514204, 0.5019751647569173, 0.4249124097885639, 0.2875171464071613, 0.2171439106790931, 0.1743136297813912, 0.11110937927605313, 0.10037244122026134, 0.08934545133594263, 0.08190429469032878, 0.0736143304488408, 0.07327006385127088, 0.0721867594925314, 0.07042527416616018, 0.0687315220763578, 0.06681937537003169, 0.06642447830364517, 0.06437836072642522, 0.0635873831512015, 0.060791248768552464, 0.057609186216970976, 0.05528245353972938, 0.05372925078899371, 0.04909830573294105, 0.04808633609087387, 0.045306406824380474, 0.04489736208567496, 0.044709846969715805, 0.04357966587574236, 0.04284931649405177, 0.04283733769362197, 0.0420623780263476, 0.040772805188195704, 0.04013167977317522, 0.03986903738847314, 0.03954931815568408, 0.03897874301162396, 0.03884934604555568, 0.0387817158798871, 0.03828887823525573, 0.03729803186228775, 0.03670448581979002, 0.03666047870806732]\n",
      "Row 49 - Column Numbers: [48 55 47 50 51 75 46 69 54 64 68 81 52 61 57 67 87 63 70 56 60 84 11 14\n",
      "  6 45 13 66 58 12 59 72 10  1 79  4 77 85 32  0 74 40 36], MI Values: [0.5536788975142031, 0.30360053691119226, 0.27768976443285975, 0.2735029225169381, 0.1755926065938338, 0.16380558437787318, 0.15828858721215955, 0.09982396156077034, 0.0899951771509615, 0.08729689308508082, 0.0805251845303161, 0.07578213385519295, 0.0734512632183959, 0.07118839940287724, 0.06818162225492586, 0.06462675171117471, 0.05826597066506878, 0.05474056322253951, 0.05205162711625633, 0.04949584081348313, 0.04890714820172626, 0.047598231033918914, 0.0471786080006531, 0.04697649944513582, 0.04612338247236547, 0.04515557347533328, 0.04394002279515519, 0.0427889260255494, 0.04277730549634029, 0.041579343265056856, 0.03968935771140636, 0.03878327857790431, 0.03721262391298552, 0.03708316769882014, 0.03707875631470614, 0.03437124492900345, 0.03420072144079178, 0.03393860185339559, 0.03373647790879719, 0.03296788902954706, 0.032940030634634354, 0.03271399526283414, 0.03233124919474406]\n",
      "Row 50 - Column Numbers: [75 49 48 69 81 57 54 47 55 68 52 46 64 84 87 51 76 45 67 10 12 14 66 63\n",
      " 60  4 74 85 17 11  6 70 33 79 83  8 36 24 21  0 88 89 40], MI Values: [0.38569583316040035, 0.273502922516939, 0.1743136297813921, 0.13649561521326792, 0.13615369070630745, 0.12386611734750641, 0.11005231669100635, 0.0978592582334139, 0.09343475605257989, 0.09313301709157429, 0.08963552340153047, 0.0891159838267166, 0.08223331555010471, 0.06909627215253966, 0.0664099664637332, 0.05717803565613533, 0.05211485875131405, 0.051636971527967646, 0.049028136696537494, 0.04645372478558407, 0.046362851486650314, 0.04624367400979423, 0.04570965837784602, 0.04395880445259959, 0.04352223482917594, 0.04297224529545307, 0.04249884332512721, 0.04210332584072418, 0.041711486256092556, 0.041695189003549515, 0.04113881744298897, 0.04104741966052927, 0.04091402778420328, 0.04064421390754891, 0.04045686991204356, 0.03995848045904005, 0.03949861996272741, 0.039383429640937884, 0.038877820203155444, 0.03883494246593333, 0.038717645473936635, 0.038634738171873906, 0.03778877017396365]\n",
      "Row 51 - Column Numbers: [55 46 48 47 49 59 64 61 56 58 68 67 50 54 84 14 87  6 44 52 75 69 63 70\n",
      " 21 76 66 60 57 89  4 32 41 40 81 38 11 23 62 74 72  0 88], MI Values: [0.4918905885238507, 0.36567183873432274, 0.2875171464071622, 0.24912743330867393, 0.1755926065938347, 0.15335403151725657, 0.14408460937434686, 0.1323322880421669, 0.09492283806278046, 0.08131092018359531, 0.06392417227606728, 0.06049342127079882, 0.05717803565613444, 0.05383149700687451, 0.050444118959005024, 0.05026820068852356, 0.04809307532768603, 0.04800319914719342, 0.0474286517687057, 0.046076652615822944, 0.04517706634337504, 0.043804660168771825, 0.042590107680609, 0.03955596847245513, 0.0389668719566183, 0.03840491710777805, 0.03826743593598536, 0.03684825881094511, 0.03623578817846784, 0.0361041768011896, 0.03552228501544441, 0.034884214114486056, 0.03474350659770309, 0.034398958953260284, 0.03368774459666746, 0.03349076627149561, 0.03327235828735464, 0.03304187113566659, 0.03265504215054538, 0.03189647338370527, 0.03187888017866847, 0.03186557598989026, 0.031744992944004125]\n",
      "Row 52 - Column Numbers: [69 32 57 54 81 75 68 34 30 64 50 46 49 33 21 17 63 88  6 61 55 35 86 28\n",
      " 47 19 66  7  4 40 48 74 41 10 72 37 84 58 38 83 70 20  1], MI Values: [0.5772799725175162, 0.5366720434860497, 0.5130885687568068, 0.3225256074571332, 0.29251898737336113, 0.193542163657888, 0.12789690664174191, 0.1277324625044658, 0.10641737910058513, 0.0948475569445888, 0.0896355234015278, 0.0823203094072067, 0.07345126321839857, 0.072159687685045, 0.06802973139084934, 0.06703671873903261, 0.06405860187379542, 0.06273572137952055, 0.06139781255903909, 0.06122875212893497, 0.06013022861701689, 0.05843192812514708, 0.057757311630738606, 0.05772311949448383, 0.05682164950861601, 0.05518017282950538, 0.05499973892547416, 0.05481337747376269, 0.054736479053383746, 0.054719591158505665, 0.05372925078899371, 0.05209049250429132, 0.05177082062384297, 0.05139303267069195, 0.05111353303252564, 0.05089562323484653, 0.05067571023863948, 0.050481480883075136, 0.05046119874022281, 0.05022240658314203, 0.05011325603669903, 0.04998115622272348, 0.04960552836869159]\n",
      "Row 53 - Column Numbers: [62 63 64 45 70 85 17 10 91 72 60  4 69 87 12 46 21 11 15 27 20 19 65  1\n",
      "  5  8  0 84 83 14 16 30 18 79 22 28 73 36 66 33 44  2  9], MI Values: [0.40877114705633577, 0.10768325129662326, 0.09142254528217908, 0.09056761307301286, 0.07763014753084896, 0.07291262831419587, 0.06894645621138817, 0.06799093673704526, 0.06654270992309375, 0.06557217989953035, 0.06551159416228547, 0.06101431583981842, 0.05994221903533248, 0.05849475346295652, 0.05643638304159726, 0.05373645940673466, 0.05359496095281546, 0.05257556822858955, 0.05145699897162004, 0.0512160780449582, 0.04985185416914284, 0.047971786345549106, 0.047543267529873035, 0.04687607939115512, 0.046211483174281476, 0.045677188956067205, 0.04379488308218882, 0.04284987062613599, 0.04248356027197353, 0.042449553699675846, 0.04223363657743473, 0.04200308548928522, 0.04179825178695129, 0.04128772798638014, 0.04072600160757123, 0.04068711874009434, 0.03933717348757071, 0.03925453370539245, 0.03848324031768957, 0.03752841617132585, 0.03638983181890776, 0.03585269752426079, 0.03562342742166713]\n",
      "Row 54 - Column Numbers: [81 69 52 75 57 68 64 46 44 32 50 62 63 84 49 47 45 66 76 70 74 55 61 87\n",
      " 48 58 72  6 60 83 30 40 21 35 17 38 36 56 28 39 88 13 51], MI Values: [0.7379530571253516, 0.6991638866458327, 0.3225256074571341, 0.28357752574033057, 0.2796508865934202, 0.2576301492482225, 0.15163383746901538, 0.14012136027135202, 0.1321626778701832, 0.11793416791373446, 0.11005231669100635, 0.09996017287947367, 0.09375651906359739, 0.09285394516933021, 0.0899951771509615, 0.08001798979213337, 0.0798331274015025, 0.07892182637938827, 0.07324275519206846, 0.07247468124904266, 0.07245070956178878, 0.07176330422608057, 0.07112370577561311, 0.07067226287875972, 0.07042527416615751, 0.06899903291146714, 0.06863149347900066, 0.06777316229745178, 0.06704206660250378, 0.06494064826102708, 0.060874758017741115, 0.05887006365191105, 0.05810380963000572, 0.05748468340966095, 0.05669604970686226, 0.05657172017433165, 0.05650255737683452, 0.0557378324255442, 0.05541299819598766, 0.055357017471672876, 0.05436024408042606, 0.05430024107788167, 0.05383149700687362]\n",
      "Row 55 - Column Numbers: [48 51 47 46 49 64 59 61 50 58 68 75 67 69 56 54 81 84 63 52 57 23 87 14\n",
      " 70  0 38 73 41  1 44 37  4  6 88 72 11 86 36 89 76 62 74], MI Values: [0.5019751647569191, 0.4918905885238507, 0.4187425231559816, 0.3141727399115961, 0.30360053691119226, 0.1455355267788132, 0.10391523768986577, 0.10320434092076614, 0.09343475605257989, 0.09039691815655626, 0.08433296148313651, 0.07894014514832115, 0.07810178261121159, 0.07626677924718717, 0.07457832871124648, 0.07176330422608146, 0.0666084572296537, 0.0649658298184459, 0.06183261687680819, 0.06013022861701511, 0.05926409456159032, 0.05849481745654206, 0.05810381930205111, 0.05661782886079081, 0.05210958027079382, 0.05151582272524369, 0.05144646558632182, 0.0513717845320274, 0.04985324468381247, 0.04872468386788853, 0.04840563532307751, 0.047905222457149677, 0.047753548931313006, 0.04774985453638614, 0.046832066350649626, 0.046337404344297006, 0.04532790922027541, 0.04508240476302117, 0.04498650870497656, 0.04457765391180146, 0.044450219960144643, 0.04410009039404095, 0.04400663644262881]\n",
      "Row 56 - Column Numbers: [61 37 64 86 29 36 46 38 28 67 74 89 41 59 39 40 33 87 47 51 21 34 88 20\n",
      " 43 35  1 17 63 55  2 68 15  0  4 85 91 24 30 77 58 48 16], MI Values: [0.43147747233694655, 0.3594022660421903, 0.22066317128273738, 0.19813479850705384, 0.1713073755137069, 0.1508160371586369, 0.14608508460096736, 0.14324753303636495, 0.14153000235829616, 0.1390223315396053, 0.12763532576626613, 0.12759658270105412, 0.11875744932887322, 0.1140267649058524, 0.11061737849190578, 0.10838563263965728, 0.10568767232682852, 0.10439486730787184, 0.10368137158256019, 0.09492283806277957, 0.09187841023316512, 0.08918579292805973, 0.08812813925290719, 0.08286165353433983, 0.08170555433368776, 0.08018360354588872, 0.07992095121214593, 0.07971577342061753, 0.07711766737948622, 0.07457832871124559, 0.07436029178819847, 0.07341505483174426, 0.07262961413738722, 0.07242362723832141, 0.0720538145634535, 0.07002602366231869, 0.06996541088145225, 0.06753872107738657, 0.06707550157230013, 0.0658465345860213, 0.06480713020071249, 0.06358738315120327, 0.06331255297437988]\n",
      "Row 57 - Column Numbers: [52 69 75 54 81 63 64 68 50 46 23 72 87 17 74 61 47  6 70 21  7 84 62 49\n",
      " 73 82 92 58 45  0 19 66 56 48 36 37 55  5 44 83 60 79 77], MI Values: [0.5130885687568085, 0.4492286562322283, 0.3175403262160419, 0.2796508865934202, 0.2386747781742029, 0.19893022670047156, 0.1706591351738478, 0.12717047965108375, 0.12386611734750552, 0.113687209028984, 0.11007546217848985, 0.1056703039813307, 0.09943857195888661, 0.09928683256670379, 0.09565681017050132, 0.09358492153412179, 0.08687796447829044, 0.08592201720969239, 0.08195684550894988, 0.08110178494543341, 0.07616119177035774, 0.07392888704485934, 0.07251648801624277, 0.06818162225492586, 0.0667097043144338, 0.06659031769662516, 0.06608857489515785, 0.06605291746158404, 0.06353587781859193, 0.061740263953568686, 0.061490900764048284, 0.06146140592633831, 0.06124498359253927, 0.060791248768552464, 0.06000224745403049, 0.0595838130800912, 0.059264094561592096, 0.058399152771426266, 0.05763128744059465, 0.05711690835432748, 0.056631880706102145, 0.05618380082027041, 0.05594599871005901]\n",
      "Row 58 - Column Numbers: [46 59 67 61 64 55 75 51 81 54 48 68 57 56 44 69  0 52 88 79  5 84 73  4\n",
      " 74 40 17 87 49 70 72  7 89 47 62 38  2 43 37 50 60 77 86], MI Values: [0.1858984961031256, 0.17684958964553754, 0.1376164223851939, 0.10259159901626358, 0.09323139589981633, 0.09039691815655537, 0.08672016085400625, 0.0813109201835962, 0.07170077496787108, 0.06899903291146536, 0.06873152207635869, 0.06709058591021666, 0.06605291746158226, 0.0648071302007116, 0.06182062594159721, 0.053739795644960786, 0.05071325731351273, 0.05048148088307869, 0.04789057473566327, 0.047499732845677656, 0.04605361797762875, 0.045749765509683904, 0.04511521302719235, 0.0451146228488728, 0.04429686953990242, 0.0436866294276701, 0.042952045110664194, 0.04293717981312373, 0.04277730549634118, 0.04249097503546562, 0.041569158118069716, 0.0414072565023762, 0.04087411787997919, 0.04008012588680554, 0.03946179272307493, 0.039370558103208886, 0.03780798205952163, 0.03731442430222387, 0.03713892176412692, 0.036719401321429146, 0.03638037155973528, 0.03628517346620885, 0.03595011355909605]\n",
      "Row 59 - Column Numbers: [80 46 61 58 51 56 55 64 67 48 75 47 44 74 68 81 73 41 33 90 43 54 40 49\n",
      " 62 84 88 57 89 38 45 21 79 70 37 50 31  3 87 52 86  5 69], MI Values: [0.2465372262762342, 0.23992709365254772, 0.18600181466110133, 0.1768495896455411, 0.1533540315172539, 0.11402676490585151, 0.10391523768986577, 0.10143685103057543, 0.07292707939904464, 0.0664244783036434, 0.05458094170480976, 0.051394876265351996, 0.048036989305325406, 0.046929431867398286, 0.0468761986306756, 0.04281709288360336, 0.041442701275810734, 0.04123745905248555, 0.04109308677692969, 0.04080241822363018, 0.0405708194427179, 0.04002737117363697, 0.039970526744237844, 0.039689357711408135, 0.03937800895674659, 0.03858909846737113, 0.038104381220402495, 0.03733929606864361, 0.037336166429184026, 0.03621910618345936, 0.036194932260467994, 0.03564645785808285, 0.03530947035182841, 0.034605332803858246, 0.034270780090086106, 0.03385625356854849, 0.033688224144492906, 0.03365099687676132, 0.03359866945243972, 0.03358824636426494, 0.033156708793527834, 0.032867078986785536, 0.03252523413328934]\n",
      "Row 60 - Column Numbers: [45 66 64 75 69 76 46 54 53 84 81 57 65 63 56 70 49 61 52  6 47 62 48 50\n",
      " 24 55 10 87  1  4 68 72 51 58  8 17 85 21 11 44  0  9  2], MI Values: [0.24105785735212315, 0.14313213465555208, 0.13185070300011947, 0.08789136339985504, 0.08538631330874047, 0.07359513171289755, 0.06886160619467585, 0.067042066602502, 0.06551159416228902, 0.062130659320295045, 0.06016542150362536, 0.056631880706101256, 0.05516399778635517, 0.05208181872897821, 0.04990175130811547, 0.04924267114111114, 0.048907148201728035, 0.04565762279498298, 0.04550928202171889, 0.04432955091321311, 0.0439619281733723, 0.043609459383989524, 0.04357966587574058, 0.04352223482917683, 0.042912718955503415, 0.04289723654803357, 0.04246041760917052, 0.041422133425950136, 0.039365018633776394, 0.03811521797273176, 0.03776259020466188, 0.03735714461537043, 0.03684825881094511, 0.0363803715597415, 0.03495408974131564, 0.034779085744490956, 0.034559288190181725, 0.03360900022740143, 0.033444948836911514, 0.032907121469348155, 0.032668405905845965, 0.0324609794611499, 0.03181022364805397]\n",
      "Row 61 - Column Numbers: [56 11 64 59 46 47 51 87 12 85 55 58 20 10 21 57  1 91 63 23 17 69  2 68\n",
      "  0  4  6 24 79 77 83 48 49 54 74 67 33 15  7 84 32 14 52], MI Values: [0.43147747233694567, 0.42117961947471017, 0.30274924109928225, 0.186001814661104, 0.17267857439960288, 0.1538487466591274, 0.1323322880421669, 0.11609849133691696, 0.11175003676089812, 0.10334008173381015, 0.10320434092076347, 0.10259159901626269, 0.10190813419336209, 0.10067720955483761, 0.09520585153423244, 0.09358492153412534, 0.0919232880302312, 0.0871403303663465, 0.08651352031480286, 0.08578580449603024, 0.0845797268571502, 0.08175995345877496, 0.0807578644808169, 0.0801785495224161, 0.07987921333337233, 0.0793639777794386, 0.07748176490715064, 0.0766084916060148, 0.07561052109916311, 0.07553429240407095, 0.07310938021788527, 0.07218675949252873, 0.07118839940287724, 0.07112370577561222, 0.07004761148596383, 0.06954426713919748, 0.06766819910745347, 0.06669711932901201, 0.06659717282749611, 0.06553165111754122, 0.06347776301673225, 0.061701359771839215, 0.06122875212893497]\n",
      "Row 62 - Column Numbers: [53 63 64 54 72 32  6 70 46 21 44 57 28 45 17 41 69 85  0 87 34 30 84 33\n",
      " 74 19 40 88 12  2 37 20  4 75 11 10  1 31 89 43 36 61 23], MI Values: [0.40877114705633755, 0.1279415691665342, 0.11842971465453456, 0.09996017287947367, 0.08923240114087871, 0.08212300251017979, 0.08134777223811351, 0.07551883001699622, 0.07403272493206625, 0.07348744391152451, 0.0730624234203292, 0.07251648801624189, 0.07174551471409796, 0.07129070394237846, 0.07054503826931224, 0.0694126384428051, 0.06494490899076766, 0.06122602061900739, 0.060570066674142886, 0.06022931405757159, 0.05971560831514555, 0.058950094823821075, 0.05873104823880926, 0.05850112049998302, 0.05785656052338606, 0.057623187032919354, 0.05477366448826526, 0.05440889071046939, 0.05387677226496379, 0.05315849709315046, 0.052254464230390596, 0.05209308293447634, 0.051951533735175026, 0.05132260781067011, 0.05125901030097513, 0.05100764313742001, 0.050656346920683326, 0.05058193701037439, 0.05028273620915957, 0.05013562158198859, 0.0501292056996574, 0.05003847734903477, 0.04962794973529405]\n",
      "Row 63 - Column Numbers: [57 64 72 87 70 62  6 45 65 53 14 54  4 61 92 46 44 84  7 47 24 56 91 74\n",
      " 66  0 85 23 18 76 69 52 82 73 68 55 11 10  1 81 48 43 17], MI Values: [0.19893022670047422, 0.16474578635889525, 0.14441268837025323, 0.14223108828764808, 0.1360734064984701, 0.12794156916653598, 0.11759316702333766, 0.1169265088990441, 0.10914449076512156, 0.10768325129662504, 0.09840075284083394, 0.09375651906359561, 0.09074112883170304, 0.08651352031480108, 0.08472994154227464, 0.08355750196953071, 0.08074364625578578, 0.07977254852835358, 0.07907681278759515, 0.0790723382731855, 0.07871775795832114, 0.07711766737948711, 0.07678764806995986, 0.0765734948289225, 0.07406004109092024, 0.07375851842512127, 0.07313981190535657, 0.07257144170705043, 0.06986318552324633, 0.06663758575631373, 0.0653233908008124, 0.06405860187379808, 0.06403591879491888, 0.06298018698645702, 0.0628392353335725, 0.0618326168768073, 0.06124640975608653, 0.05988190445075414, 0.0589489276098476, 0.057634411390770524, 0.05760918621697009, 0.05744789795037342, 0.056767715502631155]\n",
      "Row 64 - Column Numbers: [46  6 61 56 87 47 27 68 57 63 54 55 51 75 74 84 69 45 60 10  4 14 44 23\n",
      " 62 72 20 66 48 76 65 85 12 11 81 70  1  8 59 17 52  7 77], MI Values: [1.1094691017199603, 0.4786059164536729, 0.30274924109928225, 0.22066317128273738, 0.22048913023609096, 0.1987447932521187, 0.18682361749818366, 0.17760682722466647, 0.17065913517384423, 0.1647457863588926, 0.1516338374690145, 0.1455355267788141, 0.14408460937434509, 0.14236178948324518, 0.14209884783445936, 0.13984183102276582, 0.13741479855139893, 0.13477024068243804, 0.13185070300012303, 0.1299306324648466, 0.12979914510191115, 0.12701720438149788, 0.12575424005177815, 0.12382874483289896, 0.11842971465453278, 0.11641659888849265, 0.11253209164348021, 0.11225512605831867, 0.11110937927605224, 0.10732056478952767, 0.10654049307470448, 0.10591493223352533, 0.10535355610052566, 0.10500346113093073, 0.1037050834642379, 0.10306102384276805, 0.10272291690296331, 0.10254326229903832, 0.10143685103057631, 0.1003732877747634, 0.09484755694459235, 0.09462334579778542, 0.09447565520740842]\n",
      "Row 65 - Column Numbers: [27 45 63 64 66 76 60  6 84 53 62 13 46 31 74 23 57 79 15  1 61 28 90 87\n",
      " 25 18 47 35  4 10 19 22  2 16 54 17 38  5 70 43 11 71 55], MI Values: [0.6065603894953897, 0.3355390992669385, 0.10914449076511978, 0.10654049307470537, 0.07400054698096614, 0.06574940460414158, 0.05516399778635073, 0.05313625162063573, 0.05200772742261606, 0.04754326752987392, 0.04210859287540458, 0.04141383027204526, 0.04065382889106317, 0.04016739913483747, 0.03927197805547333, 0.03543013877976531, 0.03532486757824671, 0.03390511473012481, 0.03356935029377528, 0.0334370867070275, 0.03268513124965988, 0.032538341997700115, 0.03243135734308211, 0.03240600070639843, 0.03173822340394317, 0.03125147202710554, 0.030917863808890722, 0.030897225961695085, 0.03052268994560059, 0.030516181395221054, 0.030348441731518072, 0.030328529199157295, 0.030171195067245193, 0.030140476904725766, 0.029872492359135805, 0.029334903001505097, 0.029234888513575363, 0.02891810299955555, 0.02890138730320313, 0.02881055664071308, 0.028497828396734093, 0.02842485280534124, 0.028331991996227934]\n",
      "Row 66 - Column Numbers: [76 84 45 60 64 69 54 63 65 44 75 46 81 57 87 52 10  6 68 32  3 50 70 62\n",
      "  8 48 11 49 55 88 12 53 27 51 21 41 30 34 89 56 61 85 35], MI Values: [0.3276867048743224, 0.19621110110385498, 0.16669975622521527, 0.14313213465555208, 0.11225512605832044, 0.08774329941118442, 0.07892182637938827, 0.07406004109092112, 0.07400054698096792, 0.0657832364108204, 0.06574781745996905, 0.06557772498449133, 0.06464382902376808, 0.061461405926340085, 0.057380307752954884, 0.05499973892547505, 0.052649459598339554, 0.05121302295319019, 0.049935593149331936, 0.046364996147670645, 0.04601614539536314, 0.04570965837784691, 0.045050505206226, 0.044186414063735135, 0.042936712655239795, 0.042849316494054435, 0.04280397591400931, 0.0427889260255494, 0.042241733113475455, 0.039561716831260973, 0.0386714507746424, 0.038483240317686906, 0.03842749677431723, 0.03826743593598536, 0.0377725314890629, 0.03736335808473523, 0.03715626177182507, 0.03696164121794787, 0.03657013877780546, 0.03621018306623114, 0.036192436537979766, 0.03603333099672312, 0.03582784273636985]\n",
      "Row 67 - Column Numbers: [56 58 46 48 55 59 47 61 64 49 51 68 70 75 50 54 63 69 72 81 73 57 87 41\n",
      " 79  7 52 92 71  3 34 33 36 45 18 22 74  2 21 39 77 40 89], MI Values: [0.1390223315396062, 0.13761642238519123, 0.1327952209475507, 0.0819042946903279, 0.07810178261121248, 0.07292707939904286, 0.07249971148987466, 0.06954426713920014, 0.067158129948651, 0.06462675171117294, 0.06049342127079882, 0.05573066244705327, 0.05131323241564267, 0.050048166172831365, 0.04902813669653483, 0.04789187006885953, 0.04359634849634464, 0.04356102015565355, 0.042934138904747066, 0.041962299374367795, 0.03947764246554897, 0.03874132263576069, 0.0375586609402454, 0.03748203714709142, 0.03612567970739633, 0.03552096699697227, 0.03431893068828895, 0.03385542532989394, 0.03284593157964766, 0.03260253611544073, 0.03230214768395179, 0.032080902109909104, 0.032068284532125624, 0.031703696876647314, 0.03167709034729871, 0.03152308217100508, 0.0313239473107263, 0.030862122044114315, 0.030431654414645237, 0.030192101527670268, 0.03015615956557216, 0.03014741947648325, 0.030105513462540756]\n",
      "Row 68 - Column Numbers: [81 54 69 46 64 75 52 57 50 48 55 87 21 49 61 16 84 56 17 83 44 58 20 19\n",
      " 28 74 51 70  1 63 72  4  0 47 76 15 79  2 67 85 73 88 40], MI Values: [0.273919599429445, 0.25763014924822425, 0.21452460580928268, 0.19852690016740215, 0.17760682722466647, 0.13909061707178783, 0.1278969066417437, 0.12717047965108375, 0.0931330170915734, 0.0893454513359444, 0.0843329614831374, 0.08279666247431816, 0.08274897552594052, 0.08052518453031432, 0.08017854952241699, 0.08013941132973379, 0.07495229498264155, 0.07341505483174426, 0.06961403770779029, 0.06805662497684573, 0.06773250218080751, 0.06709058591021577, 0.06678931920015962, 0.06634530228217894, 0.0648958659595209, 0.06481434993591328, 0.06392417227606728, 0.06381372155874665, 0.06377396532315771, 0.06283923533357072, 0.061596290425321776, 0.06062743353392808, 0.05987241738861382, 0.05906462224581688, 0.05900909169327839, 0.05863023036643522, 0.056674954088558493, 0.05663641300834321, 0.05573066244705327, 0.05285999918476847, 0.05115265774466682, 0.05105981583143748, 0.050255155238578375]\n",
      "Row 69 - Column Numbers: [54 52 81 57 75 68 64 50 45 46 49 84 66 60 76 61 55 48 70 47 72 63 62 21\n",
      "  6 53 74 87 12 17 56 58 88 83 33 10 13 44 41 43 35 31 15], MI Values: [0.6991638866458345, 0.5772799725175153, 0.5173059047442399, 0.4492286562322283, 0.3365455824566368, 0.2145246058092809, 0.13741479855139715, 0.1364956152132697, 0.10868038934784607, 0.105422623025202, 0.09982396156077122, 0.09384699164640953, 0.08774329941118264, 0.08538631330874047, 0.08467890285416413, 0.0817599534587723, 0.07626677924718717, 0.07361433044884258, 0.06977140079906086, 0.06874455994522854, 0.06641906563649336, 0.06532339080081417, 0.06494490899076943, 0.06484185380561414, 0.06183066532204684, 0.05994221903533159, 0.05666686695618495, 0.05545803544337424, 0.05531483615886046, 0.05499612699967926, 0.05440393974544655, 0.053739795644960786, 0.0536959399704946, 0.053145985839573306, 0.05089832960081431, 0.050097225136772394, 0.04984063431350716, 0.04878869749796966, 0.04863991014106883, 0.04807444378004, 0.04771493976945074, 0.04694746829499152, 0.04658331443336472]\n",
      "Row 70 - Column Numbers: [72 71 63 46 64 57 53 62 54 47 69 87 48 68 45 36 82 56 17 61 21  4 19 13\n",
      " 74 41 55 49 67 52 60 11 15 75 28 84 32 85 66 18 44 35 31], MI Values: [0.5037025298153655, 0.1468401051584065, 0.13607340649846478, 0.13281149605317744, 0.10306102384276628, 0.08195684550894988, 0.07763014753084718, 0.07551883001699711, 0.07247468124904355, 0.07068379697728044, 0.06977140079905908, 0.0660251334839197, 0.06437836072642344, 0.06381372155874754, 0.06252081423776268, 0.05999309743629233, 0.05982269100457582, 0.057890813506117134, 0.056376474765788664, 0.055299683066056815, 0.05505815458498908, 0.05456383162511802, 0.05447668338025302, 0.05401666850898579, 0.05386607986701808, 0.053251414027695176, 0.05210958027079293, 0.05205162711625011, 0.05131323241564267, 0.050113256036700804, 0.049242671141108474, 0.049105160517478375, 0.04807318298614227, 0.047127393802390394, 0.04650128507184803, 0.046494250587683084, 0.04569125616274494, 0.04506890618240256, 0.04505050520622156, 0.04471178449303981, 0.04423971269111515, 0.044000657807371724, 0.043861067541813625]\n",
      "Row 71 - Column Numbers: [70 72 57 46 63 52 64 69 62 40 88 45 19 54 89 73 53 41 18 20 36 74 28 48\n",
      " 38 68 67 55 16 21 15 32 35 85 39 49  1 33 92 86 66 29 34], MI Values: [0.14684010515840784, 0.10642931109237441, 0.052528980782009516, 0.05241768981868278, 0.050201259190097325, 0.04467108973151124, 0.04327708127836605, 0.040533665195546575, 0.03859241843659156, 0.038561516805054374, 0.03818678028153677, 0.03813838976859696, 0.03800425250052175, 0.03790080375870186, 0.03715871144142646, 0.03588263349891774, 0.03548282442189432, 0.035353727634690024, 0.0352925510429718, 0.03441557456072353, 0.03423058910657151, 0.03397324312542693, 0.03394914598687837, 0.033806395276054335, 0.033705883841912865, 0.03342612831626557, 0.03284593157964988, 0.032719080030302106, 0.032663553226116804, 0.031987069591433936, 0.03175109221050576, 0.03144013441961224, 0.031402843954976944, 0.030959505480408822, 0.03087881443926932, 0.030695717699147362, 0.030567471549774794, 0.030379323571904315, 0.03005020752412957, 0.03002178949951162, 0.029856386276476243, 0.029726472501970136, 0.029722945487696606]\n",
      "Row 72 - Column Numbers: [70 46 63 64 71 57 62 54 87 69 53 74 36 17 47 68 19 56  6  4 21 37 18 12\n",
      " 13 79 45 52 61 14 15 85 84 11  8 83 38 55 31 10 41 48 40], MI Values: [0.5037025298153646, 0.1555945017468563, 0.14441268837025323, 0.11641659888849354, 0.10642931109237264, 0.10567030398132982, 0.08923240114088049, 0.06863149347899888, 0.06757571466233703, 0.06641906563649602, 0.06557217989953035, 0.06265296415556598, 0.06265064870036952, 0.06242048665925726, 0.06175094572082429, 0.06159629042532533, 0.06050821759756175, 0.060467185737427265, 0.059193884606223435, 0.05724329216191926, 0.054151749566812235, 0.053098326138301566, 0.05297227066477639, 0.05260851139547462, 0.052594084364699256, 0.05231208801533249, 0.05126811930396524, 0.051113533032526526, 0.050320783879531206, 0.050294567082459274, 0.049828300730804465, 0.04936721830032109, 0.04876829570450525, 0.048098306904397425, 0.04777061216579881, 0.04705935242895354, 0.04699176949630246, 0.04633740434429967, 0.04575550443701104, 0.04517050064331052, 0.04508851409560233, 0.0448973620856723, 0.04481721096307467]\n",
      "Row 73 - Column Numbers: [18 19 16 22 15 21 83 17 46 57 20 64 92  0 85 63 87  1 90 91 75 32 61 78\n",
      " 55 68 81 80  4 77 42 56  5 62  7  2 44 48 79 58 30 52 82], MI Values: [0.7893958078076446, 0.44496585631871355, 0.23365823269839314, 0.1966841939947015, 0.17737229996765524, 0.14619238110757227, 0.13046110819555246, 0.11461081534221584, 0.0669864466316632, 0.0667097043144338, 0.06621492860686029, 0.06604549816659055, 0.06534747712790967, 0.0649060502864538, 0.06342521947019009, 0.06298018698645524, 0.0611623897499598, 0.05958199657264185, 0.05918069294481576, 0.05854277511136363, 0.053336867008316524, 0.052349661683105175, 0.052132518258837024, 0.051741026293754544, 0.05137178453202651, 0.05115265774467037, 0.050731494761138585, 0.05035070457441204, 0.04944023723216873, 0.04929230770196469, 0.04884463429679364, 0.04879117015815915, 0.04871526329810205, 0.047892505862648704, 0.04712977016487141, 0.046741524692998304, 0.045420776171674504, 0.04530640682438136, 0.04518328366119828, 0.0451152130271959, 0.04476241509419232, 0.04425296906975085, 0.04269677500715918]\n",
      "Row 74 - Column Numbers: [33 30 35 43 36 86 37 29 89 38 28 40 39 31 34 88 41 32 78  5 79  2 12 64\n",
      " 44 80  4 56 46 87  0  1  3 57 42 11 13 85  8 63 10 54 90], MI Values: [1.1137204124807516, 0.6484729630309527, 0.6417520640136294, 0.624303970048989, 0.609009289588708, 0.5888147458720638, 0.5514988683591922, 0.5004203013385569, 0.4790798574401238, 0.463836147610051, 0.4637692211865332, 0.42293019416571376, 0.4188068561985556, 0.3685955153502105, 0.3551015296305451, 0.3455870286773939, 0.33199699186004406, 0.2547497346317229, 0.20415303191621437, 0.1681098351910748, 0.1650927025452713, 0.15700514453794945, 0.14286051344793105, 0.14209884783445847, 0.13751208245379942, 0.13689592489073021, 0.12952891724869087, 0.12763532576626435, 0.11736212179504246, 0.1087269697985187, 0.10670490036675684, 0.10197487194244381, 0.09931213507677228, 0.09565681017049954, 0.09219897198964855, 0.08465931443258867, 0.08012866253161377, 0.07970796683611514, 0.07707447313009208, 0.07657349482892162, 0.07645994681407764, 0.0724507095617879, 0.07133347033568604]\n",
      "Row 75 - Column Numbers: [50 69 57 81 54 52 49 46 64 68 84 48 60 58 87 55 45 47 66 74 77 79 44  0\n",
      " 19 76 37 63 86 59  2 73 13  4 36 61 17  1 62 24 88 67 10], MI Values: [0.38569583316039946, 0.3365455824566368, 0.31754032621604367, 0.299464626985233, 0.2835775257403297, 0.1935421636578889, 0.16380558437787318, 0.1598316786459506, 0.1423617894832443, 0.1390906170717887, 0.10426683306186213, 0.1003724412202649, 0.0878913633998506, 0.08672016085400713, 0.08358299144459647, 0.07894014514831671, 0.07550304956704768, 0.07403127407645904, 0.06574781745996994, 0.0641015831058036, 0.06280999904077333, 0.06198112586282889, 0.05994952546050758, 0.058932901704030094, 0.05883151968498446, 0.05840596267275, 0.05770927457101749, 0.05585066540116479, 0.05527900384734252, 0.05458094170481065, 0.054081184944083205, 0.05333686700831475, 0.053243057542840866, 0.05294436526442681, 0.05286496782731209, 0.052800446177284854, 0.052136357413616885, 0.051665821434266235, 0.05132260781066744, 0.05083179402329918, 0.05043949403648362, 0.05004816617282959, 0.049905532084435045]\n",
      "Row 76 - Column Numbers: [66 84 45 64 69 46 60 54 63 65 68 81 75 87 50 61 56 55 27 52  3 48 51 57\n",
      " 44 88 62  6 85 40  1 74 41  0 58 49 15 39  4 89 14 53 47], MI Values: [0.3276867048743197, 0.24938687538324178, 0.14089157380955797, 0.10732056478952945, 0.08467890285416502, 0.07963991449703123, 0.07359513171289844, 0.07324275519206669, 0.06663758575631462, 0.06574940460414425, 0.05900909169328106, 0.05870728910141754, 0.05840596267275089, 0.05227845227554617, 0.052114858751312276, 0.0475376914479817, 0.045768277880542385, 0.044450219960143755, 0.04331808077932564, 0.0397320107747241, 0.039450383303536896, 0.038781715879885326, 0.03840491710777716, 0.03729854865264848, 0.03695081877679929, 0.03575037533056857, 0.03553028432121241, 0.035006496062266024, 0.03479280267248619, 0.03355427583083603, 0.03330372063304132, 0.03324378852283871, 0.03314054463399074, 0.0329832469916953, 0.03260929208367003, 0.03200075462167984, 0.03142627895452854, 0.031226808565940622, 0.030530087758511293, 0.030180324229658773, 0.03013702346379077, 0.029953159421307163, 0.029614370974226034]\n",
      "Row 77 - Column Numbers: [20  1  0 17 85 21 83 87 91  2 15 79  4  5  3 11 12 19 22 16 64 78 90 10\n",
      " 24 46 61 18 31 14 33 80 74 13 56 43 75 30  8 86 37 36 29], MI Values: [0.6456828762580971, 0.3911191711403701, 0.37263024544485734, 0.2990938973597581, 0.2972324555956005, 0.2833159462922179, 0.2721591618925645, 0.2624972226636384, 0.2612330298469274, 0.23544670375940946, 0.2109149525053855, 0.19755911895090694, 0.1718626691037235, 0.17144637756480563, 0.16858842857306655, 0.15529190588759256, 0.15476368455904055, 0.14839967682173594, 0.10378871318925587, 0.09654894383117352, 0.09447565520740842, 0.0909806859788258, 0.08763090580224553, 0.0864463575035197, 0.08554737930801348, 0.0848734741910322, 0.07553429240407361, 0.07382980271187378, 0.07208828414576551, 0.07067488479129658, 0.06870563600713986, 0.06782462499272324, 0.06750317812053108, 0.06644401403919531, 0.06584653458601863, 0.06546454180161732, 0.06280999904077245, 0.06275013897899573, 0.06220005651368066, 0.061947295051053786, 0.061387189732781344, 0.061213187064223185, 0.06065012243418888]\n",
      "Row 78 - Column Numbers: [31 79  2  5 43 35  4 44 30  3  0  1 33 74 42 36 85 86 34 12 11 37 87 32\n",
      " 29 91 20 80 28 13 89 17 10 38 39 21 40 83 41 88 77 90 15], MI Values: [0.7638100129208834, 0.5291499102562947, 0.40895639584369636, 0.40195030351981753, 0.3703971113656319, 0.36035661286731635, 0.3522117773810214, 0.2940959242977499, 0.24551062402752422, 0.22968546503017695, 0.2279315500630652, 0.22306577157731855, 0.21439117181920508, 0.20415303191621348, 0.17401757617932834, 0.14656523125808896, 0.13481869307475858, 0.1340783425963794, 0.13184448924787695, 0.1251376255189447, 0.12508164598781324, 0.12299363364406979, 0.12204190372473, 0.11553471513471436, 0.11428335137809142, 0.11180728144593566, 0.11158401518017325, 0.11158379763401793, 0.10874080446091128, 0.10855159929809233, 0.10703752567566749, 0.10477670785503168, 0.10461732375843713, 0.1039286718447654, 0.1030354193690286, 0.10268663613005558, 0.09964875862896339, 0.09402627710304756, 0.09265090609569437, 0.09216904048066343, 0.09098068597882403, 0.07220152388185497, 0.06674255678354513]\n",
      "Row 79 - Column Numbers: [ 4  2  5 78  3  0 31  1 43 35 77 85 30 20 87 33 74 12 17 44 91 21 83 34\n",
      " 11 36 86 37 29 40 10 39 32 38 89 42 28 64 41 13 80 88 15], MI Values: [0.893437297964442, 0.8897537675853213, 0.8539429780686696, 0.5291499102562955, 0.5216221690633249, 0.45757637448269506, 0.3469763013969196, 0.3374236720569561, 0.2073913075411946, 0.20596754398312012, 0.19755911895090428, 0.1962347079230513, 0.1906085060616718, 0.1804159793193154, 0.17746826908973823, 0.1675397929716107, 0.1650927025452722, 0.15745268691877623, 0.15630527248319837, 0.15352082533469336, 0.14530314536725086, 0.13959981733842763, 0.13601963987999888, 0.1218215309761943, 0.12041417972820856, 0.11619314258747693, 0.11181972450478295, 0.111670136833391, 0.10420208049496171, 0.10298221946964947, 0.10144296896099547, 0.10121071598448594, 0.09567236193821316, 0.09301615106454975, 0.09254555638649187, 0.09102336506577213, 0.09026690572979756, 0.08736827809746561, 0.08676758111423233, 0.08620980383680976, 0.08466381307331439, 0.0785679892861264, 0.07750166086596]\n",
      "Row 80 - Column Numbers: [59 43 35 90 31 33 42 74 30 36 44 78 92 86 89 37 29 34 28 40 38 79  5 41\n",
      " 32 12 82 88 39  2 77 11 21  0  4 15 13  3  1 83 10 73 20], MI Values: [0.24653722627623686, 0.2276321837680122, 0.20322450593987362, 0.19218618079188143, 0.18479080672562098, 0.15136974710492979, 0.1450821651935268, 0.13689592489073021, 0.1357762064984085, 0.11571876599131237, 0.11196280971917005, 0.11158379763401705, 0.11010018137622524, 0.10493827763350172, 0.1044402309887209, 0.09822950179437395, 0.09785175941231472, 0.09689650292456431, 0.09424947908653714, 0.08752252944644034, 0.08653427377215017, 0.08466381307331616, 0.08230865790885655, 0.07854886226317959, 0.07650826602535155, 0.07494487051346166, 0.07370725535800648, 0.07253038686003155, 0.07038469791400903, 0.06970774963285731, 0.06782462499272057, 0.06530714718931119, 0.0638719053811343, 0.06157503922592156, 0.06148036084266284, 0.06004207076621082, 0.058901850104819964, 0.05522028921117084, 0.05429317094593511, 0.05309818158656032, 0.05282851504111541, 0.050350704574411154, 0.04844480590909317]\n",
      "Row 81 - Column Numbers: [54 69 75 52 68 57 50 64 46 49 58 84 74 48 55 66 87 60 45 76 77 44 36 79\n",
      " 63 86  0 61 83 37 17 33 73 38 43 39 31  4 89 47  1  2 88], MI Values: [0.7379530571253508, 0.5173059047442399, 0.29946462698523035, 0.2925189873733629, 0.27391959942944677, 0.2386747781742029, 0.136153690706311, 0.10370508346423613, 0.10140282553967683, 0.07578213385519295, 0.07170077496787108, 0.07127138714810943, 0.06860495539301592, 0.06681937537003346, 0.06660845722965725, 0.06464382902377075, 0.0635620255990954, 0.06016542150362536, 0.05993439653997257, 0.05870728910141665, 0.05853791406893283, 0.05807485470139717, 0.057863475935761244, 0.057830546664649596, 0.05763441139077141, 0.05615165444273362, 0.05562579056591499, 0.05549932064581764, 0.05488123319225746, 0.05430022036441429, 0.05358151425610025, 0.052620584599597287, 0.05073149476113681, 0.0504273983650787, 0.050018232148672404, 0.048724267224924844, 0.04741589778476474, 0.04724272848531896, 0.047045769301623075, 0.046565683993298634, 0.045974451396885385, 0.04564404577717607, 0.0445681886862177]\n",
      "Row 82 - Column Numbers: [47 92 90 80 57 63 70 64 36 41 87 74 18 42 19 85 73 86 56 43 72 78 35  6\n",
      " 31 33 29 27 44  2 21 69 34  0  5 79 15 62 30 40 23 17 46], MI Values: [0.36022650677909773, 0.20000700401697546, 0.12362127498379927, 0.07370725535800737, 0.06659031769662516, 0.06403591879492154, 0.05982269100458204, 0.048128802238390556, 0.04758120157348866, 0.04550467421470117, 0.0453016185285815, 0.04463464698039843, 0.04452332972605699, 0.043705855049582354, 0.0432350339578198, 0.042804256191230294, 0.04269677500715918, 0.042518243369825015, 0.04216181372132244, 0.041122564560073904, 0.04035249569417232, 0.040056300664696565, 0.03993065515482197, 0.039067233966030734, 0.0389505477899581, 0.038744171751281975, 0.03800177521638748, 0.037944489427784056, 0.03731345765145644, 0.03724063933802757, 0.03716957593935177, 0.037114565896340324, 0.03697025658167963, 0.03665464470504798, 0.036577827982953615, 0.035438406074370654, 0.03489171478971809, 0.03464472319516876, 0.034410902358763096, 0.034146025613621234, 0.03378679926427086, 0.033662159409545644, 0.033650920178660115]\n",
      "Row 83 - Column Numbers: [17 21 20  0  1 19 77 15 85  2 16 91 87 11 22  5  4 79 73 18  3 12 90 92\n",
      " 78 10 42 31 43 64 61 13 68 54 35 33 46 44 74  8 57 81 14], MI Values: [1.066814745597446, 0.7488876659638617, 0.4589017533899531, 0.31506896178670907, 0.29504178717312346, 0.28206410473167054, 0.2721591618925654, 0.23569399663760304, 0.19808986460266986, 0.18056529072470173, 0.16718927849869747, 0.1656431210139937, 0.15326102264911245, 0.14976259321938912, 0.1450249261206027, 0.14139989403189102, 0.1374753305211458, 0.13601963988000332, 0.13046110819555246, 0.13005610443538984, 0.12212949345012714, 0.12178764257401475, 0.09999792818939479, 0.09786512673510916, 0.09402627710304579, 0.09120163011639004, 0.08290682477634537, 0.08252825085346682, 0.08156076645929478, 0.07860224780761271, 0.07310938021788527, 0.06900697369544506, 0.06805662497684573, 0.06494064826102797, 0.06455351051612457, 0.06416764584976953, 0.06223055486476259, 0.06102533227363338, 0.05968287991838661, 0.05824405082485473, 0.05711690835432748, 0.05488123319225924, 0.05451886276258566]\n",
      "Row 84 - Column Numbers: [ 3 76 66 64 46 75 45 69 54 63 68 57 81 50 87 61 55  6 60 44 27 62 56 74\n",
      "  0 65 52  1 51 20 17 48 72 21 49 85 47 70 58 41 40 88  2], MI Values: [0.29367624960262795, 0.24938687538324178, 0.19621110110385587, 0.13984183102276848, 0.1375172592865539, 0.1042668330618639, 0.10150362847124583, 0.09384699164641042, 0.09285394516933199, 0.07977254852835536, 0.07495229498264333, 0.07392888704485934, 0.07127138714810854, 0.06909627215253789, 0.06894787220913212, 0.06553165111754211, 0.06496582981844412, 0.06491247342046069, 0.062130659320295045, 0.06139751027721019, 0.0603802858690452, 0.058731048238805705, 0.05731245332677215, 0.05441190520910766, 0.052023584398917855, 0.05200772742261517, 0.050675710238638594, 0.050658360235747324, 0.050444118959005024, 0.04966907275681187, 0.04912116274816558, 0.049098305732939274, 0.0487682957045088, 0.047929493455121985, 0.047598231033918026, 0.04751424056243447, 0.047086024603290255, 0.046494250587683084, 0.045749765509683904, 0.04533916101688806, 0.04511370164638606, 0.04442062560320448, 0.04432867747156788]\n",
      "Row 85 - Column Numbers: [91 87 11  1 20 77  0 21 15 10 16 17  2 83 79 12 13  4  5 78 19  3  8 24\n",
      " 22 31 64 61 14 23 43 33 44 46 74 42 18 35 90 92 63 53 56], MI Values: [1.0397326027081109, 0.7808738531896484, 0.4477948984444424, 0.4273072620362388, 0.42552426145736, 0.2972324555956032, 0.29292039446620866, 0.2688208314872229, 0.2607931482272816, 0.25686672570808433, 0.24952652512346507, 0.24799566598007594, 0.2191451538778244, 0.19808986460266986, 0.1962347079230522, 0.16892847033332092, 0.15241639531040452, 0.14716514799944846, 0.14129091651330672, 0.13481869307476035, 0.12862613575316306, 0.12331183579416649, 0.1197010961317595, 0.11662871191985147, 0.11578837068495584, 0.10608247049946584, 0.10591493223352089, 0.10334008173380838, 0.0977963721134758, 0.08797109748794707, 0.08744850763647705, 0.08539579380747231, 0.08318123056251547, 0.08171791357506919, 0.0797079668361178, 0.07969793759561306, 0.07840025513521187, 0.0772743628266932, 0.07673080277470046, 0.07434137186871315, 0.07313981190535657, 0.07291262831419587, 0.0700260236623178]\n",
      "Row 86 - Column Numbers: [37 36 29 38 89 28 39 33 40 74 88 41 43 35 30 34 31 32 56 78  5 79 44 80\n",
      " 12  2  4 42 90  3 87  1  0 77 14 52 64 46 81 75 85 11 63], MI Values: [1.4582722148763292, 1.0233770024292141, 0.9904397714916922, 0.7540596341394137, 0.733195425690325, 0.7092838503040939, 0.6322229406595898, 0.6078933190308362, 0.5904546129888963, 0.5888147458720656, 0.4974361490677621, 0.47456031717445146, 0.4240950333084834, 0.398460972787932, 0.37422972387261133, 0.3436127338197741, 0.22807412650458492, 0.2027410833178278, 0.1981347985070574, 0.1340783425963794, 0.1305167490968442, 0.11181972450478028, 0.10936129874318112, 0.10493827763349994, 0.10135095971922325, 0.09732347543015418, 0.0793582428961841, 0.07547417076442908, 0.07370447561000759, 0.06840077448593984, 0.06585251441988405, 0.0648701268193781, 0.06364451470636467, 0.0619472950510529, 0.06094423783477332, 0.05775731163073594, 0.057120350210864146, 0.05635429843615114, 0.0561516544427354, 0.05527900384733986, 0.053398504926430945, 0.05262110212995097, 0.05220962062188317]\n",
      "Row 87 - Column Numbers: [91 85 20  1 11 77 15  0 10 64 17 21  2 79 46 83  4 63 12  5 16 24 78 14\n",
      " 19  8 61 13 31 74  3 56 23 44 57 22 43 47 75 68 33  6  9], MI Values: [0.8254953838532577, 0.7808738531896502, 0.32604905695192254, 0.3012243820649747, 0.2965738494229102, 0.2624972226636402, 0.2236871771312554, 0.22350595260037398, 0.2210467525648223, 0.22048913023609007, 0.19689724643638407, 0.18708052814614184, 0.18419330652618005, 0.17746826908973734, 0.16549438774061542, 0.15326102264911423, 0.1467876478550867, 0.14223108828764808, 0.13558171850872913, 0.13204341952919485, 0.12870418125103367, 0.126641316562071, 0.12204190372472912, 0.12022624072505206, 0.11907016274300819, 0.11717444758841289, 0.11609849133691608, 0.11270707168404748, 0.10896037047705942, 0.10872696979851781, 0.10828482718467924, 0.10439486730786829, 0.1027970391859041, 0.10044717697416417, 0.09943857195888395, 0.08969080820395003, 0.08755593140089335, 0.08569788060934336, 0.08358299144459647, 0.0827966624743155, 0.08221603143086931, 0.07597112239010073, 0.0751232614805879]\n",
      "Row 88 - Column Numbers: [40 89 41 28 38 39 34 29 37 86 33 36 74 30 32 35 43 31 44 78 56 79  5  4\n",
      " 64 80 12 90 18  2 46 52 42  0 10  3  1 62 54 69  8 63 17], MI Values: [1.3584687582326698, 1.1135577021657408, 0.8687228214668892, 0.7614158768816592, 0.7568375359221005, 0.7414381495833346, 0.521645640678436, 0.5162986988948415, 0.5065004040074976, 0.4974361490677621, 0.4047557520194278, 0.39112029603754017, 0.3455870286773921, 0.3120618690279793, 0.27467543363149716, 0.2113827569500053, 0.2062641249804278, 0.1178467066606661, 0.0978448354860939, 0.09216904048066343, 0.0881281392529063, 0.07856798928612552, 0.07740754667316185, 0.07609992946234723, 0.07448577255951516, 0.07253038686002977, 0.07191036153530916, 0.07018600624848581, 0.06947413178679351, 0.06925480718800436, 0.0665871977414545, 0.06273572137952144, 0.06114199250922159, 0.06063371495187919, 0.06012914210785869, 0.05512401310494486, 0.05476304444835467, 0.05440889071046939, 0.05436024408042606, 0.053695939970491935, 0.05292091189701864, 0.05201826811016552, 0.05132084037915341]\n",
      "Row 89 - Column Numbers: [38 40 88 39 28 41 37 29 86 36 34 33 74 30 43 35 32 31 56 78 80  5 79 44\n",
      " 12  2 90  4 11 64  0 10  3 42 46  1  8 13 61 87 17 54 62], MI Values: [1.2419280927673935, 1.2392621662048944, 1.113557702165739, 1.0535035116401668, 1.0046755344608442, 0.9100181021852709, 0.7572524796564108, 0.7571541803206934, 0.7331954256903233, 0.5752000583378676, 0.5628237492307493, 0.5364183007679406, 0.4790798574401274, 0.37170844903925726, 0.28802774608808956, 0.2845574273495872, 0.23990089864081376, 0.15421271891570854, 0.12759658270105323, 0.1070375256756666, 0.1044402309887218, 0.1028680671126736, 0.09254555638649009, 0.09241113709100546, 0.08890082125607357, 0.08732427486063177, 0.08143911948999971, 0.07698715238078524, 0.06919349661079899, 0.06672066841319335, 0.06566309202536758, 0.0637520285116242, 0.06298051391441373, 0.06261691628512, 0.0624690478839538, 0.06095847702589374, 0.05864248331363253, 0.05740682008964981, 0.057232186056704215, 0.0568278203392758, 0.05080254511998916, 0.05074669197352755, 0.0502827362091578]\n",
      "Row 90 - Column Numbers: [42 92 80 21 82 17  1  0 83 77 40 20 19 89 30 33 43 85  5  2 79 11 86 41\n",
      " 38 12 15 78 35 74 37 88 29 36 39 34 31 91 87 28  4 32 73], MI Values: [0.5736361560630625, 0.4459659605734716, 0.19218618079188232, 0.12517520234619095, 0.1236212749837966, 0.11040902183482082, 0.10532886649482442, 0.10411775455289263, 0.09999792818939834, 0.08763090580224375, 0.08755455049272687, 0.08732179357987846, 0.08561032186586459, 0.08143911949000593, 0.07857807032348152, 0.07829650162065516, 0.07721049556759763, 0.07673080277470312, 0.07668497735520141, 0.07646301353284013, 0.07612583152068808, 0.0746333907288248, 0.07370447561000759, 0.07307672025710321, 0.07291292443408093, 0.07254758451655796, 0.0725475665380868, 0.07220152388185319, 0.07216427126334413, 0.07133347033568604, 0.07091755529673982, 0.07018600624848581, 0.07002944857802262, 0.06954945457795869, 0.06777425757346034, 0.06748508102814021, 0.06594386443864142, 0.06571885927828625, 0.06528340240650543, 0.06435233990021594, 0.06363225684698115, 0.0634542884997531, 0.059180692944813984]\n",
      "Row 91 - Column Numbers: [85 87 11 20  1 77 10 15 21  0 17 83  2 13 79 16 12  8  4  5 78 19 22  3\n",
      " 24 23 14 61 64 31 18 63 44 43 56 42 74 92 53 90 33 46 34], MI Values: [1.0397326027081135, 0.8254953838532595, 0.3865429355312866, 0.35105094399945447, 0.3192857717713009, 0.261233029846931, 0.2579871837894956, 0.2262869925209232, 0.2086854981064592, 0.20848995166817463, 0.20010695253448052, 0.1656431210139928, 0.15702895570463316, 0.15188179879224428, 0.14530314536724998, 0.13528675087576225, 0.1292188341874061, 0.12410132440415556, 0.11543451299135388, 0.11292935145386718, 0.1118072814459321, 0.10649322098528113, 0.1063924866874304, 0.09857437391434942, 0.09541744286183729, 0.09277959255307167, 0.09231436655409198, 0.08714033036634472, 0.08652458136703967, 0.08539580505606104, 0.08043542246333857, 0.07678764806996075, 0.07356394424112533, 0.07147186167010044, 0.06996541088144959, 0.06881214952706838, 0.06784461788607654, 0.06764075156292826, 0.06654270992309197, 0.06571885927828625, 0.06454231972101443, 0.060894556193985316, 0.05979450877373971]\n",
      "Row 92 - Column Numbers: [90 82 17 42 21 80 83 63  1 85  0 19 20 91 87 57 73 23  2 30 79 77  5 78\n",
      " 15 41 74 33 11 18 36  6 32  4 12 40 34 64 86 16 28 47 10], MI Values: [0.4459659605734716, 0.20000700401697458, 0.16969542448540587, 0.11438741669920915, 0.1117978672601403, 0.11010018137622612, 0.0978651267351065, 0.08472994154227287, 0.08048114102267068, 0.07434137186871048, 0.07334383362524477, 0.07083532279622062, 0.07064869314149647, 0.06764075156292648, 0.06744167818817282, 0.06608857489515962, 0.06534747712790523, 0.06377017167667542, 0.06303769631886258, 0.06244423103829355, 0.06139810833956538, 0.06009214577031052, 0.05620640348058448, 0.05570265349391068, 0.05541644764804232, 0.05389698575662827, 0.052348572626745415, 0.051905744566475676, 0.051690795509167664, 0.05057359318983057, 0.04931200112378864, 0.048166047939036005, 0.047644557437777735, 0.04702041409510738, 0.046717369248161056, 0.04610406107367648, 0.045989563524378774, 0.0458993014321587, 0.04549260487965512, 0.04529324898574405, 0.04491292878293418, 0.044605275701465885, 0.043729188914697126]\n"
     ]
    }
   ],
   "source": [
    "# load dataset\n",
    "A,X,training_set,test_set,unknow_set,full_set,know_set,training_set_s,A_s,capacity = load_data_MI('ndbc')"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-25T05:38:46.981166Z",
     "start_time": "2024-03-25T05:38:39.364935Z"
    }
   },
   "id": "d8f05601a675c8ee",
   "execution_count": 10
  },
  {
   "cell_type": "code",
   "outputs": [],
   "source": [
    "\n",
    "def test_error(STmodel, unknow_set, test_data, A_s, Missing0):\n",
    "    \"\"\"\n",
    "    :param STmodel: The graph neural networks\n",
    "    :unknow_set: The unknow locations for spatial prediction\n",
    "    :test_data: The true value test_data of shape (test_num_timesteps, num_nodes)\n",
    "    :A_s: The full adjacent matrix\n",
    "    :Missing0: True: 0 in original datasets means missing data\n",
    "    :return: NAE, MAPE and RMSE\n",
    "    \"\"\"\n",
    "    unknow_set = set(unknow_set)\n",
    "    time_dim = STmodel.time_dimension\n",
    "    test_omask = np.ones(test_data.shape)\n",
    "    if Missing0 == True:\n",
    "        test_omask[test_data == 0] = 0\n",
    "    test_inputs = (test_data * test_omask).astype('float32')\n",
    "    test_inputs_s = test_inputs\n",
    "    missing_index = np.ones(np.shape(test_data))\n",
    "    missing_index[:, list(unknow_set)] = 0\n",
    "    missing_index_s = missing_index\n",
    "    o = np.zeros([test_data.shape[0]//time_dim*time_dim, test_inputs_s.shape[1]]) #Separate the test data into several h period\n",
    "    for i in range(0, test_data.shape[0]//time_dim*time_dim, time_dim):\n",
    "        inputs = test_inputs_s[i:i+time_dim, :]\n",
    "        missing_inputs = missing_index_s[i:i+time_dim, :]\n",
    "        T_inputs = inputs*missing_inputs\n",
    "        T_inputs = T_inputs/E_maxvalue\n",
    "        T_inputs = np.expand_dims(T_inputs, axis = 0)\n",
    "        T_inputs = torch.from_numpy(T_inputs.astype('float32'))\n",
    "        A_q = torch.from_numpy((calculate_random_walk_matrix(A_s).T).astype('float32'))\n",
    "        A_h = torch.from_numpy((calculate_random_walk_matrix(A_s.T).T).astype('float32'))\n",
    "        imputation = STmodel(T_inputs, A_q, A_h)\n",
    "        imputation = imputation.data.numpy()\n",
    "        o[i:i+time_dim, :] = imputation[0, :, :]\n",
    "    if dataset == 'NREL':\n",
    "        o = o*capacities[None,:]\n",
    "    else:\n",
    "        o = o*E_maxvalue\n",
    "    truth = test_inputs_s[0:test_set.shape[0]//time_dim*time_dim]\n",
    "    o[missing_index_s[0:test_set.shape[0]//time_dim*time_dim] == 1] = truth[missing_index_s[0:test_set.shape[0]//time_dim*time_dim] == 1]\n",
    "    test_mask =  1 - missing_index_s[0:test_set.shape[0]//time_dim*time_dim]\n",
    "    if Missing0 == True:\n",
    "        test_mask[truth == 0] = 0\n",
    "        o[truth == 0] = 0\n",
    "    MAE = np.sum(np.abs(o - truth))/np.sum( test_mask)\n",
    "    RMSE = np.sqrt(np.sum((o - truth)*(o - truth))/np.sum( test_mask) )\n",
    "    MAPE = np.sum(np.abs(o - truth)/(truth + 1e-5))/np.sum( test_mask)\n",
    "    return MAE, RMSE, MAPE"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-25T05:38:46.986140Z",
     "start_time": "2024-03-25T05:38:46.981772Z"
    }
   },
   "id": "203beafa49be9aee",
   "execution_count": 11
  },
  {
   "cell_type": "code",
   "outputs": [
    {
     "data": {
