Identifier
Identifier
Values
[] => 1
[1] => 1
[1,2] => 1
[2,1] => 1
[1,2,3] => 1
[1,3,2] => 2
[2,1,3] => 1
[2,3,1] => 1
[3,1,2] => 1
[3,2,1] => 1
[1,2,3,4] => 1
[1,2,4,3] => 3
[1,3,2,4] => 2
[1,3,4,2] => 3
[1,4,2,3] => 3
[1,4,3,2] => 5
[2,1,3,4] => 1
[2,1,4,3] => 4
[2,3,1,4] => 1
[2,3,4,1] => 1
[2,4,1,3] => 2
[2,4,3,1] => 2
[3,1,2,4] => 1
[3,1,4,2] => 2
[3,2,1,4] => 1
[3,2,4,1] => 1
[3,4,1,2] => 1
[3,4,2,1] => 1
[4,1,2,3] => 1
[4,1,3,2] => 2
[4,2,1,3] => 1
[4,2,3,1] => 1
[4,3,1,2] => 1
[4,3,2,1] => 1
[1,2,3,4,5] => 1
[1,2,3,5,4] => 4
[1,2,4,3,5] => 3
[1,2,4,5,3] => 6
[1,2,5,3,4] => 6
[1,2,5,4,3] => 14
[1,3,2,4,5] => 2
[1,3,2,5,4] => 13
[1,3,4,2,5] => 3
[1,3,4,5,2] => 4
[1,3,5,2,4] => 8
[1,3,5,4,2] => 11
[1,4,2,3,5] => 3
[1,4,2,5,3] => 8
[1,4,3,2,5] => 5
[1,4,3,5,2] => 7
[1,4,5,2,3] => 6
[1,4,5,3,2] => 9
[1,5,2,3,4] => 4
[1,5,2,4,3] => 11
[1,5,3,2,4] => 7
[1,5,3,4,2] => 10
[1,5,4,2,3] => 9
[1,5,4,3,2] => 14
[2,1,3,4,5] => 1
[2,1,3,5,4] => 5
[2,1,4,3,5] => 4
[2,1,4,5,3] => 8
[2,1,5,3,4] => 8
[2,1,5,4,3] => 21
[2,3,1,4,5] => 1
[2,3,1,5,4] => 6
[2,3,4,1,5] => 1
[2,3,4,5,1] => 1
[2,3,5,1,4] => 3
[2,3,5,4,1] => 3
[2,4,1,3,5] => 2
[2,4,1,5,3] => 6
[2,4,3,1,5] => 2
[2,4,3,5,1] => 2
[2,4,5,1,3] => 3
[2,4,5,3,1] => 3
[2,5,1,3,4] => 3
[2,5,1,4,3] => 10
[2,5,3,1,4] => 3
[2,5,3,4,1] => 3
[2,5,4,1,3] => 5
[2,5,4,3,1] => 5
[3,1,2,4,5] => 1
[3,1,2,5,4] => 6
[3,1,4,2,5] => 2
[3,1,4,5,2] => 3
[3,1,5,2,4] => 6
[3,1,5,4,2] => 10
[3,2,1,4,5] => 1
[3,2,1,5,4] => 8
[3,2,4,1,5] => 1
[3,2,4,5,1] => 1
[3,2,5,1,4] => 4
[3,2,5,4,1] => 4
[3,4,1,2,5] => 1
[3,4,1,5,2] => 2
[3,4,2,1,5] => 1
[3,4,2,5,1] => 1
[3,4,5,1,2] => 1
[3,4,5,2,1] => 1
[3,5,1,2,4] => 2
[3,5,1,4,2] => 4
[3,5,2,1,4] => 2
[3,5,2,4,1] => 2
[3,5,4,1,2] => 2
[3,5,4,2,1] => 2
[4,1,2,3,5] => 1
[4,1,2,5,3] => 3
[4,1,3,2,5] => 2
[4,1,3,5,2] => 3
[4,1,5,2,3] => 3
[4,1,5,3,2] => 5
[4,2,1,3,5] => 1
[4,2,1,5,3] => 4
[4,2,3,1,5] => 1
[4,2,3,5,1] => 1
[4,2,5,1,3] => 2
[4,2,5,3,1] => 2
[4,3,1,2,5] => 1
[4,3,1,5,2] => 2
[4,3,2,1,5] => 1
[4,3,2,5,1] => 1
[4,3,5,1,2] => 1
[4,3,5,2,1] => 1
[4,5,1,2,3] => 1
[4,5,1,3,2] => 2
[4,5,2,1,3] => 1
[4,5,2,3,1] => 1
[4,5,3,1,2] => 1
[4,5,3,2,1] => 1
[5,1,2,3,4] => 1
[5,1,2,4,3] => 3
[5,1,3,2,4] => 2
[5,1,3,4,2] => 3
[5,1,4,2,3] => 3
[5,1,4,3,2] => 5
[5,2,1,3,4] => 1
[5,2,1,4,3] => 4
[5,2,3,1,4] => 1
[5,2,3,4,1] => 1
[5,2,4,1,3] => 2
[5,2,4,3,1] => 2
[5,3,1,2,4] => 1
[5,3,1,4,2] => 2
[5,3,2,1,4] => 1
[5,3,2,4,1] => 1
[5,3,4,1,2] => 1
[5,3,4,2,1] => 1
[5,4,1,2,3] => 1
[5,4,1,3,2] => 2
[5,4,2,1,3] => 1
[5,4,2,3,1] => 1
[5,4,3,1,2] => 1
[5,4,3,2,1] => 1
[1,2,3,4,5,6] => 1
[1,2,3,4,6,5] => 5
[1,2,3,5,4,6] => 4
[1,2,3,5,6,4] => 10
[1,2,3,6,4,5] => 10
[1,2,3,6,5,4] => 30
[1,2,4,3,5,6] => 3
[1,2,4,3,6,5] => 29
[1,2,4,5,3,6] => 6
[1,2,4,5,6,3] => 10
[1,2,4,6,3,5] => 20
[1,2,4,6,5,3] => 35
[1,2,5,3,4,6] => 6
[1,2,5,3,6,4] => 20
[1,2,5,4,3,6] => 14
[1,2,5,4,6,3] => 25
[1,2,5,6,3,4] => 20
[1,2,5,6,4,3] => 40
[1,2,6,3,4,5] => 10
[1,2,6,3,5,4] => 35
[1,2,6,4,3,5] => 25
[1,2,6,4,5,3] => 46
[1,2,6,5,3,4] => 40
[1,2,6,5,4,3] => 84
[1,3,2,4,5,6] => 2
[1,3,2,4,6,5] => 15
[1,3,2,5,4,6] => 13
[1,3,2,5,6,4] => 32
[1,3,2,6,4,5] => 32
[1,3,2,6,5,4] => 121
[1,3,4,2,5,6] => 3
[1,3,4,2,6,5] => 26
[1,3,4,5,2,6] => 4
[1,3,4,5,6,2] => 5
[1,3,4,6,2,5] => 15
[1,3,4,6,5,2] => 19
[1,3,5,2,4,6] => 8
[1,3,5,2,6,4] => 34
[1,3,5,4,2,6] => 11
[1,3,5,4,6,2] => 14
[1,3,5,6,2,4] => 20
[1,3,5,6,4,2] => 26
[1,3,6,2,4,5] => 15
[1,3,6,2,5,4] => 74
[1,3,6,4,2,5] => 21
[1,3,6,4,5,2] => 27
[1,3,6,5,2,4] => 44
[1,3,6,5,4,2] => 58
[1,4,2,3,5,6] => 3
[1,4,2,3,6,5] => 26
[1,4,2,5,3,6] => 8
[1,4,2,5,6,3] => 15
[1,4,2,6,3,5] => 34
[1,4,2,6,5,3] => 74
[1,4,3,2,5,6] => 5
[1,4,3,2,6,5] => 67
[1,4,3,5,2,6] => 7
[1,4,3,5,6,2] => 9
[1,4,3,6,2,5] => 40
[1,4,3,6,5,2] => 53
[1,4,5,2,3,6] => 6
[1,4,5,2,6,3] => 15
[1,4,5,3,2,6] => 9
[1,4,5,3,6,2] => 12
[1,4,5,6,2,3] => 10
[1,4,5,6,3,2] => 14
[1,4,6,2,3,5] => 15
[1,4,6,2,5,3] => 38
[1,4,6,3,2,5] => 23
[1,4,6,3,5,2] => 31
[1,4,6,5,2,3] => 26
[1,4,6,5,3,2] => 37
[1,5,2,3,4,6] => 4
[1,5,2,3,6,4] => 15
[1,5,2,4,3,6] => 11
[1,5,2,4,6,3] => 21
[1,5,2,6,3,4] => 20
[1,5,2,6,4,3] => 44
[1,5,3,2,4,6] => 7
[1,5,3,2,6,4] => 40
[1,5,3,4,2,6] => 10
[1,5,3,4,6,2] => 13
[1,5,3,6,2,4] => 24
[1,5,3,6,4,2] => 32
[1,5,4,2,3,6] => 9
[1,5,4,2,6,3] => 23
[1,5,4,3,2,6] => 14
[1,5,4,3,6,2] => 19
[1,5,4,6,2,3] => 16
[1,5,4,6,3,2] => 23
[1,5,6,2,3,4] => 10
[1,5,6,2,4,3] => 26
[1,5,6,3,2,4] => 16
[1,5,6,3,4,2] => 22
[1,5,6,4,2,3] => 19
[1,5,6,4,3,2] => 28
[1,6,2,3,4,5] => 5
[1,6,2,3,5,4] => 19
[1,6,2,4,3,5] => 14
[1,6,2,4,5,3] => 27
[1,6,2,5,3,4] => 26
[1,6,2,5,4,3] => 58
[1,6,3,2,4,5] => 9
[1,6,3,2,5,4] => 53
[1,6,3,4,2,5] => 13
[1,6,3,4,5,2] => 17
[1,6,3,5,2,4] => 32
[1,6,3,5,4,2] => 43
[1,6,4,2,3,5] => 12
[1,6,4,2,5,3] => 31
[1,6,4,3,2,5] => 19
[1,6,4,3,5,2] => 26
[1,6,4,5,2,3] => 22
