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* www.FindStat.org - The Combinatorial Statistic Finder *
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* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
* *
* This information is distributed in the hope that it will be useful, *
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. *
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-----------------------------------------------------------------------------
Statistic identifier: St000518
-----------------------------------------------------------------------------
Collection: Binary words
-----------------------------------------------------------------------------
Description: The number of distinct subsequences in a binary word.
In contrast to the subword complexity [[St000294]] this is the cardinality of the set of all subsequences of not necessarily consecutive letters.
-----------------------------------------------------------------------------
References: [1] Flaxman, A., Harrow, A. W., Sorkin, G. B. Strings with maximally many distinct subsequences and substrings [[MathSciNet:2034422]]
[2] Elzinga, C., Rahmann, S., Wang, H. Algorithms for subsequence combinatorics [[MathSciNet:2473913]]
-----------------------------------------------------------------------------
Code:
def statistic(w):
return len(Set(Subwords(w)))
-----------------------------------------------------------------------------
Statistic values:
0 => 2
1 => 2
00 => 3
01 => 4
10 => 4
11 => 3
000 => 4
001 => 6
010 => 7
011 => 6
100 => 6
101 => 7
110 => 6
111 => 4
0000 => 5
0001 => 8
0010 => 10
0011 => 9
0100 => 10
0101 => 12
0110 => 11
0111 => 8
1000 => 8
1001 => 11
1010 => 12
1011 => 10
1100 => 9
1101 => 10
1110 => 8
1111 => 5
00000 => 6
00001 => 10
00010 => 13
00011 => 12
00100 => 14
00101 => 17
00110 => 16
00111 => 12
01000 => 13
01001 => 18
01010 => 20
01011 => 17
01100 => 16
01101 => 18
01110 => 15
01111 => 10
10000 => 10
10001 => 15
10010 => 18
10011 => 16
10100 => 17
10101 => 20
10110 => 18
10111 => 13
11000 => 12
11001 => 16
11010 => 17
11011 => 14
11100 => 12
11101 => 13
11110 => 10
11111 => 6
000000 => 7
000001 => 12
000010 => 16
000011 => 15
000100 => 18
000101 => 22
000110 => 21
000111 => 16
001000 => 18
001001 => 25
001010 => 28
001011 => 24
001100 => 23
001101 => 26
001110 => 22
001111 => 15
010000 => 16
010001 => 24
010010 => 29
010011 => 26
010100 => 28
010101 => 33
010110 => 30
010111 => 22
011000 => 21
011001 => 28
011010 => 30
011011 => 25
011100 => 22
011101 => 24
011110 => 19
011111 => 12
100000 => 12
100001 => 19
100010 => 24
100011 => 22
100100 => 25
100101 => 30
100110 => 28
100111 => 21
101000 => 22
101001 => 30
101010 => 33
101011 => 28
101100 => 26
101101 => 29
101110 => 24
101111 => 16
110000 => 15
110001 => 22
110010 => 26
110011 => 23
110100 => 24
110101 => 28
110110 => 25
110111 => 18
111000 => 16
111001 => 21
111010 => 22
111011 => 18
111100 => 15
111101 => 16
111110 => 12
111111 => 7
0000000 => 8
0000001 => 14
0000010 => 19
0000011 => 18
0000100 => 22
0000101 => 27
0000110 => 26
0000111 => 20
0001000 => 23
0001001 => 32
0001010 => 36
0001011 => 31
0001100 => 30
0001101 => 34
0001110 => 29
0001111 => 20
0010000 => 22
0010001 => 33
0010010 => 40
0010011 => 36
0010100 => 39
0010101 => 46
0010110 => 42
0010111 => 31
0011000 => 30
0011001 => 40
0011010 => 43
0011011 => 36
0011100 => 32
