ripple.py

import math
import time
from operator import itemgetter
import numpy as np

def graphConv(filename):
    graph = {}
    size = 0
    with open(filename, 'r') as file:
        for line in file:
            contents = line.split()
            if contents[0] == 'p':
                size = int(contents[2])
                break
    for i in range(1, size + 1):
        graph[i] = []
    with open(filename, 'r') as file:
        for line in file:
            edge = line.split()
            if edge[0] == 'e':
                e1 = int(edge[1])
                e2 = int(edge[2])
                graph[e1].append(e2)
                graph[e2].append(e1)
    return graph
def makeGraphCopy(graph):
    copy = {}
    for key in graph.keys():
        temp = []
        for n in graph[key]:
            temp.append(n)
        copy[key] = temp
    return copy
def closedNeighborhood(node, graph):
    antiNeigh = []
    for key in graph.keys():
        if key not in graph[node]:
            antiNeigh.append(key)
    for anti in antiNeigh:
        neighbors = graph[anti]
        for n in neighbors:
            graph[n].remove(anti)
        graph.pop(anti, None)
    return graph
#'''
very_first_ordering = {1: [114, 99, 104, 54, 60, 29, 49, 98, 8, 19, 7, 110, 45, 111, 39, 40, 125, 80, 101, 48, 34, 10, 92, 22, 11, 122, 44, 115, 9, 2, 41, 96, 82, 123, 18, 70, 47, 24, 66, 26, 84, 107, 5, 57, 79, 25, 30, 46, 85, 119, 59, 65, 77, 14, 55, 93, 43, 121, 13, 58, 31, 91, 117, 6, 52, 74, 86, 103, 32, 61, 124, 20, 23, 72, 35, 69, 4, 81, 63, 28, 27, 62, 3, 33, 17, 68, 116, 38, 78, 89, 102, 71, 120, 15, 88, 94, 100, 21, 105, 112, 113, 50, 75, 51, 73, 16, 97, 76, 64, 90, 36, 83], 
2: [54, 60, 114, 19, 80, 110, 45, 104, 111, 77, 29, 40, 67, 11, 8, 7, 101, 99, 35, 91, 74, 65, 34, 92, 24, 39, 70, 49, 98, 125, 84, 44, 57, 48, 119, 22, 59, 10, 123, 18, 47, 1, 79, 115, 6, 41, 86, 96, 82, 71, 32, 121, 122, 58, 5, 31, 72, 109, 117, 118, 9, 25, 52, 30, 46, 85, 61, 93, 124, 26, 37, 106, 107, 4, 69, 81, 100, 63, 78, 102, 87, 23, 27, 43, 62, 116, 14, 38, 21, 89, 112, 105, 28, 97, 94, 113, 12, 17, 68, 103, 108, 16, 88, 95, 50, 33, 51, 42, 76, 73, 64, 36, 83], 
3: [111, 54, 45, 60, 114, 67, 19, 101, 7, 104, 82, 39, 18, 29, 40, 49, 125, 8, 99, 110, 4, 6, 25, 96, 10, 123, 47, 70, 24, 11, 98, 61, 20, 66, 106, 44, 58, 1, 13, 118, 46, 74, 86, 119, 59, 92, 53, 121, 5, 91, 69, 72, 79, 9, 30, 41, 48, 85, 77, 14, 32, 26, 23, 27, 62, 52, 33, 55, 28, 120, 37, 84, 107, 43, 122, 76, 109, 17, 103, 81, 63, 21, 112, 87, 93, 64, 113, 68, 38, 105, 71, 124, 15, 12, 50, 100, 78, 102, 73, 97, 116, 75, 51, 90, 88, 95, 36], 
4: [45, 111, 60, 54, 114, 19, 80, 110, 104, 39, 29, 49, 40, 125, 8, 99, 7, 101, 10, 47, 24, 28, 67, 11, 98, 109, 6, 70, 18, 62, 23, 106, 91, 35, 9, 30, 46, 52, 86, 119, 59, 65, 82, 92, 123, 89, 27, 37, 121, 5, 72, 13, 57, 58, 117, 118, 2, 74, 41, 96, 61, 87, 32, 120, 53, 107, 26, 43, 44, 1, 79, 115, 3, 100, 103, 55, 63, 38, 78, 105, 21, 56, 124, 66, 84, 20, 122, 64, 50, 12, 17, 116, 14, 112, 71, 42, 16, 33, 81, 102, 73, 94, 113, 51, 90, 15, 88, 95, 75, 97, 36, 108], 
5: [99, 104, 54, 60, 114, 70, 98, 125, 19, 7, 45, 111, 10, 40, 11, 8, 80, 101, 110, 25, 39, 18, 24, 47, 49, 67, 29, 66, 107, 31, 91, 9, 41, 48, 77, 82, 92, 26, 57, 44, 1, 79, 115, 13, 52, 46, 85, 2, 30, 86, 96, 119, 59, 65, 34, 123, 62, 37, 122, 58, 69, 72, 117, 118, 4, 35, 6, 61, 32, 53, 106, 121, 109, 116, 63, 55, 14, 21, 112, 71, 56, 93, 124, 43, 94, 50, 12, 17, 100, 102, 89, 105, 87, 120, 3, 81, 78, 51, 64, 16, 113, 68, 103, 73, 90, 15, 76, 75, 42, 88, 36, 83], 
6: [111, 7, 54, 60, 24, 19, 101, 45, 18, 67, 49, 11, 29, 99, 8, 80, 110, 77, 47, 40, 98, 13, 46, 119, 41, 22, 59, 10, 39, 43, 4, 2, 25, 86, 96, 34, 92, 123, 82, 27, 121, 106, 69, 57, 58, 72, 91, 117, 35, 79, 109, 48, 52, 85, 9, 74, 30, 12, 38, 112, 71, 28, 87, 20, 23, 26, 107, 122, 84, 5, 44, 1, 115, 118, 89, 61, 124, 32, 93, 66, 37, 53, 62, 3, 68, 81, 100, 103, 63, 21, 55, 56, 120, 94, 17, 102, 64, 42, 33, 50, 116, 51, 73, 90, 95, 113, 76, 88, 16, 97, 75, 36, 108], 
7: [54, 114, 45, 60, 80, 8, 104, 111, 29, 98, 11, 99, 110, 19, 101, 24, 18, 49, 40, 67, 125, 13, 6, 34, 65, 123, 70, 39, 47, 35, 25, 41, 119, 9, 92, 77, 22, 59, 82, 10, 5, 79, 44, 115, 117, 1, 46, 48, 52, 74, 85, 96, 2, 21, 28, 71, 87, 124, 84, 66, 20, 53, 106, 121, 122, 107, 72, 91, 57, 69, 109, 118, 4, 31, 68, 105, 112, 32, 93, 120, 62, 26, 37, 23, 27, 43, 50, 33, 38, 55, 63, 89, 61, 56, 12, 17, 102, 73, 42, 64, 3, 116, 103, 100, 90, 88, 94, 113, 75, 51, 95, 97, 15, 16, 36, 76, 83], 
8: [114, 104, 54, 60, 19, 80, 7, 45, 111, 98, 101, 99, 18, 29, 67, 11, 49, 125, 30, 10, 22, 34, 65, 92, 123, 24, 39, 47, 70, 43, 9, 46, 74, 85, 119, 59, 82, 77, 37, 53, 13, 57, 69, 91, 117, 1, 109, 25, 48, 41, 2, 6, 52, 86, 96, 56, 124, 20, 26, 27, 84, 106, 107, 122, 35, 72, 5, 31, 4, 79, 115, 118, 78, 89, 102, 23, 62, 66, 68, 38, 21, 105, 112, 28, 32, 61, 71, 87, 93, 120, 50, 33, 14, 55, 63, 90, 64, 16, 88, 17, 81, 103, 100, 116, 15, 42, 97, 3, 75, 76, 51, 73, 94, 95, 108, 83, 36], 