[1,6,4,5,3,2] => 32
[1,6,5,2,3,4] => 14
[1,6,5,2,4,3] => 37
[1,6,5,3,2,4] => 23
[1,6,5,3,4,2] => 32
[1,6,5,4,2,3] => 28
[1,6,5,4,3,2] => 42
[2,1,3,4,5,6] => 1
[2,1,3,4,6,5] => 6
[2,1,3,5,4,6] => 5
[2,1,3,5,6,4] => 13
[2,1,3,6,4,5] => 13
[2,1,3,6,5,4] => 42
[2,1,4,3,5,6] => 4
[2,1,4,3,6,5] => 41
[2,1,4,5,3,6] => 8
[2,1,4,5,6,3] => 13
[2,1,4,6,3,5] => 29
[2,1,4,6,5,3] => 51
[2,1,5,3,4,6] => 8
[2,1,5,3,6,4] => 29
[2,1,5,4,3,6] => 21
[2,1,5,4,6,3] => 38
[2,1,5,6,3,4] => 29
[2,1,5,6,4,3] => 60
[2,1,6,3,4,5] => 13
[2,1,6,3,5,4] => 51
[2,1,6,4,3,5] => 38
[2,1,6,4,5,3] => 71
[2,1,6,5,3,4] => 60
[2,1,6,5,4,3] => 135
[2,3,1,4,5,6] => 1
[2,3,1,4,6,5] => 7
[2,3,1,5,4,6] => 6
[2,3,1,5,6,4] => 15
[2,3,1,6,4,5] => 15
[2,3,1,6,5,4] => 56
[2,3,4,1,5,6] => 1
[2,3,4,1,6,5] => 8
[2,3,4,5,1,6] => 1
[2,3,4,5,6,1] => 1
[2,3,4,6,1,5] => 4
[2,3,4,6,5,1] => 4
[2,3,5,1,4,6] => 3
[2,3,5,1,6,4] => 12
[2,3,5,4,1,6] => 3
[2,3,5,4,6,1] => 3
[2,3,5,6,1,4] => 6
[2,3,5,6,4,1] => 6
[2,3,6,1,4,5] => 6
[2,3,6,1,5,4] => 28
[2,3,6,4,1,5] => 6
[2,3,6,4,5,1] => 6
[2,3,6,5,1,4] => 14
[2,3,6,5,4,1] => 14
[2,4,1,3,5,6] => 2
[2,4,1,3,6,5] => 21
[2,4,1,5,3,6] => 6
[2,4,1,5,6,3] => 11
[2,4,1,6,3,5] => 24
[2,4,1,6,5,3] => 52
[2,4,3,1,5,6] => 2
[2,4,3,1,6,5] => 26
[2,4,3,5,1,6] => 2
[2,4,3,5,6,1] => 2
[2,4,3,6,1,5] => 13
[2,4,3,6,5,1] => 13
[2,4,5,1,3,6] => 3
[2,4,5,1,6,3] => 8
[2,4,5,3,1,6] => 3
[2,4,5,3,6,1] => 3
[2,4,5,6,1,3] => 4
[2,4,5,6,3,1] => 4
[2,4,6,1,3,5] => 8
[2,4,6,1,5,3] => 22
[2,4,6,3,1,5] => 8
[2,4,6,3,5,1] => 8
[2,4,6,5,1,3] => 11
[2,4,6,5,3,1] => 11
[2,5,1,3,4,6] => 3
[2,5,1,3,6,4] => 13
[2,5,1,4,3,6] => 10
[2,5,1,4,6,3] => 19
[2,5,1,6,3,4] => 17
[2,5,1,6,4,3] => 40
[2,5,3,1,4,6] => 3
[2,5,3,1,6,4] => 16
[2,5,3,4,1,6] => 3
[2,5,3,4,6,1] => 3
[2,5,3,6,1,4] => 8
[2,5,3,6,4,1] => 8
[2,5,4,1,3,6] => 5
[2,5,4,1,6,3] => 14
[2,5,4,3,1,6] => 5
[2,5,4,3,6,1] => 5
[2,5,4,6,1,3] => 7
[2,5,4,6,3,1] => 7
[2,5,6,1,3,4] => 6
[2,5,6,1,4,3] => 18
[2,5,6,3,1,4] => 6
[2,5,6,3,4,1] => 6
[2,5,6,4,1,3] => 9
[2,5,6,4,3,1] => 9
[2,6,1,3,4,5] => 4
[2,6,1,3,5,4] => 18
[2,6,1,4,3,5] => 14
[2,6,1,4,5,3] => 27
[2,6,1,5,3,4] => 25
[2,6,1,5,4,3] => 61
[2,6,3,1,4,5] => 4
[2,6,3,1,5,4] => 22
[2,6,3,4,1,5] => 4
[2,6,3,4,5,1] => 4
[2,6,3,5,1,4] => 11
[2,6,3,5,4,1] => 11
[2,6,4,1,3,5] => 7
[2,6,4,1,5,3] => 20
[2,6,4,3,1,5] => 7
[2,6,4,3,5,1] => 7
[2,6,4,5,1,3] => 10
[2,6,4,5,3,1] => 10
[2,6,5,1,3,4] => 9
[2,6,5,1,4,3] => 28
[2,6,5,3,1,4] => 9
[2,6,5,3,4,1] => 9
[2,6,5,4,1,3] => 14
[2,6,5,4,3,1] => 14
[3,1,2,4,5,6] => 1
[3,1,2,4,6,5] => 7
[3,1,2,5,4,6] => 6
[3,1,2,5,6,4] => 15
[3,1,2,6,4,5] => 15
[3,1,2,6,5,4] => 56
[3,1,4,2,5,6] => 2
[3,1,4,2,6,5] => 21
[3,1,4,5,2,6] => 3
[3,1,4,5,6,2] => 4
[3,1,4,6,2,5] => 13
[3,1,4,6,5,2] => 18
[3,1,5,2,4,6] => 6
[3,1,5,2,6,4] => 24
[3,1,5,4,2,6] => 10
[3,1,5,4,6,2] => 14
[3,1,5,6,2,4] => 17
[3,1,5,6,4,2] => 25
[3,1,6,2,4,5] => 11
[3,1,6,2,5,4] => 52
[3,1,6,4,2,5] => 19
[3,1,6,4,5,2] => 27
[3,1,6,5,2,4] => 40
[3,1,6,5,4,2] => 61
[3,2,1,4,5,6] => 1
[3,2,1,4,6,5] => 9
[3,2,1,5,4,6] => 8
[3,2,1,5,6,4] => 20
[3,2,1,6,4,5] => 20
[3,2,1,6,5,4] => 82
[3,2,4,1,5,6] => 1
[3,2,4,1,6,5] => 10
[3,2,4,5,1,6] => 1
[3,2,4,5,6,1] => 1
[3,2,4,6,1,5] => 5
[3,2,4,6,5,1] => 5
[3,2,5,1,4,6] => 4
[3,2,5,1,6,4] => 16
[3,2,5,4,1,6] => 4
[3,2,5,4,6,1] => 4
[3,2,5,6,1,4] => 8
[3,2,5,6,4,1] => 8
[3,2,6,1,4,5] => 8
[3,2,6,1,5,4] => 42
[3,2,6,4,1,5] => 8
[3,2,6,4,5,1] => 8
[3,2,6,5,1,4] => 21
[3,2,6,5,4,1] => 21
[3,4,1,2,5,6] => 1
[3,4,1,2,6,5] => 9
[3,4,1,5,2,6] => 2
[3,4,1,5,6,2] => 3
[3,4,1,6,2,5] => 9
[3,4,1,6,5,2] => 15
[3,4,2,1,5,6] => 1
[3,4,2,1,6,5] => 12
[3,4,2,5,1,6] => 1
[3,4,2,5,6,1] => 1
[3,4,2,6,1,5] => 6
[3,4,2,6,5,1] => 6
[3,4,5,1,2,6] => 1
[3,4,5,1,6,2] => 2
[3,4,5,2,1,6] => 1
[3,4,5,2,6,1] => 1
[3,4,5,6,1,2] => 1
[3,4,5,6,2,1] => 1
[3,4,6,1,2,5] => 3
[3,4,6,1,5,2] => 6
[3,4,6,2,1,5] => 3
[3,4,6,2,5,1] => 3
[3,4,6,5,1,2] => 3
[3,4,6,5,2,1] => 3
[3,5,1,2,4,6] => 2
[3,5,1,2,6,4] => 9
[3,5,1,4,2,6] => 4
[3,5,1,4,6,2] => 6
[3,5,1,6,2,4] => 9
[3,5,1,6,4,2] => 15
[3,5,2,1,4,6] => 2
[3,5,2,1,6,4] => 12
[3,5,2,4,1,6] => 2
[3,5,2,4,6,1] => 2
[3,5,2,6,1,4] => 6
[3,5,2,6,4,1] => 6
[3,5,4,1,2,6] => 2
[3,5,4,1,6,2] => 4
[3,5,4,2,1,6] => 2
[3,5,4,2,6,1] => 2
[3,5,4,6,1,2] => 2
[3,5,4,6,2,1] => 2
[3,5,6,1,2,4] => 3
[3,5,6,1,4,2] => 6
[3,5,6,2,1,4] => 3
[3,5,6,2,4,1] => 3
[3,5,6,4,1,2] => 3
[3,5,6,4,2,1] => 3
[3,6,1,2,4,5] => 3
[3,6,1,2,5,4] => 15
[3,6,1,4,2,5] => 6
[3,6,1,4,5,2] => 9
[3,6,1,5,2,4] => 15
[3,6,1,5,4,2] => 25
[3,6,2,1,4,5] => 3
[3,6,2,1,5,4] => 20
[3,6,2,4,1,5] => 3
[3,6,2,4,5,1] => 3
[3,6,2,5,1,4] => 10
[3,6,2,5,4,1] => 10
[3,6,4,1,2,5] => 3
[3,6,4,1,5,2] => 6
[3,6,4,2,1,5] => 3
[3,6,4,2,5,1] => 3
[3,6,4,5,1,2] => 3
[3,6,4,5,2,1] => 3
[3,6,5,1,2,4] => 5
[3,6,5,1,4,2] => 10
[3,6,5,2,1,4] => 5
[3,6,5,2,4,1] => 5
[3,6,5,4,1,2] => 5
[3,6,5,4,2,1] => 5
[4,1,2,3,5,6] => 1