0011101 => 35
0011110 => 28
0011111 => 18
0100000 => 19
0100001 => 30
0100010 => 38
0100011 => 35
0100100 => 40
0100101 => 48
0100110 => 45
0100111 => 34
0101000 => 36
0101001 => 49
0101010 => 54
0101011 => 46
0101100 => 43
0101101 => 48
0101110 => 40
0101111 => 27
0110000 => 26
0110001 => 38
0110010 => 45
0110011 => 40
0110100 => 42
0110101 => 49
0110110 => 44
0110111 => 32
0111000 => 29
0111001 => 38
0111010 => 40
0111011 => 33
0111100 => 28
0111101 => 30
0111110 => 23
0111111 => 14
1000000 => 14
1000001 => 23
1000010 => 30
1000011 => 28
1000100 => 33
1000101 => 40
1000110 => 38
1000111 => 29
1001000 => 32
1001001 => 44
1001010 => 49
1001011 => 42
1001100 => 40
1001101 => 45
1001110 => 38
1001111 => 26
1010000 => 27
1010001 => 40
1010010 => 48
1010011 => 43
1010100 => 46
1010101 => 54
1010110 => 49
1010111 => 36
1011000 => 34
1011001 => 45
1011010 => 48
1011011 => 40
1011100 => 35
1011101 => 38
1011110 => 30
1011111 => 19
1100000 => 18
1100001 => 28
1100010 => 35
1100011 => 32
1100100 => 36
1100101 => 43
1100110 => 40
1100111 => 30
1101000 => 31
1101001 => 42
1101010 => 46
1101011 => 39
1101100 => 36
1101101 => 40
1101110 => 33
1101111 => 22
1110000 => 20
1110001 => 29
1110010 => 34
1110011 => 30
1110100 => 31
1110101 => 36
1110110 => 32
1110111 => 23
1111000 => 20
1111001 => 26
1111010 => 27
1111011 => 22
1111100 => 18
1111101 => 19
1111110 => 14
1111111 => 8
00000000 => 9
00000001 => 16
00000010 => 22
00000011 => 21
00000100 => 26
00000101 => 32
00000110 => 31
00000111 => 24
00001000 => 28
00001001 => 39
00001010 => 44
00001011 => 38
00001100 => 37
00001101 => 42
00001110 => 36
00001111 => 25
00010000 => 28
00010001 => 42
00010010 => 51
00010011 => 46
00010100 => 50
00010101 => 59
00010110 => 54
00010111 => 40
00011000 => 39
00011001 => 52
00011010 => 56
00011011 => 47
00011100 => 42
00011101 => 46
00011110 => 37
00011111 => 24
00100000 => 26
00100001 => 41
00100010 => 52
00100011 => 48
00100100 => 55
00100101 => 66
00100110 => 62
00100111 => 47
00101000 => 50
00101001 => 68
00101010 => 75
00101011 => 64
00101100 => 60
00101101 => 67
00101110 => 56
00101111 => 38
00110000 => 37
00110001 => 54
00110010 => 64
00110011 => 57
00110100 => 60
00110101 => 70
00110110 => 63
00110111 => 46
00111000 => 42
00111001 => 55
00111010 => 58
00111011 => 48
00111100 => 41
00111101 => 44
00111110 => 34
00111111 => 21
01000000 => 22
01000001 => 36
01000010 => 47
01000011 => 44
01000100 => 52
01000101 => 63
01000110 => 60
01000111 => 46
01001000 => 51
01001001 => 70
01001010 => 78
01001011 => 67
01001100 => 64
01001101 => 72
01001110 => 61
01001111 => 42
01010000 => 44
01010001 => 65
01010010 => 78
01010011 => 70
01010100 => 75
01010101 => 88
01010110 => 80
01010111 => 59
01011000 => 56
01011001 => 74
01011010 => 79
01011011 => 66
01011100 => 58
01011101 => 63
01011110 => 50
01011111 => 32
01100000 => 31
01100001 => 48
01100010 => 60
01100011 => 55
01100100 => 62
01100101 => 74
01100110 => 69
01100111 => 52
01101000 => 54
01101001 => 73
01101010 => 80
01101011 => 68
01101100 => 63
01101101 => 70
01101110 => 58
01101111 => 39
01110000 => 36
01110001 => 52
01110010 => 61
01110011 => 54
01110100 => 56
01110101 => 65
01110110 => 58
01110111 => 42
01111000 => 37
01111001 => 48
01111010 => 50
01111011 => 41
01111100 => 34
01111101 => 36
01111110 => 27
01111111 => 16
10000000 => 16
10000001 => 27
10000010 => 36
10000011 => 34