9: [114, 104, 60, 54, 67, 11, 8, 19, 80, 99, 110, 7, 45, 111, 49, 40, 29, 98, 101, 52, 85, 41, 34, 92, 47, 125, 13, 86, 82, 123, 39, 18, 70, 24, 27, 121, 5, 58, 1, 79, 115, 25, 30, 59, 10, 22, 65, 77, 87, 62, 66, 20, 37, 23, 84, 57, 44, 72, 4, 117, 118, 2, 6, 48, 96, 119, 33, 63, 28, 93, 120, 43, 107, 31, 35, 91, 109, 68, 17, 55, 14, 38, 56, 61, 71, 53, 106, 122, 50, 100, 78, 89, 102, 105, 15, 81, 103, 21, 112, 51, 16, 94, 97, 113, 3, 42, 95, 75, 73, 90, 83, 76, 36], 
10: [19, 114, 60, 125, 8, 99, 104, 111, 45, 98, 101, 110, 7, 80, 91, 46, 47, 24, 70, 49, 11, 40, 67, 5, 119, 86, 30, 22, 65, 77, 18, 39, 106, 107, 4, 1, 13, 69, 2, 6, 48, 52, 74, 123, 82, 92, 59, 53, 26, 43, 115, 117, 109, 58, 57, 79, 35, 9, 25, 96, 85, 41, 100, 61, 23, 66, 122, 62, 37, 31, 72, 44, 78, 89, 55, 124, 32, 27, 84, 103, 116, 17, 14, 21, 63, 120, 87, 93, 28, 56, 94, 3, 12, 112, 105, 102, 38, 113, 88, 42, 50, 68, 81, 75, 73, 15, 64, 97, 16, 76, 51, 108, 90, 36], 
11: [45, 114, 54, 60, 98, 67, 101, 19, 7, 104, 111, 125, 40, 49, 110, 80, 99, 8, 39, 70, 24, 29, 85, 9, 52, 92, 123, 77, 65, 82, 18, 47, 117, 44, 79, 96, 2, 6, 74, 119, 41, 48, 34, 10, 22, 107, 62, 118, 72, 109, 5, 13, 57, 58, 69, 25, 30, 46, 38, 120, 32, 122, 27, 66, 37, 91, 35, 115, 1, 4, 31, 81, 89, 28, 87, 71, 56, 106, 121, 23, 53, 84, 20, 43, 33, 102, 21, 63, 78, 105, 93, 61, 100, 103, 116, 12, 17, 55, 14, 75, 73, 94, 113, 95, 50, 68, 88, 16, 42, 64, 3, 90, 36, 83, 76, 108], 
12: [110, 60, 80, 45, 54, 29, 67, 99, 101, 7, 111, 6, 119, 70, 39, 18, 24, 11, 40, 125, 121, 19, 13, 77, 47, 49, 98, 52, 86, 96, 123, 10, 65, 82, 71, 120, 53, 37, 5, 31, 109, 4, 25, 30, 41, 46, 85, 2, 74, 22, 34, 59, 17, 87, 32, 124, 62, 106, 107, 57, 58, 72, 91, 44, 79, 115, 117, 118, 35, 69, 48, 50, 38, 105, 56, 23, 122, 26, 66, 116, 81, 63, 112, 21, 93, 28, 27, 20, 64, 14, 61, 113, 16, 55, 51, 94, 3, 103, 100, 73, 90, 42, 95, 97, 108, 75, 36, 83], 
13: [7, 111, 54, 60, 114, 8, 19, 99, 110, 45, 104, 18, 29, 67, 11, 80, 101, 41, 52, 6, 9, 10, 47, 39, 70, 24, 40, 49, 98, 125, 30, 59, 92, 22, 123, 43, 53, 5, 58, 25, 46, 85, 86, 119, 34, 77, 82, 28, 87, 120, 66, 20, 37, 106, 107, 44, 4, 57, 1, 35, 69, 72, 79, 115, 109, 74, 96, 12, 63, 21, 56, 62, 23, 122, 31, 118, 91, 117, 33, 81, 55, 89, 32, 93, 26, 27, 3, 50, 68, 103, 17, 38, 112, 105, 61, 15, 64, 116, 100, 90, 75, 51, 73, 42, 94, 95, 113, 16, 97, 36, 76, 83], 
14: [114, 45, 104, 25, 60, 54, 29, 19, 80, 110, 101, 31, 115, 79, 111, 96, 82, 40, 49, 67, 125, 8, 99, 1, 30, 85, 86, 34, 65, 39, 70, 11, 98, 9, 48, 10, 22, 59, 92, 77, 123, 18, 24, 47, 121, 43, 122, 5, 58, 41, 2, 46, 52, 74, 84, 20, 4, 117, 72, 109, 119, 81, 78, 61, 32, 56, 124, 62, 27, 66, 107, 44, 57, 69, 91, 118, 88, 3, 103, 33, 68, 38, 55, 112, 102, 120, 23, 37, 26, 53, 116, 17, 50, 100, 21, 105, 51, 90, 94, 12, 15, 95, 113, 16, 76, 75, 97, 83, 36], 
15: [104, 114, 54, 99, 45, 60, 125, 49, 19, 8, 101, 111, 70, 40, 98, 110, 7, 80, 44, 115, 118, 9, 48, 34, 59, 82, 18, 39, 29, 13, 1, 74, 85, 10, 65, 123, 92, 24, 47, 120, 107, 43, 117, 35, 31, 69, 30, 25, 46, 41, 52, 86, 22, 33, 103, 63, 28, 87, 20, 26, 53, 5, 4, 58, 72, 21, 112, 78, 89, 105, 23, 27, 37, 106, 62, 66, 84, 91, 100, 81, 14, 102, 55, 61, 56, 93, 121, 122, 3, 68, 113, 97, 50, 108, 76, 90, 73, 88, 95, 17, 116, 36, 42, 16, 64, 83], 
16: [110, 45, 114, 8, 57, 104, 85, 60, 54, 111, 70, 11, 99, 19, 7, 30, 22, 34, 65, 24, 39, 47, 67, 98, 125, 49, 28, 31, 35, 4, 96, 119, 2, 9, 86, 92, 123, 10, 82, 18, 78, 62, 106, 27, 109, 115, 117, 5, 69, 48, 52, 41, 46, 59, 77, 38, 121, 122, 37, 66, 84, 58, 91, 1, 6, 50, 105, 63, 32, 56, 71, 107, 20, 26, 79, 118, 13, 81, 12, 17, 55, 102, 14, 93, 61, 87, 120, 124, 43, 100, 75, 33, 51, 73, 113, 42, 88, 116, 95, 97, 94, 90, 15, 83, 108, 36], 
17: [54, 114, 110, 19, 101, 45, 92, 123, 24, 125, 80, 99, 7, 104, 52, 86, 65, 82, 18, 98, 11, 8, 46, 9, 41, 10, 34, 70, 39, 47, 67, 29, 40, 49, 93, 26, 44, 115, 25, 77, 71, 62, 106, 107, 69, 5, 91, 1, 4, 13, 118, 113, 6, 2, 85, 119, 59, 22, 12, 61, 120, 66, 37, 122, 27, 84, 23, 121, 58, 79, 117, 31, 48, 74, 96, 63, 55, 89, 28, 87, 57, 35, 109, 14, 21, 124, 32, 53, 20, 3, 81, 103, 100, 78, 105, 16, 38, 112, 36, 94, 76, 51, 73, 90, 75, 95, 15, 108], 
18: [54, 111, 60, 114, 8, 7, 19, 99, 101, 110, 45, 49, 125, 80, 123, 24, 47, 11, 29, 67, 40, 98, 44, 6, 48, 74, 59, 92, 34, 21, 70, 39, 26, 13, 72, 117, 41, 46, 10, 22, 77, 82, 43, 5, 31, 91, 118, 9, 2, 25, 86, 85, 96, 119, 71, 93, 20, 53, 23, 121, 58, 1, 4, 35, 69, 79, 109, 115, 50, 68, 38, 56, 61, 32, 120, 66, 37, 84, 106, 107, 122, 17, 12, 116, 63, 105, 112, 28, 87, 124, 3, 81, 103, 14, 55, 78, 89, 97, 33, 100, 51, 64, 15, 42, 88, 16, 95, 94, 75, 73, 90, 108, 76, 83, 36], 
19: [114, 54, 8, 80, 111, 104, 45, 47, 29, 67, 98, 11, 125, 110, 99, 101, 7, 22, 10, 39, 18, 24, 70, 40, 49, 91, 92, 123, 35, 6, 9, 30, 41, 52, 2, 46, 74, 85, 86, 65, 34, 59, 77, 82, 26, 107, 69, 5, 117, 1, 4, 13, 44, 58, 79, 96, 25, 48, 119, 56, 66, 43, 121, 122, 57, 115, 31, 72, 109, 118, 120, 87, 62, 23, 27, 37, 53, 84, 68, 100, 103, 17, 55, 14, 38, 93, 28, 71, 32, 42, 33, 116, 81, 63, 21, 112, 78, 102, 89, 105, 94, 3, 12, 50, 64, 95, 15, 51, 16, 88, 97, 75, 76, 73, 90, 36, 108], 