[4,1,2,3,6,5] => 8
[4,1,2,5,3,6] => 3
[4,1,2,5,6,3] => 6
[4,1,2,6,3,5] => 12
[4,1,2,6,5,3] => 28
[4,1,3,2,5,6] => 2
[4,1,3,2,6,5] => 26
[4,1,3,5,2,6] => 3
[4,1,3,5,6,2] => 4
[4,1,3,6,2,5] => 16
[4,1,3,6,5,2] => 22
[4,1,5,2,3,6] => 3
[4,1,5,2,6,3] => 8
[4,1,5,3,2,6] => 5
[4,1,5,3,6,2] => 7
[4,1,5,6,2,3] => 6
[4,1,5,6,3,2] => 9
[4,1,6,2,3,5] => 8
[4,1,6,2,5,3] => 22
[4,1,6,3,2,5] => 14
[4,1,6,3,5,2] => 20
[4,1,6,5,2,3] => 18
[4,1,6,5,3,2] => 28
[4,2,1,3,5,6] => 1
[4,2,1,3,6,5] => 10
[4,2,1,5,3,6] => 4
[4,2,1,5,6,3] => 8
[4,2,1,6,3,5] => 16
[4,2,1,6,5,3] => 42
[4,2,3,1,5,6] => 1
[4,2,3,1,6,5] => 12
[4,2,3,5,1,6] => 1
[4,2,3,5,6,1] => 1
[4,2,3,6,1,5] => 6
[4,2,3,6,5,1] => 6
[4,2,5,1,3,6] => 2
[4,2,5,1,6,3] => 6
[4,2,5,3,1,6] => 2
[4,2,5,3,6,1] => 2
[4,2,5,6,1,3] => 3
[4,2,5,6,3,1] => 3
[4,2,6,1,3,5] => 6
[4,2,6,1,5,3] => 20
[4,2,6,3,1,5] => 6
[4,2,6,3,5,1] => 6
[4,2,6,5,1,3] => 10
[4,2,6,5,3,1] => 10
[4,3,1,2,5,6] => 1
[4,3,1,2,6,5] => 12
[4,3,1,5,2,6] => 2
[4,3,1,5,6,2] => 3
[4,3,1,6,2,5] => 12
[4,3,1,6,5,2] => 20
[4,3,2,1,5,6] => 1
[4,3,2,1,6,5] => 16
[4,3,2,5,1,6] => 1
[4,3,2,5,6,1] => 1
[4,3,2,6,1,5] => 8
[4,3,2,6,5,1] => 8
[4,3,5,1,2,6] => 1
[4,3,5,1,6,2] => 2
[4,3,5,2,1,6] => 1
[4,3,5,2,6,1] => 1
[4,3,5,6,1,2] => 1
[4,3,5,6,2,1] => 1
[4,3,6,1,2,5] => 4
[4,3,6,1,5,2] => 8
[4,3,6,2,1,5] => 4
[4,3,6,2,5,1] => 4
[4,3,6,5,1,2] => 4
[4,3,6,5,2,1] => 4
[4,5,1,2,3,6] => 1
[4,5,1,2,6,3] => 3
[4,5,1,3,2,6] => 2
[4,5,1,3,6,2] => 3
[4,5,1,6,2,3] => 3
[4,5,1,6,3,2] => 5
[4,5,2,1,3,6] => 1
[4,5,2,1,6,3] => 4
[4,5,2,3,1,6] => 1
[4,5,2,3,6,1] => 1
[4,5,2,6,1,3] => 2
[4,5,2,6,3,1] => 2
[4,5,3,1,2,6] => 1
[4,5,3,1,6,2] => 2
[4,5,3,2,1,6] => 1
[4,5,3,2,6,1] => 1
[4,5,3,6,1,2] => 1
[4,5,3,6,2,1] => 1
[4,5,6,1,2,3] => 1
[4,5,6,1,3,2] => 2
[4,5,6,2,1,3] => 1
[4,5,6,2,3,1] => 1
[4,5,6,3,1,2] => 1
[4,5,6,3,2,1] => 1
[4,6,1,2,3,5] => 2
[4,6,1,2,5,3] => 6
[4,6,1,3,2,5] => 4
[4,6,1,3,5,2] => 6
[4,6,1,5,2,3] => 6
[4,6,1,5,3,2] => 10
[4,6,2,1,3,5] => 2
[4,6,2,1,5,3] => 8
[4,6,2,3,1,5] => 2
[4,6,2,3,5,1] => 2
[4,6,2,5,1,3] => 4
[4,6,2,5,3,1] => 4
[4,6,3,1,2,5] => 2
[4,6,3,1,5,2] => 4
[4,6,3,2,1,5] => 2
[4,6,3,2,5,1] => 2
[4,6,3,5,1,2] => 2
[4,6,3,5,2,1] => 2
[4,6,5,1,2,3] => 2
[4,6,5,1,3,2] => 4
[4,6,5,2,1,3] => 2
[4,6,5,2,3,1] => 2
[4,6,5,3,1,2] => 2
[4,6,5,3,2,1] => 2
[5,1,2,3,4,6] => 1
[5,1,2,3,6,4] => 4
[5,1,2,4,3,6] => 3
[5,1,2,4,6,3] => 6
[5,1,2,6,3,4] => 6
[5,1,2,6,4,3] => 14
[5,1,3,2,4,6] => 2
[5,1,3,2,6,4] => 13
[5,1,3,4,2,6] => 3
[5,1,3,4,6,2] => 4
[5,1,3,6,2,4] => 8
[5,1,3,6,4,2] => 11
[5,1,4,2,3,6] => 3
[5,1,4,2,6,3] => 8
[5,1,4,3,2,6] => 5
[5,1,4,3,6,2] => 7
[5,1,4,6,2,3] => 6
[5,1,4,6,3,2] => 9
[5,1,6,2,3,4] => 4
[5,1,6,2,4,3] => 11
[5,1,6,3,2,4] => 7
[5,1,6,3,4,2] => 10
[5,1,6,4,2,3] => 9
[5,1,6,4,3,2] => 14
[5,2,1,3,4,6] => 1
[5,2,1,3,6,4] => 5
[5,2,1,4,3,6] => 4
[5,2,1,4,6,3] => 8
[5,2,1,6,3,4] => 8
[5,2,1,6,4,3] => 21
[5,2,3,1,4,6] => 1
[5,2,3,1,6,4] => 6
[5,2,3,4,1,6] => 1
[5,2,3,4,6,1] => 1
[5,2,3,6,1,4] => 3
[5,2,3,6,4,1] => 3
[5,2,4,1,3,6] => 2
[5,2,4,1,6,3] => 6
[5,2,4,3,1,6] => 2
[5,2,4,3,6,1] => 2
[5,2,4,6,1,3] => 3
[5,2,4,6,3,1] => 3
[5,2,6,1,3,4] => 3
[5,2,6,1,4,3] => 10
[5,2,6,3,1,4] => 3
[5,2,6,3,4,1] => 3
[5,2,6,4,1,3] => 5
[5,2,6,4,3,1] => 5
[5,3,1,2,4,6] => 1
[5,3,1,2,6,4] => 6
[5,3,1,4,2,6] => 2
[5,3,1,4,6,2] => 3
[5,3,1,6,2,4] => 6
[5,3,1,6,4,2] => 10
[5,3,2,1,4,6] => 1
[5,3,2,1,6,4] => 8
[5,3,2,4,1,6] => 1
[5,3,2,4,6,1] => 1
[5,3,2,6,1,4] => 4
[5,3,2,6,4,1] => 4
[5,3,4,1,2,6] => 1
[5,3,4,1,6,2] => 2
[5,3,4,2,1,6] => 1
[5,3,4,2,6,1] => 1
[5,3,4,6,1,2] => 1
[5,3,4,6,2,1] => 1
[5,3,6,1,2,4] => 2
[5,3,6,1,4,2] => 4
[5,3,6,2,1,4] => 2
[5,3,6,2,4,1] => 2
[5,3,6,4,1,2] => 2
[5,3,6,4,2,1] => 2
[5,4,1,2,3,6] => 1
[5,4,1,2,6,3] => 3
[5,4,1,3,2,6] => 2
[5,4,1,3,6,2] => 3
[5,4,1,6,2,3] => 3
[5,4,1,6,3,2] => 5
[5,4,2,1,3,6] => 1
[5,4,2,1,6,3] => 4
[5,4,2,3,1,6] => 1
[5,4,2,3,6,1] => 1
[5,4,2,6,1,3] => 2
[5,4,2,6,3,1] => 2
[5,4,3,1,2,6] => 1
[5,4,3,1,6,2] => 2
[5,4,3,2,1,6] => 1
[5,4,3,2,6,1] => 1
[5,4,3,6,1,2] => 1
[5,4,3,6,2,1] => 1
[5,4,6,1,2,3] => 1
[5,4,6,1,3,2] => 2
[5,4,6,2,1,3] => 1
[5,4,6,2,3,1] => 1
[5,4,6,3,1,2] => 1
[5,4,6,3,2,1] => 1
[5,6,1,2,3,4] => 1
[5,6,1,2,4,3] => 3
[5,6,1,3,2,4] => 2
[5,6,1,3,4,2] => 3
[5,6,1,4,2,3] => 3
[5,6,1,4,3,2] => 5
[5,6,2,1,3,4] => 1
[5,6,2,1,4,3] => 4
[5,6,2,3,1,4] => 1
[5,6,2,3,4,1] => 1
[5,6,2,4,1,3] => 2
[5,6,2,4,3,1] => 2
[5,6,3,1,2,4] => 1
[5,6,3,1,4,2] => 2
[5,6,3,2,1,4] => 1
[5,6,3,2,4,1] => 1
[5,6,3,4,1,2] => 1
[5,6,3,4,2,1] => 1
[5,6,4,1,2,3] => 1
[5,6,4,1,3,2] => 2
[5,6,4,2,1,3] => 1
[5,6,4,2,3,1] => 1
[5,6,4,3,1,2] => 1
[5,6,4,3,2,1] => 1
[6,1,2,3,4,5] => 1
[6,1,2,3,5,4] => 4
[6,1,2,4,3,5] => 3
[6,1,2,4,5,3] => 6
[6,1,2,5,3,4] => 6
[6,1,2,5,4,3] => 14
[6,1,3,2,4,5] => 2
[6,1,3,2,5,4] => 13
[6,1,3,4,2,5] => 3
[6,1,3,4,5,2] => 4
[6,1,3,5,2,4] => 8
[6,1,3,5,4,2] => 11