      "text/plain": "OrderedDict([('GNN1.Theta1',\n              tensor([[-0.0565, -0.0106,  0.0122,  ..., -0.0457, -0.0026, -0.0830],\n                      [ 0.0296, -0.0353, -0.0647,  ...,  0.0538,  0.0159, -0.0188],\n                      [ 0.0064,  0.0306, -0.0617,  ...,  0.0932, -0.0761, -0.0050],\n                      ...,\n                      [ 0.0333, -0.0776, -0.0641,  ...,  0.0298,  0.0085,  0.0693],\n                      [-0.0389,  0.0677, -0.0106,  ...,  0.0133, -0.0053, -0.0038],\n                      [-0.0375,  0.0726, -0.0529,  ..., -0.0637, -0.0726, -0.0040]])),\n             ('GNN1.bias',\n              tensor([ 0.0516, -0.0006, -0.0130,  0.0840,  0.0660,  0.0443,  0.0540, -0.0252,\n                      -0.0925, -0.0581, -0.0634,  0.0417,  0.0515,  0.0052,  0.0355, -0.0728,\n                       0.0627, -0.0744, -0.0446, -0.0263, -0.0756, -0.0776, -0.0634, -0.0239,\n                       0.0590,  0.0439, -0.0400,  0.0145,  0.0888,  0.0073,  0.0227, -0.0540,\n                      -0.0872, -0.0992,  0.0475, -0.0820, -0.0984, -0.0692,  0.0724, -0.0417,\n                       0.0668, -0.0414,  0.0339,  0.0137,  0.0011, -0.0526,  0.0210, -0.0262,\n                       0.0749, -0.0601, -0.0162,  0.0542,  0.0724, -0.0444,  0.0651,  0.0915,\n                       0.0048, -0.0015, -0.0426,  0.0635,  0.0820,  0.0294,  0.0324, -0.0931,\n                      -0.0734,  0.0822, -0.0886, -0.0334, -0.0698, -0.0083,  0.0269,  0.0006,\n                      -0.0401,  0.0696, -0.0615,  0.0699, -0.0520, -0.0625,  0.0696, -0.0215,\n                       0.0129, -0.0317,  0.0597, -0.0398, -0.0923, -0.0538,  0.0496, -0.0791,\n                       0.0490, -0.0771, -0.0001, -0.0259,  0.0181, -0.0473, -0.0796, -0.0288,\n                      -0.0064, -0.0589, -0.0536,  0.0770])),\n             ('GNN2.Theta1',\n              tensor([[ 4.6268e-02, -9.8626e-02,  2.7627e-02,  ..., -2.9514e-03,\n                        5.8540e-02, -1.3019e-02],\n                      [ 4.1872e-02,  4.1520e-02, -2.2070e-02,  ..., -5.8264e-02,\n                       -6.1578e-02,  1.6352e-02],\n                      [-6.9415e-02,  6.1551e-02,  8.3853e-02,  ...,  3.8959e-02,\n                       -5.9732e-02,  1.0200e-01],\n                      ...,\n                      [-4.8975e-02,  1.4918e-02,  5.1484e-02,  ...,  3.6636e-02,\n                       -5.0734e-02,  7.5326e-05],\n                      [-4.8546e-02,  7.9341e-02, -6.3893e-02,  ...,  1.1551e-02,\n                       -4.4514e-02, -4.4674e-02],\n                      [ 6.0419e-02, -2.0798e-02, -9.4230e-02,  ..., -9.7350e-02,\n                       -2.4461e-02,  2.1006e-02]])),\n             ('GNN2.bias',\n              tensor([ 0.0177, -0.0746,  0.0350, -0.0174, -0.0563,  0.0485,  0.0150, -0.0915,\n                      -0.0295,  0.0358,  0.0259, -0.0293, -0.0541, -0.0356,  0.0128, -0.0260,\n                      -0.0636,  0.0697,  0.0453,  0.0784, -0.0245,  0.0358, -0.0036, -0.0630,\n                       0.0329, -0.0133,  0.0746,  0.0736,  0.0528,  0.0873, -0.0888,  0.0247,\n                      -0.0665,  0.0952,  0.0157, -0.0284, -0.0596,  0.0084,  0.0552, -0.0565,\n                      -0.0388, -0.0100, -0.0128,  0.0197,  0.0765,  0.0958, -0.0186,  0.0010,\n                       0.0749, -0.0680, -0.0307,  0.0109,  0.0869,  0.0215, -0.0042, -0.0777,\n                      -0.0901, -0.0625, -0.0070, -0.0093,  0.0897,  0.0104,  0.0510, -0.0885,\n                       0.0321, -0.0784,  0.0316,  0.0691,  0.0793,  0.0682,  0.0083,  0.0113,\n                      -0.0188, -0.0041,  0.0288, -0.0282,  0.0307,  0.0600, -0.0464,  0.0374,\n                      -0.0596, -0.0489, -0.0106,  0.0649, -0.0239,  0.0906,  0.0824,  0.0754,\n                       0.0023, -0.0016, -0.0064, -0.0402, -0.0014,  0.0939, -0.0792, -0.0018,\n                      -0.0469,  0.0228,  0.0029,  0.0289])),\n             ('GNN3.Theta1',\n              tensor([[-8.6958e-02,  6.0510e-05,  1.2429e-01,  ..., -1.8818e-01,\n                       -4.4837e-02,  2.0627e-02],\n                      [-1.2923e-01,  1.1233e-01,  1.9289e-01,  ..., -1.6892e-01,\n                       -1.6594e-01, -1.1280e-01],\n                      [ 2.0175e-01,  7.2647e-02,  1.5074e-01,  ...,  6.1872e-02,\n                       -5.5003e-02,  2.7887e-02],\n                      ...,\n                      [-4.2309e-02,  1.5929e-01,  9.9748e-02,  ..., -5.8982e-03,\n                        4.4111e-02,  8.6019e-02],\n                      [ 1.0578e-02,  1.9126e-02,  1.5627e-01,  ...,  7.6835e-02,\n                       -1.5088e-01, -1.5989e-02],\n                      [-1.5302e-01, -1.8086e-01,  5.0090e-02,  ...,  1.2376e-01,\n                        2.0829e-01, -1.7325e-01]])),\n             ('GNN3.bias',\n              tensor([ 0.0935,  0.1179, -0.0241, -0.0323,  0.0742,  0.0812, -0.0614, -0.1525,\n                      -0.1081, -0.0233,  0.0400, -0.0600, -0.1705,  0.1574, -0.1592,  0.0565,\n                      -0.1738, -0.0986,  0.0384,  0.1196,  0.1111,  0.0855,  0.0568, -0.0584]))])"
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#torch.save(STmodel.state_dict(), '/content/Spatial-interpolation/model/IGNNK_{:}_{:}iter_{:}.pth'.format(dataset,max_iter,time.strftime(\"%Y-%m-%d %H:%M:%S\", time.localtime()))) # Save the model\n",
    "torch.save(STmodel.state_dict(), '/home/xren451/rxb/phd/Spatial_interpolation/XBSPA/ModIGNNK/IGNNK_{:}iter_{:}.pth'.format(max_iter,time.strftime(\"%Y-%m-%d %H:%M:%S\", time.localtime()))) # Save the model\n",
    "STmodel.state_dict()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-25T05:38:47.006321Z",
     "start_time": "2024-03-25T05:38:46.987359Z"
    }
   },
   "id": "998b8469d02754e4",
   "execution_count": 12
  },
  {
   "cell_type": "markdown",
   "source": [
    "Inference"
   ],
   "metadata": {
    "collapsed": false
   },
   "id": "6377c6e09748cc8a"
  },
  {
   "cell_type": "code",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 1.6149224443523984 2.52955289554241 879.9701738180798\n",
      "1 0.7877490398799057 1.3121267842842288 583.4288385626284\n",
      "2 0.7352291173601594 1.2137979559888692 546.4334157530495\n",
      "3 0.6888332073379644 1.125183008665543 510.9577476332256\n",
      "4 0.641995979954657 1.0370048625319204 476.1958675750768\n",
      "5 0.5977678576006255 0.9552627899781174 440.5831677556239\n",
      "6 0.5567252959623211 0.8819417846689256 403.694635704134\n",
      "7 0.5214402970455466 0.8134062462720038 378.4143287479428\n",
      "8 0.47611740132883323 0.7391244577464788 341.8123945082279\n",
      "9 0.4528726404718752 0.6848395230386973 325.185460233376\n",
      "10 0.42336753970541635 0.6311392415894838 301.29145656436145\n",
      "11 0.40836183967637163 0.5929155654196876 294.07332932421974\n",
      "12 0.3877241664606062 0.5518707327273531 278.76200143827924\n",
      "13 0.3662003603967178 0.5112564697171508 262.60388374292415\n",
      "14 0.3524175333197208 0.48089751027599903 251.9919828560895\n",
      "15 0.34367277984964323 0.457486771092555 250.77718985802\n",
      "16 0.3337708614801255 0.4372562880959559 246.82251732890475\n",
      "17 0.3317443767758332 0.4258543983976938 243.43977886643907\n",
      "18 0.31317153465208014 0.39958779136149697 226.6470406391484\n",
      "19 0.3086356439916307 0.3888138244218538 222.36527346248639\n",
      "20 0.3055337735631418 0.38140985032574587 222.88900685346957\n",
      "21 0.296028081457843 0.36721521463314777 210.83846915808408\n",
      "22 0.2948824322277581 0.3646651620595067 207.84327737363938\n",
      "23 0.2884944058197927 0.3543211441763053 205.39929235571083\n",
      "24 0.29097149595042404 0.35651135269626333 209.96759229277234\n",
      "25 0.27980820574354637 0.34211814761274134 191.4138987971492\n",
      "26 0.2822285253967074 0.34383713203341215 198.19985522919916\n",
      "27 0.28724449081831455 0.34902331461809893 211.40504998977207\n",
      "28 0.2817110591045804 0.3421129496976459 204.2561416774376\n",
      "29 0.2784053949865997 0.33871738697328285 194.76628462968404\n",
      "30 0.27980078434572514 0.33956477133931123 199.0056283316695\n",
      "31 0.27903571642537434 0.33850429845789914 198.22350291876648\n",
      "32 0.2760960196095696 0.33431118863958426 199.07261413053882\n",
      "33 0.27436461653051486 0.33185675242214246 193.64225399595298\n",
      "34 0.27594790731363933 0.3332330391072468 200.27962521815832\n",
      "35 0.27779110244206695 0.3357396919273261 201.70778826671665\n",
      "36 0.27520070131395874 0.33204712797129676 199.58133814349998\n",
      "37 0.2711820729180016 0.3273746327730555 189.421266484855\n",
      "38 0.27295710761448055 0.32912921004130785 197.90926975791876\n",
      "39 0.27435718917530505 0.331446039122741 198.26101458578347\n",
      "40 0.27015197394365004 0.32542116302470125 193.00542644565846\n",
      "41 0.272932535614368 0.3276612598010059 199.5360121584501\n",
      "42 0.27226334237986827 0.3266059482047661 201.72589759566384\n",
      "43 0.269238831824842 0.323720110216172 191.07242368189074\n",
      "44 0.2664277213226077 0.3204788487662763 185.2296394654966\n",
      "45 0.2732393668803642 0.32833290968507617 199.77610757192502\n",
      "46 0.2663239659388982 0.32019054786754264 185.92146118254607\n",
      "47 0.2704375546600222 0.3262993525732299 190.23103368573663\n",
      "48 0.2719968922995084 0.32610881581094675 199.80950260935703\n",
      "49 0.26721889392535997 0.32072388457077433 189.2203628883211\n",
      "50 0.26927863663004603 0.3217930362048295 196.83929803085087\n",
      "51 0.27172739236970717 0.32611471045235363 198.33692763205605\n",
      "52 0.2667469893543271 0.3180480768652933 193.8269071185952\n",
      "53 0.26837423443977776 0.32043834024495593 197.8299699253348\n",
      "54 0.26356279419702855 0.3168373737604832 176.5553477432329\n",
      "55 0.2624631576557891 0.3131162284878576 184.08349992427904\n",
      "56 0.26632737274792023 0.31904834961848416 192.14300786921453\n",
      "57 0.26880330754831167 0.3193202692782935 200.49407387555362\n",
      "58 0.26327189311524535 0.31429862141868287 187.45532048955172\n",
      "59 0.26588375657557445 0.31627145609592194 197.1080206246656\n",
      "60 0.2624025790224586 0.3129592593535125 186.56184597608078\n",
      "61 0.2583354791624892 0.3079842682985334 180.30569157773297\n",
      "62 0.2565376115057155 0.3061505040228604 177.26436189335865\n",
      "63 0.25741104695641054 0.3061645291560485 181.0759125495275\n",
      "64 0.2623774064852787 0.3126604137498141 189.48946652950326\n",
      "65 0.2574517759178827 0.3070339668638788 180.89936356971637\n",
      "66 0.26204451944442453 0.31050880376799833 193.42664218945384\n",
      "67 0.25811033724305765 0.3051443696496984 188.71092943807557\n",
      "68 0.2578113109806025 0.30502836364461877 186.37926138113147\n",
      "69 0.2584383845399543 0.30709865236130185 184.8416633023217\n",
      "70 0.26131424445441576 0.30906983198497073 192.95432835469833\n",
      "71 0.2524033818849336 0.29990387381549855 171.85405526242778\n",
      "72 0.26076834747521316 0.3078376441148229 194.53649867199007\n",
      "73 0.2597401796682472 0.30743993553793164 191.07323720362706\n",
      "74 0.25357557435855177 0.3004944067779157 178.89888001559638\n",
      "75 0.2679680097443945 0.31656751750110196 207.3653762684951\n",
      "76 0.2693564985634525 0.31711725914549954 207.80303455369292\n",
      "77 0.26143937336290735 0.30772303543199736 197.15292236750585\n",
      "78 0.25322113771801663 0.30023448848349815 175.82964839937716\n",
      "79 0.25996036813097234 0.30714650261786874 194.63936827137263\n",
      "80 0.26028914659014735 0.3063034141433206 195.7772358279343\n",
      "81 0.2628882687774808 0.30864819472461413 200.201768180746\n",
      "82 0.2538385820667461 0.3021382478595761 175.41098305032673\n",
      "83 0.2633334274488179 0.30937836299093163 203.5926053632767\n",
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      "85 0.25549866956958955 0.30243665877472437 182.46800129101058\n",
      "86 0.2541845187588238 0.30029598406613256 181.78359412076315\n",
      "87 0.2538090759636076 0.29886165046529745 184.25195428758067\n",
      "88 0.2502189664609445 0.29642381163657117 171.32679431013122\n",
      "89 0.2503925559805996 0.2966762046931643 173.64781002678916\n",
      "90 0.2515597517118666 0.29565859473594225 181.90549890739015\n",
      "91 0.2503975031510211 0.29542863771412037 177.59966278807698\n",
      "92 0.25437616991740547 0.29950222426286904 183.7588688725753\n",
      "93 0.26285873774172624 0.30756291177957773 202.08758588294984\n",
      "94 0.26061912634852663 0.3055930124202392 198.87669842139073\n",
      "95 0.25935183761141367 0.30384777038283217 196.8482860294203\n",
      "96 0.2505126791076136 0.29528389760448703 176.52740069395688\n",
      "97 0.26732491100555683 0.3122885736954822 208.24536563334917\n",
      "98 0.24988071136548082 0.2949968677329763 175.33279039852687\n",
      "99 0.2602471209426367 0.30627333131909606 194.03695421359288\n"
     ]
    }
   ],
   "source": [
    " # Define model and train\n",
    "STmodel = IGNNK(h, z, K)  # The graph neural networks\n",
    "criterion = nn.MSELoss()\n",
    "optimizer = optim.Adam(STmodel.parameters(), lr=learning_rate)\n",
    "RMSE_list = []\n",
    "MAE_list = []\n",
    "MAPE_list = []\n",
    "for epoch in range(max_iter):\n",
    "    for i in range(training_set.shape[0]//(h * batch_size)):  #using time_length as reference to record test_error\n",
    "        t_random = np.random.randint(0, high=(training_set_s.shape[0] - h), size=batch_size, dtype='l')\n",
    "        know_mask = set(random.sample(range(0,training_set_s.shape[1]),n_o_n_m)) #sample n_o + n_m nodes\n",
    "        feed_batch = []\n",
    "        for j in range(batch_size):\n",
    "            feed_batch.append(training_set_s[t_random[j]: t_random[j] + h, :][:, list(know_mask)]) #generate 8 time batches\n",
    "        inputs = np.array(feed_batch)\n",
    "        inputs_omask = np.ones(np.shape(inputs))\n",
    "        if not dataset == 'NREL':\n",
    "            inputs_omask[inputs == 0] = 0           # We found that there are irregular 0 values for METR-LA, so we treat those 0 values as missing data,\n",
    "                                                    # For other datasets, it is not necessary to mask 0 values\n",
    "        missing_index = np.ones((inputs.shape))\n",
    "        for j in range(batch_size):\n",
    "            missing_mask = random.sample(range(0,n_o_n_m),n_m) #Masked locations\n",
    "            missing_index[j, :, missing_mask] = 0\n",
    "        if dataset == 'NREL':\n",
    "            Mf_inputs = inputs * inputs_omask * missing_index / capacities[:, None]\n",
    "        else:\n",
    "            Mf_inputs = inputs * inputs_omask * missing_index / E_maxvalue #normalize the value according to experience\n",
    "        Mf_inputs = torch.from_numpy(Mf_inputs.astype('float32'))\n",
    "        mask = torch.from_numpy(inputs_omask.astype('float32'))   #The reconstruction errors on irregular 0s are not used for training\n",
    "        A_dynamic = A_s[list(know_mask), :][:, list(know_mask)]   #Obtain the dynamic adjacent matrix\n",
    "        A_q = torch.from_numpy((calculate_random_walk_matrix(A_dynamic).T).astype('float32'))\n",
    "        A_h = torch.from_numpy((calculate_random_walk_matrix(A_dynamic.T).T).astype('float32'))\n",
    "        if dataset == 'NREL':\n",
    "            outputs = torch.from_numpy(inputs/capacities[:, None])\n",
    "        else:\n",
    "            outputs = torch.from_numpy(inputs/E_maxvalue) #The label\n",
    "        optimizer.zero_grad()\n",
    "        X_res = STmodel(Mf_inputs, A_q, A_h)  #Obtain the reconstruction\n",
    "        loss = criterion(X_res*mask, outputs*mask)\n",
    "        loss.backward()\n",
    "        optimizer.step()        #Errors backward\n",
    "    if not dataset == 'NREL':\n",
    "        flags = parse_args(sys.argv[1:])\n",
    "        E_maxvalue = flags.E_maxvalue\n",
    "        MAE_t, RMSE_t, MAPE_t = test_error(STmodel, unknow_set, test_set, A, E_maxvalue)\n",
    "    else:\n",
    "        MAE_t, RMSE_t, MAPE_t= test_error(STmodel, unknow_set, test_set, A,E_maxvalue)\n",
    "    RMSE_list.append(RMSE_t)\n",
    "    MAE_list.append(MAE_t)\n",
    "    MAPE_list.append(MAPE_t)\n",
    "    print(epoch, MAE_t, RMSE_t, MAPE_t)\n"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-25T05:39:27.748991Z",
     "start_time": "2024-03-25T05:38:47.007185Z"
    }
   },
   "id": "d71cd2be5893116",
   "execution_count": 13
  },
  {
   "cell_type": "code",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1, 93)\n",
      "(1, 93)\n",
      "Best model in the 5 -th column is 0.3963973298993473 0.4965677424469117 -1.8583974139128197\n",
      "(1, 96)\n",
      "(1, 96)\n",
      "Best model in the 6 -th column is 0.15896444868640408 0.19401845596661563 -2.4753977707385815\n",
      "(1, 94)\n",
      "(1, 94)\n",
      "Best model in the 7 -th column is 0.1268784930729019 0.15618160090515343 -2.443852504411656\n",
      "(1, 72)\n",
      "(1, 72)\n",
      "Best model in the 8 -th column is 0.08986223805704768 0.1183024403392515 -1.3732976811914015\n",
      "(1, 72)\n",
      "(1, 72)\n",
      "Best model in the 9 -th column is 0.24969313192053522 0.29853945729939213 -2.880217721458145\n",
      "(1, 65)\n",
      "(1, 65)\n",
      "Best model in the 10 -th column is 0.15529648691880432 0.17784814729769147 -4.080004130222068\n",
      "(1, 40)\n",
      "(1, 40)\n",
      "Best model in the 11 -th column is 0.4535547051545998 0.5359839978249362 -2.4894681217241015\n",
      "(1, 98)\n",
      "(1, 98)\n",
      "Best model in the 12 -th column is 0.052289027167505615 0.05821623130649479 -21.317503459953613\n",
      "(1, 99)\n",
      "(1, 99)\n",
      "Best model in the 13 -th column is 0.538051544351029 0.6326040877792422 -35.790758184725895\n",
      "(1, 77)\n",
      "(1, 77)\n",
      "Best model in the 14 -th column is 0.438707544183882 0.5165909500028942 -4.69548736884733\n",
      "(1, 39)\n",
      "(1, 39)\n",
      "Best model in the 15 -th column is 0.6228129687522254 0.6488404434238706 -16.746925416597673\n",
      "(1, 7)\n",
      "(1, 7)\n",
      "Best model in the 16 -th column is 0.9225954244917297 0.9380242775063401 -28.96493155173652\n"
     ]
    }
   ],
   "source": [
    "#Adj---Determined by tSNE\n",
    "#Raw data and raw adjacency matrix without mapminmax\n",
    "X_raw\n",
    "# X_raw=normalize_3d_array(X_raw)\n",
    "\n",
    "for j in range(5,X_raw.shape[1]-1):\n",
    "    NDBC_lat=pd.DataFrame(Station_info.iloc[:,1])\n",
    "    NDBC_long=pd.DataFrame(Station_info.iloc[:,3])\n",
    "    NDBC_ID=pd.DataFrame(Station_info.iloc[:,0])\n",
    "    Adj_dist=adj_dist(NDBC_lat,NDBC_long)\n",
    "    X_raw_0=X_raw[:,j,:]#GET the first feature\n",
    "    #print(X_raw_0.shape)\n",
    "    # Count the num of missing values in each column\n",
    "    missing_counts_per_column = np.sum(np.isnan(X_raw_0), axis=0)\n",
    "    # print results\n",
    "    # print(\"Incomplete data number in each column：\", missing_counts_per_column)\n",
    "\n",
    "    #Get the index if the value is not zero\n",
    "    # Find the columns where missing values exist.\n",
    "    columns_with_missing_data = np.any(np.isnan(X_raw_0), axis=0)\n",
    "\n",
    "    # Get the column numbers when missing value exist.\n",
    "    missing_columns = np.where(columns_with_missing_data)[0]\n",
    "\n",
    "    # Print results\n",
    "    #print(\"The column numbers with missing values are：\", missing_columns)\n",
    "\n",
    "    #Get new data after deletion.\n",
    "    #Delete those columns(Stations) if there is not any features.\n",
    "    result = np.delete(X_raw_0, missing_columns, axis=1)\n",
    "    result = (result - np.min(result)) / (np.max(result) - np.min(result))\n",
    "    #Mean results---for SNE\n",
    "    mean_result_axis_1=np.mean(result,axis=0)\n",
    "    mean_result_axis_1=mean_result_axis_1.reshape(-1,1)\n",
    "\n",
    "    #Get new adjacency matrix after deletion.\n",
    "    NDBC_long=NDBC_long.transpose()\n",
    "    NDBC_long_aft=NDBC_long.drop(columns=missing_columns)\n",
    "    # Reconstruct the index in the DataFrame and get the longitude after deletion.\n",
    "    NDBC_long_aft = NDBC_long_aft.reset_index(drop=True)\n",
    "    print(NDBC_long_aft.shape)\n",
    "    Temp_long=NDBC_long_aft.values\n",
    "\n",
    "    NDBC_lat=NDBC_lat.transpose()\n",
    "    NDBC_lat_aft=NDBC_lat.drop(columns=missing_columns)\n",
    "    # Reconstruct the index in the DataFrame and get the latitude after deletion.\n",
    "    NDBC_lat_aft = NDBC_lat_aft.reset_index(drop=True)\n",
    "    print(NDBC_lat_aft.shape)\n",
    "    Temp_lat=NDBC_lat_aft.values\n",
    "\n",
    "    merged_array = np.concatenate([mean_result_axis_1, Temp_long.T,Temp_lat.T], axis=1)\n",
    "    tsne = TSNE(n_components=2, random_state=30,perplexity=1) #Make sure random seed to be the same for the reproducibility.\n",
    "    array_aft = tsne.fit_transform(merged_array)\n",
    "\n",
    "    #GEt the new ADJ matrix.\n",
    "    Adj_dist=adj_dist(pd.DataFrame(array_aft[:,0]),pd.DataFrame(array_aft[:,1]))\n",
    "    capacities=np.ones((Adj_dist.shape[0], 1))\n",
    "    capacities=capacities.flatten()\n",
    "    split_line1 = int(result.shape[0] * 0.7)\n",
    "    training_set = result[:split_line1, :]\n",
    "    test_set = result[split_line1:, :]\n",
    "    rand = np.random.RandomState(0) # Fixed random output, just an example when seed = 0.\n",
    "    unknow_set = rand.choice(list(range(0,result.shape[1])),N_u,replace=True)#Stations to be predicted\n",
    "    unknow_set = set(unknow_set)\n",
    "    full_set = set(range(0,result.shape[1]))\n",
    "    know_set = full_set - unknow_set\n",
    "    training_set_s = training_set[:, list(know_set)]   # get the training data in the sample time period\n",
    "    A_s = Adj_dist[:, list(know_set)][list(know_set), :]\n",
    "    MAE_t, RMSE_t, R2_t, nrel_ignnk_res  = test_error_cap(STmodel, unknow_set, full_set,test_set, Adj_dist,h,capacities)\n",
    "    print('Best model in the',j, '-th column is', MAE_t, RMSE_t, R2_t)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-25T05:39:42.134888Z",
     "start_time": "2024-03-25T05:39:27.749824Z"
    }
   },
   "id": "4d2c8f6fb14dea14",
   "execution_count": 14
  },
  {
   "cell_type": "markdown",
   "source": [
    "Experiment 3.2: IGNNK-dis-MIsubgrh-3DGNN (Format:Metd-Adj-a node can constrct multiple subgraphs-3DGNN)"
   ],
   "metadata": {
    "collapsed": false
   },
   "id": "d6ed47a13f30bb2b"
  },
  {
   "cell_type": "code",
   "outputs": [],
   "source": [
    "if __name__ == \"__main__\":\n",
    "    \"\"\"\n",
    "    Model training\n",
    "    \"\"\"\n",
    "    flags = parse_args(sys.argv[1:])\n",
    "    dataset=flags.dataset\n",
    "    n_o_n_m = flags.n_o\n",
    "    h = flags.h\n",
    "    z = flags.z\n",
    "    K = flags.K\n",
    "    n_m = flags.n_m\n",
    "    n_u = flags.n_u\n",
    "    max_iter = flags.max_iter\n",
    "    learning_rate = flags.learning_rate\n",
    "    E_maxvalue = flags.E_maxvalue\n",
    "    batch_size = flags.batch_size\n",
    "    to_plot = flags.to_plot"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-25T05:39:42.138194Z",
     "start_time": "2024-03-25T05:39:42.135642Z"
    }
   },
   "id": "7965804188f1338e",
   "execution_count": 15
  },
  {
   "cell_type": "code",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1, 93)\n",
      "A's shape is: (93, 93)\n",
      "X's shape is: (93, 8784)\n",
      "(8784, 103)\n",
      "Incomplete data number in each column： [8784    0    0    0    0    0    0    0    0    0    0    0    0    0\n",
      "    0    0    0    0    0    0    0    0    0    0    0    0    0    0\n",
      "    0    0    0    0    0    0 8784    0    0    0 8784    0    0    0\n",
      "    0    0    0    0    0    0    0 8784 8784    0    0    0    0 8784\n",
      " 8784    0    0    0    0    0    0    0    0    0    0    0    0    0\n",
      "    0    0    0 8784    0    0    0    0    0    0    0 8784    0 8784\n",
      "    0    0    0    0    0    0    0    0    0    0    0    0    0    0\n",
      "    0    0    0    0    0]\n",
      "The column numbers with missing values are： [ 0 34 38 49 50 55 56 73 81 83]\n",
      "(8784, 93)\n",
      "Row 0 - Column Numbers: [ 1  2  4 79  5 20  3 77 21 17 83 85 78 87 91 12 15 31 11 43 19 44 35 30\n",
      " 74 90 16 10 33 64 42 34 61 13 32 46 22 63 92 56 18  8 41], MI Values: [0.8272601132894586, 0.6901375697065202, 0.4673606483958732, 0.45757637448269683, 0.4363240338301644, 0.4190235175463517, 0.37428008133733837, 0.37263024544485734, 0.33215728219304985, 0.3299090634675217, 0.3150689617867082, 0.29292039446620866, 0.22793155006306698, 0.22350595260037576, 0.2084899516681764, 0.19725693559810153, 0.16436438822998234, 0.1621107642515911, 0.15513395543730368, 0.13586993979589845, 0.13409996608400565, 0.12631372813239938, 0.11361591888716127, 0.10962686909974106, 0.10670490036675684, 0.10411775455289352, 0.10173701560948789, 0.10125880394889375, 0.0966457877057838, 0.0917156023777439, 0.08872664637913985, 0.08750394746818291, 0.07987921333337233, 0.0779097501756647, 0.07772961987272176, 0.07681250087322766, 0.07596636122032496, 0.07375851842511771, 0.07334383362524477, 0.0724236272383223, 0.06937049801544504, 0.06869053966721506, 0.06665335877298872]\n",
      "Row 1 - Column Numbers: [ 0 20  2 85 21 77  4 79 17  5 91 87 83  3 11 15 12 78 31 19 10 16 43 35\n",
      " 30 33 13 90 64 74 44 22 42 61 18 34 92  8 46 56 24 28 36], MI Values: [0.8272601132894577, 0.5324618722588088, 0.52600823699178, 0.4273072620362397, 0.4023069759074378, 0.39111917114037187, 0.34043212687770286, 0.33742367205695434, 0.3283135513911546, 0.32209271522604777, 0.3192857717713018, 0.3012243820649747, 0.2950417871731199, 0.25018137359531334, 0.2344515509245717, 0.23100847367209631, 0.22954525563754213, 0.22306577157731855, 0.161217443157323, 0.16120899606897954, 0.14396039237957936, 0.13986782406464826, 0.12913107009156644, 0.11642248941903688, 0.1150059734774116, 0.10934085523256787, 0.10726653658897867, 0.10532886649482887, 0.10272291690296598, 0.10197487194243937, 0.09756958090356083, 0.0945249676245794, 0.09265639520815494, 0.09192328803022942, 0.09060525299304167, 0.09049841174829254, 0.08048114102267423, 0.08040105111154183, 0.08010342629738876, 0.07992095121214415, 0.07658487183692309, 0.07617110541908634, 0.07458627225738823]\n",
      "Row 2 - Column Numbers: [ 4 79  5  0  3  1 78 31 20 77 85 21 17 12 35 43 87 83 30 33 91 74 11 44\n",
      " 34 10 36 15 13 86 29 39 19 42 37 32 40 38 89 64 28 61 41], MI Values: [1.0421298348636876, 0.889753767585324, 0.8252189069592397, 0.6901375697065175, 0.6346295603606373, 0.52600823699178, 0.4089563958436999, 0.2885791692349038, 0.26984073230595396, 0.23544670375941035, 0.21914515387782174, 0.2125857191397058, 0.20709995929092173, 0.19750308970805186, 0.18701920286034568, 0.18681968571483498, 0.18419330652618005, 0.1805652907247035, 0.15876062884895603, 0.158099218500249, 0.15702895570463316, 0.15700514453794945, 0.15460225559136997, 0.14614605566375083, 0.11747560005255142, 0.1108491328808272, 0.1096084538611164, 0.10428901675494728, 0.10194617541772022, 0.09732347543015507, 0.09469648273846154, 0.09409837181553105, 0.09214628161064109, 0.09190658625377424, 0.0914136839587858, 0.09002264997452336, 0.08826839034197409, 0.08794009077204912, 0.08732427486062821, 0.08295219935787657, 0.08247104503342495, 0.08075786448081335, 0.07942866688885175]\n",
      "Row 3 - Column Numbers: [ 2  5 79  4  0 84  1 78 77 31 20 17 85 83 21 87 43 35 12 74 91 33 44 30\n",
      " 11 34 64 36 86 10 46 37 41 89 39 32 38 15 29 42 40 19 56], MI Values: [0.6346295603606364, 0.6014752255233811, 0.5216221690633258, 0.5005956595959162, 0.37428008133733837, 0.29367624960262795, 0.2501813735953151, 0.22968546503017784, 0.168588428573063, 0.15053120343368054, 0.14918195632018705, 0.135719601508959, 0.12331183579416383, 0.12212949345012802, 0.12006037445413753, 0.10828482718467836, 0.1038170751558507, 0.10166237481487972, 0.10067391244311352, 0.0993121350767705, 0.09857437391434942, 0.09072061229028172, 0.09034618967547559, 0.08507553529173251, 0.08430822621926293, 0.07711971317009514, 0.0732968907767324, 0.07188834325973747, 0.06840077448593984, 0.06747669748327834, 0.0662602861970365, 0.06558274587027046, 0.06306413363040075, 0.06298051391441817, 0.06157433149594205, 0.06126513617121354, 0.06113916617078008, 0.06068970280665109, 0.06048824178377199, 0.05799913453610728, 0.057212613678012225, 0.05676014452040157, 0.05643454058528263]\n",
      "Row 4 - Column Numbers: [ 2  5 79  3  0 78  1 44 31 20 77 17 85 12 87 21 83 35 43 11 64 74 30 33\n",
      " 91 10 34 63 36 32 13 19 61 86 24 23 38 46 89 29 15 88 40], MI Values: [1.0421298348636858, 0.9112659905285279, 0.893437297964442, 0.5005956595959136, 0.4673606483958741, 0.3522117773810223, 0.34043212687770286, 0.25771696574601854, 0.227791945861342, 0.17593949417667076, 0.1718626691037226, 0.15309018167041533, 0.14716514799944758, 0.1468250597240388, 0.1467876478550929, 0.14440832752750676, 0.1374753305211449, 0.13262659195667847, 0.13167838609283677, 0.1303296358704138, 0.1297991451019085, 0.1295289172486882, 0.12417935392990831, 0.12068089113273661, 0.11543451299135477, 0.09954623668022755, 0.09367692420842033, 0.09074112883170127, 0.08771441417981674, 0.08734619315226588, 0.08641934307043808, 0.08049320130510296, 0.0793639777794386, 0.07935824289618232, 0.07926789355999908, 0.07907845045093165, 0.07857614620487485, 0.07856401142111924, 0.07698715238078346, 0.07666467817423595, 0.07652558554478439, 0.07609992946234811, 0.07604174073334136]\n",
      "Row 5 - Column Numbers: [ 4 79  2  3  0 78  1 31 43 36 35  7 77 33 20 74 17 30 21 83 85 44 87 86\n",
      " 37 12 29 91 38 89 39 11 28 40 34 42 32 10 41 80 88 90 15], MI Values: [0.9112659905285261, 0.8539429780686714, 0.8252189069592406, 0.6014752255233793, 0.4363240338301635, 0.40195030351981753, 0.32209271522605043, 0.2760329582147678, 0.20819529046906293, 0.20674579006625127, 0.19563347399244257, 0.18293846291297733, 0.17144637756480563, 0.17076852453711044, 0.1697430692708517, 0.16810983519107303, 0.16129782284088812, 0.14845254677791608, 0.1420832575295341, 0.14139989403188924, 0.14129091651330405, 0.13308552892848002, 0.13204341952919751, 0.1305167490968433, 0.12301925557245497, 0.12297734107820624, 0.11470618022646395, 0.11292935145386807, 0.10350223849688867, 0.1028680671126736, 0.10050281527196514, 0.09942878741363614, 0.09875071075038111, 0.09746128685535993, 0.09670112680553178, 0.09376382987344023, 0.09331795784564356, 0.08681805312730084, 0.08605778397885011, 0.08230865790885478, 0.07740754667316363, 0.07668497735519875, 0.07561477718424658]\n",
      "Row 6 - Column Numbers: [64 14 46 63 12 23  8 57  9 62 11 61 32 45 87 13 44  4 10 54 28 47  7 84\n",
      " 27 69 52 72 36 30 35 79 65 74 41  2 56 26 66 34  1 85 92], MI Values: [0.478605916453672, 0.1659311007796953, 0.13099684473508688, 0.11759316702334122, 0.11209322621671447, 0.09453623691659319, 0.08865574838552437, 0.0859220172096915, 0.08576932695849138, 0.08134777223811529, 0.07911821580729761, 0.07748176490715508, 0.07727934830261152, 0.07607959090818373, 0.07597112239010162, 0.07148486877965077, 0.07123886187653383, 0.07119374646681464, 0.06986362657552991, 0.067773162297458, 0.06638342779498618, 0.06549702884688458, 0.0654621562897697, 0.0649124734204598, 0.06278134191716767, 0.06183066532204595, 0.0613978125590382, 0.05919388460622166, 0.05838254740344251, 0.05558434696104264, 0.055331827053077376, 0.05403814410428076, 0.053136251620639285, 0.0529400614221025, 0.05243412828986749, 0.052066717960047804, 0.0518643235699745, 0.05140858603128606, 0.05121302295318664, 0.0509936262443027, 0.05053181341582125, 0.05019818795246955, 0.04816604793903778]\n",
      "Row 7 - Column Numbers: [ 5 17 64 21 63 57 23 46 61  6 79  2  4 52 87 12 27  3 62  9  0  8  1 73\n",
      " 10 20 69 19 47 54 58 11 14 68 88 74 30 32 33 67 31 72 34], MI Values: [0.1829384629129791, 0.10524195919111623, 0.0946233457977872, 0.09121449964563944, 0.07907681278759338, 0.07616119177035774, 0.0681607842361398, 0.06676341580429312, 0.066597172827497, 0.06546215628976793, 0.059427428725374654, 0.05901064569144587, 0.05558987853756037, 0.054813377473760916, 0.05399825056106078, 0.053976980524889306, 0.05053310241240361, 0.05009254312144673, 0.0482538265970307, 0.04809050593593689, 0.047727363031476955, 0.047556140122899215, 0.0474209934989922, 0.047129770164868745, 0.04693364118155152, 0.04555598545496231, 0.04435919441098868, 0.04338328445526862, 0.0431716643311324, 0.04278103642929665, 0.041407256502377976, 0.040946924073455904, 0.04074963195215808, 0.03718480535959223, 0.03666191730525448, 0.036462534916334555, 0.03612339642617801, 0.03608454747954237, 0.03558055210133837, 0.035520966996969605, 0.035348553502023705, 0.03526695646017597, 0.035145156518217036]\n",
      "Row 8 - Column Numbers: [10  9 14 26 11 13 25 91 85 87 12 32 64 24 27 20 21 34 17  6 23 15  1 74\n",
      " 33 30 44  0 28  4  2 77 46  5 89 31 83 78 79 35 88 63 19], MI Values: [0.48698986391151955, 0.375802297419666, 0.2819697411476927, 0.2524540408417879, 0.2289457453068362, 0.21963152219072413, 0.16233774299458315, 0.12410132440415467, 0.11970109613176039, 0.11717444758841289, 0.10941441927598472, 0.10441158737263923, 0.10254326229904187, 0.10209066826928259, 0.09968544490658893, 0.09860668116430737, 0.09797349325439786, 0.09279000891834333, 0.08886645776288304, 0.08865574838552615, 0.08474539401989478, 0.08043587263141738, 0.0804010511115445, 0.07707447313008853, 0.07565747720513727, 0.07521271366405902, 0.0702725389356953, 0.06869053966721772, 0.06518271250260987, 0.06434639902210026, 0.06327216027249083, 0.062200056513681545, 0.06204077732827784, 0.060054597826602496, 0.05864248331363431, 0.05824452931784396, 0.05824405082485651, 0.0575396306220366, 0.05661802684946515, 0.055954172623136955, 0.05292091189701953, 0.052721647755728185, 0.05241070031981643]\n",
      "Row 9 - Column Numbers: [ 8 10 26 13 14 11 32  6 12 25 87 34 64 20 27 91 24 21 17 85 36  1 23  0\n",
      " 28 41 74 63  7 30 62 83 15 61 54  2 72 19 57 79 40 89 78], MI Values: [0.37580229741966775, 0.2739374700127568, 0.1888349353819665, 0.18881791101212642, 0.17302647019022377, 0.14827272551388315, 0.08690570143561605, 0.08576932695849404, 0.08575515951341117, 0.07942615953296617, 0.07512326148058257, 0.06858253221368038, 0.06743046912400352, 0.0606112133373804, 0.060249930177727506, 0.05872512110265582, 0.05556219929455963, 0.05510777850993431, 0.053827948456972585, 0.05356332489102211, 0.05062803388903436, 0.05042486996980955, 0.04914461256289693, 0.04911468770996663, 0.04892501848965658, 0.04833957062141003, 0.04817579082966983, 0.04815235147500374, 0.048090505935939554, 0.047497107903827995, 0.046442659973216394, 0.04500640957005597, 0.044571645079205524, 0.04384180562593176, 0.04255922801340173, 0.04239438289088415, 0.041960240322472586, 0.04195403205745141, 0.04175321361746853, 0.041721734850988845, 0.041382496982518724, 0.039247318738780734, 0.03916411448757362]\n",
      "Row 10 - Column Numbers: [11  8 13  9 91 85 14 87 12 26  1 20 64 25 24  2 21 17 78 79  0 61  4 23\n",
      " 83 15 34  5 77 31 44 32 27 33 30 74 28 43 35  6 41 46 53], MI Values: [0.4993554128442783, 0.4869898639115231, 0.4066358068899456, 0.27393747001275504, 0.2579871837894956, 0.25686672570808167, 0.2251698714598369, 0.22104675256482142, 0.17468399623417863, 0.1595045585205188, 0.14396039237957758, 0.13028693835191518, 0.12993063246484482, 0.1129190817547916, 0.11268616419256361, 0.1108491328808281, 0.10815686636048127, 0.10750415858836693, 0.10461732375843713, 0.10144296896099103, 0.10125880394889109, 0.10067720955484294, 0.09954623668022666, 0.09526800567615812, 0.09120163011638649, 0.09068210425726964, 0.08709868991881109, 0.08681805312730351, 0.08644635750351704, 0.08544174110632596, 0.08386645043593433, 0.08091774681887642, 0.07918640410680755, 0.077949740915769, 0.07776056152449495, 0.07645994681407409, 0.07299784236684648, 0.07182439963604015, 0.07091448732899508, 0.06986362657553258, 0.06936075480536807, 0.06801559120089085, 0.06799093673704792]\n",
      "Row 11 - Column Numbers: [10 85 61 12 13 91 87  1  8 20 21 17 77  0  2 83  9  4 78 14 79 31 24 15\n",
      " 64  5 35 43 44 74  3 33  6 42 30 28 90 34 19 89 22 23 80], MI Values: [0.499355412844281, 0.447794898444446, 0.4211796194747075, 0.4197051791498847, 0.40682029470780456, 0.3865429355312857, 0.296573849422912, 0.23445155092457082, 0.22894574530684064, 0.21618413086183974, 0.17612200358653762, 0.1627161637347161, 0.15529190588759256, 0.15513395543730546, 0.15460225559137086, 0.14976259321938645, 0.1482727255138805, 0.13032963587041646, 0.12508164598781324, 0.12287505739090143, 0.12041417972820945, 0.11341149652601601, 0.10784355126935719, 0.10663625668288024, 0.10500346113093073, 0.09942878741363259, 0.096740469127222, 0.09481730555193213, 0.08789263097170963, 0.08465931443259134, 0.08430822621926115, 0.0819176206772605, 0.0791182158072985, 0.07587529502254231, 0.0758563574615021, 0.07518085992455958, 0.07463339072882835, 0.0729801592932775, 0.06976258783125644, 0.0691934966107981, 0.06893504056359223, 0.06614162517794231, 0.06530714718931119]\n",
      "Row 12 - Column Numbers: [11 13  1  2  0 20 10 85 79 77 21  4 31 74 43 30 87 33 91 35 17 78  5 83\n",
      "  6 61  8 64 86  3 34 36 14 37 28 40 39 29 42 89 44 38  9], MI Values: [0.41970517914988204, 0.2820044236370247, 0.22954525563754302, 0.19750308970805097, 0.19725693559809976, 0.19049650601974388, 0.17468399623417863, 0.16892847033331915, 0.15745268691877712, 0.15476368455904232, 0.1470253698180608, 0.1468250597240388, 0.14662969753092625, 0.14286051344793105, 0.14156956810136734, 0.13732974337876414, 0.13558171850873002, 0.13072864694938868, 0.12921883418740698, 0.12855491233259286, 0.12797358847181428, 0.1251376255189447, 0.12297734107820624, 0.12178764257401742, 0.11209322621671713, 0.11175003676089723, 0.10941441927598472, 0.10535355610052655, 0.10135095971922237, 0.10067391244311619, 0.09993696526051199, 0.09709484343702979, 0.09629848458173385, 0.09592473158963521, 0.09501229751970186, 0.09185969685608963, 0.09122469199042715, 0.08955815291430014, 0.08912140713055461, 0.08890082125607712, 0.08654874505815524, 0.08621577314512052, 0.08575515951341028]\n",
      "Row 13 - Column Numbers: [11 10 12  8  9 85 91 87 78  1 20  2 31 14 35 30 43 33 44  4 79 21 28 74\n",
      " 25  0 34 17 26  6 64 83  5 15 77 36 42 32 80 89 61 54 70], MI Values: [0.406820294707801, 0.40663580688994827, 0.28200442363702294, 0.21963152219071969, 0.18881791101212642, 0.15241639531040452, 0.15188179879224428, 0.11270707168405014, 0.10855159929809766, 0.10726653658897689, 0.10347968403017482, 0.10194617541771755, 0.10045734833963227, 0.09715275871665696, 0.095142371568528, 0.09258617061155316, 0.09195467760153075, 0.08878636983820609, 0.08824878688846738, 0.08641934307043897, 0.08620980383680887, 0.08274041805652033, 0.08202421217934308, 0.08012866253161732, 0.07985596483401824, 0.07790975017566382, 0.07495306478076014, 0.07488041542475532, 0.07181363072769464, 0.07148486877965166, 0.07002602341222808, 0.06900697369544506, 0.06846734306451818, 0.0666776158158564, 0.0664440140391962, 0.06379802149536751, 0.062408309849672605, 0.062004348452000535, 0.05890185010481819, 0.057406820089648924, 0.05485204269998434, 0.05430024107788256, 0.054016668508986676]\n",
      "Row 14 - Column Numbers: [ 8 10  9 26  6 27 64 11 87 25 63 85 13 12 46 91 47 24 20 77 34 17 37 61\n",
      " 36 86 56 29 23 55 79  0 48 83  4 74  2  5 57 32 72 51 30], MI Values: [0.2819697411476918, 0.22516987145983425, 0.17302647019022466, 0.17093143981882442, 0.16593110077969708, 0.1515567092969663, 0.12701720438150055, 0.12287505739089966, 0.12022624072505117, 0.10808026792929493, 0.09840075284083127, 0.09779637211347314, 0.0971527587166543, 0.09629848458173651, 0.09266115822732779, 0.09231436655408931, 0.09074348902636675, 0.07873666169272209, 0.07681486761087797, 0.07067488479129924, 0.06725286085851412, 0.06554506282266725, 0.0641664994737523, 0.06170135977184188, 0.061668865682766416, 0.06094423783477776, 0.05952118983744992, 0.0587014765905316, 0.0585240406935128, 0.05661782886078903, 0.056059091866146105, 0.05562693284596332, 0.05528245353972583, 0.05451886276258566, 0.05432706381529773, 0.05401613896216251, 0.05270106891950288, 0.05173567448447702, 0.05167205271928932, 0.05104880529890021, 0.050294567082459274, 0.05026820068852178, 0.04979484407518253]\n",
      "Row 15 - Column Numbers: [21 16 22 20 17 19 18 85 83  1 91 87 77 73  0 11  2 10  8 12 79  4  5 56\n",
      " 90 23 42 78 61 13 24 35 43 31  3 80 68 32 46 92 57 33 53], MI Values: [0.48722604389986746, 0.47765933545984574, 0.42274734051130114, 0.3684773490976543, 0.3095265239658307, 0.30125231966110366, 0.27326227718117746, 0.2607931482272843, 0.23569399663760038, 0.23100847367209187, 0.226286992520925, 0.22368717713125363, 0.2109149525053864, 0.17737229996765436, 0.16436438822998056, 0.10663625668287935, 0.10428901675494551, 0.09068210425726964, 0.08043587263142005, 0.07994733324017389, 0.07750166086596355, 0.07652558554478794, 0.07561477718424747, 0.07262961413739166, 0.07254756653808414, 0.07129603115169658, 0.06699419564638731, 0.06674255678354601, 0.06669711932901201, 0.0666776158158564, 0.06508609948717492, 0.06380756444094082, 0.06258859383481585, 0.06209333159081609, 0.06068970280665109, 0.06004207076621171, 0.05863023036643167, 0.05587065130398727, 0.05560717684994554, 0.055416447648041434, 0.054577733516099514, 0.051477381196054495, 0.05145699897161915]\n",
      "Row 16 - Column Numbers: [15 18 22 19 21 85 73 17 20 83  1 91 87  0 77 68  2 42 10 23 56 61  5 11\n",
      "  4 90 13 78 57 63 79  3 64 46 92 52 84 80 24 53  8 47 32], MI Values: [0.47765933545984485, 0.39646468501385357, 0.3870402149910266, 0.3091588054074448, 0.28541688685649813, 0.2495265251234624, 0.23365823269839403, 0.19302253406145908, 0.17044387506372072, 0.16718927849869658, 0.13986782406464915, 0.13528675087576136, 0.12870418125103722, 0.101737015609487, 0.09654894383117263, 0.08013941132973557, 0.07497954269839457, 0.0675083713658422, 0.06746525386392133, 0.06694340591739856, 0.06331255297438165, 0.06108123440198021, 0.059929091775576815, 0.05975370525344825, 0.05524048992921937, 0.052897766030480575, 0.051451103064484194, 0.050915937056171146, 0.049854047095866605, 0.049689454222085594, 0.04856746770346909, 0.04659548808807035, 0.046006140165719245, 0.04556275492620987, 0.04529324898574405, 0.04328046495819304, 0.04310793055946416, 0.04279362459041813, 0.04234654693679207, 0.04223363657743562, 0.04159168613493058, 0.040768941888324584, 0.04067108310344292]\n",
      "Row 17 - Column Numbers: [83 21 20  0  1 15 77 19 85  2 91 87 16 92 11  5 22 79  4 18  3 12 73 46\n",
      " 90 10  7 78 64 57 31  8 42 61 56 43 13 62 68 74 35 53 52], MI Values: [1.0668147455974486, 1.021617623019086, 0.4934266968283074, 0.3299090634675217, 0.3283135513911546, 0.30952652396583336, 0.299093897359759, 0.2719089149660965, 0.24799566598007683, 0.20709995929092084, 0.2001069525344823, 0.19689724643638318, 0.1930225340614582, 0.16969542448540675, 0.16271616373471876, 0.16129782284088456, 0.15874125412953077, 0.15630527248319748, 0.153090181670418, 0.13764098894343224, 0.13571960150895812, 0.1279735884718134, 0.11461081534221496, 0.11280369881762375, 0.11040902183482348, 0.1075041585883687, 0.10524195919111712, 0.1047767078550299, 0.10037328777475985, 0.0992868325667029, 0.09616040667204562, 0.0888664577628866, 0.0846645868325373, 0.08457972685715465, 0.07971577342061753, 0.07861749607301505, 0.07488041542475354, 0.07054503826931136, 0.06961403770779029, 0.06954563307844097, 0.06903264964802336, 0.06894645621138906, 0.06703671873903527]\n",
      "Row 18 - Column Numbers: [73 19 16 22 15 21 17 83 20  1 91 85 87 77 63 88  0 57 46 72 32 64 90 92\n",
      " 56 78  2 68 42 61 11 70 82  4 62 10 52  5 48 36 75 53 55], MI Values: [0.7893958078076464, 0.5505196890502351, 0.39646468501385357, 0.32015585431856763, 0.27326227718117746, 0.1986950339873701, 0.1376409889434349, 0.1300561044353925, 0.1028199239054004, 0.09060525299304434, 0.08043542246333768, 0.07840025513521187, 0.07415089398027508, 0.073829802711872, 0.0698631855232481, 0.06947413178679618, 0.06937049801544681, 0.0555089312872461, 0.05501723067444342, 0.05297227066477728, 0.05286118816878638, 0.05264544534878457, 0.052266576769972595, 0.050573593189831456, 0.05004107750332221, 0.04951922140218912, 0.04704017567014063, 0.04656039319276406, 0.04583471052896382, 0.04531110745527123, 0.0452698374916638, 0.044711784493036255, 0.04452332972605788, 0.04430454607192402, 0.04406838905054933, 0.04345714793886302, 0.04316032552696658, 0.04294014239589039, 0.04283733769362108, 0.042177627147790275, 0.04216690271784085, 0.04179825178695218, 0.041337731296333224]\n",
      "Row 19 - Column Numbers: [18 73 21 16 15 83 17 22 20  1 77  0 85 87 91  2 90 64 12  4 46 79 92  5\n",
      " 11 68 78 42 10 57 72 75 62  3 31 52 70 56 32  8 30 35 43], MI Values: [0.5505196890502289, 0.4449658563187162, 0.3588428833857771, 0.3091588054074439, 0.301252319661101, 0.28206410473166965, 0.2719089149661009, 0.23610468619476066, 0.2076473979554514, 0.16120899606897776, 0.1483996768217315, 0.13409996608400476, 0.12862613575316484, 0.11907016274300641, 0.10649322098528025, 0.09214628161063843, 0.08561032186586814, 0.08194120218001011, 0.0811618444653357, 0.08049320130510296, 0.07977684117637374, 0.07277800134663526, 0.0708353227962224, 0.07067602202174772, 0.06976258783125466, 0.06634530228217983, 0.06322232364202662, 0.06322090154945581, 0.06289596277964993, 0.06149090076405361, 0.06050821759755998, 0.058831519684985345, 0.05762318703291758, 0.05676014452040601, 0.055853509021861925, 0.05518017282950449, 0.0544766833802548, 0.05387141021679831, 0.05309676005317332, 0.05241070031981998, 0.052023287162046294, 0.05003592431078108, 0.04839550757959277]\n",
      "Row 20 - Column Numbers: [77 21  1 17 83 85  0 15 91 87  2 11 19 12 79  4 16  5 22  3 10 64 78 13\n",
      " 18 61  8 90 31 56 24 46 14 30 92 74 68 34 73 33 42 44 43], MI Values: [0.6456828762580988, 0.5615054795942642, 0.5324618722588088, 0.49342669682830653, 0.4589017533899522, 0.42552426145736355, 0.4190235175463517, 0.3684773490976534, 0.3510509439994527, 0.3260490569519252, 0.26984073230595484, 0.21618413086183885, 0.20764739795544962, 0.190496506019743, 0.18041597931931808, 0.17593949417666988, 0.1704438750637216, 0.16974306927085436, 0.1497647957772532, 0.14918195632018527, 0.13028693835191607, 0.11253209164347666, 0.11158401518017502, 0.10347968403017305, 0.10281992390539951, 0.10190813419336298, 0.09860668116430649, 0.08732179357987757, 0.0842263209541052, 0.0828616535343425, 0.08129397459731802, 0.07862828607228867, 0.0768148676108753, 0.07673835654706895, 0.07064869314149558, 0.06733550911625219, 0.0667893192001614, 0.06677633392818816, 0.06621492860686207, 0.06372475882601236, 0.06355486571293412, 0.061150149623385275, 0.060827899523522966]\n",
      "Row 21 - Column Numbers: [17 83 20 15  1 19  0 16 77 85 22  2 91 18 87 11 12 73  4  5 79 90  3 92\n",
      " 10 78  8 42 61 64 56  7 46 31 68 13 57 43 62 44 35 52 26], MI Values: [1.0216176230190834, 0.7488876659638635, 0.5615054795942669, 0.48722604389986657, 0.4023069759074396, 0.3588428833857771, 0.33215728219305163, 0.2854168868564999, 0.28331594629221524, 0.2688208314872229, 0.22456476967975902, 0.2125857191397058, 0.2086854981064592, 0.19869503398736654, 0.18708052814614362, 0.1761220035865394, 0.14702536981806258, 0.14619238110757227, 0.144408327527505, 0.142083257529535, 0.13959981733842852, 0.12517520234618917, 0.12006037445413664, 0.1117978672601394, 0.10815686636048305, 0.10268663613005469, 0.09797349325439786, 0.09722563185672684, 0.09520585153422978, 0.09236995631917555, 0.09187841023316423, 0.09121449964563855, 0.08964547025689651, 0.08819779567887132, 0.08274897552593963, 0.08274041805651944, 0.08110178494543518, 0.07911198418960996, 0.07348744391152273, 0.06846944162919932, 0.06815788789081711, 0.06802973139084845, 0.06522771175571496]\n",
      "Row 22 - Column Numbers: [15 16 18 19 21 73 17 20 83 85 91 77  1 87 23  0 11  2 56 10 79 13 57  5\n",
      " 42 32 61  8  3 74 64 34 70 24 78 63 68 90 43 72 35 53 62], MI Values: [0.4227473405113029, 0.3870402149910266, 0.32015585431856763, 0.23610468619476155, 0.22456476967976258, 0.19668419399470238, 0.15874125412953077, 0.14976479577725232, 0.14502492612060003, 0.11578837068495584, 0.1063924866874304, 0.10378871318925587, 0.09452496762458118, 0.08969080820395181, 0.07632786384865842, 0.07596636122032496, 0.06893504056359401, 0.06328881794610464, 0.06098127462148906, 0.05727822396969895, 0.054970003136741497, 0.051323177882335536, 0.05062976172811151, 0.050465669694910176, 0.05027063548670352, 0.049760788383411025, 0.047233204160109565, 0.04542566347070398, 0.04382301867003058, 0.04368901502755573, 0.04358675196225281, 0.042850022291132994, 0.04278545874037132, 0.04263132941212078, 0.04245227781570726, 0.04240480524732426, 0.04177115423568889, 0.04146334279107311, 0.041258234396297944, 0.04113645596182369, 0.040745425400359636, 0.040726001607573004, 0.040577710389676724]\n",
      "Row 23 - Column Numbers: [64 57 87 44 10  6 24 91 85 61  8  4 22 63 15  7 16  0 11 17 92  2 12 21\n",
      " 14 55 47  1 74 56  5 13 79 62  9 31 25 77 26 83 32 20 46], MI Values: [0.1238287448328963, 0.11007546217848985, 0.10279703918589878, 0.09985139888774786, 0.09526800567615457, 0.09453623691659319, 0.09442643580457855, 0.092779592553069, 0.08797109748794085, 0.08578580449603201, 0.08474539401989523, 0.07907845045093076, 0.07632786384865975, 0.07257144170704688, 0.07129603115169214, 0.06816078423614158, 0.06694340591739678, 0.06631267495817283, 0.06614162517793609, 0.06462454817737662, 0.06377017167667276, 0.06238952944812581, 0.06198182224754323, 0.06102500139047695, 0.05852404069351369, 0.058494817456543835, 0.057048950299178, 0.056427588090688374, 0.05575798124214959, 0.05424612918912608, 0.053944258296575676, 0.053394179519995255, 0.05090816537458753, 0.049627949735287835, 0.04914461256289693, 0.04830377167633948, 0.0479154062061089, 0.047404493128977876, 0.04534942266509967, 0.044620281399040174, 0.04423650621570019, 0.04399862638296703, 0.04319511791377284]\n",
      "Row 24 - Column Numbers: [87 25 85 10 11  8 26 91 23 77 64 12 20  4 14 63 61  1 56  0 15 46  2 44\n",
      "  9 27 21 30 75 32 79 62  5 31  3 78 68 60 22 34 16 17  6], MI Values: [0.12664131656206834, 0.12184764568086237, 0.11662871191984614, 0.1126861641925645, 0.10784355126935541, 0.10209066826928304, 0.09988104072929094, 0.09541744286183551, 0.09442643580457988, 0.08554737930800638, 0.08433207450633073, 0.08382766133586106, 0.08129397459731003, 0.07926789356000175, 0.07873666169272342, 0.07871775795832381, 0.07660849160601568, 0.07658487183691687, 0.06753872107738834, 0.06575943129935258, 0.06508609948716693, 0.06378754370319006, 0.06196951220919278, 0.05575375327102261, 0.055562199294558745, 0.05318120567191542, 0.05262117138877809, 0.05116230585414172, 0.05083179402329918, 0.049254453905052564, 0.04814401145309244, 0.04665448807793737, 0.04619072869628571, 0.0458151748730149, 0.044434685459121326, 0.043901624829374875, 0.04323480914173228, 0.04291271895550075, 0.04263132941212122, 0.04238722505216597, 0.042346546936791185, 0.041908005215020694, 0.04135516870134959]\n",
      "Row 25 - Column Numbers: [26  8 24 10 14 13  9 27 64 20 32 30 63 11 21 12 74 33 17 56 23 85 91 15\n",
      " 87 28 61 89 34 38  1 40 43 52 36 80 35 37 41 83 86 88 16], MI Values: [0.22448983276060552, 0.16233774299458315, 0.12184764568086015, 0.11291908175479026, 0.10808026792929493, 0.07985596483401203, 0.07942615953296661, 0.06742082698712792, 0.057769002718598195, 0.05586583465511197, 0.054965263207836124, 0.05443370142787174, 0.053776458305056174, 0.05343401191718833, 0.05308655380792704, 0.05045720325549752, 0.05034647749383048, 0.04992384501594582, 0.0492451891629031, 0.04834454363245477, 0.0479154062061089, 0.047684160601328074, 0.047297099255485975, 0.04577736523629383, 0.0457726787254078, 0.045771120375120766, 0.04566515411493954, 0.043420484714855156, 0.043385152301504526, 0.04150956737140632, 0.04116356278905453, 0.040902739036422275, 0.039271536657020434, 0.03872861083601631, 0.03870735899101785, 0.03823640170302056, 0.03689051731253823, 0.03648924728638114, 0.03594012672179936, 0.03543675472183061, 0.0353375347334941, 0.033978841582392505, 0.033213377245050246]\n",
      "Row 26 - Column Numbers: [ 8 25  9 14 10 27 24 64 13 30 32 21 11 17 20 91 74 85 87 33 34 46  6 43\n",
      " 15 36 35  1 12 63 23 83 41 80 31 72 56 86 84 52 37 28 61], MI Values: [0.25245404084178746, 0.22448983276060552, 0.1888349353819665, 0.1709314398188191, 0.15950455852051704, 0.10013893815186226, 0.09988104072928916, 0.08361194904788949, 0.07181363072768843, 0.06658416020495395, 0.06642109881221003, 0.06522771175571318, 0.06133706698861552, 0.060864275396509626, 0.06030983748989538, 0.05855558719449405, 0.058118774994220246, 0.05502112683089955, 0.054955567957541085, 0.0548802691847472, 0.05446576296866468, 0.05385131209205429, 0.05140858603128562, 0.04892271442605356, 0.048556550337056414, 0.047843331021867996, 0.04718698058252446, 0.04666834102500239, 0.04641197580127887, 0.04620099613250428, 0.045349422665099226, 0.045142856596432246, 0.04487870650962478, 0.04102053350114243, 0.03975973670425059, 0.039456412404046404, 0.03926146380477791, 0.03883323698171193, 0.038101405951134204, 0.03717014915810957, 0.03702701389699303, 0.03678714727422072, 0.036512909297854]\n",
      "Row 27 - Column Numbers: [65 64 14 46 45 26  8 10 25  6 84  9 12 38 11 13 24 53 74  7 44 21 63 85\n",
      " 47 91 62  0 86  4  3  5 31 43 61 87 76 20 80  1 77 37 29], MI Values: [0.6065603894953897, 0.18682361749818366, 0.1515567092969663, 0.13632308186498676, 0.10364354834176126, 0.10013893815186492, 0.09968544490658893, 0.07918640410680577, 0.06742082698712792, 0.06278134191716767, 0.06038028586904787, 0.06024993017772662, 0.05954908040441431, 0.05566701959818321, 0.05365543785469562, 0.05349787902327563, 0.053181205671913645, 0.05121607804495909, 0.05107317746817763, 0.050533102412405384, 0.05024731173365815, 0.04849977979742892, 0.04791989593709012, 0.04765153600392935, 0.04741748068507423, 0.04718827956837135, 0.04704704797821968, 0.046555580550760034, 0.045963625687851284, 0.0458714770575126, 0.04550892471748291, 0.04427143864075678, 0.044267360807431544, 0.04422157037556218, 0.044030392965271226, 0.043659800788907965, 0.04331808077932564, 0.04308091954790427, 0.04297197397555763, 0.042923144439217076, 0.04277349385328666, 0.04153155742864545, 0.040719138411590805]\n",
      "Row 28 - Column Numbers: [89 38 88 37 40 86 29 41 39 36 33 74 30 34 35 43 32 31 56 78  5 44 12 80\n",
      " 79  2 13 42  1 11 10  4 62  6  8 68 90 64 52 17  0 54 61], MI Values: [1.0046755344608442, 0.8668221841314496, 0.7614158768816583, 0.7435037784407115, 0.7401508914135695, 0.7092838503040948, 0.6969500914396249, 0.6683242642188869, 0.6188553437563042, 0.5887599355969604, 0.573378254007582, 0.4637692211865332, 0.44110042693832696, 0.43990166348400894, 0.3542576214733666, 0.3130926126664333, 0.3038339983430083, 0.1631475034181804, 0.14153000235829616, 0.10874080446091217, 0.09875071075037845, 0.0973992316948431, 0.09501229751970275, 0.09424947908653536, 0.09026690572979579, 0.08247104503342673, 0.08202421217934486, 0.08020834452426495, 0.07617110541908723, 0.0751808599245587, 0.07299784236684648, 0.07194026557628508, 0.07174551471409618, 0.06638342779498885, 0.06518271250260632, 0.06489586595952179, 0.0643523399002186, 0.06270446068020075, 0.05772311949448383, 0.056954572674678516, 0.05644466945878257, 0.05541299819598944, 0.05407556787339285]\n",
      "Row 29 - Column Numbers: [37 86 38 89 39 28 40 36 88 74 33 41 43 35 30 34 31 56 32  5 78 79 44 80\n",
      "  2 12  4 90  1  0 87 42 46 77  3 14 64 11 85 62 63 57 13], MI Values: [1.124331483930141, 0.9904397714916939, 0.8561076404645682, 0.7571541803206943, 0.7394482075767632, 0.6969500914396267, 0.6243050233062002, 0.6127287729060686, 0.5162986988948424, 0.5004203013385551, 0.4839723248105665, 0.44277394507430223, 0.3862199704096003, 0.3611089233159852, 0.3044944524915385, 0.30210464330076015, 0.20191448281292157, 0.171307375513706, 0.1557361930389609, 0.11470618022646129, 0.1142833513780932, 0.10420208049496082, 0.10392751587923588, 0.09785175941231206, 0.09469648273846332, 0.08955815291429925, 0.07666467817423417, 0.07002944857802351, 0.06654779481397011, 0.06576826886766884, 0.06531253837083639, 0.06416664878429135, 0.06302637459570448, 0.06065012243418977, 0.06048824178377199, 0.058701476590528046, 0.05802769428221577, 0.049098105017652216, 0.04872740090602523, 0.04751490159093841, 0.04718646229756551, 0.047177310303764486, 0.04510718141365366]\n",