20: [54, 60, 45, 114, 67, 8, 7, 104, 111, 123, 29, 49, 125, 40, 80, 99, 110, 101, 22, 59, 77, 47, 18, 24, 98, 11, 66, 23, 118, 115, 30, 41, 96, 9, 82, 34, 33, 39, 84, 13, 58, 69, 79, 6, 25, 65, 92, 120, 43, 106, 53, 27, 1, 57, 117, 31, 46, 48, 52, 85, 86, 119, 55, 38, 56, 61, 124, 28, 71, 121, 26, 44, 72, 4, 109, 3, 14, 32, 37, 62, 122, 63, 112, 87, 93, 50, 68, 81, 78, 102, 21, 89, 105, 90, 95, 15, 42, 64, 97, 103, 12, 116, 17, 83, 75, 51, 16, 73, 88, 76, 36], 
21: [18, 7, 54, 114, 99, 104, 111, 60, 40, 29, 80, 8, 101, 45, 74, 123, 11, 49, 98, 125, 19, 44, 47, 67, 13, 52, 10, 34, 92, 70, 39, 112, 23, 5, 117, 4, 6, 41, 48, 119, 2, 46, 65, 77, 82, 22, 59, 120, 28, 53, 69, 72, 31, 91, 109, 115, 35, 118, 9, 96, 68, 93, 26, 121, 37, 43, 58, 1, 79, 64, 50, 103, 63, 89, 105, 56, 32, 61, 124, 84, 106, 107, 122, 20, 12, 17, 33, 100, 14, 87, 88, 15, 97, 3, 116, 55, 90, 113, 81, 76, 51, 95, 42, 108, 73, 94, 36, 75, 83], 
22: [54, 19, 80, 111, 60, 114, 8, 110, 45, 104, 29, 40, 98, 99, 101, 7, 34, 65, 39, 70, 47, 24, 49, 67, 11, 125, 69, 25, 41, 48, 10, 77, 123, 18, 35, 1, 52, 6, 74, 2, 46, 85, 59, 82, 92, 53, 27, 43, 20, 57, 79, 13, 115, 117, 30, 96, 9, 86, 119, 89, 28, 56, 120, 66, 26, 84, 122, 107, 72, 58, 44, 109, 118, 32, 87, 93, 62, 95, 33, 68, 103, 38, 78, 102, 14, 71, 124, 94, 50, 100, 116, 55, 63, 21, 105, 112, 42, 88, 16, 81, 12, 17, 83, 97, 113, 76, 73, 90, 64, 15, 108, 75, 51, 36], 
23: [125, 49, 99, 101, 111, 114, 54, 60, 67, 80, 110, 104, 45, 98, 40, 29, 8, 7, 19, 77, 59, 82, 47, 18, 11, 20, 4, 9, 74, 123, 10, 34, 39, 24, 84, 37, 118, 58, 96, 6, 85, 46, 48, 119, 52, 30, 92, 65, 63, 121, 66, 27, 91, 117, 72, 79, 1, 44, 13, 35, 31, 86, 2, 55, 21, 120, 124, 61, 28, 106, 122, 53, 62, 43, 26, 115, 109, 57, 89, 112, 38, 93, 71, 68, 116, 103, 33, 17, 78, 87, 56, 51, 64, 3, 12, 105, 14, 94, 42, 81, 88, 97, 15, 108, 76, 73, 113, 75, 90, 83, 36], 
24: [54, 45, 60, 110, 7, 19, 104, 47, 29, 125, 11, 8, 99, 101, 80, 6, 86, 92, 18, 40, 67, 98, 49, 25, 34, 123, 10, 22, 65, 77, 82, 39, 70, 117, 119, 2, 30, 41, 46, 52, 85, 59, 66, 27, 26, 5, 13, 35, 57, 118, 4, 31, 44, 69, 9, 74, 96, 48, 32, 61, 121, 20, 53, 106, 109, 115, 1, 58, 72, 79, 17, 68, 112, 55, 102, 93, 71, 23, 43, 84, 107, 122, 37, 12, 105, 38, 28, 56, 124, 87, 33, 100, 103, 116, 81, 14, 89, 63, 90, 88, 113, 3, 50, 42, 94, 16, 64, 51, 15, 95, 36, 75, 76, 73, 108], 
25: [114, 80, 101, 110, 104, 54, 60, 29, 99, 7, 45, 111, 85, 34, 24, 40, 98, 8, 19, 115, 77, 22, 70, 11, 67, 49, 125, 5, 79, 46, 48, 74, 86, 82, 123, 47, 39, 18, 14, 69, 72, 31, 6, 9, 30, 41, 96, 119, 65, 10, 59, 92, 112, 107, 44, 13, 57, 1, 52, 2, 102, 93, 61, 32, 62, 66, 53, 20, 84, 122, 27, 121, 58, 91, 117, 118, 109, 68, 105, 71, 120, 26, 37, 43, 106, 3, 17, 81, 100, 55, 89, 87, 56, 124, 76, 113, 12, 50, 103, 51, 90, 95, 88, 33, 116, 15, 94, 97, 108, 73, 83, 75, 36], 
26: [60, 125, 19, 54, 114, 18, 8, 101, 110, 99, 45, 104, 111, 123, 24, 40, 80, 7, 46, 48, 59, 92, 10, 39, 47, 29, 49, 67, 5, 44, 1, 74, 86, 65, 82, 22, 70, 61, 66, 69, 117, 91, 118, 41, 2, 6, 30, 119, 77, 34, 62, 43, 106, 122, 31, 58, 4, 35, 57, 25, 85, 96, 17, 116, 55, 28, 93, 124, 20, 23, 84, 13, 115, 109, 103, 63, 38, 71, 32, 53, 107, 121, 50, 21, 112, 102, 120, 87, 75, 3, 68, 12, 100, 14, 78, 89, 105, 51, 42, 64, 15, 88, 33, 81, 73, 16, 94, 76, 90, 36, 108], 
27: [111, 104, 45, 114, 60, 54, 110, 101, 8, 30, 24, 98, 11, 40, 49, 80, 99, 19, 7, 9, 52, 22, 47, 29, 67, 6, 41, 82, 123, 34, 65, 39, 70, 118, 79, 109, 4, 85, 86, 119, 25, 46, 48, 77, 92, 59, 10, 87, 56, 66, 23, 53, 20, 43, 117, 69, 58, 72, 96, 2, 102, 28, 84, 107, 37, 91, 115, 1, 13, 35, 97, 89, 55, 38, 124, 71, 61, 32, 122, 106, 121, 17, 33, 112, 78, 63, 14, 120, 88, 95, 16, 3, 100, 103, 68, 105, 90, 113, 81, 12, 51, 73, 94, 64, 15, 76, 42, 83, 108, 75, 36], 
28: [101, 45, 114, 7, 110, 80, 104, 111, 54, 60, 40, 99, 4, 11, 29, 98, 19, 8, 35, 22, 89, 39, 70, 49, 67, 125, 13, 115, 109, 6, 9, 52, 119, 34, 65, 123, 18, 24, 47, 46, 74, 30, 41, 86, 92, 10, 59, 82, 77, 87, 23, 26, 20, 27, 84, 1, 57, 58, 117, 69, 118, 2, 21, 63, 93, 37, 53, 62, 66, 122, 106, 91, 44, 16, 78, 105, 61, 124, 32, 71, 107, 121, 43, 73, 17, 50, 100, 33, 103, 55, 120, 56, 75, 15, 94, 3, 12, 81, 102, 95, 113, 42, 68, 116, 51, 88, 97, 90, 36, 83], 
29: [54, 80, 45, 60, 114, 40, 19, 101, 110, 7, 99, 104, 111, 39, 121, 8, 47, 24, 49, 67, 11, 98, 125, 25, 119, 59, 22, 34, 82, 70, 18, 122, 44, 72, 31, 1, 117, 9, 6, 2, 52, 74, 96, 86, 65, 92, 77, 123, 57, 91, 13, 79, 118, 4, 35, 41, 30, 48, 85, 68, 23, 84, 43, 20, 5, 58, 69, 109, 115, 14, 21, 38, 89, 112, 105, 28, 71, 93, 56, 27, 26, 37, 62, 66, 107, 12, 50, 103, 55, 87, 61, 120, 124, 32, 33, 81, 63, 102, 95, 3, 17, 100, 116, 90, 42, 64, 94, 83, 51, 88, 97, 15, 113, 75, 36, 108], 