[6,1,4,2,3,5] => 3
[6,1,4,2,5,3] => 8
[6,1,4,3,2,5] => 5
[6,1,4,3,5,2] => 7
[6,1,4,5,2,3] => 6
[6,1,4,5,3,2] => 9
[6,1,5,2,3,4] => 4
[6,1,5,2,4,3] => 11
[6,1,5,3,2,4] => 7
[6,1,5,3,4,2] => 10
[6,1,5,4,2,3] => 9
[6,1,5,4,3,2] => 14
[6,2,1,3,4,5] => 1
[6,2,1,3,5,4] => 5
[6,2,1,4,3,5] => 4
[6,2,1,4,5,3] => 8
[6,2,1,5,3,4] => 8
[6,2,1,5,4,3] => 21
[6,2,3,1,4,5] => 1
[6,2,3,1,5,4] => 6
[6,2,3,4,1,5] => 1
[6,2,3,4,5,1] => 1
[6,2,3,5,1,4] => 3
[6,2,3,5,4,1] => 3
[6,2,4,1,3,5] => 2
[6,2,4,1,5,3] => 6
[6,2,4,3,1,5] => 2
[6,2,4,3,5,1] => 2
[6,2,4,5,1,3] => 3
[6,2,4,5,3,1] => 3
[6,2,5,1,3,4] => 3
[6,2,5,1,4,3] => 10
[6,2,5,3,1,4] => 3
[6,2,5,3,4,1] => 3
[6,2,5,4,1,3] => 5
[6,2,5,4,3,1] => 5
[6,3,1,2,4,5] => 1
[6,3,1,2,5,4] => 6
[6,3,1,4,2,5] => 2
[6,3,1,4,5,2] => 3
[6,3,1,5,2,4] => 6
[6,3,1,5,4,2] => 10
[6,3,2,1,4,5] => 1
[6,3,2,1,5,4] => 8
[6,3,2,4,1,5] => 1
[6,3,2,4,5,1] => 1
[6,3,2,5,1,4] => 4
[6,3,2,5,4,1] => 4
[6,3,4,1,2,5] => 1
[6,3,4,1,5,2] => 2
[6,3,4,2,1,5] => 1
[6,3,4,2,5,1] => 1
[6,3,4,5,1,2] => 1
[6,3,4,5,2,1] => 1
[6,3,5,1,2,4] => 2
[6,3,5,1,4,2] => 4
[6,3,5,2,1,4] => 2
[6,3,5,2,4,1] => 2
[6,3,5,4,1,2] => 2
[6,3,5,4,2,1] => 2
[6,4,1,2,3,5] => 1
[6,4,1,2,5,3] => 3
[6,4,1,3,2,5] => 2
[6,4,1,3,5,2] => 3
[6,4,1,5,2,3] => 3
[6,4,1,5,3,2] => 5
[6,4,2,1,3,5] => 1
[6,4,2,1,5,3] => 4
[6,4,2,3,1,5] => 1
[6,4,2,3,5,1] => 1
[6,4,2,5,1,3] => 2
[6,4,2,5,3,1] => 2
[6,4,3,1,2,5] => 1
[6,4,3,1,5,2] => 2
[6,4,3,2,1,5] => 1
[6,4,3,2,5,1] => 1
[6,4,3,5,1,2] => 1
[6,4,3,5,2,1] => 1
[6,4,5,1,2,3] => 1
[6,4,5,1,3,2] => 2
[6,4,5,2,1,3] => 1
[6,4,5,2,3,1] => 1
[6,4,5,3,1,2] => 1
[6,4,5,3,2,1] => 1
[6,5,1,2,3,4] => 1
[6,5,1,2,4,3] => 3
[6,5,1,3,2,4] => 2
[6,5,1,3,4,2] => 3
[6,5,1,4,2,3] => 3
[6,5,1,4,3,2] => 5
[6,5,2,1,3,4] => 1
[6,5,2,1,4,3] => 4
[6,5,2,3,1,4] => 1
[6,5,2,3,4,1] => 1
[6,5,2,4,1,3] => 2
[6,5,2,4,3,1] => 2
[6,5,3,1,2,4] => 1
[6,5,3,1,4,2] => 2
[6,5,3,2,1,4] => 1
[6,5,3,2,4,1] => 1
[6,5,3,4,1,2] => 1
[6,5,3,4,2,1] => 1
[6,5,4,1,2,3] => 1
[6,5,4,1,3,2] => 2
[6,5,4,2,1,3] => 1
[6,5,4,2,3,1] => 1
[6,5,4,3,1,2] => 1
[6,5,4,3,2,1] => 1
[1,2,3,4,5,6,7] => 1
[1,2,3,4,5,7,6] => 6
[1,2,3,4,6,5,7] => 5
[1,2,3,4,6,7,5] => 15
[1,2,3,4,7,5,6] => 15
[1,2,3,4,7,6,5] => 55
[1,2,3,5,4,6,7] => 4
[1,2,3,5,4,7,6] => 54
[1,2,3,5,6,4,7] => 10
[1,2,3,5,6,7,4] => 20
[1,2,3,5,7,4,6] => 40
[1,2,3,5,7,6,4] => 85
[1,2,3,6,4,5,7] => 10
[1,2,3,6,4,7,5] => 40
[1,2,3,6,5,4,7] => 30
[1,2,3,6,5,7,4] => 65
[1,2,3,6,7,4,5] => 50
[1,2,3,6,7,5,4] => 125
[1,2,3,7,4,5,6] => 20
[1,2,3,7,4,6,5] => 85
[1,2,3,7,5,4,6] => 65
[1,2,3,7,5,6,4] => 146
[1,2,3,7,6,4,5] => 125
[1,2,3,7,6,5,4] => 330
[1,2,4,3,5,6,7] => 3
[1,2,4,3,5,7,6] => 32
[1,2,4,3,6,5,7] => 29
[1,2,4,3,6,7,5] => 84
[1,2,4,3,7,5,6] => 84
[1,2,4,3,7,6,5] => 439
[1,2,4,5,3,6,7] => 6
[1,2,4,5,3,7,6] => 71
[1,2,4,5,6,3,7] => 10
[1,2,4,5,6,7,3] => 15
[1,2,4,5,7,3,6] => 45
[1,2,4,5,7,6,3] => 69
[1,2,4,6,3,5,7] => 20
[1,2,4,6,3,7,5] => 115
[1,2,4,6,5,3,7] => 35
[1,2,4,6,5,7,3] => 54
[1,2,4,6,7,3,5] => 75
[1,2,4,6,7,5,3] => 120
[1,2,4,7,3,5,6] => 45
[1,2,4,7,3,6,5] => 310
[1,2,4,7,5,3,6] => 81
[1,2,4,7,5,6,3] => 127
[1,2,4,7,6,3,5] => 205
[1,2,4,7,6,5,3] => 335
[1,2,5,3,4,6,7] => 6
[1,2,5,3,4,7,6] => 71
[1,2,5,3,6,4,7] => 20
[1,2,5,3,6,7,4] => 45
[1,2,5,3,7,4,6] => 115
[1,2,5,3,7,6,4] => 310
[1,2,5,4,3,6,7] => 14
[1,2,5,4,3,7,6] => 294
[1,2,5,4,6,3,7] => 25
[1,2,5,4,6,7,3] => 39
[1,2,5,4,7,3,6] => 195
[1,2,5,4,7,6,3] => 320
[1,2,5,6,3,4,7] => 20
[1,2,5,6,3,7,4] => 60
[1,2,5,6,4,3,7] => 40
[1,2,5,6,4,7,3] => 66
[1,2,5,6,7,3,4] => 50
[1,2,5,6,7,4,3] => 90
[1,2,5,7,3,4,6] => 60
[1,2,5,7,3,6,4] => 184
[1,2,5,7,4,3,6] => 124
[1,2,5,7,4,6,3] => 208
[1,2,5,7,6,3,4] => 160
[1,2,5,7,6,4,3] => 295
[1,2,6,3,4,5,7] => 10
[1,2,6,3,4,7,5] => 45
[1,2,6,3,5,4,7] => 35
[1,2,6,3,5,7,4] => 81
[1,2,6,3,7,4,5] => 75
[1,2,6,3,7,5,4] => 205
[1,2,6,4,3,5,7] => 25
[1,2,6,4,3,7,5] => 195
[1,2,6,4,5,3,7] => 46
[1,2,6,4,5,7,3] => 73
[1,2,6,4,7,3,5] => 130
[1,2,6,4,7,5,3] => 215
[1,2,6,5,3,4,7] => 40
[1,2,6,5,3,7,4] => 124
[1,2,6,5,4,3,7] => 84
[1,2,6,5,4,7,3] => 142
[1,2,6,5,7,3,4] => 110
[1,2,6,5,7,4,3] => 205
[1,2,6,7,3,4,5] => 50
[1,2,6,7,3,5,4] => 160
[1,2,6,7,4,3,5] => 110
[1,2,6,7,4,5,3] => 190
[1,2,6,7,5,3,4] => 155
[1,2,6,7,5,4,3] => 300
[1,2,7,3,4,5,6] => 15
[1,2,7,3,4,6,5] => 69
[1,2,7,3,5,4,6] => 54
[1,2,7,3,5,6,4] => 127
[1,2,7,3,6,4,5] => 120
[1,2,7,3,6,5,4] => 335
[1,2,7,4,3,5,6] => 39
[1,2,7,4,3,6,5] => 320
[1,2,7,4,5,3,6] => 73
[1,2,7,4,5,6,3] => 117
[1,2,7,4,6,3,5] => 215
[1,2,7,4,6,5,3] => 360
[1,2,7,5,3,4,6] => 66
[1,2,7,5,3,6,4] => 208
[1,2,7,5,4,3,6] => 142
[1,2,7,5,4,6,3] => 243
[1,2,7,5,6,3,4] => 190
[1,2,7,5,6,4,3] => 360
[1,2,7,6,3,4,5] => 90
[1,2,7,6,3,5,4] => 295
[1,2,7,6,4,3,5] => 205
[1,2,7,6,4,5,3] => 360
[1,2,7,6,5,3,4] => 300
[1,2,7,6,5,4,3] => 594
[1,3,2,4,5,6,7] => 2
[1,3,2,4,5,7,6] => 17
[1,3,2,4,6,5,7] => 15