      "Row 30 - Column Numbers: [33 35 74 32 34 43 28 31 36 86 89 40 37 38 41 88 29 39 78 79  2 44  5 12\n",
      " 80  4 42  1  0 52 13  3 64 90 10 20 11  8 87 56 85 26 77], MI Values: [0.8392067051587295, 0.6637829223064537, 0.6484729630309518, 0.5649484715892896, 0.5416346036080313, 0.4933942675879779, 0.4411004269383261, 0.4130016958463507, 0.38187736651662174, 0.3742297238726069, 0.3717084490392537, 0.3527990507831582, 0.33036985608766933, 0.32508215731131695, 0.315969342937767, 0.3120618690279784, 0.3044944524915376, 0.2926134592339231, 0.245510624027526, 0.1906085060616709, 0.15876062884895248, 0.15101976681000995, 0.14845254677791608, 0.1373297433787659, 0.13577620649841027, 0.1241793539299092, 0.11531395362702757, 0.1150059734774116, 0.10962686909974106, 0.10641737910058513, 0.09258617061154961, 0.08507553529173606, 0.08219023403697623, 0.07857807032348152, 0.07776056152449762, 0.0767383565470654, 0.0758563574615021, 0.07521271366405902, 0.07367325277221859, 0.06707550157230102, 0.06691537715915796, 0.06658416020495572, 0.06275013897899484]\n",
      "Row 31 - Column Numbers: [43 78 35 30 33 44 74 79  2  5 36 42 86  4 37 29 34 80 32 38 28  0  1 89\n",
      " 39  3 12 40 41 88 11 87 85 13 17 21 10 91 20 83 77 64 90], MI Values: [0.8121927311946013, 0.7638100129208842, 0.7457506706593477, 0.41300169584634716, 0.40367630493282647, 0.3834036968008201, 0.36859551535020874, 0.3469763013969196, 0.288579169234902, 0.2760329582147696, 0.2539363056818278, 0.2480981515670253, 0.22807412650458492, 0.22779194586134022, 0.21452991980362057, 0.20191448281292157, 0.1870476252617994, 0.18479080672561743, 0.17115190570613592, 0.167611070828948, 0.16314750341817774, 0.16211076425159288, 0.16121744315732478, 0.15421271891570942, 0.1526762354992739, 0.15053120343368143, 0.14662969753092536, 0.1369994315782277, 0.12987048179875593, 0.1178467066606661, 0.11341149652601867, 0.10896037047705764, 0.1060824704994614, 0.10045734833963404, 0.09616040667204917, 0.08819779567887043, 0.08544174110632508, 0.08539580505605926, 0.0842263209541061, 0.08252825085347038, 0.07208828414576374, 0.06851019554836757, 0.06594386443863964]\n",
      "Row 32 - Column Numbers: [34 30 52 33 28 88 40 74 35 89 41 86 38 43 39 37 36 31 29 44 54 78  8 79\n",
      "  5  2  4  9 62 10 12 42  0  6 80 64  1 26 87 61 90 13  3], MI Values: [0.6589132113122833, 0.5649484715892905, 0.5366720434860506, 0.31429643099880256, 0.3038339983430083, 0.2746754336314945, 0.264343537327707, 0.254749734631722, 0.24376381697460836, 0.23990089864081465, 0.2315338746347546, 0.2027410833178278, 0.197909157760205, 0.19253106758836758, 0.1831205200479813, 0.17952444982802795, 0.17752977924984759, 0.1711519057061368, 0.15573619303895825, 0.12104168683611505, 0.11793416791373534, 0.1155347151347117, 0.10441158737263923, 0.09567236193821138, 0.09331795784564623, 0.09002264997452247, 0.087346193152265, 0.08690570143561605, 0.08212300251017712, 0.08091774681887465, 0.07909381487392952, 0.07802938607998389, 0.07772961987272353, 0.0772793483026124, 0.07650826602535332, 0.07345476684191166, 0.07062525451403978, 0.06642109881221536, 0.06429935007831045, 0.06347776301673225, 0.06345428849975132, 0.06200434845199787, 0.061265136171211765]\n",
      "Row 33 - Column Numbers: [74 30 36 35 43 86 28 37 89 38 29 40 34 39 41 88 31 32 78  5 79  2 44 80\n",
      " 12  4 42  1 56  0  3 13 85 64 87 11 90 10  8 52 77 61 91], MI Values: [1.1137204124807507, 0.8392067051587295, 0.7259968303690219, 0.676225408758059, 0.6277452858407466, 0.6078933190308362, 0.5733782540075802, 0.5576286905708168, 0.5364183007679388, 0.49716674763380553, 0.4839723248105665, 0.4791060933274043, 0.45408232882174193, 0.4358859922207907, 0.4346502711337248, 0.4047557520194287, 0.40367630493282647, 0.31429643099880256, 0.21439117181920508, 0.1707685245371131, 0.1675397929716098, 0.1580992185002481, 0.1558944425895863, 0.1513697471049289, 0.13072864694939046, 0.12068089113273839, 0.11403454812488523, 0.10934085523256698, 0.10568767232683207, 0.09664578770578203, 0.09072061229028083, 0.08878636983820609, 0.0853957938074732, 0.08444826940177563, 0.0822160314308702, 0.08191762067726316, 0.07829650162065782, 0.07794974091576812, 0.07565747720513549, 0.0721596876850441, 0.06870563600714075, 0.06766819910745436, 0.06454231972101443]\n",
      "Row 34 - Column Numbers: [32 41 40 89 30 88 33 28 38 39 74 86 37 36 29 35 43 31 78 52 79  2 12 80\n",
      "  5  4  8 44  1 56  0 10 42  3 13 11  9 85 90 14 20 87 91], MI Values: [0.6589132113122842, 0.6479726613644816, 0.6043685240765004, 0.5628237492307457, 0.5416346036080313, 0.521645640678436, 0.45408232882174193, 0.43990166348400983, 0.4368469340751924, 0.39158474017250366, 0.3551015296305442, 0.3436127338197732, 0.3342616147154853, 0.30793458819287167, 0.30210464330076015, 0.2547895016786663, 0.25147509845387006, 0.18704762526179852, 0.1318444892478734, 0.12773246250446846, 0.12182153097619519, 0.11747560005254787, 0.09993696526051377, 0.09689650292456253, 0.09670112680552911, 0.09367692420841855, 0.09279000891834333, 0.09093985620778966, 0.09049841174829432, 0.08918579292805706, 0.08750394746818113, 0.08709868991881464, 0.08002420593659476, 0.07711971317009425, 0.07495306478075747, 0.07298015929327839, 0.0685825322136786, 0.06771394965493194, 0.06748508102814021, 0.06725286085851323, 0.06677633392818727, 0.06352632300524341, 0.05979450877373882]\n",
      "Row 35 - Column Numbers: [43 31 33 30 74 36 86 37 29 78 28 38 89 44 39 34 40 32 88 79 80 41  5  2\n",
      " 42  4 12  1  0  3 11 13 56 85 87 90 10 64 17 21 83 15 91], MI Values: [1.3860244468954068, 0.7457506706593469, 0.676225408758059, 0.6637829223064564, 0.6417520640136267, 0.41003162791165604, 0.39846097278793113, 0.37245697314779047, 0.36110892331598254, 0.36035661286731724, 0.3542576214733648, 0.28812166153925034, 0.28455742734958633, 0.2744838416218025, 0.25908379307944696, 0.2547895016786681, 0.2444710266515937, 0.24376381697461103, 0.2113827569500044, 0.20596754398312012, 0.2032245059398745, 0.20034425775401932, 0.1956334739924417, 0.1870192028603448, 0.18522516757732976, 0.13262659195667936, 0.1285549123325911, 0.11642248941903688, 0.11361591888716038, 0.1016623748148815, 0.09674046912721845, 0.095142371568528, 0.0801836035458896, 0.07727436282669675, 0.07446311599579492, 0.07216427126333969, 0.07091448732899774, 0.06950218448865986, 0.06903264964802514, 0.06815788789081711, 0.06455351051612634, 0.06380756444093993, 0.05848415311997446]\n",
      "Row 36 - Column Numbers: [86 37 33 29 74 28 89 41 38 40 39 43 35 88 30 34 31  5 32 56 78 79 80 44\n",
      "  2 12  4 42  1  3 90 10  0 13 72 14 77 64 87 57 70 46  6], MI Values: [1.0233770024292177, 0.8615166885581989, 0.7259968303690219, 0.6127287729060713, 0.6090092895887054, 0.5887599355969613, 0.5752000583378694, 0.5713794920745894, 0.5355098016260644, 0.47454758830574484, 0.4665352887983394, 0.4335648849167999, 0.41003162791165515, 0.39112029603754017, 0.38187736651661996, 0.30793458819287167, 0.2539363056818287, 0.20674579006625216, 0.1775297792498458, 0.15081603715863867, 0.14656523125808896, 0.11619314258747515, 0.11571876599131148, 0.1145234869763252, 0.10960845386111995, 0.0970948434370289, 0.0877144141798194, 0.07775809933113642, 0.07458627225738823, 0.07188834325973659, 0.06954945457795603, 0.06702934232361812, 0.06656537960473763, 0.0637980214953684, 0.06265064870037129, 0.06166886568276819, 0.06121318706422585, 0.06076563582838368, 0.0603698282500984, 0.0600022474540296, 0.05999309743629677, 0.059587362304820424, 0.05838254740343718]\n",
      "Row 37 - Column Numbers: [86 29 36 38 89 28 39 40 33 74 88 41 43 35 56 34 30 31 32  5 78 79 44 80\n",
      " 12  2  4 90  1 42 87 46  3  0 14 77 57 64 75 10 81 85 72], MI Values: [1.45827221487633, 1.1243314839301428, 0.8615166885582006, 0.8339552318828192, 0.75725247965641, 0.7435037784407115, 0.6894104126018572, 0.6269405732545383, 0.557628690570815, 0.5514988683591895, 0.5065004040074994, 0.4944806219210722, 0.4048082990644746, 0.37245697314779047, 0.35940226604219117, 0.3342616147154871, 0.3303698560876711, 0.21452991980362324, 0.17952444982802884, 0.12301925557245674, 0.1229936336440689, 0.11167013683338922, 0.10660787110909098, 0.09822950179437395, 0.09592473158963699, 0.09141368395878491, 0.07514331037207178, 0.07091755529673804, 0.06883285800983607, 0.06871969299735081, 0.066765545099301, 0.06572403954205441, 0.06558274587026869, 0.06455866987752579, 0.06416649947375319, 0.06138718973277957, 0.05958381308008942, 0.0586839187321484, 0.05770927457102015, 0.05541200876063623, 0.0543002203644134, 0.053567885640179114, 0.053098326138301566]\n",
      "Row 38 - Column Numbers: [89 39 40 28 29 37 88 86 41 36 33 74 34 30 43 35 32 31 56 78  5 79 44  2\n",
      " 80 12  4 90 42 87 64 10  3  0 46 54 27 63  1 55 61 52 81], MI Values: [1.2419280927673926, 0.9495031915623935, 0.9353087992452069, 0.8668221841314478, 0.8561076404645709, 0.8339552318828174, 0.7568375359220987, 0.7540596341394155, 0.6590139783160547, 0.5355098016260609, 0.49716674763380464, 0.4638361476100483, 0.4368469340751897, 0.32508215731131607, 0.2970750486302043, 0.28812166153925034, 0.19790915776020768, 0.16761107082894533, 0.14324753303636406, 0.10392867184476451, 0.10350223849689133, 0.09301615106454886, 0.08916423701914233, 0.08794009077204823, 0.08653427377214928, 0.08621577314512141, 0.07857614620487752, 0.07291292443408093, 0.06775644455948626, 0.06587368807998661, 0.06444153292271437, 0.06239411896947633, 0.0611391661707783, 0.05890813572238418, 0.05743119615494585, 0.05657172017433254, 0.0556670195981841, 0.052999594620209756, 0.05251122766241956, 0.05144646558632271, 0.050525831605085614, 0.05046119874021926, 0.050427398365081366]\n",
      "Row 39 - Column Numbers: [89 40 38 88 29 37 86 28 41 36 33 74 34 30 43 35 32 31 56 78 79  5  2 44\n",
      " 12  4 80 90 46 64 42  0  3  1 87 54 57 10 85 81 11 75 13], MI Values: [1.0535035116401659, 0.980751027799518, 0.9495031915623944, 0.7414381495833338, 0.7394482075767623, 0.6894104126018581, 0.6322229406595952, 0.6188553437562998, 0.597892725921354, 0.46653528879833495, 0.4358859922207863, 0.41880685619855296, 0.3915847401725019, 0.29261345923392224, 0.2629228824826715, 0.2590837930794496, 0.18312052004798485, 0.15267623549927567, 0.11061737849190223, 0.10303541936903038, 0.10121071598448683, 0.10050281527196514, 0.09409837181553016, 0.09268755609898616, 0.09122469199042627, 0.07574221883219856, 0.07038469791400459, 0.06777425757345945, 0.06718928231977817, 0.06637371235615408, 0.06470157204124849, 0.06376207874312012, 0.06157433149594027, 0.059317843630458, 0.056927475789509074, 0.0553570174716711, 0.050475458950668184, 0.049665682066896366, 0.048873507505192926, 0.048724267224924844, 0.048532049612547645, 0.045653657389332025, 0.045387402202069715]\n",
      "Row 40 - Column Numbers: [88 89 39 38 41 28 37 29 34 86 33 36 74 30 32 35 43 31 56 79 78  5 12  2\n",
      " 90 80 44  4 64 46 10 42 11  0 54  3 87 62 52  8  1 61 13], MI Values: [1.358468758232667, 1.2392621662048944, 0.9807510277995188, 0.935308799245206, 0.926520358369948, 0.7401508914135668, 0.6269405732545383, 0.624305023306202, 0.6043685240764987, 0.5904546129889008, 0.4791060933274034, 0.47454758830574484, 0.42293019416571376, 0.3527990507831582, 0.2643435373277079, 0.24447102665159282, 0.24139738990497683, 0.13699943157822414, 0.10838563263965639, 0.1029822194696477, 0.09964875862896427, 0.09746128685535993, 0.09185969685609141, 0.08826839034197231, 0.08755455049272953, 0.08752252944643946, 0.08181196297427373, 0.07604174073333958, 0.072912801172893, 0.07131829013591684, 0.06301067329213339, 0.06159199509503921, 0.0600744169282601, 0.05966325856990995, 0.05887006365191372, 0.05721261367801134, 0.05676698284365411, 0.05477366448826615, 0.054719591158505665, 0.0521148561565834, 0.05184786967249444, 0.05173422697187924, 0.050382935130099504]\n",
      "Row 41 - Column Numbers: [40 89 88 28 38 34 39 36 37 86 29 33 74 30 32 43 35 31 56 78 79  5 44  2\n",
      " 80 12 90 62 10  0  1  3 42  4 61 64 92 11 70  6  8 52 13], MI Values: [0.9265203583699506, 0.9100181021852727, 0.8687228214668874, 0.6683242642188896, 0.6590139783160538, 0.6479726613644816, 0.5978927259213549, 0.5713794920745912, 0.4944806219210731, 0.47456031717445235, 0.44277394507429957, 0.4346502711337239, 0.33199699186004406, 0.3159693429377697, 0.23153387463475372, 0.21422375662965543, 0.20034425775401843, 0.1298704817987586, 0.11875744932887322, 0.0926509060956926, 0.08676758111423233, 0.086057783978851, 0.08262255635642912, 0.07942866688885086, 0.0785488622631787, 0.0742530711565692, 0.07307672025710232, 0.06941263844280599, 0.06936075480536719, 0.06665335877299139, 0.06410363270210784, 0.06306413363039987, 0.06207958706935557, 0.05954608451087129, 0.0593461118278249, 0.057899646129423665, 0.05389698575662916, 0.053384856694632, 0.05325141402769873, 0.05243412828986749, 0.052078907698307475, 0.05177082062384475, 0.050887404336976694]\n",
      "Row 42 - Column Numbers: [90 31 44 43 35 78 80 30 92 33 21  5  1 74  2 79 12  0 17 83 28 34 85 32\n",
      " 36 11 86 91 37 38 16  4 15 10 39 29 20 19 87 89 13 41 40], MI Values: [0.5736361560630607, 0.24809815156702442, 0.237501584176659, 0.2123646632862819, 0.18522516757733065, 0.17401757617932745, 0.14508216519352857, 0.11531395362702668, 0.11438741669921182, 0.11403454812488256, 0.09722563185672684, 0.09376382987344112, 0.09265639520815316, 0.09219897198964677, 0.09190658625377246, 0.09102336506577036, 0.08912140713055283, 0.08872664637914252, 0.08466458683253641, 0.08290682477634803, 0.08020834452426406, 0.08002420593659121, 0.07969793759561306, 0.07802938607998477, 0.07775809933113642, 0.07587529502253965, 0.0754741707644273, 0.06881214952706838, 0.06871969299735348, 0.06775644455948715, 0.06750837136584042, 0.06712048581871777, 0.06699419564638998, 0.06547249101527441, 0.06470157204125115, 0.06416664878429224, 0.06355486571293678, 0.0632209015494567, 0.0630884431737817, 0.06261691628512, 0.06240830984967349, 0.06207958706935468, 0.0615919950950401]\n",
      "Row 43 - Column Numbers: [35 31 33 74 30 36 86 37 29 78 28 44 38 89 39 34 40 80 41 42  5 79 88 32\n",
      "  2 12  0  4  1  3 11 13 87 85 56 83 21 17 90 10 91 77 64], MI Values: [1.386024446895405, 0.8121927311945987, 0.6277452858407475, 0.6243039700489881, 0.4933942675879788, 0.433564884916799, 0.4240950333084843, 0.4048082990644737, 0.38621997040959855, 0.370397111365631, 0.3130926126664342, 0.30395671539799096, 0.2970750486302043, 0.28802774608809134, 0.2629228824826706, 0.25147509845387095, 0.24139738990497772, 0.2276321837680122, 0.21422375662965365, 0.21236466328628278, 0.20819529046906204, 0.20739130754119195, 0.20626412498042956, 0.1925310675883667, 0.18681968571483676, 0.14156956810137, 0.1358699397958949, 0.1316783860928359, 0.12913107009156466, 0.1038170751558507, 0.09481730555192946, 0.09195467760152898, 0.08755593140089069, 0.08744850763647793, 0.08170555433368687, 0.081560766459293, 0.07911198418961085, 0.07861749607301682, 0.07721049556759585, 0.07182439963604015, 0.07147186167010044, 0.06546454180161465, 0.06421723199729623]\n",
      "Row 44 - Column Numbers: [31 43 78 35  4 42 33 79 30  2 74  5 54  0 64 32 36 80 86 37 29 87 23 88\n",
      "  1 28 39 89 34  3 38 13 11 12 10 85 46 41 40 63 91 62  6], MI Values: [0.38340369680082365, 0.3039567153979892, 0.2940959242977499, 0.27448384162180073, 0.2577169657460203, 0.23750158417665634, 0.15589444258958807, 0.1535208253346898, 0.15101976681000817, 0.14614605566374905, 0.13751208245379942, 0.1330855289284827, 0.13216267787018499, 0.12631372813240205, 0.12575424005177993, 0.12104168683611682, 0.11452348697632786, 0.11196280971917094, 0.10936129874317668, 0.10660787110909098, 0.10392751587923676, 0.10044717697415884, 0.09985139888775052, 0.09784483548609302, 0.09756958090355994, 0.0973992316948431, 0.09268755609898616, 0.09241113709100457, 0.09093985620779232, 0.0903461896754747, 0.08916423701913878, 0.0882487868884656, 0.08789263097170785, 0.0865487450581588, 0.08386645043593699, 0.08318123056251459, 0.08302480760550157, 0.08262255635642735, 0.08181196297427551, 0.08074364625578223, 0.07356394424112711, 0.07306242342033098, 0.07123886187653294]\n",
      "Row 45 - Column Numbers: [65 60 66 76 64 63 69 27 84 53 54  6 75 62 57 70 81 12 46 61 11 50 72 87\n",
      "  1 10 85 52 49 68 13 77  3 48 21 24 32 90 91  8 30 79 15], MI Values: [0.3355390992669385, 0.24105785735212137, 0.16669975622521527, 0.14089157380955708, 0.13477024068243892, 0.11692650889904499, 0.10868038934784607, 0.10364354834175771, 0.10150362847124583, 0.09056761307301286, 0.0798331274015025, 0.07607959090818639, 0.07550304956704501, 0.07129070394238113, 0.06353587781859105, 0.06252081423776445, 0.05993439653997168, 0.05696539251436761, 0.05614165957912931, 0.05305353245500477, 0.05289097853795344, 0.05163697152796942, 0.05126811930396258, 0.049018668863451076, 0.048759179040770206, 0.04826951163990145, 0.04548841097074785, 0.045170627201460256, 0.04515557347533239, 0.04505498244851758, 0.04468423892141704, 0.04437075080106645, 0.04344271363863772, 0.042062378026346714, 0.041189709960936405, 0.04052516260945005, 0.04034464006210747, 0.04008368476259694, 0.039929482136464856, 0.039675854506701747, 0.039107723692991314, 0.038854237195490526, 0.038161379909507964]\n",
      "Row 46 - Column Numbers: [64 51 55 59 48 68 47 58 61 87 75 49 72 56 54 84 27 70 67  6 74 57 17 69\n",
      " 81 14 21 50 77 63 44 52 85  1 19 76 20  4  0 79 62  2 40], MI Values: [1.1094691017199603, 0.36567183873432274, 0.3141727399115952, 0.23992709365254683, 0.2171439106790931, 0.19852690016740127, 0.18923509125775695, 0.1858984961031256, 0.17267857439960022, 0.16549438774061187, 0.15983167864594883, 0.15828858721216044, 0.15559450174685807, 0.1460850846009656, 0.14012136027135202, 0.13751725928655478, 0.13632308186498943, 0.1328114960531792, 0.13279522094755158, 0.13099684473508688, 0.11736212179504424, 0.11368720902898488, 0.11280369881762642, 0.105422623025202, 0.10140282553967683, 0.09266115822732957, 0.08964547025689651, 0.08911598382671393, 0.08487347419103042, 0.08355750196952805, 0.08302480760550068, 0.08232030940720492, 0.08171791357507097, 0.08010342629738698, 0.07977684117637374, 0.07963991449703212, 0.07862828607228867, 0.07856401142112102, 0.07681250087322677, 0.07650530330583649, 0.07403272493206359, 0.07325788085011453, 0.07131829013591773]\n",
      "Row 47 - Column Numbers: [48 55 82 49 51 64 46 61 56 50 14 57 87 54 63 75 67 70 69  6 72 74 68 23\n",
      "  4 52 20 59 38 27 85 84 11 81 33 92 89 60 41  7 36 77 19], MI Values: [0.4249124097885648, 0.4187425231559816, 0.3602265067790995, 0.2776897644328633, 0.24912743330867393, 0.1987447932521178, 0.18923509125775695, 0.15384874665912562, 0.10368137158256019, 0.09785925823341302, 0.09074348902636764, 0.08687796447828866, 0.08569788060934425, 0.08001798979213337, 0.07907233827318905, 0.07403127407645904, 0.07249971148987289, 0.07068379697727956, 0.06874455994522588, 0.06549702884688635, 0.06175094572082518, 0.06009771362514993, 0.05906462224581688, 0.05704895029918333, 0.056865014508378664, 0.05682164950861601, 0.05161482461035316, 0.05139487626535377, 0.050000458629791744, 0.047417480685076896, 0.04726109720318572, 0.04708602460329292, 0.0467491462024574, 0.04656568399330041, 0.045808067196454694, 0.04460527570146677, 0.04416183571061527, 0.043961928173374076, 0.04334931626754024, 0.043171664331128845, 0.04285749863832411, 0.041651660789991496, 0.040805913716284614]\n",
      "Row 48 - Column Numbers: [49 55 47 51 46 50 64 75 68 67 69 87 61 54 58 81 59 70 56 57 63 14 52 84\n",
      "  6 73 72 91 60 66 18 45 85 11 74 21 17  4 76 38 19 32 44], MI Values: [0.553678897514204, 0.5019751647569173, 0.4249124097885639, 0.2875171464071613, 0.2171439106790931, 0.1743136297813912, 0.11110937927605313, 0.10037244122026134, 0.08934545133594263, 0.08190429469032878, 0.0736143304488408, 0.07327006385127088, 0.0721867594925314, 0.07042527416616018, 0.0687315220763578, 0.06681937537003169, 0.06642447830364517, 0.06437836072642522, 0.0635873831512015, 0.060791248768552464, 0.057609186216970976, 0.05528245353972938, 0.05372925078899371, 0.04909830573294105, 0.04808633609087387, 0.045306406824380474, 0.04489736208567496, 0.044709846969715805, 0.04357966587574236, 0.04284931649405177, 0.04283733769362197, 0.0420623780263476, 0.040772805188195704, 0.04013167977317522, 0.03986903738847314, 0.03954931815568408, 0.03897874301162396, 0.03884934604555568, 0.0387817158798871, 0.03828887823525573, 0.03729803186228775, 0.03670448581979002, 0.03666047870806732]\n",
      "Row 49 - Column Numbers: [48 55 47 50 51 75 46 69 54 64 68 81 52 61 57 67 87 63 70 56 60 84 11 14\n",
      "  6 45 13 66 58 12 59 72 10  1 79  4 77 85 32  0 74 40 36], MI Values: [0.5536788975142031, 0.30360053691119226, 0.27768976443285975, 0.2735029225169381, 0.1755926065938338, 0.16380558437787318, 0.15828858721215955, 0.09982396156077034, 0.0899951771509615, 0.08729689308508082, 0.0805251845303161, 0.07578213385519295, 0.0734512632183959, 0.07118839940287724, 0.06818162225492586, 0.06462675171117471, 0.05826597066506878, 0.05474056322253951, 0.05205162711625633, 0.04949584081348313, 0.04890714820172626, 0.047598231033918914, 0.0471786080006531, 0.04697649944513582, 0.04612338247236547, 0.04515557347533328, 0.04394002279515519, 0.0427889260255494, 0.04277730549634029, 0.041579343265056856, 0.03968935771140636, 0.03878327857790431, 0.03721262391298552, 0.03708316769882014, 0.03707875631470614, 0.03437124492900345, 0.03420072144079178, 0.03393860185339559, 0.03373647790879719, 0.03296788902954706, 0.032940030634634354, 0.03271399526283414, 0.03233124919474406]\n",
      "Row 50 - Column Numbers: [75 49 48 69 81 57 54 47 55 68 52 46 64 84 87 51 76 45 67 10 12 14 66 63\n",
      " 60  4 74 85 17 11  6 70 33 79 83  8 36 24 21  0 88 89 40], MI Values: [0.38569583316040035, 0.273502922516939, 0.1743136297813921, 0.13649561521326792, 0.13615369070630745, 0.12386611734750641, 0.11005231669100635, 0.0978592582334139, 0.09343475605257989, 0.09313301709157429, 0.08963552340153047, 0.0891159838267166, 0.08223331555010471, 0.06909627215253966, 0.0664099664637332, 0.05717803565613533, 0.05211485875131405, 0.051636971527967646, 0.049028136696537494, 0.04645372478558407, 0.046362851486650314, 0.04624367400979423, 0.04570965837784602, 0.04395880445259959, 0.04352223482917594, 0.04297224529545307, 0.04249884332512721, 0.04210332584072418, 0.041711486256092556, 0.041695189003549515, 0.04113881744298897, 0.04104741966052927, 0.04091402778420328, 0.04064421390754891, 0.04045686991204356, 0.03995848045904005, 0.03949861996272741, 0.039383429640937884, 0.038877820203155444, 0.03883494246593333, 0.038717645473936635, 0.038634738171873906, 0.03778877017396365]\n",
      "Row 51 - Column Numbers: [55 46 48 47 49 59 64 61 56 58 68 67 50 54 84 14 87  6 44 52 75 69 63 70\n",
      " 21 76 66 60 57 89  4 32 41 40 81 38 11 23 62 74 72  0 88], MI Values: [0.4918905885238507, 0.36567183873432274, 0.2875171464071622, 0.24912743330867393, 0.1755926065938347, 0.15335403151725657, 0.14408460937434686, 0.1323322880421669, 0.09492283806278046, 0.08131092018359531, 0.06392417227606728, 0.06049342127079882, 0.05717803565613444, 0.05383149700687451, 0.050444118959005024, 0.05026820068852356, 0.04809307532768603, 0.04800319914719342, 0.0474286517687057, 0.046076652615822944, 0.04517706634337504, 0.043804660168771825, 0.042590107680609, 0.03955596847245513, 0.0389668719566183, 0.03840491710777805, 0.03826743593598536, 0.03684825881094511, 0.03623578817846784, 0.0361041768011896, 0.03552228501544441, 0.034884214114486056, 0.03474350659770309, 0.034398958953260284, 0.03368774459666746, 0.03349076627149561, 0.03327235828735464, 0.03304187113566659, 0.03265504215054538, 0.03189647338370527, 0.03187888017866847, 0.03186557598989026, 0.031744992944004125]\n",
      "Row 52 - Column Numbers: [69 32 57 54 81 75 68 34 30 64 50 46 49 33 21 17 63 88  6 61 55 35 86 28\n",
      " 47 19 66  7  4 40 48 74 41 10 72 37 84 58 38 83 70 20  1], MI Values: [0.5772799725175162, 0.5366720434860497, 0.5130885687568068, 0.3225256074571332, 0.29251898737336113, 0.193542163657888, 0.12789690664174191, 0.1277324625044658, 0.10641737910058513, 0.0948475569445888, 0.0896355234015278, 0.0823203094072067, 0.07345126321839857, 0.072159687685045, 0.06802973139084934, 0.06703671873903261, 0.06405860187379542, 0.06273572137952055, 0.06139781255903909, 0.06122875212893497, 0.06013022861701689, 0.05843192812514708, 0.057757311630738606, 0.05772311949448383, 0.05682164950861601, 0.05518017282950538, 0.05499973892547416, 0.05481337747376269, 0.054736479053383746, 0.054719591158505665, 0.05372925078899371, 0.05209049250429132, 0.05177082062384297, 0.05139303267069195, 0.05111353303252564, 0.05089562323484653, 0.05067571023863948, 0.050481480883075136, 0.05046119874022281, 0.05022240658314203, 0.05011325603669903, 0.04998115622272348, 0.04960552836869159]\n",
      "Row 53 - Column Numbers: [62 63 64 45 70 85 17 10 91 72 60  4 69 87 12 46 21 11 15 27 20 19 65  1\n",
      "  5  8  0 84 83 14 16 30 18 79 22 28 73 36 66 33 44  2  9], MI Values: [0.40877114705633577, 0.10768325129662326, 0.09142254528217908, 0.09056761307301286, 0.07763014753084896, 0.07291262831419587, 0.06894645621138817, 0.06799093673704526, 0.06654270992309375, 0.06557217989953035, 0.06551159416228547, 0.06101431583981842, 0.05994221903533248, 0.05849475346295652, 0.05643638304159726, 0.05373645940673466, 0.05359496095281546, 0.05257556822858955, 0.05145699897162004, 0.0512160780449582, 0.04985185416914284, 0.047971786345549106, 0.047543267529873035, 0.04687607939115512, 0.046211483174281476, 0.045677188956067205, 0.04379488308218882, 0.04284987062613599, 0.04248356027197353, 0.042449553699675846, 0.04223363657743473, 0.04200308548928522, 0.04179825178695129, 0.04128772798638014, 0.04072600160757123, 0.04068711874009434, 0.03933717348757071, 0.03925453370539245, 0.03848324031768957, 0.03752841617132585, 0.03638983181890776, 0.03585269752426079, 0.03562342742166713]\n",
      "Row 54 - Column Numbers: [81 69 52 75 57 68 64 46 44 32 50 62 63 84 49 47 45 66 76 70 74 55 61 87\n",
      " 48 58 72  6 60 83 30 40 21 35 17 38 36 56 28 39 88 13 51], MI Values: [0.7379530571253516, 0.6991638866458327, 0.3225256074571341, 0.28357752574033057, 0.2796508865934202, 0.2576301492482225, 0.15163383746901538, 0.14012136027135202, 0.1321626778701832, 0.11793416791373446, 0.11005231669100635, 0.09996017287947367, 0.09375651906359739, 0.09285394516933021, 0.0899951771509615, 0.08001798979213337, 0.0798331274015025, 0.07892182637938827, 0.07324275519206846, 0.07247468124904266, 0.07245070956178878, 0.07176330422608057, 0.07112370577561311, 0.07067226287875972, 0.07042527416615751, 0.06899903291146714, 0.06863149347900066, 0.06777316229745178, 0.06704206660250378, 0.06494064826102708, 0.060874758017741115, 0.05887006365191105, 0.05810380963000572, 0.05748468340966095, 0.05669604970686226, 0.05657172017433165, 0.05650255737683452, 0.0557378324255442, 0.05541299819598766, 0.055357017471672876, 0.05436024408042606, 0.05430024107788167, 0.05383149700687362]\n",
      "Row 55 - Column Numbers: [48 51 47 46 49 64 59 61 50 58 68 75 67 69 56 54 81 84 63 52 57 23 87 14\n",
      " 70  0 38 73 41  1 44 37  4  6 88 72 11 86 36 89 76 62 74], MI Values: [0.5019751647569191, 0.4918905885238507, 0.4187425231559816, 0.3141727399115961, 0.30360053691119226, 0.1455355267788132, 0.10391523768986577, 0.10320434092076614, 0.09343475605257989, 0.09039691815655626, 0.08433296148313651, 0.07894014514832115, 0.07810178261121159, 0.07626677924718717, 0.07457832871124648, 0.07176330422608146, 0.0666084572296537, 0.0649658298184459, 0.06183261687680819, 0.06013022861701511, 0.05926409456159032, 0.05849481745654206, 0.05810381930205111, 0.05661782886079081, 0.05210958027079382, 0.05151582272524369, 0.05144646558632182, 0.0513717845320274, 0.04985324468381247, 0.04872468386788853, 0.04840563532307751, 0.047905222457149677, 0.047753548931313006, 0.04774985453638614, 0.046832066350649626, 0.046337404344297006, 0.04532790922027541, 0.04508240476302117, 0.04498650870497656, 0.04457765391180146, 0.044450219960144643, 0.04410009039404095, 0.04400663644262881]\n",
      "Row 56 - Column Numbers: [61 37 64 86 29 36 46 38 28 67 74 89 41 59 39 40 33 87 47 51 21 34 88 20\n",
      " 43 35  1 17 63 55  2 68 15  0  4 85 91 24 30 77 58 48 16], MI Values: [0.43147747233694655, 0.3594022660421903, 0.22066317128273738, 0.19813479850705384, 0.1713073755137069, 0.1508160371586369, 0.14608508460096736, 0.14324753303636495, 0.14153000235829616, 0.1390223315396053, 0.12763532576626613, 0.12759658270105412, 0.11875744932887322, 0.1140267649058524, 0.11061737849190578, 0.10838563263965728, 0.10568767232682852, 0.10439486730787184, 0.10368137158256019, 0.09492283806277957, 0.09187841023316512, 0.08918579292805973, 0.08812813925290719, 0.08286165353433983, 0.08170555433368776, 0.08018360354588872, 0.07992095121214593, 0.07971577342061753, 0.07711766737948622, 0.07457832871124559, 0.07436029178819847, 0.07341505483174426, 0.07262961413738722, 0.07242362723832141, 0.0720538145634535, 0.07002602366231869, 0.06996541088145225, 0.06753872107738657, 0.06707550157230013, 0.0658465345860213, 0.06480713020071249, 0.06358738315120327, 0.06331255297437988]\n",
      "Row 57 - Column Numbers: [52 69 75 54 81 63 64 68 50 46 23 72 87 17 74 61 47  6 70 21  7 84 62 49\n",
      " 73 82 92 58 45  0 19 66 56 48 36 37 55  5 44 83 60 79 77], MI Values: [0.5130885687568085, 0.4492286562322283, 0.3175403262160419, 0.2796508865934202, 0.2386747781742029, 0.19893022670047156, 0.1706591351738478, 0.12717047965108375, 0.12386611734750552, 0.113687209028984, 0.11007546217848985, 0.1056703039813307, 0.09943857195888661, 0.09928683256670379, 0.09565681017050132, 0.09358492153412179, 0.08687796447829044, 0.08592201720969239, 0.08195684550894988, 0.08110178494543341, 0.07616119177035774, 0.07392888704485934, 0.07251648801624277, 0.06818162225492586, 0.0667097043144338, 0.06659031769662516, 0.06608857489515785, 0.06605291746158404, 0.06353587781859193, 0.061740263953568686, 0.061490900764048284, 0.06146140592633831, 0.06124498359253927, 0.060791248768552464, 0.06000224745403049, 0.0595838130800912, 0.059264094561592096, 0.058399152771426266, 0.05763128744059465, 0.05711690835432748, 0.056631880706102145, 0.05618380082027041, 0.05594599871005901]\n",
      "Row 58 - Column Numbers: [46 59 67 61 64 55 75 51 81 54 48 68 57 56 44 69  0 52 88 79  5 84 73  4\n",
      " 74 40 17 87 49 70 72  7 89 47 62 38  2 43 37 50 60 77 86], MI Values: [0.1858984961031256, 0.17684958964553754, 0.1376164223851939, 0.10259159901626358, 0.09323139589981633, 0.09039691815655537, 0.08672016085400625, 0.0813109201835962, 0.07170077496787108, 0.06899903291146536, 0.06873152207635869, 0.06709058591021666, 0.06605291746158226, 0.0648071302007116, 0.06182062594159721, 0.053739795644960786, 0.05071325731351273, 0.05048148088307869, 0.04789057473566327, 0.047499732845677656, 0.04605361797762875, 0.045749765509683904, 0.04511521302719235, 0.0451146228488728, 0.04429686953990242, 0.0436866294276701, 0.042952045110664194, 0.04293717981312373, 0.04277730549634118, 0.04249097503546562, 0.041569158118069716, 0.0414072565023762, 0.04087411787997919, 0.04008012588680554, 0.03946179272307493, 0.039370558103208886, 0.03780798205952163, 0.03731442430222387, 0.03713892176412692, 0.036719401321429146, 0.03638037155973528, 0.03628517346620885, 0.03595011355909605]\n",
      "Row 59 - Column Numbers: [80 46 61 58 51 56 55 64 67 48 75 47 44 74 68 81 73 41 33 90 43 54 40 49\n",
      " 62 84 88 57 89 38 45 21 79 70 37 50 31  3 87 52 86  5 69], MI Values: [0.2465372262762342, 0.23992709365254772, 0.18600181466110133, 0.1768495896455411, 0.1533540315172539, 0.11402676490585151, 0.10391523768986577, 0.10143685103057543, 0.07292707939904464, 0.0664244783036434, 0.05458094170480976, 0.051394876265351996, 0.048036989305325406, 0.046929431867398286, 0.0468761986306756, 0.04281709288360336, 0.041442701275810734, 0.04123745905248555, 0.04109308677692969, 0.04080241822363018, 0.0405708194427179, 0.04002737117363697, 0.039970526744237844, 0.039689357711408135, 0.03937800895674659, 0.03858909846737113, 0.038104381220402495, 0.03733929606864361, 0.037336166429184026, 0.03621910618345936, 0.036194932260467994, 0.03564645785808285, 0.03530947035182841, 0.034605332803858246, 0.034270780090086106, 0.03385625356854849, 0.033688224144492906, 0.03365099687676132, 0.03359866945243972, 0.03358824636426494, 0.033156708793527834, 0.032867078986785536, 0.03252523413328934]\n",
      "Row 60 - Column Numbers: [45 66 64 75 69 76 46 54 53 84 81 57 65 63 56 70 49 61 52  6 47 62 48 50\n",
      " 24 55 10 87  1  4 68 72 51 58  8 17 85 21 11 44  0  9  2], MI Values: [0.24105785735212315, 0.14313213465555208, 0.13185070300011947, 0.08789136339985504, 0.08538631330874047, 0.07359513171289755, 0.06886160619467585, 0.067042066602502, 0.06551159416228902, 0.062130659320295045, 0.06016542150362536, 0.056631880706101256, 0.05516399778635517, 0.05208181872897821, 0.04990175130811547, 0.04924267114111114, 0.048907148201728035, 0.04565762279498298, 0.04550928202171889, 0.04432955091321311, 0.0439619281733723, 0.043609459383989524, 0.04357966587574058, 0.04352223482917683, 0.042912718955503415, 0.04289723654803357, 0.04246041760917052, 0.041422133425950136, 0.039365018633776394, 0.03811521797273176, 0.03776259020466188, 0.03735714461537043, 0.03684825881094511, 0.0363803715597415, 0.03495408974131564, 0.034779085744490956, 0.034559288190181725, 0.03360900022740143, 0.033444948836911514, 0.032907121469348155, 0.032668405905845965, 0.0324609794611499, 0.03181022364805397]\n",
      "Row 61 - Column Numbers: [56 11 64 59 46 47 51 87 12 85 55 58 20 10 21 57  1 91 63 23 17 69  2 68\n",
      "  0  4  6 24 79 77 83 48 49 54 74 67 33 15  7 84 32 14 52], MI Values: [0.43147747233694567, 0.42117961947471017, 0.30274924109928225, 0.186001814661104, 0.17267857439960288, 0.1538487466591274, 0.1323322880421669, 0.11609849133691696, 0.11175003676089812, 0.10334008173381015, 0.10320434092076347, 0.10259159901626269, 0.10190813419336209, 0.10067720955483761, 0.09520585153423244, 0.09358492153412534, 0.0919232880302312, 0.0871403303663465, 0.08651352031480286, 0.08578580449603024, 0.0845797268571502, 0.08175995345877496, 0.0807578644808169, 0.0801785495224161, 0.07987921333337233, 0.0793639777794386, 0.07748176490715064, 0.0766084916060148, 0.07561052109916311, 0.07553429240407095, 0.07310938021788527, 0.07218675949252873, 0.07118839940287724, 0.07112370577561222, 0.07004761148596383, 0.06954426713919748, 0.06766819910745347, 0.06669711932901201, 0.06659717282749611, 0.06553165111754122, 0.06347776301673225, 0.061701359771839215, 0.06122875212893497]\n",
      "Row 62 - Column Numbers: [53 63 64 54 72 32  6 70 46 21 44 57 28 45 17 41 69 85  0 87 34 30 84 33\n",
      " 74 19 40 88 12  2 37 20  4 75 11 10  1 31 89 43 36 61 23], MI Values: [0.40877114705633755, 0.1279415691665342, 0.11842971465453456, 0.09996017287947367, 0.08923240114087871, 0.08212300251017979, 0.08134777223811351, 0.07551883001699622, 0.07403272493206625, 0.07348744391152451, 0.0730624234203292, 0.07251648801624189, 0.07174551471409796, 0.07129070394237846, 0.07054503826931224, 0.0694126384428051, 0.06494490899076766, 0.06122602061900739, 0.060570066674142886, 0.06022931405757159, 0.05971560831514555, 0.058950094823821075, 0.05873104823880926, 0.05850112049998302, 0.05785656052338606, 0.057623187032919354, 0.05477366448826526, 0.05440889071046939, 0.05387677226496379, 0.05315849709315046, 0.052254464230390596, 0.05209308293447634, 0.051951533735175026, 0.05132260781067011, 0.05125901030097513, 0.05100764313742001, 0.050656346920683326, 0.05058193701037439, 0.05028273620915957, 0.05013562158198859, 0.0501292056996574, 0.05003847734903477, 0.04962794973529405]\n",
      "Row 63 - Column Numbers: [57 64 72 87 70 62  6 45 65 53 14 54  4 61 92 46 44 84  7 47 24 56 91 74\n",
      " 66  0 85 23 18 76 69 52 82 73 68 55 11 10  1 81 48 43 17], MI Values: [0.19893022670047422, 0.16474578635889525, 0.14441268837025323, 0.14223108828764808, 0.1360734064984701, 0.12794156916653598, 0.11759316702333766, 0.1169265088990441, 0.10914449076512156, 0.10768325129662504, 0.09840075284083394, 0.09375651906359561, 0.09074112883170304, 0.08651352031480108, 0.08472994154227464, 0.08355750196953071, 0.08074364625578578, 0.07977254852835358, 0.07907681278759515, 0.0790723382731855, 0.07871775795832114, 0.07711766737948711, 0.07678764806995986, 0.0765734948289225, 0.07406004109092024, 0.07375851842512127, 0.07313981190535657, 0.07257144170705043, 0.06986318552324633, 0.06663758575631373, 0.0653233908008124, 0.06405860187379808, 0.06403591879491888, 0.06298018698645702, 0.0628392353335725, 0.0618326168768073, 0.06124640975608653, 0.05988190445075414, 0.0589489276098476, 0.057634411390770524, 0.05760918621697009, 0.05744789795037342, 0.056767715502631155]\n",
      "Row 64 - Column Numbers: [46  6 61 56 87 47 27 68 57 63 54 55 51 75 74 84 69 45 60 10  4 14 44 23\n",
      " 62 72 20 66 48 76 65 85 12 11 81 70  1  8 59 17 52  7 77], MI Values: [1.1094691017199603, 0.4786059164536729, 0.30274924109928225, 0.22066317128273738, 0.22048913023609096, 0.1987447932521187, 0.18682361749818366, 0.17760682722466647, 0.17065913517384423, 0.1647457863588926, 0.1516338374690145, 0.1455355267788141, 0.14408460937434509, 0.14236178948324518, 0.14209884783445936, 0.13984183102276582, 0.13741479855139893, 0.13477024068243804, 0.13185070300012303, 0.1299306324648466, 0.12979914510191115, 0.12701720438149788, 0.12575424005177815, 0.12382874483289896, 0.11842971465453278, 0.11641659888849265, 0.11253209164348021, 0.11225512605831867, 0.11110937927605224, 0.10732056478952767, 0.10654049307470448, 0.10591493223352533, 0.10535355610052566, 0.10500346113093073, 0.1037050834642379, 0.10306102384276805, 0.10272291690296331, 0.10254326229903832, 0.10143685103057631, 0.1003732877747634, 0.09484755694459235, 0.09462334579778542, 0.09447565520740842]\n",
      "Row 65 - Column Numbers: [27 45 63 64 66 76 60  6 84 53 62 13 46 31 74 23 57 79 15  1 61 28 90 87\n",
      " 25 18 47 35  4 10 19 22  2 16 54 17 38  5 70 43 11 71 55], MI Values: [0.6065603894953897, 0.3355390992669385, 0.10914449076511978, 0.10654049307470537, 0.07400054698096614, 0.06574940460414158, 0.05516399778635073, 0.05313625162063573, 0.05200772742261606, 0.04754326752987392, 0.04210859287540458, 0.04141383027204526, 0.04065382889106317, 0.04016739913483747, 0.03927197805547333, 0.03543013877976531, 0.03532486757824671, 0.03390511473012481, 0.03356935029377528, 0.0334370867070275, 0.03268513124965988, 0.032538341997700115, 0.03243135734308211, 0.03240600070639843, 0.03173822340394317, 0.03125147202710554, 0.030917863808890722, 0.030897225961695085, 0.03052268994560059, 0.030516181395221054, 0.030348441731518072, 0.030328529199157295, 0.030171195067245193, 0.030140476904725766, 0.029872492359135805, 0.029334903001505097, 0.029234888513575363, 0.02891810299955555, 0.02890138730320313, 0.02881055664071308, 0.028497828396734093, 0.02842485280534124, 0.028331991996227934]\n",
      "Row 66 - Column Numbers: [76 84 45 60 64 69 54 63 65 44 75 46 81 57 87 52 10  6 68 32  3 50 70 62\n",
      "  8 48 11 49 55 88 12 53 27 51 21 41 30 34 89 56 61 85 35], MI Values: [0.3276867048743224, 0.19621110110385498, 0.16669975622521527, 0.14313213465555208, 0.11225512605832044, 0.08774329941118442, 0.07892182637938827, 0.07406004109092112, 0.07400054698096792, 0.0657832364108204, 0.06574781745996905, 0.06557772498449133, 0.06464382902376808, 0.061461405926340085, 0.057380307752954884, 0.05499973892547505, 0.052649459598339554, 0.05121302295319019, 0.049935593149331936, 0.046364996147670645, 0.04601614539536314, 0.04570965837784691, 0.045050505206226, 0.044186414063735135, 0.042936712655239795, 0.042849316494054435, 0.04280397591400931, 0.0427889260255494, 0.042241733113475455, 0.039561716831260973, 0.0386714507746424, 0.038483240317686906, 0.03842749677431723, 0.03826743593598536, 0.0377725314890629, 0.03736335808473523, 0.03715626177182507, 0.03696164121794787, 0.03657013877780546, 0.03621018306623114, 0.036192436537979766, 0.03603333099672312, 0.03582784273636985]\n",
      "Row 67 - Column Numbers: [56 58 46 48 55 59 47 61 64 49 51 68 70 75 50 54 63 69 72 81 73 57 87 41\n",
      " 79  7 52 92 71  3 34 33 36 45 18 22 74  2 21 39 77 40 89], MI Values: [0.1390223315396062, 0.13761642238519123, 0.1327952209475507, 0.0819042946903279, 0.07810178261121248, 0.07292707939904286, 0.07249971148987466, 0.06954426713920014, 0.067158129948651, 0.06462675171117294, 0.06049342127079882, 0.05573066244705327, 0.05131323241564267, 0.050048166172831365, 0.04902813669653483, 0.04789187006885953, 0.04359634849634464, 0.04356102015565355, 0.042934138904747066, 0.041962299374367795, 0.03947764246554897, 0.03874132263576069, 0.0375586609402454, 0.03748203714709142, 0.03612567970739633, 0.03552096699697227, 0.03431893068828895, 0.03385542532989394, 0.03284593157964766, 0.03260253611544073, 0.03230214768395179, 0.032080902109909104, 0.032068284532125624, 0.031703696876647314, 0.03167709034729871, 0.03152308217100508, 0.0313239473107263, 0.030862122044114315, 0.030431654414645237, 0.030192101527670268, 0.03015615956557216, 0.03014741947648325, 0.030105513462540756]\n",
      "Row 68 - Column Numbers: [81 54 69 46 64 75 52 57 50 48 55 87 21 49 61 16 84 56 17 83 44 58 20 19\n",
      " 28 74 51 70  1 63 72  4  0 47 76 15 79  2 67 85 73 88 40], MI Values: [0.273919599429445, 0.25763014924822425, 0.21452460580928268, 0.19852690016740215, 0.17760682722466647, 0.13909061707178783, 0.1278969066417437, 0.12717047965108375, 0.0931330170915734, 0.0893454513359444, 0.0843329614831374, 0.08279666247431816, 0.08274897552594052, 0.08052518453031432, 0.08017854952241699, 0.08013941132973379, 0.07495229498264155, 0.07341505483174426, 0.06961403770779029, 0.06805662497684573, 0.06773250218080751, 0.06709058591021577, 0.06678931920015962, 0.06634530228217894, 0.0648958659595209, 0.06481434993591328, 0.06392417227606728, 0.06381372155874665, 0.06377396532315771, 0.06283923533357072, 0.061596290425321776, 0.06062743353392808, 0.05987241738861382, 0.05906462224581688, 0.05900909169327839, 0.05863023036643522, 0.056674954088558493, 0.05663641300834321, 0.05573066244705327, 0.05285999918476847, 0.05115265774466682, 0.05105981583143748, 0.050255155238578375]\n",
      "Row 69 - Column Numbers: [54 52 81 57 75 68 64 50 45 46 49 84 66 60 76 61 55 48 70 47 72 63 62 21\n",
      "  6 53 74 87 12 17 56 58 88 83 33 10 13 44 41 43 35 31 15], MI Values: [0.6991638866458345, 0.5772799725175153, 0.5173059047442399, 0.4492286562322283, 0.3365455824566368, 0.2145246058092809, 0.13741479855139715, 0.1364956152132697, 0.10868038934784607, 0.105422623025202, 0.09982396156077122, 0.09384699164640953, 0.08774329941118264, 0.08538631330874047, 0.08467890285416413, 0.0817599534587723, 0.07626677924718717, 0.07361433044884258, 0.06977140079906086, 0.06874455994522854, 0.06641906563649336, 0.06532339080081417, 0.06494490899076943, 0.06484185380561414, 0.06183066532204684, 0.05994221903533159, 0.05666686695618495, 0.05545803544337424, 0.05531483615886046, 0.05499612699967926, 0.05440393974544655, 0.053739795644960786, 0.0536959399704946, 0.053145985839573306, 0.05089832960081431, 0.050097225136772394, 0.04984063431350716, 0.04878869749796966, 0.04863991014106883, 0.04807444378004, 0.04771493976945074, 0.04694746829499152, 0.04658331443336472]\n",
      "Row 70 - Column Numbers: [72 71 63 46 64 57 53 62 54 47 69 87 48 68 45 36 82 56 17 61 21  4 19 13\n",
      " 74 41 55 49 67 52 60 11 15 75 28 84 32 85 66 18 44 35 31], MI Values: [0.5037025298153655, 0.1468401051584065, 0.13607340649846478, 0.13281149605317744, 0.10306102384276628, 0.08195684550894988, 0.07763014753084718, 0.07551883001699711, 0.07247468124904355, 0.07068379697728044, 0.06977140079905908, 0.0660251334839197, 0.06437836072642344, 0.06381372155874754, 0.06252081423776268, 0.05999309743629233, 0.05982269100457582, 0.057890813506117134, 0.056376474765788664, 0.055299683066056815, 0.05505815458498908, 0.05456383162511802, 0.05447668338025302, 0.05401666850898579, 0.05386607986701808, 0.053251414027695176, 0.05210958027079293, 0.05205162711625011, 0.05131323241564267, 0.050113256036700804, 0.049242671141108474, 0.049105160517478375, 0.04807318298614227, 0.047127393802390394, 0.04650128507184803, 0.046494250587683084, 0.04569125616274494, 0.04506890618240256, 0.04505050520622156, 0.04471178449303981, 0.04423971269111515, 0.044000657807371724, 0.043861067541813625]\n",
      "Row 71 - Column Numbers: [70 72 57 46 63 52 64 69 62 40 88 45 19 54 89 73 53 41 18 20 36 74 28 48\n",
      " 38 68 67 55 16 21 15 32 35 85 39 49  1 33 92 86 66 29 34], MI Values: [0.14684010515840784, 0.10642931109237441, 0.052528980782009516, 0.05241768981868278, 0.050201259190097325, 0.04467108973151124, 0.04327708127836605, 0.040533665195546575, 0.03859241843659156, 0.038561516805054374, 0.03818678028153677, 0.03813838976859696, 0.03800425250052175, 0.03790080375870186, 0.03715871144142646, 0.03588263349891774, 0.03548282442189432, 0.035353727634690024, 0.0352925510429718, 0.03441557456072353, 0.03423058910657151, 0.03397324312542693, 0.03394914598687837, 0.033806395276054335, 0.033705883841912865, 0.03342612831626557, 0.03284593157964988, 0.032719080030302106, 0.032663553226116804, 0.031987069591433936, 0.03175109221050576, 0.03144013441961224, 0.031402843954976944, 0.030959505480408822, 0.03087881443926932, 0.030695717699147362, 0.030567471549774794, 0.030379323571904315, 0.03005020752412957, 0.03002178949951162, 0.029856386276476243, 0.029726472501970136, 0.029722945487696606]\n",
      "Row 72 - Column Numbers: [70 46 63 64 71 57 62 54 87 69 53 74 36 17 47 68 19 56  6  4 21 37 18 12\n",
      " 13 79 45 52 61 14 15 85 84 11  8 83 38 55 31 10 41 48 40], MI Values: [0.5037025298153646, 0.1555945017468563, 0.14441268837025323, 0.11641659888849354, 0.10642931109237264, 0.10567030398132982, 0.08923240114088049, 0.06863149347899888, 0.06757571466233703, 0.06641906563649602, 0.06557217989953035, 0.06265296415556598, 0.06265064870036952, 0.06242048665925726, 0.06175094572082429, 0.06159629042532533, 0.06050821759756175, 0.060467185737427265, 0.059193884606223435, 0.05724329216191926, 0.054151749566812235, 0.053098326138301566, 0.05297227066477639, 0.05260851139547462, 0.052594084364699256, 0.05231208801533249, 0.05126811930396524, 0.051113533032526526, 0.050320783879531206, 0.050294567082459274, 0.049828300730804465, 0.04936721830032109, 0.04876829570450525, 0.048098306904397425, 0.04777061216579881, 0.04705935242895354, 0.04699176949630246, 0.04633740434429967, 0.04575550443701104, 0.04517050064331052, 0.04508851409560233, 0.0448973620856723, 0.04481721096307467]\n",
      "Row 73 - Column Numbers: [18 19 16 22 15 21 83 17 46 57 20 64 92  0 85 63 87  1 90 91 75 32 61 78\n",
      " 55 68 81 80  4 77 42 56  5 62  7  2 44 48 79 58 30 52 82], MI Values: [0.7893958078076446, 0.44496585631871355, 0.23365823269839314, 0.1966841939947015, 0.17737229996765524, 0.14619238110757227, 0.13046110819555246, 0.11461081534221584, 0.0669864466316632, 0.0667097043144338, 0.06621492860686029, 0.06604549816659055, 0.06534747712790967, 0.0649060502864538, 0.06342521947019009, 0.06298018698645524, 0.0611623897499598, 0.05958199657264185, 0.05918069294481576, 0.05854277511136363, 0.053336867008316524, 0.052349661683105175, 0.052132518258837024, 0.051741026293754544, 0.05137178453202651, 0.05115265774467037, 0.050731494761138585, 0.05035070457441204, 0.04944023723216873, 0.04929230770196469, 0.04884463429679364, 0.04879117015815915, 0.04871526329810205, 0.047892505862648704, 0.04712977016487141, 0.046741524692998304, 0.045420776171674504, 0.04530640682438136, 0.04518328366119828, 0.0451152130271959, 0.04476241509419232, 0.04425296906975085, 0.04269677500715918]\n",
      "Row 74 - Column Numbers: [33 30 35 43 36 86 37 29 89 38 28 40 39 31 34 88 41 32 78  5 79  2 12 64\n",
      " 44 80  4 56 46 87  0  1  3 57 42 11 13 85  8 63 10 54 90], MI Values: [1.1137204124807516, 0.6484729630309527, 0.6417520640136294, 0.624303970048989, 0.609009289588708, 0.5888147458720638, 0.5514988683591922, 0.5004203013385569, 0.4790798574401238, 0.463836147610051, 0.4637692211865332, 0.42293019416571376, 0.4188068561985556, 0.3685955153502105, 0.3551015296305451, 0.3455870286773939, 0.33199699186004406, 0.2547497346317229, 0.20415303191621437, 0.1681098351910748, 0.1650927025452713, 0.15700514453794945, 0.14286051344793105, 0.14209884783445847, 0.13751208245379942, 0.13689592489073021, 0.12952891724869087, 0.12763532576626435, 0.11736212179504246, 0.1087269697985187, 0.10670490036675684, 0.10197487194244381, 0.09931213507677228, 0.09565681017049954, 0.09219897198964855, 0.08465931443258867, 0.08012866253161377, 0.07970796683611514, 0.07707447313009208, 0.07657349482892162, 0.07645994681407764, 0.0724507095617879, 0.07133347033568604]\n",
      "Row 75 - Column Numbers: [50 69 57 81 54 52 49 46 64 68 84 48 60 58 87 55 45 47 66 74 77 79 44  0\n",
      " 19 76 37 63 86 59  2 73 13  4 36 61 17  1 62 24 88 67 10], MI Values: [0.38569583316039946, 0.3365455824566368, 0.31754032621604367, 0.299464626985233, 0.2835775257403297, 0.1935421636578889, 0.16380558437787318, 0.1598316786459506, 0.1423617894832443, 0.1390906170717887, 0.10426683306186213, 0.1003724412202649, 0.0878913633998506, 0.08672016085400713, 0.08358299144459647, 0.07894014514831671, 0.07550304956704768, 0.07403127407645904, 0.06574781745996994, 0.0641015831058036, 0.06280999904077333, 0.06198112586282889, 0.05994952546050758, 0.058932901704030094, 0.05883151968498446, 0.05840596267275, 0.05770927457101749, 0.05585066540116479, 0.05527900384734252, 0.05458094170481065, 0.054081184944083205, 0.05333686700831475, 0.053243057542840866, 0.05294436526442681, 0.05286496782731209, 0.052800446177284854, 0.052136357413616885, 0.051665821434266235, 0.05132260781066744, 0.05083179402329918, 0.05043949403648362, 0.05004816617282959, 0.049905532084435045]\n",
      "Row 76 - Column Numbers: [66 84 45 64 69 46 60 54 63 65 68 81 75 87 50 61 56 55 27 52  3 48 51 57\n",
      " 44 88 62  6 85 40  1 74 41  0 58 49 15 39  4 89 14 53 47], MI Values: [0.3276867048743197, 0.24938687538324178, 0.14089157380955797, 0.10732056478952945, 0.08467890285416502, 0.07963991449703123, 0.07359513171289844, 0.07324275519206669, 0.06663758575631462, 0.06574940460414425, 0.05900909169328106, 0.05870728910141754, 0.05840596267275089, 0.05227845227554617, 0.052114858751312276, 0.0475376914479817, 0.045768277880542385, 0.044450219960143755, 0.04331808077932564, 0.0397320107747241, 0.039450383303536896, 0.038781715879885326, 0.03840491710777716, 0.03729854865264848, 0.03695081877679929, 0.03575037533056857, 0.03553028432121241, 0.035006496062266024, 0.03479280267248619, 0.03355427583083603, 0.03330372063304132, 0.03324378852283871, 0.03314054463399074, 0.0329832469916953, 0.03260929208367003, 0.03200075462167984, 0.03142627895452854, 0.031226808565940622, 0.030530087758511293, 0.030180324229658773, 0.03013702346379077, 0.029953159421307163, 0.029614370974226034]\n",
      "Row 77 - Column Numbers: [20  1  0 17 85 21 83 87 91  2 15 79  4  5  3 11 12 19 22 16 64 78 90 10\n",
      " 24 46 61 18 31 14 33 80 74 13 56 43 75 30  8 86 37 36 29], MI Values: [0.6456828762580971, 0.3911191711403701, 0.37263024544485734, 0.2990938973597581, 0.2972324555956005, 0.2833159462922179, 0.2721591618925645, 0.2624972226636384, 0.2612330298469274, 0.23544670375940946, 0.2109149525053855, 0.19755911895090694, 0.1718626691037235, 0.17144637756480563, 0.16858842857306655, 0.15529190588759256, 0.15476368455904055, 0.14839967682173594, 0.10378871318925587, 0.09654894383117352, 0.09447565520740842, 0.0909806859788258, 0.08763090580224553, 0.0864463575035197, 0.08554737930801348, 0.0848734741910322, 0.07553429240407361, 0.07382980271187378, 0.07208828414576551, 0.07067488479129658, 0.06870563600713986, 0.06782462499272324, 0.06750317812053108, 0.06644401403919531, 0.06584653458601863, 0.06546454180161732, 0.06280999904077245, 0.06275013897899573, 0.06220005651368066, 0.061947295051053786, 0.061387189732781344, 0.061213187064223185, 0.06065012243418888]\n",
      "Row 78 - Column Numbers: [31 79  2  5 43 35  4 44 30  3  0  1 33 74 42 36 85 86 34 12 11 37 87 32\n",
      " 29 91 20 80 28 13 89 17 10 38 39 21 40 83 41 88 77 90 15], MI Values: [0.7638100129208834, 0.5291499102562947, 0.40895639584369636, 0.40195030351981753, 0.3703971113656319, 0.36035661286731635, 0.3522117773810214, 0.2940959242977499, 0.24551062402752422, 0.22968546503017695, 0.2279315500630652, 0.22306577157731855, 0.21439117181920508, 0.20415303191621348, 0.17401757617932834, 0.14656523125808896, 0.13481869307475858, 0.1340783425963794, 0.13184448924787695, 0.1251376255189447, 0.12508164598781324, 0.12299363364406979, 0.12204190372473, 0.11553471513471436, 0.11428335137809142, 0.11180728144593566, 0.11158401518017325, 0.11158379763401793, 0.10874080446091128, 0.10855159929809233, 0.10703752567566749, 0.10477670785503168, 0.10461732375843713, 0.1039286718447654, 0.1030354193690286, 0.10268663613005558, 0.09964875862896339, 0.09402627710304756, 0.09265090609569437, 0.09216904048066343, 0.09098068597882403, 0.07220152388185497, 0.06674255678354513]\n",
      "Row 79 - Column Numbers: [ 4  2  5 78  3  0 31  1 43 35 77 85 30 20 87 33 74 12 17 44 91 21 83 34\n",
      " 11 36 86 37 29 40 10 39 32 38 89 42 28 64 41 13 80 88 15], MI Values: [0.893437297964442, 0.8897537675853213, 0.8539429780686696, 0.5291499102562955, 0.5216221690633249, 0.45757637448269506, 0.3469763013969196, 0.3374236720569561, 0.2073913075411946, 0.20596754398312012, 0.19755911895090428, 0.1962347079230513, 0.1906085060616718, 0.1804159793193154, 0.17746826908973823, 0.1675397929716107, 0.1650927025452722, 0.15745268691877623, 0.15630527248319837, 0.15352082533469336, 0.14530314536725086, 0.13959981733842763, 0.13601963987999888, 0.1218215309761943, 0.12041417972820856, 0.11619314258747693, 0.11181972450478295, 0.111670136833391, 0.10420208049496171, 0.10298221946964947, 0.10144296896099547, 0.10121071598448594, 0.09567236193821316, 0.09301615106454975, 0.09254555638649187, 0.09102336506577213, 0.09026690572979756, 0.08736827809746561, 0.08676758111423233, 0.08620980383680976, 0.08466381307331439, 0.0785679892861264, 0.07750166086596]\n",
      "Row 80 - Column Numbers: [59 43 35 90 31 33 42 74 30 36 44 78 92 86 89 37 29 34 28 40 38 79  5 41\n",