30: [60, 8, 104, 111, 114, 19, 101, 110, 45, 80, 99, 10, 24, 11, 29, 67, 40, 49, 98, 125, 27, 57, 58, 52, 86, 119, 65, 82, 123, 47, 39, 70, 62, 43, 13, 91, 79, 9, 25, 41, 46, 85, 59, 77, 22, 34, 92, 102, 56, 66, 20, 5, 1, 4, 72, 115, 117, 109, 6, 2, 48, 74, 96, 14, 38, 78, 32, 53, 26, 23, 106, 107, 31, 69, 35, 118, 33, 89, 28, 93, 120, 124, 37, 84, 122, 121, 88, 81, 105, 61, 87, 16, 12, 116, 100, 103, 55, 63, 112, 64, 42, 94, 97, 3, 75, 73, 15, 51, 90, 95, 76, 36, 83], 
31: [45, 54, 114, 80, 104, 96, 60, 29, 67, 125, 110, 82, 65, 70, 49, 40, 19, 8, 99, 101, 7, 85, 34, 18, 24, 39, 98, 11, 5, 35, 117, 48, 25, 59, 77, 92, 123, 47, 14, 93, 57, 79, 69, 115, 72, 41, 74, 86, 2, 119, 10, 106, 121, 1, 44, 91, 9, 46, 52, 30, 62, 20, 23, 26, 43, 53, 122, 37, 58, 13, 118, 109, 50, 68, 38, 112, 56, 61, 124, 66, 84, 107, 12, 33, 116, 55, 78, 21, 105, 32, 71, 120, 16, 17, 81, 103, 63, 102, 15, 100, 108, 51, 42, 64, 88, 97, 95, 83, 90, 113, 75, 36], 
32: [114, 54, 60, 11, 99, 101, 7, 104, 111, 45, 77, 39, 47, 24, 40, 125, 8, 110, 80, 19, 79, 74, 2, 18, 70, 29, 98, 49, 115, 118, 69, 119, 25, 30, 41, 86, 10, 22, 59, 92, 5, 1, 4, 58, 6, 96, 46, 48, 123, 65, 102, 124, 107, 91, 35, 57, 72, 109, 13, 85, 52, 38, 89, 71, 27, 37, 106, 20, 26, 66, 44, 31, 88, 12, 81, 55, 112, 14, 105, 87, 28, 61, 93, 53, 43, 84, 121, 122, 73, 94, 97, 113, 42, 3, 50, 103, 21, 78, 56, 95, 33, 116, 17, 100, 16, 64, 90, 76, 36, 83], 
33: [54, 60, 67, 114, 7, 104, 111, 45, 123, 11, 20, 8, 19, 9, 70, 29, 80, 99, 110, 101, 41, 85, 96, 30, 82, 22, 39, 24, 40, 98, 125, 49, 58, 118, 13, 52, 59, 34, 92, 47, 18, 43, 84, 79, 1, 31, 35, 69, 74, 119, 65, 120, 23, 66, 121, 27, 44, 4, 72, 117, 109, 25, 2, 6, 46, 48, 88, 50, 14, 87, 28, 56, 61, 53, 106, 122, 57, 15, 97, 3, 68, 100, 38, 63, 78, 102, 21, 105, 93, 32, 37, 62, 26, 81, 103, 55, 112, 90, 64, 42, 73, 95, 75, 51, 16, 113, 83, 76], 
34: [80, 54, 114, 60, 8, 7, 110, 45, 104, 111, 29, 40, 67, 98, 19, 101, 99, 117, 25, 22, 82, 24, 47, 18, 11, 49, 125, 115, 9, 85, 2, 77, 59, 65, 123, 39, 70, 107, 31, 1, 57, 79, 86, 46, 48, 92, 93, 122, 72, 35, 69, 109, 6, 41, 30, 52, 74, 96, 119, 71, 27, 23, 37, 20, 84, 121, 5, 44, 13, 91, 68, 14, 63, 112, 28, 56, 61, 120, 124, 26, 43, 53, 66, 106, 17, 81, 100, 89, 21, 105, 87, 97, 113, 33, 50, 103, 116, 38, 55, 78, 102, 16, 88, 15, 12, 108, 90, 51, 95, 94, 83, 76, 73, 36], 
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100: [60, 114, 19, 54, 10, 80, 99, 101, 110, 45, 104, 111, 41, 39, 70, 11, 98, 107, 7, 8, 109, 2, 74, 85, 34, 24, 67, 29, 40, 91, 4, 115, 6, 25, 9, 46, 86, 119, 22, 65, 82, 92, 123, 18, 61, 5, 57, 79, 30, 52, 48, 103, 87, 56, 43, 84, 122, 13, 1, 117, 35, 105, 28, 120, 27, 26, 53, 62, 106, 121, 31, 58, 72, 44, 33, 116, 14, 63, 21, 32, 93, 37, 95, 17, 50, 81, 102, 89, 78, 124, 15, 88, 94, 97, 113, 38, 112, 75, 51, 73, 90, 16, 3, 12, 68, 42, 108, 76], 
101: [45, 54, 60, 114, 40, 80, 111, 11, 29, 7, 8, 19, 99, 110, 18, 70, 67, 49, 98, 125, 74, 25, 65, 77, 82, 123, 39, 47, 24, 79, 115, 6, 30, 46, 52, 85, 119, 59, 10, 34, 92, 22, 89, 28, 23, 44, 58, 109, 2, 86, 9, 48, 41, 26, 27, 53, 62, 107, 122, 5, 13, 57, 1, 4, 31, 35, 69, 91, 117, 118, 38, 102, 105, 32, 87, 93, 66, 37, 43, 20, 106, 84, 121, 17, 103, 14, 55, 21, 78, 56, 61, 71, 120, 124, 12, 68, 81, 100, 88, 3, 33, 116, 76, 15, 64, 42, 94, 95, 75, 51, 73, 90, 97, 113, 36, 108, 83], 
102: [104, 111, 60, 114, 8, 101, 54, 125, 45, 30, 92, 70, 24, 11, 49, 98, 7, 19, 80, 46, 48, 25, 86, 65, 82, 77, 47, 29, 67, 40, 72, 74, 2, 22, 39, 32, 27, 69, 57, 91, 79, 9, 85, 10, 34, 59, 71, 66, 62, 37, 43, 84, 107, 1, 5, 35, 58, 109, 115, 6, 96, 119, 88, 116, 38, 55, 78, 89, 61, 124, 26, 121, 31, 44, 4, 118, 117, 68, 14, 56, 93, 53, 20, 106, 122, 42, 95, 33, 28, 87, 113, 100, 103, 81, 105, 112, 15, 64, 16, 97, 76, 90, 94, 3, 73, 108, 36, 75, 83], 
103: [49, 60, 40, 19, 99, 101, 104, 54, 114, 29, 125, 80, 110, 111, 45, 11, 67, 98, 7, 8, 1, 74, 52, 46, 85, 10, 22, 39, 24, 18, 122, 4, 44, 118, 6, 96, 65, 34, 59, 92, 77, 82, 123, 70, 26, 13, 91, 79, 9, 25, 30, 41, 2, 86, 100, 61, 43, 53, 23, 121, 31, 58, 117, 119, 81, 14, 55, 21, 112, 28, 32, 93, 56, 27, 62, 84, 5, 35, 115, 15, 68, 38, 78, 89, 120, 124, 66, 20, 107, 88, 3, 17, 33, 116, 63, 102, 95, 113, 50, 76, 90, 42, 97, 94, 12, 73, 64, 108], 
104: [114, 54, 60, 8, 99, 45, 111, 49, 98, 125, 7, 19, 80, 110, 65, 70, 11, 40, 29, 67, 46, 92, 77, 39, 24, 47, 9, 25, 30, 52, 96, 10, 59, 34, 22, 82, 123, 1, 5, 57, 31, 58, 72, 117, 2, 41, 48, 86, 74, 119, 85, 112, 78, 43, 27, 62, 84, 122, 13, 4, 35, 44, 69, 79, 91, 109, 115, 118, 102, 28, 23, 37, 20, 26, 53, 66, 106, 107, 121, 68, 14, 63, 89, 21, 32, 56, 71, 93, 61, 87, 120, 124, 15, 33, 50, 103, 55, 113, 17, 116, 81, 100, 16, 88, 3, 76, 51, 90, 42, 64, 95, 97, 94, 73, 108, 75, 36, 83], 
105: [60, 114, 7, 101, 99, 45, 54, 39, 29, 98, 8, 80, 110, 111, 70, 47, 40, 11, 125, 19, 59, 18, 24, 67, 109, 25, 119, 85, 65, 34, 62, 106, 72, 4, 57, 69, 91, 2, 52, 30, 48, 9, 86, 41, 10, 22, 82, 92, 123, 84, 107, 121, 5, 31, 35, 44, 118, 13, 79, 74, 96, 71, 32, 87, 28, 120, 66, 37, 53, 1, 115, 50, 12, 81, 100, 63, 21, 89, 56, 61, 124, 93, 23, 26, 27, 20, 43, 73, 33, 14, 16, 15, 97, 113, 17, 116, 55, 102, 75, 51, 42, 88, 3, 95, 76, 64, 94, 83, 108], 