[1,3,2,4,6,7,5] => 47
[1,3,2,4,7,5,6] => 47
[1,3,2,4,7,6,5] => 200
[1,3,2,5,4,6,7] => 13
[1,3,2,5,4,7,6] => 198
[1,3,2,5,6,4,7] => 32
[1,3,2,5,6,7,4] => 61
[1,3,2,5,7,4,6] => 153
[1,3,2,5,7,6,4] => 328
[1,3,2,6,4,5,7] => 32
[1,3,2,6,4,7,5] => 153
[1,3,2,6,5,4,7] => 121
[1,3,2,6,5,7,4] => 267
[1,3,2,6,7,4,5] => 185
[1,3,2,6,7,5,4] => 496
[1,3,2,7,4,5,6] => 61
[1,3,2,7,4,6,5] => 328
[1,3,2,7,5,4,6] => 267
[1,3,2,7,5,6,4] => 610
[1,3,2,7,6,4,5] => 496
[1,3,2,7,6,5,4] => 1514
[1,3,4,2,5,6,7] => 3
[1,3,4,2,5,7,6] => 29
[1,3,4,2,6,5,7] => 26
[1,3,4,2,6,7,5] => 79
[1,3,4,2,7,5,6] => 77
[1,3,4,2,7,6,5] => 398
[1,3,4,5,2,6,7] => 4
[1,3,4,5,2,7,6] => 43
[1,3,4,5,6,2,7] => 5
[1,3,4,5,6,7,2] => 6
[1,3,4,5,7,2,6] => 24
[1,3,4,5,7,6,2] => 29
[1,3,4,6,2,5,7] => 15
[1,3,4,6,2,7,5] => 80
[1,3,4,6,5,2,7] => 19
[1,3,4,6,5,7,2] => 23
[1,3,4,6,7,2,5] => 45
[1,3,4,6,7,5,2] => 55
[1,3,4,7,2,5,6] => 36
[1,3,4,7,2,6,5] => 230
[1,3,4,7,5,2,6] => 46
[1,3,4,7,5,6,2] => 56
[1,3,4,7,6,2,5] => 130
[1,3,4,7,6,5,2] => 160
[1,3,5,2,4,6,7] => 8
[1,3,5,2,4,7,6] => 131
[1,3,5,2,6,4,7] => 34
[1,3,5,2,6,7,4] => 75
[1,3,5,2,7,4,6] => 172
[1,3,5,2,7,6,4] => 480
[1,3,5,4,2,6,7] => 11
[1,3,5,4,2,7,6] => 221
[1,3,5,4,6,2,7] => 14
[1,3,5,4,6,7,2] => 17
[1,3,5,4,7,2,6] => 125
[1,3,5,4,7,6,2] => 154
[1,3,5,6,2,4,7] => 20
[1,3,5,6,2,7,4] => 70
[1,3,5,6,4,2,7] => 26
[1,3,5,6,4,7,2] => 32
[1,3,5,6,7,2,4] => 40
[1,3,5,6,7,4,2] => 50
[1,3,5,7,2,4,6] => 64
[1,3,5,7,2,6,4] => 235
[1,3,5,7,4,2,6] => 84
[1,3,5,7,4,6,2] => 104
[1,3,5,7,6,2,4] => 135
[1,3,5,7,6,4,2] => 170
[1,3,6,2,4,5,7] => 15
[1,3,6,2,4,7,5] => 89
[1,3,6,2,5,4,7] => 74
[1,3,6,2,5,7,4] => 170
[1,3,6,2,7,4,5] => 144
[1,3,6,2,7,5,4] => 456
[1,3,6,4,2,5,7] => 21
[1,3,6,4,2,7,5] => 150
[1,3,6,4,5,2,7] => 27
[1,3,6,4,5,7,2] => 33
[1,3,6,4,7,2,5] => 85
[1,3,6,4,7,5,2] => 105
[1,3,6,5,2,4,7] => 44
[1,3,6,5,2,7,4] => 165
[1,3,6,5,4,2,7] => 58
[1,3,6,5,4,7,2] => 72
[1,3,6,5,7,2,4] => 95
[1,3,6,5,7,4,2] => 120
[1,3,6,7,2,4,5] => 60
[1,3,6,7,2,5,4] => 250
[1,3,6,7,4,2,5] => 80
[1,3,6,7,4,5,2] => 100
[1,3,6,7,5,2,4] => 145
[1,3,6,7,5,4,2] => 185
[1,3,7,2,4,5,6] => 24
[1,3,7,2,4,6,5] => 151
[1,3,7,2,5,4,6] => 127
[1,3,7,2,5,6,4] => 297
[1,3,7,2,6,4,5] => 266
[1,3,7,2,6,5,4] => 888
[1,3,7,4,2,5,6] => 34
[1,3,7,4,2,6,5] => 255
[1,3,7,4,5,2,6] => 44
[1,3,7,4,5,6,2] => 54
[1,3,7,4,6,2,5] => 145
[1,3,7,4,6,5,2] => 180
[1,3,7,5,2,4,6] => 76
[1,3,7,5,2,6,4] => 294
[1,3,7,5,4,2,6] => 101
[1,3,7,5,4,6,2] => 126
[1,3,7,5,6,2,4] => 170
[1,3,7,5,6,4,2] => 216
[1,3,7,6,2,4,5] => 115
[1,3,7,6,2,5,4] => 504
[1,3,7,6,4,2,5] => 155
[1,3,7,6,4,5,2] => 195
[1,3,7,6,5,2,4] => 294
[1,3,7,6,5,4,2] => 378
[1,4,2,3,5,6,7] => 3
[1,4,2,3,5,7,6] => 29
[1,4,2,3,6,5,7] => 26
[1,4,2,3,6,7,5] => 77
[1,4,2,3,7,5,6] => 79
[1,4,2,3,7,6,5] => 398
[1,4,2,5,3,6,7] => 8
[1,4,2,5,3,7,6] => 131
[1,4,2,5,6,3,7] => 15
[1,4,2,5,6,7,3] => 24
[1,4,2,5,7,3,6] => 89
[1,4,2,5,7,6,3] => 151
[1,4,2,6,3,5,7] => 34
[1,4,2,6,3,7,5] => 172
[1,4,2,6,5,3,7] => 74
[1,4,2,6,5,7,3] => 127
[1,4,2,6,7,3,5] => 144
[1,4,2,6,7,5,3] => 266
[1,4,2,7,3,5,6] => 75
[1,4,2,7,3,6,5] => 480
[1,4,2,7,5,3,6] => 170
[1,4,2,7,5,6,3] => 297
[1,4,2,7,6,3,5] => 456
[1,4,2,7,6,5,3] => 888
[1,4,3,2,5,6,7] => 5
[1,4,3,2,5,7,6] => 72
[1,4,3,2,6,5,7] => 67
[1,4,3,2,6,7,5] => 198
[1,4,3,2,7,5,6] => 198
[1,4,3,2,7,6,5] => 1186
[1,4,3,5,2,6,7] => 7
[1,4,3,5,2,7,6] => 109
[1,4,3,5,6,2,7] => 9
[1,4,3,5,6,7,2] => 11
[1,4,3,5,7,2,6] => 62
[1,4,3,5,7,6,2] => 77
[1,4,3,6,2,5,7] => 40
[1,4,3,6,2,7,5] => 212
[1,4,3,6,5,2,7] => 53
[1,4,3,6,5,7,2] => 66
[1,4,3,6,7,2,5] => 122
[1,4,3,6,7,5,2] => 154
[1,4,3,7,2,5,6] => 95
[1,4,3,7,2,6,5] => 743
[1,4,3,7,5,2,6] => 127
[1,4,3,7,5,6,2] => 159
[1,4,3,7,6,2,5] => 432
[1,4,3,7,6,5,2] => 553
[1,4,5,2,3,6,7] => 6
[1,4,5,2,3,7,6] => 74
[1,4,5,2,6,3,7] => 15
[1,4,5,2,6,7,3] => 27
[1,4,5,2,7,3,6] => 89
[1,4,5,2,7,6,3] => 183
[1,4,5,3,2,6,7] => 9
[1,4,5,3,2,7,6] => 162
[1,4,5,3,6,2,7] => 12
[1,4,5,3,6,7,2] => 15
[1,4,5,3,7,2,6] => 94
[1,4,5,3,7,6,2] => 120
[1,4,5,6,2,3,7] => 10
[1,4,5,6,2,7,3] => 24
[1,4,5,6,3,2,7] => 14
[1,4,5,6,3,7,2] => 18
[1,4,5,6,7,2,3] => 15
[1,4,5,6,7,3,2] => 20
[1,4,5,7,2,3,6] => 36
[1,4,5,7,2,6,3] => 87
[1,4,5,7,3,2,6] => 51
[1,4,5,7,3,6,2] => 66
[1,4,5,7,6,2,3] => 55
[1,4,5,7,6,3,2] => 74
[1,4,6,2,3,5,7] => 15
[1,4,6,2,3,7,5] => 89
[1,4,6,2,5,3,7] => 38
[1,4,6,2,5,7,3] => 69
[1,4,6,2,7,3,5] => 109
[1,4,6,2,7,5,3] => 227
[1,4,6,3,2,5,7] => 23
[1,4,6,3,2,7,5] => 202
[1,4,6,3,5,2,7] => 31
[1,4,6,3,5,7,2] => 39
[1,4,6,3,7,2,5] => 118
[1,4,6,3,7,5,2] => 152
[1,4,6,5,2,3,7] => 26
[1,4,6,5,2,7,3] => 63
[1,4,6,5,3,2,7] => 37
[1,4,6,5,3,7,2] => 48
[1,4,6,5,7,2,3] => 40
[1,4,6,5,7,3,2] => 54
[1,4,6,7,2,3,5] => 45
[1,4,6,7,2,5,3] => 110
[1,4,6,7,3,2,5] => 65
[1,4,6,7,3,5,2] => 85
[1,4,6,7,5,2,3] => 71
[1,4,6,7,5,3,2] => 97
[1,4,7,2,3,5,6] => 27