      " 32 12 82 88 39  2 77 11 21  0  4 15 13  3  1 83 10 73 20], MI Values: [0.24653722627623686, 0.2276321837680122, 0.20322450593987362, 0.19218618079188143, 0.18479080672562098, 0.15136974710492979, 0.1450821651935268, 0.13689592489073021, 0.1357762064984085, 0.11571876599131237, 0.11196280971917005, 0.11158379763401705, 0.11010018137622524, 0.10493827763350172, 0.1044402309887209, 0.09822950179437395, 0.09785175941231472, 0.09689650292456431, 0.09424947908653714, 0.08752252944644034, 0.08653427377215017, 0.08466381307331616, 0.08230865790885655, 0.07854886226317959, 0.07650826602535155, 0.07494487051346166, 0.07370725535800648, 0.07253038686003155, 0.07038469791400903, 0.06970774963285731, 0.06782462499272057, 0.06530714718931119, 0.0638719053811343, 0.06157503922592156, 0.06148036084266284, 0.06004207076621082, 0.058901850104819964, 0.05522028921117084, 0.05429317094593511, 0.05309818158656032, 0.05282851504111541, 0.050350704574411154, 0.04844480590909317]\n",
      "Row 81 - Column Numbers: [54 69 75 52 68 57 50 64 46 49 58 84 74 48 55 66 87 60 45 76 77 44 36 79\n",
      " 63 86  0 61 83 37 17 33 73 38 43 39 31  4 89 47  1  2 88], MI Values: [0.7379530571253508, 0.5173059047442399, 0.29946462698523035, 0.2925189873733629, 0.27391959942944677, 0.2386747781742029, 0.136153690706311, 0.10370508346423613, 0.10140282553967683, 0.07578213385519295, 0.07170077496787108, 0.07127138714810943, 0.06860495539301592, 0.06681937537003346, 0.06660845722965725, 0.06464382902377075, 0.0635620255990954, 0.06016542150362536, 0.05993439653997257, 0.05870728910141665, 0.05853791406893283, 0.05807485470139717, 0.057863475935761244, 0.057830546664649596, 0.05763441139077141, 0.05615165444273362, 0.05562579056591499, 0.05549932064581764, 0.05488123319225746, 0.05430022036441429, 0.05358151425610025, 0.052620584599597287, 0.05073149476113681, 0.0504273983650787, 0.050018232148672404, 0.048724267224924844, 0.04741589778476474, 0.04724272848531896, 0.047045769301623075, 0.046565683993298634, 0.045974451396885385, 0.04564404577717607, 0.0445681886862177]\n",
      "Row 82 - Column Numbers: [47 92 90 80 57 63 70 64 36 41 87 74 18 42 19 85 73 86 56 43 72 78 35  6\n",
      " 31 33 29 27 44  2 21 69 34  0  5 79 15 62 30 40 23 17 46], MI Values: [0.36022650677909773, 0.20000700401697546, 0.12362127498379927, 0.07370725535800737, 0.06659031769662516, 0.06403591879492154, 0.05982269100458204, 0.048128802238390556, 0.04758120157348866, 0.04550467421470117, 0.0453016185285815, 0.04463464698039843, 0.04452332972605699, 0.043705855049582354, 0.0432350339578198, 0.042804256191230294, 0.04269677500715918, 0.042518243369825015, 0.04216181372132244, 0.041122564560073904, 0.04035249569417232, 0.040056300664696565, 0.03993065515482197, 0.039067233966030734, 0.0389505477899581, 0.038744171751281975, 0.03800177521638748, 0.037944489427784056, 0.03731345765145644, 0.03724063933802757, 0.03716957593935177, 0.037114565896340324, 0.03697025658167963, 0.03665464470504798, 0.036577827982953615, 0.035438406074370654, 0.03489171478971809, 0.03464472319516876, 0.034410902358763096, 0.034146025613621234, 0.03378679926427086, 0.033662159409545644, 0.033650920178660115]\n",
      "Row 83 - Column Numbers: [17 21 20  0  1 19 77 15 85  2 16 91 87 11 22  5  4 79 73 18  3 12 90 92\n",
      " 78 10 42 31 43 64 61 13 68 54 35 33 46 44 74  8 57 81 14], MI Values: [1.066814745597446, 0.7488876659638617, 0.4589017533899531, 0.31506896178670907, 0.29504178717312346, 0.28206410473167054, 0.2721591618925654, 0.23569399663760304, 0.19808986460266986, 0.18056529072470173, 0.16718927849869747, 0.1656431210139937, 0.15326102264911245, 0.14976259321938912, 0.1450249261206027, 0.14139989403189102, 0.1374753305211458, 0.13601963988000332, 0.13046110819555246, 0.13005610443538984, 0.12212949345012714, 0.12178764257401475, 0.09999792818939479, 0.09786512673510916, 0.09402627710304579, 0.09120163011639004, 0.08290682477634537, 0.08252825085346682, 0.08156076645929478, 0.07860224780761271, 0.07310938021788527, 0.06900697369544506, 0.06805662497684573, 0.06494064826102797, 0.06455351051612457, 0.06416764584976953, 0.06223055486476259, 0.06102533227363338, 0.05968287991838661, 0.05824405082485473, 0.05711690835432748, 0.05488123319225924, 0.05451886276258566]\n",
      "Row 84 - Column Numbers: [ 3 76 66 64 46 75 45 69 54 63 68 57 81 50 87 61 55  6 60 44 27 62 56 74\n",
      "  0 65 52  1 51 20 17 48 72 21 49 85 47 70 58 41 40 88  2], MI Values: [0.29367624960262795, 0.24938687538324178, 0.19621110110385587, 0.13984183102276848, 0.1375172592865539, 0.1042668330618639, 0.10150362847124583, 0.09384699164641042, 0.09285394516933199, 0.07977254852835536, 0.07495229498264333, 0.07392888704485934, 0.07127138714810854, 0.06909627215253789, 0.06894787220913212, 0.06553165111754211, 0.06496582981844412, 0.06491247342046069, 0.062130659320295045, 0.06139751027721019, 0.0603802858690452, 0.058731048238805705, 0.05731245332677215, 0.05441190520910766, 0.052023584398917855, 0.05200772742261517, 0.050675710238638594, 0.050658360235747324, 0.050444118959005024, 0.04966907275681187, 0.04912116274816558, 0.049098305732939274, 0.0487682957045088, 0.047929493455121985, 0.047598231033918026, 0.04751424056243447, 0.047086024603290255, 0.046494250587683084, 0.045749765509683904, 0.04533916101688806, 0.04511370164638606, 0.04442062560320448, 0.04432867747156788]\n",
      "Row 85 - Column Numbers: [91 87 11  1 20 77  0 21 15 10 16 17  2 83 79 12 13  4  5 78 19  3  8 24\n",
      " 22 31 64 61 14 23 43 33 44 46 74 42 18 35 90 92 63 53 56], MI Values: [1.0397326027081109, 0.7808738531896484, 0.4477948984444424, 0.4273072620362388, 0.42552426145736, 0.2972324555956032, 0.29292039446620866, 0.2688208314872229, 0.2607931482272816, 0.25686672570808433, 0.24952652512346507, 0.24799566598007594, 0.2191451538778244, 0.19808986460266986, 0.1962347079230522, 0.16892847033332092, 0.15241639531040452, 0.14716514799944846, 0.14129091651330672, 0.13481869307476035, 0.12862613575316306, 0.12331183579416649, 0.1197010961317595, 0.11662871191985147, 0.11578837068495584, 0.10608247049946584, 0.10591493223352089, 0.10334008173380838, 0.0977963721134758, 0.08797109748794707, 0.08744850763647705, 0.08539579380747231, 0.08318123056251547, 0.08171791357506919, 0.0797079668361178, 0.07969793759561306, 0.07840025513521187, 0.0772743628266932, 0.07673080277470046, 0.07434137186871315, 0.07313981190535657, 0.07291262831419587, 0.0700260236623178]\n",
      "Row 86 - Column Numbers: [37 36 29 38 89 28 39 33 40 74 88 41 43 35 30 34 31 32 56 78  5 79 44 80\n",
      " 12  2  4 42 90  3 87  1  0 77 14 52 64 46 81 75 85 11 63], MI Values: [1.4582722148763292, 1.0233770024292141, 0.9904397714916922, 0.7540596341394137, 0.733195425690325, 0.7092838503040939, 0.6322229406595898, 0.6078933190308362, 0.5904546129888963, 0.5888147458720656, 0.4974361490677621, 0.47456031717445146, 0.4240950333084834, 0.398460972787932, 0.37422972387261133, 0.3436127338197741, 0.22807412650458492, 0.2027410833178278, 0.1981347985070574, 0.1340783425963794, 0.1305167490968442, 0.11181972450478028, 0.10936129874318112, 0.10493827763349994, 0.10135095971922325, 0.09732347543015418, 0.0793582428961841, 0.07547417076442908, 0.07370447561000759, 0.06840077448593984, 0.06585251441988405, 0.0648701268193781, 0.06364451470636467, 0.0619472950510529, 0.06094423783477332, 0.05775731163073594, 0.057120350210864146, 0.05635429843615114, 0.0561516544427354, 0.05527900384733986, 0.053398504926430945, 0.05262110212995097, 0.05220962062188317]\n",
      "Row 87 - Column Numbers: [91 85 20  1 11 77 15  0 10 64 17 21  2 79 46 83  4 63 12  5 16 24 78 14\n",
      " 19  8 61 13 31 74  3 56 23 44 57 22 43 47 75 68 33  6  9], MI Values: [0.8254953838532577, 0.7808738531896502, 0.32604905695192254, 0.3012243820649747, 0.2965738494229102, 0.2624972226636402, 0.2236871771312554, 0.22350595260037398, 0.2210467525648223, 0.22048913023609007, 0.19689724643638407, 0.18708052814614184, 0.18419330652618005, 0.17746826908973734, 0.16549438774061542, 0.15326102264911423, 0.1467876478550867, 0.14223108828764808, 0.13558171850872913, 0.13204341952919485, 0.12870418125103367, 0.126641316562071, 0.12204190372472912, 0.12022624072505206, 0.11907016274300819, 0.11717444758841289, 0.11609849133691608, 0.11270707168404748, 0.10896037047705942, 0.10872696979851781, 0.10828482718467924, 0.10439486730786829, 0.1027970391859041, 0.10044717697416417, 0.09943857195888395, 0.08969080820395003, 0.08755593140089335, 0.08569788060934336, 0.08358299144459647, 0.0827966624743155, 0.08221603143086931, 0.07597112239010073, 0.0751232614805879]\n",
      "Row 88 - Column Numbers: [40 89 41 28 38 39 34 29 37 86 33 36 74 30 32 35 43 31 44 78 56 79  5  4\n",
      " 64 80 12 90 18  2 46 52 42  0 10  3  1 62 54 69  8 63 17], MI Values: [1.3584687582326698, 1.1135577021657408, 0.8687228214668892, 0.7614158768816592, 0.7568375359221005, 0.7414381495833346, 0.521645640678436, 0.5162986988948415, 0.5065004040074976, 0.4974361490677621, 0.4047557520194278, 0.39112029603754017, 0.3455870286773921, 0.3120618690279793, 0.27467543363149716, 0.2113827569500053, 0.2062641249804278, 0.1178467066606661, 0.0978448354860939, 0.09216904048066343, 0.0881281392529063, 0.07856798928612552, 0.07740754667316185, 0.07609992946234723, 0.07448577255951516, 0.07253038686002977, 0.07191036153530916, 0.07018600624848581, 0.06947413178679351, 0.06925480718800436, 0.0665871977414545, 0.06273572137952144, 0.06114199250922159, 0.06063371495187919, 0.06012914210785869, 0.05512401310494486, 0.05476304444835467, 0.05440889071046939, 0.05436024408042606, 0.053695939970491935, 0.05292091189701864, 0.05201826811016552, 0.05132084037915341]\n",
      "Row 89 - Column Numbers: [38 40 88 39 28 41 37 29 86 36 34 33 74 30 43 35 32 31 56 78 80  5 79 44\n",
      " 12  2 90  4 11 64  0 10  3 42 46  1  8 13 61 87 17 54 62], MI Values: [1.2419280927673935, 1.2392621662048944, 1.113557702165739, 1.0535035116401668, 1.0046755344608442, 0.9100181021852709, 0.7572524796564108, 0.7571541803206934, 0.7331954256903233, 0.5752000583378676, 0.5628237492307493, 0.5364183007679406, 0.4790798574401274, 0.37170844903925726, 0.28802774608808956, 0.2845574273495872, 0.23990089864081376, 0.15421271891570854, 0.12759658270105323, 0.1070375256756666, 0.1044402309887218, 0.1028680671126736, 0.09254555638649009, 0.09241113709100546, 0.08890082125607357, 0.08732427486063177, 0.08143911948999971, 0.07698715238078524, 0.06919349661079899, 0.06672066841319335, 0.06566309202536758, 0.0637520285116242, 0.06298051391441373, 0.06261691628512, 0.0624690478839538, 0.06095847702589374, 0.05864248331363253, 0.05740682008964981, 0.057232186056704215, 0.0568278203392758, 0.05080254511998916, 0.05074669197352755, 0.0502827362091578]\n",
      "Row 90 - Column Numbers: [42 92 80 21 82 17  1  0 83 77 40 20 19 89 30 33 43 85  5  2 79 11 86 41\n",
      " 38 12 15 78 35 74 37 88 29 36 39 34 31 91 87 28  4 32 73], MI Values: [0.5736361560630625, 0.4459659605734716, 0.19218618079188232, 0.12517520234619095, 0.1236212749837966, 0.11040902183482082, 0.10532886649482442, 0.10411775455289263, 0.09999792818939834, 0.08763090580224375, 0.08755455049272687, 0.08732179357987846, 0.08561032186586459, 0.08143911949000593, 0.07857807032348152, 0.07829650162065516, 0.07721049556759763, 0.07673080277470312, 0.07668497735520141, 0.07646301353284013, 0.07612583152068808, 0.0746333907288248, 0.07370447561000759, 0.07307672025710321, 0.07291292443408093, 0.07254758451655796, 0.0725475665380868, 0.07220152388185319, 0.07216427126334413, 0.07133347033568604, 0.07091755529673982, 0.07018600624848581, 0.07002944857802262, 0.06954945457795869, 0.06777425757346034, 0.06748508102814021, 0.06594386443864142, 0.06571885927828625, 0.06528340240650543, 0.06435233990021594, 0.06363225684698115, 0.0634542884997531, 0.059180692944813984]\n",
      "Row 91 - Column Numbers: [85 87 11 20  1 77 10 15 21  0 17 83  2 13 79 16 12  8  4  5 78 19 22  3\n",
      " 24 23 14 61 64 31 18 63 44 43 56 42 74 92 53 90 33 46 34], MI Values: [1.0397326027081135, 0.8254953838532595, 0.3865429355312866, 0.35105094399945447, 0.3192857717713009, 0.261233029846931, 0.2579871837894956, 0.2262869925209232, 0.2086854981064592, 0.20848995166817463, 0.20010695253448052, 0.1656431210139928, 0.15702895570463316, 0.15188179879224428, 0.14530314536724998, 0.13528675087576225, 0.1292188341874061, 0.12410132440415556, 0.11543451299135388, 0.11292935145386718, 0.1118072814459321, 0.10649322098528113, 0.1063924866874304, 0.09857437391434942, 0.09541744286183729, 0.09277959255307167, 0.09231436655409198, 0.08714033036634472, 0.08652458136703967, 0.08539580505606104, 0.08043542246333857, 0.07678764806996075, 0.07356394424112533, 0.07147186167010044, 0.06996541088144959, 0.06881214952706838, 0.06784461788607654, 0.06764075156292826, 0.06654270992309197, 0.06571885927828625, 0.06454231972101443, 0.060894556193985316, 0.05979450877373971]\n",
      "Row 92 - Column Numbers: [90 82 17 42 21 80 83 63  1 85  0 19 20 91 87 57 73 23  2 30 79 77  5 78\n",
      " 15 41 74 33 11 18 36  6 32  4 12 40 34 64 86 16 28 47 10], MI Values: [0.4459659605734716, 0.20000700401697458, 0.16969542448540587, 0.11438741669920915, 0.1117978672601403, 0.11010018137622612, 0.0978651267351065, 0.08472994154227287, 0.08048114102267068, 0.07434137186871048, 0.07334383362524477, 0.07083532279622062, 0.07064869314149647, 0.06764075156292648, 0.06744167818817282, 0.06608857489515962, 0.06534747712790523, 0.06377017167667542, 0.06303769631886258, 0.06244423103829355, 0.06139810833956538, 0.06009214577031052, 0.05620640348058448, 0.05570265349391068, 0.05541644764804232, 0.05389698575662827, 0.052348572626745415, 0.051905744566475676, 0.051690795509167664, 0.05057359318983057, 0.04931200112378864, 0.048166047939036005, 0.047644557437777735, 0.04702041409510738, 0.046717369248161056, 0.04610406107367648, 0.045989563524378774, 0.0458993014321587, 0.04549260487965512, 0.04529324898574405, 0.04491292878293418, 0.044605275701465885, 0.043729188914697126]\n"
     ]
    }
   ],
   "source": [
    "# load dataset\n",
    "A,X,training_set,test_set,unknow_set,full_set,know_set,training_set_s,A_s,capacity = load_data_MI('ndbc')\n"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-25T05:39:50.192307Z",
     "start_time": "2024-03-25T05:39:42.138868Z"
    }
   },
   "id": "56f799b3338eef29",
   "execution_count": 16
  },
  {
   "cell_type": "code",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "1 1.1407583723690777 1.6731743752803818 287.9954207174686\n",
      "2 0.8410641901960044 1.2965538153562406 258.23561098245483\n",
      "3 0.8042294406434464 1.2441544397055262 249.52167323996295\n",
      "4 0.7690821432277976 1.191330875839847 242.3903908139965\n",
      "5 0.7343648175601256 1.14138187062066 234.8007328148832\n",
      "6 0.7081538409445882 1.0994694293175673 231.7585617444324\n",
      "7 0.6744996838025722 1.0514412728108185 223.01737992427692\n",
      "8 0.6417277524543326 1.0027990996717413 215.3846594854217\n",
      "9 0.6226871449710973 0.9640124686764253 214.50746662669982\n",
      "10 0.5951804885339449 0.9198348661887882 208.52073563708137\n",
      "11 0.5751930741760104 0.8815028207899035 204.8874928431642\n",
      "12 0.5487821315066919 0.838443613423531 197.00615331863636\n",
      "13 0.5186939860098042 0.7942799926185324 185.32205643427218\n",
      "14 0.5060034769538516 0.7643362966250455 186.4185160215653\n",
      "15 0.49156862955579933 0.7323854964418166 185.2633752260314\n",
      "16 0.4693259495285707 0.6959184948697634 177.99538015186326\n",
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      "97 0.24831445786333714 0.29245645009693577 127.79128258286961\n",
      "98 0.2516840029162759 0.29614862509626744 131.02199756380304\n",
      "99 0.24871047163456936 0.293961864386571 127.69297571363973\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division\n",
    "import torch\n",
    "import numpy as np\n",
    "import torch.optim as optim\n",
    "from torch import nn\n",
    "import matplotlib.pyplot as plt\n",
    "from utils import *\n",
    "import random\n",
    "import pandas as pd\n",
    "from basic_structure import IGNNK\n",
    "from basic_process import *\n",
    "import argparse\n",
    "import sys\n",
    "import os\n",
    "import time\n",
    "import pdb\n",
    " # Define model and train\n",
    "STmodel = IGNNK(h, z, K)  # The graph neural networks\n",
    "criterion = nn.MSELoss()\n",
    "optimizer = optim.Adam(STmodel.parameters(), lr=learning_rate)\n",
    "RMSE_list = []\n",
    "MAE_list = []\n",
    "MAPE_list = []\n",
    "for epoch in range(max_iter):\n",
    "    for i in range(training_set.shape[0]//(h * batch_size)):  #using time_length as reference to record test_error\n",
    "        t_random = np.random.randint(0, high=(training_set_s.shape[0] - h), size=batch_size, dtype='l')\n",
    "        know_mask = set(random.sample(range(0,training_set_s.shape[1]),n_o_n_m)) #sample n_o + n_m nodes\n",
    "        feed_batch = []\n",
    "        for j in range(batch_size):\n",
    "            feed_batch.append(training_set_s[t_random[j]: t_random[j] + h, :][:, list(know_mask)]) #generate 8 time batches\n",
    "        inputs = np.array(feed_batch)\n",
    "        inputs_omask = np.ones(np.shape(inputs))\n",
    "        if not dataset == 'NREL':\n",
    "            inputs_omask[inputs == 0] = 0           # We found that there are irregular 0 values for METR-LA, so we treat those 0 values as missing data,\n",
    "                                                    # For other datasets, it is not necessary to mask 0 values\n",
    "        missing_index = np.ones((inputs.shape))\n",
    "        for j in range(batch_size):\n",
    "            missing_mask = random.sample(range(0,n_o_n_m),n_m) #Masked locations\n",
    "            missing_index[j, :, missing_mask] = 0\n",
    "        if dataset == 'NREL':\n",
    "            Mf_inputs = inputs * inputs_omask * missing_index / capacities[:, None]\n",
    "        else:\n",
    "            Mf_inputs = inputs * inputs_omask * missing_index / E_maxvalue #normalize the value according to experience\n",
    "        Mf_inputs = torch.from_numpy(Mf_inputs.astype('float32'))\n",
    "        mask = torch.from_numpy(inputs_omask.astype('float32'))   #The reconstruction errors on irregular 0s are not used for training\n",
    "        A_dynamic = A_s[list(know_mask), :][:, list(know_mask)]   #Obtain the dynamic adjacent matrix\n",
    "        A_q = torch.from_numpy((calculate_random_walk_matrix(A_dynamic).T).astype('float32'))\n",
    "        A_h = torch.from_numpy((calculate_random_walk_matrix(A_dynamic.T).T).astype('float32'))\n",
    "        if dataset == 'NREL':\n",
    "            outputs = torch.from_numpy(inputs/capacities[:, None])\n",
    "        else:\n",
    "            outputs = torch.from_numpy(inputs/E_maxvalue) #The label\n",
    "        optimizer.zero_grad()\n",
    "        X_res = STmodel(Mf_inputs, A_q, A_h)  #Obtain the reconstruction\n",
    "        loss = criterion(X_res*mask, outputs*mask)\n",
    "        loss.backward()\n",
    "        optimizer.step()        #Errors backward\n",
    "    if not dataset == 'NREL':\n",
    "        MAE_t, RMSE_t, MAPE_t= test_error_new(STmodel, unknow_set, test_set, A, E_maxvalue)\n",
    "    else:\n",
    "        MAE_t, RMSE_t, MAPE_t= test_error_new(STmodel, unknow_set, test_set, A,E_maxvalue)\n",
    "    RMSE_list.append(RMSE_t)\n",
    "    MAE_list.append(MAE_t)\n",
    "    MAPE_list.append(MAPE_t)\n",
    "    print(epoch, MAE_t, RMSE_t, MAPE_t)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-25T05:40:29.834830Z",
     "start_time": "2024-03-25T05:39:50.193157Z"
    }
   },
   "id": "391adb596049f69",
   "execution_count": 17
  },
  {
   "cell_type": "code",
   "outputs": [
    {
     "data": {
      "text/plain": "OrderedDict([('GNN1.Theta1',\n              tensor([[-0.0440, -0.0673, -0.0438,  ..., -0.0012,  0.0591,  0.0705],\n                      [ 0.0722, -0.0447,  0.0257,  ...,  0.0501,  0.0713,  0.0928],\n                      [-0.0005, -0.0707,  0.0231,  ...,  0.0752,  0.0472, -0.0439],\n                      ...,\n                      [ 0.0833,  0.0616,  0.0626,  ..., -0.0187,  0.0021,  0.0268],\n                      [ 0.0508,  0.0226,  0.0365,  ...,  0.0546, -0.0051, -0.0511],\n                      [ 0.0192,  0.0621, -0.0710,  ..., -0.0031, -0.0175, -0.0462]])),\n             ('GNN1.bias',\n              tensor([-0.0814, -0.0938,  0.0013,  0.0030, -0.0714,  0.0373,  0.0529, -0.0372,\n                      -0.0622,  0.0740,  0.0082,  0.0435,  0.0460, -0.0990,  0.0869, -0.0136,\n                       0.0699,  0.0312, -0.0013,  0.0455, -0.0116, -0.0793,  0.0195, -0.0312,\n                      -0.0824,  0.0638,  0.0369,  0.0384,  0.0679,  0.0545, -0.0176, -0.0291,\n                       0.0313,  0.0626, -0.0162, -0.0812,  0.0111,  0.0372,  0.0474,  0.0656,\n                       0.0890, -0.0193,  0.0293, -0.0339, -0.0065,  0.0721,  0.0802,  0.0193,\n                      -0.0722, -0.0165, -0.0912, -0.0099,  0.0492,  0.0175,  0.0242,  0.0819,\n                       0.0577,  0.0267, -0.0658,  0.0378,  0.0575,  0.0760,  0.0137,  0.0654,\n                      -0.0202, -0.0644,  0.0832, -0.0752,  0.0286,  0.0713,  0.0005, -0.0753,\n                       0.0304,  0.0144,  0.0552,  0.0889, -0.0776,  0.0468,  0.0661, -0.0234,\n                       0.0213,  0.0752, -0.0174, -0.0482, -0.0111,  0.0359,  0.0271,  0.1151,\n                       0.0711,  0.0771, -0.0892,  0.0779, -0.0801,  0.0580, -0.0338, -0.0327,\n                       0.0392, -0.0115,  0.0213, -0.0729])),\n             ('GNN2.Theta1',\n              tensor([[ 0.0828, -0.0608,  0.0740,  ...,  0.0667, -0.0824,  0.0838],\n                      [-0.0773,  0.0989,  0.0520,  ..., -0.0299,  0.0462, -0.0128],\n                      [ 0.0459, -0.0409, -0.0458,  ..., -0.0183, -0.0361,  0.0678],\n                      ...,\n                      [-0.0422, -0.0628,  0.0749,  ...,  0.0137, -0.0018, -0.0842],\n                      [ 0.0511, -0.0997, -0.0134,  ...,  0.0775, -0.0056,  0.0548],\n                      [ 0.0109,  0.0471,  0.0989,  ...,  0.0080,  0.0117,  0.0718]])),\n             ('GNN2.bias',\n              tensor([-0.0341,  0.0993,  0.0128, -0.0492, -0.0260, -0.0626, -0.0700, -0.0250,\n                       0.0592,  0.0486,  0.0262, -0.0855, -0.0982, -0.0513,  0.0692, -0.0697,\n                      -0.0356,  0.0054,  0.0090, -0.0752, -0.0419, -0.0945, -0.0439, -0.0661,\n                      -0.0914, -0.0182,  0.1114,  0.0259,  0.0393,  0.0795,  0.0763,  0.0743,\n                       0.0608,  0.0090,  0.1069,  0.0215, -0.0894,  0.0179, -0.0517,  0.0120,\n                       0.0766,  0.1183,  0.0917, -0.0115, -0.0653, -0.0074, -0.0804, -0.0586,\n                      -0.0844, -0.0989, -0.0703, -0.0593,  0.0040, -0.0924,  0.0357,  0.0420,\n                       0.0436,  0.0424,  0.0900,  0.0778,  0.0702,  0.0746, -0.0263,  0.0083,\n                      -0.0894, -0.0749,  0.0584,  0.0131, -0.0572, -0.0481,  0.0116, -0.0090,\n                      -0.0805,  0.0308, -0.0988,  0.0434,  0.0639,  0.0404, -0.0798, -0.0869,\n                       0.0409, -0.0521,  0.0479,  0.1220, -0.0625, -0.0004,  0.0430, -0.0490,\n                       0.0302, -0.0242,  0.0870, -0.0364, -0.0844,  0.0944, -0.0875, -0.0306,\n                       0.0041, -0.0785,  0.0750,  0.0206])),\n             ('GNN3.Theta1',\n              tensor([[-0.0002, -0.1101,  0.0801,  ..., -0.1216,  0.1861,  0.0140],\n                      [-0.1954,  0.0051,  0.1889,  ..., -0.1120,  0.0758,  0.1288],\n                      [ 0.1422, -0.1590, -0.0911,  ..., -0.0427, -0.1007, -0.0633],\n                      ...,\n                      [-0.0976, -0.0120, -0.1861,  ...,  0.1978,  0.0893,  0.0035],\n                      [-0.1395,  0.0066,  0.0072,  ..., -0.0327, -0.1354,  0.1403],\n                      [ 0.0332,  0.1705, -0.1976,  ..., -0.1290, -0.1766,  0.1522]])),\n             ('GNN3.bias',\n              tensor([-0.1674, -0.1533, -0.0798,  0.1141, -0.1190, -0.1071, -0.0851,  0.0098,\n                      -0.0541, -0.0542, -0.0701, -0.1499,  0.0144, -0.0671,  0.1727,  0.1765,\n                      -0.1231,  0.0107, -0.0895,  0.0589,  0.0459,  0.1289,  0.0953,  0.0281]))])"
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#torch.save(STmodel.state_dict(), '/content/Spatial-interpolation/model/IGNNK_{:}_{:}iter_{:}.pth'.format(dataset,max_iter,time.strftime(\"%Y-%m-%d %H:%M:%S\", time.localtime()))) # Save the model\n",
    "torch.save(STmodel.state_dict(), '/home/xren451/rxb/phd/Spatial_interpolation/XBSPA/ModIGNNK/model/IGNNK_{:}iter_{:}.pth'.format(max_iter,time.strftime(\"%Y-%m-%d %H:%M:%S\", time.localtime()))) # Save the model\n",
    "STmodel.state_dict()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-25T05:40:29.839971Z",
     "start_time": "2024-03-25T05:40:29.835418Z"
    }
   },
   "id": "9270e6f581636cc",
   "execution_count": 18
  },
  {
   "cell_type": "code",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(8784, 103)\n",
      "Incomplete data number in each column： [8784    0    0    0    0    0    0    0    0    0    0    0    0    0\n",
      "    0    0    0    0    0    0    0    0    0    0    0    0    0    0\n",
      "    0    0    0    0    0    0 8784    0    0    0 8784    0    0    0\n",
      "    0    0    0    0    0    0    0 8784 8784    0    0    0    0 8784\n",
      " 8784    0    0    0    0    0    0    0    0    0    0    0    0    0\n",
      "    0    0    0 8784    0    0    0    0    0    0    0 8784    0 8784\n",
      "    0    0    0    0    0    0    0    0    0    0    0    0    0    0\n",
      "    0    0    0    0    0]\n",
      "The column numbers with missing values are： [ 0 34 38 49 50 55 56 73 81 83]\n",
      "(8784, 93)\n",
      "Row 0 - Column Numbers: [ 1  2  4 79  5 20  3 77 21 17 83 85 78 87 91 12 15 31 11 43 19 44 35 30\n",
      " 74 90 16 10 33 64 42 34 61 13 32 46 22 63 92 56 18  8 41], MI Values: [0.8272601132894586, 0.6901375697065202, 0.4673606483958732, 0.45757637448269683, 0.4363240338301644, 0.4190235175463517, 0.37428008133733837, 0.37263024544485734, 0.33215728219304985, 0.3299090634675217, 0.3150689617867082, 0.29292039446620866, 0.22793155006306698, 0.22350595260037576, 0.2084899516681764, 0.19725693559810153, 0.16436438822998234, 0.1621107642515911, 0.15513395543730368, 0.13586993979589845, 0.13409996608400565, 0.12631372813239938, 0.11361591888716127, 0.10962686909974106, 0.10670490036675684, 0.10411775455289352, 0.10173701560948789, 0.10125880394889375, 0.0966457877057838, 0.0917156023777439, 0.08872664637913985, 0.08750394746818291, 0.07987921333337233, 0.0779097501756647, 0.07772961987272176, 0.07681250087322766, 0.07596636122032496, 0.07375851842511771, 0.07334383362524477, 0.0724236272383223, 0.06937049801544504, 0.06869053966721506, 0.06665335877298872]\n",
      "Row 1 - Column Numbers: [ 0 20  2 85 21 77  4 79 17  5 91 87 83  3 11 15 12 78 31 19 10 16 43 35\n",
      " 30 33 13 90 64 74 44 22 42 61 18 34 92  8 46 56 24 28 36], MI Values: [0.8272601132894577, 0.5324618722588088, 0.52600823699178, 0.4273072620362397, 0.4023069759074378, 0.39111917114037187, 0.34043212687770286, 0.33742367205695434, 0.3283135513911546, 0.32209271522604777, 0.3192857717713018, 0.3012243820649747, 0.2950417871731199, 0.25018137359531334, 0.2344515509245717, 0.23100847367209631, 0.22954525563754213, 0.22306577157731855, 0.161217443157323, 0.16120899606897954, 0.14396039237957936, 0.13986782406464826, 0.12913107009156644, 0.11642248941903688, 0.1150059734774116, 0.10934085523256787, 0.10726653658897867, 0.10532886649482887, 0.10272291690296598, 0.10197487194243937, 0.09756958090356083, 0.0945249676245794, 0.09265639520815494, 0.09192328803022942, 0.09060525299304167, 0.09049841174829254, 0.08048114102267423, 0.08040105111154183, 0.08010342629738876, 0.07992095121214415, 0.07658487183692309, 0.07617110541908634, 0.07458627225738823]\n",
      "Row 2 - Column Numbers: [ 4 79  5  0  3  1 78 31 20 77 85 21 17 12 35 43 87 83 30 33 91 74 11 44\n",
      " 34 10 36 15 13 86 29 39 19 42 37 32 40 38 89 64 28 61 41], MI Values: [1.0421298348636876, 0.889753767585324, 0.8252189069592397, 0.6901375697065175, 0.6346295603606373, 0.52600823699178, 0.4089563958436999, 0.2885791692349038, 0.26984073230595396, 0.23544670375941035, 0.21914515387782174, 0.2125857191397058, 0.20709995929092173, 0.19750308970805186, 0.18701920286034568, 0.18681968571483498, 0.18419330652618005, 0.1805652907247035, 0.15876062884895603, 0.158099218500249, 0.15702895570463316, 0.15700514453794945, 0.15460225559136997, 0.14614605566375083, 0.11747560005255142, 0.1108491328808272, 0.1096084538611164, 0.10428901675494728, 0.10194617541772022, 0.09732347543015507, 0.09469648273846154, 0.09409837181553105, 0.09214628161064109, 0.09190658625377424, 0.0914136839587858, 0.09002264997452336, 0.08826839034197409, 0.08794009077204912, 0.08732427486062821, 0.08295219935787657, 0.08247104503342495, 0.08075786448081335, 0.07942866688885175]\n",
      "Row 3 - Column Numbers: [ 2  5 79  4  0 84  1 78 77 31 20 17 85 83 21 87 43 35 12 74 91 33 44 30\n",
      " 11 34 64 36 86 10 46 37 41 89 39 32 38 15 29 42 40 19 56], MI Values: [0.6346295603606364, 0.6014752255233811, 0.5216221690633258, 0.5005956595959162, 0.37428008133733837, 0.29367624960262795, 0.2501813735953151, 0.22968546503017784, 0.168588428573063, 0.15053120343368054, 0.14918195632018705, 0.135719601508959, 0.12331183579416383, 0.12212949345012802, 0.12006037445413753, 0.10828482718467836, 0.1038170751558507, 0.10166237481487972, 0.10067391244311352, 0.0993121350767705, 0.09857437391434942, 0.09072061229028172, 0.09034618967547559, 0.08507553529173251, 0.08430822621926293, 0.07711971317009514, 0.0732968907767324, 0.07188834325973747, 0.06840077448593984, 0.06747669748327834, 0.0662602861970365, 0.06558274587027046, 0.06306413363040075, 0.06298051391441817, 0.06157433149594205, 0.06126513617121354, 0.06113916617078008, 0.06068970280665109, 0.06048824178377199, 0.05799913453610728, 0.057212613678012225, 0.05676014452040157, 0.05643454058528263]\n",
      "Row 4 - Column Numbers: [ 2  5 79  3  0 78  1 44 31 20 77 17 85 12 87 21 83 35 43 11 64 74 30 33\n",
      " 91 10 34 63 36 32 13 19 61 86 24 23 38 46 89 29 15 88 40], MI Values: [1.0421298348636858, 0.9112659905285279, 0.893437297964442, 0.5005956595959136, 0.4673606483958741, 0.3522117773810223, 0.34043212687770286, 0.25771696574601854, 0.227791945861342, 0.17593949417667076, 0.1718626691037226, 0.15309018167041533, 0.14716514799944758, 0.1468250597240388, 0.1467876478550929, 0.14440832752750676, 0.1374753305211449, 0.13262659195667847, 0.13167838609283677, 0.1303296358704138, 0.1297991451019085, 0.1295289172486882, 0.12417935392990831, 0.12068089113273661, 0.11543451299135477, 0.09954623668022755, 0.09367692420842033, 0.09074112883170127, 0.08771441417981674, 0.08734619315226588, 0.08641934307043808, 0.08049320130510296, 0.0793639777794386, 0.07935824289618232, 0.07926789355999908, 0.07907845045093165, 0.07857614620487485, 0.07856401142111924, 0.07698715238078346, 0.07666467817423595, 0.07652558554478439, 0.07609992946234811, 0.07604174073334136]\n",
      "Row 5 - Column Numbers: [ 4 79  2  3  0 78  1 31 43 36 35  7 77 33 20 74 17 30 21 83 85 44 87 86\n",
      " 37 12 29 91 38 89 39 11 28 40 34 42 32 10 41 80 88 90 15], MI Values: [0.9112659905285261, 0.8539429780686714, 0.8252189069592406, 0.6014752255233793, 0.4363240338301635, 0.40195030351981753, 0.32209271522605043, 0.2760329582147678, 0.20819529046906293, 0.20674579006625127, 0.19563347399244257, 0.18293846291297733, 0.17144637756480563, 0.17076852453711044, 0.1697430692708517, 0.16810983519107303, 0.16129782284088812, 0.14845254677791608, 0.1420832575295341, 0.14139989403188924, 0.14129091651330405, 0.13308552892848002, 0.13204341952919751, 0.1305167490968433, 0.12301925557245497, 0.12297734107820624, 0.11470618022646395, 0.11292935145386807, 0.10350223849688867, 0.1028680671126736, 0.10050281527196514, 0.09942878741363614, 0.09875071075038111, 0.09746128685535993, 0.09670112680553178, 0.09376382987344023, 0.09331795784564356, 0.08681805312730084, 0.08605778397885011, 0.08230865790885478, 0.07740754667316363, 0.07668497735519875, 0.07561477718424658]\n",
      "Row 6 - Column Numbers: [64 14 46 63 12 23  8 57  9 62 11 61 32 45 87 13 44  4 10 54 28 47  7 84\n",
      " 27 69 52 72 36 30 35 79 65 74 41  2 56 26 66 34  1 85 92], MI Values: [0.478605916453672, 0.1659311007796953, 0.13099684473508688, 0.11759316702334122, 0.11209322621671447, 0.09453623691659319, 0.08865574838552437, 0.0859220172096915, 0.08576932695849138, 0.08134777223811529, 0.07911821580729761, 0.07748176490715508, 0.07727934830261152, 0.07607959090818373, 0.07597112239010162, 0.07148486877965077, 0.07123886187653383, 0.07119374646681464, 0.06986362657552991, 0.067773162297458, 0.06638342779498618, 0.06549702884688458, 0.0654621562897697, 0.0649124734204598, 0.06278134191716767, 0.06183066532204595, 0.0613978125590382, 0.05919388460622166, 0.05838254740344251, 0.05558434696104264, 0.055331827053077376, 0.05403814410428076, 0.053136251620639285, 0.0529400614221025, 0.05243412828986749, 0.052066717960047804, 0.0518643235699745, 0.05140858603128606, 0.05121302295318664, 0.0509936262443027, 0.05053181341582125, 0.05019818795246955, 0.04816604793903778]\n",
      "Row 7 - Column Numbers: [ 5 17 64 21 63 57 23 46 61  6 79  2  4 52 87 12 27  3 62  9  0  8  1 73\n",
      " 10 20 69 19 47 54 58 11 14 68 88 74 30 32 33 67 31 72 34], MI Values: [0.1829384629129791, 0.10524195919111623, 0.0946233457977872, 0.09121449964563944, 0.07907681278759338, 0.07616119177035774, 0.0681607842361398, 0.06676341580429312, 0.066597172827497, 0.06546215628976793, 0.059427428725374654, 0.05901064569144587, 0.05558987853756037, 0.054813377473760916, 0.05399825056106078, 0.053976980524889306, 0.05053310241240361, 0.05009254312144673, 0.0482538265970307, 0.04809050593593689, 0.047727363031476955, 0.047556140122899215, 0.0474209934989922, 0.047129770164868745, 0.04693364118155152, 0.04555598545496231, 0.04435919441098868, 0.04338328445526862, 0.0431716643311324, 0.04278103642929665, 0.041407256502377976, 0.040946924073455904, 0.04074963195215808, 0.03718480535959223, 0.03666191730525448, 0.036462534916334555, 0.03612339642617801, 0.03608454747954237, 0.03558055210133837, 0.035520966996969605, 0.035348553502023705, 0.03526695646017597, 0.035145156518217036]\n",
      "Row 8 - Column Numbers: [10  9 14 26 11 13 25 91 85 87 12 32 64 24 27 20 21 34 17  6 23 15  1 74\n",
      " 33 30 44  0 28  4  2 77 46  5 89 31 83 78 79 35 88 63 19], MI Values: [0.48698986391151955, 0.375802297419666, 0.2819697411476927, 0.2524540408417879, 0.2289457453068362, 0.21963152219072413, 0.16233774299458315, 0.12410132440415467, 0.11970109613176039, 0.11717444758841289, 0.10941441927598472, 0.10441158737263923, 0.10254326229904187, 0.10209066826928259, 0.09968544490658893, 0.09860668116430737, 0.09797349325439786, 0.09279000891834333, 0.08886645776288304, 0.08865574838552615, 0.08474539401989478, 0.08043587263141738, 0.0804010511115445, 0.07707447313008853, 0.07565747720513727, 0.07521271366405902, 0.0702725389356953, 0.06869053966721772, 0.06518271250260987, 0.06434639902210026, 0.06327216027249083, 0.062200056513681545, 0.06204077732827784, 0.060054597826602496, 0.05864248331363431, 0.05824452931784396, 0.05824405082485651, 0.0575396306220366, 0.05661802684946515, 0.055954172623136955, 0.05292091189701953, 0.052721647755728185, 0.05241070031981643]\n",
      "Row 9 - Column Numbers: [ 8 10 26 13 14 11 32  6 12 25 87 34 64 20 27 91 24 21 17 85 36  1 23  0\n",
      " 28 41 74 63  7 30 62 83 15 61 54  2 72 19 57 79 40 89 78], MI Values: [0.37580229741966775, 0.2739374700127568, 0.1888349353819665, 0.18881791101212642, 0.17302647019022377, 0.14827272551388315, 0.08690570143561605, 0.08576932695849404, 0.08575515951341117, 0.07942615953296617, 0.07512326148058257, 0.06858253221368038, 0.06743046912400352, 0.0606112133373804, 0.060249930177727506, 0.05872512110265582, 0.05556219929455963, 0.05510777850993431, 0.053827948456972585, 0.05356332489102211, 0.05062803388903436, 0.05042486996980955, 0.04914461256289693, 0.04911468770996663, 0.04892501848965658, 0.04833957062141003, 0.04817579082966983, 0.04815235147500374, 0.048090505935939554, 0.047497107903827995, 0.046442659973216394, 0.04500640957005597, 0.044571645079205524, 0.04384180562593176, 0.04255922801340173, 0.04239438289088415, 0.041960240322472586, 0.04195403205745141, 0.04175321361746853, 0.041721734850988845, 0.041382496982518724, 0.039247318738780734, 0.03916411448757362]\n",
      "Row 10 - Column Numbers: [11  8 13  9 91 85 14 87 12 26  1 20 64 25 24  2 21 17 78 79  0 61  4 23\n",
      " 83 15 34  5 77 31 44 32 27 33 30 74 28 43 35  6 41 46 53], MI Values: [0.4993554128442783, 0.4869898639115231, 0.4066358068899456, 0.27393747001275504, 0.2579871837894956, 0.25686672570808167, 0.2251698714598369, 0.22104675256482142, 0.17468399623417863, 0.1595045585205188, 0.14396039237957758, 0.13028693835191518, 0.12993063246484482, 0.1129190817547916, 0.11268616419256361, 0.1108491328808281, 0.10815686636048127, 0.10750415858836693, 0.10461732375843713, 0.10144296896099103, 0.10125880394889109, 0.10067720955484294, 0.09954623668022666, 0.09526800567615812, 0.09120163011638649, 0.09068210425726964, 0.08709868991881109, 0.08681805312730351, 0.08644635750351704, 0.08544174110632596, 0.08386645043593433, 0.08091774681887642, 0.07918640410680755, 0.077949740915769, 0.07776056152449495, 0.07645994681407409, 0.07299784236684648, 0.07182439963604015, 0.07091448732899508, 0.06986362657553258, 0.06936075480536807, 0.06801559120089085, 0.06799093673704792]\n",
      "Row 11 - Column Numbers: [10 85 61 12 13 91 87  1  8 20 21 17 77  0  2 83  9  4 78 14 79 31 24 15\n",
      " 64  5 35 43 44 74  3 33  6 42 30 28 90 34 19 89 22 23 80], MI Values: [0.499355412844281, 0.447794898444446, 0.4211796194747075, 0.4197051791498847, 0.40682029470780456, 0.3865429355312857, 0.296573849422912, 0.23445155092457082, 0.22894574530684064, 0.21618413086183974, 0.17612200358653762, 0.1627161637347161, 0.15529190588759256, 0.15513395543730546, 0.15460225559137086, 0.14976259321938645, 0.1482727255138805, 0.13032963587041646, 0.12508164598781324, 0.12287505739090143, 0.12041417972820945, 0.11341149652601601, 0.10784355126935719, 0.10663625668288024, 0.10500346113093073, 0.09942878741363259, 0.096740469127222, 0.09481730555193213, 0.08789263097170963, 0.08465931443259134, 0.08430822621926115, 0.0819176206772605, 0.0791182158072985, 0.07587529502254231, 0.0758563574615021, 0.07518085992455958, 0.07463339072882835, 0.0729801592932775, 0.06976258783125644, 0.0691934966107981, 0.06893504056359223, 0.06614162517794231, 0.06530714718931119]\n",
      "Row 12 - Column Numbers: [11 13  1  2  0 20 10 85 79 77 21  4 31 74 43 30 87 33 91 35 17 78  5 83\n",
      "  6 61  8 64 86  3 34 36 14 37 28 40 39 29 42 89 44 38  9], MI Values: [0.41970517914988204, 0.2820044236370247, 0.22954525563754302, 0.19750308970805097, 0.19725693559809976, 0.19049650601974388, 0.17468399623417863, 0.16892847033331915, 0.15745268691877712, 0.15476368455904232, 0.1470253698180608, 0.1468250597240388, 0.14662969753092625, 0.14286051344793105, 0.14156956810136734, 0.13732974337876414, 0.13558171850873002, 0.13072864694938868, 0.12921883418740698, 0.12855491233259286, 0.12797358847181428, 0.1251376255189447, 0.12297734107820624, 0.12178764257401742, 0.11209322621671713, 0.11175003676089723, 0.10941441927598472, 0.10535355610052655, 0.10135095971922237, 0.10067391244311619, 0.09993696526051199, 0.09709484343702979, 0.09629848458173385, 0.09592473158963521, 0.09501229751970186, 0.09185969685608963, 0.09122469199042715, 0.08955815291430014, 0.08912140713055461, 0.08890082125607712, 0.08654874505815524, 0.08621577314512052, 0.08575515951341028]\n",
      "Row 13 - Column Numbers: [11 10 12  8  9 85 91 87 78  1 20  2 31 14 35 30 43 33 44  4 79 21 28 74\n",
      " 25  0 34 17 26  6 64 83  5 15 77 36 42 32 80 89 61 54 70], MI Values: [0.406820294707801, 0.40663580688994827, 0.28200442363702294, 0.21963152219071969, 0.18881791101212642, 0.15241639531040452, 0.15188179879224428, 0.11270707168405014, 0.10855159929809766, 0.10726653658897689, 0.10347968403017482, 0.10194617541771755, 0.10045734833963227, 0.09715275871665696, 0.095142371568528, 0.09258617061155316, 0.09195467760153075, 0.08878636983820609, 0.08824878688846738, 0.08641934307043897, 0.08620980383680887, 0.08274041805652033, 0.08202421217934308, 0.08012866253161732, 0.07985596483401824, 0.07790975017566382, 0.07495306478076014, 0.07488041542475532, 0.07181363072769464, 0.07148486877965166, 0.07002602341222808, 0.06900697369544506, 0.06846734306451818, 0.0666776158158564, 0.0664440140391962, 0.06379802149536751, 0.062408309849672605, 0.062004348452000535, 0.05890185010481819, 0.057406820089648924, 0.05485204269998434, 0.05430024107788256, 0.054016668508986676]\n",
      "Row 14 - Column Numbers: [ 8 10  9 26  6 27 64 11 87 25 63 85 13 12 46 91 47 24 20 77 34 17 37 61\n",
      " 36 86 56 29 23 55 79  0 48 83  4 74  2  5 57 32 72 51 30], MI Values: [0.2819697411476918, 0.22516987145983425, 0.17302647019022466, 0.17093143981882442, 0.16593110077969708, 0.1515567092969663, 0.12701720438150055, 0.12287505739089966, 0.12022624072505117, 0.10808026792929493, 0.09840075284083127, 0.09779637211347314, 0.0971527587166543, 0.09629848458173651, 0.09266115822732779, 0.09231436655408931, 0.09074348902636675, 0.07873666169272209, 0.07681486761087797, 0.07067488479129924, 0.06725286085851412, 0.06554506282266725, 0.0641664994737523, 0.06170135977184188, 0.061668865682766416, 0.06094423783477776, 0.05952118983744992, 0.0587014765905316, 0.0585240406935128, 0.05661782886078903, 0.056059091866146105, 0.05562693284596332, 0.05528245353972583, 0.05451886276258566, 0.05432706381529773, 0.05401613896216251, 0.05270106891950288, 0.05173567448447702, 0.05167205271928932, 0.05104880529890021, 0.050294567082459274, 0.05026820068852178, 0.04979484407518253]\n",
      "Row 15 - Column Numbers: [21 16 22 20 17 19 18 85 83  1 91 87 77 73  0 11  2 10  8 12 79  4  5 56\n",
      " 90 23 42 78 61 13 24 35 43 31  3 80 68 32 46 92 57 33 53], MI Values: [0.48722604389986746, 0.47765933545984574, 0.42274734051130114, 0.3684773490976543, 0.3095265239658307, 0.30125231966110366, 0.27326227718117746, 0.2607931482272843, 0.23569399663760038, 0.23100847367209187, 0.226286992520925, 0.22368717713125363, 0.2109149525053864, 0.17737229996765436, 0.16436438822998056, 0.10663625668287935, 0.10428901675494551, 0.09068210425726964, 0.08043587263142005, 0.07994733324017389, 0.07750166086596355, 0.07652558554478794, 0.07561477718424747, 0.07262961413739166, 0.07254756653808414, 0.07129603115169658, 0.06699419564638731, 0.06674255678354601, 0.06669711932901201, 0.0666776158158564, 0.06508609948717492, 0.06380756444094082, 0.06258859383481585, 0.06209333159081609, 0.06068970280665109, 0.06004207076621171, 0.05863023036643167, 0.05587065130398727, 0.05560717684994554, 0.055416447648041434, 0.054577733516099514, 0.051477381196054495, 0.05145699897161915]\n",
      "Row 16 - Column Numbers: [15 18 22 19 21 85 73 17 20 83  1 91 87  0 77 68  2 42 10 23 56 61  5 11\n",
      "  4 90 13 78 57 63 79  3 64 46 92 52 84 80 24 53  8 47 32], MI Values: [0.47765933545984485, 0.39646468501385357, 0.3870402149910266, 0.3091588054074448, 0.28541688685649813, 0.2495265251234624, 0.23365823269839403, 0.19302253406145908, 0.17044387506372072, 0.16718927849869658, 0.13986782406464915, 0.13528675087576136, 0.12870418125103722, 0.101737015609487, 0.09654894383117263, 0.08013941132973557, 0.07497954269839457, 0.0675083713658422, 0.06746525386392133, 0.06694340591739856, 0.06331255297438165, 0.06108123440198021, 0.059929091775576815, 0.05975370525344825, 0.05524048992921937, 0.052897766030480575, 0.051451103064484194, 0.050915937056171146, 0.049854047095866605, 0.049689454222085594, 0.04856746770346909, 0.04659548808807035, 0.046006140165719245, 0.04556275492620987, 0.04529324898574405, 0.04328046495819304, 0.04310793055946416, 0.04279362459041813, 0.04234654693679207, 0.04223363657743562, 0.04159168613493058, 0.040768941888324584, 0.04067108310344292]\n",
      "Row 17 - Column Numbers: [83 21 20  0  1 15 77 19 85  2 91 87 16 92 11  5 22 79  4 18  3 12 73 46\n",
      " 90 10  7 78 64 57 31  8 42 61 56 43 13 62 68 74 35 53 52], MI Values: [1.0668147455974486, 1.021617623019086, 0.4934266968283074, 0.3299090634675217, 0.3283135513911546, 0.30952652396583336, 0.299093897359759, 0.2719089149660965, 0.24799566598007683, 0.20709995929092084, 0.2001069525344823, 0.19689724643638318, 0.1930225340614582, 0.16969542448540675, 0.16271616373471876, 0.16129782284088456, 0.15874125412953077, 0.15630527248319748, 0.153090181670418, 0.13764098894343224, 0.13571960150895812, 0.1279735884718134, 0.11461081534221496, 0.11280369881762375, 0.11040902183482348, 0.1075041585883687, 0.10524195919111712, 0.1047767078550299, 0.10037328777475985, 0.0992868325667029, 0.09616040667204562, 0.0888664577628866, 0.0846645868325373, 0.08457972685715465, 0.07971577342061753, 0.07861749607301505, 0.07488041542475354, 0.07054503826931136, 0.06961403770779029, 0.06954563307844097, 0.06903264964802336, 0.06894645621138906, 0.06703671873903527]\n",
      "Row 18 - Column Numbers: [73 19 16 22 15 21 17 83 20  1 91 85 87 77 63 88  0 57 46 72 32 64 90 92\n",
      " 56 78  2 68 42 61 11 70 82  4 62 10 52  5 48 36 75 53 55], MI Values: [0.7893958078076464, 0.5505196890502351, 0.39646468501385357, 0.32015585431856763, 0.27326227718117746, 0.1986950339873701, 0.1376409889434349, 0.1300561044353925, 0.1028199239054004, 0.09060525299304434, 0.08043542246333768, 0.07840025513521187, 0.07415089398027508, 0.073829802711872, 0.0698631855232481, 0.06947413178679618, 0.06937049801544681, 0.0555089312872461, 0.05501723067444342, 0.05297227066477728, 0.05286118816878638, 0.05264544534878457, 0.052266576769972595, 0.050573593189831456, 0.05004107750332221, 0.04951922140218912, 0.04704017567014063, 0.04656039319276406, 0.04583471052896382, 0.04531110745527123, 0.0452698374916638, 0.044711784493036255, 0.04452332972605788, 0.04430454607192402, 0.04406838905054933, 0.04345714793886302, 0.04316032552696658, 0.04294014239589039, 0.04283733769362108, 0.042177627147790275, 0.04216690271784085, 0.04179825178695218, 0.041337731296333224]\n",
      "Row 19 - Column Numbers: [18 73 21 16 15 83 17 22 20  1 77  0 85 87 91  2 90 64 12  4 46 79 92  5\n",
      " 11 68 78 42 10 57 72 75 62  3 31 52 70 56 32  8 30 35 43], MI Values: [0.5505196890502289, 0.4449658563187162, 0.3588428833857771, 0.3091588054074439, 0.301252319661101, 0.28206410473166965, 0.2719089149661009, 0.23610468619476066, 0.2076473979554514, 0.16120899606897776, 0.1483996768217315, 0.13409996608400476, 0.12862613575316484, 0.11907016274300641, 0.10649322098528025, 0.09214628161063843, 0.08561032186586814, 0.08194120218001011, 0.0811618444653357, 0.08049320130510296, 0.07977684117637374, 0.07277800134663526, 0.0708353227962224, 0.07067602202174772, 0.06976258783125466, 0.06634530228217983, 0.06322232364202662, 0.06322090154945581, 0.06289596277964993, 0.06149090076405361, 0.06050821759755998, 0.058831519684985345, 0.05762318703291758, 0.05676014452040601, 0.055853509021861925, 0.05518017282950449, 0.0544766833802548, 0.05387141021679831, 0.05309676005317332, 0.05241070031981998, 0.052023287162046294, 0.05003592431078108, 0.04839550757959277]\n",
      "Row 20 - Column Numbers: [77 21  1 17 83 85  0 15 91 87  2 11 19 12 79  4 16  5 22  3 10 64 78 13\n",
      " 18 61  8 90 31 56 24 46 14 30 92 74 68 34 73 33 42 44 43], MI Values: [0.6456828762580988, 0.5615054795942642, 0.5324618722588088, 0.49342669682830653, 0.4589017533899522, 0.42552426145736355, 0.4190235175463517, 0.3684773490976534, 0.3510509439994527, 0.3260490569519252, 0.26984073230595484, 0.21618413086183885, 0.20764739795544962, 0.190496506019743, 0.18041597931931808, 0.17593949417666988, 0.1704438750637216, 0.16974306927085436, 0.1497647957772532, 0.14918195632018527, 0.13028693835191607, 0.11253209164347666, 0.11158401518017502, 0.10347968403017305, 0.10281992390539951, 0.10190813419336298, 0.09860668116430649, 0.08732179357987757, 0.0842263209541052, 0.0828616535343425, 0.08129397459731802, 0.07862828607228867, 0.0768148676108753, 0.07673835654706895, 0.07064869314149558, 0.06733550911625219, 0.0667893192001614, 0.06677633392818816, 0.06621492860686207, 0.06372475882601236, 0.06355486571293412, 0.061150149623385275, 0.060827899523522966]\n",
      "Row 21 - Column Numbers: [17 83 20 15  1 19  0 16 77 85 22  2 91 18 87 11 12 73  4  5 79 90  3 92\n",
      " 10 78  8 42 61 64 56  7 46 31 68 13 57 43 62 44 35 52 26], MI Values: [1.0216176230190834, 0.7488876659638635, 0.5615054795942669, 0.48722604389986657, 0.4023069759074396, 0.3588428833857771, 0.33215728219305163, 0.2854168868564999, 0.28331594629221524, 0.2688208314872229, 0.22456476967975902, 0.2125857191397058, 0.2086854981064592, 0.19869503398736654, 0.18708052814614362, 0.1761220035865394, 0.14702536981806258, 0.14619238110757227, 0.144408327527505, 0.142083257529535, 0.13959981733842852, 0.12517520234618917, 0.12006037445413664, 0.1117978672601394, 0.10815686636048305, 0.10268663613005469, 0.09797349325439786, 0.09722563185672684, 0.09520585153422978, 0.09236995631917555, 0.09187841023316423, 0.09121449964563855, 0.08964547025689651, 0.08819779567887132, 0.08274897552593963, 0.08274041805651944, 0.08110178494543518, 0.07911198418960996, 0.07348744391152273, 0.06846944162919932, 0.06815788789081711, 0.06802973139084845, 0.06522771175571496]\n",
      "Row 22 - Column Numbers: [15 16 18 19 21 73 17 20 83 85 91 77  1 87 23  0 11  2 56 10 79 13 57  5\n",
      " 42 32 61  8  3 74 64 34 70 24 78 63 68 90 43 72 35 53 62], MI Values: [0.4227473405113029, 0.3870402149910266, 0.32015585431856763, 0.23610468619476155, 0.22456476967976258, 0.19668419399470238, 0.15874125412953077, 0.14976479577725232, 0.14502492612060003, 0.11578837068495584, 0.1063924866874304, 0.10378871318925587, 0.09452496762458118, 0.08969080820395181, 0.07632786384865842, 0.07596636122032496, 0.06893504056359401, 0.06328881794610464, 0.06098127462148906, 0.05727822396969895, 0.054970003136741497, 0.051323177882335536, 0.05062976172811151, 0.050465669694910176, 0.05027063548670352, 0.049760788383411025, 0.047233204160109565, 0.04542566347070398, 0.04382301867003058, 0.04368901502755573, 0.04358675196225281, 0.042850022291132994, 0.04278545874037132, 0.04263132941212078, 0.04245227781570726, 0.04240480524732426, 0.04177115423568889, 0.04146334279107311, 0.041258234396297944, 0.04113645596182369, 0.040745425400359636, 0.040726001607573004, 0.040577710389676724]\n",
      "Row 23 - Column Numbers: [64 57 87 44 10  6 24 91 85 61  8  4 22 63 15  7 16  0 11 17 92  2 12 21\n",
      " 14 55 47  1 74 56  5 13 79 62  9 31 25 77 26 83 32 20 46], MI Values: [0.1238287448328963, 0.11007546217848985, 0.10279703918589878, 0.09985139888774786, 0.09526800567615457, 0.09453623691659319, 0.09442643580457855, 0.092779592553069, 0.08797109748794085, 0.08578580449603201, 0.08474539401989523, 0.07907845045093076, 0.07632786384865975, 0.07257144170704688, 0.07129603115169214, 0.06816078423614158, 0.06694340591739678, 0.06631267495817283, 0.06614162517793609, 0.06462454817737662, 0.06377017167667276, 0.06238952944812581, 0.06198182224754323, 0.06102500139047695, 0.05852404069351369, 0.058494817456543835, 0.057048950299178, 0.056427588090688374, 0.05575798124214959, 0.05424612918912608, 0.053944258296575676, 0.053394179519995255, 0.05090816537458753, 0.049627949735287835, 0.04914461256289693, 0.04830377167633948, 0.0479154062061089, 0.047404493128977876, 0.04534942266509967, 0.044620281399040174, 0.04423650621570019, 0.04399862638296703, 0.04319511791377284]\n",
      "Row 24 - Column Numbers: [87 25 85 10 11  8 26 91 23 77 64 12 20  4 14 63 61  1 56  0 15 46  2 44\n",
      "  9 27 21 30 75 32 79 62  5 31  3 78 68 60 22 34 16 17  6], MI Values: [0.12664131656206834, 0.12184764568086237, 0.11662871191984614, 0.1126861641925645, 0.10784355126935541, 0.10209066826928304, 0.09988104072929094, 0.09541744286183551, 0.09442643580457988, 0.08554737930800638, 0.08433207450633073, 0.08382766133586106, 0.08129397459731003, 0.07926789356000175, 0.07873666169272342, 0.07871775795832381, 0.07660849160601568, 0.07658487183691687, 0.06753872107738834, 0.06575943129935258, 0.06508609948716693, 0.06378754370319006, 0.06196951220919278, 0.05575375327102261, 0.055562199294558745, 0.05318120567191542, 0.05262117138877809, 0.05116230585414172, 0.05083179402329918, 0.049254453905052564, 0.04814401145309244, 0.04665448807793737, 0.04619072869628571, 0.0458151748730149, 0.044434685459121326, 0.043901624829374875, 0.04323480914173228, 0.04291271895550075, 0.04263132941212122, 0.04238722505216597, 0.042346546936791185, 0.041908005215020694, 0.04135516870134959]\n",
      "Row 25 - Column Numbers: [26  8 24 10 14 13  9 27 64 20 32 30 63 11 21 12 74 33 17 56 23 85 91 15\n",
      " 87 28 61 89 34 38  1 40 43 52 36 80 35 37 41 83 86 88 16], MI Values: [0.22448983276060552, 0.16233774299458315, 0.12184764568086015, 0.11291908175479026, 0.10808026792929493, 0.07985596483401203, 0.07942615953296661, 0.06742082698712792, 0.057769002718598195, 0.05586583465511197, 0.054965263207836124, 0.05443370142787174, 0.053776458305056174, 0.05343401191718833, 0.05308655380792704, 0.05045720325549752, 0.05034647749383048, 0.04992384501594582, 0.0492451891629031, 0.04834454363245477, 0.0479154062061089, 0.047684160601328074, 0.047297099255485975, 0.04577736523629383, 0.0457726787254078, 0.045771120375120766, 0.04566515411493954, 0.043420484714855156, 0.043385152301504526, 0.04150956737140632, 0.04116356278905453, 0.040902739036422275, 0.039271536657020434, 0.03872861083601631, 0.03870735899101785, 0.03823640170302056, 0.03689051731253823, 0.03648924728638114, 0.03594012672179936, 0.03543675472183061, 0.0353375347334941, 0.033978841582392505, 0.033213377245050246]\n",
      "Row 26 - Column Numbers: [ 8 25  9 14 10 27 24 64 13 30 32 21 11 17 20 91 74 85 87 33 34 46  6 43\n",
      " 15 36 35  1 12 63 23 83 41 80 31 72 56 86 84 52 37 28 61], MI Values: [0.25245404084178746, 0.22448983276060552, 0.1888349353819665, 0.1709314398188191, 0.15950455852051704, 0.10013893815186226, 0.09988104072928916, 0.08361194904788949, 0.07181363072768843, 0.06658416020495395, 0.06642109881221003, 0.06522771175571318, 0.06133706698861552, 0.060864275396509626, 0.06030983748989538, 0.05855558719449405, 0.058118774994220246, 0.05502112683089955, 0.054955567957541085, 0.0548802691847472, 0.05446576296866468, 0.05385131209205429, 0.05140858603128562, 0.04892271442605356, 0.048556550337056414, 0.047843331021867996, 0.04718698058252446, 0.04666834102500239, 0.04641197580127887, 0.04620099613250428, 0.045349422665099226, 0.045142856596432246, 0.04487870650962478, 0.04102053350114243, 0.03975973670425059, 0.039456412404046404, 0.03926146380477791, 0.03883323698171193, 0.038101405951134204, 0.03717014915810957, 0.03702701389699303, 0.03678714727422072, 0.036512909297854]\n",