10000100 => 41
10000101 => 50
10000110 => 48
10000111 => 37
10001000 => 42
10001001 => 58
10001010 => 65
10001011 => 56
10001100 => 54
10001101 => 61
10001110 => 52
10001111 => 36
10010000 => 39
10010001 => 58
10010010 => 70
10010011 => 63
10010100 => 68
10010101 => 80
10010110 => 73
10010111 => 54
10011000 => 52
10011001 => 69
10011010 => 74
10011011 => 62
10011100 => 55
10011101 => 60
10011110 => 48
10011111 => 31
10100000 => 32
10100001 => 50
10100010 => 63
10100011 => 58
10100100 => 66
10100101 => 79
10100110 => 74
10100111 => 56
10101000 => 59
10101001 => 80
10101010 => 88
10101011 => 75
10101100 => 70
10101101 => 78
10101110 => 65
10101111 => 44
10110000 => 42
10110001 => 61
10110010 => 72
10110011 => 64
10110100 => 67
10110101 => 78
10110110 => 70
10110111 => 51
10111000 => 46
10111001 => 60
10111010 => 63
10111011 => 52
10111100 => 44
10111101 => 47
10111110 => 36
10111111 => 22
11000000 => 21
11000001 => 34
11000010 => 44
11000011 => 41
11000100 => 48
11000101 => 58
11000110 => 55
11000111 => 42
11001000 => 46
11001001 => 63
11001010 => 70
11001011 => 60
11001100 => 57
11001101 => 64
11001110 => 54
11001111 => 37
11010000 => 38
11010001 => 56
11010010 => 67
11010011 => 60
11010100 => 64
11010101 => 75
11010110 => 68
11010111 => 50
11011000 => 47
11011001 => 62
11011010 => 66
11011011 => 55
11011100 => 48
11011101 => 52
11011110 => 41
11011111 => 26
11100000 => 24
11100001 => 37
11100010 => 46
11100011 => 42
11100100 => 47
11100101 => 56
11100110 => 52
11100111 => 39
11101000 => 40
11101001 => 54
11101010 => 59
11101011 => 50
11101100 => 46
11101101 => 51
11101110 => 42
11101111 => 28
11110000 => 25
11110001 => 36
11110010 => 42
11110011 => 37
11110100 => 38
11110101 => 44
11110110 => 39
11110111 => 28
11111000 => 24
11111001 => 31
11111010 => 32
11111011 => 26
11111100 => 21
11111101 => 22
11111110 => 16
11111111 => 9
000000000 => 10
000000001 => 18
000000010 => 25
000000011 => 24
000000100 => 30
000000101 => 37
000000110 => 36
000000111 => 28
000001000 => 33
000001001 => 46
000001010 => 52
000001011 => 45
000001100 => 44
000001101 => 50
000001110 => 43
000001111 => 30
000010000 => 34
000010001 => 51
000010010 => 62
000010011 => 56
000010100 => 61
000010101 => 72
000010110 => 66
000010111 => 49
000011000 => 48
000011001 => 64
000011010 => 69
000011011 => 58
000011100 => 52
000011101 => 57
000011110 => 46
000011111 => 30
000100000 => 33
000100001 => 52
000100010 => 66
000100011 => 61
000100100 => 70
000100101 => 84
000100110 => 79
000100111 => 60
000101000 => 64
000101001 => 87
000101010 => 96
000101011 => 82
000101100 => 77
000101101 => 86
000101110 => 72
000101111 => 49
000110000 => 48
000110001 => 70
000110010 => 83
000110011 => 74
000110100 => 78
000110101 => 91
000110110 => 82
000110111 => 60
000111000 => 55
000111001 => 72
000111010 => 76
000111011 => 63
000111100 => 54
000111101 => 58
000111110 => 45
000111111 => 28
001000000 => 30
001000001 => 49
001000010 => 64
001000011 => 60
001000100 => 71
001000101 => 86
001000110 => 82
001000111 => 63
001001000 => 70
001001001 => 96
001001010 => 107
001001011 => 92
001001100 => 88
001001101 => 99
001001110 => 84
001001111 => 58
001010000 => 61
001010001 => 90
001010010 => 108
001010011 => 97
001010100 => 104
001010101 => 122
001010110 => 111
001010111 => 82
001011000 => 78
001011001 => 103
001011010 => 110
001011011 => 92
001011100 => 81
001011101 => 88