[1,4,7,2,3,6,5] => 183
[1,4,7,2,5,3,6] => 69
[1,4,7,2,5,6,3] => 126
[1,4,7,2,6,3,5] => 227
[1,4,7,2,6,5,3] => 477
[1,4,7,3,2,5,6] => 42
[1,4,7,3,2,6,5] => 426
[1,4,7,3,5,2,6] => 57
[1,4,7,3,5,6,2] => 72
[1,4,7,3,6,2,5] => 250
[1,4,7,3,6,5,2] => 324
[1,4,7,5,2,3,6] => 48
[1,4,7,5,2,6,3] => 117
[1,4,7,5,3,2,6] => 69
[1,4,7,5,3,6,2] => 90
[1,4,7,5,6,2,3] => 75
[1,4,7,5,6,3,2] => 102
[1,4,7,6,2,3,5] => 95
[1,4,7,6,2,5,3] => 234
[1,4,7,6,3,2,5] => 139
[1,4,7,6,3,5,2] => 183
[1,4,7,6,5,2,3] => 153
[1,4,7,6,5,3,2] => 211
[1,5,2,3,4,6,7] => 4
[1,5,2,3,4,7,6] => 43
[1,5,2,3,6,4,7] => 15
[1,5,2,3,6,7,4] => 36
[1,5,2,3,7,4,6] => 80
[1,5,2,3,7,6,4] => 230
[1,5,2,4,3,6,7] => 11
[1,5,2,4,3,7,6] => 221
[1,5,2,4,6,3,7] => 21
[1,5,2,4,6,7,3] => 34
[1,5,2,4,7,3,6] => 150
[1,5,2,4,7,6,3] => 255
[1,5,2,6,3,4,7] => 20
[1,5,2,6,3,7,4] => 64
[1,5,2,6,4,3,7] => 44
[1,5,2,6,4,7,3] => 76
[1,5,2,6,7,3,4] => 60
[1,5,2,6,7,4,3] => 115
[1,5,2,7,3,4,6] => 70
[1,5,2,7,3,6,4] => 235
[1,5,2,7,4,3,6] => 165
[1,5,2,7,4,6,3] => 294
[1,5,2,7,6,3,4] => 250
[1,5,2,7,6,4,3] => 504
[1,5,3,2,4,6,7] => 7
[1,5,3,2,4,7,6] => 109
[1,5,3,2,6,4,7] => 40
[1,5,3,2,6,7,4] => 95
[1,5,3,2,7,4,6] => 212
[1,5,3,2,7,6,4] => 743
[1,5,3,4,2,6,7] => 10
[1,5,3,4,2,7,6] => 184
[1,5,3,4,6,2,7] => 13
[1,5,3,4,6,7,2] => 16
[1,5,3,4,7,2,6] => 105
[1,5,3,4,7,6,2] => 131
[1,5,3,6,2,4,7] => 24
[1,5,3,6,2,7,4] => 95
[1,5,3,6,4,2,7] => 32
[1,5,3,6,4,7,2] => 40
[1,5,3,6,7,2,4] => 55
[1,5,3,6,7,4,2] => 70
[1,5,3,7,2,4,6] => 95
[1,5,3,7,2,6,4] => 434
[1,5,3,7,4,2,6] => 129
[1,5,3,7,4,6,2] => 163
[1,5,3,7,6,2,4] => 254
[1,5,3,7,6,4,2] => 328
[1,5,4,2,3,6,7] => 9
[1,5,4,2,3,7,6] => 162
[1,5,4,2,6,3,7] => 23
[1,5,4,2,6,7,3] => 42
[1,5,4,2,7,3,6] => 202
[1,5,4,2,7,6,3] => 426
[1,5,4,3,2,6,7] => 14
[1,5,4,3,2,7,6] => 381
[1,5,4,3,6,2,7] => 19
[1,5,4,3,6,7,2] => 24
[1,5,4,3,7,2,6] => 224
[1,5,4,3,7,6,2] => 291
[1,5,4,6,2,3,7] => 16
[1,5,4,6,2,7,3] => 39
[1,5,4,6,3,2,7] => 23
[1,5,4,6,3,7,2] => 30
[1,5,4,6,7,2,3] => 25
[1,5,4,6,7,3,2] => 34
[1,5,4,7,2,3,6] => 85
[1,5,4,7,2,6,3] => 210
[1,5,4,7,3,2,6] => 125
[1,5,4,7,3,6,2] => 165
[1,5,4,7,6,2,3] => 138
[1,5,4,7,6,3,2] => 191
[1,5,6,2,3,4,7] => 10
[1,5,6,2,3,7,4] => 36
[1,5,6,2,4,3,7] => 26
[1,5,6,2,4,7,3] => 48
[1,5,6,2,7,3,4] => 45
[1,5,6,2,7,4,3] => 95
[1,5,6,3,2,4,7] => 16
[1,5,6,3,2,7,4] => 85
[1,5,6,3,4,2,7] => 22
[1,5,6,3,4,7,2] => 28
[1,5,6,3,7,2,4] => 50
[1,5,6,3,7,4,2] => 65
[1,5,6,4,2,3,7] => 19
[1,5,6,4,2,7,3] => 47
[1,5,6,4,3,2,7] => 28
[1,5,6,4,3,7,2] => 37
[1,5,6,4,7,2,3] => 31
[1,5,6,4,7,3,2] => 43
[1,5,6,7,2,3,4] => 20
[1,5,6,7,2,4,3] => 50
[1,5,6,7,3,2,4] => 30
[1,5,6,7,3,4,2] => 40
[1,5,6,7,4,2,3] => 34
[1,5,6,7,4,3,2] => 48
[1,5,7,2,3,4,6] => 24
[1,5,7,2,3,6,4] => 87
[1,5,7,2,4,3,6] => 63
[1,5,7,2,4,6,3] => 117
[1,5,7,2,6,3,4] => 110
[1,5,7,2,6,4,3] => 234
[1,5,7,3,2,4,6] => 39
[1,5,7,3,2,6,4] => 210
[1,5,7,3,4,2,6] => 54
[1,5,7,3,4,6,2] => 69
[1,5,7,3,6,2,4] => 124
[1,5,7,3,6,4,2] => 162
[1,5,7,4,2,3,6] => 47
[1,5,7,4,2,6,3] => 117
[1,5,7,4,3,2,6] => 70
[1,5,7,4,3,6,2] => 93
[1,5,7,4,6,2,3] => 78
[1,5,7,4,6,3,2] => 109
[1,5,7,6,2,3,4] => 50
[1,5,7,6,2,4,3] => 126
[1,5,7,6,3,2,4] => 76
[1,5,7,6,3,4,2] => 102
[1,5,7,6,4,2,3] => 87
[1,5,7,6,4,3,2] => 124
[1,6,2,3,4,5,7] => 5
[1,6,2,3,4,7,5] => 24
[1,6,2,3,5,4,7] => 19
[1,6,2,3,5,7,4] => 46
[1,6,2,3,7,4,5] => 45
[1,6,2,3,7,5,4] => 130
[1,6,2,4,3,5,7] => 14
[1,6,2,4,3,7,5] => 125
[1,6,2,4,5,3,7] => 27
[1,6,2,4,5,7,3] => 44
[1,6,2,4,7,3,5] => 85
[1,6,2,4,7,5,3] => 145
[1,6,2,5,3,4,7] => 26
[1,6,2,5,3,7,4] => 84
[1,6,2,5,4,3,7] => 58
[1,6,2,5,4,7,3] => 101
[1,6,2,5,7,3,4] => 80
[1,6,2,5,7,4,3] => 155
[1,6,2,7,3,4,5] => 40
[1,6,2,7,3,5,4] => 135
[1,6,2,7,4,3,5] => 95
[1,6,2,7,4,5,3] => 170
[1,6,2,7,5,3,4] => 145
[1,6,2,7,5,4,3] => 294
[1,6,3,2,4,5,7] => 9
[1,6,3,2,4,7,5] => 62
[1,6,3,2,5,4,7] => 53
[1,6,3,2,5,7,4] => 127
[1,6,3,2,7,4,5] => 122
[1,6,3,2,7,5,4] => 432
[1,6,3,4,2,5,7] => 13
[1,6,3,4,2,7,5] => 105
[1,6,3,4,5,2,7] => 17
[1,6,3,4,5,7,2] => 21
[1,6,3,4,7,2,5] => 60
[1,6,3,4,7,5,2] => 75
[1,6,3,5,2,4,7] => 32
[1,6,3,5,2,7,4] => 129
[1,6,3,5,4,2,7] => 43
[1,6,3,5,4,7,2] => 54
[1,6,3,5,7,2,4] => 75
[1,6,3,5,7,4,2] => 96
[1,6,3,7,2,4,5] => 55
[1,6,3,7,2,5,4] => 254
[1,6,3,7,4,2,5] => 75
[1,6,3,7,4,5,2] => 95
[1,6,3,7,5,2,4] => 149
[1,6,3,7,5,4,2] => 193
[1,6,4,2,3,5,7] => 12
[1,6,4,2,3,7,5] => 94
[1,6,4,2,5,3,7] => 31
[1,6,4,2,5,7,3] => 57
[1,6,4,2,7,3,5] => 118
[1,6,4,2,7,5,3] => 250
[1,6,4,3,2,5,7] => 19
[1,6,4,3,2,7,5] => 224
[1,6,4,3,5,2,7] => 26
[1,6,4,3,5,7,2] => 33
[1,6,4,3,7,2,5] => 132
[1,6,4,3,7,5,2] => 172
[1,6,4,5,2,3,7] => 22
[1,6,4,5,2,7,3] => 54
[1,6,4,5,3,2,7] => 32
[1,6,4,5,3,7,2] => 42
[1,6,4,5,7,2,3] => 35
[1,6,4,5,7,3,2] => 48
[1,6,4,7,2,3,5] => 50
[1,6,4,7,2,5,3] => 124
[1,6,4,7,3,2,5] => 74
[1,6,4,7,3,5,2] => 98
[1,6,4,7,5,2,3] => 82
[1,6,4,7,5,3,2] => 114