106: [54, 60, 45, 114, 67, 8, 7, 104, 111, 10, 47, 125, 80, 99, 101, 110, 69, 46, 59, 82, 24, 70, 11, 40, 49, 98, 53, 4, 6, 65, 77, 123, 18, 37, 84, 31, 13, 35, 91, 72, 109, 30, 86, 2, 48, 96, 34, 92, 87, 61, 20, 26, 5, 57, 44, 58, 115, 117, 118, 9, 25, 41, 52, 74, 85, 119, 78, 89, 105, 71, 93, 23, 43, 62, 66, 79, 3, 17, 55, 28, 32, 124, 120, 27, 107, 42, 113, 12, 63, 73, 16, 33, 81, 100, 21, 38, 102, 112, 95, 88, 50, 116, 76, 64, 15, 97, 108, 51, 90, 36, 75], 
107: [19, 54, 60, 114, 39, 11, 98, 8, 7, 80, 101, 45, 104, 111, 10, 34, 49, 110, 99, 5, 41, 82, 47, 40, 29, 125, 122, 1, 115, 25, 46, 22, 65, 123, 18, 24, 91, 79, 13, 6, 2, 9, 30, 74, 85, 86, 92, 100, 57, 4, 35, 44, 69, 109, 117, 48, 52, 96, 119, 32, 87, 27, 53, 43, 31, 72, 17, 81, 63, 89, 102, 105, 71, 56, 61, 93, 120, 26, 62, 37, 66, 106, 121, 94, 12, 116, 14, 112, 28, 15, 21, 38, 55, 78, 90, 113, 3, 68, 103, 16, 64, 95, 97, 88, 108, 75, 51, 73, 76, 36, 83], 
108: [54, 67, 80, 35, 45, 104, 111, 2, 60, 114, 34, 70, 40, 98, 8, 19, 99, 74, 96, 82, 29, 49, 125, 101, 110, 31, 86, 10, 59, 65, 22, 123, 18, 11, 71, 124, 117, 118, 48, 25, 46, 77, 92, 47, 24, 39, 23, 37, 106, 107, 69, 72, 91, 6, 85, 119, 63, 56, 26, 84, 122, 57, 44, 109, 52, 89, 21, 112, 61, 87, 93, 53, 27, 43, 62, 121, 4, 15, 68, 12, 50, 116, 78, 102, 105, 120, 64, 95, 42, 97, 113, 17, 81, 100, 55, 90, 103, 51, 88, 76, 16, 36, 83], 
109: [60, 57, 45, 54, 114, 67, 8, 101, 104, 111, 47, 40, 11, 7, 19, 80, 110, 119, 87, 29, 98, 125, 4, 79, 69, 77, 10, 34, 59, 82, 18, 24, 39, 70, 56, 37, 52, 6, 30, 46, 2, 41, 22, 65, 92, 123, 28, 71, 124, 53, 27, 106, 13, 72, 91, 117, 115, 9, 25, 86, 74, 100, 105, 43, 62, 107, 122, 5, 58, 31, 35, 38, 89, 32, 61, 26, 23, 66, 20, 84, 121, 50, 12, 116, 14, 55, 21, 78, 102, 112, 120, 51, 95, 97, 33, 81, 63, 75, 73, 90, 16, 64, 94, 17, 68, 42, 88, 3, 113, 108, 76, 83], 
110: [114, 80, 45, 54, 60, 40, 99, 104, 111, 29, 98, 19, 7, 101, 18, 39, 24, 11, 49, 67, 125, 41, 25, 85, 86, 22, 34, 77, 123, 47, 70, 44, 35, 58, 48, 2, 9, 30, 52, 119, 10, 65, 59, 82, 92, 66, 84, 72, 1, 31, 57, 91, 4, 13, 115, 117, 6, 46, 74, 96, 28, 93, 23, 53, 62, 26, 27, 43, 121, 122, 69, 5, 79, 109, 118, 12, 63, 38, 78, 71, 120, 20, 106, 107, 17, 50, 14, 89, 105, 32, 61, 87, 56, 124, 16, 100, 103, 116, 55, 112, 88, 113, 33, 68, 81, 75, 95, 97, 3, 51, 73, 42, 15, 94, 83, 36, 108], 
111: [60, 114, 54, 104, 49, 125, 8, 7, 80, 19, 99, 101, 110, 70, 18, 67, 11, 29, 40, 98, 6, 22, 59, 47, 39, 72, 30, 77, 10, 34, 82, 92, 123, 43, 4, 13, 91, 25, 9, 46, 48, 52, 74, 2, 85, 86, 96, 119, 37, 62, 23, 27, 121, 5, 1, 35, 44, 57, 58, 69, 79, 115, 117, 118, 109, 102, 28, 56, 87, 93, 120, 124, 66, 53, 26, 84, 106, 107, 20, 122, 81, 116, 55, 89, 78, 112, 21, 32, 71, 61, 3, 68, 33, 50, 63, 14, 38, 105, 94, 97, 12, 100, 103, 64, 42, 88, 76, 73, 16, 15, 113, 95, 51, 90, 83, 108, 75, 36], 
112: [104, 114, 7, 111, 60, 54, 29, 8, 80, 99, 25, 24, 49, 98, 19, 110, 72, 6, 96, 59, 34, 18, 47, 67, 125, 46, 74, 65, 77, 82, 68, 39, 21, 5, 31, 79, 117, 41, 48, 2, 86, 119, 22, 92, 10, 123, 124, 23, 37, 53, 84, 121, 13, 58, 69, 4, 35, 44, 109, 118, 9, 30, 52, 32, 93, 27, 26, 43, 20, 107, 122, 57, 91, 1, 115, 103, 14, 71, 87, 66, 106, 76, 12, 50, 63, 55, 61, 56, 120, 51, 15, 64, 97, 3, 33, 102, 90, 94, 113, 17, 116, 100, 36, 42, 88, 108, 73, 95, 83], 
113: [54, 104, 60, 114, 98, 125, 110, 11, 40, 7, 80, 99, 45, 111, 86, 34, 24, 70, 39, 101, 25, 46, 2, 10, 65, 17, 47, 29, 49, 67, 106, 72, 44, 52, 74, 9, 119, 59, 22, 92, 82, 32, 62, 37, 5, 69, 1, 4, 79, 115, 118, 48, 85, 6, 77, 71, 61, 93, 120, 27, 66, 84, 107, 121, 58, 35, 57, 41, 96, 81, 102, 105, 28, 53, 122, 13, 31, 109, 3, 12, 103, 100, 55, 14, 21, 63, 89, 112, 124, 23, 78, 87, 73, 15, 97, 33, 50, 116, 76, 16, 95, 88, 94, 108, 90, 36], 
114: [104, 45, 111, 54, 60, 8, 7, 80, 110, 125, 19, 99, 101, 65, 70, 11, 29, 40, 67, 49, 98, 9, 34, 92, 18, 39, 47, 84, 25, 85, 86, 59, 22, 10, 82, 123, 77, 1, 31, 35, 91, 115, 2, 30, 41, 48, 52, 46, 74, 96, 119, 78, 53, 62, 43, 58, 4, 5, 13, 57, 69, 72, 44, 79, 109, 117, 118, 14, 28, 87, 124, 93, 120, 23, 26, 66, 20, 27, 37, 107, 106, 121, 122, 68, 55, 89, 21, 102, 105, 112, 32, 56, 61, 71, 17, 33, 100, 63, 38, 15, 88, 50, 103, 116, 16, 42, 97, 113, 3, 51, 95, 94, 76, 75, 73, 90, 83, 36, 108], 
115: [54, 114, 80, 101, 45, 60, 7, 110, 104, 111, 25, 34, 123, 8, 19, 99, 77, 82, 70, 11, 49, 29, 40, 125, 98, 1, 79, 2, 9, 74, 86, 10, 65, 22, 92, 47, 18, 24, 39, 14, 20, 107, 5, 31, 117, 46, 30, 41, 85, 59, 61, 28, 32, 13, 44, 57, 58, 69, 91, 109, 6, 48, 52, 89, 56, 87, 124, 43, 122, 84, 106, 4, 72, 118, 17, 100, 55, 71, 120, 93, 62, 23, 26, 27, 53, 121, 37, 15, 81, 38, 21, 78, 102, 95, 12, 116, 105, 112, 90, 16, 88, 113, 97, 68, 50, 103, 51, 73, 76, 75, 83, 36], 
116: [111, 60, 49, 45, 54, 114, 92, 125, 19, 80, 110, 104, 18, 11, 67, 98, 8, 7, 99, 101, 74, 86, 10, 77, 47, 24, 70, 40, 29, 26, 62, 66, 5, 72, 91, 44, 2, 46, 48, 22, 34, 82, 39, 124, 1, 31, 117, 4, 35, 57, 79, 109, 30, 85, 119, 96, 59, 65, 102, 56, 71, 120, 23, 37, 43, 121, 107, 13, 58, 115, 6, 25, 50, 63, 53, 122, 84, 12, 100, 14, 32, 20, 106, 64, 94, 68, 81, 103, 89, 21, 78, 105, 28, 42, 38, 112, 95, 36, 75, 73, 113, 3, 83, 108, 51, 15, 16, 76], 