      "Row 27 - Column Numbers: [65 64 14 46 45 26  8 10 25  6 84  9 12 38 11 13 24 53 74  7 44 21 63 85\n",
      " 47 91 62  0 86  4  3  5 31 43 61 87 76 20 80  1 77 37 29], MI Values: [0.6065603894953897, 0.18682361749818366, 0.1515567092969663, 0.13632308186498676, 0.10364354834176126, 0.10013893815186492, 0.09968544490658893, 0.07918640410680577, 0.06742082698712792, 0.06278134191716767, 0.06038028586904787, 0.06024993017772662, 0.05954908040441431, 0.05566701959818321, 0.05365543785469562, 0.05349787902327563, 0.053181205671913645, 0.05121607804495909, 0.05107317746817763, 0.050533102412405384, 0.05024731173365815, 0.04849977979742892, 0.04791989593709012, 0.04765153600392935, 0.04741748068507423, 0.04718827956837135, 0.04704704797821968, 0.046555580550760034, 0.045963625687851284, 0.0458714770575126, 0.04550892471748291, 0.04427143864075678, 0.044267360807431544, 0.04422157037556218, 0.044030392965271226, 0.043659800788907965, 0.04331808077932564, 0.04308091954790427, 0.04297197397555763, 0.042923144439217076, 0.04277349385328666, 0.04153155742864545, 0.040719138411590805]\n",
      "Row 28 - Column Numbers: [89 38 88 37 40 86 29 41 39 36 33 74 30 34 35 43 32 31 56 78  5 44 12 80\n",
      " 79  2 13 42  1 11 10  4 62  6  8 68 90 64 52 17  0 54 61], MI Values: [1.0046755344608442, 0.8668221841314496, 0.7614158768816583, 0.7435037784407115, 0.7401508914135695, 0.7092838503040948, 0.6969500914396249, 0.6683242642188869, 0.6188553437563042, 0.5887599355969604, 0.573378254007582, 0.4637692211865332, 0.44110042693832696, 0.43990166348400894, 0.3542576214733666, 0.3130926126664333, 0.3038339983430083, 0.1631475034181804, 0.14153000235829616, 0.10874080446091217, 0.09875071075037845, 0.0973992316948431, 0.09501229751970275, 0.09424947908653536, 0.09026690572979579, 0.08247104503342673, 0.08202421217934486, 0.08020834452426495, 0.07617110541908723, 0.0751808599245587, 0.07299784236684648, 0.07194026557628508, 0.07174551471409618, 0.06638342779498885, 0.06518271250260632, 0.06489586595952179, 0.0643523399002186, 0.06270446068020075, 0.05772311949448383, 0.056954572674678516, 0.05644466945878257, 0.05541299819598944, 0.05407556787339285]\n",
      "Row 29 - Column Numbers: [37 86 38 89 39 28 40 36 88 74 33 41 43 35 30 34 31 56 32  5 78 79 44 80\n",
      "  2 12  4 90  1  0 87 42 46 77  3 14 64 11 85 62 63 57 13], MI Values: [1.124331483930141, 0.9904397714916939, 0.8561076404645682, 0.7571541803206943, 0.7394482075767632, 0.6969500914396267, 0.6243050233062002, 0.6127287729060686, 0.5162986988948424, 0.5004203013385551, 0.4839723248105665, 0.44277394507430223, 0.3862199704096003, 0.3611089233159852, 0.3044944524915385, 0.30210464330076015, 0.20191448281292157, 0.171307375513706, 0.1557361930389609, 0.11470618022646129, 0.1142833513780932, 0.10420208049496082, 0.10392751587923588, 0.09785175941231206, 0.09469648273846332, 0.08955815291429925, 0.07666467817423417, 0.07002944857802351, 0.06654779481397011, 0.06576826886766884, 0.06531253837083639, 0.06416664878429135, 0.06302637459570448, 0.06065012243418977, 0.06048824178377199, 0.058701476590528046, 0.05802769428221577, 0.049098105017652216, 0.04872740090602523, 0.04751490159093841, 0.04718646229756551, 0.047177310303764486, 0.04510718141365366]\n",
      "Row 30 - Column Numbers: [33 35 74 32 34 43 28 31 36 86 89 40 37 38 41 88 29 39 78 79  2 44  5 12\n",
      " 80  4 42  1  0 52 13  3 64 90 10 20 11  8 87 56 85 26 77], MI Values: [0.8392067051587295, 0.6637829223064537, 0.6484729630309518, 0.5649484715892896, 0.5416346036080313, 0.4933942675879779, 0.4411004269383261, 0.4130016958463507, 0.38187736651662174, 0.3742297238726069, 0.3717084490392537, 0.3527990507831582, 0.33036985608766933, 0.32508215731131695, 0.315969342937767, 0.3120618690279784, 0.3044944524915376, 0.2926134592339231, 0.245510624027526, 0.1906085060616709, 0.15876062884895248, 0.15101976681000995, 0.14845254677791608, 0.1373297433787659, 0.13577620649841027, 0.1241793539299092, 0.11531395362702757, 0.1150059734774116, 0.10962686909974106, 0.10641737910058513, 0.09258617061154961, 0.08507553529173606, 0.08219023403697623, 0.07857807032348152, 0.07776056152449762, 0.0767383565470654, 0.0758563574615021, 0.07521271366405902, 0.07367325277221859, 0.06707550157230102, 0.06691537715915796, 0.06658416020495572, 0.06275013897899484]\n",
      "Row 31 - Column Numbers: [43 78 35 30 33 44 74 79  2  5 36 42 86  4 37 29 34 80 32 38 28  0  1 89\n",
      " 39  3 12 40 41 88 11 87 85 13 17 21 10 91 20 83 77 64 90], MI Values: [0.8121927311946013, 0.7638100129208842, 0.7457506706593477, 0.41300169584634716, 0.40367630493282647, 0.3834036968008201, 0.36859551535020874, 0.3469763013969196, 0.288579169234902, 0.2760329582147696, 0.2539363056818278, 0.2480981515670253, 0.22807412650458492, 0.22779194586134022, 0.21452991980362057, 0.20191448281292157, 0.1870476252617994, 0.18479080672561743, 0.17115190570613592, 0.167611070828948, 0.16314750341817774, 0.16211076425159288, 0.16121744315732478, 0.15421271891570942, 0.1526762354992739, 0.15053120343368143, 0.14662969753092536, 0.1369994315782277, 0.12987048179875593, 0.1178467066606661, 0.11341149652601867, 0.10896037047705764, 0.1060824704994614, 0.10045734833963404, 0.09616040667204917, 0.08819779567887043, 0.08544174110632508, 0.08539580505605926, 0.0842263209541061, 0.08252825085347038, 0.07208828414576374, 0.06851019554836757, 0.06594386443863964]\n",
      "Row 32 - Column Numbers: [34 30 52 33 28 88 40 74 35 89 41 86 38 43 39 37 36 31 29 44 54 78  8 79\n",
      "  5  2  4  9 62 10 12 42  0  6 80 64  1 26 87 61 90 13  3], MI Values: [0.6589132113122833, 0.5649484715892905, 0.5366720434860506, 0.31429643099880256, 0.3038339983430083, 0.2746754336314945, 0.264343537327707, 0.254749734631722, 0.24376381697460836, 0.23990089864081465, 0.2315338746347546, 0.2027410833178278, 0.197909157760205, 0.19253106758836758, 0.1831205200479813, 0.17952444982802795, 0.17752977924984759, 0.1711519057061368, 0.15573619303895825, 0.12104168683611505, 0.11793416791373534, 0.1155347151347117, 0.10441158737263923, 0.09567236193821138, 0.09331795784564623, 0.09002264997452247, 0.087346193152265, 0.08690570143561605, 0.08212300251017712, 0.08091774681887465, 0.07909381487392952, 0.07802938607998389, 0.07772961987272353, 0.0772793483026124, 0.07650826602535332, 0.07345476684191166, 0.07062525451403978, 0.06642109881221536, 0.06429935007831045, 0.06347776301673225, 0.06345428849975132, 0.06200434845199787, 0.061265136171211765]\n",
      "Row 33 - Column Numbers: [74 30 36 35 43 86 28 37 89 38 29 40 34 39 41 88 31 32 78  5 79  2 44 80\n",
      " 12  4 42  1 56  0  3 13 85 64 87 11 90 10  8 52 77 61 91], MI Values: [1.1137204124807507, 0.8392067051587295, 0.7259968303690219, 0.676225408758059, 0.6277452858407466, 0.6078933190308362, 0.5733782540075802, 0.5576286905708168, 0.5364183007679388, 0.49716674763380553, 0.4839723248105665, 0.4791060933274043, 0.45408232882174193, 0.4358859922207907, 0.4346502711337248, 0.4047557520194287, 0.40367630493282647, 0.31429643099880256, 0.21439117181920508, 0.1707685245371131, 0.1675397929716098, 0.1580992185002481, 0.1558944425895863, 0.1513697471049289, 0.13072864694939046, 0.12068089113273839, 0.11403454812488523, 0.10934085523256698, 0.10568767232683207, 0.09664578770578203, 0.09072061229028083, 0.08878636983820609, 0.0853957938074732, 0.08444826940177563, 0.0822160314308702, 0.08191762067726316, 0.07829650162065782, 0.07794974091576812, 0.07565747720513549, 0.0721596876850441, 0.06870563600714075, 0.06766819910745436, 0.06454231972101443]\n",
      "Row 34 - Column Numbers: [32 41 40 89 30 88 33 28 38 39 74 86 37 36 29 35 43 31 78 52 79  2 12 80\n",
      "  5  4  8 44  1 56  0 10 42  3 13 11  9 85 90 14 20 87 91], MI Values: [0.6589132113122842, 0.6479726613644816, 0.6043685240765004, 0.5628237492307457, 0.5416346036080313, 0.521645640678436, 0.45408232882174193, 0.43990166348400983, 0.4368469340751924, 0.39158474017250366, 0.3551015296305442, 0.3436127338197732, 0.3342616147154853, 0.30793458819287167, 0.30210464330076015, 0.2547895016786663, 0.25147509845387006, 0.18704762526179852, 0.1318444892478734, 0.12773246250446846, 0.12182153097619519, 0.11747560005254787, 0.09993696526051377, 0.09689650292456253, 0.09670112680552911, 0.09367692420841855, 0.09279000891834333, 0.09093985620778966, 0.09049841174829432, 0.08918579292805706, 0.08750394746818113, 0.08709868991881464, 0.08002420593659476, 0.07711971317009425, 0.07495306478075747, 0.07298015929327839, 0.0685825322136786, 0.06771394965493194, 0.06748508102814021, 0.06725286085851323, 0.06677633392818727, 0.06352632300524341, 0.05979450877373882]\n",
      "Row 35 - Column Numbers: [43 31 33 30 74 36 86 37 29 78 28 38 89 44 39 34 40 32 88 79 80 41  5  2\n",
      " 42  4 12  1  0  3 11 13 56 85 87 90 10 64 17 21 83 15 91], MI Values: [1.3860244468954068, 0.7457506706593469, 0.676225408758059, 0.6637829223064564, 0.6417520640136267, 0.41003162791165604, 0.39846097278793113, 0.37245697314779047, 0.36110892331598254, 0.36035661286731724, 0.3542576214733648, 0.28812166153925034, 0.28455742734958633, 0.2744838416218025, 0.25908379307944696, 0.2547895016786681, 0.2444710266515937, 0.24376381697461103, 0.2113827569500044, 0.20596754398312012, 0.2032245059398745, 0.20034425775401932, 0.1956334739924417, 0.1870192028603448, 0.18522516757732976, 0.13262659195667936, 0.1285549123325911, 0.11642248941903688, 0.11361591888716038, 0.1016623748148815, 0.09674046912721845, 0.095142371568528, 0.0801836035458896, 0.07727436282669675, 0.07446311599579492, 0.07216427126333969, 0.07091448732899774, 0.06950218448865986, 0.06903264964802514, 0.06815788789081711, 0.06455351051612634, 0.06380756444093993, 0.05848415311997446]\n",
      "Row 36 - Column Numbers: [86 37 33 29 74 28 89 41 38 40 39 43 35 88 30 34 31  5 32 56 78 79 80 44\n",
      "  2 12  4 42  1  3 90 10  0 13 72 14 77 64 87 57 70 46  6], MI Values: [1.0233770024292177, 0.8615166885581989, 0.7259968303690219, 0.6127287729060713, 0.6090092895887054, 0.5887599355969613, 0.5752000583378694, 0.5713794920745894, 0.5355098016260644, 0.47454758830574484, 0.4665352887983394, 0.4335648849167999, 0.41003162791165515, 0.39112029603754017, 0.38187736651661996, 0.30793458819287167, 0.2539363056818287, 0.20674579006625216, 0.1775297792498458, 0.15081603715863867, 0.14656523125808896, 0.11619314258747515, 0.11571876599131148, 0.1145234869763252, 0.10960845386111995, 0.0970948434370289, 0.0877144141798194, 0.07775809933113642, 0.07458627225738823, 0.07188834325973659, 0.06954945457795603, 0.06702934232361812, 0.06656537960473763, 0.0637980214953684, 0.06265064870037129, 0.06166886568276819, 0.06121318706422585, 0.06076563582838368, 0.0603698282500984, 0.0600022474540296, 0.05999309743629677, 0.059587362304820424, 0.05838254740343718]\n",
      "Row 37 - Column Numbers: [86 29 36 38 89 28 39 40 33 74 88 41 43 35 56 34 30 31 32  5 78 79 44 80\n",
      " 12  2  4 90  1 42 87 46  3  0 14 77 57 64 75 10 81 85 72], MI Values: [1.45827221487633, 1.1243314839301428, 0.8615166885582006, 0.8339552318828192, 0.75725247965641, 0.7435037784407115, 0.6894104126018572, 0.6269405732545383, 0.557628690570815, 0.5514988683591895, 0.5065004040074994, 0.4944806219210722, 0.4048082990644746, 0.37245697314779047, 0.35940226604219117, 0.3342616147154871, 0.3303698560876711, 0.21452991980362324, 0.17952444982802884, 0.12301925557245674, 0.1229936336440689, 0.11167013683338922, 0.10660787110909098, 0.09822950179437395, 0.09592473158963699, 0.09141368395878491, 0.07514331037207178, 0.07091755529673804, 0.06883285800983607, 0.06871969299735081, 0.066765545099301, 0.06572403954205441, 0.06558274587026869, 0.06455866987752579, 0.06416649947375319, 0.06138718973277957, 0.05958381308008942, 0.0586839187321484, 0.05770927457102015, 0.05541200876063623, 0.0543002203644134, 0.053567885640179114, 0.053098326138301566]\n",
      "Row 38 - Column Numbers: [89 39 40 28 29 37 88 86 41 36 33 74 34 30 43 35 32 31 56 78  5 79 44  2\n",
      " 80 12  4 90 42 87 64 10  3  0 46 54 27 63  1 55 61 52 81], MI Values: [1.2419280927673926, 0.9495031915623935, 0.9353087992452069, 0.8668221841314478, 0.8561076404645709, 0.8339552318828174, 0.7568375359220987, 0.7540596341394155, 0.6590139783160547, 0.5355098016260609, 0.49716674763380464, 0.4638361476100483, 0.4368469340751897, 0.32508215731131607, 0.2970750486302043, 0.28812166153925034, 0.19790915776020768, 0.16761107082894533, 0.14324753303636406, 0.10392867184476451, 0.10350223849689133, 0.09301615106454886, 0.08916423701914233, 0.08794009077204823, 0.08653427377214928, 0.08621577314512141, 0.07857614620487752, 0.07291292443408093, 0.06775644455948626, 0.06587368807998661, 0.06444153292271437, 0.06239411896947633, 0.0611391661707783, 0.05890813572238418, 0.05743119615494585, 0.05657172017433254, 0.0556670195981841, 0.052999594620209756, 0.05251122766241956, 0.05144646558632271, 0.050525831605085614, 0.05046119874021926, 0.050427398365081366]\n",
      "Row 39 - Column Numbers: [89 40 38 88 29 37 86 28 41 36 33 74 34 30 43 35 32 31 56 78 79  5  2 44\n",
      " 12  4 80 90 46 64 42  0  3  1 87 54 57 10 85 81 11 75 13], MI Values: [1.0535035116401659, 0.980751027799518, 0.9495031915623944, 0.7414381495833338, 0.7394482075767623, 0.6894104126018581, 0.6322229406595952, 0.6188553437562998, 0.597892725921354, 0.46653528879833495, 0.4358859922207863, 0.41880685619855296, 0.3915847401725019, 0.29261345923392224, 0.2629228824826715, 0.2590837930794496, 0.18312052004798485, 0.15267623549927567, 0.11061737849190223, 0.10303541936903038, 0.10121071598448683, 0.10050281527196514, 0.09409837181553016, 0.09268755609898616, 0.09122469199042627, 0.07574221883219856, 0.07038469791400459, 0.06777425757345945, 0.06718928231977817, 0.06637371235615408, 0.06470157204124849, 0.06376207874312012, 0.06157433149594027, 0.059317843630458, 0.056927475789509074, 0.0553570174716711, 0.050475458950668184, 0.049665682066896366, 0.048873507505192926, 0.048724267224924844, 0.048532049612547645, 0.045653657389332025, 0.045387402202069715]\n",
      "Row 40 - Column Numbers: [88 89 39 38 41 28 37 29 34 86 33 36 74 30 32 35 43 31 56 79 78  5 12  2\n",
      " 90 80 44  4 64 46 10 42 11  0 54  3 87 62 52  8  1 61 13], MI Values: [1.358468758232667, 1.2392621662048944, 0.9807510277995188, 0.935308799245206, 0.926520358369948, 0.7401508914135668, 0.6269405732545383, 0.624305023306202, 0.6043685240764987, 0.5904546129889008, 0.4791060933274034, 0.47454758830574484, 0.42293019416571376, 0.3527990507831582, 0.2643435373277079, 0.24447102665159282, 0.24139738990497683, 0.13699943157822414, 0.10838563263965639, 0.1029822194696477, 0.09964875862896427, 0.09746128685535993, 0.09185969685609141, 0.08826839034197231, 0.08755455049272953, 0.08752252944643946, 0.08181196297427373, 0.07604174073333958, 0.072912801172893, 0.07131829013591684, 0.06301067329213339, 0.06159199509503921, 0.0600744169282601, 0.05966325856990995, 0.05887006365191372, 0.05721261367801134, 0.05676698284365411, 0.05477366448826615, 0.054719591158505665, 0.0521148561565834, 0.05184786967249444, 0.05173422697187924, 0.050382935130099504]\n",
      "Row 41 - Column Numbers: [40 89 88 28 38 34 39 36 37 86 29 33 74 30 32 43 35 31 56 78 79  5 44  2\n",
      " 80 12 90 62 10  0  1  3 42  4 61 64 92 11 70  6  8 52 13], MI Values: [0.9265203583699506, 0.9100181021852727, 0.8687228214668874, 0.6683242642188896, 0.6590139783160538, 0.6479726613644816, 0.5978927259213549, 0.5713794920745912, 0.4944806219210731, 0.47456031717445235, 0.44277394507429957, 0.4346502711337239, 0.33199699186004406, 0.3159693429377697, 0.23153387463475372, 0.21422375662965543, 0.20034425775401843, 0.1298704817987586, 0.11875744932887322, 0.0926509060956926, 0.08676758111423233, 0.086057783978851, 0.08262255635642912, 0.07942866688885086, 0.0785488622631787, 0.0742530711565692, 0.07307672025710232, 0.06941263844280599, 0.06936075480536719, 0.06665335877299139, 0.06410363270210784, 0.06306413363039987, 0.06207958706935557, 0.05954608451087129, 0.0593461118278249, 0.057899646129423665, 0.05389698575662916, 0.053384856694632, 0.05325141402769873, 0.05243412828986749, 0.052078907698307475, 0.05177082062384475, 0.050887404336976694]\n",
      "Row 42 - Column Numbers: [90 31 44 43 35 78 80 30 92 33 21  5  1 74  2 79 12  0 17 83 28 34 85 32\n",
      " 36 11 86 91 37 38 16  4 15 10 39 29 20 19 87 89 13 41 40], MI Values: [0.5736361560630607, 0.24809815156702442, 0.237501584176659, 0.2123646632862819, 0.18522516757733065, 0.17401757617932745, 0.14508216519352857, 0.11531395362702668, 0.11438741669921182, 0.11403454812488256, 0.09722563185672684, 0.09376382987344112, 0.09265639520815316, 0.09219897198964677, 0.09190658625377246, 0.09102336506577036, 0.08912140713055283, 0.08872664637914252, 0.08466458683253641, 0.08290682477634803, 0.08020834452426406, 0.08002420593659121, 0.07969793759561306, 0.07802938607998477, 0.07775809933113642, 0.07587529502253965, 0.0754741707644273, 0.06881214952706838, 0.06871969299735348, 0.06775644455948715, 0.06750837136584042, 0.06712048581871777, 0.06699419564638998, 0.06547249101527441, 0.06470157204125115, 0.06416664878429224, 0.06355486571293678, 0.0632209015494567, 0.0630884431737817, 0.06261691628512, 0.06240830984967349, 0.06207958706935468, 0.0615919950950401]\n",
      "Row 43 - Column Numbers: [35 31 33 74 30 36 86 37 29 78 28 44 38 89 39 34 40 80 41 42  5 79 88 32\n",
      "  2 12  0  4  1  3 11 13 87 85 56 83 21 17 90 10 91 77 64], MI Values: [1.386024446895405, 0.8121927311945987, 0.6277452858407475, 0.6243039700489881, 0.4933942675879788, 0.433564884916799, 0.4240950333084843, 0.4048082990644737, 0.38621997040959855, 0.370397111365631, 0.3130926126664342, 0.30395671539799096, 0.2970750486302043, 0.28802774608809134, 0.2629228824826706, 0.25147509845387095, 0.24139738990497772, 0.2276321837680122, 0.21422375662965365, 0.21236466328628278, 0.20819529046906204, 0.20739130754119195, 0.20626412498042956, 0.1925310675883667, 0.18681968571483676, 0.14156956810137, 0.1358699397958949, 0.1316783860928359, 0.12913107009156466, 0.1038170751558507, 0.09481730555192946, 0.09195467760152898, 0.08755593140089069, 0.08744850763647793, 0.08170555433368687, 0.081560766459293, 0.07911198418961085, 0.07861749607301682, 0.07721049556759585, 0.07182439963604015, 0.07147186167010044, 0.06546454180161465, 0.06421723199729623]\n",
      "Row 44 - Column Numbers: [31 43 78 35  4 42 33 79 30  2 74  5 54  0 64 32 36 80 86 37 29 87 23 88\n",
      "  1 28 39 89 34  3 38 13 11 12 10 85 46 41 40 63 91 62  6], MI Values: [0.38340369680082365, 0.3039567153979892, 0.2940959242977499, 0.27448384162180073, 0.2577169657460203, 0.23750158417665634, 0.15589444258958807, 0.1535208253346898, 0.15101976681000817, 0.14614605566374905, 0.13751208245379942, 0.1330855289284827, 0.13216267787018499, 0.12631372813240205, 0.12575424005177993, 0.12104168683611682, 0.11452348697632786, 0.11196280971917094, 0.10936129874317668, 0.10660787110909098, 0.10392751587923676, 0.10044717697415884, 0.09985139888775052, 0.09784483548609302, 0.09756958090355994, 0.0973992316948431, 0.09268755609898616, 0.09241113709100457, 0.09093985620779232, 0.0903461896754747, 0.08916423701913878, 0.0882487868884656, 0.08789263097170785, 0.0865487450581588, 0.08386645043593699, 0.08318123056251459, 0.08302480760550157, 0.08262255635642735, 0.08181196297427551, 0.08074364625578223, 0.07356394424112711, 0.07306242342033098, 0.07123886187653294]\n",
      "Row 45 - Column Numbers: [65 60 66 76 64 63 69 27 84 53 54  6 75 62 57 70 81 12 46 61 11 50 72 87\n",
      "  1 10 85 52 49 68 13 77  3 48 21 24 32 90 91  8 30 79 15], MI Values: [0.3355390992669385, 0.24105785735212137, 0.16669975622521527, 0.14089157380955708, 0.13477024068243892, 0.11692650889904499, 0.10868038934784607, 0.10364354834175771, 0.10150362847124583, 0.09056761307301286, 0.0798331274015025, 0.07607959090818639, 0.07550304956704501, 0.07129070394238113, 0.06353587781859105, 0.06252081423776445, 0.05993439653997168, 0.05696539251436761, 0.05614165957912931, 0.05305353245500477, 0.05289097853795344, 0.05163697152796942, 0.05126811930396258, 0.049018668863451076, 0.048759179040770206, 0.04826951163990145, 0.04548841097074785, 0.045170627201460256, 0.04515557347533239, 0.04505498244851758, 0.04468423892141704, 0.04437075080106645, 0.04344271363863772, 0.042062378026346714, 0.041189709960936405, 0.04052516260945005, 0.04034464006210747, 0.04008368476259694, 0.039929482136464856, 0.039675854506701747, 0.039107723692991314, 0.038854237195490526, 0.038161379909507964]\n",
      "Row 46 - Column Numbers: [64 51 55 59 48 68 47 58 61 87 75 49 72 56 54 84 27 70 67  6 74 57 17 69\n",
      " 81 14 21 50 77 63 44 52 85  1 19 76 20  4  0 79 62  2 40], MI Values: [1.1094691017199603, 0.36567183873432274, 0.3141727399115952, 0.23992709365254683, 0.2171439106790931, 0.19852690016740127, 0.18923509125775695, 0.1858984961031256, 0.17267857439960022, 0.16549438774061187, 0.15983167864594883, 0.15828858721216044, 0.15559450174685807, 0.1460850846009656, 0.14012136027135202, 0.13751725928655478, 0.13632308186498943, 0.1328114960531792, 0.13279522094755158, 0.13099684473508688, 0.11736212179504424, 0.11368720902898488, 0.11280369881762642, 0.105422623025202, 0.10140282553967683, 0.09266115822732957, 0.08964547025689651, 0.08911598382671393, 0.08487347419103042, 0.08355750196952805, 0.08302480760550068, 0.08232030940720492, 0.08171791357507097, 0.08010342629738698, 0.07977684117637374, 0.07963991449703212, 0.07862828607228867, 0.07856401142112102, 0.07681250087322677, 0.07650530330583649, 0.07403272493206359, 0.07325788085011453, 0.07131829013591773]\n",
      "Row 47 - Column Numbers: [48 55 82 49 51 64 46 61 56 50 14 57 87 54 63 75 67 70 69  6 72 74 68 23\n",
      "  4 52 20 59 38 27 85 84 11 81 33 92 89 60 41  7 36 77 19], MI Values: [0.4249124097885648, 0.4187425231559816, 0.3602265067790995, 0.2776897644328633, 0.24912743330867393, 0.1987447932521178, 0.18923509125775695, 0.15384874665912562, 0.10368137158256019, 0.09785925823341302, 0.09074348902636764, 0.08687796447828866, 0.08569788060934425, 0.08001798979213337, 0.07907233827318905, 0.07403127407645904, 0.07249971148987289, 0.07068379697727956, 0.06874455994522588, 0.06549702884688635, 0.06175094572082518, 0.06009771362514993, 0.05906462224581688, 0.05704895029918333, 0.056865014508378664, 0.05682164950861601, 0.05161482461035316, 0.05139487626535377, 0.050000458629791744, 0.047417480685076896, 0.04726109720318572, 0.04708602460329292, 0.0467491462024574, 0.04656568399330041, 0.045808067196454694, 0.04460527570146677, 0.04416183571061527, 0.043961928173374076, 0.04334931626754024, 0.043171664331128845, 0.04285749863832411, 0.041651660789991496, 0.040805913716284614]\n",
      "Row 48 - Column Numbers: [49 55 47 51 46 50 64 75 68 67 69 87 61 54 58 81 59 70 56 57 63 14 52 84\n",
      "  6 73 72 91 60 66 18 45 85 11 74 21 17  4 76 38 19 32 44], MI Values: [0.553678897514204, 0.5019751647569173, 0.4249124097885639, 0.2875171464071613, 0.2171439106790931, 0.1743136297813912, 0.11110937927605313, 0.10037244122026134, 0.08934545133594263, 0.08190429469032878, 0.0736143304488408, 0.07327006385127088, 0.0721867594925314, 0.07042527416616018, 0.0687315220763578, 0.06681937537003169, 0.06642447830364517, 0.06437836072642522, 0.0635873831512015, 0.060791248768552464, 0.057609186216970976, 0.05528245353972938, 0.05372925078899371, 0.04909830573294105, 0.04808633609087387, 0.045306406824380474, 0.04489736208567496, 0.044709846969715805, 0.04357966587574236, 0.04284931649405177, 0.04283733769362197, 0.0420623780263476, 0.040772805188195704, 0.04013167977317522, 0.03986903738847314, 0.03954931815568408, 0.03897874301162396, 0.03884934604555568, 0.0387817158798871, 0.03828887823525573, 0.03729803186228775, 0.03670448581979002, 0.03666047870806732]\n",
      "Row 49 - Column Numbers: [48 55 47 50 51 75 46 69 54 64 68 81 52 61 57 67 87 63 70 56 60 84 11 14\n",
      "  6 45 13 66 58 12 59 72 10  1 79  4 77 85 32  0 74 40 36], MI Values: [0.5536788975142031, 0.30360053691119226, 0.27768976443285975, 0.2735029225169381, 0.1755926065938338, 0.16380558437787318, 0.15828858721215955, 0.09982396156077034, 0.0899951771509615, 0.08729689308508082, 0.0805251845303161, 0.07578213385519295, 0.0734512632183959, 0.07118839940287724, 0.06818162225492586, 0.06462675171117471, 0.05826597066506878, 0.05474056322253951, 0.05205162711625633, 0.04949584081348313, 0.04890714820172626, 0.047598231033918914, 0.0471786080006531, 0.04697649944513582, 0.04612338247236547, 0.04515557347533328, 0.04394002279515519, 0.0427889260255494, 0.04277730549634029, 0.041579343265056856, 0.03968935771140636, 0.03878327857790431, 0.03721262391298552, 0.03708316769882014, 0.03707875631470614, 0.03437124492900345, 0.03420072144079178, 0.03393860185339559, 0.03373647790879719, 0.03296788902954706, 0.032940030634634354, 0.03271399526283414, 0.03233124919474406]\n",
      "Row 50 - Column Numbers: [75 49 48 69 81 57 54 47 55 68 52 46 64 84 87 51 76 45 67 10 12 14 66 63\n",
      " 60  4 74 85 17 11  6 70 33 79 83  8 36 24 21  0 88 89 40], MI Values: [0.38569583316040035, 0.273502922516939, 0.1743136297813921, 0.13649561521326792, 0.13615369070630745, 0.12386611734750641, 0.11005231669100635, 0.0978592582334139, 0.09343475605257989, 0.09313301709157429, 0.08963552340153047, 0.0891159838267166, 0.08223331555010471, 0.06909627215253966, 0.0664099664637332, 0.05717803565613533, 0.05211485875131405, 0.051636971527967646, 0.049028136696537494, 0.04645372478558407, 0.046362851486650314, 0.04624367400979423, 0.04570965837784602, 0.04395880445259959, 0.04352223482917594, 0.04297224529545307, 0.04249884332512721, 0.04210332584072418, 0.041711486256092556, 0.041695189003549515, 0.04113881744298897, 0.04104741966052927, 0.04091402778420328, 0.04064421390754891, 0.04045686991204356, 0.03995848045904005, 0.03949861996272741, 0.039383429640937884, 0.038877820203155444, 0.03883494246593333, 0.038717645473936635, 0.038634738171873906, 0.03778877017396365]\n",
      "Row 51 - Column Numbers: [55 46 48 47 49 59 64 61 56 58 68 67 50 54 84 14 87  6 44 52 75 69 63 70\n",
      " 21 76 66 60 57 89  4 32 41 40 81 38 11 23 62 74 72  0 88], MI Values: [0.4918905885238507, 0.36567183873432274, 0.2875171464071622, 0.24912743330867393, 0.1755926065938347, 0.15335403151725657, 0.14408460937434686, 0.1323322880421669, 0.09492283806278046, 0.08131092018359531, 0.06392417227606728, 0.06049342127079882, 0.05717803565613444, 0.05383149700687451, 0.050444118959005024, 0.05026820068852356, 0.04809307532768603, 0.04800319914719342, 0.0474286517687057, 0.046076652615822944, 0.04517706634337504, 0.043804660168771825, 0.042590107680609, 0.03955596847245513, 0.0389668719566183, 0.03840491710777805, 0.03826743593598536, 0.03684825881094511, 0.03623578817846784, 0.0361041768011896, 0.03552228501544441, 0.034884214114486056, 0.03474350659770309, 0.034398958953260284, 0.03368774459666746, 0.03349076627149561, 0.03327235828735464, 0.03304187113566659, 0.03265504215054538, 0.03189647338370527, 0.03187888017866847, 0.03186557598989026, 0.031744992944004125]\n",
      "Row 52 - Column Numbers: [69 32 57 54 81 75 68 34 30 64 50 46 49 33 21 17 63 88  6 61 55 35 86 28\n",
      " 47 19 66  7  4 40 48 74 41 10 72 37 84 58 38 83 70 20  1], MI Values: [0.5772799725175162, 0.5366720434860497, 0.5130885687568068, 0.3225256074571332, 0.29251898737336113, 0.193542163657888, 0.12789690664174191, 0.1277324625044658, 0.10641737910058513, 0.0948475569445888, 0.0896355234015278, 0.0823203094072067, 0.07345126321839857, 0.072159687685045, 0.06802973139084934, 0.06703671873903261, 0.06405860187379542, 0.06273572137952055, 0.06139781255903909, 0.06122875212893497, 0.06013022861701689, 0.05843192812514708, 0.057757311630738606, 0.05772311949448383, 0.05682164950861601, 0.05518017282950538, 0.05499973892547416, 0.05481337747376269, 0.054736479053383746, 0.054719591158505665, 0.05372925078899371, 0.05209049250429132, 0.05177082062384297, 0.05139303267069195, 0.05111353303252564, 0.05089562323484653, 0.05067571023863948, 0.050481480883075136, 0.05046119874022281, 0.05022240658314203, 0.05011325603669903, 0.04998115622272348, 0.04960552836869159]\n",
      "Row 53 - Column Numbers: [62 63 64 45 70 85 17 10 91 72 60  4 69 87 12 46 21 11 15 27 20 19 65  1\n",
      "  5  8  0 84 83 14 16 30 18 79 22 28 73 36 66 33 44  2  9], MI Values: [0.40877114705633577, 0.10768325129662326, 0.09142254528217908, 0.09056761307301286, 0.07763014753084896, 0.07291262831419587, 0.06894645621138817, 0.06799093673704526, 0.06654270992309375, 0.06557217989953035, 0.06551159416228547, 0.06101431583981842, 0.05994221903533248, 0.05849475346295652, 0.05643638304159726, 0.05373645940673466, 0.05359496095281546, 0.05257556822858955, 0.05145699897162004, 0.0512160780449582, 0.04985185416914284, 0.047971786345549106, 0.047543267529873035, 0.04687607939115512, 0.046211483174281476, 0.045677188956067205, 0.04379488308218882, 0.04284987062613599, 0.04248356027197353, 0.042449553699675846, 0.04223363657743473, 0.04200308548928522, 0.04179825178695129, 0.04128772798638014, 0.04072600160757123, 0.04068711874009434, 0.03933717348757071, 0.03925453370539245, 0.03848324031768957, 0.03752841617132585, 0.03638983181890776, 0.03585269752426079, 0.03562342742166713]\n",
      "Row 54 - Column Numbers: [81 69 52 75 57 68 64 46 44 32 50 62 63 84 49 47 45 66 76 70 74 55 61 87\n",
      " 48 58 72  6 60 83 30 40 21 35 17 38 36 56 28 39 88 13 51], MI Values: [0.7379530571253516, 0.6991638866458327, 0.3225256074571341, 0.28357752574033057, 0.2796508865934202, 0.2576301492482225, 0.15163383746901538, 0.14012136027135202, 0.1321626778701832, 0.11793416791373446, 0.11005231669100635, 0.09996017287947367, 0.09375651906359739, 0.09285394516933021, 0.0899951771509615, 0.08001798979213337, 0.0798331274015025, 0.07892182637938827, 0.07324275519206846, 0.07247468124904266, 0.07245070956178878, 0.07176330422608057, 0.07112370577561311, 0.07067226287875972, 0.07042527416615751, 0.06899903291146714, 0.06863149347900066, 0.06777316229745178, 0.06704206660250378, 0.06494064826102708, 0.060874758017741115, 0.05887006365191105, 0.05810380963000572, 0.05748468340966095, 0.05669604970686226, 0.05657172017433165, 0.05650255737683452, 0.0557378324255442, 0.05541299819598766, 0.055357017471672876, 0.05436024408042606, 0.05430024107788167, 0.05383149700687362]\n",
      "Row 55 - Column Numbers: [48 51 47 46 49 64 59 61 50 58 68 75 67 69 56 54 81 84 63 52 57 23 87 14\n",
      " 70  0 38 73 41  1 44 37  4  6 88 72 11 86 36 89 76 62 74], MI Values: [0.5019751647569191, 0.4918905885238507, 0.4187425231559816, 0.3141727399115961, 0.30360053691119226, 0.1455355267788132, 0.10391523768986577, 0.10320434092076614, 0.09343475605257989, 0.09039691815655626, 0.08433296148313651, 0.07894014514832115, 0.07810178261121159, 0.07626677924718717, 0.07457832871124648, 0.07176330422608146, 0.0666084572296537, 0.0649658298184459, 0.06183261687680819, 0.06013022861701511, 0.05926409456159032, 0.05849481745654206, 0.05810381930205111, 0.05661782886079081, 0.05210958027079382, 0.05151582272524369, 0.05144646558632182, 0.0513717845320274, 0.04985324468381247, 0.04872468386788853, 0.04840563532307751, 0.047905222457149677, 0.047753548931313006, 0.04774985453638614, 0.046832066350649626, 0.046337404344297006, 0.04532790922027541, 0.04508240476302117, 0.04498650870497656, 0.04457765391180146, 0.044450219960144643, 0.04410009039404095, 0.04400663644262881]\n",
      "Row 56 - Column Numbers: [61 37 64 86 29 36 46 38 28 67 74 89 41 59 39 40 33 87 47 51 21 34 88 20\n",
      " 43 35  1 17 63 55  2 68 15  0  4 85 91 24 30 77 58 48 16], MI Values: [0.43147747233694655, 0.3594022660421903, 0.22066317128273738, 0.19813479850705384, 0.1713073755137069, 0.1508160371586369, 0.14608508460096736, 0.14324753303636495, 0.14153000235829616, 0.1390223315396053, 0.12763532576626613, 0.12759658270105412, 0.11875744932887322, 0.1140267649058524, 0.11061737849190578, 0.10838563263965728, 0.10568767232682852, 0.10439486730787184, 0.10368137158256019, 0.09492283806277957, 0.09187841023316512, 0.08918579292805973, 0.08812813925290719, 0.08286165353433983, 0.08170555433368776, 0.08018360354588872, 0.07992095121214593, 0.07971577342061753, 0.07711766737948622, 0.07457832871124559, 0.07436029178819847, 0.07341505483174426, 0.07262961413738722, 0.07242362723832141, 0.0720538145634535, 0.07002602366231869, 0.06996541088145225, 0.06753872107738657, 0.06707550157230013, 0.0658465345860213, 0.06480713020071249, 0.06358738315120327, 0.06331255297437988]\n",
      "Row 57 - Column Numbers: [52 69 75 54 81 63 64 68 50 46 23 72 87 17 74 61 47  6 70 21  7 84 62 49\n",
      " 73 82 92 58 45  0 19 66 56 48 36 37 55  5 44 83 60 79 77], MI Values: [0.5130885687568085, 0.4492286562322283, 0.3175403262160419, 0.2796508865934202, 0.2386747781742029, 0.19893022670047156, 0.1706591351738478, 0.12717047965108375, 0.12386611734750552, 0.113687209028984, 0.11007546217848985, 0.1056703039813307, 0.09943857195888661, 0.09928683256670379, 0.09565681017050132, 0.09358492153412179, 0.08687796447829044, 0.08592201720969239, 0.08195684550894988, 0.08110178494543341, 0.07616119177035774, 0.07392888704485934, 0.07251648801624277, 0.06818162225492586, 0.0667097043144338, 0.06659031769662516, 0.06608857489515785, 0.06605291746158404, 0.06353587781859193, 0.061740263953568686, 0.061490900764048284, 0.06146140592633831, 0.06124498359253927, 0.060791248768552464, 0.06000224745403049, 0.0595838130800912, 0.059264094561592096, 0.058399152771426266, 0.05763128744059465, 0.05711690835432748, 0.056631880706102145, 0.05618380082027041, 0.05594599871005901]\n",
      "Row 58 - Column Numbers: [46 59 67 61 64 55 75 51 81 54 48 68 57 56 44 69  0 52 88 79  5 84 73  4\n",
      " 74 40 17 87 49 70 72  7 89 47 62 38  2 43 37 50 60 77 86], MI Values: [0.1858984961031256, 0.17684958964553754, 0.1376164223851939, 0.10259159901626358, 0.09323139589981633, 0.09039691815655537, 0.08672016085400625, 0.0813109201835962, 0.07170077496787108, 0.06899903291146536, 0.06873152207635869, 0.06709058591021666, 0.06605291746158226, 0.0648071302007116, 0.06182062594159721, 0.053739795644960786, 0.05071325731351273, 0.05048148088307869, 0.04789057473566327, 0.047499732845677656, 0.04605361797762875, 0.045749765509683904, 0.04511521302719235, 0.0451146228488728, 0.04429686953990242, 0.0436866294276701, 0.042952045110664194, 0.04293717981312373, 0.04277730549634118, 0.04249097503546562, 0.041569158118069716, 0.0414072565023762, 0.04087411787997919, 0.04008012588680554, 0.03946179272307493, 0.039370558103208886, 0.03780798205952163, 0.03731442430222387, 0.03713892176412692, 0.036719401321429146, 0.03638037155973528, 0.03628517346620885, 0.03595011355909605]\n",
      "Row 59 - Column Numbers: [80 46 61 58 51 56 55 64 67 48 75 47 44 74 68 81 73 41 33 90 43 54 40 49\n",
      " 62 84 88 57 89 38 45 21 79 70 37 50 31  3 87 52 86  5 69], MI Values: [0.2465372262762342, 0.23992709365254772, 0.18600181466110133, 0.1768495896455411, 0.1533540315172539, 0.11402676490585151, 0.10391523768986577, 0.10143685103057543, 0.07292707939904464, 0.0664244783036434, 0.05458094170480976, 0.051394876265351996, 0.048036989305325406, 0.046929431867398286, 0.0468761986306756, 0.04281709288360336, 0.041442701275810734, 0.04123745905248555, 0.04109308677692969, 0.04080241822363018, 0.0405708194427179, 0.04002737117363697, 0.039970526744237844, 0.039689357711408135, 0.03937800895674659, 0.03858909846737113, 0.038104381220402495, 0.03733929606864361, 0.037336166429184026, 0.03621910618345936, 0.036194932260467994, 0.03564645785808285, 0.03530947035182841, 0.034605332803858246, 0.034270780090086106, 0.03385625356854849, 0.033688224144492906, 0.03365099687676132, 0.03359866945243972, 0.03358824636426494, 0.033156708793527834, 0.032867078986785536, 0.03252523413328934]\n",
      "Row 60 - Column Numbers: [45 66 64 75 69 76 46 54 53 84 81 57 65 63 56 70 49 61 52  6 47 62 48 50\n",
      " 24 55 10 87  1  4 68 72 51 58  8 17 85 21 11 44  0  9  2], MI Values: [0.24105785735212315, 0.14313213465555208, 0.13185070300011947, 0.08789136339985504, 0.08538631330874047, 0.07359513171289755, 0.06886160619467585, 0.067042066602502, 0.06551159416228902, 0.062130659320295045, 0.06016542150362536, 0.056631880706101256, 0.05516399778635517, 0.05208181872897821, 0.04990175130811547, 0.04924267114111114, 0.048907148201728035, 0.04565762279498298, 0.04550928202171889, 0.04432955091321311, 0.0439619281733723, 0.043609459383989524, 0.04357966587574058, 0.04352223482917683, 0.042912718955503415, 0.04289723654803357, 0.04246041760917052, 0.041422133425950136, 0.039365018633776394, 0.03811521797273176, 0.03776259020466188, 0.03735714461537043, 0.03684825881094511, 0.0363803715597415, 0.03495408974131564, 0.034779085744490956, 0.034559288190181725, 0.03360900022740143, 0.033444948836911514, 0.032907121469348155, 0.032668405905845965, 0.0324609794611499, 0.03181022364805397]\n",
      "Row 61 - Column Numbers: [56 11 64 59 46 47 51 87 12 85 55 58 20 10 21 57  1 91 63 23 17 69  2 68\n",
      "  0  4  6 24 79 77 83 48 49 54 74 67 33 15  7 84 32 14 52], MI Values: [0.43147747233694567, 0.42117961947471017, 0.30274924109928225, 0.186001814661104, 0.17267857439960288, 0.1538487466591274, 0.1323322880421669, 0.11609849133691696, 0.11175003676089812, 0.10334008173381015, 0.10320434092076347, 0.10259159901626269, 0.10190813419336209, 0.10067720955483761, 0.09520585153423244, 0.09358492153412534, 0.0919232880302312, 0.0871403303663465, 0.08651352031480286, 0.08578580449603024, 0.0845797268571502, 0.08175995345877496, 0.0807578644808169, 0.0801785495224161, 0.07987921333337233, 0.0793639777794386, 0.07748176490715064, 0.0766084916060148, 0.07561052109916311, 0.07553429240407095, 0.07310938021788527, 0.07218675949252873, 0.07118839940287724, 0.07112370577561222, 0.07004761148596383, 0.06954426713919748, 0.06766819910745347, 0.06669711932901201, 0.06659717282749611, 0.06553165111754122, 0.06347776301673225, 0.061701359771839215, 0.06122875212893497]\n",
      "Row 62 - Column Numbers: [53 63 64 54 72 32  6 70 46 21 44 57 28 45 17 41 69 85  0 87 34 30 84 33\n",
      " 74 19 40 88 12  2 37 20  4 75 11 10  1 31 89 43 36 61 23], MI Values: [0.40877114705633755, 0.1279415691665342, 0.11842971465453456, 0.09996017287947367, 0.08923240114087871, 0.08212300251017979, 0.08134777223811351, 0.07551883001699622, 0.07403272493206625, 0.07348744391152451, 0.0730624234203292, 0.07251648801624189, 0.07174551471409796, 0.07129070394237846, 0.07054503826931224, 0.0694126384428051, 0.06494490899076766, 0.06122602061900739, 0.060570066674142886, 0.06022931405757159, 0.05971560831514555, 0.058950094823821075, 0.05873104823880926, 0.05850112049998302, 0.05785656052338606, 0.057623187032919354, 0.05477366448826526, 0.05440889071046939, 0.05387677226496379, 0.05315849709315046, 0.052254464230390596, 0.05209308293447634, 0.051951533735175026, 0.05132260781067011, 0.05125901030097513, 0.05100764313742001, 0.050656346920683326, 0.05058193701037439, 0.05028273620915957, 0.05013562158198859, 0.0501292056996574, 0.05003847734903477, 0.04962794973529405]\n",
      "Row 63 - Column Numbers: [57 64 72 87 70 62  6 45 65 53 14 54  4 61 92 46 44 84  7 47 24 56 91 74\n",
      " 66  0 85 23 18 76 69 52 82 73 68 55 11 10  1 81 48 43 17], MI Values: [0.19893022670047422, 0.16474578635889525, 0.14441268837025323, 0.14223108828764808, 0.1360734064984701, 0.12794156916653598, 0.11759316702333766, 0.1169265088990441, 0.10914449076512156, 0.10768325129662504, 0.09840075284083394, 0.09375651906359561, 0.09074112883170304, 0.08651352031480108, 0.08472994154227464, 0.08355750196953071, 0.08074364625578578, 0.07977254852835358, 0.07907681278759515, 0.0790723382731855, 0.07871775795832114, 0.07711766737948711, 0.07678764806995986, 0.0765734948289225, 0.07406004109092024, 0.07375851842512127, 0.07313981190535657, 0.07257144170705043, 0.06986318552324633, 0.06663758575631373, 0.0653233908008124, 0.06405860187379808, 0.06403591879491888, 0.06298018698645702, 0.0628392353335725, 0.0618326168768073, 0.06124640975608653, 0.05988190445075414, 0.0589489276098476, 0.057634411390770524, 0.05760918621697009, 0.05744789795037342, 0.056767715502631155]\n",
      "Row 64 - Column Numbers: [46  6 61 56 87 47 27 68 57 63 54 55 51 75 74 84 69 45 60 10  4 14 44 23\n",
      " 62 72 20 66 48 76 65 85 12 11 81 70  1  8 59 17 52  7 77], MI Values: [1.1094691017199603, 0.4786059164536729, 0.30274924109928225, 0.22066317128273738, 0.22048913023609096, 0.1987447932521187, 0.18682361749818366, 0.17760682722466647, 0.17065913517384423, 0.1647457863588926, 0.1516338374690145, 0.1455355267788141, 0.14408460937434509, 0.14236178948324518, 0.14209884783445936, 0.13984183102276582, 0.13741479855139893, 0.13477024068243804, 0.13185070300012303, 0.1299306324648466, 0.12979914510191115, 0.12701720438149788, 0.12575424005177815, 0.12382874483289896, 0.11842971465453278, 0.11641659888849265, 0.11253209164348021, 0.11225512605831867, 0.11110937927605224, 0.10732056478952767, 0.10654049307470448, 0.10591493223352533, 0.10535355610052566, 0.10500346113093073, 0.1037050834642379, 0.10306102384276805, 0.10272291690296331, 0.10254326229903832, 0.10143685103057631, 0.1003732877747634, 0.09484755694459235, 0.09462334579778542, 0.09447565520740842]\n",
      "Row 65 - Column Numbers: [27 45 63 64 66 76 60  6 84 53 62 13 46 31 74 23 57 79 15  1 61 28 90 87\n",
      " 25 18 47 35  4 10 19 22  2 16 54 17 38  5 70 43 11 71 55], MI Values: [0.6065603894953897, 0.3355390992669385, 0.10914449076511978, 0.10654049307470537, 0.07400054698096614, 0.06574940460414158, 0.05516399778635073, 0.05313625162063573, 0.05200772742261606, 0.04754326752987392, 0.04210859287540458, 0.04141383027204526, 0.04065382889106317, 0.04016739913483747, 0.03927197805547333, 0.03543013877976531, 0.03532486757824671, 0.03390511473012481, 0.03356935029377528, 0.0334370867070275, 0.03268513124965988, 0.032538341997700115, 0.03243135734308211, 0.03240600070639843, 0.03173822340394317, 0.03125147202710554, 0.030917863808890722, 0.030897225961695085, 0.03052268994560059, 0.030516181395221054, 0.030348441731518072, 0.030328529199157295, 0.030171195067245193, 0.030140476904725766, 0.029872492359135805, 0.029334903001505097, 0.029234888513575363, 0.02891810299955555, 0.02890138730320313, 0.02881055664071308, 0.028497828396734093, 0.02842485280534124, 0.028331991996227934]\n",
      "Row 66 - Column Numbers: [76 84 45 60 64 69 54 63 65 44 75 46 81 57 87 52 10  6 68 32  3 50 70 62\n",
      "  8 48 11 49 55 88 12 53 27 51 21 41 30 34 89 56 61 85 35], MI Values: [0.3276867048743224, 0.19621110110385498, 0.16669975622521527, 0.14313213465555208, 0.11225512605832044, 0.08774329941118442, 0.07892182637938827, 0.07406004109092112, 0.07400054698096792, 0.0657832364108204, 0.06574781745996905, 0.06557772498449133, 0.06464382902376808, 0.061461405926340085, 0.057380307752954884, 0.05499973892547505, 0.052649459598339554, 0.05121302295319019, 0.049935593149331936, 0.046364996147670645, 0.04601614539536314, 0.04570965837784691, 0.045050505206226, 0.044186414063735135, 0.042936712655239795, 0.042849316494054435, 0.04280397591400931, 0.0427889260255494, 0.042241733113475455, 0.039561716831260973, 0.0386714507746424, 0.038483240317686906, 0.03842749677431723, 0.03826743593598536, 0.0377725314890629, 0.03736335808473523, 0.03715626177182507, 0.03696164121794787, 0.03657013877780546, 0.03621018306623114, 0.036192436537979766, 0.03603333099672312, 0.03582784273636985]\n",
      "Row 67 - Column Numbers: [56 58 46 48 55 59 47 61 64 49 51 68 70 75 50 54 63 69 72 81 73 57 87 41\n",
      " 79  7 52 92 71  3 34 33 36 45 18 22 74  2 21 39 77 40 89], MI Values: [0.1390223315396062, 0.13761642238519123, 0.1327952209475507, 0.0819042946903279, 0.07810178261121248, 0.07292707939904286, 0.07249971148987466, 0.06954426713920014, 0.067158129948651, 0.06462675171117294, 0.06049342127079882, 0.05573066244705327, 0.05131323241564267, 0.050048166172831365, 0.04902813669653483, 0.04789187006885953, 0.04359634849634464, 0.04356102015565355, 0.042934138904747066, 0.041962299374367795, 0.03947764246554897, 0.03874132263576069, 0.0375586609402454, 0.03748203714709142, 0.03612567970739633, 0.03552096699697227, 0.03431893068828895, 0.03385542532989394, 0.03284593157964766, 0.03260253611544073, 0.03230214768395179, 0.032080902109909104, 0.032068284532125624, 0.031703696876647314, 0.03167709034729871, 0.03152308217100508, 0.0313239473107263, 0.030862122044114315, 0.030431654414645237, 0.030192101527670268, 0.03015615956557216, 0.03014741947648325, 0.030105513462540756]\n",
      "Row 68 - Column Numbers: [81 54 69 46 64 75 52 57 50 48 55 87 21 49 61 16 84 56 17 83 44 58 20 19\n",
      " 28 74 51 70  1 63 72  4  0 47 76 15 79  2 67 85 73 88 40], MI Values: [0.273919599429445, 0.25763014924822425, 0.21452460580928268, 0.19852690016740215, 0.17760682722466647, 0.13909061707178783, 0.1278969066417437, 0.12717047965108375, 0.0931330170915734, 0.0893454513359444, 0.0843329614831374, 0.08279666247431816, 0.08274897552594052, 0.08052518453031432, 0.08017854952241699, 0.08013941132973379, 0.07495229498264155, 0.07341505483174426, 0.06961403770779029, 0.06805662497684573, 0.06773250218080751, 0.06709058591021577, 0.06678931920015962, 0.06634530228217894, 0.0648958659595209, 0.06481434993591328, 0.06392417227606728, 0.06381372155874665, 0.06377396532315771, 0.06283923533357072, 0.061596290425321776, 0.06062743353392808, 0.05987241738861382, 0.05906462224581688, 0.05900909169327839, 0.05863023036643522, 0.056674954088558493, 0.05663641300834321, 0.05573066244705327, 0.05285999918476847, 0.05115265774466682, 0.05105981583143748, 0.050255155238578375]\n",
      "Row 69 - Column Numbers: [54 52 81 57 75 68 64 50 45 46 49 84 66 60 76 61 55 48 70 47 72 63 62 21\n",
      "  6 53 74 87 12 17 56 58 88 83 33 10 13 44 41 43 35 31 15], MI Values: [0.6991638866458345, 0.5772799725175153, 0.5173059047442399, 0.4492286562322283, 0.3365455824566368, 0.2145246058092809, 0.13741479855139715, 0.1364956152132697, 0.10868038934784607, 0.105422623025202, 0.09982396156077122, 0.09384699164640953, 0.08774329941118264, 0.08538631330874047, 0.08467890285416413, 0.0817599534587723, 0.07626677924718717, 0.07361433044884258, 0.06977140079906086, 0.06874455994522854, 0.06641906563649336, 0.06532339080081417, 0.06494490899076943, 0.06484185380561414, 0.06183066532204684, 0.05994221903533159, 0.05666686695618495, 0.05545803544337424, 0.05531483615886046, 0.05499612699967926, 0.05440393974544655, 0.053739795644960786, 0.0536959399704946, 0.053145985839573306, 0.05089832960081431, 0.050097225136772394, 0.04984063431350716, 0.04878869749796966, 0.04863991014106883, 0.04807444378004, 0.04771493976945074, 0.04694746829499152, 0.04658331443336472]\n",
      "Row 70 - Column Numbers: [72 71 63 46 64 57 53 62 54 47 69 87 48 68 45 36 82 56 17 61 21  4 19 13\n",
      " 74 41 55 49 67 52 60 11 15 75 28 84 32 85 66 18 44 35 31], MI Values: [0.5037025298153655, 0.1468401051584065, 0.13607340649846478, 0.13281149605317744, 0.10306102384276628, 0.08195684550894988, 0.07763014753084718, 0.07551883001699711, 0.07247468124904355, 0.07068379697728044, 0.06977140079905908, 0.0660251334839197, 0.06437836072642344, 0.06381372155874754, 0.06252081423776268, 0.05999309743629233, 0.05982269100457582, 0.057890813506117134, 0.056376474765788664, 0.055299683066056815, 0.05505815458498908, 0.05456383162511802, 0.05447668338025302, 0.05401666850898579, 0.05386607986701808, 0.053251414027695176, 0.05210958027079293, 0.05205162711625011, 0.05131323241564267, 0.050113256036700804, 0.049242671141108474, 0.049105160517478375, 0.04807318298614227, 0.047127393802390394, 0.04650128507184803, 0.046494250587683084, 0.04569125616274494, 0.04506890618240256, 0.04505050520622156, 0.04471178449303981, 0.04423971269111515, 0.044000657807371724, 0.043861067541813625]\n",
      "Row 71 - Column Numbers: [70 72 57 46 63 52 64 69 62 40 88 45 19 54 89 73 53 41 18 20 36 74 28 48\n",
      " 38 68 67 55 16 21 15 32 35 85 39 49  1 33 92 86 66 29 34], MI Values: [0.14684010515840784, 0.10642931109237441, 0.052528980782009516, 0.05241768981868278, 0.050201259190097325, 0.04467108973151124, 0.04327708127836605, 0.040533665195546575, 0.03859241843659156, 0.038561516805054374, 0.03818678028153677, 0.03813838976859696, 0.03800425250052175, 0.03790080375870186, 0.03715871144142646, 0.03588263349891774, 0.03548282442189432, 0.035353727634690024, 0.0352925510429718, 0.03441557456072353, 0.03423058910657151, 0.03397324312542693, 0.03394914598687837, 0.033806395276054335, 0.033705883841912865, 0.03342612831626557, 0.03284593157964988, 0.032719080030302106, 0.032663553226116804, 0.031987069591433936, 0.03175109221050576, 0.03144013441961224, 0.031402843954976944, 0.030959505480408822, 0.03087881443926932, 0.030695717699147362, 0.030567471549774794, 0.030379323571904315, 0.03005020752412957, 0.03002178949951162, 0.029856386276476243, 0.029726472501970136, 0.029722945487696606]\n",
      "Row 72 - Column Numbers: [70 46 63 64 71 57 62 54 87 69 53 74 36 17 47 68 19 56  6  4 21 37 18 12\n",
      " 13 79 45 52 61 14 15 85 84 11  8 83 38 55 31 10 41 48 40], MI Values: [0.5037025298153646, 0.1555945017468563, 0.14441268837025323, 0.11641659888849354, 0.10642931109237264, 0.10567030398132982, 0.08923240114088049, 0.06863149347899888, 0.06757571466233703, 0.06641906563649602, 0.06557217989953035, 0.06265296415556598, 0.06265064870036952, 0.06242048665925726, 0.06175094572082429, 0.06159629042532533, 0.06050821759756175, 0.060467185737427265, 0.059193884606223435, 0.05724329216191926, 0.054151749566812235, 0.053098326138301566, 0.05297227066477639, 0.05260851139547462, 0.052594084364699256, 0.05231208801533249, 0.05126811930396524, 0.051113533032526526, 0.050320783879531206, 0.050294567082459274, 0.049828300730804465, 0.04936721830032109, 0.04876829570450525, 0.048098306904397425, 0.04777061216579881, 0.04705935242895354, 0.04699176949630246, 0.04633740434429967, 0.04575550443701104, 0.04517050064331052, 0.04508851409560233, 0.0448973620856723, 0.04481721096307467]\n",
      "Row 73 - Column Numbers: [18 19 16 22 15 21 83 17 46 57 20 64 92  0 85 63 87  1 90 91 75 32 61 78\n",
      " 55 68 81 80  4 77 42 56  5 62  7  2 44 48 79 58 30 52 82], MI Values: [0.7893958078076446, 0.44496585631871355, 0.23365823269839314, 0.1966841939947015, 0.17737229996765524, 0.14619238110757227, 0.13046110819555246, 0.11461081534221584, 0.0669864466316632, 0.0667097043144338, 0.06621492860686029, 0.06604549816659055, 0.06534747712790967, 0.0649060502864538, 0.06342521947019009, 0.06298018698645524, 0.0611623897499598, 0.05958199657264185, 0.05918069294481576, 0.05854277511136363, 0.053336867008316524, 0.052349661683105175, 0.052132518258837024, 0.051741026293754544, 0.05137178453202651, 0.05115265774467037, 0.050731494761138585, 0.05035070457441204, 0.04944023723216873, 0.04929230770196469, 0.04884463429679364, 0.04879117015815915, 0.04871526329810205, 0.047892505862648704, 0.04712977016487141, 0.046741524692998304, 0.045420776171674504, 0.04530640682438136, 0.04518328366119828, 0.0451152130271959, 0.04476241509419232, 0.04425296906975085, 0.04269677500715918]\n",
      "Row 74 - Column Numbers: [33 30 35 43 36 86 37 29 89 38 28 40 39 31 34 88 41 32 78  5 79  2 12 64\n",
      " 44 80  4 56 46 87  0  1  3 57 42 11 13 85  8 63 10 54 90], MI Values: [1.1137204124807516, 0.6484729630309527, 0.6417520640136294, 0.624303970048989, 0.609009289588708, 0.5888147458720638, 0.5514988683591922, 0.5004203013385569, 0.4790798574401238, 0.463836147610051, 0.4637692211865332, 0.42293019416571376, 0.4188068561985556, 0.3685955153502105, 0.3551015296305451, 0.3455870286773939, 0.33199699186004406, 0.2547497346317229, 0.20415303191621437, 0.1681098351910748, 0.1650927025452713, 0.15700514453794945, 0.14286051344793105, 0.14209884783445847, 0.13751208245379942, 0.13689592489073021, 0.12952891724869087, 0.12763532576626435, 0.11736212179504246, 0.1087269697985187, 0.10670490036675684, 0.10197487194244381, 0.09931213507677228, 0.09565681017049954, 0.09219897198964855, 0.08465931443258867, 0.08012866253161377, 0.07970796683611514, 0.07707447313009208, 0.07657349482892162, 0.07645994681407764, 0.0724507095617879, 0.07133347033568604]\n",
      "Row 75 - Column Numbers: [50 69 57 81 54 52 49 46 64 68 84 48 60 58 87 55 45 47 66 74 77 79 44  0\n",
      " 19 76 37 63 86 59  2 73 13  4 36 61 17  1 62 24 88 67 10], MI Values: [0.38569583316039946, 0.3365455824566368, 0.31754032621604367, 0.299464626985233, 0.2835775257403297, 0.1935421636578889, 0.16380558437787318, 0.1598316786459506, 0.1423617894832443, 0.1390906170717887, 0.10426683306186213, 0.1003724412202649, 0.0878913633998506, 0.08672016085400713, 0.08358299144459647, 0.07894014514831671, 0.07550304956704768, 0.07403127407645904, 0.06574781745996994, 0.0641015831058036, 0.06280999904077333, 0.06198112586282889, 0.05994952546050758, 0.058932901704030094, 0.05883151968498446, 0.05840596267275, 0.05770927457101749, 0.05585066540116479, 0.05527900384734252, 0.05458094170481065, 0.054081184944083205, 0.05333686700831475, 0.053243057542840866, 0.05294436526442681, 0.05286496782731209, 0.052800446177284854, 0.052136357413616885, 0.051665821434266235, 0.05132260781066744, 0.05083179402329918, 0.05043949403648362, 0.05004816617282959, 0.049905532084435045]\n",
      "Row 76 - Column Numbers: [66 84 45 64 69 46 60 54 63 65 68 81 75 87 50 61 56 55 27 52  3 48 51 57\n",
      " 44 88 62  6 85 40  1 74 41  0 58 49 15 39  4 89 14 53 47], MI Values: [0.3276867048743197, 0.24938687538324178, 0.14089157380955797, 0.10732056478952945, 0.08467890285416502, 0.07963991449703123, 0.07359513171289844, 0.07324275519206669, 0.06663758575631462, 0.06574940460414425, 0.05900909169328106, 0.05870728910141754, 0.05840596267275089, 0.05227845227554617, 0.052114858751312276, 0.0475376914479817, 0.045768277880542385, 0.044450219960143755, 0.04331808077932564, 0.0397320107747241, 0.039450383303536896, 0.038781715879885326, 0.03840491710777716, 0.03729854865264848, 0.03695081877679929, 0.03575037533056857, 0.03553028432121241, 0.035006496062266024, 0.03479280267248619, 0.03355427583083603, 0.03330372063304132, 0.03324378852283871, 0.03314054463399074, 0.0329832469916953, 0.03260929208367003, 0.03200075462167984, 0.03142627895452854, 0.031226808565940622, 0.030530087758511293, 0.030180324229658773, 0.03013702346379077, 0.029953159421307163, 0.029614370974226034]\n",