[1,6,5,2,3,4,7] => 14
[1,6,5,2,3,7,4] => 51
[1,6,5,2,4,3,7] => 37
[1,6,5,2,4,7,3] => 69
[1,6,5,2,7,3,4] => 65
[1,6,5,2,7,4,3] => 139
[1,6,5,3,2,4,7] => 23
[1,6,5,3,2,7,4] => 125
[1,6,5,3,4,2,7] => 32
[1,6,5,3,4,7,2] => 41
[1,6,5,3,7,2,4] => 74
[1,6,5,3,7,4,2] => 97
[1,6,5,4,2,3,7] => 28
[1,6,5,4,2,7,3] => 70
[1,6,5,4,3,2,7] => 42
[1,6,5,4,3,7,2] => 56
[1,6,5,4,7,2,3] => 47
[1,6,5,4,7,3,2] => 66
[1,6,5,7,2,3,4] => 30
[1,6,5,7,2,4,3] => 76
[1,6,5,7,3,2,4] => 46
[1,6,5,7,3,4,2] => 62
[1,6,5,7,4,2,3] => 53
[1,6,5,7,4,3,2] => 76
[1,6,7,2,3,4,5] => 15
[1,6,7,2,3,5,4] => 55
[1,6,7,2,4,3,5] => 40
[1,6,7,2,4,5,3] => 75
[1,6,7,2,5,3,4] => 71
[1,6,7,2,5,4,3] => 153
[1,6,7,3,2,4,5] => 25
[1,6,7,3,2,5,4] => 138
[1,6,7,3,4,2,5] => 35
[1,6,7,3,4,5,2] => 45
[1,6,7,3,5,2,4] => 82
[1,6,7,3,5,4,2] => 108
[1,6,7,4,2,3,5] => 31
[1,6,7,4,2,5,3] => 78
[1,6,7,4,3,2,5] => 47
[1,6,7,4,3,5,2] => 63
[1,6,7,4,5,2,3] => 53
[1,6,7,4,5,3,2] => 75
[1,6,7,5,2,3,4] => 34
[1,6,7,5,2,4,3] => 87
[1,6,7,5,3,2,4] => 53
[1,6,7,5,3,4,2] => 72
[1,6,7,5,4,2,3] => 62
[1,6,7,5,4,3,2] => 90
[1,7,2,3,4,5,6] => 6
[1,7,2,3,4,6,5] => 29
[1,7,2,3,5,4,6] => 23
[1,7,2,3,5,6,4] => 56
[1,7,2,3,6,4,5] => 55
[1,7,2,3,6,5,4] => 160
[1,7,2,4,3,5,6] => 17
[1,7,2,4,3,6,5] => 154
[1,7,2,4,5,3,6] => 33
[1,7,2,4,5,6,3] => 54
[1,7,2,4,6,3,5] => 105
[1,7,2,4,6,5,3] => 180
[1,7,2,5,3,4,6] => 32
[1,7,2,5,3,6,4] => 104
[1,7,2,5,4,3,6] => 72
[1,7,2,5,4,6,3] => 126
[1,7,2,5,6,3,4] => 100
[1,7,2,5,6,4,3] => 195
[1,7,2,6,3,4,5] => 50
[1,7,2,6,3,5,4] => 170
[1,7,2,6,4,3,5] => 120
[1,7,2,6,4,5,3] => 216
[1,7,2,6,5,3,4] => 185
[1,7,2,6,5,4,3] => 378
[1,7,3,2,4,5,6] => 11
[1,7,3,2,4,6,5] => 77
[1,7,3,2,5,4,6] => 66
[1,7,3,2,5,6,4] => 159
[1,7,3,2,6,4,5] => 154
[1,7,3,2,6,5,4] => 553
[1,7,3,4,2,5,6] => 16
[1,7,3,4,2,6,5] => 131
[1,7,3,4,5,2,6] => 21
[1,7,3,4,5,6,2] => 26
[1,7,3,4,6,2,5] => 75
[1,7,3,4,6,5,2] => 94
[1,7,3,5,2,4,6] => 40
[1,7,3,5,2,6,4] => 163
[1,7,3,5,4,2,6] => 54
[1,7,3,5,4,6,2] => 68
[1,7,3,5,6,2,4] => 95
[1,7,3,5,6,4,2] => 122
[1,7,3,6,2,4,5] => 70
[1,7,3,6,2,5,4] => 328
[1,7,3,6,4,2,5] => 96
[1,7,3,6,4,5,2] => 122
[1,7,3,6,5,2,4] => 193
[1,7,3,6,5,4,2] => 251
[1,7,4,2,3,5,6] => 15
[1,7,4,2,3,6,5] => 120
[1,7,4,2,5,3,6] => 39
[1,7,4,2,5,6,3] => 72
[1,7,4,2,6,3,5] => 152
[1,7,4,2,6,5,3] => 324
[1,7,4,3,2,5,6] => 24
[1,7,4,3,2,6,5] => 291
[1,7,4,3,5,2,6] => 33
[1,7,4,3,5,6,2] => 42
[1,7,4,3,6,2,5] => 172
[1,7,4,3,6,5,2] => 225
[1,7,4,5,2,3,6] => 28
[1,7,4,5,2,6,3] => 69
[1,7,4,5,3,2,6] => 41
[1,7,4,5,3,6,2] => 54
[1,7,4,5,6,2,3] => 45
[1,7,4,5,6,3,2] => 62
[1,7,4,6,2,3,5] => 65
[1,7,4,6,2,5,3] => 162
[1,7,4,6,3,2,5] => 97
[1,7,4,6,3,5,2] => 129
[1,7,4,6,5,2,3] => 108
[1,7,4,6,5,3,2] => 151
[1,7,5,2,3,4,6] => 18
[1,7,5,2,3,6,4] => 66
[1,7,5,2,4,3,6] => 48
[1,7,5,2,4,6,3] => 90
[1,7,5,2,6,3,4] => 85
[1,7,5,2,6,4,3] => 183
[1,7,5,3,2,4,6] => 30
[1,7,5,3,2,6,4] => 165
[1,7,5,3,4,2,6] => 42
[1,7,5,3,4,6,2] => 54
[1,7,5,3,6,2,4] => 98
[1,7,5,3,6,4,2] => 129
[1,7,5,4,2,3,6] => 37
[1,7,5,4,2,6,3] => 93
[1,7,5,4,3,2,6] => 56
[1,7,5,4,3,6,2] => 75
[1,7,5,4,6,2,3] => 63
[1,7,5,4,6,3,2] => 89
[1,7,5,6,2,3,4] => 40
[1,7,5,6,2,4,3] => 102
[1,7,5,6,3,2,4] => 62
[1,7,5,6,3,4,2] => 84
[1,7,5,6,4,2,3] => 72
[1,7,5,6,4,3,2] => 104
[1,7,6,2,3,4,5] => 20
[1,7,6,2,3,5,4] => 74
[1,7,6,2,4,3,5] => 54
[1,7,6,2,4,5,3] => 102
[1,7,6,2,5,3,4] => 97
[1,7,6,2,5,4,3] => 211
[1,7,6,3,2,4,5] => 34
[1,7,6,3,2,5,4] => 191
[1,7,6,3,4,2,5] => 48
[1,7,6,3,4,5,2] => 62
[1,7,6,3,5,2,4] => 114
[1,7,6,3,5,4,2] => 151
[1,7,6,4,2,3,5] => 43
[1,7,6,4,2,5,3] => 109
[1,7,6,4,3,2,5] => 66
[1,7,6,4,3,5,2] => 89
[1,7,6,4,5,2,3] => 75
[1,7,6,4,5,3,2] => 107
[1,7,6,5,2,3,4] => 48
[1,7,6,5,2,4,3] => 124
[1,7,6,5,3,2,4] => 76
[1,7,6,5,3,4,2] => 104
[1,7,6,5,4,2,3] => 90
[1,7,6,5,4,3,2] => 132
[2,1,3,4,5,6,7] => 1
[2,1,3,4,5,7,6] => 7
[2,1,3,4,6,5,7] => 6
[2,1,3,4,6,7,5] => 19
[2,1,3,4,7,5,6] => 19
[2,1,3,4,7,6,5] => 74
[2,1,3,5,4,6,7] => 5
[2,1,3,5,4,7,6] => 73
[2,1,3,5,6,4,7] => 13
[2,1,3,5,6,7,4] => 26
[2,1,3,5,7,4,6] => 55
[2,1,3,5,7,6,4] => 119
[2,1,3,6,4,5,7] => 13
[2,1,3,6,4,7,5] => 55
[2,1,3,6,5,4,7] => 42
[2,1,3,6,5,7,4] => 93
[2,1,3,6,7,4,5] => 71
[2,1,3,6,7,5,4] => 182
[2,1,3,7,4,5,6] => 26
[2,1,3,7,4,6,5] => 119
[2,1,3,7,5,4,6] => 93
[2,1,3,7,5,6,4] => 215
[2,1,3,7,6,4,5] => 182
[2,1,3,7,6,5,4] => 499
[2,1,4,3,5,6,7] => 4
[2,1,4,3,5,7,6] => 45
[2,1,4,3,6,5,7] => 41
[2,1,4,3,6,7,5] => 121
[2,1,4,3,7,5,6] => 121
[2,1,4,3,7,6,5] => 658
[2,1,4,5,3,6,7] => 8
[2,1,4,5,3,7,6] => 101
[2,1,4,5,6,3,7] => 13
[2,1,4,5,6,7,3] => 19
[2,1,4,5,7,3,6] => 64
[2,1,4,5,7,6,3] => 97
[2,1,4,6,3,5,7] => 29
[2,1,4,6,3,7,5] => 169
[2,1,4,6,5,3,7] => 51
[2,1,4,6,5,7,3] => 78
[2,1,4,6,7,3,5] => 111
[2,1,4,6,7,5,3] => 177
[2,1,4,7,3,5,6] => 67
[2,1,4,7,3,6,5] => 473
[2,1,4,7,5,3,6] => 122
[2,1,4,7,5,6,3] => 190
[2,1,4,7,6,3,5] => 317
[2,1,4,7,6,5,3] => 520