117: [54, 80, 45, 104, 60, 114, 34, 82, 11, 29, 8, 19, 7, 110, 111, 24, 18, 40, 49, 67, 99, 101, 59, 77, 123, 47, 98, 125, 31, 96, 10, 65, 92, 22, 70, 43, 122, 44, 57, 79, 35, 115, 6, 52, 9, 46, 2, 30, 68, 56, 26, 5, 91, 4, 58, 72, 1, 109, 25, 41, 48, 85, 74, 38, 93, 120, 20, 27, 53, 66, 84, 23, 106, 107, 13, 69, 21, 78, 89, 112, 28, 37, 121, 116, 14, 55, 63, 61, 71, 87, 124, 75, 12, 50, 17, 33, 103, 100, 102, 51, 90, 64, 15, 94, 16, 42, 88, 95, 81, 83, 108, 36], 
118: [54, 49, 60, 114, 67, 99, 111, 45, 104, 59, 11, 40, 29, 125, 8, 19, 80, 7, 101, 110, 77, 18, 24, 39, 47, 70, 98, 44, 52, 48, 96, 82, 92, 123, 62, 20, 69, 58, 86, 9, 2, 41, 74, 119, 85, 65, 22, 32, 71, 23, 26, 27, 37, 66, 53, 72, 5, 35, 4, 6, 25, 30, 46, 61, 87, 93, 84, 106, 121, 13, 31, 91, 115, 33, 103, 55, 56, 28, 124, 43, 122, 15, 3, 17, 50, 63, 21, 105, 112, 120, 42, 12, 81, 14, 38, 78, 89, 102, 90, 64, 95, 113, 68, 36, 73, 88, 94, 108, 76, 16, 51, 83], 
119: [45, 60, 114, 67, 29, 125, 7, 8, 80, 110, 99, 101, 104, 111, 39, 11, 98, 19, 10, 24, 70, 40, 49, 109, 6, 48, 2, 30, 65, 77, 92, 47, 18, 53, 35, 57, 25, 41, 86, 74, 59, 22, 34, 82, 123, 66, 37, 121, 5, 4, 13, 31, 72, 1, 79, 91, 118, 46, 52, 9, 85, 12, 63, 56, 28, 71, 87, 124, 32, 62, 23, 26, 27, 122, 58, 69, 38, 89, 105, 61, 93, 120, 84, 107, 20, 106, 94, 100, 21, 112, 73, 3, 50, 33, 68, 17, 81, 116, 14, 102, 16, 97, 113, 103, 51, 90, 64, 42, 75, 88, 83, 108, 36], 
120: [54, 60, 114, 80, 111, 11, 19, 7, 99, 110, 45, 104, 123, 67, 125, 8, 101, 52, 22, 63, 47, 39, 18, 40, 49, 29, 98, 62, 13, 48, 41, 74, 9, 34, 82, 70, 20, 53, 66, 4, 79, 117, 25, 30, 119, 59, 65, 10, 87, 23, 69, 115, 46, 6, 85, 96, 12, 81, 21, 56, 37, 43, 106, 107, 121, 57, 58, 72, 1, 5, 31, 44, 109, 118, 33, 17, 116, 89, 105, 78, 71, 27, 26, 84, 122, 15, 50, 100, 14, 38, 93, 124, 28, 90, 95, 113, 3, 103, 112, 73, 42, 64, 97, 83, 16, 94, 36, 75, 76, 108], 
121: [29, 54, 111, 60, 114, 19, 7, 99, 110, 45, 104, 40, 49, 125, 80, 101, 9, 92, 47, 18, 39, 24, 70, 11, 67, 98, 6, 2, 85, 119, 59, 34, 82, 71, 37, 1, 4, 44, 91, 31, 25, 48, 52, 86, 96, 77, 123, 12, 23, 122, 84, 5, 57, 58, 72, 118, 30, 41, 74, 68, 14, 62, 20, 35, 79, 117, 115, 109, 50, 105, 112, 56, 61, 87, 93, 124, 120, 26, 27, 66, 107, 3, 116, 17, 33, 81, 103, 55, 63, 21, 38, 102, 28, 32, 100, 16, 94, 113, 51, 64, 95, 42, 83, 76, 73, 90, 15, 97, 36, 108, 75], 
122: [60, 29, 98, 104, 54, 114, 49, 7, 8, 19, 80, 99, 101, 110, 45, 111, 77, 82, 11, 40, 125, 1, 65, 34, 123, 47, 70, 67, 107, 91, 117, 46, 2, 10, 22, 24, 18, 56, 44, 5, 79, 6, 25, 48, 52, 86, 85, 96, 119, 92, 61, 26, 66, 121, 13, 57, 31, 35, 109, 115, 41, 9, 30, 74, 103, 81, 63, 14, 78, 93, 43, 23, 37, 4, 118, 69, 68, 55, 71, 28, 124, 62, 20, 27, 50, 17, 100, 38, 112, 32, 87, 120, 51, 12, 33, 116, 21, 89, 102, 75, 16, 97, 3, 76, 64, 94, 88, 113, 15, 108, 83], 
123: [54, 60, 45, 114, 8, 19, 7, 99, 110, 101, 104, 111, 18, 11, 67, 80, 52, 82, 24, 70, 29, 40, 49, 125, 115, 41, 65, 22, 59, 92, 34, 47, 39, 26, 20, 69, 117, 25, 46, 2, 9, 74, 30, 96, 10, 77, 61, 120, 122, 1, 13, 35, 31, 58, 118, 6, 48, 85, 119, 33, 17, 21, 56, 23, 27, 37, 43, 53, 106, 107, 5, 44, 4, 57, 79, 109, 63, 38, 28, 87, 93, 62, 84, 121, 14, 55, 71, 32, 124, 97, 3, 50, 68, 12, 81, 103, 100, 112, 78, 89, 105, 51, 90, 64, 95, 88, 16, 15, 83, 75, 73, 108, 76, 36], 
124: [60, 114, 8, 7, 45, 111, 54, 49, 80, 104, 77, 70, 40, 98, 125, 110, 99, 101, 65, 59, 29, 109, 2, 86, 96, 119, 10, 34, 92, 18, 39, 24, 47, 84, 69, 57, 1, 115, 6, 30, 46, 48, 74, 22, 82, 123, 71, 32, 20, 23, 26, 53, 4, 31, 35, 79, 91, 5, 118, 25, 52, 116, 55, 112, 27, 37, 121, 122, 106, 72, 117, 12, 14, 89, 102, 61, 28, 56, 93, 62, 66, 43, 50, 21, 38, 78, 105, 120, 88, 94, 68, 17, 103, 63, 108, 51, 64, 42, 97, 100, 90, 16, 113, 3, 75, 95, 36, 73, 76, 83], 
125: [114, 111, 104, 54, 60, 70, 49, 19, 99, 45, 47, 11, 98, 8, 80, 7, 101, 110, 10, 65, 24, 18, 40, 29, 67, 69, 48, 74, 119, 59, 77, 92, 39, 23, 26, 37, 5, 31, 46, 86, 96, 82, 22, 34, 123, 55, 66, 44, 1, 4, 57, 91, 118, 52, 2, 9, 25, 30, 85, 61, 71, 93, 20, 62, 106, 121, 122, 13, 58, 72, 79, 35, 109, 115, 117, 63, 102, 120, 32, 124, 53, 84, 107, 17, 116, 103, 14, 38, 78, 89, 21, 105, 56, 28, 87, 113, 12, 50, 81, 112, 73, 42, 15, 3, 33, 68, 64, 16, 88, 94, 97, 76, 90, 36, 108, 75], 
}
#'''
def disconnected(graph):    
    for key in graph.keys():
        if len(graph[key]) > 0:
            return False
    return True
#def rippling(ordering, iterations, origSize, weights):
def rippling(ordering, iterations, origSize):
    if disconnected(ordering):
        temp = []
        for key in ordering.keys():
            temp.append((key,0.0))
        return temp
    #def ripple(ordering, value, origSize, weight):
    def ripple(ordering, value, origSize, ith):
        updates = {}
        for key in ordering.keys():#this is assuming ordering.keys() is ordered
            update = np.zeros(origSize)#done this way for numpy optimization