      "Row 77 - Column Numbers: [20  1  0 17 85 21 83 87 91  2 15 79  4  5  3 11 12 19 22 16 64 78 90 10\n",
      " 24 46 61 18 31 14 33 80 74 13 56 43 75 30  8 86 37 36 29], MI Values: [0.6456828762580971, 0.3911191711403701, 0.37263024544485734, 0.2990938973597581, 0.2972324555956005, 0.2833159462922179, 0.2721591618925645, 0.2624972226636384, 0.2612330298469274, 0.23544670375940946, 0.2109149525053855, 0.19755911895090694, 0.1718626691037235, 0.17144637756480563, 0.16858842857306655, 0.15529190588759256, 0.15476368455904055, 0.14839967682173594, 0.10378871318925587, 0.09654894383117352, 0.09447565520740842, 0.0909806859788258, 0.08763090580224553, 0.0864463575035197, 0.08554737930801348, 0.0848734741910322, 0.07553429240407361, 0.07382980271187378, 0.07208828414576551, 0.07067488479129658, 0.06870563600713986, 0.06782462499272324, 0.06750317812053108, 0.06644401403919531, 0.06584653458601863, 0.06546454180161732, 0.06280999904077245, 0.06275013897899573, 0.06220005651368066, 0.061947295051053786, 0.061387189732781344, 0.061213187064223185, 0.06065012243418888]\n",
      "Row 78 - Column Numbers: [31 79  2  5 43 35  4 44 30  3  0  1 33 74 42 36 85 86 34 12 11 37 87 32\n",
      " 29 91 20 80 28 13 89 17 10 38 39 21 40 83 41 88 77 90 15], MI Values: [0.7638100129208834, 0.5291499102562947, 0.40895639584369636, 0.40195030351981753, 0.3703971113656319, 0.36035661286731635, 0.3522117773810214, 0.2940959242977499, 0.24551062402752422, 0.22968546503017695, 0.2279315500630652, 0.22306577157731855, 0.21439117181920508, 0.20415303191621348, 0.17401757617932834, 0.14656523125808896, 0.13481869307475858, 0.1340783425963794, 0.13184448924787695, 0.1251376255189447, 0.12508164598781324, 0.12299363364406979, 0.12204190372473, 0.11553471513471436, 0.11428335137809142, 0.11180728144593566, 0.11158401518017325, 0.11158379763401793, 0.10874080446091128, 0.10855159929809233, 0.10703752567566749, 0.10477670785503168, 0.10461732375843713, 0.1039286718447654, 0.1030354193690286, 0.10268663613005558, 0.09964875862896339, 0.09402627710304756, 0.09265090609569437, 0.09216904048066343, 0.09098068597882403, 0.07220152388185497, 0.06674255678354513]\n",
      "Row 79 - Column Numbers: [ 4  2  5 78  3  0 31  1 43 35 77 85 30 20 87 33 74 12 17 44 91 21 83 34\n",
      " 11 36 86 37 29 40 10 39 32 38 89 42 28 64 41 13 80 88 15], MI Values: [0.893437297964442, 0.8897537675853213, 0.8539429780686696, 0.5291499102562955, 0.5216221690633249, 0.45757637448269506, 0.3469763013969196, 0.3374236720569561, 0.2073913075411946, 0.20596754398312012, 0.19755911895090428, 0.1962347079230513, 0.1906085060616718, 0.1804159793193154, 0.17746826908973823, 0.1675397929716107, 0.1650927025452722, 0.15745268691877623, 0.15630527248319837, 0.15352082533469336, 0.14530314536725086, 0.13959981733842763, 0.13601963987999888, 0.1218215309761943, 0.12041417972820856, 0.11619314258747693, 0.11181972450478295, 0.111670136833391, 0.10420208049496171, 0.10298221946964947, 0.10144296896099547, 0.10121071598448594, 0.09567236193821316, 0.09301615106454975, 0.09254555638649187, 0.09102336506577213, 0.09026690572979756, 0.08736827809746561, 0.08676758111423233, 0.08620980383680976, 0.08466381307331439, 0.0785679892861264, 0.07750166086596]\n",
      "Row 80 - Column Numbers: [59 43 35 90 31 33 42 74 30 36 44 78 92 86 89 37 29 34 28 40 38 79  5 41\n",
      " 32 12 82 88 39  2 77 11 21  0  4 15 13  3  1 83 10 73 20], MI Values: [0.24653722627623686, 0.2276321837680122, 0.20322450593987362, 0.19218618079188143, 0.18479080672562098, 0.15136974710492979, 0.1450821651935268, 0.13689592489073021, 0.1357762064984085, 0.11571876599131237, 0.11196280971917005, 0.11158379763401705, 0.11010018137622524, 0.10493827763350172, 0.1044402309887209, 0.09822950179437395, 0.09785175941231472, 0.09689650292456431, 0.09424947908653714, 0.08752252944644034, 0.08653427377215017, 0.08466381307331616, 0.08230865790885655, 0.07854886226317959, 0.07650826602535155, 0.07494487051346166, 0.07370725535800648, 0.07253038686003155, 0.07038469791400903, 0.06970774963285731, 0.06782462499272057, 0.06530714718931119, 0.0638719053811343, 0.06157503922592156, 0.06148036084266284, 0.06004207076621082, 0.058901850104819964, 0.05522028921117084, 0.05429317094593511, 0.05309818158656032, 0.05282851504111541, 0.050350704574411154, 0.04844480590909317]\n",
      "Row 81 - Column Numbers: [54 69 75 52 68 57 50 64 46 49 58 84 74 48 55 66 87 60 45 76 77 44 36 79\n",
      " 63 86  0 61 83 37 17 33 73 38 43 39 31  4 89 47  1  2 88], MI Values: [0.7379530571253508, 0.5173059047442399, 0.29946462698523035, 0.2925189873733629, 0.27391959942944677, 0.2386747781742029, 0.136153690706311, 0.10370508346423613, 0.10140282553967683, 0.07578213385519295, 0.07170077496787108, 0.07127138714810943, 0.06860495539301592, 0.06681937537003346, 0.06660845722965725, 0.06464382902377075, 0.0635620255990954, 0.06016542150362536, 0.05993439653997257, 0.05870728910141665, 0.05853791406893283, 0.05807485470139717, 0.057863475935761244, 0.057830546664649596, 0.05763441139077141, 0.05615165444273362, 0.05562579056591499, 0.05549932064581764, 0.05488123319225746, 0.05430022036441429, 0.05358151425610025, 0.052620584599597287, 0.05073149476113681, 0.0504273983650787, 0.050018232148672404, 0.048724267224924844, 0.04741589778476474, 0.04724272848531896, 0.047045769301623075, 0.046565683993298634, 0.045974451396885385, 0.04564404577717607, 0.0445681886862177]\n",
      "Row 82 - Column Numbers: [47 92 90 80 57 63 70 64 36 41 87 74 18 42 19 85 73 86 56 43 72 78 35  6\n",
      " 31 33 29 27 44  2 21 69 34  0  5 79 15 62 30 40 23 17 46], MI Values: [0.36022650677909773, 0.20000700401697546, 0.12362127498379927, 0.07370725535800737, 0.06659031769662516, 0.06403591879492154, 0.05982269100458204, 0.048128802238390556, 0.04758120157348866, 0.04550467421470117, 0.0453016185285815, 0.04463464698039843, 0.04452332972605699, 0.043705855049582354, 0.0432350339578198, 0.042804256191230294, 0.04269677500715918, 0.042518243369825015, 0.04216181372132244, 0.041122564560073904, 0.04035249569417232, 0.040056300664696565, 0.03993065515482197, 0.039067233966030734, 0.0389505477899581, 0.038744171751281975, 0.03800177521638748, 0.037944489427784056, 0.03731345765145644, 0.03724063933802757, 0.03716957593935177, 0.037114565896340324, 0.03697025658167963, 0.03665464470504798, 0.036577827982953615, 0.035438406074370654, 0.03489171478971809, 0.03464472319516876, 0.034410902358763096, 0.034146025613621234, 0.03378679926427086, 0.033662159409545644, 0.033650920178660115]\n",
      "Row 83 - Column Numbers: [17 21 20  0  1 19 77 15 85  2 16 91 87 11 22  5  4 79 73 18  3 12 90 92\n",
      " 78 10 42 31 43 64 61 13 68 54 35 33 46 44 74  8 57 81 14], MI Values: [1.066814745597446, 0.7488876659638617, 0.4589017533899531, 0.31506896178670907, 0.29504178717312346, 0.28206410473167054, 0.2721591618925654, 0.23569399663760304, 0.19808986460266986, 0.18056529072470173, 0.16718927849869747, 0.1656431210139937, 0.15326102264911245, 0.14976259321938912, 0.1450249261206027, 0.14139989403189102, 0.1374753305211458, 0.13601963988000332, 0.13046110819555246, 0.13005610443538984, 0.12212949345012714, 0.12178764257401475, 0.09999792818939479, 0.09786512673510916, 0.09402627710304579, 0.09120163011639004, 0.08290682477634537, 0.08252825085346682, 0.08156076645929478, 0.07860224780761271, 0.07310938021788527, 0.06900697369544506, 0.06805662497684573, 0.06494064826102797, 0.06455351051612457, 0.06416764584976953, 0.06223055486476259, 0.06102533227363338, 0.05968287991838661, 0.05824405082485473, 0.05711690835432748, 0.05488123319225924, 0.05451886276258566]\n",
      "Row 84 - Column Numbers: [ 3 76 66 64 46 75 45 69 54 63 68 57 81 50 87 61 55  6 60 44 27 62 56 74\n",
      "  0 65 52  1 51 20 17 48 72 21 49 85 47 70 58 41 40 88  2], MI Values: [0.29367624960262795, 0.24938687538324178, 0.19621110110385587, 0.13984183102276848, 0.1375172592865539, 0.1042668330618639, 0.10150362847124583, 0.09384699164641042, 0.09285394516933199, 0.07977254852835536, 0.07495229498264333, 0.07392888704485934, 0.07127138714810854, 0.06909627215253789, 0.06894787220913212, 0.06553165111754211, 0.06496582981844412, 0.06491247342046069, 0.062130659320295045, 0.06139751027721019, 0.0603802858690452, 0.058731048238805705, 0.05731245332677215, 0.05441190520910766, 0.052023584398917855, 0.05200772742261517, 0.050675710238638594, 0.050658360235747324, 0.050444118959005024, 0.04966907275681187, 0.04912116274816558, 0.049098305732939274, 0.0487682957045088, 0.047929493455121985, 0.047598231033918026, 0.04751424056243447, 0.047086024603290255, 0.046494250587683084, 0.045749765509683904, 0.04533916101688806, 0.04511370164638606, 0.04442062560320448, 0.04432867747156788]\n",
      "Row 85 - Column Numbers: [91 87 11  1 20 77  0 21 15 10 16 17  2 83 79 12 13  4  5 78 19  3  8 24\n",
      " 22 31 64 61 14 23 43 33 44 46 74 42 18 35 90 92 63 53 56], MI Values: [1.0397326027081109, 0.7808738531896484, 0.4477948984444424, 0.4273072620362388, 0.42552426145736, 0.2972324555956032, 0.29292039446620866, 0.2688208314872229, 0.2607931482272816, 0.25686672570808433, 0.24952652512346507, 0.24799566598007594, 0.2191451538778244, 0.19808986460266986, 0.1962347079230522, 0.16892847033332092, 0.15241639531040452, 0.14716514799944846, 0.14129091651330672, 0.13481869307476035, 0.12862613575316306, 0.12331183579416649, 0.1197010961317595, 0.11662871191985147, 0.11578837068495584, 0.10608247049946584, 0.10591493223352089, 0.10334008173380838, 0.0977963721134758, 0.08797109748794707, 0.08744850763647705, 0.08539579380747231, 0.08318123056251547, 0.08171791357506919, 0.0797079668361178, 0.07969793759561306, 0.07840025513521187, 0.0772743628266932, 0.07673080277470046, 0.07434137186871315, 0.07313981190535657, 0.07291262831419587, 0.0700260236623178]\n",
      "Row 86 - Column Numbers: [37 36 29 38 89 28 39 33 40 74 88 41 43 35 30 34 31 32 56 78  5 79 44 80\n",
      " 12  2  4 42 90  3 87  1  0 77 14 52 64 46 81 75 85 11 63], MI Values: [1.4582722148763292, 1.0233770024292141, 0.9904397714916922, 0.7540596341394137, 0.733195425690325, 0.7092838503040939, 0.6322229406595898, 0.6078933190308362, 0.5904546129888963, 0.5888147458720656, 0.4974361490677621, 0.47456031717445146, 0.4240950333084834, 0.398460972787932, 0.37422972387261133, 0.3436127338197741, 0.22807412650458492, 0.2027410833178278, 0.1981347985070574, 0.1340783425963794, 0.1305167490968442, 0.11181972450478028, 0.10936129874318112, 0.10493827763349994, 0.10135095971922325, 0.09732347543015418, 0.0793582428961841, 0.07547417076442908, 0.07370447561000759, 0.06840077448593984, 0.06585251441988405, 0.0648701268193781, 0.06364451470636467, 0.0619472950510529, 0.06094423783477332, 0.05775731163073594, 0.057120350210864146, 0.05635429843615114, 0.0561516544427354, 0.05527900384733986, 0.053398504926430945, 0.05262110212995097, 0.05220962062188317]\n",
      "Row 87 - Column Numbers: [91 85 20  1 11 77 15  0 10 64 17 21  2 79 46 83  4 63 12  5 16 24 78 14\n",
      " 19  8 61 13 31 74  3 56 23 44 57 22 43 47 75 68 33  6  9], MI Values: [0.8254953838532577, 0.7808738531896502, 0.32604905695192254, 0.3012243820649747, 0.2965738494229102, 0.2624972226636402, 0.2236871771312554, 0.22350595260037398, 0.2210467525648223, 0.22048913023609007, 0.19689724643638407, 0.18708052814614184, 0.18419330652618005, 0.17746826908973734, 0.16549438774061542, 0.15326102264911423, 0.1467876478550867, 0.14223108828764808, 0.13558171850872913, 0.13204341952919485, 0.12870418125103367, 0.126641316562071, 0.12204190372472912, 0.12022624072505206, 0.11907016274300819, 0.11717444758841289, 0.11609849133691608, 0.11270707168404748, 0.10896037047705942, 0.10872696979851781, 0.10828482718467924, 0.10439486730786829, 0.1027970391859041, 0.10044717697416417, 0.09943857195888395, 0.08969080820395003, 0.08755593140089335, 0.08569788060934336, 0.08358299144459647, 0.0827966624743155, 0.08221603143086931, 0.07597112239010073, 0.0751232614805879]\n",
      "Row 88 - Column Numbers: [40 89 41 28 38 39 34 29 37 86 33 36 74 30 32 35 43 31 44 78 56 79  5  4\n",
      " 64 80 12 90 18  2 46 52 42  0 10  3  1 62 54 69  8 63 17], MI Values: [1.3584687582326698, 1.1135577021657408, 0.8687228214668892, 0.7614158768816592, 0.7568375359221005, 0.7414381495833346, 0.521645640678436, 0.5162986988948415, 0.5065004040074976, 0.4974361490677621, 0.4047557520194278, 0.39112029603754017, 0.3455870286773921, 0.3120618690279793, 0.27467543363149716, 0.2113827569500053, 0.2062641249804278, 0.1178467066606661, 0.0978448354860939, 0.09216904048066343, 0.0881281392529063, 0.07856798928612552, 0.07740754667316185, 0.07609992946234723, 0.07448577255951516, 0.07253038686002977, 0.07191036153530916, 0.07018600624848581, 0.06947413178679351, 0.06925480718800436, 0.0665871977414545, 0.06273572137952144, 0.06114199250922159, 0.06063371495187919, 0.06012914210785869, 0.05512401310494486, 0.05476304444835467, 0.05440889071046939, 0.05436024408042606, 0.053695939970491935, 0.05292091189701864, 0.05201826811016552, 0.05132084037915341]\n",
      "Row 89 - Column Numbers: [38 40 88 39 28 41 37 29 86 36 34 33 74 30 43 35 32 31 56 78 80  5 79 44\n",
      " 12  2 90  4 11 64  0 10  3 42 46  1  8 13 61 87 17 54 62], MI Values: [1.2419280927673935, 1.2392621662048944, 1.113557702165739, 1.0535035116401668, 1.0046755344608442, 0.9100181021852709, 0.7572524796564108, 0.7571541803206934, 0.7331954256903233, 0.5752000583378676, 0.5628237492307493, 0.5364183007679406, 0.4790798574401274, 0.37170844903925726, 0.28802774608808956, 0.2845574273495872, 0.23990089864081376, 0.15421271891570854, 0.12759658270105323, 0.1070375256756666, 0.1044402309887218, 0.1028680671126736, 0.09254555638649009, 0.09241113709100546, 0.08890082125607357, 0.08732427486063177, 0.08143911948999971, 0.07698715238078524, 0.06919349661079899, 0.06672066841319335, 0.06566309202536758, 0.0637520285116242, 0.06298051391441373, 0.06261691628512, 0.0624690478839538, 0.06095847702589374, 0.05864248331363253, 0.05740682008964981, 0.057232186056704215, 0.0568278203392758, 0.05080254511998916, 0.05074669197352755, 0.0502827362091578]\n",
      "Row 90 - Column Numbers: [42 92 80 21 82 17  1  0 83 77 40 20 19 89 30 33 43 85  5  2 79 11 86 41\n",
      " 38 12 15 78 35 74 37 88 29 36 39 34 31 91 87 28  4 32 73], MI Values: [0.5736361560630625, 0.4459659605734716, 0.19218618079188232, 0.12517520234619095, 0.1236212749837966, 0.11040902183482082, 0.10532886649482442, 0.10411775455289263, 0.09999792818939834, 0.08763090580224375, 0.08755455049272687, 0.08732179357987846, 0.08561032186586459, 0.08143911949000593, 0.07857807032348152, 0.07829650162065516, 0.07721049556759763, 0.07673080277470312, 0.07668497735520141, 0.07646301353284013, 0.07612583152068808, 0.0746333907288248, 0.07370447561000759, 0.07307672025710321, 0.07291292443408093, 0.07254758451655796, 0.0725475665380868, 0.07220152388185319, 0.07216427126334413, 0.07133347033568604, 0.07091755529673982, 0.07018600624848581, 0.07002944857802262, 0.06954945457795869, 0.06777425757346034, 0.06748508102814021, 0.06594386443864142, 0.06571885927828625, 0.06528340240650543, 0.06435233990021594, 0.06363225684698115, 0.0634542884997531, 0.059180692944813984]\n",
      "Row 91 - Column Numbers: [85 87 11 20  1 77 10 15 21  0 17 83  2 13 79 16 12  8  4  5 78 19 22  3\n",
      " 24 23 14 61 64 31 18 63 44 43 56 42 74 92 53 90 33 46 34], MI Values: [1.0397326027081135, 0.8254953838532595, 0.3865429355312866, 0.35105094399945447, 0.3192857717713009, 0.261233029846931, 0.2579871837894956, 0.2262869925209232, 0.2086854981064592, 0.20848995166817463, 0.20010695253448052, 0.1656431210139928, 0.15702895570463316, 0.15188179879224428, 0.14530314536724998, 0.13528675087576225, 0.1292188341874061, 0.12410132440415556, 0.11543451299135388, 0.11292935145386718, 0.1118072814459321, 0.10649322098528113, 0.1063924866874304, 0.09857437391434942, 0.09541744286183729, 0.09277959255307167, 0.09231436655409198, 0.08714033036634472, 0.08652458136703967, 0.08539580505606104, 0.08043542246333857, 0.07678764806996075, 0.07356394424112533, 0.07147186167010044, 0.06996541088144959, 0.06881214952706838, 0.06784461788607654, 0.06764075156292826, 0.06654270992309197, 0.06571885927828625, 0.06454231972101443, 0.060894556193985316, 0.05979450877373971]\n",
      "Row 92 - Column Numbers: [90 82 17 42 21 80 83 63  1 85  0 19 20 91 87 57 73 23  2 30 79 77  5 78\n",
      " 15 41 74 33 11 18 36  6 32  4 12 40 34 64 86 16 28 47 10], MI Values: [0.4459659605734716, 0.20000700401697458, 0.16969542448540587, 0.11438741669920915, 0.1117978672601403, 0.11010018137622612, 0.0978651267351065, 0.08472994154227287, 0.08048114102267068, 0.07434137186871048, 0.07334383362524477, 0.07083532279622062, 0.07064869314149647, 0.06764075156292648, 0.06744167818817282, 0.06608857489515962, 0.06534747712790523, 0.06377017167667542, 0.06303769631886258, 0.06244423103829355, 0.06139810833956538, 0.06009214577031052, 0.05620640348058448, 0.05570265349391068, 0.05541644764804232, 0.05389698575662827, 0.052348572626745415, 0.051905744566475676, 0.051690795509167664, 0.05057359318983057, 0.04931200112378864, 0.048166047939036005, 0.047644557437777735, 0.04702041409510738, 0.046717369248161056, 0.04610406107367648, 0.045989563524378774, 0.0458993014321587, 0.04549260487965512, 0.04529324898574405, 0.04491292878293418, 0.044605275701465885, 0.043729188914697126]\n"
     ]
    }
   ],
   "source": [
    "#Subgraph generation module 1 --->Giving raw series, and generate a series of subgraph based on MI.\n",
    "NDBC_lat=pd.DataFrame(Station_info.iloc[:,1])\n",
    "NDBC_long=pd.DataFrame(Station_info.iloc[:,3])\n",
    "NDBC_ID=pd.DataFrame(Station_info.iloc[:,0])\n",
    "Adj_dist=adj_dist(NDBC_lat,NDBC_long)\n",
    "j=5#J-th colum, start from 5 as the first feature.\n",
    "X_raw_0=X_raw[:,j,:]#GET the first feature\n",
    "print(X_raw_0.shape)\n",
    "# Count the num of missing values in each column\n",
    "missing_counts_per_column = np.sum(np.isnan(X_raw_0), axis=0)\n",
    "# print results\n",
    "print(\"Incomplete data number in each column：\", missing_counts_per_column)\n",
    "\n",
    "#Get the index if the value is not zero\n",
    "# Find the columns where missing values exist.\n",
    "columns_with_missing_data = np.any(np.isnan(X_raw_0), axis=0)\n",
    "\n",
    "# Get the column numbers when missing value exist.\n",
    "missing_columns = np.where(columns_with_missing_data)[0]\n",
    "\n",
    "# Print results\n",
    "print(\"The column numbers with missing values are：\", missing_columns)\n",
    "\n",
    "# Get new data after deletion.\n",
    "# Delete those columns (Stations) if there is not any features.\n",
    "result = np.delete(X_raw_0, missing_columns, axis=1)\n",
    "result = (result - np.min(result)) / (np.max(result) - np.min(result))\n",
    "print(result.shape)#(8784, 93)\n",
    "\n",
    "#Determine group num here\n",
    "group_num=result.shape[1]-N_u\n",
    "\n",
    "# Initialize MI_store\n",
    "MI_store = np.zeros((result.shape[1], result.shape[1]))\n",
    "\n",
    "# Calculate mutual information\n",
    "for i in range(result.shape[1]):\n",
    "    for j in range(result.shape[1]):\n",
    "        MI_store[i, j] = calc_MI(result[:, i], result[:, j], 10)\n",
    "\n",
    "# Return column numbers and corresponding mutual information\n",
    "column_numbers = []\n",
    "MI_values = []\n",
    "\n",
    "for i in range(MI_store.shape[0]):\n",
    "    row = MI_store[i, :]\n",
    "    row_index = np.arange(MI_store.shape[0])\n",
    "    row_index = np.delete(row_index, i)  # Exclude the current row's index\n",
    "    sorted_indices = np.argsort(row[row_index])\n",
    "    max_indices = row_index[sorted_indices[-group_num:][::-1]]  # Get largest column_num\n",
    "    column_numbers.append(max_indices)\n",
    "    MI_values.append([row[j] for j in max_indices])\n",
    "\n",
    "# Output results\n",
    "for i, (columns, values) in enumerate(zip(column_numbers, MI_values)):\n",
    "    print(f\"Row {i} - Column Numbers: {columns}, MI Values: {values}\")"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-25T05:40:34.143437Z",
     "start_time": "2024-03-25T05:40:29.840562Z"
    }
   },
   "id": "7578d20606c9d51d",
   "execution_count": 19
  },
  {
   "cell_type": "code",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1, 93)\n",
      "A's shape is: (93, 93)\n",
      "X's shape is: (93, 8784)\n",
      "(8784, 103)\n",
      "Incomplete data number in each column： [8784    0    0    0    0    0    0    0    0    0    0    0    0    0\n",
      "    0    0    0    0    0    0    0    0    0    0    0    0    0    0\n",
      "    0    0    0    0    0    0 8784    0    0    0 8784    0    0    0\n",
      "    0    0    0    0    0    0    0 8784 8784    0    0    0    0 8784\n",
      " 8784    0    0    0    0    0    0    0    0    0    0    0    0    0\n",
      "    0    0    0 8784    0    0    0    0    0    0    0 8784    0 8784\n",
      "    0    0    0    0    0    0    0    0    0    0    0    0    0    0\n",
      "    0    0    0    0    0]\n",
      "The column numbers with missing values are： [ 0 34 38 49 50 55 56 73 81 83]\n",
      "(8784, 93)\n",
      "Row 0 - Column Numbers: [ 1  2  4 79  5 20  3 77 21 17 83 85 78 87 91 12 15 31 11 43 19 44 35 30\n",
      " 74 90 16 10 33 64 42 34 61 13 32 46 22 63 92 56 18  8 41], MI Values: [0.8272601132894586, 0.6901375697065202, 0.4673606483958732, 0.45757637448269683, 0.4363240338301644, 0.4190235175463517, 0.37428008133733837, 0.37263024544485734, 0.33215728219304985, 0.3299090634675217, 0.3150689617867082, 0.29292039446620866, 0.22793155006306698, 0.22350595260037576, 0.2084899516681764, 0.19725693559810153, 0.16436438822998234, 0.1621107642515911, 0.15513395543730368, 0.13586993979589845, 0.13409996608400565, 0.12631372813239938, 0.11361591888716127, 0.10962686909974106, 0.10670490036675684, 0.10411775455289352, 0.10173701560948789, 0.10125880394889375, 0.0966457877057838, 0.0917156023777439, 0.08872664637913985, 0.08750394746818291, 0.07987921333337233, 0.0779097501756647, 0.07772961987272176, 0.07681250087322766, 0.07596636122032496, 0.07375851842511771, 0.07334383362524477, 0.0724236272383223, 0.06937049801544504, 0.06869053966721506, 0.06665335877298872]\n",
      "Row 1 - Column Numbers: [ 0 20  2 85 21 77  4 79 17  5 91 87 83  3 11 15 12 78 31 19 10 16 43 35\n",
      " 30 33 13 90 64 74 44 22 42 61 18 34 92  8 46 56 24 28 36], MI Values: [0.8272601132894577, 0.5324618722588088, 0.52600823699178, 0.4273072620362397, 0.4023069759074378, 0.39111917114037187, 0.34043212687770286, 0.33742367205695434, 0.3283135513911546, 0.32209271522604777, 0.3192857717713018, 0.3012243820649747, 0.2950417871731199, 0.25018137359531334, 0.2344515509245717, 0.23100847367209631, 0.22954525563754213, 0.22306577157731855, 0.161217443157323, 0.16120899606897954, 0.14396039237957936, 0.13986782406464826, 0.12913107009156644, 0.11642248941903688, 0.1150059734774116, 0.10934085523256787, 0.10726653658897867, 0.10532886649482887, 0.10272291690296598, 0.10197487194243937, 0.09756958090356083, 0.0945249676245794, 0.09265639520815494, 0.09192328803022942, 0.09060525299304167, 0.09049841174829254, 0.08048114102267423, 0.08040105111154183, 0.08010342629738876, 0.07992095121214415, 0.07658487183692309, 0.07617110541908634, 0.07458627225738823]\n",
      "Row 2 - Column Numbers: [ 4 79  5  0  3  1 78 31 20 77 85 21 17 12 35 43 87 83 30 33 91 74 11 44\n",
      " 34 10 36 15 13 86 29 39 19 42 37 32 40 38 89 64 28 61 41], MI Values: [1.0421298348636876, 0.889753767585324, 0.8252189069592397, 0.6901375697065175, 0.6346295603606373, 0.52600823699178, 0.4089563958436999, 0.2885791692349038, 0.26984073230595396, 0.23544670375941035, 0.21914515387782174, 0.2125857191397058, 0.20709995929092173, 0.19750308970805186, 0.18701920286034568, 0.18681968571483498, 0.18419330652618005, 0.1805652907247035, 0.15876062884895603, 0.158099218500249, 0.15702895570463316, 0.15700514453794945, 0.15460225559136997, 0.14614605566375083, 0.11747560005255142, 0.1108491328808272, 0.1096084538611164, 0.10428901675494728, 0.10194617541772022, 0.09732347543015507, 0.09469648273846154, 0.09409837181553105, 0.09214628161064109, 0.09190658625377424, 0.0914136839587858, 0.09002264997452336, 0.08826839034197409, 0.08794009077204912, 0.08732427486062821, 0.08295219935787657, 0.08247104503342495, 0.08075786448081335, 0.07942866688885175]\n",
      "Row 3 - Column Numbers: [ 2  5 79  4  0 84  1 78 77 31 20 17 85 83 21 87 43 35 12 74 91 33 44 30\n",
      " 11 34 64 36 86 10 46 37 41 89 39 32 38 15 29 42 40 19 56], MI Values: [0.6346295603606364, 0.6014752255233811, 0.5216221690633258, 0.5005956595959162, 0.37428008133733837, 0.29367624960262795, 0.2501813735953151, 0.22968546503017784, 0.168588428573063, 0.15053120343368054, 0.14918195632018705, 0.135719601508959, 0.12331183579416383, 0.12212949345012802, 0.12006037445413753, 0.10828482718467836, 0.1038170751558507, 0.10166237481487972, 0.10067391244311352, 0.0993121350767705, 0.09857437391434942, 0.09072061229028172, 0.09034618967547559, 0.08507553529173251, 0.08430822621926293, 0.07711971317009514, 0.0732968907767324, 0.07188834325973747, 0.06840077448593984, 0.06747669748327834, 0.0662602861970365, 0.06558274587027046, 0.06306413363040075, 0.06298051391441817, 0.06157433149594205, 0.06126513617121354, 0.06113916617078008, 0.06068970280665109, 0.06048824178377199, 0.05799913453610728, 0.057212613678012225, 0.05676014452040157, 0.05643454058528263]\n",
      "Row 4 - Column Numbers: [ 2  5 79  3  0 78  1 44 31 20 77 17 85 12 87 21 83 35 43 11 64 74 30 33\n",
      " 91 10 34 63 36 32 13 19 61 86 24 23 38 46 89 29 15 88 40], MI Values: [1.0421298348636858, 0.9112659905285279, 0.893437297964442, 0.5005956595959136, 0.4673606483958741, 0.3522117773810223, 0.34043212687770286, 0.25771696574601854, 0.227791945861342, 0.17593949417667076, 0.1718626691037226, 0.15309018167041533, 0.14716514799944758, 0.1468250597240388, 0.1467876478550929, 0.14440832752750676, 0.1374753305211449, 0.13262659195667847, 0.13167838609283677, 0.1303296358704138, 0.1297991451019085, 0.1295289172486882, 0.12417935392990831, 0.12068089113273661, 0.11543451299135477, 0.09954623668022755, 0.09367692420842033, 0.09074112883170127, 0.08771441417981674, 0.08734619315226588, 0.08641934307043808, 0.08049320130510296, 0.0793639777794386, 0.07935824289618232, 0.07926789355999908, 0.07907845045093165, 0.07857614620487485, 0.07856401142111924, 0.07698715238078346, 0.07666467817423595, 0.07652558554478439, 0.07609992946234811, 0.07604174073334136]\n",
      "Row 5 - Column Numbers: [ 4 79  2  3  0 78  1 31 43 36 35  7 77 33 20 74 17 30 21 83 85 44 87 86\n",
      " 37 12 29 91 38 89 39 11 28 40 34 42 32 10 41 80 88 90 15], MI Values: [0.9112659905285261, 0.8539429780686714, 0.8252189069592406, 0.6014752255233793, 0.4363240338301635, 0.40195030351981753, 0.32209271522605043, 0.2760329582147678, 0.20819529046906293, 0.20674579006625127, 0.19563347399244257, 0.18293846291297733, 0.17144637756480563, 0.17076852453711044, 0.1697430692708517, 0.16810983519107303, 0.16129782284088812, 0.14845254677791608, 0.1420832575295341, 0.14139989403188924, 0.14129091651330405, 0.13308552892848002, 0.13204341952919751, 0.1305167490968433, 0.12301925557245497, 0.12297734107820624, 0.11470618022646395, 0.11292935145386807, 0.10350223849688867, 0.1028680671126736, 0.10050281527196514, 0.09942878741363614, 0.09875071075038111, 0.09746128685535993, 0.09670112680553178, 0.09376382987344023, 0.09331795784564356, 0.08681805312730084, 0.08605778397885011, 0.08230865790885478, 0.07740754667316363, 0.07668497735519875, 0.07561477718424658]\n",
      "Row 6 - Column Numbers: [64 14 46 63 12 23  8 57  9 62 11 61 32 45 87 13 44  4 10 54 28 47  7 84\n",
      " 27 69 52 72 36 30 35 79 65 74 41  2 56 26 66 34  1 85 92], MI Values: [0.478605916453672, 0.1659311007796953, 0.13099684473508688, 0.11759316702334122, 0.11209322621671447, 0.09453623691659319, 0.08865574838552437, 0.0859220172096915, 0.08576932695849138, 0.08134777223811529, 0.07911821580729761, 0.07748176490715508, 0.07727934830261152, 0.07607959090818373, 0.07597112239010162, 0.07148486877965077, 0.07123886187653383, 0.07119374646681464, 0.06986362657552991, 0.067773162297458, 0.06638342779498618, 0.06549702884688458, 0.0654621562897697, 0.0649124734204598, 0.06278134191716767, 0.06183066532204595, 0.0613978125590382, 0.05919388460622166, 0.05838254740344251, 0.05558434696104264, 0.055331827053077376, 0.05403814410428076, 0.053136251620639285, 0.0529400614221025, 0.05243412828986749, 0.052066717960047804, 0.0518643235699745, 0.05140858603128606, 0.05121302295318664, 0.0509936262443027, 0.05053181341582125, 0.05019818795246955, 0.04816604793903778]\n",
      "Row 7 - Column Numbers: [ 5 17 64 21 63 57 23 46 61  6 79  2  4 52 87 12 27  3 62  9  0  8  1 73\n",
      " 10 20 69 19 47 54 58 11 14 68 88 74 30 32 33 67 31 72 34], MI Values: [0.1829384629129791, 0.10524195919111623, 0.0946233457977872, 0.09121449964563944, 0.07907681278759338, 0.07616119177035774, 0.0681607842361398, 0.06676341580429312, 0.066597172827497, 0.06546215628976793, 0.059427428725374654, 0.05901064569144587, 0.05558987853756037, 0.054813377473760916, 0.05399825056106078, 0.053976980524889306, 0.05053310241240361, 0.05009254312144673, 0.0482538265970307, 0.04809050593593689, 0.047727363031476955, 0.047556140122899215, 0.0474209934989922, 0.047129770164868745, 0.04693364118155152, 0.04555598545496231, 0.04435919441098868, 0.04338328445526862, 0.0431716643311324, 0.04278103642929665, 0.041407256502377976, 0.040946924073455904, 0.04074963195215808, 0.03718480535959223, 0.03666191730525448, 0.036462534916334555, 0.03612339642617801, 0.03608454747954237, 0.03558055210133837, 0.035520966996969605, 0.035348553502023705, 0.03526695646017597, 0.035145156518217036]\n",
      "Row 8 - Column Numbers: [10  9 14 26 11 13 25 91 85 87 12 32 64 24 27 20 21 34 17  6 23 15  1 74\n",
      " 33 30 44  0 28  4  2 77 46  5 89 31 83 78 79 35 88 63 19], MI Values: [0.48698986391151955, 0.375802297419666, 0.2819697411476927, 0.2524540408417879, 0.2289457453068362, 0.21963152219072413, 0.16233774299458315, 0.12410132440415467, 0.11970109613176039, 0.11717444758841289, 0.10941441927598472, 0.10441158737263923, 0.10254326229904187, 0.10209066826928259, 0.09968544490658893, 0.09860668116430737, 0.09797349325439786, 0.09279000891834333, 0.08886645776288304, 0.08865574838552615, 0.08474539401989478, 0.08043587263141738, 0.0804010511115445, 0.07707447313008853, 0.07565747720513727, 0.07521271366405902, 0.0702725389356953, 0.06869053966721772, 0.06518271250260987, 0.06434639902210026, 0.06327216027249083, 0.062200056513681545, 0.06204077732827784, 0.060054597826602496, 0.05864248331363431, 0.05824452931784396, 0.05824405082485651, 0.0575396306220366, 0.05661802684946515, 0.055954172623136955, 0.05292091189701953, 0.052721647755728185, 0.05241070031981643]\n",
      "Row 9 - Column Numbers: [ 8 10 26 13 14 11 32  6 12 25 87 34 64 20 27 91 24 21 17 85 36  1 23  0\n",
      " 28 41 74 63  7 30 62 83 15 61 54  2 72 19 57 79 40 89 78], MI Values: [0.37580229741966775, 0.2739374700127568, 0.1888349353819665, 0.18881791101212642, 0.17302647019022377, 0.14827272551388315, 0.08690570143561605, 0.08576932695849404, 0.08575515951341117, 0.07942615953296617, 0.07512326148058257, 0.06858253221368038, 0.06743046912400352, 0.0606112133373804, 0.060249930177727506, 0.05872512110265582, 0.05556219929455963, 0.05510777850993431, 0.053827948456972585, 0.05356332489102211, 0.05062803388903436, 0.05042486996980955, 0.04914461256289693, 0.04911468770996663, 0.04892501848965658, 0.04833957062141003, 0.04817579082966983, 0.04815235147500374, 0.048090505935939554, 0.047497107903827995, 0.046442659973216394, 0.04500640957005597, 0.044571645079205524, 0.04384180562593176, 0.04255922801340173, 0.04239438289088415, 0.041960240322472586, 0.04195403205745141, 0.04175321361746853, 0.041721734850988845, 0.041382496982518724, 0.039247318738780734, 0.03916411448757362]\n",
      "Row 10 - Column Numbers: [11  8 13  9 91 85 14 87 12 26  1 20 64 25 24  2 21 17 78 79  0 61  4 23\n",
      " 83 15 34  5 77 31 44 32 27 33 30 74 28 43 35  6 41 46 53], MI Values: [0.4993554128442783, 0.4869898639115231, 0.4066358068899456, 0.27393747001275504, 0.2579871837894956, 0.25686672570808167, 0.2251698714598369, 0.22104675256482142, 0.17468399623417863, 0.1595045585205188, 0.14396039237957758, 0.13028693835191518, 0.12993063246484482, 0.1129190817547916, 0.11268616419256361, 0.1108491328808281, 0.10815686636048127, 0.10750415858836693, 0.10461732375843713, 0.10144296896099103, 0.10125880394889109, 0.10067720955484294, 0.09954623668022666, 0.09526800567615812, 0.09120163011638649, 0.09068210425726964, 0.08709868991881109, 0.08681805312730351, 0.08644635750351704, 0.08544174110632596, 0.08386645043593433, 0.08091774681887642, 0.07918640410680755, 0.077949740915769, 0.07776056152449495, 0.07645994681407409, 0.07299784236684648, 0.07182439963604015, 0.07091448732899508, 0.06986362657553258, 0.06936075480536807, 0.06801559120089085, 0.06799093673704792]\n",
      "Row 11 - Column Numbers: [10 85 61 12 13 91 87  1  8 20 21 17 77  0  2 83  9  4 78 14 79 31 24 15\n",
      " 64  5 35 43 44 74  3 33  6 42 30 28 90 34 19 89 22 23 80], MI Values: [0.499355412844281, 0.447794898444446, 0.4211796194747075, 0.4197051791498847, 0.40682029470780456, 0.3865429355312857, 0.296573849422912, 0.23445155092457082, 0.22894574530684064, 0.21618413086183974, 0.17612200358653762, 0.1627161637347161, 0.15529190588759256, 0.15513395543730546, 0.15460225559137086, 0.14976259321938645, 0.1482727255138805, 0.13032963587041646, 0.12508164598781324, 0.12287505739090143, 0.12041417972820945, 0.11341149652601601, 0.10784355126935719, 0.10663625668288024, 0.10500346113093073, 0.09942878741363259, 0.096740469127222, 0.09481730555193213, 0.08789263097170963, 0.08465931443259134, 0.08430822621926115, 0.0819176206772605, 0.0791182158072985, 0.07587529502254231, 0.0758563574615021, 0.07518085992455958, 0.07463339072882835, 0.0729801592932775, 0.06976258783125644, 0.0691934966107981, 0.06893504056359223, 0.06614162517794231, 0.06530714718931119]\n",
      "Row 12 - Column Numbers: [11 13  1  2  0 20 10 85 79 77 21  4 31 74 43 30 87 33 91 35 17 78  5 83\n",
      "  6 61  8 64 86  3 34 36 14 37 28 40 39 29 42 89 44 38  9], MI Values: [0.41970517914988204, 0.2820044236370247, 0.22954525563754302, 0.19750308970805097, 0.19725693559809976, 0.19049650601974388, 0.17468399623417863, 0.16892847033331915, 0.15745268691877712, 0.15476368455904232, 0.1470253698180608, 0.1468250597240388, 0.14662969753092625, 0.14286051344793105, 0.14156956810136734, 0.13732974337876414, 0.13558171850873002, 0.13072864694938868, 0.12921883418740698, 0.12855491233259286, 0.12797358847181428, 0.1251376255189447, 0.12297734107820624, 0.12178764257401742, 0.11209322621671713, 0.11175003676089723, 0.10941441927598472, 0.10535355610052655, 0.10135095971922237, 0.10067391244311619, 0.09993696526051199, 0.09709484343702979, 0.09629848458173385, 0.09592473158963521, 0.09501229751970186, 0.09185969685608963, 0.09122469199042715, 0.08955815291430014, 0.08912140713055461, 0.08890082125607712, 0.08654874505815524, 0.08621577314512052, 0.08575515951341028]\n",
      "Row 13 - Column Numbers: [11 10 12  8  9 85 91 87 78  1 20  2 31 14 35 30 43 33 44  4 79 21 28 74\n",
      " 25  0 34 17 26  6 64 83  5 15 77 36 42 32 80 89 61 54 70], MI Values: [0.406820294707801, 0.40663580688994827, 0.28200442363702294, 0.21963152219071969, 0.18881791101212642, 0.15241639531040452, 0.15188179879224428, 0.11270707168405014, 0.10855159929809766, 0.10726653658897689, 0.10347968403017482, 0.10194617541771755, 0.10045734833963227, 0.09715275871665696, 0.095142371568528, 0.09258617061155316, 0.09195467760153075, 0.08878636983820609, 0.08824878688846738, 0.08641934307043897, 0.08620980383680887, 0.08274041805652033, 0.08202421217934308, 0.08012866253161732, 0.07985596483401824, 0.07790975017566382, 0.07495306478076014, 0.07488041542475532, 0.07181363072769464, 0.07148486877965166, 0.07002602341222808, 0.06900697369544506, 0.06846734306451818, 0.0666776158158564, 0.0664440140391962, 0.06379802149536751, 0.062408309849672605, 0.062004348452000535, 0.05890185010481819, 0.057406820089648924, 0.05485204269998434, 0.05430024107788256, 0.054016668508986676]\n",
      "Row 14 - Column Numbers: [ 8 10  9 26  6 27 64 11 87 25 63 85 13 12 46 91 47 24 20 77 34 17 37 61\n",
      " 36 86 56 29 23 55 79  0 48 83  4 74  2  5 57 32 72 51 30], MI Values: [0.2819697411476918, 0.22516987145983425, 0.17302647019022466, 0.17093143981882442, 0.16593110077969708, 0.1515567092969663, 0.12701720438150055, 0.12287505739089966, 0.12022624072505117, 0.10808026792929493, 0.09840075284083127, 0.09779637211347314, 0.0971527587166543, 0.09629848458173651, 0.09266115822732779, 0.09231436655408931, 0.09074348902636675, 0.07873666169272209, 0.07681486761087797, 0.07067488479129924, 0.06725286085851412, 0.06554506282266725, 0.0641664994737523, 0.06170135977184188, 0.061668865682766416, 0.06094423783477776, 0.05952118983744992, 0.0587014765905316, 0.0585240406935128, 0.05661782886078903, 0.056059091866146105, 0.05562693284596332, 0.05528245353972583, 0.05451886276258566, 0.05432706381529773, 0.05401613896216251, 0.05270106891950288, 0.05173567448447702, 0.05167205271928932, 0.05104880529890021, 0.050294567082459274, 0.05026820068852178, 0.04979484407518253]\n",
      "Row 15 - Column Numbers: [21 16 22 20 17 19 18 85 83  1 91 87 77 73  0 11  2 10  8 12 79  4  5 56\n",
      " 90 23 42 78 61 13 24 35 43 31  3 80 68 32 46 92 57 33 53], MI Values: [0.48722604389986746, 0.47765933545984574, 0.42274734051130114, 0.3684773490976543, 0.3095265239658307, 0.30125231966110366, 0.27326227718117746, 0.2607931482272843, 0.23569399663760038, 0.23100847367209187, 0.226286992520925, 0.22368717713125363, 0.2109149525053864, 0.17737229996765436, 0.16436438822998056, 0.10663625668287935, 0.10428901675494551, 0.09068210425726964, 0.08043587263142005, 0.07994733324017389, 0.07750166086596355, 0.07652558554478794, 0.07561477718424747, 0.07262961413739166, 0.07254756653808414, 0.07129603115169658, 0.06699419564638731, 0.06674255678354601, 0.06669711932901201, 0.0666776158158564, 0.06508609948717492, 0.06380756444094082, 0.06258859383481585, 0.06209333159081609, 0.06068970280665109, 0.06004207076621171, 0.05863023036643167, 0.05587065130398727, 0.05560717684994554, 0.055416447648041434, 0.054577733516099514, 0.051477381196054495, 0.05145699897161915]\n",
      "Row 16 - Column Numbers: [15 18 22 19 21 85 73 17 20 83  1 91 87  0 77 68  2 42 10 23 56 61  5 11\n",
      "  4 90 13 78 57 63 79  3 64 46 92 52 84 80 24 53  8 47 32], MI Values: [0.47765933545984485, 0.39646468501385357, 0.3870402149910266, 0.3091588054074448, 0.28541688685649813, 0.2495265251234624, 0.23365823269839403, 0.19302253406145908, 0.17044387506372072, 0.16718927849869658, 0.13986782406464915, 0.13528675087576136, 0.12870418125103722, 0.101737015609487, 0.09654894383117263, 0.08013941132973557, 0.07497954269839457, 0.0675083713658422, 0.06746525386392133, 0.06694340591739856, 0.06331255297438165, 0.06108123440198021, 0.059929091775576815, 0.05975370525344825, 0.05524048992921937, 0.052897766030480575, 0.051451103064484194, 0.050915937056171146, 0.049854047095866605, 0.049689454222085594, 0.04856746770346909, 0.04659548808807035, 0.046006140165719245, 0.04556275492620987, 0.04529324898574405, 0.04328046495819304, 0.04310793055946416, 0.04279362459041813, 0.04234654693679207, 0.04223363657743562, 0.04159168613493058, 0.040768941888324584, 0.04067108310344292]\n",
      "Row 17 - Column Numbers: [83 21 20  0  1 15 77 19 85  2 91 87 16 92 11  5 22 79  4 18  3 12 73 46\n",
      " 90 10  7 78 64 57 31  8 42 61 56 43 13 62 68 74 35 53 52], MI Values: [1.0668147455974486, 1.021617623019086, 0.4934266968283074, 0.3299090634675217, 0.3283135513911546, 0.30952652396583336, 0.299093897359759, 0.2719089149660965, 0.24799566598007683, 0.20709995929092084, 0.2001069525344823, 0.19689724643638318, 0.1930225340614582, 0.16969542448540675, 0.16271616373471876, 0.16129782284088456, 0.15874125412953077, 0.15630527248319748, 0.153090181670418, 0.13764098894343224, 0.13571960150895812, 0.1279735884718134, 0.11461081534221496, 0.11280369881762375, 0.11040902183482348, 0.1075041585883687, 0.10524195919111712, 0.1047767078550299, 0.10037328777475985, 0.0992868325667029, 0.09616040667204562, 0.0888664577628866, 0.0846645868325373, 0.08457972685715465, 0.07971577342061753, 0.07861749607301505, 0.07488041542475354, 0.07054503826931136, 0.06961403770779029, 0.06954563307844097, 0.06903264964802336, 0.06894645621138906, 0.06703671873903527]\n",
      "Row 18 - Column Numbers: [73 19 16 22 15 21 17 83 20  1 91 85 87 77 63 88  0 57 46 72 32 64 90 92\n",
      " 56 78  2 68 42 61 11 70 82  4 62 10 52  5 48 36 75 53 55], MI Values: [0.7893958078076464, 0.5505196890502351, 0.39646468501385357, 0.32015585431856763, 0.27326227718117746, 0.1986950339873701, 0.1376409889434349, 0.1300561044353925, 0.1028199239054004, 0.09060525299304434, 0.08043542246333768, 0.07840025513521187, 0.07415089398027508, 0.073829802711872, 0.0698631855232481, 0.06947413178679618, 0.06937049801544681, 0.0555089312872461, 0.05501723067444342, 0.05297227066477728, 0.05286118816878638, 0.05264544534878457, 0.052266576769972595, 0.050573593189831456, 0.05004107750332221, 0.04951922140218912, 0.04704017567014063, 0.04656039319276406, 0.04583471052896382, 0.04531110745527123, 0.0452698374916638, 0.044711784493036255, 0.04452332972605788, 0.04430454607192402, 0.04406838905054933, 0.04345714793886302, 0.04316032552696658, 0.04294014239589039, 0.04283733769362108, 0.042177627147790275, 0.04216690271784085, 0.04179825178695218, 0.041337731296333224]\n",
      "Row 19 - Column Numbers: [18 73 21 16 15 83 17 22 20  1 77  0 85 87 91  2 90 64 12  4 46 79 92  5\n",
      " 11 68 78 42 10 57 72 75 62  3 31 52 70 56 32  8 30 35 43], MI Values: [0.5505196890502289, 0.4449658563187162, 0.3588428833857771, 0.3091588054074439, 0.301252319661101, 0.28206410473166965, 0.2719089149661009, 0.23610468619476066, 0.2076473979554514, 0.16120899606897776, 0.1483996768217315, 0.13409996608400476, 0.12862613575316484, 0.11907016274300641, 0.10649322098528025, 0.09214628161063843, 0.08561032186586814, 0.08194120218001011, 0.0811618444653357, 0.08049320130510296, 0.07977684117637374, 0.07277800134663526, 0.0708353227962224, 0.07067602202174772, 0.06976258783125466, 0.06634530228217983, 0.06322232364202662, 0.06322090154945581, 0.06289596277964993, 0.06149090076405361, 0.06050821759755998, 0.058831519684985345, 0.05762318703291758, 0.05676014452040601, 0.055853509021861925, 0.05518017282950449, 0.0544766833802548, 0.05387141021679831, 0.05309676005317332, 0.05241070031981998, 0.052023287162046294, 0.05003592431078108, 0.04839550757959277]\n",
      "Row 20 - Column Numbers: [77 21  1 17 83 85  0 15 91 87  2 11 19 12 79  4 16  5 22  3 10 64 78 13\n",
      " 18 61  8 90 31 56 24 46 14 30 92 74 68 34 73 33 42 44 43], MI Values: [0.6456828762580988, 0.5615054795942642, 0.5324618722588088, 0.49342669682830653, 0.4589017533899522, 0.42552426145736355, 0.4190235175463517, 0.3684773490976534, 0.3510509439994527, 0.3260490569519252, 0.26984073230595484, 0.21618413086183885, 0.20764739795544962, 0.190496506019743, 0.18041597931931808, 0.17593949417666988, 0.1704438750637216, 0.16974306927085436, 0.1497647957772532, 0.14918195632018527, 0.13028693835191607, 0.11253209164347666, 0.11158401518017502, 0.10347968403017305, 0.10281992390539951, 0.10190813419336298, 0.09860668116430649, 0.08732179357987757, 0.0842263209541052, 0.0828616535343425, 0.08129397459731802, 0.07862828607228867, 0.0768148676108753, 0.07673835654706895, 0.07064869314149558, 0.06733550911625219, 0.0667893192001614, 0.06677633392818816, 0.06621492860686207, 0.06372475882601236, 0.06355486571293412, 0.061150149623385275, 0.060827899523522966]\n",
      "Row 21 - Column Numbers: [17 83 20 15  1 19  0 16 77 85 22  2 91 18 87 11 12 73  4  5 79 90  3 92\n",
      " 10 78  8 42 61 64 56  7 46 31 68 13 57 43 62 44 35 52 26], MI Values: [1.0216176230190834, 0.7488876659638635, 0.5615054795942669, 0.48722604389986657, 0.4023069759074396, 0.3588428833857771, 0.33215728219305163, 0.2854168868564999, 0.28331594629221524, 0.2688208314872229, 0.22456476967975902, 0.2125857191397058, 0.2086854981064592, 0.19869503398736654, 0.18708052814614362, 0.1761220035865394, 0.14702536981806258, 0.14619238110757227, 0.144408327527505, 0.142083257529535, 0.13959981733842852, 0.12517520234618917, 0.12006037445413664, 0.1117978672601394, 0.10815686636048305, 0.10268663613005469, 0.09797349325439786, 0.09722563185672684, 0.09520585153422978, 0.09236995631917555, 0.09187841023316423, 0.09121449964563855, 0.08964547025689651, 0.08819779567887132, 0.08274897552593963, 0.08274041805651944, 0.08110178494543518, 0.07911198418960996, 0.07348744391152273, 0.06846944162919932, 0.06815788789081711, 0.06802973139084845, 0.06522771175571496]\n",
      "Row 22 - Column Numbers: [15 16 18 19 21 73 17 20 83 85 91 77  1 87 23  0 11  2 56 10 79 13 57  5\n",
      " 42 32 61  8  3 74 64 34 70 24 78 63 68 90 43 72 35 53 62], MI Values: [0.4227473405113029, 0.3870402149910266, 0.32015585431856763, 0.23610468619476155, 0.22456476967976258, 0.19668419399470238, 0.15874125412953077, 0.14976479577725232, 0.14502492612060003, 0.11578837068495584, 0.1063924866874304, 0.10378871318925587, 0.09452496762458118, 0.08969080820395181, 0.07632786384865842, 0.07596636122032496, 0.06893504056359401, 0.06328881794610464, 0.06098127462148906, 0.05727822396969895, 0.054970003136741497, 0.051323177882335536, 0.05062976172811151, 0.050465669694910176, 0.05027063548670352, 0.049760788383411025, 0.047233204160109565, 0.04542566347070398, 0.04382301867003058, 0.04368901502755573, 0.04358675196225281, 0.042850022291132994, 0.04278545874037132, 0.04263132941212078, 0.04245227781570726, 0.04240480524732426, 0.04177115423568889, 0.04146334279107311, 0.041258234396297944, 0.04113645596182369, 0.040745425400359636, 0.040726001607573004, 0.040577710389676724]\n",
      "Row 23 - Column Numbers: [64 57 87 44 10  6 24 91 85 61  8  4 22 63 15  7 16  0 11 17 92  2 12 21\n",
      " 14 55 47  1 74 56  5 13 79 62  9 31 25 77 26 83 32 20 46], MI Values: [0.1238287448328963, 0.11007546217848985, 0.10279703918589878, 0.09985139888774786, 0.09526800567615457, 0.09453623691659319, 0.09442643580457855, 0.092779592553069, 0.08797109748794085, 0.08578580449603201, 0.08474539401989523, 0.07907845045093076, 0.07632786384865975, 0.07257144170704688, 0.07129603115169214, 0.06816078423614158, 0.06694340591739678, 0.06631267495817283, 0.06614162517793609, 0.06462454817737662, 0.06377017167667276, 0.06238952944812581, 0.06198182224754323, 0.06102500139047695, 0.05852404069351369, 0.058494817456543835, 0.057048950299178, 0.056427588090688374, 0.05575798124214959, 0.05424612918912608, 0.053944258296575676, 0.053394179519995255, 0.05090816537458753, 0.049627949735287835, 0.04914461256289693, 0.04830377167633948, 0.0479154062061089, 0.047404493128977876, 0.04534942266509967, 0.044620281399040174, 0.04423650621570019, 0.04399862638296703, 0.04319511791377284]\n",
      "Row 24 - Column Numbers: [87 25 85 10 11  8 26 91 23 77 64 12 20  4 14 63 61  1 56  0 15 46  2 44\n",
      "  9 27 21 30 75 32 79 62  5 31  3 78 68 60 22 34 16 17  6], MI Values: [0.12664131656206834, 0.12184764568086237, 0.11662871191984614, 0.1126861641925645, 0.10784355126935541, 0.10209066826928304, 0.09988104072929094, 0.09541744286183551, 0.09442643580457988, 0.08554737930800638, 0.08433207450633073, 0.08382766133586106, 0.08129397459731003, 0.07926789356000175, 0.07873666169272342, 0.07871775795832381, 0.07660849160601568, 0.07658487183691687, 0.06753872107738834, 0.06575943129935258, 0.06508609948716693, 0.06378754370319006, 0.06196951220919278, 0.05575375327102261, 0.055562199294558745, 0.05318120567191542, 0.05262117138877809, 0.05116230585414172, 0.05083179402329918, 0.049254453905052564, 0.04814401145309244, 0.04665448807793737, 0.04619072869628571, 0.0458151748730149, 0.044434685459121326, 0.043901624829374875, 0.04323480914173228, 0.04291271895550075, 0.04263132941212122, 0.04238722505216597, 0.042346546936791185, 0.041908005215020694, 0.04135516870134959]\n",
      "Row 25 - Column Numbers: [26  8 24 10 14 13  9 27 64 20 32 30 63 11 21 12 74 33 17 56 23 85 91 15\n",
      " 87 28 61 89 34 38  1 40 43 52 36 80 35 37 41 83 86 88 16], MI Values: [0.22448983276060552, 0.16233774299458315, 0.12184764568086015, 0.11291908175479026, 0.10808026792929493, 0.07985596483401203, 0.07942615953296661, 0.06742082698712792, 0.057769002718598195, 0.05586583465511197, 0.054965263207836124, 0.05443370142787174, 0.053776458305056174, 0.05343401191718833, 0.05308655380792704, 0.05045720325549752, 0.05034647749383048, 0.04992384501594582, 0.0492451891629031, 0.04834454363245477, 0.0479154062061089, 0.047684160601328074, 0.047297099255485975, 0.04577736523629383, 0.0457726787254078, 0.045771120375120766, 0.04566515411493954, 0.043420484714855156, 0.043385152301504526, 0.04150956737140632, 0.04116356278905453, 0.040902739036422275, 0.039271536657020434, 0.03872861083601631, 0.03870735899101785, 0.03823640170302056, 0.03689051731253823, 0.03648924728638114, 0.03594012672179936, 0.03543675472183061, 0.0353375347334941, 0.033978841582392505, 0.033213377245050246]\n",
      "Row 26 - Column Numbers: [ 8 25  9 14 10 27 24 64 13 30 32 21 11 17 20 91 74 85 87 33 34 46  6 43\n",
      " 15 36 35  1 12 63 23 83 41 80 31 72 56 86 84 52 37 28 61], MI Values: [0.25245404084178746, 0.22448983276060552, 0.1888349353819665, 0.1709314398188191, 0.15950455852051704, 0.10013893815186226, 0.09988104072928916, 0.08361194904788949, 0.07181363072768843, 0.06658416020495395, 0.06642109881221003, 0.06522771175571318, 0.06133706698861552, 0.060864275396509626, 0.06030983748989538, 0.05855558719449405, 0.058118774994220246, 0.05502112683089955, 0.054955567957541085, 0.0548802691847472, 0.05446576296866468, 0.05385131209205429, 0.05140858603128562, 0.04892271442605356, 0.048556550337056414, 0.047843331021867996, 0.04718698058252446, 0.04666834102500239, 0.04641197580127887, 0.04620099613250428, 0.045349422665099226, 0.045142856596432246, 0.04487870650962478, 0.04102053350114243, 0.03975973670425059, 0.039456412404046404, 0.03926146380477791, 0.03883323698171193, 0.038101405951134204, 0.03717014915810957, 0.03702701389699303, 0.03678714727422072, 0.036512909297854]\n",
      "Row 27 - Column Numbers: [65 64 14 46 45 26  8 10 25  6 84  9 12 38 11 13 24 53 74  7 44 21 63 85\n",
      " 47 91 62  0 86  4  3  5 31 43 61 87 76 20 80  1 77 37 29], MI Values: [0.6065603894953897, 0.18682361749818366, 0.1515567092969663, 0.13632308186498676, 0.10364354834176126, 0.10013893815186492, 0.09968544490658893, 0.07918640410680577, 0.06742082698712792, 0.06278134191716767, 0.06038028586904787, 0.06024993017772662, 0.05954908040441431, 0.05566701959818321, 0.05365543785469562, 0.05349787902327563, 0.053181205671913645, 0.05121607804495909, 0.05107317746817763, 0.050533102412405384, 0.05024731173365815, 0.04849977979742892, 0.04791989593709012, 0.04765153600392935, 0.04741748068507423, 0.04718827956837135, 0.04704704797821968, 0.046555580550760034, 0.045963625687851284, 0.0458714770575126, 0.04550892471748291, 0.04427143864075678, 0.044267360807431544, 0.04422157037556218, 0.044030392965271226, 0.043659800788907965, 0.04331808077932564, 0.04308091954790427, 0.04297197397555763, 0.042923144439217076, 0.04277349385328666, 0.04153155742864545, 0.040719138411590805]\n",
      "Row 28 - Column Numbers: [89 38 88 37 40 86 29 41 39 36 33 74 30 34 35 43 32 31 56 78  5 44 12 80\n",
      " 79  2 13 42  1 11 10  4 62  6  8 68 90 64 52 17  0 54 61], MI Values: [1.0046755344608442, 0.8668221841314496, 0.7614158768816583, 0.7435037784407115, 0.7401508914135695, 0.7092838503040948, 0.6969500914396249, 0.6683242642188869, 0.6188553437563042, 0.5887599355969604, 0.573378254007582, 0.4637692211865332, 0.44110042693832696, 0.43990166348400894, 0.3542576214733666, 0.3130926126664333, 0.3038339983430083, 0.1631475034181804, 0.14153000235829616, 0.10874080446091217, 0.09875071075037845, 0.0973992316948431, 0.09501229751970275, 0.09424947908653536, 0.09026690572979579, 0.08247104503342673, 0.08202421217934486, 0.08020834452426495, 0.07617110541908723, 0.0751808599245587, 0.07299784236684648, 0.07194026557628508, 0.07174551471409618, 0.06638342779498885, 0.06518271250260632, 0.06489586595952179, 0.0643523399002186, 0.06270446068020075, 0.05772311949448383, 0.056954572674678516, 0.05644466945878257, 0.05541299819598944, 0.05407556787339285]\n",
      "Row 29 - Column Numbers: [37 86 38 89 39 28 40 36 88 74 33 41 43 35 30 34 31 56 32  5 78 79 44 80\n",
      "  2 12  4 90  1  0 87 42 46 77  3 14 64 11 85 62 63 57 13], MI Values: [1.124331483930141, 0.9904397714916939, 0.8561076404645682, 0.7571541803206943, 0.7394482075767632, 0.6969500914396267, 0.6243050233062002, 0.6127287729060686, 0.5162986988948424, 0.5004203013385551, 0.4839723248105665, 0.44277394507430223, 0.3862199704096003, 0.3611089233159852, 0.3044944524915385, 0.30210464330076015, 0.20191448281292157, 0.171307375513706, 0.1557361930389609, 0.11470618022646129, 0.1142833513780932, 0.10420208049496082, 0.10392751587923588, 0.09785175941231206, 0.09469648273846332, 0.08955815291429925, 0.07666467817423417, 0.07002944857802351, 0.06654779481397011, 0.06576826886766884, 0.06531253837083639, 0.06416664878429135, 0.06302637459570448, 0.06065012243418977, 0.06048824178377199, 0.058701476590528046, 0.05802769428221577, 0.049098105017652216, 0.04872740090602523, 0.04751490159093841, 0.04718646229756551, 0.047177310303764486, 0.04510718141365366]\n",
      "Row 30 - Column Numbers: [33 35 74 32 34 43 28 31 36 86 89 40 37 38 41 88 29 39 78 79  2 44  5 12\n",
      " 80  4 42  1  0 52 13  3 64 90 10 20 11  8 87 56 85 26 77], MI Values: [0.8392067051587295, 0.6637829223064537, 0.6484729630309518, 0.5649484715892896, 0.5416346036080313, 0.4933942675879779, 0.4411004269383261, 0.4130016958463507, 0.38187736651662174, 0.3742297238726069, 0.3717084490392537, 0.3527990507831582, 0.33036985608766933, 0.32508215731131695, 0.315969342937767, 0.3120618690279784, 0.3044944524915376, 0.2926134592339231, 0.245510624027526, 0.1906085060616709, 0.15876062884895248, 0.15101976681000995, 0.14845254677791608, 0.1373297433787659, 0.13577620649841027, 0.1241793539299092, 0.11531395362702757, 0.1150059734774116, 0.10962686909974106, 0.10641737910058513, 0.09258617061154961, 0.08507553529173606, 0.08219023403697623, 0.07857807032348152, 0.07776056152449762, 0.0767383565470654, 0.0758563574615021, 0.07521271366405902, 0.07367325277221859, 0.06707550157230102, 0.06691537715915796, 0.06658416020495572, 0.06275013897899484]\n",