001011110 => 70
001011111 => 45
001100000 => 44
001100001 => 68
001100010 => 85
001100011 => 78
001100100 => 88
001100101 => 105
001100110 => 98
001100111 => 74
001101000 => 77
001101001 => 104
001101010 => 114
001101011 => 97
001101100 => 90
001101101 => 100
001101110 => 83
001101111 => 56
001110000 => 52
001110001 => 75
001110010 => 88
001110011 => 78
001110100 => 81
001110101 => 94
001110110 => 84
001110111 => 61
001111000 => 54
001111001 => 70
001111010 => 73
001111011 => 60
001111100 => 50
001111101 => 53
001111110 => 40
001111111 => 24
010000000 => 25
010000001 => 42
010000010 => 56
010000011 => 53
010000100 => 64
010000101 => 78
010000110 => 75
010000111 => 58
010001000 => 66
010001001 => 91
010001010 => 102
010001011 => 88
010001100 => 85
010001101 => 96
010001110 => 82
010001111 => 57
010010000 => 62
010010001 => 92
010010010 => 111
010010011 => 100
010010100 => 108
010010101 => 127
010010110 => 116
010010111 => 86
010011000 => 83
010011001 => 110
010011010 => 118
010011011 => 99
010011100 => 88
010011101 => 96
010011110 => 77
010011111 => 50
010100000 => 52
010100001 => 81
010100010 => 102
010100011 => 94
010100100 => 107
010100101 => 128
010100110 => 120
010100111 => 91
010101000 => 96
010101001 => 130
010101010 => 143
010101011 => 122
010101100 => 114
010101101 => 127
010101110 => 106
010101111 => 72
010110000 => 69
010110001 => 100
010110010 => 118
010110011 => 105
010110100 => 110
010110101 => 128
010110110 => 115
010110111 => 84
010111000 => 76
010111001 => 99
010111010 => 104
010111011 => 86
010111100 => 73
010111101 => 78
010111110 => 60
010111111 => 37
011000000 => 36
011000001 => 58
011000010 => 75
011000011 => 70
011000100 => 82
011000101 => 99
011000110 => 94
011000111 => 72
011001000 => 79
011001001 => 108
011001010 => 120
011001011 => 103
011001100 => 98
011001101 => 110
011001110 => 93
011001111 => 64
011010000 => 66
011010001 => 97
011010010 => 116
011010011 => 104
011010100 => 111
011010101 => 130
011010110 => 118
011010111 => 87
011011000 => 82
011011001 => 108
011011010 => 115
011011011 => 96
011011100 => 84
011011101 => 91
011011110 => 72
011011111 => 46
011100000 => 43
011100001 => 66
011100010 => 82
011100011 => 75
011100100 => 84
011100101 => 100
011100110 => 93
011100111 => 70
011101000 => 72
011101001 => 97
011101010 => 106
011101011 => 90
011101100 => 83
011101101 => 92
011101110 => 76
011101111 => 51
011110000 => 46
011110001 => 66
011110010 => 77
011110011 => 68
011110100 => 70
011110101 => 81
011110110 => 72
011110111 => 52
011111000 => 45
011111001 => 58
011111010 => 60
011111011 => 49
011111100 => 40
011111101 => 42
011111110 => 31
011111111 => 18
100000000 => 18
100000001 => 31
100000010 => 42
100000011 => 40
100000100 => 49
100000101 => 60
100000110 => 58
100000111 => 45
100001000 => 52
100001001 => 72
100001010 => 81
100001011 => 70
100001100 => 68
100001101 => 77
100001110 => 66
100001111 => 46
100010000 => 51
100010001 => 76
100010010 => 92
100010011 => 83
100010100 => 90
100010101 => 106
100010110 => 97
100010111 => 72
100011000 => 70
100011001 => 93
100011010 => 100
100011011 => 84
100011100 => 75
100011101 => 82
100011110 => 66
100011111 => 43
100100000 => 46
100100001 => 72
100100010 => 91
100100011 => 84
100100100 => 96
100100101 => 115
100100110 => 108
100100111 => 82
100101000 => 87
100101001 => 118
100101010 => 130
100101011 => 111
100101100 => 104