            '''Implementation Detail -- what function to use for factor?'''
            #factor = math.sqrt(value[key]) # --> Perhaps a better option?
            factor = value[key]
            
            rankings = ordering[key]
            size = float(len(rankings))
            for i in range(len(rankings)):
                '''Implementation Detail -- how to choose how to apply factor?'''
                update[rankings[i]-1] = factor*(size-i)/float(size) # --> Overflows kind of fast
                #update[rankings[i]-1] = factor*(size-i)/float(size)*weight[key][i][1]
                #update[rankings[i]-1] = factor*(size-i)/float(size)*(weight[key][i][1] ** ith)
                #update[rankings[i]-1] = factor*(size-i)/float(size)*value[rankings[i]] #--> Overflows too fast
                #update[rankings[i]-1] = factor*(size-i)/float(size)*value[rankings[i]]*weight[key][i][1]
                #update[rankings[i]-1] = factor*(size-i)/float(size)*value[rankings[i]]*(weight[key][i][1] ** ith)
            
            updates[key] = update
        totalUpdate = np.zeros(origSize)
        for key in updates.keys():
            totalUpdate += updates[key]
        for key in value.keys():
            value[key] += totalUpdate[key-1]
            '''Implementation Detail -- divide each key by its number of neighbors? -- makes sure that just the nodes w/
            the most neighbors don't "rise" the fastest'''
            #if len(ordering[key]) > 0:
            #   value[key] /= len(ordering[key])
    #def initRipple(ordering, value, weight):
    def initRipple(ordering, value):
        for key in ordering.keys():
            rankings = ordering[key]
            size = float(len(rankings))
            for i in range(len(rankings)):
                value[rankings[i]] += (size-i)/float(size)
                #value[rankings[i]] += (size-i)/float(size)*weight[key][i][1]
        '''Implementation Detail -- divide each key by its number of neighbors?'''
        #for key in ordering.keys():
        #   if len(ordering[key]) > 0:
        #       value[key] /= len(ordering[key])

    value = {}
    for key in ordering.keys():
        value[key] = 0.0
    initRipple(ordering, value)
    #initRipple(ordering, value, weights)
    for i in range(iterations):
        ripple(ordering, value, origSize, i)
        #ripple(ordering, value, origSize, weights)

    rank = []
    for key in value.keys():
        rank.append((key,value[key]))
    rank = sorted(rank, key=itemgetter(1), reverse=True)
    #rank = sorted(rank, key=itemgetter(1), reverse=False)

    #if printing:
    #    for item in rank:
    #        print(item)
    return rank