      "Row 31 - Column Numbers: [43 78 35 30 33 44 74 79  2  5 36 42 86  4 37 29 34 80 32 38 28  0  1 89\n",
      " 39  3 12 40 41 88 11 87 85 13 17 21 10 91 20 83 77 64 90], MI Values: [0.8121927311946013, 0.7638100129208842, 0.7457506706593477, 0.41300169584634716, 0.40367630493282647, 0.3834036968008201, 0.36859551535020874, 0.3469763013969196, 0.288579169234902, 0.2760329582147696, 0.2539363056818278, 0.2480981515670253, 0.22807412650458492, 0.22779194586134022, 0.21452991980362057, 0.20191448281292157, 0.1870476252617994, 0.18479080672561743, 0.17115190570613592, 0.167611070828948, 0.16314750341817774, 0.16211076425159288, 0.16121744315732478, 0.15421271891570942, 0.1526762354992739, 0.15053120343368143, 0.14662969753092536, 0.1369994315782277, 0.12987048179875593, 0.1178467066606661, 0.11341149652601867, 0.10896037047705764, 0.1060824704994614, 0.10045734833963404, 0.09616040667204917, 0.08819779567887043, 0.08544174110632508, 0.08539580505605926, 0.0842263209541061, 0.08252825085347038, 0.07208828414576374, 0.06851019554836757, 0.06594386443863964]\n",
      "Row 32 - Column Numbers: [34 30 52 33 28 88 40 74 35 89 41 86 38 43 39 37 36 31 29 44 54 78  8 79\n",
      "  5  2  4  9 62 10 12 42  0  6 80 64  1 26 87 61 90 13  3], MI Values: [0.6589132113122833, 0.5649484715892905, 0.5366720434860506, 0.31429643099880256, 0.3038339983430083, 0.2746754336314945, 0.264343537327707, 0.254749734631722, 0.24376381697460836, 0.23990089864081465, 0.2315338746347546, 0.2027410833178278, 0.197909157760205, 0.19253106758836758, 0.1831205200479813, 0.17952444982802795, 0.17752977924984759, 0.1711519057061368, 0.15573619303895825, 0.12104168683611505, 0.11793416791373534, 0.1155347151347117, 0.10441158737263923, 0.09567236193821138, 0.09331795784564623, 0.09002264997452247, 0.087346193152265, 0.08690570143561605, 0.08212300251017712, 0.08091774681887465, 0.07909381487392952, 0.07802938607998389, 0.07772961987272353, 0.0772793483026124, 0.07650826602535332, 0.07345476684191166, 0.07062525451403978, 0.06642109881221536, 0.06429935007831045, 0.06347776301673225, 0.06345428849975132, 0.06200434845199787, 0.061265136171211765]\n",
      "Row 33 - Column Numbers: [74 30 36 35 43 86 28 37 89 38 29 40 34 39 41 88 31 32 78  5 79  2 44 80\n",
      " 12  4 42  1 56  0  3 13 85 64 87 11 90 10  8 52 77 61 91], MI Values: [1.1137204124807507, 0.8392067051587295, 0.7259968303690219, 0.676225408758059, 0.6277452858407466, 0.6078933190308362, 0.5733782540075802, 0.5576286905708168, 0.5364183007679388, 0.49716674763380553, 0.4839723248105665, 0.4791060933274043, 0.45408232882174193, 0.4358859922207907, 0.4346502711337248, 0.4047557520194287, 0.40367630493282647, 0.31429643099880256, 0.21439117181920508, 0.1707685245371131, 0.1675397929716098, 0.1580992185002481, 0.1558944425895863, 0.1513697471049289, 0.13072864694939046, 0.12068089113273839, 0.11403454812488523, 0.10934085523256698, 0.10568767232683207, 0.09664578770578203, 0.09072061229028083, 0.08878636983820609, 0.0853957938074732, 0.08444826940177563, 0.0822160314308702, 0.08191762067726316, 0.07829650162065782, 0.07794974091576812, 0.07565747720513549, 0.0721596876850441, 0.06870563600714075, 0.06766819910745436, 0.06454231972101443]\n",
      "Row 34 - Column Numbers: [32 41 40 89 30 88 33 28 38 39 74 86 37 36 29 35 43 31 78 52 79  2 12 80\n",
      "  5  4  8 44  1 56  0 10 42  3 13 11  9 85 90 14 20 87 91], MI Values: [0.6589132113122842, 0.6479726613644816, 0.6043685240765004, 0.5628237492307457, 0.5416346036080313, 0.521645640678436, 0.45408232882174193, 0.43990166348400983, 0.4368469340751924, 0.39158474017250366, 0.3551015296305442, 0.3436127338197732, 0.3342616147154853, 0.30793458819287167, 0.30210464330076015, 0.2547895016786663, 0.25147509845387006, 0.18704762526179852, 0.1318444892478734, 0.12773246250446846, 0.12182153097619519, 0.11747560005254787, 0.09993696526051377, 0.09689650292456253, 0.09670112680552911, 0.09367692420841855, 0.09279000891834333, 0.09093985620778966, 0.09049841174829432, 0.08918579292805706, 0.08750394746818113, 0.08709868991881464, 0.08002420593659476, 0.07711971317009425, 0.07495306478075747, 0.07298015929327839, 0.0685825322136786, 0.06771394965493194, 0.06748508102814021, 0.06725286085851323, 0.06677633392818727, 0.06352632300524341, 0.05979450877373882]\n",
      "Row 35 - Column Numbers: [43 31 33 30 74 36 86 37 29 78 28 38 89 44 39 34 40 32 88 79 80 41  5  2\n",
      " 42  4 12  1  0  3 11 13 56 85 87 90 10 64 17 21 83 15 91], MI Values: [1.3860244468954068, 0.7457506706593469, 0.676225408758059, 0.6637829223064564, 0.6417520640136267, 0.41003162791165604, 0.39846097278793113, 0.37245697314779047, 0.36110892331598254, 0.36035661286731724, 0.3542576214733648, 0.28812166153925034, 0.28455742734958633, 0.2744838416218025, 0.25908379307944696, 0.2547895016786681, 0.2444710266515937, 0.24376381697461103, 0.2113827569500044, 0.20596754398312012, 0.2032245059398745, 0.20034425775401932, 0.1956334739924417, 0.1870192028603448, 0.18522516757732976, 0.13262659195667936, 0.1285549123325911, 0.11642248941903688, 0.11361591888716038, 0.1016623748148815, 0.09674046912721845, 0.095142371568528, 0.0801836035458896, 0.07727436282669675, 0.07446311599579492, 0.07216427126333969, 0.07091448732899774, 0.06950218448865986, 0.06903264964802514, 0.06815788789081711, 0.06455351051612634, 0.06380756444093993, 0.05848415311997446]\n",
      "Row 36 - Column Numbers: [86 37 33 29 74 28 89 41 38 40 39 43 35 88 30 34 31  5 32 56 78 79 80 44\n",
      "  2 12  4 42  1  3 90 10  0 13 72 14 77 64 87 57 70 46  6], MI Values: [1.0233770024292177, 0.8615166885581989, 0.7259968303690219, 0.6127287729060713, 0.6090092895887054, 0.5887599355969613, 0.5752000583378694, 0.5713794920745894, 0.5355098016260644, 0.47454758830574484, 0.4665352887983394, 0.4335648849167999, 0.41003162791165515, 0.39112029603754017, 0.38187736651661996, 0.30793458819287167, 0.2539363056818287, 0.20674579006625216, 0.1775297792498458, 0.15081603715863867, 0.14656523125808896, 0.11619314258747515, 0.11571876599131148, 0.1145234869763252, 0.10960845386111995, 0.0970948434370289, 0.0877144141798194, 0.07775809933113642, 0.07458627225738823, 0.07188834325973659, 0.06954945457795603, 0.06702934232361812, 0.06656537960473763, 0.0637980214953684, 0.06265064870037129, 0.06166886568276819, 0.06121318706422585, 0.06076563582838368, 0.0603698282500984, 0.0600022474540296, 0.05999309743629677, 0.059587362304820424, 0.05838254740343718]\n",
      "Row 37 - Column Numbers: [86 29 36 38 89 28 39 40 33 74 88 41 43 35 56 34 30 31 32  5 78 79 44 80\n",
      " 12  2  4 90  1 42 87 46  3  0 14 77 57 64 75 10 81 85 72], MI Values: [1.45827221487633, 1.1243314839301428, 0.8615166885582006, 0.8339552318828192, 0.75725247965641, 0.7435037784407115, 0.6894104126018572, 0.6269405732545383, 0.557628690570815, 0.5514988683591895, 0.5065004040074994, 0.4944806219210722, 0.4048082990644746, 0.37245697314779047, 0.35940226604219117, 0.3342616147154871, 0.3303698560876711, 0.21452991980362324, 0.17952444982802884, 0.12301925557245674, 0.1229936336440689, 0.11167013683338922, 0.10660787110909098, 0.09822950179437395, 0.09592473158963699, 0.09141368395878491, 0.07514331037207178, 0.07091755529673804, 0.06883285800983607, 0.06871969299735081, 0.066765545099301, 0.06572403954205441, 0.06558274587026869, 0.06455866987752579, 0.06416649947375319, 0.06138718973277957, 0.05958381308008942, 0.0586839187321484, 0.05770927457102015, 0.05541200876063623, 0.0543002203644134, 0.053567885640179114, 0.053098326138301566]\n",
      "Row 38 - Column Numbers: [89 39 40 28 29 37 88 86 41 36 33 74 34 30 43 35 32 31 56 78  5 79 44  2\n",
      " 80 12  4 90 42 87 64 10  3  0 46 54 27 63  1 55 61 52 81], MI Values: [1.2419280927673926, 0.9495031915623935, 0.9353087992452069, 0.8668221841314478, 0.8561076404645709, 0.8339552318828174, 0.7568375359220987, 0.7540596341394155, 0.6590139783160547, 0.5355098016260609, 0.49716674763380464, 0.4638361476100483, 0.4368469340751897, 0.32508215731131607, 0.2970750486302043, 0.28812166153925034, 0.19790915776020768, 0.16761107082894533, 0.14324753303636406, 0.10392867184476451, 0.10350223849689133, 0.09301615106454886, 0.08916423701914233, 0.08794009077204823, 0.08653427377214928, 0.08621577314512141, 0.07857614620487752, 0.07291292443408093, 0.06775644455948626, 0.06587368807998661, 0.06444153292271437, 0.06239411896947633, 0.0611391661707783, 0.05890813572238418, 0.05743119615494585, 0.05657172017433254, 0.0556670195981841, 0.052999594620209756, 0.05251122766241956, 0.05144646558632271, 0.050525831605085614, 0.05046119874021926, 0.050427398365081366]\n",
      "Row 39 - Column Numbers: [89 40 38 88 29 37 86 28 41 36 33 74 34 30 43 35 32 31 56 78 79  5  2 44\n",
      " 12  4 80 90 46 64 42  0  3  1 87 54 57 10 85 81 11 75 13], MI Values: [1.0535035116401659, 0.980751027799518, 0.9495031915623944, 0.7414381495833338, 0.7394482075767623, 0.6894104126018581, 0.6322229406595952, 0.6188553437562998, 0.597892725921354, 0.46653528879833495, 0.4358859922207863, 0.41880685619855296, 0.3915847401725019, 0.29261345923392224, 0.2629228824826715, 0.2590837930794496, 0.18312052004798485, 0.15267623549927567, 0.11061737849190223, 0.10303541936903038, 0.10121071598448683, 0.10050281527196514, 0.09409837181553016, 0.09268755609898616, 0.09122469199042627, 0.07574221883219856, 0.07038469791400459, 0.06777425757345945, 0.06718928231977817, 0.06637371235615408, 0.06470157204124849, 0.06376207874312012, 0.06157433149594027, 0.059317843630458, 0.056927475789509074, 0.0553570174716711, 0.050475458950668184, 0.049665682066896366, 0.048873507505192926, 0.048724267224924844, 0.048532049612547645, 0.045653657389332025, 0.045387402202069715]\n",
      "Row 40 - Column Numbers: [88 89 39 38 41 28 37 29 34 86 33 36 74 30 32 35 43 31 56 79 78  5 12  2\n",
      " 90 80 44  4 64 46 10 42 11  0 54  3 87 62 52  8  1 61 13], MI Values: [1.358468758232667, 1.2392621662048944, 0.9807510277995188, 0.935308799245206, 0.926520358369948, 0.7401508914135668, 0.6269405732545383, 0.624305023306202, 0.6043685240764987, 0.5904546129889008, 0.4791060933274034, 0.47454758830574484, 0.42293019416571376, 0.3527990507831582, 0.2643435373277079, 0.24447102665159282, 0.24139738990497683, 0.13699943157822414, 0.10838563263965639, 0.1029822194696477, 0.09964875862896427, 0.09746128685535993, 0.09185969685609141, 0.08826839034197231, 0.08755455049272953, 0.08752252944643946, 0.08181196297427373, 0.07604174073333958, 0.072912801172893, 0.07131829013591684, 0.06301067329213339, 0.06159199509503921, 0.0600744169282601, 0.05966325856990995, 0.05887006365191372, 0.05721261367801134, 0.05676698284365411, 0.05477366448826615, 0.054719591158505665, 0.0521148561565834, 0.05184786967249444, 0.05173422697187924, 0.050382935130099504]\n",
      "Row 41 - Column Numbers: [40 89 88 28 38 34 39 36 37 86 29 33 74 30 32 43 35 31 56 78 79  5 44  2\n",
      " 80 12 90 62 10  0  1  3 42  4 61 64 92 11 70  6  8 52 13], MI Values: [0.9265203583699506, 0.9100181021852727, 0.8687228214668874, 0.6683242642188896, 0.6590139783160538, 0.6479726613644816, 0.5978927259213549, 0.5713794920745912, 0.4944806219210731, 0.47456031717445235, 0.44277394507429957, 0.4346502711337239, 0.33199699186004406, 0.3159693429377697, 0.23153387463475372, 0.21422375662965543, 0.20034425775401843, 0.1298704817987586, 0.11875744932887322, 0.0926509060956926, 0.08676758111423233, 0.086057783978851, 0.08262255635642912, 0.07942866688885086, 0.0785488622631787, 0.0742530711565692, 0.07307672025710232, 0.06941263844280599, 0.06936075480536719, 0.06665335877299139, 0.06410363270210784, 0.06306413363039987, 0.06207958706935557, 0.05954608451087129, 0.0593461118278249, 0.057899646129423665, 0.05389698575662916, 0.053384856694632, 0.05325141402769873, 0.05243412828986749, 0.052078907698307475, 0.05177082062384475, 0.050887404336976694]\n",
      "Row 42 - Column Numbers: [90 31 44 43 35 78 80 30 92 33 21  5  1 74  2 79 12  0 17 83 28 34 85 32\n",
      " 36 11 86 91 37 38 16  4 15 10 39 29 20 19 87 89 13 41 40], MI Values: [0.5736361560630607, 0.24809815156702442, 0.237501584176659, 0.2123646632862819, 0.18522516757733065, 0.17401757617932745, 0.14508216519352857, 0.11531395362702668, 0.11438741669921182, 0.11403454812488256, 0.09722563185672684, 0.09376382987344112, 0.09265639520815316, 0.09219897198964677, 0.09190658625377246, 0.09102336506577036, 0.08912140713055283, 0.08872664637914252, 0.08466458683253641, 0.08290682477634803, 0.08020834452426406, 0.08002420593659121, 0.07969793759561306, 0.07802938607998477, 0.07775809933113642, 0.07587529502253965, 0.0754741707644273, 0.06881214952706838, 0.06871969299735348, 0.06775644455948715, 0.06750837136584042, 0.06712048581871777, 0.06699419564638998, 0.06547249101527441, 0.06470157204125115, 0.06416664878429224, 0.06355486571293678, 0.0632209015494567, 0.0630884431737817, 0.06261691628512, 0.06240830984967349, 0.06207958706935468, 0.0615919950950401]\n",
      "Row 43 - Column Numbers: [35 31 33 74 30 36 86 37 29 78 28 44 38 89 39 34 40 80 41 42  5 79 88 32\n",
      "  2 12  0  4  1  3 11 13 87 85 56 83 21 17 90 10 91 77 64], MI Values: [1.386024446895405, 0.8121927311945987, 0.6277452858407475, 0.6243039700489881, 0.4933942675879788, 0.433564884916799, 0.4240950333084843, 0.4048082990644737, 0.38621997040959855, 0.370397111365631, 0.3130926126664342, 0.30395671539799096, 0.2970750486302043, 0.28802774608809134, 0.2629228824826706, 0.25147509845387095, 0.24139738990497772, 0.2276321837680122, 0.21422375662965365, 0.21236466328628278, 0.20819529046906204, 0.20739130754119195, 0.20626412498042956, 0.1925310675883667, 0.18681968571483676, 0.14156956810137, 0.1358699397958949, 0.1316783860928359, 0.12913107009156466, 0.1038170751558507, 0.09481730555192946, 0.09195467760152898, 0.08755593140089069, 0.08744850763647793, 0.08170555433368687, 0.081560766459293, 0.07911198418961085, 0.07861749607301682, 0.07721049556759585, 0.07182439963604015, 0.07147186167010044, 0.06546454180161465, 0.06421723199729623]\n",
      "Row 44 - Column Numbers: [31 43 78 35  4 42 33 79 30  2 74  5 54  0 64 32 36 80 86 37 29 87 23 88\n",
      "  1 28 39 89 34  3 38 13 11 12 10 85 46 41 40 63 91 62  6], MI Values: [0.38340369680082365, 0.3039567153979892, 0.2940959242977499, 0.27448384162180073, 0.2577169657460203, 0.23750158417665634, 0.15589444258958807, 0.1535208253346898, 0.15101976681000817, 0.14614605566374905, 0.13751208245379942, 0.1330855289284827, 0.13216267787018499, 0.12631372813240205, 0.12575424005177993, 0.12104168683611682, 0.11452348697632786, 0.11196280971917094, 0.10936129874317668, 0.10660787110909098, 0.10392751587923676, 0.10044717697415884, 0.09985139888775052, 0.09784483548609302, 0.09756958090355994, 0.0973992316948431, 0.09268755609898616, 0.09241113709100457, 0.09093985620779232, 0.0903461896754747, 0.08916423701913878, 0.0882487868884656, 0.08789263097170785, 0.0865487450581588, 0.08386645043593699, 0.08318123056251459, 0.08302480760550157, 0.08262255635642735, 0.08181196297427551, 0.08074364625578223, 0.07356394424112711, 0.07306242342033098, 0.07123886187653294]\n",
      "Row 45 - Column Numbers: [65 60 66 76 64 63 69 27 84 53 54  6 75 62 57 70 81 12 46 61 11 50 72 87\n",
      "  1 10 85 52 49 68 13 77  3 48 21 24 32 90 91  8 30 79 15], MI Values: [0.3355390992669385, 0.24105785735212137, 0.16669975622521527, 0.14089157380955708, 0.13477024068243892, 0.11692650889904499, 0.10868038934784607, 0.10364354834175771, 0.10150362847124583, 0.09056761307301286, 0.0798331274015025, 0.07607959090818639, 0.07550304956704501, 0.07129070394238113, 0.06353587781859105, 0.06252081423776445, 0.05993439653997168, 0.05696539251436761, 0.05614165957912931, 0.05305353245500477, 0.05289097853795344, 0.05163697152796942, 0.05126811930396258, 0.049018668863451076, 0.048759179040770206, 0.04826951163990145, 0.04548841097074785, 0.045170627201460256, 0.04515557347533239, 0.04505498244851758, 0.04468423892141704, 0.04437075080106645, 0.04344271363863772, 0.042062378026346714, 0.041189709960936405, 0.04052516260945005, 0.04034464006210747, 0.04008368476259694, 0.039929482136464856, 0.039675854506701747, 0.039107723692991314, 0.038854237195490526, 0.038161379909507964]\n",
      "Row 46 - Column Numbers: [64 51 55 59 48 68 47 58 61 87 75 49 72 56 54 84 27 70 67  6 74 57 17 69\n",
      " 81 14 21 50 77 63 44 52 85  1 19 76 20  4  0 79 62  2 40], MI Values: [1.1094691017199603, 0.36567183873432274, 0.3141727399115952, 0.23992709365254683, 0.2171439106790931, 0.19852690016740127, 0.18923509125775695, 0.1858984961031256, 0.17267857439960022, 0.16549438774061187, 0.15983167864594883, 0.15828858721216044, 0.15559450174685807, 0.1460850846009656, 0.14012136027135202, 0.13751725928655478, 0.13632308186498943, 0.1328114960531792, 0.13279522094755158, 0.13099684473508688, 0.11736212179504424, 0.11368720902898488, 0.11280369881762642, 0.105422623025202, 0.10140282553967683, 0.09266115822732957, 0.08964547025689651, 0.08911598382671393, 0.08487347419103042, 0.08355750196952805, 0.08302480760550068, 0.08232030940720492, 0.08171791357507097, 0.08010342629738698, 0.07977684117637374, 0.07963991449703212, 0.07862828607228867, 0.07856401142112102, 0.07681250087322677, 0.07650530330583649, 0.07403272493206359, 0.07325788085011453, 0.07131829013591773]\n",
      "Row 47 - Column Numbers: [48 55 82 49 51 64 46 61 56 50 14 57 87 54 63 75 67 70 69  6 72 74 68 23\n",
      "  4 52 20 59 38 27 85 84 11 81 33 92 89 60 41  7 36 77 19], MI Values: [0.4249124097885648, 0.4187425231559816, 0.3602265067790995, 0.2776897644328633, 0.24912743330867393, 0.1987447932521178, 0.18923509125775695, 0.15384874665912562, 0.10368137158256019, 0.09785925823341302, 0.09074348902636764, 0.08687796447828866, 0.08569788060934425, 0.08001798979213337, 0.07907233827318905, 0.07403127407645904, 0.07249971148987289, 0.07068379697727956, 0.06874455994522588, 0.06549702884688635, 0.06175094572082518, 0.06009771362514993, 0.05906462224581688, 0.05704895029918333, 0.056865014508378664, 0.05682164950861601, 0.05161482461035316, 0.05139487626535377, 0.050000458629791744, 0.047417480685076896, 0.04726109720318572, 0.04708602460329292, 0.0467491462024574, 0.04656568399330041, 0.045808067196454694, 0.04460527570146677, 0.04416183571061527, 0.043961928173374076, 0.04334931626754024, 0.043171664331128845, 0.04285749863832411, 0.041651660789991496, 0.040805913716284614]\n",
      "Row 48 - Column Numbers: [49 55 47 51 46 50 64 75 68 67 69 87 61 54 58 81 59 70 56 57 63 14 52 84\n",
      "  6 73 72 91 60 66 18 45 85 11 74 21 17  4 76 38 19 32 44], MI Values: [0.553678897514204, 0.5019751647569173, 0.4249124097885639, 0.2875171464071613, 0.2171439106790931, 0.1743136297813912, 0.11110937927605313, 0.10037244122026134, 0.08934545133594263, 0.08190429469032878, 0.0736143304488408, 0.07327006385127088, 0.0721867594925314, 0.07042527416616018, 0.0687315220763578, 0.06681937537003169, 0.06642447830364517, 0.06437836072642522, 0.0635873831512015, 0.060791248768552464, 0.057609186216970976, 0.05528245353972938, 0.05372925078899371, 0.04909830573294105, 0.04808633609087387, 0.045306406824380474, 0.04489736208567496, 0.044709846969715805, 0.04357966587574236, 0.04284931649405177, 0.04283733769362197, 0.0420623780263476, 0.040772805188195704, 0.04013167977317522, 0.03986903738847314, 0.03954931815568408, 0.03897874301162396, 0.03884934604555568, 0.0387817158798871, 0.03828887823525573, 0.03729803186228775, 0.03670448581979002, 0.03666047870806732]\n",
      "Row 49 - Column Numbers: [48 55 47 50 51 75 46 69 54 64 68 81 52 61 57 67 87 63 70 56 60 84 11 14\n",
      "  6 45 13 66 58 12 59 72 10  1 79  4 77 85 32  0 74 40 36], MI Values: [0.5536788975142031, 0.30360053691119226, 0.27768976443285975, 0.2735029225169381, 0.1755926065938338, 0.16380558437787318, 0.15828858721215955, 0.09982396156077034, 0.0899951771509615, 0.08729689308508082, 0.0805251845303161, 0.07578213385519295, 0.0734512632183959, 0.07118839940287724, 0.06818162225492586, 0.06462675171117471, 0.05826597066506878, 0.05474056322253951, 0.05205162711625633, 0.04949584081348313, 0.04890714820172626, 0.047598231033918914, 0.0471786080006531, 0.04697649944513582, 0.04612338247236547, 0.04515557347533328, 0.04394002279515519, 0.0427889260255494, 0.04277730549634029, 0.041579343265056856, 0.03968935771140636, 0.03878327857790431, 0.03721262391298552, 0.03708316769882014, 0.03707875631470614, 0.03437124492900345, 0.03420072144079178, 0.03393860185339559, 0.03373647790879719, 0.03296788902954706, 0.032940030634634354, 0.03271399526283414, 0.03233124919474406]\n",
      "Row 50 - Column Numbers: [75 49 48 69 81 57 54 47 55 68 52 46 64 84 87 51 76 45 67 10 12 14 66 63\n",
      " 60  4 74 85 17 11  6 70 33 79 83  8 36 24 21  0 88 89 40], MI Values: [0.38569583316040035, 0.273502922516939, 0.1743136297813921, 0.13649561521326792, 0.13615369070630745, 0.12386611734750641, 0.11005231669100635, 0.0978592582334139, 0.09343475605257989, 0.09313301709157429, 0.08963552340153047, 0.0891159838267166, 0.08223331555010471, 0.06909627215253966, 0.0664099664637332, 0.05717803565613533, 0.05211485875131405, 0.051636971527967646, 0.049028136696537494, 0.04645372478558407, 0.046362851486650314, 0.04624367400979423, 0.04570965837784602, 0.04395880445259959, 0.04352223482917594, 0.04297224529545307, 0.04249884332512721, 0.04210332584072418, 0.041711486256092556, 0.041695189003549515, 0.04113881744298897, 0.04104741966052927, 0.04091402778420328, 0.04064421390754891, 0.04045686991204356, 0.03995848045904005, 0.03949861996272741, 0.039383429640937884, 0.038877820203155444, 0.03883494246593333, 0.038717645473936635, 0.038634738171873906, 0.03778877017396365]\n",
      "Row 51 - Column Numbers: [55 46 48 47 49 59 64 61 56 58 68 67 50 54 84 14 87  6 44 52 75 69 63 70\n",
      " 21 76 66 60 57 89  4 32 41 40 81 38 11 23 62 74 72  0 88], MI Values: [0.4918905885238507, 0.36567183873432274, 0.2875171464071622, 0.24912743330867393, 0.1755926065938347, 0.15335403151725657, 0.14408460937434686, 0.1323322880421669, 0.09492283806278046, 0.08131092018359531, 0.06392417227606728, 0.06049342127079882, 0.05717803565613444, 0.05383149700687451, 0.050444118959005024, 0.05026820068852356, 0.04809307532768603, 0.04800319914719342, 0.0474286517687057, 0.046076652615822944, 0.04517706634337504, 0.043804660168771825, 0.042590107680609, 0.03955596847245513, 0.0389668719566183, 0.03840491710777805, 0.03826743593598536, 0.03684825881094511, 0.03623578817846784, 0.0361041768011896, 0.03552228501544441, 0.034884214114486056, 0.03474350659770309, 0.034398958953260284, 0.03368774459666746, 0.03349076627149561, 0.03327235828735464, 0.03304187113566659, 0.03265504215054538, 0.03189647338370527, 0.03187888017866847, 0.03186557598989026, 0.031744992944004125]\n",
      "Row 52 - Column Numbers: [69 32 57 54 81 75 68 34 30 64 50 46 49 33 21 17 63 88  6 61 55 35 86 28\n",
      " 47 19 66  7  4 40 48 74 41 10 72 37 84 58 38 83 70 20  1], MI Values: [0.5772799725175162, 0.5366720434860497, 0.5130885687568068, 0.3225256074571332, 0.29251898737336113, 0.193542163657888, 0.12789690664174191, 0.1277324625044658, 0.10641737910058513, 0.0948475569445888, 0.0896355234015278, 0.0823203094072067, 0.07345126321839857, 0.072159687685045, 0.06802973139084934, 0.06703671873903261, 0.06405860187379542, 0.06273572137952055, 0.06139781255903909, 0.06122875212893497, 0.06013022861701689, 0.05843192812514708, 0.057757311630738606, 0.05772311949448383, 0.05682164950861601, 0.05518017282950538, 0.05499973892547416, 0.05481337747376269, 0.054736479053383746, 0.054719591158505665, 0.05372925078899371, 0.05209049250429132, 0.05177082062384297, 0.05139303267069195, 0.05111353303252564, 0.05089562323484653, 0.05067571023863948, 0.050481480883075136, 0.05046119874022281, 0.05022240658314203, 0.05011325603669903, 0.04998115622272348, 0.04960552836869159]\n",
      "Row 53 - Column Numbers: [62 63 64 45 70 85 17 10 91 72 60  4 69 87 12 46 21 11 15 27 20 19 65  1\n",
      "  5  8  0 84 83 14 16 30 18 79 22 28 73 36 66 33 44  2  9], MI Values: [0.40877114705633577, 0.10768325129662326, 0.09142254528217908, 0.09056761307301286, 0.07763014753084896, 0.07291262831419587, 0.06894645621138817, 0.06799093673704526, 0.06654270992309375, 0.06557217989953035, 0.06551159416228547, 0.06101431583981842, 0.05994221903533248, 0.05849475346295652, 0.05643638304159726, 0.05373645940673466, 0.05359496095281546, 0.05257556822858955, 0.05145699897162004, 0.0512160780449582, 0.04985185416914284, 0.047971786345549106, 0.047543267529873035, 0.04687607939115512, 0.046211483174281476, 0.045677188956067205, 0.04379488308218882, 0.04284987062613599, 0.04248356027197353, 0.042449553699675846, 0.04223363657743473, 0.04200308548928522, 0.04179825178695129, 0.04128772798638014, 0.04072600160757123, 0.04068711874009434, 0.03933717348757071, 0.03925453370539245, 0.03848324031768957, 0.03752841617132585, 0.03638983181890776, 0.03585269752426079, 0.03562342742166713]\n",
      "Row 54 - Column Numbers: [81 69 52 75 57 68 64 46 44 32 50 62 63 84 49 47 45 66 76 70 74 55 61 87\n",
      " 48 58 72  6 60 83 30 40 21 35 17 38 36 56 28 39 88 13 51], MI Values: [0.7379530571253516, 0.6991638866458327, 0.3225256074571341, 0.28357752574033057, 0.2796508865934202, 0.2576301492482225, 0.15163383746901538, 0.14012136027135202, 0.1321626778701832, 0.11793416791373446, 0.11005231669100635, 0.09996017287947367, 0.09375651906359739, 0.09285394516933021, 0.0899951771509615, 0.08001798979213337, 0.0798331274015025, 0.07892182637938827, 0.07324275519206846, 0.07247468124904266, 0.07245070956178878, 0.07176330422608057, 0.07112370577561311, 0.07067226287875972, 0.07042527416615751, 0.06899903291146714, 0.06863149347900066, 0.06777316229745178, 0.06704206660250378, 0.06494064826102708, 0.060874758017741115, 0.05887006365191105, 0.05810380963000572, 0.05748468340966095, 0.05669604970686226, 0.05657172017433165, 0.05650255737683452, 0.0557378324255442, 0.05541299819598766, 0.055357017471672876, 0.05436024408042606, 0.05430024107788167, 0.05383149700687362]\n",
      "Row 55 - Column Numbers: [48 51 47 46 49 64 59 61 50 58 68 75 67 69 56 54 81 84 63 52 57 23 87 14\n",
      " 70  0 38 73 41  1 44 37  4  6 88 72 11 86 36 89 76 62 74], MI Values: [0.5019751647569191, 0.4918905885238507, 0.4187425231559816, 0.3141727399115961, 0.30360053691119226, 0.1455355267788132, 0.10391523768986577, 0.10320434092076614, 0.09343475605257989, 0.09039691815655626, 0.08433296148313651, 0.07894014514832115, 0.07810178261121159, 0.07626677924718717, 0.07457832871124648, 0.07176330422608146, 0.0666084572296537, 0.0649658298184459, 0.06183261687680819, 0.06013022861701511, 0.05926409456159032, 0.05849481745654206, 0.05810381930205111, 0.05661782886079081, 0.05210958027079382, 0.05151582272524369, 0.05144646558632182, 0.0513717845320274, 0.04985324468381247, 0.04872468386788853, 0.04840563532307751, 0.047905222457149677, 0.047753548931313006, 0.04774985453638614, 0.046832066350649626, 0.046337404344297006, 0.04532790922027541, 0.04508240476302117, 0.04498650870497656, 0.04457765391180146, 0.044450219960144643, 0.04410009039404095, 0.04400663644262881]\n",
      "Row 56 - Column Numbers: [61 37 64 86 29 36 46 38 28 67 74 89 41 59 39 40 33 87 47 51 21 34 88 20\n",
      " 43 35  1 17 63 55  2 68 15  0  4 85 91 24 30 77 58 48 16], MI Values: [0.43147747233694655, 0.3594022660421903, 0.22066317128273738, 0.19813479850705384, 0.1713073755137069, 0.1508160371586369, 0.14608508460096736, 0.14324753303636495, 0.14153000235829616, 0.1390223315396053, 0.12763532576626613, 0.12759658270105412, 0.11875744932887322, 0.1140267649058524, 0.11061737849190578, 0.10838563263965728, 0.10568767232682852, 0.10439486730787184, 0.10368137158256019, 0.09492283806277957, 0.09187841023316512, 0.08918579292805973, 0.08812813925290719, 0.08286165353433983, 0.08170555433368776, 0.08018360354588872, 0.07992095121214593, 0.07971577342061753, 0.07711766737948622, 0.07457832871124559, 0.07436029178819847, 0.07341505483174426, 0.07262961413738722, 0.07242362723832141, 0.0720538145634535, 0.07002602366231869, 0.06996541088145225, 0.06753872107738657, 0.06707550157230013, 0.0658465345860213, 0.06480713020071249, 0.06358738315120327, 0.06331255297437988]\n",
      "Row 57 - Column Numbers: [52 69 75 54 81 63 64 68 50 46 23 72 87 17 74 61 47  6 70 21  7 84 62 49\n",
      " 73 82 92 58 45  0 19 66 56 48 36 37 55  5 44 83 60 79 77], MI Values: [0.5130885687568085, 0.4492286562322283, 0.3175403262160419, 0.2796508865934202, 0.2386747781742029, 0.19893022670047156, 0.1706591351738478, 0.12717047965108375, 0.12386611734750552, 0.113687209028984, 0.11007546217848985, 0.1056703039813307, 0.09943857195888661, 0.09928683256670379, 0.09565681017050132, 0.09358492153412179, 0.08687796447829044, 0.08592201720969239, 0.08195684550894988, 0.08110178494543341, 0.07616119177035774, 0.07392888704485934, 0.07251648801624277, 0.06818162225492586, 0.0667097043144338, 0.06659031769662516, 0.06608857489515785, 0.06605291746158404, 0.06353587781859193, 0.061740263953568686, 0.061490900764048284, 0.06146140592633831, 0.06124498359253927, 0.060791248768552464, 0.06000224745403049, 0.0595838130800912, 0.059264094561592096, 0.058399152771426266, 0.05763128744059465, 0.05711690835432748, 0.056631880706102145, 0.05618380082027041, 0.05594599871005901]\n",
      "Row 58 - Column Numbers: [46 59 67 61 64 55 75 51 81 54 48 68 57 56 44 69  0 52 88 79  5 84 73  4\n",
      " 74 40 17 87 49 70 72  7 89 47 62 38  2 43 37 50 60 77 86], MI Values: [0.1858984961031256, 0.17684958964553754, 0.1376164223851939, 0.10259159901626358, 0.09323139589981633, 0.09039691815655537, 0.08672016085400625, 0.0813109201835962, 0.07170077496787108, 0.06899903291146536, 0.06873152207635869, 0.06709058591021666, 0.06605291746158226, 0.0648071302007116, 0.06182062594159721, 0.053739795644960786, 0.05071325731351273, 0.05048148088307869, 0.04789057473566327, 0.047499732845677656, 0.04605361797762875, 0.045749765509683904, 0.04511521302719235, 0.0451146228488728, 0.04429686953990242, 0.0436866294276701, 0.042952045110664194, 0.04293717981312373, 0.04277730549634118, 0.04249097503546562, 0.041569158118069716, 0.0414072565023762, 0.04087411787997919, 0.04008012588680554, 0.03946179272307493, 0.039370558103208886, 0.03780798205952163, 0.03731442430222387, 0.03713892176412692, 0.036719401321429146, 0.03638037155973528, 0.03628517346620885, 0.03595011355909605]\n",
      "Row 59 - Column Numbers: [80 46 61 58 51 56 55 64 67 48 75 47 44 74 68 81 73 41 33 90 43 54 40 49\n",
      " 62 84 88 57 89 38 45 21 79 70 37 50 31  3 87 52 86  5 69], MI Values: [0.2465372262762342, 0.23992709365254772, 0.18600181466110133, 0.1768495896455411, 0.1533540315172539, 0.11402676490585151, 0.10391523768986577, 0.10143685103057543, 0.07292707939904464, 0.0664244783036434, 0.05458094170480976, 0.051394876265351996, 0.048036989305325406, 0.046929431867398286, 0.0468761986306756, 0.04281709288360336, 0.041442701275810734, 0.04123745905248555, 0.04109308677692969, 0.04080241822363018, 0.0405708194427179, 0.04002737117363697, 0.039970526744237844, 0.039689357711408135, 0.03937800895674659, 0.03858909846737113, 0.038104381220402495, 0.03733929606864361, 0.037336166429184026, 0.03621910618345936, 0.036194932260467994, 0.03564645785808285, 0.03530947035182841, 0.034605332803858246, 0.034270780090086106, 0.03385625356854849, 0.033688224144492906, 0.03365099687676132, 0.03359866945243972, 0.03358824636426494, 0.033156708793527834, 0.032867078986785536, 0.03252523413328934]\n",
      "Row 60 - Column Numbers: [45 66 64 75 69 76 46 54 53 84 81 57 65 63 56 70 49 61 52  6 47 62 48 50\n",
      " 24 55 10 87  1  4 68 72 51 58  8 17 85 21 11 44  0  9  2], MI Values: [0.24105785735212315, 0.14313213465555208, 0.13185070300011947, 0.08789136339985504, 0.08538631330874047, 0.07359513171289755, 0.06886160619467585, 0.067042066602502, 0.06551159416228902, 0.062130659320295045, 0.06016542150362536, 0.056631880706101256, 0.05516399778635517, 0.05208181872897821, 0.04990175130811547, 0.04924267114111114, 0.048907148201728035, 0.04565762279498298, 0.04550928202171889, 0.04432955091321311, 0.0439619281733723, 0.043609459383989524, 0.04357966587574058, 0.04352223482917683, 0.042912718955503415, 0.04289723654803357, 0.04246041760917052, 0.041422133425950136, 0.039365018633776394, 0.03811521797273176, 0.03776259020466188, 0.03735714461537043, 0.03684825881094511, 0.0363803715597415, 0.03495408974131564, 0.034779085744490956, 0.034559288190181725, 0.03360900022740143, 0.033444948836911514, 0.032907121469348155, 0.032668405905845965, 0.0324609794611499, 0.03181022364805397]\n",
      "Row 61 - Column Numbers: [56 11 64 59 46 47 51 87 12 85 55 58 20 10 21 57  1 91 63 23 17 69  2 68\n",
      "  0  4  6 24 79 77 83 48 49 54 74 67 33 15  7 84 32 14 52], MI Values: [0.43147747233694567, 0.42117961947471017, 0.30274924109928225, 0.186001814661104, 0.17267857439960288, 0.1538487466591274, 0.1323322880421669, 0.11609849133691696, 0.11175003676089812, 0.10334008173381015, 0.10320434092076347, 0.10259159901626269, 0.10190813419336209, 0.10067720955483761, 0.09520585153423244, 0.09358492153412534, 0.0919232880302312, 0.0871403303663465, 0.08651352031480286, 0.08578580449603024, 0.0845797268571502, 0.08175995345877496, 0.0807578644808169, 0.0801785495224161, 0.07987921333337233, 0.0793639777794386, 0.07748176490715064, 0.0766084916060148, 0.07561052109916311, 0.07553429240407095, 0.07310938021788527, 0.07218675949252873, 0.07118839940287724, 0.07112370577561222, 0.07004761148596383, 0.06954426713919748, 0.06766819910745347, 0.06669711932901201, 0.06659717282749611, 0.06553165111754122, 0.06347776301673225, 0.061701359771839215, 0.06122875212893497]\n",
      "Row 62 - Column Numbers: [53 63 64 54 72 32  6 70 46 21 44 57 28 45 17 41 69 85  0 87 34 30 84 33\n",
      " 74 19 40 88 12  2 37 20  4 75 11 10  1 31 89 43 36 61 23], MI Values: [0.40877114705633755, 0.1279415691665342, 0.11842971465453456, 0.09996017287947367, 0.08923240114087871, 0.08212300251017979, 0.08134777223811351, 0.07551883001699622, 0.07403272493206625, 0.07348744391152451, 0.0730624234203292, 0.07251648801624189, 0.07174551471409796, 0.07129070394237846, 0.07054503826931224, 0.0694126384428051, 0.06494490899076766, 0.06122602061900739, 0.060570066674142886, 0.06022931405757159, 0.05971560831514555, 0.058950094823821075, 0.05873104823880926, 0.05850112049998302, 0.05785656052338606, 0.057623187032919354, 0.05477366448826526, 0.05440889071046939, 0.05387677226496379, 0.05315849709315046, 0.052254464230390596, 0.05209308293447634, 0.051951533735175026, 0.05132260781067011, 0.05125901030097513, 0.05100764313742001, 0.050656346920683326, 0.05058193701037439, 0.05028273620915957, 0.05013562158198859, 0.0501292056996574, 0.05003847734903477, 0.04962794973529405]\n",
      "Row 63 - Column Numbers: [57 64 72 87 70 62  6 45 65 53 14 54  4 61 92 46 44 84  7 47 24 56 91 74\n",
      " 66  0 85 23 18 76 69 52 82 73 68 55 11 10  1 81 48 43 17], MI Values: [0.19893022670047422, 0.16474578635889525, 0.14441268837025323, 0.14223108828764808, 0.1360734064984701, 0.12794156916653598, 0.11759316702333766, 0.1169265088990441, 0.10914449076512156, 0.10768325129662504, 0.09840075284083394, 0.09375651906359561, 0.09074112883170304, 0.08651352031480108, 0.08472994154227464, 0.08355750196953071, 0.08074364625578578, 0.07977254852835358, 0.07907681278759515, 0.0790723382731855, 0.07871775795832114, 0.07711766737948711, 0.07678764806995986, 0.0765734948289225, 0.07406004109092024, 0.07375851842512127, 0.07313981190535657, 0.07257144170705043, 0.06986318552324633, 0.06663758575631373, 0.0653233908008124, 0.06405860187379808, 0.06403591879491888, 0.06298018698645702, 0.0628392353335725, 0.0618326168768073, 0.06124640975608653, 0.05988190445075414, 0.0589489276098476, 0.057634411390770524, 0.05760918621697009, 0.05744789795037342, 0.056767715502631155]\n",
      "Row 64 - Column Numbers: [46  6 61 56 87 47 27 68 57 63 54 55 51 75 74 84 69 45 60 10  4 14 44 23\n",
      " 62 72 20 66 48 76 65 85 12 11 81 70  1  8 59 17 52  7 77], MI Values: [1.1094691017199603, 0.4786059164536729, 0.30274924109928225, 0.22066317128273738, 0.22048913023609096, 0.1987447932521187, 0.18682361749818366, 0.17760682722466647, 0.17065913517384423, 0.1647457863588926, 0.1516338374690145, 0.1455355267788141, 0.14408460937434509, 0.14236178948324518, 0.14209884783445936, 0.13984183102276582, 0.13741479855139893, 0.13477024068243804, 0.13185070300012303, 0.1299306324648466, 0.12979914510191115, 0.12701720438149788, 0.12575424005177815, 0.12382874483289896, 0.11842971465453278, 0.11641659888849265, 0.11253209164348021, 0.11225512605831867, 0.11110937927605224, 0.10732056478952767, 0.10654049307470448, 0.10591493223352533, 0.10535355610052566, 0.10500346113093073, 0.1037050834642379, 0.10306102384276805, 0.10272291690296331, 0.10254326229903832, 0.10143685103057631, 0.1003732877747634, 0.09484755694459235, 0.09462334579778542, 0.09447565520740842]\n",
      "Row 65 - Column Numbers: [27 45 63 64 66 76 60  6 84 53 62 13 46 31 74 23 57 79 15  1 61 28 90 87\n",
      " 25 18 47 35  4 10 19 22  2 16 54 17 38  5 70 43 11 71 55], MI Values: [0.6065603894953897, 0.3355390992669385, 0.10914449076511978, 0.10654049307470537, 0.07400054698096614, 0.06574940460414158, 0.05516399778635073, 0.05313625162063573, 0.05200772742261606, 0.04754326752987392, 0.04210859287540458, 0.04141383027204526, 0.04065382889106317, 0.04016739913483747, 0.03927197805547333, 0.03543013877976531, 0.03532486757824671, 0.03390511473012481, 0.03356935029377528, 0.0334370867070275, 0.03268513124965988, 0.032538341997700115, 0.03243135734308211, 0.03240600070639843, 0.03173822340394317, 0.03125147202710554, 0.030917863808890722, 0.030897225961695085, 0.03052268994560059, 0.030516181395221054, 0.030348441731518072, 0.030328529199157295, 0.030171195067245193, 0.030140476904725766, 0.029872492359135805, 0.029334903001505097, 0.029234888513575363, 0.02891810299955555, 0.02890138730320313, 0.02881055664071308, 0.028497828396734093, 0.02842485280534124, 0.028331991996227934]\n",
      "Row 66 - Column Numbers: [76 84 45 60 64 69 54 63 65 44 75 46 81 57 87 52 10  6 68 32  3 50 70 62\n",
      "  8 48 11 49 55 88 12 53 27 51 21 41 30 34 89 56 61 85 35], MI Values: [0.3276867048743224, 0.19621110110385498, 0.16669975622521527, 0.14313213465555208, 0.11225512605832044, 0.08774329941118442, 0.07892182637938827, 0.07406004109092112, 0.07400054698096792, 0.0657832364108204, 0.06574781745996905, 0.06557772498449133, 0.06464382902376808, 0.061461405926340085, 0.057380307752954884, 0.05499973892547505, 0.052649459598339554, 0.05121302295319019, 0.049935593149331936, 0.046364996147670645, 0.04601614539536314, 0.04570965837784691, 0.045050505206226, 0.044186414063735135, 0.042936712655239795, 0.042849316494054435, 0.04280397591400931, 0.0427889260255494, 0.042241733113475455, 0.039561716831260973, 0.0386714507746424, 0.038483240317686906, 0.03842749677431723, 0.03826743593598536, 0.0377725314890629, 0.03736335808473523, 0.03715626177182507, 0.03696164121794787, 0.03657013877780546, 0.03621018306623114, 0.036192436537979766, 0.03603333099672312, 0.03582784273636985]\n",
      "Row 67 - Column Numbers: [56 58 46 48 55 59 47 61 64 49 51 68 70 75 50 54 63 69 72 81 73 57 87 41\n",
      " 79  7 52 92 71  3 34 33 36 45 18 22 74  2 21 39 77 40 89], MI Values: [0.1390223315396062, 0.13761642238519123, 0.1327952209475507, 0.0819042946903279, 0.07810178261121248, 0.07292707939904286, 0.07249971148987466, 0.06954426713920014, 0.067158129948651, 0.06462675171117294, 0.06049342127079882, 0.05573066244705327, 0.05131323241564267, 0.050048166172831365, 0.04902813669653483, 0.04789187006885953, 0.04359634849634464, 0.04356102015565355, 0.042934138904747066, 0.041962299374367795, 0.03947764246554897, 0.03874132263576069, 0.0375586609402454, 0.03748203714709142, 0.03612567970739633, 0.03552096699697227, 0.03431893068828895, 0.03385542532989394, 0.03284593157964766, 0.03260253611544073, 0.03230214768395179, 0.032080902109909104, 0.032068284532125624, 0.031703696876647314, 0.03167709034729871, 0.03152308217100508, 0.0313239473107263, 0.030862122044114315, 0.030431654414645237, 0.030192101527670268, 0.03015615956557216, 0.03014741947648325, 0.030105513462540756]\n",
      "Row 68 - Column Numbers: [81 54 69 46 64 75 52 57 50 48 55 87 21 49 61 16 84 56 17 83 44 58 20 19\n",
      " 28 74 51 70  1 63 72  4  0 47 76 15 79  2 67 85 73 88 40], MI Values: [0.273919599429445, 0.25763014924822425, 0.21452460580928268, 0.19852690016740215, 0.17760682722466647, 0.13909061707178783, 0.1278969066417437, 0.12717047965108375, 0.0931330170915734, 0.0893454513359444, 0.0843329614831374, 0.08279666247431816, 0.08274897552594052, 0.08052518453031432, 0.08017854952241699, 0.08013941132973379, 0.07495229498264155, 0.07341505483174426, 0.06961403770779029, 0.06805662497684573, 0.06773250218080751, 0.06709058591021577, 0.06678931920015962, 0.06634530228217894, 0.0648958659595209, 0.06481434993591328, 0.06392417227606728, 0.06381372155874665, 0.06377396532315771, 0.06283923533357072, 0.061596290425321776, 0.06062743353392808, 0.05987241738861382, 0.05906462224581688, 0.05900909169327839, 0.05863023036643522, 0.056674954088558493, 0.05663641300834321, 0.05573066244705327, 0.05285999918476847, 0.05115265774466682, 0.05105981583143748, 0.050255155238578375]\n",
      "Row 69 - Column Numbers: [54 52 81 57 75 68 64 50 45 46 49 84 66 60 76 61 55 48 70 47 72 63 62 21\n",
      "  6 53 74 87 12 17 56 58 88 83 33 10 13 44 41 43 35 31 15], MI Values: [0.6991638866458345, 0.5772799725175153, 0.5173059047442399, 0.4492286562322283, 0.3365455824566368, 0.2145246058092809, 0.13741479855139715, 0.1364956152132697, 0.10868038934784607, 0.105422623025202, 0.09982396156077122, 0.09384699164640953, 0.08774329941118264, 0.08538631330874047, 0.08467890285416413, 0.0817599534587723, 0.07626677924718717, 0.07361433044884258, 0.06977140079906086, 0.06874455994522854, 0.06641906563649336, 0.06532339080081417, 0.06494490899076943, 0.06484185380561414, 0.06183066532204684, 0.05994221903533159, 0.05666686695618495, 0.05545803544337424, 0.05531483615886046, 0.05499612699967926, 0.05440393974544655, 0.053739795644960786, 0.0536959399704946, 0.053145985839573306, 0.05089832960081431, 0.050097225136772394, 0.04984063431350716, 0.04878869749796966, 0.04863991014106883, 0.04807444378004, 0.04771493976945074, 0.04694746829499152, 0.04658331443336472]\n",
      "Row 70 - Column Numbers: [72 71 63 46 64 57 53 62 54 47 69 87 48 68 45 36 82 56 17 61 21  4 19 13\n",
      " 74 41 55 49 67 52 60 11 15 75 28 84 32 85 66 18 44 35 31], MI Values: [0.5037025298153655, 0.1468401051584065, 0.13607340649846478, 0.13281149605317744, 0.10306102384276628, 0.08195684550894988, 0.07763014753084718, 0.07551883001699711, 0.07247468124904355, 0.07068379697728044, 0.06977140079905908, 0.0660251334839197, 0.06437836072642344, 0.06381372155874754, 0.06252081423776268, 0.05999309743629233, 0.05982269100457582, 0.057890813506117134, 0.056376474765788664, 0.055299683066056815, 0.05505815458498908, 0.05456383162511802, 0.05447668338025302, 0.05401666850898579, 0.05386607986701808, 0.053251414027695176, 0.05210958027079293, 0.05205162711625011, 0.05131323241564267, 0.050113256036700804, 0.049242671141108474, 0.049105160517478375, 0.04807318298614227, 0.047127393802390394, 0.04650128507184803, 0.046494250587683084, 0.04569125616274494, 0.04506890618240256, 0.04505050520622156, 0.04471178449303981, 0.04423971269111515, 0.044000657807371724, 0.043861067541813625]\n",
      "Row 71 - Column Numbers: [70 72 57 46 63 52 64 69 62 40 88 45 19 54 89 73 53 41 18 20 36 74 28 48\n",
      " 38 68 67 55 16 21 15 32 35 85 39 49  1 33 92 86 66 29 34], MI Values: [0.14684010515840784, 0.10642931109237441, 0.052528980782009516, 0.05241768981868278, 0.050201259190097325, 0.04467108973151124, 0.04327708127836605, 0.040533665195546575, 0.03859241843659156, 0.038561516805054374, 0.03818678028153677, 0.03813838976859696, 0.03800425250052175, 0.03790080375870186, 0.03715871144142646, 0.03588263349891774, 0.03548282442189432, 0.035353727634690024, 0.0352925510429718, 0.03441557456072353, 0.03423058910657151, 0.03397324312542693, 0.03394914598687837, 0.033806395276054335, 0.033705883841912865, 0.03342612831626557, 0.03284593157964988, 0.032719080030302106, 0.032663553226116804, 0.031987069591433936, 0.03175109221050576, 0.03144013441961224, 0.031402843954976944, 0.030959505480408822, 0.03087881443926932, 0.030695717699147362, 0.030567471549774794, 0.030379323571904315, 0.03005020752412957, 0.03002178949951162, 0.029856386276476243, 0.029726472501970136, 0.029722945487696606]\n",
      "Row 72 - Column Numbers: [70 46 63 64 71 57 62 54 87 69 53 74 36 17 47 68 19 56  6  4 21 37 18 12\n",
      " 13 79 45 52 61 14 15 85 84 11  8 83 38 55 31 10 41 48 40], MI Values: [0.5037025298153646, 0.1555945017468563, 0.14441268837025323, 0.11641659888849354, 0.10642931109237264, 0.10567030398132982, 0.08923240114088049, 0.06863149347899888, 0.06757571466233703, 0.06641906563649602, 0.06557217989953035, 0.06265296415556598, 0.06265064870036952, 0.06242048665925726, 0.06175094572082429, 0.06159629042532533, 0.06050821759756175, 0.060467185737427265, 0.059193884606223435, 0.05724329216191926, 0.054151749566812235, 0.053098326138301566, 0.05297227066477639, 0.05260851139547462, 0.052594084364699256, 0.05231208801533249, 0.05126811930396524, 0.051113533032526526, 0.050320783879531206, 0.050294567082459274, 0.049828300730804465, 0.04936721830032109, 0.04876829570450525, 0.048098306904397425, 0.04777061216579881, 0.04705935242895354, 0.04699176949630246, 0.04633740434429967, 0.04575550443701104, 0.04517050064331052, 0.04508851409560233, 0.0448973620856723, 0.04481721096307467]\n",
      "Row 73 - Column Numbers: [18 19 16 22 15 21 83 17 46 57 20 64 92  0 85 63 87  1 90 91 75 32 61 78\n",
      " 55 68 81 80  4 77 42 56  5 62  7  2 44 48 79 58 30 52 82], MI Values: [0.7893958078076446, 0.44496585631871355, 0.23365823269839314, 0.1966841939947015, 0.17737229996765524, 0.14619238110757227, 0.13046110819555246, 0.11461081534221584, 0.0669864466316632, 0.0667097043144338, 0.06621492860686029, 0.06604549816659055, 0.06534747712790967, 0.0649060502864538, 0.06342521947019009, 0.06298018698645524, 0.0611623897499598, 0.05958199657264185, 0.05918069294481576, 0.05854277511136363, 0.053336867008316524, 0.052349661683105175, 0.052132518258837024, 0.051741026293754544, 0.05137178453202651, 0.05115265774467037, 0.050731494761138585, 0.05035070457441204, 0.04944023723216873, 0.04929230770196469, 0.04884463429679364, 0.04879117015815915, 0.04871526329810205, 0.047892505862648704, 0.04712977016487141, 0.046741524692998304, 0.045420776171674504, 0.04530640682438136, 0.04518328366119828, 0.0451152130271959, 0.04476241509419232, 0.04425296906975085, 0.04269677500715918]\n",
      "Row 74 - Column Numbers: [33 30 35 43 36 86 37 29 89 38 28 40 39 31 34 88 41 32 78  5 79  2 12 64\n",
      " 44 80  4 56 46 87  0  1  3 57 42 11 13 85  8 63 10 54 90], MI Values: [1.1137204124807516, 0.6484729630309527, 0.6417520640136294, 0.624303970048989, 0.609009289588708, 0.5888147458720638, 0.5514988683591922, 0.5004203013385569, 0.4790798574401238, 0.463836147610051, 0.4637692211865332, 0.42293019416571376, 0.4188068561985556, 0.3685955153502105, 0.3551015296305451, 0.3455870286773939, 0.33199699186004406, 0.2547497346317229, 0.20415303191621437, 0.1681098351910748, 0.1650927025452713, 0.15700514453794945, 0.14286051344793105, 0.14209884783445847, 0.13751208245379942, 0.13689592489073021, 0.12952891724869087, 0.12763532576626435, 0.11736212179504246, 0.1087269697985187, 0.10670490036675684, 0.10197487194244381, 0.09931213507677228, 0.09565681017049954, 0.09219897198964855, 0.08465931443258867, 0.08012866253161377, 0.07970796683611514, 0.07707447313009208, 0.07657349482892162, 0.07645994681407764, 0.0724507095617879, 0.07133347033568604]\n",
      "Row 75 - Column Numbers: [50 69 57 81 54 52 49 46 64 68 84 48 60 58 87 55 45 47 66 74 77 79 44  0\n",
      " 19 76 37 63 86 59  2 73 13  4 36 61 17  1 62 24 88 67 10], MI Values: [0.38569583316039946, 0.3365455824566368, 0.31754032621604367, 0.299464626985233, 0.2835775257403297, 0.1935421636578889, 0.16380558437787318, 0.1598316786459506, 0.1423617894832443, 0.1390906170717887, 0.10426683306186213, 0.1003724412202649, 0.0878913633998506, 0.08672016085400713, 0.08358299144459647, 0.07894014514831671, 0.07550304956704768, 0.07403127407645904, 0.06574781745996994, 0.0641015831058036, 0.06280999904077333, 0.06198112586282889, 0.05994952546050758, 0.058932901704030094, 0.05883151968498446, 0.05840596267275, 0.05770927457101749, 0.05585066540116479, 0.05527900384734252, 0.05458094170481065, 0.054081184944083205, 0.05333686700831475, 0.053243057542840866, 0.05294436526442681, 0.05286496782731209, 0.052800446177284854, 0.052136357413616885, 0.051665821434266235, 0.05132260781066744, 0.05083179402329918, 0.05043949403648362, 0.05004816617282959, 0.049905532084435045]\n",
      "Row 76 - Column Numbers: [66 84 45 64 69 46 60 54 63 65 68 81 75 87 50 61 56 55 27 52  3 48 51 57\n",
      " 44 88 62  6 85 40  1 74 41  0 58 49 15 39  4 89 14 53 47], MI Values: [0.3276867048743197, 0.24938687538324178, 0.14089157380955797, 0.10732056478952945, 0.08467890285416502, 0.07963991449703123, 0.07359513171289844, 0.07324275519206669, 0.06663758575631462, 0.06574940460414425, 0.05900909169328106, 0.05870728910141754, 0.05840596267275089, 0.05227845227554617, 0.052114858751312276, 0.0475376914479817, 0.045768277880542385, 0.044450219960143755, 0.04331808077932564, 0.0397320107747241, 0.039450383303536896, 0.038781715879885326, 0.03840491710777716, 0.03729854865264848, 0.03695081877679929, 0.03575037533056857, 0.03553028432121241, 0.035006496062266024, 0.03479280267248619, 0.03355427583083603, 0.03330372063304132, 0.03324378852283871, 0.03314054463399074, 0.0329832469916953, 0.03260929208367003, 0.03200075462167984, 0.03142627895452854, 0.031226808565940622, 0.030530087758511293, 0.030180324229658773, 0.03013702346379077, 0.029953159421307163, 0.029614370974226034]\n",
      "Row 77 - Column Numbers: [20  1  0 17 85 21 83 87 91  2 15 79  4  5  3 11 12 19 22 16 64 78 90 10\n",
      " 24 46 61 18 31 14 33 80 74 13 56 43 75 30  8 86 37 36 29], MI Values: [0.6456828762580971, 0.3911191711403701, 0.37263024544485734, 0.2990938973597581, 0.2972324555956005, 0.2833159462922179, 0.2721591618925645, 0.2624972226636384, 0.2612330298469274, 0.23544670375940946, 0.2109149525053855, 0.19755911895090694, 0.1718626691037235, 0.17144637756480563, 0.16858842857306655, 0.15529190588759256, 0.15476368455904055, 0.14839967682173594, 0.10378871318925587, 0.09654894383117352, 0.09447565520740842, 0.0909806859788258, 0.08763090580224553, 0.0864463575035197, 0.08554737930801348, 0.0848734741910322, 0.07553429240407361, 0.07382980271187378, 0.07208828414576551, 0.07067488479129658, 0.06870563600713986, 0.06782462499272324, 0.06750317812053108, 0.06644401403919531, 0.06584653458601863, 0.06546454180161732, 0.06280999904077245, 0.06275013897899573, 0.06220005651368066, 0.061947295051053786, 0.061387189732781344, 0.061213187064223185, 0.06065012243418888]\n",
      "Row 78 - Column Numbers: [31 79  2  5 43 35  4 44 30  3  0  1 33 74 42 36 85 86 34 12 11 37 87 32\n",
      " 29 91 20 80 28 13 89 17 10 38 39 21 40 83 41 88 77 90 15], MI Values: [0.7638100129208834, 0.5291499102562947, 0.40895639584369636, 0.40195030351981753, 0.3703971113656319, 0.36035661286731635, 0.3522117773810214, 0.2940959242977499, 0.24551062402752422, 0.22968546503017695, 0.2279315500630652, 0.22306577157731855, 0.21439117181920508, 0.20415303191621348, 0.17401757617932834, 0.14656523125808896, 0.13481869307475858, 0.1340783425963794, 0.13184448924787695, 0.1251376255189447, 0.12508164598781324, 0.12299363364406979, 0.12204190372473, 0.11553471513471436, 0.11428335137809142, 0.11180728144593566, 0.11158401518017325, 0.11158379763401793, 0.10874080446091128, 0.10855159929809233, 0.10703752567566749, 0.10477670785503168, 0.10461732375843713, 0.1039286718447654, 0.1030354193690286, 0.10268663613005558, 0.09964875862896339, 0.09402627710304756, 0.09265090609569437, 0.09216904048066343, 0.09098068597882403, 0.07220152388185497, 0.06674255678354513]\n",
      "Row 79 - Column Numbers: [ 4  2  5 78  3  0 31  1 43 35 77 85 30 20 87 33 74 12 17 44 91 21 83 34\n",
      " 11 36 86 37 29 40 10 39 32 38 89 42 28 64 41 13 80 88 15], MI Values: [0.893437297964442, 0.8897537675853213, 0.8539429780686696, 0.5291499102562955, 0.5216221690633249, 0.45757637448269506, 0.3469763013969196, 0.3374236720569561, 0.2073913075411946, 0.20596754398312012, 0.19755911895090428, 0.1962347079230513, 0.1906085060616718, 0.1804159793193154, 0.17746826908973823, 0.1675397929716107, 0.1650927025452722, 0.15745268691877623, 0.15630527248319837, 0.15352082533469336, 0.14530314536725086, 0.13959981733842763, 0.13601963987999888, 0.1218215309761943, 0.12041417972820856, 0.11619314258747693, 0.11181972450478295, 0.111670136833391, 0.10420208049496171, 0.10298221946964947, 0.10144296896099547, 0.10121071598448594, 0.09567236193821316, 0.09301615106454975, 0.09254555638649187, 0.09102336506577213, 0.09026690572979756, 0.08736827809746561, 0.08676758111423233, 0.08620980383680976, 0.08466381307331439, 0.0785679892861264, 0.07750166086596]\n",
      "Row 80 - Column Numbers: [59 43 35 90 31 33 42 74 30 36 44 78 92 86 89 37 29 34 28 40 38 79  5 41\n",
      " 32 12 82 88 39  2 77 11 21  0  4 15 13  3  1 83 10 73 20], MI Values: [0.24653722627623686, 0.2276321837680122, 0.20322450593987362, 0.19218618079188143, 0.18479080672562098, 0.15136974710492979, 0.1450821651935268, 0.13689592489073021, 0.1357762064984085, 0.11571876599131237, 0.11196280971917005, 0.11158379763401705, 0.11010018137622524, 0.10493827763350172, 0.1044402309887209, 0.09822950179437395, 0.09785175941231472, 0.09689650292456431, 0.09424947908653714, 0.08752252944644034, 0.08653427377215017, 0.08466381307331616, 0.08230865790885655, 0.07854886226317959, 0.07650826602535155, 0.07494487051346166, 0.07370725535800648, 0.07253038686003155, 0.07038469791400903, 0.06970774963285731, 0.06782462499272057, 0.06530714718931119, 0.0638719053811343, 0.06157503922592156, 0.06148036084266284, 0.06004207076621082, 0.058901850104819964, 0.05522028921117084, 0.05429317094593511, 0.05309818158656032, 0.05282851504111541, 0.050350704574411154, 0.04844480590909317]\n",