100101101 => 116
100101110 => 97
100101111 => 66
100110000 => 64
100110001 => 93
100110010 => 110
100110011 => 98
100110100 => 103
100110101 => 120
100110110 => 108
100110111 => 79
100111000 => 72
100111001 => 94
100111010 => 99
100111011 => 82
100111100 => 70
100111101 => 75
100111110 => 58
100111111 => 36
101000000 => 37
101000001 => 60
101000010 => 78
101000011 => 73
101000100 => 86
101000101 => 104
101000110 => 99
101000111 => 76
101001000 => 84
101001001 => 115
101001010 => 128
101001011 => 110
101001100 => 105
101001101 => 118
101001110 => 100
101001111 => 69
101010000 => 72
101010001 => 106
101010010 => 127
101010011 => 114
101010100 => 122
101010101 => 143
101010110 => 130
101010111 => 96
101011000 => 91
101011001 => 120
101011010 => 128
101011011 => 107
101011100 => 94
101011101 => 102
101011110 => 81
101011111 => 52
101100000 => 50
101100001 => 77
101100010 => 96
101100011 => 88
101100100 => 99
101100101 => 118
101100110 => 110
101100111 => 83
101101000 => 86
101101001 => 116
101101010 => 127
101101011 => 108
101101100 => 100
101101101 => 111
101101110 => 92
101101111 => 62
101110000 => 57
101110001 => 82
101110010 => 96
101110011 => 85
101110100 => 88
101110101 => 102
101110110 => 91
101110111 => 66
101111000 => 58
101111001 => 75
101111010 => 78
101111011 => 64
101111100 => 53
101111101 => 56
101111110 => 42
101111111 => 25
110000000 => 24
110000001 => 40
110000010 => 53
110000011 => 50
110000100 => 60
110000101 => 73
110000110 => 70
110000111 => 54
110001000 => 61
110001001 => 84
110001010 => 94
110001011 => 81
110001100 => 78
110001101 => 88
110001110 => 75
110001111 => 52
110010000 => 56
110010001 => 83
110010010 => 100
110010011 => 90
110010100 => 97
110010101 => 114
110010110 => 104
110010111 => 77
110011000 => 74
110011001 => 98
110011010 => 105
110011011 => 88
110011100 => 78
110011101 => 85
110011110 => 68
110011111 => 44
110100000 => 45
110100001 => 70
110100010 => 88
110100011 => 81
110100100 => 92
110100101 => 110
110100110 => 103
110100111 => 78
110101000 => 82
110101001 => 111
110101010 => 122
110101011 => 104
110101100 => 97
110101101 => 108
110101110 => 90
110101111 => 61
110110000 => 58
110110001 => 84
110110010 => 99
110110011 => 88
110110100 => 92
110110101 => 107
110110110 => 96
110110111 => 70
110111000 => 63
110111001 => 82
110111010 => 86
110111011 => 71
110111100 => 60
110111101 => 64
110111110 => 49
110111111 => 30
111000000 => 28
111000001 => 45
111000010 => 58
111000011 => 54
111000100 => 63
111000101 => 76
111000110 => 72
111000111 => 55
111001000 => 60
111001001 => 82
111001010 => 91
111001011 => 78
111001100 => 74
111001101 => 83
111001110 => 70
111001111 => 48
111010000 => 49
111010001 => 72
111010010 => 86
111010011 => 77
111010100 => 82
111010101 => 96
111010110 => 87
111010111 => 64
111011000 => 60
111011001 => 79
111011010 => 84
111011011 => 70
111011100 => 61
111011101 => 66
111011110 => 52
111011111 => 33
111100000 => 30
111100001 => 46
111100010 => 57
111100011 => 52
111100100 => 58
111100101 => 69
111100110 => 64
111100111 => 48
111101000 => 49
111101001 => 66
111101010 => 72
111101011 => 61
111101100 => 56
111101101 => 62
111101110 => 51
111101111 => 34
111110000 => 30
111110001 => 43
111110010 => 50
111110011 => 44
111110100 => 45
111110101 => 52
111110110 => 46
111110111 => 33
111111000 => 28
111111001 => 36
111111010 => 37
111111011 => 30
111111100 => 24