#def reverseRippling(ordering, iterations, origSize, weights):
def reverseRippling(ordering, iterations, origSize):
    if disconnected(ordering):
        temp = []
        for key in ordering.keys():
            temp.append((key,0.0))
        return temp
    #def rriple(ordering, value, origSize, weight):
    def rripple(ordering, value, origSize, ith):
        updates = {}
        for key in ordering.keys():#this is assuming ordering.keys() is ordered
            #update = [0.0]*len(ordering.keys())#done this way for numpy optimization
            update = np.zeros(origSize)
            
            #factor = math.sqrt(value[key]) # --> Perhaps a better option?
            factor = value[key]
            
            rankings = ordering[key]
            size = float(len(rankings))
            for i in range(len(rankings)):
                update[rankings[i]-1] = factor*(i+1)/float(size) # --> Overflows kind of fast
                #update[rankings[i]-1] = factor*(i+1)/float(size)*weight[key][i][1]
                #update[rankings[i]-1] = factor*(i+1)/float(size)*(weight[key][i][1] ** ith)
                #update[rankings[i]-1] = factor*(i+1)/float(size)*value[rankings[i]] # --> Overflows too fast
                #update[rankings[i]-1] = factor*(i+1)/float(size)*value[rankings[i]]*weight[key][i][1]
                #update[rankings[i]-1] = factor*(i+1)/float(size)*value[rankings[i]]*(weight[key][i][1] ** ith)

            updates[key] = update
        '''
        for key in updates.keys():
            update = updates[key]
            for i in range(len(update)):
                value[i+1] += update[i]'''
        totalUpdate = np.zeros(origSize)
        for key in updates.keys():
            totalUpdate += updates[key]
        for key in value.keys():
            value[key] += totalUpdate[key-1]
            #if len(ordering[key]) > 0:
            #   value[key] /= len(ordering[key])
    #def initRRiple(ordering, value, weight):
    def initRRipple(ordering, value):
        for key in ordering.keys():
            rankings = ordering[key]
            size = float(len(rankings))
            for i in range(len(rankings)):
                value[rankings[i]] += (i+1)/float(size)
                #value[rankings[i]] += (i+1)/float(size)*weight[key][i][1]
        #for key in ordering.keys():
        #   if len(ordering[key]) > 0:
        #       value[key] /= len(ordering[key])
        
    value = {}
    for key in ordering.keys():
        value[key] = 0.0
    initRRipple(ordering, value)
    #initRRiple(ordering, value, weights)
    for i in range(iterations):
        rripple(ordering, value, origSize, i)
        #rripple(ordering, value, origSize, weights)

    rank = []
    for key in value.keys():
        rank.append((key,value[key]))
    rank = sorted(rank, key=itemgetter(1))

    #if printing:
    #    for item in rank:
    #        print(item)
    return rank

#[36, 83, 108, 76, 51, 90, 64, 15, 95, 68, 42, 97, 88, 16, 94, 75, 102, 55, 27, 33, 43, 112, 87, 56, 100, 21, 73, 121, 107, 105, 3, 14]
#[113, 61, 109, 50, 124, 84, 72, 32, 37, 4, 57, 78, 20, 116, 28, 12, 53, 120, 106, 65, 98, 46, 115, 23, 62, 30, 118, 74, 52, 39, 111, 6]
#[58, 103, 91, 89, 38, 86, 63, 81, 119, 10, 49, 92, 26]
'''
greedy = [(36, 0.816),
(83, 0.816),
(108, 0.824),
(75, 0.832),
(76, 0.832),
(51, 0.84),
(73, 0.84),
(90, 0.84),
(15, 0.848),
(16, 0.848),
(42, 0.848),
(64, 0.848),
(88, 0.848),
(94, 0.848),
(95, 0.848),
(97, 0.848),
(113, 0.848),
(3, 0.856),
(12, 0.864),
(17, 0.864),
(33, 0.864),
(50, 0.864),
(68, 0.864),
(81, 0.864),
(100, 0.864),
(103, 0.864),
(116, 0.864),
(14, 0.872),
(21, 0.872),
(38, 0.872),
(55, 0.872),
(63, 0.872),
(78, 0.872),
(89, 0.872),
(102, 0.872),
(105, 0.872),
(112, 0.872),
(28, 0.88),
(32, 0.88),
(56, 0.88),
(61, 0.88),
(71, 0.88),
(87, 0.88),
(93, 0.88),
(120, 0.88),
(124, 0.88),
(20, 0.888),
(23, 0.888),
(26, 0.888),
(27, 0.888),
(37, 0.888),
(43, 0.888),
(53, 0.888),
(62, 0.888),
(66, 0.888),
(84, 0.888),
(106, 0.888),
(107, 0.888),
(121, 0.888),
(122, 0.888),
(1, 0.896),
(4, 0.896),
(5, 0.896),
(13, 0.896),
(31, 0.896),
(35, 0.896),
(44, 0.896),
(57, 0.896),
(58, 0.896),
(69, 0.896),
(72, 0.896),
(79, 0.896),
(91, 0.896),
(109, 0.896),
(115, 0.896),
(117, 0.896),
(118, 0.896),
(2, 0.904),
(6, 0.904),
(9, 0.904),
(25, 0.904),
(30, 0.904),
(41, 0.904),
(46, 0.904),
(48, 0.904),
(52, 0.904),
(74, 0.904),
(85, 0.904),
(86, 0.904),
(96, 0.904),
(119, 0.904),
(10, 0.912),
(22, 0.912),
(34, 0.912),
(59, 0.912),
(65, 0.912),
(77, 0.912),
(82, 0.912),
(92, 0.912),
(123, 0.912),
(18, 0.92),
(24, 0.92),
(39, 0.92),
(47, 0.92),
(70, 0.92),
(11, 0.928),
(29, 0.928),
(40, 0.928),
(49, 0.928),
(67, 0.928),
(98, 0.928),
(125, 0.928),
(7, 0.936),
(8, 0.936),
(19, 0.936),
(80, 0.936),
(99, 0.936),
(101, 0.936),
(110, 0.936),
(45, 0.944),
(104, 0.944),
(111, 0.944),
(54, 0.952),
(60, 0.952),
(114, 0.952),]'''
'''
greedyGroup = []
i = 0
while i != 124:
    temp = []
    for j in range(i, 124):
        if greedy[j][1] == greedy[j+1][1]:
            temp.append(greedy[j][0])
        else:
            temp.append(greedy[j][0])
            i += 1
            break
        i += 1
    if i == 124:
        temp.append(greedy[124][0])
    greedyGroup.append(temp)

greedyOrder = []
for item in greedy:
    greedyOrder.append(item[0])

r = rippling(very_first_ordering, 10)
j = 0
for i in range(len(r)):
    sofar = sum([len(greedyGroup[x]) for x in range(j)])
    if i == sofar:
        print("{0}\t{1}\t{2}".format(r[i], greedyOrder[i], greedyGroup[j]))
        if r[i][0] not in greedyGroup[j]:
            print("Something's wrong")
        j += 1
    else:
        print("{0}\t{1}".format(r[i], greedyOrder[i]))
        if r[i][0] not in greedyGroup[j-1]:
            print("Something's wrong")
'''
#print(reverseRippling(very_first_ordering, 30, 125))
#print(rippling(very_first_ordering, 30, 125))

#Holy shit, this is so interesting...
#If I set the update to divide by its number of neighbors after each update,
#+ the regular factor set to value[key]
#+ the update being your factor * their factor
#... I get a shift of values from 10, to 50, to something pretty consistent @100+...
#... AND, if I change the function to being factor = math.sqrt(value[key])... things change differently too!
#print(rippling(very_first_ordering, 150, 125))

#...What if I just keep this going over time? And I keep multiplying everything by some e^+k of the (biggest number -1)?
#What would happen?





def findMaximal(graph):
    base = []
    while True:
        temp = makeGraphCopy(graph)
        temp = closedCliqueNeighborhood(base, temp)
        if len(temp.keys()) == 0:
            break
        select = random.randint(0, len(temp.keys()))
        base.append(graph.keys()[select])
    return base