      "Row 81 - Column Numbers: [54 69 75 52 68 57 50 64 46 49 58 84 74 48 55 66 87 60 45 76 77 44 36 79\n",
      " 63 86  0 61 83 37 17 33 73 38 43 39 31  4 89 47  1  2 88], MI Values: [0.7379530571253508, 0.5173059047442399, 0.29946462698523035, 0.2925189873733629, 0.27391959942944677, 0.2386747781742029, 0.136153690706311, 0.10370508346423613, 0.10140282553967683, 0.07578213385519295, 0.07170077496787108, 0.07127138714810943, 0.06860495539301592, 0.06681937537003346, 0.06660845722965725, 0.06464382902377075, 0.0635620255990954, 0.06016542150362536, 0.05993439653997257, 0.05870728910141665, 0.05853791406893283, 0.05807485470139717, 0.057863475935761244, 0.057830546664649596, 0.05763441139077141, 0.05615165444273362, 0.05562579056591499, 0.05549932064581764, 0.05488123319225746, 0.05430022036441429, 0.05358151425610025, 0.052620584599597287, 0.05073149476113681, 0.0504273983650787, 0.050018232148672404, 0.048724267224924844, 0.04741589778476474, 0.04724272848531896, 0.047045769301623075, 0.046565683993298634, 0.045974451396885385, 0.04564404577717607, 0.0445681886862177]\n",
      "Row 82 - Column Numbers: [47 92 90 80 57 63 70 64 36 41 87 74 18 42 19 85 73 86 56 43 72 78 35  6\n",
      " 31 33 29 27 44  2 21 69 34  0  5 79 15 62 30 40 23 17 46], MI Values: [0.36022650677909773, 0.20000700401697546, 0.12362127498379927, 0.07370725535800737, 0.06659031769662516, 0.06403591879492154, 0.05982269100458204, 0.048128802238390556, 0.04758120157348866, 0.04550467421470117, 0.0453016185285815, 0.04463464698039843, 0.04452332972605699, 0.043705855049582354, 0.0432350339578198, 0.042804256191230294, 0.04269677500715918, 0.042518243369825015, 0.04216181372132244, 0.041122564560073904, 0.04035249569417232, 0.040056300664696565, 0.03993065515482197, 0.039067233966030734, 0.0389505477899581, 0.038744171751281975, 0.03800177521638748, 0.037944489427784056, 0.03731345765145644, 0.03724063933802757, 0.03716957593935177, 0.037114565896340324, 0.03697025658167963, 0.03665464470504798, 0.036577827982953615, 0.035438406074370654, 0.03489171478971809, 0.03464472319516876, 0.034410902358763096, 0.034146025613621234, 0.03378679926427086, 0.033662159409545644, 0.033650920178660115]\n",
      "Row 83 - Column Numbers: [17 21 20  0  1 19 77 15 85  2 16 91 87 11 22  5  4 79 73 18  3 12 90 92\n",
      " 78 10 42 31 43 64 61 13 68 54 35 33 46 44 74  8 57 81 14], MI Values: [1.066814745597446, 0.7488876659638617, 0.4589017533899531, 0.31506896178670907, 0.29504178717312346, 0.28206410473167054, 0.2721591618925654, 0.23569399663760304, 0.19808986460266986, 0.18056529072470173, 0.16718927849869747, 0.1656431210139937, 0.15326102264911245, 0.14976259321938912, 0.1450249261206027, 0.14139989403189102, 0.1374753305211458, 0.13601963988000332, 0.13046110819555246, 0.13005610443538984, 0.12212949345012714, 0.12178764257401475, 0.09999792818939479, 0.09786512673510916, 0.09402627710304579, 0.09120163011639004, 0.08290682477634537, 0.08252825085346682, 0.08156076645929478, 0.07860224780761271, 0.07310938021788527, 0.06900697369544506, 0.06805662497684573, 0.06494064826102797, 0.06455351051612457, 0.06416764584976953, 0.06223055486476259, 0.06102533227363338, 0.05968287991838661, 0.05824405082485473, 0.05711690835432748, 0.05488123319225924, 0.05451886276258566]\n",
      "Row 84 - Column Numbers: [ 3 76 66 64 46 75 45 69 54 63 68 57 81 50 87 61 55  6 60 44 27 62 56 74\n",
      "  0 65 52  1 51 20 17 48 72 21 49 85 47 70 58 41 40 88  2], MI Values: [0.29367624960262795, 0.24938687538324178, 0.19621110110385587, 0.13984183102276848, 0.1375172592865539, 0.1042668330618639, 0.10150362847124583, 0.09384699164641042, 0.09285394516933199, 0.07977254852835536, 0.07495229498264333, 0.07392888704485934, 0.07127138714810854, 0.06909627215253789, 0.06894787220913212, 0.06553165111754211, 0.06496582981844412, 0.06491247342046069, 0.062130659320295045, 0.06139751027721019, 0.0603802858690452, 0.058731048238805705, 0.05731245332677215, 0.05441190520910766, 0.052023584398917855, 0.05200772742261517, 0.050675710238638594, 0.050658360235747324, 0.050444118959005024, 0.04966907275681187, 0.04912116274816558, 0.049098305732939274, 0.0487682957045088, 0.047929493455121985, 0.047598231033918026, 0.04751424056243447, 0.047086024603290255, 0.046494250587683084, 0.045749765509683904, 0.04533916101688806, 0.04511370164638606, 0.04442062560320448, 0.04432867747156788]\n",
      "Row 85 - Column Numbers: [91 87 11  1 20 77  0 21 15 10 16 17  2 83 79 12 13  4  5 78 19  3  8 24\n",
      " 22 31 64 61 14 23 43 33 44 46 74 42 18 35 90 92 63 53 56], MI Values: [1.0397326027081109, 0.7808738531896484, 0.4477948984444424, 0.4273072620362388, 0.42552426145736, 0.2972324555956032, 0.29292039446620866, 0.2688208314872229, 0.2607931482272816, 0.25686672570808433, 0.24952652512346507, 0.24799566598007594, 0.2191451538778244, 0.19808986460266986, 0.1962347079230522, 0.16892847033332092, 0.15241639531040452, 0.14716514799944846, 0.14129091651330672, 0.13481869307476035, 0.12862613575316306, 0.12331183579416649, 0.1197010961317595, 0.11662871191985147, 0.11578837068495584, 0.10608247049946584, 0.10591493223352089, 0.10334008173380838, 0.0977963721134758, 0.08797109748794707, 0.08744850763647705, 0.08539579380747231, 0.08318123056251547, 0.08171791357506919, 0.0797079668361178, 0.07969793759561306, 0.07840025513521187, 0.0772743628266932, 0.07673080277470046, 0.07434137186871315, 0.07313981190535657, 0.07291262831419587, 0.0700260236623178]\n",
      "Row 86 - Column Numbers: [37 36 29 38 89 28 39 33 40 74 88 41 43 35 30 34 31 32 56 78  5 79 44 80\n",
      " 12  2  4 42 90  3 87  1  0 77 14 52 64 46 81 75 85 11 63], MI Values: [1.4582722148763292, 1.0233770024292141, 0.9904397714916922, 0.7540596341394137, 0.733195425690325, 0.7092838503040939, 0.6322229406595898, 0.6078933190308362, 0.5904546129888963, 0.5888147458720656, 0.4974361490677621, 0.47456031717445146, 0.4240950333084834, 0.398460972787932, 0.37422972387261133, 0.3436127338197741, 0.22807412650458492, 0.2027410833178278, 0.1981347985070574, 0.1340783425963794, 0.1305167490968442, 0.11181972450478028, 0.10936129874318112, 0.10493827763349994, 0.10135095971922325, 0.09732347543015418, 0.0793582428961841, 0.07547417076442908, 0.07370447561000759, 0.06840077448593984, 0.06585251441988405, 0.0648701268193781, 0.06364451470636467, 0.0619472950510529, 0.06094423783477332, 0.05775731163073594, 0.057120350210864146, 0.05635429843615114, 0.0561516544427354, 0.05527900384733986, 0.053398504926430945, 0.05262110212995097, 0.05220962062188317]\n",
      "Row 87 - Column Numbers: [91 85 20  1 11 77 15  0 10 64 17 21  2 79 46 83  4 63 12  5 16 24 78 14\n",
      " 19  8 61 13 31 74  3 56 23 44 57 22 43 47 75 68 33  6  9], MI Values: [0.8254953838532577, 0.7808738531896502, 0.32604905695192254, 0.3012243820649747, 0.2965738494229102, 0.2624972226636402, 0.2236871771312554, 0.22350595260037398, 0.2210467525648223, 0.22048913023609007, 0.19689724643638407, 0.18708052814614184, 0.18419330652618005, 0.17746826908973734, 0.16549438774061542, 0.15326102264911423, 0.1467876478550867, 0.14223108828764808, 0.13558171850872913, 0.13204341952919485, 0.12870418125103367, 0.126641316562071, 0.12204190372472912, 0.12022624072505206, 0.11907016274300819, 0.11717444758841289, 0.11609849133691608, 0.11270707168404748, 0.10896037047705942, 0.10872696979851781, 0.10828482718467924, 0.10439486730786829, 0.1027970391859041, 0.10044717697416417, 0.09943857195888395, 0.08969080820395003, 0.08755593140089335, 0.08569788060934336, 0.08358299144459647, 0.0827966624743155, 0.08221603143086931, 0.07597112239010073, 0.0751232614805879]\n",
      "Row 88 - Column Numbers: [40 89 41 28 38 39 34 29 37 86 33 36 74 30 32 35 43 31 44 78 56 79  5  4\n",
      " 64 80 12 90 18  2 46 52 42  0 10  3  1 62 54 69  8 63 17], MI Values: [1.3584687582326698, 1.1135577021657408, 0.8687228214668892, 0.7614158768816592, 0.7568375359221005, 0.7414381495833346, 0.521645640678436, 0.5162986988948415, 0.5065004040074976, 0.4974361490677621, 0.4047557520194278, 0.39112029603754017, 0.3455870286773921, 0.3120618690279793, 0.27467543363149716, 0.2113827569500053, 0.2062641249804278, 0.1178467066606661, 0.0978448354860939, 0.09216904048066343, 0.0881281392529063, 0.07856798928612552, 0.07740754667316185, 0.07609992946234723, 0.07448577255951516, 0.07253038686002977, 0.07191036153530916, 0.07018600624848581, 0.06947413178679351, 0.06925480718800436, 0.0665871977414545, 0.06273572137952144, 0.06114199250922159, 0.06063371495187919, 0.06012914210785869, 0.05512401310494486, 0.05476304444835467, 0.05440889071046939, 0.05436024408042606, 0.053695939970491935, 0.05292091189701864, 0.05201826811016552, 0.05132084037915341]\n",
      "Row 89 - Column Numbers: [38 40 88 39 28 41 37 29 86 36 34 33 74 30 43 35 32 31 56 78 80  5 79 44\n",
      " 12  2 90  4 11 64  0 10  3 42 46  1  8 13 61 87 17 54 62], MI Values: [1.2419280927673935, 1.2392621662048944, 1.113557702165739, 1.0535035116401668, 1.0046755344608442, 0.9100181021852709, 0.7572524796564108, 0.7571541803206934, 0.7331954256903233, 0.5752000583378676, 0.5628237492307493, 0.5364183007679406, 0.4790798574401274, 0.37170844903925726, 0.28802774608808956, 0.2845574273495872, 0.23990089864081376, 0.15421271891570854, 0.12759658270105323, 0.1070375256756666, 0.1044402309887218, 0.1028680671126736, 0.09254555638649009, 0.09241113709100546, 0.08890082125607357, 0.08732427486063177, 0.08143911948999971, 0.07698715238078524, 0.06919349661079899, 0.06672066841319335, 0.06566309202536758, 0.0637520285116242, 0.06298051391441373, 0.06261691628512, 0.0624690478839538, 0.06095847702589374, 0.05864248331363253, 0.05740682008964981, 0.057232186056704215, 0.0568278203392758, 0.05080254511998916, 0.05074669197352755, 0.0502827362091578]\n",
      "Row 90 - Column Numbers: [42 92 80 21 82 17  1  0 83 77 40 20 19 89 30 33 43 85  5  2 79 11 86 41\n",
      " 38 12 15 78 35 74 37 88 29 36 39 34 31 91 87 28  4 32 73], MI Values: [0.5736361560630625, 0.4459659605734716, 0.19218618079188232, 0.12517520234619095, 0.1236212749837966, 0.11040902183482082, 0.10532886649482442, 0.10411775455289263, 0.09999792818939834, 0.08763090580224375, 0.08755455049272687, 0.08732179357987846, 0.08561032186586459, 0.08143911949000593, 0.07857807032348152, 0.07829650162065516, 0.07721049556759763, 0.07673080277470312, 0.07668497735520141, 0.07646301353284013, 0.07612583152068808, 0.0746333907288248, 0.07370447561000759, 0.07307672025710321, 0.07291292443408093, 0.07254758451655796, 0.0725475665380868, 0.07220152388185319, 0.07216427126334413, 0.07133347033568604, 0.07091755529673982, 0.07018600624848581, 0.07002944857802262, 0.06954945457795869, 0.06777425757346034, 0.06748508102814021, 0.06594386443864142, 0.06571885927828625, 0.06528340240650543, 0.06435233990021594, 0.06363225684698115, 0.0634542884997531, 0.059180692944813984]\n",
      "Row 91 - Column Numbers: [85 87 11 20  1 77 10 15 21  0 17 83  2 13 79 16 12  8  4  5 78 19 22  3\n",
      " 24 23 14 61 64 31 18 63 44 43 56 42 74 92 53 90 33 46 34], MI Values: [1.0397326027081135, 0.8254953838532595, 0.3865429355312866, 0.35105094399945447, 0.3192857717713009, 0.261233029846931, 0.2579871837894956, 0.2262869925209232, 0.2086854981064592, 0.20848995166817463, 0.20010695253448052, 0.1656431210139928, 0.15702895570463316, 0.15188179879224428, 0.14530314536724998, 0.13528675087576225, 0.1292188341874061, 0.12410132440415556, 0.11543451299135388, 0.11292935145386718, 0.1118072814459321, 0.10649322098528113, 0.1063924866874304, 0.09857437391434942, 0.09541744286183729, 0.09277959255307167, 0.09231436655409198, 0.08714033036634472, 0.08652458136703967, 0.08539580505606104, 0.08043542246333857, 0.07678764806996075, 0.07356394424112533, 0.07147186167010044, 0.06996541088144959, 0.06881214952706838, 0.06784461788607654, 0.06764075156292826, 0.06654270992309197, 0.06571885927828625, 0.06454231972101443, 0.060894556193985316, 0.05979450877373971]\n",
      "Row 92 - Column Numbers: [90 82 17 42 21 80 83 63  1 85  0 19 20 91 87 57 73 23  2 30 79 77  5 78\n",
      " 15 41 74 33 11 18 36  6 32  4 12 40 34 64 86 16 28 47 10], MI Values: [0.4459659605734716, 0.20000700401697458, 0.16969542448540587, 0.11438741669920915, 0.1117978672601403, 0.11010018137622612, 0.0978651267351065, 0.08472994154227287, 0.08048114102267068, 0.07434137186871048, 0.07334383362524477, 0.07083532279622062, 0.07064869314149647, 0.06764075156292648, 0.06744167818817282, 0.06608857489515962, 0.06534747712790523, 0.06377017167667542, 0.06303769631886258, 0.06244423103829355, 0.06139810833956538, 0.06009214577031052, 0.05620640348058448, 0.05570265349391068, 0.05541644764804232, 0.05389698575662827, 0.052348572626745415, 0.051905744566475676, 0.051690795509167664, 0.05057359318983057, 0.04931200112378864, 0.048166047939036005, 0.047644557437777735, 0.04702041409510738, 0.046717369248161056, 0.04610406107367648, 0.045989563524378774, 0.0458993014321587, 0.04549260487965512, 0.04529324898574405, 0.04491292878293418, 0.044605275701465885, 0.043729188914697126]\n"
     ]
    }
   ],
   "source": [
    "A,X,training_set,test_set,unknow_set,full_set,know_set,training_set_s,A_s,capacity,unknow_set_2D,know_set_2D,training_set_s_3D = load_data_MI_3D('ndbc')"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-25T05:40:42.064994Z",
     "start_time": "2024-03-25T05:40:34.144053Z"
    }
   },
   "id": "120f3df14ccc0fa9",
   "execution_count": 20
  },
  {
   "cell_type": "code",
   "outputs": [
    {
     "data": {
      "text/plain": "(93, 6148, 43)"
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "training_set_s_3D.shape"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-25T05:40:42.070445Z",
     "start_time": "2024-03-25T05:40:42.066858Z"
    }
   },
   "id": "96bb3dc3ece5e59",
   "execution_count": 21
  },
  {
   "cell_type": "code",
   "outputs": [],
   "source": [
    "unknow_set_2D\n",
    "know_set_2D"
   ],
   "metadata": {
    "collapsed": false
   },
   "id": "e1355598e89ee073",
   "execution_count": null
  },
  {
   "cell_type": "code",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "1 1.016575022307287 1.698995022539805 207.46193650197083\n",
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      "3 0.9370821843085656 1.5669263176289367 196.96721365542646\n",
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      "5 0.8559166753035169 1.4303165874599781 181.52387070809758\n",
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      "9 0.7180243509588887 1.184085372380192 159.37613515440384\n",
      "10 0.6838944854046982 1.127367374102417 152.03956999932592\n",
      "11 0.6508450035564441 1.0677169742097425 148.76547198815862\n",
      "12 0.6170224747284075 1.0086684916956152 141.15633374776584\n",
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      "50 0.2900374938626948 0.34688941630657805 100.06742139836761\n",
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      "59 0.2816912677497421 0.3358431910576191 97.99543911514735\n",
      "60 0.283623446296092 0.3349305340294747 103.0049153596992\n",
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      "65 0.2772941896033531 0.32810775419652694 101.42667211855206\n",
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      "69 0.27264123272520474 0.3225095728311679 99.14032678736888\n",
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      "73 0.27332847094528745 0.32063282616340677 103.28098751215919\n",
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      "75 0.27081309356394373 0.3175304534468914 101.89192237016606\n",
      "76 0.27169941099998024 0.31885714356324557 102.16314343143185\n",
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      "78 0.27266074856057365 0.31543748461084115 109.36691218729963\n",
      "79 0.2716895890113202 0.3155400830060626 107.13866209770205\n",
      "80 0.27163860710062027 0.31585974337036665 107.84786507706373\n",
      "81 0.2701845940210823 0.3136815993418224 107.59761660654596\n",
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      "83 0.2658228117608396 0.31104257432629256 101.88643923854627\n",
      "84 0.2644121689001146 0.3125022590457382 96.75839110283933\n",
      "85 0.27104444889565865 0.3135555790232091 108.62637602904566\n",
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      "87 0.2705053667878267 0.31239348187170485 108.49022888066906\n",
      "88 0.2685451729151699 0.3107673299375787 106.50057324731475\n",
      "89 0.26380821640222135 0.3101525712848127 99.85605859276824\n",
      "90 0.2656833796219424 0.3083219470987358 106.33501202828472\n",
      "91 0.26667271395482156 0.30800419996732903 108.33022397666967\n",
      "92 0.2666581026494659 0.30855989737017697 107.49039674306685\n",
      "93 0.26196993710562005 0.3051153640971322 102.40554716991473\n",
      "94 0.2582360568611056 0.30432125110496233 98.3057668281272\n",
      "95 0.2634093782590864 0.30446114781614275 105.8495998985478\n",
      "96 0.26180303743699196 0.3042273381601463 103.70883962522453\n",
      "97 0.2672409737978571 0.3068765667625773 111.93175688118485\n",
      "98 0.2625237648517505 0.3077391877821057 99.54603434729543\n",
      "99 0.2602665249021658 0.3038290136966475 100.74571516528073\n",
      "(1, 93)\n",
      "(1, 93)\n",
      "Best model in the 5 -th column is 0.4015517612882144 0.5059065306594789 -1.9669223065523695\n",
      "(1, 96)\n",
      "(1, 96)\n",
      "Best model in the 6 -th column is 0.14480805116593193 0.18179759763743775 -2.0513688608533176\n",
      "(1, 94)\n",
      "(1, 94)\n",
      "Best model in the 7 -th column is 0.10991636774971732 0.1411886580964847 -1.8143909381009284\n",
      "(1, 72)\n",
      "(1, 72)\n",
      "Best model in the 8 -th column is 0.07779215507213218 0.10666074827156423 -0.9291858173252963\n",
      "(1, 72)\n",
      "(1, 72)\n",
      "Best model in the 9 -th column is 0.2311749604284762 0.28685871530868085 -2.582520754197486\n",
      "(1, 65)\n",
      "(1, 65)\n",
      "Best model in the 10 -th column is 0.1344308813709083 0.1599871699675866 -3.1108884006039865\n",
      "(1, 40)\n",
      "(1, 40)\n",
      "Best model in the 11 -th column is 0.43027969182787423 0.5163125455865013 -2.238030561298572\n",
      "(1, 98)\n",
      "(1, 98)\n",
      "Best model in the 12 -th column is 0.03703741100292766 0.04418316849736164 -11.854972445155814\n",
      "(1, 99)\n",
      "(1, 99)\n",
      "Best model in the 13 -th column is 0.5726557396684747 0.6766950533174347 -41.097931156896415\n",
      "(1, 77)\n",
      "(1, 77)\n",
      "Best model in the 14 -th column is 0.42619955461428605 0.5159420829340473 -4.681188654377783\n",
      "(1, 39)\n",
      "(1, 39)\n",
      "Best model in the 15 -th column is 0.5806069870751259 0.6185104359679522 -15.126546115297234\n",
      "(1, 7)\n",
      "(1, 7)\n",
      "Best model in the 16 -th column is 0.9225075870167216 0.9379391458934557 -28.959492785904636\n"
     ]
    }
   ],
   "source": [
    "if __name__ == \"__main__\":\n",
    "    \"\"\"\n",
    "    Model training\n",
    "    \"\"\"\n",
    "    flags = parse_args(sys.argv[1:])\n",
    "    dataset=flags.dataset\n",
    "    n_o_n_m = flags.n_o\n",
    "    h = flags.h\n",
    "    z = flags.z\n",
    "    K = flags.K\n",
    "    n_m = flags.n_m\n",
    "    n_u = flags.n_u\n",
    "    max_iter = flags.max_iter\n",
    "    learning_rate = flags.learning_rate\n",
    "    E_maxvalue = flags.E_maxvalue\n",
    "    batch_size = flags.batch_size\n",
    "    to_plot = flags.to_plot\n",
    "\n",
    "# Define model and train\n",
    "STmodel = IGNNK(h, z, K)  # The graph neural networks\n",
    "criterion = nn.MSELoss()\n",
    "optimizer = optim.Adam(STmodel.parameters(), lr=learning_rate)\n",
    "RMSE_list = []\n",
    "MAE_list = []\n",
    "MAPE_list = []\n",
    "for epoch in range(max_iter):\n",
    "    for i in range(training_set.shape[0]//(h * batch_size)):  #using time_length as reference to record test_error\n",
    "        t_random = np.random.randint(0, high=(training_set_s.shape[0] - h), size=batch_size, dtype='l')\n",
    "        know_mask = set(random.sample(range(0,training_set_s.shape[1]),n_o_n_m)) #sample n_o + n_m nodes\n",
    "        feed_batch = []\n",
    "        for j in range(batch_size):\n",
    "            feed_batch.append(training_set_s[t_random[j]: t_random[j] + h, :][:, list(know_mask)]) #generate 8 time batches\n",
    "        inputs = np.array(feed_batch)\n",
    "        inputs_omask = np.ones(np.shape(inputs))\n",
    "        if not dataset == 'NREL':\n",
    "            inputs_omask[inputs == 0] = 0           # We found that there are irregular 0 values for METR-LA, so we treat those 0 values as missing data,\n",
    "                                                    # For other datasets, it is not necessary to mask 0 values\n",
    "        missing_index = np.ones((inputs.shape))\n",
    "        for j in range(batch_size):\n",
    "            missing_mask = random.sample(range(0,n_o_n_m),n_m) #Masked locations\n",
    "            missing_index[j, :, missing_mask] = 0\n",
    "        if dataset == 'NREL':\n",
    "            Mf_inputs = inputs * inputs_omask * missing_index / capacities[:, None]\n",
    "        else:\n",
    "            Mf_inputs = inputs * inputs_omask * missing_index / E_maxvalue #normalize the value according to experience\n",
    "        Mf_inputs = torch.from_numpy(Mf_inputs.astype('float32'))\n",
    "        mask = torch.from_numpy(inputs_omask.astype('float32'))   #The reconstruction errors on irregular 0s are not used for training\n",
    "        A_dynamic = A_s[list(know_mask), :][:, list(know_mask)]   #Obtain the dynamic adjacent matrix\n",
    "        A_q = torch.from_numpy((calculate_random_walk_matrix(A_dynamic).T).astype('float32'))\n",
    "        A_h = torch.from_numpy((calculate_random_walk_matrix(A_dynamic.T).T).astype('float32'))\n",
    "        if dataset == 'NREL':\n",
    "            outputs = torch.from_numpy(inputs/capacities[:, None])\n",
    "        else:\n",
    "            outputs = torch.from_numpy(inputs/E_maxvalue) #The label\n",
    "        optimizer.zero_grad()\n",
    "        X_res = STmodel(Mf_inputs, A_q, A_h)  #Obtain the reconstruction\n",
    "        loss = criterion(X_res*mask, outputs*mask)\n",
    "        loss.backward()\n",
    "        optimizer.step()        #Errors backward\n",
    "    if not dataset == 'NREL':\n",
    "        flags = parse_args(sys.argv[1:])\n",
    "        E_maxvalue = flags.E_maxvalue\n",
    "        MAE_t, RMSE_t, MAPE_t = test_error_new(STmodel, unknow_set, test_set, A, E_maxvalue)\n",
    "    else:\n",
    "        MAE_t, RMSE_t, MAPE_t= test_error_new(STmodel, unknow_set, test_set, A,E_maxvalue)\n",
    "    RMSE_list.append(RMSE_t)\n",
    "    MAE_list.append(MAE_t)\n",
    "    MAPE_list.append(MAPE_t)\n",
    "    print(epoch, MAE_t, RMSE_t, MAPE_t)\n",
    "\n",
    "\n",
    "#Adj---Determined by tSNE\n",
    "#Raw data and raw adjacency matrix without mapminmax\n",
    "X_raw\n",
    "# X_raw=normalize_3d_array(X_raw)\n",
    "\n",
    "for j in range(5,X_raw.shape[1]-1):\n",
    "    NDBC_lat=pd.DataFrame(Station_info.iloc[:,1])\n",
    "    NDBC_long=pd.DataFrame(Station_info.iloc[:,3])\n",
    "    NDBC_ID=pd.DataFrame(Station_info.iloc[:,0])\n",
    "    Adj_dist=adj_dist(NDBC_lat,NDBC_long)\n",
    "    X_raw_0=X_raw[:,j,:]#GET the first feature\n",
    "    #print(X_raw_0.shape)\n",
    "    # Count the num of missing values in each column\n",
    "    missing_counts_per_column = np.sum(np.isnan(X_raw_0), axis=0)\n",
    "    # print results\n",
    "    # print(\"Incomplete data number in each column：\", missing_counts_per_column)\n",
    "\n",
    "    #Get the index if the value is not zero\n",
    "    # Find the columns where missing values exist.\n",
    "    columns_with_missing_data = np.any(np.isnan(X_raw_0), axis=0)\n",
    "\n",
    "    # Get the column numbers when missing value exist.\n",
    "    missing_columns = np.where(columns_with_missing_data)[0]\n",
    "\n",
    "    # Print results\n",
    "    #print(\"The column numbers with missing values are：\", missing_columns)\n",
    "\n",
    "    #Get new data after deletion.\n",
    "    #Delete those columns(Stations) if there is not any features.\n",
    "    result = np.delete(X_raw_0, missing_columns, axis=1)\n",
    "    result = (result - np.min(result)) / (np.max(result) - np.min(result))\n",
    "    #Mean results---for SNE\n",
    "    mean_result_axis_1=np.mean(result,axis=0)\n",
    "    mean_result_axis_1=mean_result_axis_1.reshape(-1,1)\n",
    "\n",
    "    #Get new adjacency matrix after deletion.\n",
    "    NDBC_long=NDBC_long.transpose()\n",
    "    NDBC_long_aft=NDBC_long.drop(columns=missing_columns)\n",
    "    # Reconstruct the index in the DataFrame and get the longitude after deletion.\n",
    "    NDBC_long_aft = NDBC_long_aft.reset_index(drop=True)\n",
    "    print(NDBC_long_aft.shape)\n",
    "    Temp_long=NDBC_long_aft.values\n",
    "\n",
    "    NDBC_lat=NDBC_lat.transpose()\n",
    "    NDBC_lat_aft=NDBC_lat.drop(columns=missing_columns)\n",
    "    # Reconstruct the index in the DataFrame and get the latitude after deletion.\n",
    "    NDBC_lat_aft = NDBC_lat_aft.reset_index(drop=True)\n",
    "    print(NDBC_lat_aft.shape)\n",
    "    Temp_lat=NDBC_lat_aft.values\n",
    "\n",
    "    merged_array = np.concatenate([mean_result_axis_1, Temp_long.T,Temp_lat.T], axis=1)\n",
    "    tsne = TSNE(n_components=2, random_state=30,perplexity=1) #Make sure random seed to be the same for the reproducibility.\n",
    "    array_aft = tsne.fit_transform(merged_array)\n",
    "\n",
    "    #GEt the new ADJ matrix.\n",
    "    Adj_dist=adj_dist(pd.DataFrame(array_aft[:,0]),pd.DataFrame(array_aft[:,1]))\n",
    "    capacities=np.ones((Adj_dist.shape[0], 1))\n",
    "    capacities=capacities.flatten()\n",
    "    split_line1 = int(result.shape[0] * 0.7)\n",
    "    training_set = result[:split_line1, :]\n",
    "    test_set = result[split_line1:, :]\n",
    "    rand = np.random.RandomState(0) # Fixed random output, just an example when seed = 0.\n",
    "    unknow_set = rand.choice(list(range(0,result.shape[1])),N_u,replace=True)#Stations to be predicted\n",
    "    unknow_set = set(unknow_set)\n",
    "    full_set = set(range(0,result.shape[1]))\n",
    "    know_set = full_set - unknow_set\n",
    "    training_set_s = training_set[:, list(know_set)]   # get the training data in the sample time period\n",
    "    A_s = Adj_dist[:, list(know_set)][list(know_set), :]\n",
    "    MAE_t, RMSE_t, R2_t, nrel_ignnk_res  = test_error_cap(STmodel, unknow_set, full_set,test_set, Adj_dist,h,capacities)\n",
    "    print('Best model in the',j, '-th column is', MAE_t, RMSE_t, R2_t)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-25T06:49:56.537840Z",
     "start_time": "2024-03-25T06:49:00.923447Z"
    }
   },
   "id": "2be7e7c0a51c988d",
   "execution_count": 26
  },
  {
   "cell_type": "code",
   "outputs": [],
   "source": [
    "if __name__ == \"__main__\":\n",
    "    \"\"\"\n",
    "    Model training\n",
    "    \"\"\"\n",
    "    flags = parse_args(sys.argv[1:])\n",
    "    dataset=flags.dataset\n",
    "    n_o_n_m = flags.n_o\n",
    "    h = flags.h\n",
    "    z = flags.z\n",
    "    K = flags.K\n",
    "    n_m = flags.n_m\n",
    "    n_u = flags.n_u\n",
    "    max_iter = flags.max_iter\n",
    "    learning_rate = flags.learning_rate\n",
    "    E_maxvalue = flags.E_maxvalue\n",
    "    batch_size = flags.batch_size\n",
    "    to_plot = flags.to_plot\n",
    "\n",
    "# Define model and train\n",
    "STmodel = IGNNK(h, z, K)  # The graph neural networks\n",
    "criterion = nn.MSELoss()\n",
    "optimizer = optim.Adam(STmodel.parameters(), lr=learning_rate)\n",
    "RMSE_list = []\n",
    "MAE_list = []\n",
    "MAPE_list = []\n",
    "for epoch in range(max_iter):\n",
    "    for i in range(training_set.shape[0]//(h * batch_size)):  #using time_length as reference to record test_error\n",
    "        t_random = np.random.randint(0, high=(training_set_s.shape[0] - h), size=batch_size, dtype='l')\n",
    "        know_mask = set(random.sample(range(0,training_set_s.shape[1]),n_o_n_m)) #sample n_o + n_m nodes\n",
    "        feed_batch = []\n",
    "        for j in range(batch_size):\n",
    "            feed_batch.append(training_set_s[t_random[j]: t_random[j] + h, :][:, list(know_mask)]) #generate 8 time batches\n",
    "        inputs = np.array(feed_batch)\n",
    "        inputs_omask = np.ones(np.shape(inputs))\n",
    "        if not dataset == 'NREL':\n",
    "            inputs_omask[inputs == 0] = 0           # We found that there are irregular 0 values for METR-LA, so we treat those 0 values as missing data,\n",
    "                                                    # For other datasets, it is not necessary to mask 0 values\n",
    "        missing_index = np.ones((inputs.shape))\n",
    "        for j in range(batch_size):\n",
    "            missing_mask = random.sample(range(0,n_o_n_m),n_m) #Masked locations\n",
    "            missing_index[j, :, missing_mask] = 0\n",
    "        if dataset == 'NREL':\n",
    "            Mf_inputs = inputs * inputs_omask * missing_index / capacities[:, None]\n",
    "        else:\n",
    "            Mf_inputs = inputs * inputs_omask * missing_index / E_maxvalue #normalize the value according to experience\n",
    "        Mf_inputs = torch.from_numpy(Mf_inputs.astype('float32'))\n",
    "        mask = torch.from_numpy(inputs_omask.astype('float32'))   #The reconstruction errors on irregular 0s are not used for training\n",
    "        A_dynamic = A_s[list(know_mask), :][:, list(know_mask)]   #Obtain the dynamic adjacent matrix\n",
    "        A_q = torch.from_numpy((calculate_random_walk_matrix(A_dynamic).T).astype('float32'))\n",
    "        A_h = torch.from_numpy((calculate_random_walk_matrix(A_dynamic.T).T).astype('float32'))\n",
    "        if dataset == 'NREL':\n",
    "            outputs = torch.from_numpy(inputs/capacities[:, None])\n",
    "        else:\n",
    "            outputs = torch.from_numpy(inputs/E_maxvalue) #The label\n",
    "        optimizer.zero_grad()\n",
    "        X_res = STmodel(Mf_inputs, A_q, A_h)  #Obtain the reconstruction\n",
    "        loss = criterion(X_res*mask, outputs*mask)\n",
    "        loss.backward()\n",
    "        optimizer.step()        #Errors backward\n",
    "    if not dataset == 'NREL':\n",
    "        flags = parse_args(sys.argv[1:])\n",
    "        E_maxvalue = flags.E_maxvalue\n",
    "        MAE_t, RMSE_t, MAPE_t = test_error_new(STmodel, unknow_set, test_set, A, E_maxvalue)\n",
    "    else:\n",
    "        MAE_t, RMSE_t, MAPE_t= test_error_new(STmodel, unknow_set, test_set, A,E_maxvalue)\n",
    "    RMSE_list.append(RMSE_t)\n",
    "    MAE_list.append(MAE_t)\n",
    "    MAPE_list.append(MAPE_t)\n",
    "    print(epoch, MAE_t, RMSE_t, MAPE_t)\n",
    "\n",
    "\n",
    "#Adj---Determined by tSNE\n",
    "#Raw data and raw adjacency matrix without mapminmax\n",
    "X_raw\n",
    "# X_raw=normalize_3d_array(X_raw)\n",
    "\n",
    "for j in range(5,X_raw.shape[1]-1):\n",
    "    NDBC_lat=pd.DataFrame(Station_info.iloc[:,1])\n",
    "    NDBC_long=pd.DataFrame(Station_info.iloc[:,3])\n",
    "    NDBC_ID=pd.DataFrame(Station_info.iloc[:,0])\n",
    "    Adj_dist=adj_dist(NDBC_lat,NDBC_long)\n",
    "    X_raw_0=X_raw[:,j,:]#GET the first feature\n",
    "    #print(X_raw_0.shape)\n",
    "    # Count the num of missing values in each column\n",
    "    missing_counts_per_column = np.sum(np.isnan(X_raw_0), axis=0)\n",
    "    # print results\n",
    "    # print(\"Incomplete data number in each column：\", missing_counts_per_column)\n",
    "\n",
    "    #Get the index if the value is not zero\n",
    "    # Find the columns where missing values exist.\n",
    "    columns_with_missing_data = np.any(np.isnan(X_raw_0), axis=0)\n",
    "\n",
    "    # Get the column numbers when missing value exist.\n",
    "    missing_columns = np.where(columns_with_missing_data)[0]\n",
    "\n",
    "    # Print results\n",
    "    #print(\"The column numbers with missing values are：\", missing_columns)\n",
    "\n",
    "    #Get new data after deletion.\n",
    "    #Delete those columns(Stations) if there is not any features.\n",
    "    result = np.delete(X_raw_0, missing_columns, axis=1)\n",
    "    result = (result - np.min(result)) / (np.max(result) - np.min(result))\n",
    "    #Mean results---for SNE\n",
    "    mean_result_axis_1=np.mean(result,axis=0)\n",
    "    mean_result_axis_1=mean_result_axis_1.reshape(-1,1)\n",
    "\n",
    "    #Get new adjacency matrix after deletion.\n",
    "    NDBC_long=NDBC_long.transpose()\n",
    "    NDBC_long_aft=NDBC_long.drop(columns=missing_columns)\n",
    "    # Reconstruct the index in the DataFrame and get the longitude after deletion.\n",
    "    NDBC_long_aft = NDBC_long_aft.reset_index(drop=True)\n",
    "    print(NDBC_long_aft.shape)\n",
    "    Temp_long=NDBC_long_aft.values\n",
    "\n",
    "    NDBC_lat=NDBC_lat.transpose()\n",
    "    NDBC_lat_aft=NDBC_lat.drop(columns=missing_columns)\n",
    "    # Reconstruct the index in the DataFrame and get the latitude after deletion.\n",
    "    NDBC_lat_aft = NDBC_lat_aft.reset_index(drop=True)\n",
    "    print(NDBC_lat_aft.shape)\n",
    "    Temp_lat=NDBC_lat_aft.values\n",
    "\n",
    "    merged_array = np.concatenate([mean_result_axis_1, Temp_long.T,Temp_lat.T], axis=1)\n",
    "    tsne = TSNE(n_components=2, random_state=30,perplexity=1) #Make sure random seed to be the same for the reproducibility.\n",
    "    array_aft = tsne.fit_transform(merged_array)\n",
    "\n",
    "    #GEt the new ADJ matrix.\n",
    "    Adj_dist=adj_dist(pd.DataFrame(array_aft[:,0]),pd.DataFrame(array_aft[:,1]))\n",
    "    capacities=np.ones((Adj_dist.shape[0], 1))\n",
    "    capacities=capacities.flatten()\n",
    "    split_line1 = int(result.shape[0] * 0.7)\n",
    "    training_set = result[:split_line1, :]\n",
    "    test_set = result[split_line1:, :]\n",
    "    rand = np.random.RandomState(0) # Fixed random output, just an example when seed = 0.\n",
    "    unknow_set = rand.choice(list(range(0,result.shape[1])),N_u,replace=True)#Stations to be predicted\n",
    "    unknow_set = set(unknow_set)\n",
    "    full_set = set(range(0,result.shape[1]))\n",
    "    know_set = full_set - unknow_set\n",
    "    training_set_s = training_set[:, list(know_set)]   # get the training data in the sample time period\n",
    "    A_s = Adj_dist[:, list(know_set)][list(know_set), :]\n",
    "    MAE_t, RMSE_t, R2_t, nrel_ignnk_res  = test_error_cap(STmodel, unknow_set, full_set,test_set, Adj_dist,h,capacities)\n",
    "    print('Best model in the',j, '-th column is', MAE_t, RMSE_t, R2_t)"
   ],
   "metadata": {
    "collapsed": false
   },
   "id": "2469b250c7eec57d",
   "execution_count": null
  },
  {
   "cell_type": "code",
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "__init__() missing 1 required positional argument: 'experts_bn'",
     "output_type": "error",
     "traceback": [
      "\u001B[0;31m---------------------------------------------------------------------------\u001B[0m",
      "\u001B[0;31mTypeError\u001B[0m                                 Traceback (most recent call last)",
      "Cell \u001B[0;32mIn[27], line 315\u001B[0m\n\u001B[1;32m    312\u001B[0m         out \u001B[38;5;241m=\u001B[39m \u001B[38;5;28mself\u001B[39m\u001B[38;5;241m.\u001B[39msoft(out)\n\u001B[1;32m    313\u001B[0m         \u001B[38;5;28;01mreturn\u001B[39;00m out\n\u001B[0;32m--> 315\u001B[0m moe_model \u001B[38;5;241m=\u001B[39m \u001B[43mMoE\u001B[49m\u001B[43m(\u001B[49m\u001B[38;5;241;43m10\u001B[39;49m\u001B[43m,\u001B[49m\u001B[43m \u001B[49m\u001B[38;5;241;43m10\u001B[39;49m\u001B[43m,\u001B[49m\u001B[43m \u001B[49m\u001B[38;5;241;43m3\u001B[39;49m\u001B[43m,\u001B[49m\u001B[43m \u001B[49m\u001B[43m[\u001B[49m\u001B[43mMLP\u001B[49m\u001B[43m(\u001B[49m\u001B[38;5;241;43m10\u001B[39;49m\u001B[43m,\u001B[49m\u001B[38;5;241;43m10\u001B[39;49m\u001B[43m,\u001B[49m\u001B[38;5;241;43m10\u001B[39;49m\u001B[43m)\u001B[49m\u001B[43m,\u001B[49m\u001B[43m \u001B[49m\u001B[43mMLP\u001B[49m\u001B[43m(\u001B[49m\u001B[38;5;241;43m10\u001B[39;49m\u001B[43m,\u001B[49m\u001B[38;5;241;43m10\u001B[39;49m\u001B[43m,\u001B[49m\u001B[38;5;241;43m10\u001B[39;49m\u001B[43m)\u001B[49m\u001B[43m,\u001B[49m\u001B[43m \u001B[49m\u001B[43mMLP\u001B[49m\u001B[43m(\u001B[49m\u001B[38;5;241;43m10\u001B[39;49m\u001B[43m,\u001B[49m\u001B[38;5;241;43m10\u001B[39;49m\u001B[43m,\u001B[49m\u001B[38;5;241;43m10\u001B[39;49m\u001B[43m)\u001B[49m\u001B[43m]\u001B[49m\u001B[43m,\u001B[49m\u001B[43m \u001B[49m\u001B[43mk\u001B[49m\u001B[38;5;241;43m=\u001B[39;49m\u001B[38;5;241;43m1\u001B[39;49m\u001B[43m)\u001B[49m\n\u001B[1;32m    316\u001B[0m x \u001B[38;5;241m=\u001B[39m torch\u001B[38;5;241m.\u001B[39mones((\u001B[38;5;241m8\u001B[39m,\u001B[38;5;241m10\u001B[39m))\n\u001B[1;32m    317\u001B[0m h \u001B[38;5;241m=\u001B[39m moe_model(x)\n",
      "\u001B[0;31mTypeError\u001B[0m: __init__() missing 1 required positional argument: 'experts_bn'"
     ]
    }
   ],
   "source": [
    "\n",
    "\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "from torch.distributions.normal import Normal\n",
    "import numpy as np\n",
    "\n",
    "\n",
    "class SparseDispatcher(object):\n",
    "    \"\"\"Helper for implementing a mixture of experts.\n",
    "    The purpose of this class is to create input minibatches for the\n",
    "    experts and to combine the results of the experts to form a unified\n",
    "    output tensor.\n",
    "    There are two functions:\n",
    "    dispatch - take an input Tensor and create input Tensors for each expert.\n",
    "    combine - take output Tensors from each expert and form a combined output\n",
    "      Tensor.  Outputs from different experts for the same batch element are\n",
    "      summed together, weighted by the provided \"gates\".\n",
    "    The class is initialized with a \"gates\" Tensor, which specifies which\n",
    "    batch elements go to which experts, and the weights to use when combining\n",
    "    the outputs.  Batch element b is sent to expert e iff gates[b, e] != 0.\n",
    "    The inputs and outputs are all two-dimensional [batch, depth].\n",
    "    Caller is responsible for collapsing additional dimensions prior to\n",
    "    calling this class and reshaping the output to the original shape.\n",
    "    See common_layers.reshape_like().\n",
    "    Example use:\n",
    "    gates: a float32 `Tensor` with shape `[batch_size, num_experts]`\n",
    "    inputs: a float32 `Tensor` with shape `[batch_size, input_size]`\n",
    "    experts: a list of length `num_experts` containing sub-networks.\n",
    "    dispatcher = SparseDispatcher(num_experts, gates)\n",
    "    expert_inputs = dispatcher.dispatch(inputs)\n",
    "    expert_outputs = [experts[i](expert_inputs[i]) for i in range(num_experts)]\n",
    "    outputs = dispatcher.combine(expert_outputs)\n",
    "    The preceding code sets the output for a particular example b to:\n",
    "    output[b] = Sum_i(gates[b, i] * experts[i](inputs[b]))\n",
    "    This class takes advantage of sparsity in the gate matrix by including in the\n",
    "    `Tensor`s for expert i only the batch elements for which `gates[b, i] > 0`.\n",
    "    \"\"\"\n",
    "\n",
    "    def __init__(self, num_experts, gates):\n",
    "        \"\"\"Create a SparseDispatcher.\"\"\"\n",
    "\n",
    "        self._gates = gates\n",
    "        self._num_experts = num_experts\n",
    "        # sort experts\n",
    "        sorted_experts, index_sorted_experts = torch.nonzero(gates).sort(0)\n",
    "        # drop indices\n",
    "        _, self._expert_index = sorted_experts.split(1, dim=1)\n",
    "        # get according batch index for each expert\n",
    "        self._batch_index = torch.nonzero(gates)[index_sorted_experts[:, 1], 0]\n",
    "        # calculate num samples that each expert gets\n",
    "        self._part_sizes = (gates > 0).sum(0).tolist()\n",
    "        # expand gates to match with self._batch_index\n",
    "        gates_exp = gates[self._batch_index.flatten()]\n",
    "        self._nonzero_gates = torch.gather(gates_exp, 1, self._expert_index)\n",
    "\n",
    "    def dispatch(self, inp, edge_index, edge_attr):\n",
    "        \"\"\"Create one input Tensor for each expert.\n",
    "        The `Tensor` for a expert `i` contains the slices of `inp` corresponding\n",
    "        to the batch elements `b` where `gates[b, i] > 0`.\n",
    "        Args:\n",
    "          inp: a `Tensor` of shape \"[batch_size, <extra_input_dims>]`\n",
    "        Returns:\n",
    "          a list of `num_experts` `Tensor`s with shapes\n",
    "            `[expert_batch_size_i, <extra_input_dims>]`.\n",
    "        \"\"\"\n",
    "\n",
    "        # Note by Haotao:\n",
    "        # self._batch_index: shape=(N_batch). The re-order indices from 0 to N_batch-1.\n",
    "        # inp_exp: shape=inp.shape. The input Tensor re-ordered by self._batch_index along the batch dimension.\n",
    "        # self._part_sizes: shape=(N_experts), sum=N_batch. self._part_sizes[i] is the number of samples routed towards expert[i].\n",
    "        # return value: list [Tensor with shape[0]=self._part_sizes[i] for i in range(N_experts)] \n",
    "\n",
    "        # assigns samples to experts whose gate is nonzero\n",
    "\n",
    "        # expand according to batch index so we can just split by _part_sizes\n",
    "        inp_exp = inp[self._batch_index].squeeze(1)\n",
    "        edge_index_exp = edge_index[:,self._batch_index]\n",
    "        edge_attr_exp = edge_attr[self._batch_index]\n",
    "        return torch.split(inp_exp, self._part_sizes, dim=0), torch.split(edge_index_exp, self._part_sizes, dim=1), torch.split(edge_attr_exp, self._part_sizes, dim=0)\n",
    "\n",
    "    def combine(self, expert_out, multiply_by_gates=True):\n",
    "        \"\"\"Sum together the expert output, weighted by the gates.\n",
    "        The slice corresponding to a particular batch element `b` is computed\n",
    "        as the sum over all experts `i` of the expert output, weighted by the\n",
    "        corresponding gate values.  If `multiply_by_gates` is set to False, the\n",
    "        gate values are ignored.\n",
    "        Args:\n",
    "          expert_out: a list of `num_experts` `Tensor`s, each with shape\n",
    "            `[expert_batch_size_i, <extra_output_dims>]`.\n",
    "          multiply_by_gates: a boolean\n",
    "        Returns:\n",
    "          a `Tensor` with shape `[batch_size, <extra_output_dims>]`.\n",
    "        \"\"\"\n",
    "        # apply exp to expert outputs, so we are not longer in log space\n",
    "        stitched = torch.cat(expert_out, 0).exp()\n",
    "\n",
    "        if multiply_by_gates:\n",
    "            stitched = stitched.mul(self._nonzero_gates)\n",
    "        zeros = torch.zeros(self._gates.size(0), expert_out[-1].size(1), requires_grad=True, device=stitched.device)\n",
    "        # combine samples that have been processed by the same k experts\n",
    "        combined = zeros.index_add(0, self._batch_index, stitched.float())\n",
    "        # add eps to all zero values in order to avoid nans when going back to log space\n",
    "        combined[combined == 0] = np.finfo(float).eps\n",
    "        # back to log space\n",
    "        return combined.log()\n",
    "\n",
    "    def expert_to_gates(self):\n",
    "        \"\"\"Gate values corresponding to the examples in the per-expert `Tensor`s.\n",
    "        Returns:\n",
    "          a list of `num_experts` one-dimensional `Tensor`s with type `tf.float32`\n",
    "              and shapes `[expert_batch_size_i]`\n",
    "        \"\"\"\n",
    "        # split nonzero gates for each expert\n",
    "        return torch.split(self._nonzero_gates, self._part_sizes, dim=0)\n",
    "\n",
    "class MoE(nn.Module):\n",
    "\n",
    "    \"\"\"Call a Sparsely gated mixture of experts layer with 1-layer Feed-Forward networks as experts.\n",
    "    Args:\n",
    "    input_size: integer - size of the input\n",
    "    output_size: integer - size of the input\n",
    "    num_experts: an integer - number of experts\n",
    "    hidden_size: an integer - hidden size of the experts\n",
    "    noisy_gating: a boolean\n",
    "    k: an integer - how many experts to use for each batch element\n",
    "    \"\"\"\n",
    "\n",
    "    def __init__(self, input_size, output_size, num_experts, experts_conv, experts_bn, noisy_gating=True, k=4, coef=1e-2, num_experts_1hop=None):\n",
    "        super(MoE, self).__init__()\n",
    "        self.noisy_gating = noisy_gating\n",
    "        self.num_experts = num_experts\n",
    "        self.output_size = output_size\n",
    "        self.input_size = input_size\n",
    "        self.k = k\n",
    "        self.loss_coef = coef\n",
    "        if not num_experts_1hop:\n",
    "            self.num_experts_1hop = num_experts # by default, all experts are hop-1 experts.\n",
    "        else:\n",
    "            assert num_experts_1hop <= num_experts\n",
    "            self.num_experts_1hop = num_experts_1hop\n",
    "        # instantiate experts\n",
    "        # self.experts = nn.ModuleList([MLP(self.input_size, self.output_size, self.hidden_size) for i in range(self.num_experts)])\n",
    "        self.experts_conv = experts_conv\n",
    "        self.experts_bn = experts_bn\n",
    "        self.w_gate = nn.Parameter(torch.zeros(input_size, num_experts), requires_grad=True)\n",
    "        self.w_noise = nn.Parameter(torch.zeros(input_size, num_experts), requires_grad=True)\n",
    "\n",
    "        self.softplus = nn.Softplus()\n",
    "        self.softmax = nn.Softmax(1)\n",
    "        self.register_buffer(\"mean\", torch.tensor([0.0]))\n",
    "        self.register_buffer(\"std\", torch.tensor([1.0]))\n",
    "        assert(self.k <= self.num_experts)\n",
    "\n",
    "    def cv_squared(self, x):\n",
    "        \"\"\"The squared coefficient of variation of a sample.\n",
    "        Useful as a loss to encourage a positive distribution to be more uniform.\n",
    "        Epsilons added for numerical stability.\n",
    "        Returns 0 for an empty Tensor.\n",
    "        Args:\n",
    "        x: a `Tensor`.\n",
    "        Returns:\n",
    "        a `Scalar`.\n",
    "        \"\"\"\n",
    "        eps = 1e-10\n",
    "        # if only num_experts = 1\n",
    "\n",
    "        if x.shape[0] == 1:\n",
    "            return torch.tensor([0], device=x.device, dtype=x.dtype)\n",
    "        return x.float().var() / (x.float().mean()**2 + eps)\n",
    "\n",
    "    def _gates_to_load(self, gates):\n",
    "        \"\"\"Compute the true load per expert, given the gates.\n",
    "        The load is the number of examples for which the corresponding gate is >0.\n",
    "        Args:\n",
    "        gates: a `Tensor` of shape [batch_size, n]\n",
    "        Returns:\n",
    "        a float32 `Tensor` of shape [n]\n",
    "        \"\"\"\n",
    "        return (gates > 0).sum(0)\n",
    "\n",
    "    def _prob_in_top_k(self, clean_values, noisy_values, noise_stddev, noisy_top_values):\n",
    "        \"\"\"Helper function to NoisyTopKGating.\n",
    "        Computes the probability that value is in top k, given different random noise.\n",
    "        This gives us a way of backpropagating from a loss that balances the number\n",
    "        of times each expert is in the top k experts per example.\n",
    "        In the case of no noise, pass in None for noise_stddev, and the result will\n",
    "        not be differentiable.\n",
    "        Args:\n",
    "        clean_values: a `Tensor` of shape [batch, n].\n",
    "        noisy_values: a `Tensor` of shape [batch, n].  Equal to clean values plus\n",
    "          normally distributed noise with standard deviation noise_stddev.\n",
    "        noise_stddev: a `Tensor` of shape [batch, n], or None\n",
    "        noisy_top_values: a `Tensor` of shape [batch, m].\n",
    "           \"values\" Output of tf.top_k(noisy_top_values, m).  m >= k+1\n",
    "        Returns:\n",
    "        a `Tensor` of shape [batch, n].\n",
    "        \"\"\"\n",
    "        batch = clean_values.size(0)\n",
    "        m = noisy_top_values.size(1)\n",
    "        top_values_flat = noisy_top_values.flatten()\n",
    "\n",
    "        threshold_positions_if_in = torch.arange(batch, device=clean_values.device) * m + self.k\n",
    "        threshold_if_in = torch.unsqueeze(torch.gather(top_values_flat, 0, threshold_positions_if_in), 1)\n",
    "        is_in = torch.gt(noisy_values, threshold_if_in)\n",
    "        threshold_positions_if_out = threshold_positions_if_in - 1\n",
    "        threshold_if_out = torch.unsqueeze(torch.gather(top_values_flat, 0, threshold_positions_if_out), 1)\n",
    "        # is each value currently in the top k.\n",
    "        normal = Normal(self.mean, self.std)\n",
    "        prob_if_in = normal.cdf((clean_values - threshold_if_in)/noise_stddev)\n",
    "        prob_if_out = normal.cdf((clean_values - threshold_if_out)/noise_stddev)\n",
    "        prob = torch.where(is_in, prob_if_in, prob_if_out)\n",
    "        return prob\n",
    "\n",
    "    def noisy_top_k_gating(self, x, train, noise_epsilon=1e-2):\n",
    "        \"\"\"Noisy top-k gating.\n",
    "          See paper: https://arxiv.org/abs/1701.06538.\n",
    "          Args:\n",
    "            x: input Tensor with shape [batch_size, input_size]\n",
    "            train: a boolean - we only add noise at training time.\n",
    "            noise_epsilon: a float\n",
    "          Returns:\n",
    "            gates: a Tensor with shape [batch_size, num_experts]\n",
    "            load: a Tensor with shape [num_experts]\n",
    "        \"\"\"\n",
    "        clean_logits = x @ self.w_gate\n",
    "        if self.noisy_gating and train:\n",
    "            raw_noise_stddev = x @ self.w_noise\n",
    "            noise_stddev = ((self.softplus(raw_noise_stddev) + noise_epsilon))\n",
    "            noisy_logits = clean_logits + (torch.randn_like(clean_logits) * noise_stddev)\n",
    "            logits = noisy_logits\n",
    "        else:\n",
    "            logits = clean_logits\n",
    "\n",
    "        # calculate topk + 1 that will be needed for the noisy gates\n",
    "        top_logits, top_indices = logits.topk(min(self.k + 1, self.num_experts), dim=1)\n",
    "        top_k_logits = top_logits[:, :self.k]\n",
    "        top_k_indices = top_indices[:, :self.k]\n",
    "        top_k_gates = self.softmax(top_k_logits)\n",
    "\n",
    "        zeros = torch.zeros_like(logits, requires_grad=True)\n",
    "        gates = zeros.scatter(1, top_k_indices, top_k_gates)\n",
    "\n",
    "        if self.noisy_gating and self.k < self.num_experts and train:\n",
    "            load = (self._prob_in_top_k(clean_logits, noisy_logits, noise_stddev, top_logits)).sum(0)\n",
    "        else:\n",
    "            load = self._gates_to_load(gates)\n",
    "        return gates, load\n",
    "\n",
    "    def forward(self, x, edge_index, edge_attr, edge_index_2hop=None, edge_attr_2hop=None):\n",
    "        \"\"\"Args:\n",
    "        x: tensor shape [batch_size, input_size]\n",
    "        train: a boolean scalar.\n",
    "        loss_coef: a scalar - multiplier on load-balancing losses\n",
    "\n",
    "        Returns:\n",
    "        y: a tensor with shape [batch_size, output_size].\n",
    "        extra_training_loss: a scalar.  This should be added into the overall\n",
    "        training loss of the model.  The backpropagation of this loss\n",
    "        encourages all experts to be approximately equally used across a batch.\n",
    "        \"\"\"\n",
    "        gates, load = self.noisy_top_k_gating(x, self.training)\n",
    "        # calculate importance loss\n",
    "        importance = gates.sum(0)\n",
    "        #\n",
    "        loss = self.cv_squared(importance) + self.cv_squared(load)\n",
    "        loss *= self.loss_coef\n",
    "\n",
    "\n",
    "\n",
    "        expert_outputs = []\n",
    "        for i in range(self.num_experts):\n",
    "            if i < self.num_experts_1hop:\n",
    "                expert_i_output = self.experts_conv[i](x, edge_index, edge_attr)\n",
    "            else:\n",
    "                expert_i_output = self.experts_conv[i](x, edge_index_2hop, edge_attr_2hop)\n",
    "            expert_i_output = self.experts_bn[i](expert_i_output)\n",
    "            expert_outputs.append(expert_i_output)\n",
    "        expert_outputs = torch.stack(expert_outputs, dim=1) # shape=[num_nodes, num_experts, d_feature]\n",
    "\n",
    "        # gates: shape=[num_nodes, num_experts]\n",
    "        y = gates.unsqueeze(dim=-1) * expert_outputs\n",
    "        y = y.mean(dim=1)\n",
    "\n",
    "        return y, loss\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    class MLP(nn.Module):\n",
    "        def __init__(self, input_size, output_size, hidden_size):\n",
    "            super(MLP, self).__init__()\n",
    "            self.fc1 = nn.Linear(input_size, hidden_size)\n",
    "            self.fc2 = nn.Linear(hidden_size, output_size)\n",
    "            self.relu = nn.ReLU()\n",
    "            self.soft = nn.Softmax(1)\n",
    "\n",
    "        def forward(self, x):\n",
    "            out = self.fc1(x)\n",
    "            out = self.relu(out)\n",
    "            out = self.fc2(out)\n",
    "            out = self.soft(out)\n",
    "            return out\n",
    "\n",
    "    moe_model = MoE(10, 10, 3, [MLP(10,10,10), MLP(10,10,10), MLP(10,10,10)], k=1)\n",
    "    x = torch.ones((8,10))\n",
    "    h = moe_model(x)\n",
    "    print(h.shape)"
   ],
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    "ExecuteTime": {
     "end_time": "2024-03-25T07:05:23.344801Z",
     "start_time": "2024-03-25T07:05:23.288134Z"
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   },
   "id": "2e1bfd24b3ed1b5",
   "execution_count": 27
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   "source": [],
   "metadata": {
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   },
   "id": "7eb4032a53ebb8b7",
   "execution_count": null
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