111111101 => 25
111111110 => 18
111111111 => 10
0000000001 => 20
0010000001 => 57
0010101101 => 176
0010101011 => 169
0010100111 => 126
0010011101 => 132
0010011011 => 136
0010010111 => 118
0010001111 => 78
0001110101 => 123
0001110011 => 102
0001101101 => 130
0001101011 => 126
0001100111 => 96
0001011101 => 113
0001011011 => 118
0001010111 => 105
0001001111 => 74
0000111101 => 72
0000111011 => 78
0000110111 => 74
0000101111 => 60
0000011111 => 36
0000000000 => 11
0000000110 => 41
0000011000 => 57
0000011110 => 55
0000010010 => 73
0001100000 => 57
0001100110 => 127
0001111000 => 71
0001111110 => 53
0001110010 => 115
0001001000 => 89
0001001110 => 107
0001000010 => 81
0001011010 => 141
0010101010 => 198
0010101000 => 133
0010101100 => 158
0010100100 => 148
0010010100 => 148
0001010100 => 133
0010101110 => 147
0010100000 => 72
0010000100 => 87
0000010100 => 72
0000000010 => 28
0000001110 => 50
0000111110 => 56
0000000100 => 34
0000001010 => 60
0000010110 => 78
0000101110 => 88
0001011110 => 90
0001101110 => 108
0001110110 => 110
0001111010 => 96
0001111100 => 66
0000000101 => 42
0000001101 => 58
0000011101 => 68
0001111101 => 70
0000001001 => 53
0000010101 => 85
0000101101 => 105
0010110001 => 139
0001100001 => 88
0001000001 => 62
0000111111 => 35
0001110100 => 106
0001101100 => 117
0010011100 => 121
0001011100 => 104
0000111100 => 67
0001101010 => 148
0010011010 => 162
0000111010 => 94
0010100110 => 166
0010010110 => 159
0001010110 => 142
0000110110 => 101
0010001110 => 112
0001101001 => 135
0000110001 => 86
0000010001 => 60
0000001100 => 51
0000011001 => 76
0000110011 => 91
0000110100 => 96
0000000011 => 27
0000011011 => 69
0001101111 => 73
0000110101 => 112
0010000010 => 76
0001000011 => 76
0010011110 => 106
0001010000 => 78
0001000100 => 90
0001010101 => 156
0001001011 => 117
0001100011 => 101
0001110111 => 80
0010000000 => 34
0000000111 => 32
0000001111 => 35
0001111111 => 32
0000001011 => 52
0000010111 => 58
0001011111 => 58
0001111001 => 92
0000011010 => 82
0000101010 => 117
0000100101 => 102
0010010001 => 126
0010000101 => 106
0010010101 => 174
0010010011 => 137
0000101011 => 100
0001000111 => 80
0000100111 => 73
0010010010 => 152
0001001010 => 136
0001001001 => 122
0001000101 => 109
0000100011 => 74
0000100100 => 85
0000100010 => 80
0010110000 => 96
0000011100 => 62
0000001000 => 38
0000101100 => 94
0010101111 => 100
0000101000 => 78
0010001000 => 90
0001001100 => 112
0001000110 => 104
0001100100 => 114
0001100010 => 110
0000100110 => 96
0000110010 => 102
0010010000 => 85
0001010010 => 138
0001000000 => 38
0001011001 => 132
0001100101 => 136
0001110001 => 98
0010011001 => 151
0010100101 => 177
0010101001 => 180
0010011111 => 69
0000111001 => 89
0010001101 => 131
0001001101 => 126
0001010001 => 115
0001010011 => 124
0001111011 => 79
0010011000 => 114
0001011000 => 100
0000100000 => 40
0010001011 => 120
0010000111 => 79
0000010011 => 66
0010001100 => 116
0010000110 => 102
0000110000 => 59
0000100001 => 63
0010100011 => 130
0010100001 => 112
0000111000 => 68
0001101000 => 100
0000010000 => 40
0000101001 => 106
0010100010 => 141
0010001001 => 124
0010000011 => 72
0010001010 => 139
0001110000 => 68
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Created: Jun 01, 2016 at 09:30 by Martin Rubey
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Last Updated: Jun 01, 2016 at 09:30 by Martin Rubey