[2,1,5,3,4,6,7] => 8
[2,1,5,3,4,7,6] => 101
[2,1,5,3,6,4,7] => 29
[2,1,5,3,6,7,4] => 67
[2,1,5,3,7,4,6] => 169
[2,1,5,3,7,6,4] => 473
[2,1,5,4,3,6,7] => 21
[2,1,5,4,3,7,6] => 452
[2,1,5,4,6,3,7] => 38
[2,1,5,4,6,7,3] => 59
[2,1,5,4,7,3,6] => 304
[2,1,5,4,7,6,3] => 501
[2,1,5,6,3,4,7] => 29
[2,1,5,6,3,7,4] => 89
[2,1,5,6,4,3,7] => 60
[2,1,5,6,4,7,3] => 99
[2,1,5,6,7,3,4] => 73
[2,1,5,6,7,4,3] => 132
[2,1,5,7,3,4,6] => 89
[2,1,5,7,3,6,4] => 284
[2,1,5,7,4,3,6] => 195
[2,1,5,7,4,6,3] => 330
[2,1,5,7,6,3,4] => 247
[2,1,5,7,6,4,3] => 465
[2,1,6,3,4,5,7] => 13
[2,1,6,3,4,7,5] => 64
[2,1,6,3,5,4,7] => 51
[2,1,6,3,5,7,4] => 122
[2,1,6,3,7,4,5] => 111
[2,1,6,3,7,5,4] => 317
[2,1,6,4,3,5,7] => 38
[2,1,6,4,3,7,5] => 304
[2,1,6,4,5,3,7] => 71
[2,1,6,4,5,7,3] => 112
[2,1,6,4,7,3,5] => 206
[2,1,6,4,7,5,3] => 343
[2,1,6,5,3,4,7] => 60
[2,1,6,5,3,7,4] => 195
[2,1,6,5,4,3,7] => 135
[2,1,6,5,4,7,3] => 231
[2,1,6,5,7,3,4] => 174
[2,1,6,5,7,4,3] => 333
[2,1,6,7,3,4,5] => 73
[2,1,6,7,3,5,4] => 247
[2,1,6,7,4,3,5] => 174
[2,1,6,7,4,5,3] => 304
[2,1,6,7,5,3,4] => 240
[2,1,6,7,5,4,3] => 481
[2,1,7,3,4,5,6] => 19
[2,1,7,3,4,6,5] => 97
[2,1,7,3,5,4,6] => 78
[2,1,7,3,5,6,4] => 190
[2,1,7,3,6,4,5] => 177
[2,1,7,3,6,5,4] => 520
[2,1,7,4,3,5,6] => 59
[2,1,7,4,3,6,5] => 501
[2,1,7,4,5,3,6] => 112
[2,1,7,4,5,6,3] => 178
[2,1,7,4,6,3,5] => 343
[2,1,7,4,6,5,3] => 579
[2,1,7,5,3,4,6] => 99
[2,1,7,5,3,6,4] => 330
[2,1,7,5,4,3,6] => 231
[2,1,7,5,4,6,3] => 401
[2,1,7,5,6,3,4] => 304
[2,1,7,5,6,4,3] => 594
[2,1,7,6,3,4,5] => 132
[2,1,7,6,3,5,4] => 465
[2,1,7,6,4,3,5] => 333
[2,1,7,6,4,5,3] => 594
[2,1,7,6,5,3,4] => 481
[2,1,7,6,5,4,3] => 1000
[2,3,1,4,5,6,7] => 1
[2,3,1,4,5,7,6] => 8
[2,3,1,4,6,5,7] => 7
[2,3,1,4,6,7,5] => 22
[2,3,1,4,7,5,6] => 22
[2,3,1,4,7,6,5] => 93
[2,3,1,5,4,6,7] => 6
[2,3,1,5,4,7,6] => 92
[2,3,1,5,6,4,7] => 15
[2,3,1,5,6,7,4] => 29
[2,3,1,5,7,4,6] => 71
[2,3,1,5,7,6,4] => 154
[2,3,1,6,4,5,7] => 15
[2,3,1,6,4,7,5] => 71
[2,3,1,6,5,4,7] => 56
[2,3,1,6,5,7,4] => 125
[2,3,1,6,7,4,5] => 87
[2,3,1,6,7,5,4] => 232
[2,3,1,7,4,5,6] => 29
[2,3,1,7,4,6,5] => 153
[2,3,1,7,5,4,6] => 124
[2,3,1,7,5,6,4] => 287
[2,3,1,7,6,4,5] => 235
[2,3,1,7,6,5,4] => 709
[2,3,4,1,5,6,7] => 1
[2,3,4,1,5,7,6] => 9
[2,3,4,1,6,5,7] => 8
[2,3,4,1,6,7,5] => 24
[2,3,4,1,7,5,6] => 24
[2,3,4,1,7,6,5] => 118
[2,3,4,5,1,6,7] => 1
[2,3,4,5,1,7,6] => 10
[2,3,4,5,6,1,7] => 1
[2,3,4,5,6,7,1] => 1
[2,3,4,5,7,1,6] => 5
[2,3,4,5,7,6,1] => 5
[2,3,4,6,1,5,7] => 4
[2,3,4,6,1,7,5] => 20
[2,3,4,6,5,1,7] => 4
[2,3,4,6,5,7,1] => 4
[2,3,4,6,7,1,5] => 10
[2,3,4,6,7,5,1] => 10
[2,3,4,7,1,5,6] => 10
[2,3,4,7,1,6,5] => 60
[2,3,4,7,5,1,6] => 10
[2,3,4,7,5,6,1] => 10
[2,3,4,7,6,1,5] => 30
[2,3,4,7,6,5,1] => 30
[2,3,5,1,4,6,7] => 3
[2,3,5,1,4,7,6] => 49
[2,3,5,1,6,4,7] => 12
[2,3,5,1,6,7,4] => 26
[2,3,5,1,7,4,6] => 60
[2,3,5,1,7,6,4] => 160
[2,3,5,4,1,6,7] => 3
[2,3,5,4,1,7,6] => 58
[2,3,5,4,6,1,7] => 3
[2,3,5,4,6,7,1] => 3
[2,3,5,4,7,1,6] => 29
[2,3,5,4,7,6,1] => 29
[2,3,5,6,1,4,7] => 6
[2,3,5,6,1,7,4] => 20
[2,3,5,6,4,1,7] => 6
[2,3,5,6,4,7,1] => 6
[2,3,5,6,7,1,4] => 10
[2,3,5,6,7,4,1] => 10
[2,3,5,7,1,4,6] => 20
[2,3,5,7,1,6,4] => 70
[2,3,5,7,4,1,6] => 20
[2,3,5,7,4,6,1] => 20
[2,3,5,7,6,1,4] => 35
[2,3,5,7,6,4,1] => 35
[2,3,6,1,4,5,7] => 6
[2,3,6,1,4,7,5] => 34
[2,3,6,1,5,4,7] => 28
[2,3,6,1,5,7,4] => 64
[2,3,6,1,7,4,5] => 54
[2,3,6,1,7,5,4] => 168
[2,3,6,4,1,5,7] => 6
[2,3,6,4,1,7,5] => 40
[2,3,6,4,5,1,7] => 6
[2,3,6,4,5,7,1] => 6
[2,3,6,4,7,1,5] => 20
[2,3,6,4,7,5,1] => 20
[2,3,6,5,1,4,7] => 14
[2,3,6,5,1,7,4] => 50
[2,3,6,5,4,1,7] => 14
[2,3,6,5,4,7,1] => 14
[2,3,6,5,7,1,4] => 25
[2,3,6,5,7,4,1] => 25
[2,3,6,7,1,4,5] => 20
[2,3,6,7,1,5,4] => 80
[2,3,6,7,4,1,5] => 20
[2,3,6,7,4,5,1] => 20
[2,3,6,7,5,1,4] => 40
[2,3,6,7,5,4,1] => 40
[2,3,7,1,4,5,6] => 10
[2,3,7,1,4,6,5] => 60
[2,3,7,1,5,4,6] => 50
[2,3,7,1,5,6,4] => 117
[2,3,7,1,6,4,5] => 105
[2,3,7,1,6,5,4] => 346
[2,3,7,4,1,5,6] => 10
[2,3,7,4,1,6,5] => 70
[2,3,7,4,5,1,6] => 10
[2,3,7,4,5,6,1] => 10
[2,3,7,4,6,1,5] => 35
[2,3,7,4,6,5,1] => 35
[2,3,7,5,1,4,6] => 25
[2,3,7,5,1,6,4] => 92
[2,3,7,5,4,1,6] => 25
[2,3,7,5,4,6,1] => 25
[2,3,7,5,6,1,4] => 46
[2,3,7,5,6,4,1] => 46
[2,3,7,6,1,4,5] => 40
[2,3,7,6,1,5,4] => 168
[2,3,7,6,4,1,5] => 40
[2,3,7,6,4,5,1] => 40
[2,3,7,6,5,1,4] => 84
[2,3,7,6,5,4,1] => 84
[2,4,1,3,5,6,7] => 2
[2,4,1,3,5,7,6] => 23
[2,4,1,3,6,5,7] => 21
[2,4,1,3,6,7,5] => 64
[2,4,1,3,7,5,6] => 63
[2,4,1,3,7,6,5] => 346
[2,4,1,5,3,6,7] => 6
[2,4,1,5,3,7,6] => 93
[2,4,1,5,6,3,7] => 11
[2,4,1,5,6,7,3] => 17
[2,4,1,5,7,3,6] => 63
[2,4,1,5,7,6,3] => 103
[2,4,1,6,3,5,7] => 24
[2,4,1,6,3,7,5] => 133
[2,4,1,6,5,3,7] => 52
[2,4,1,6,5,7,3] => 86
[2,4,1,6,7,3,5] => 103
[2,4,1,6,7,5,3] => 183
[2,4,1,7,3,5,6] => 53
[2,4,1,7,3,6,5] => 378
[2,4,1,7,5,3,6] => 121
[2,4,1,7,5,6,3] => 204
[2,4,1,7,6,3,5] => 323
[2,4,1,7,6,5,3] => 609
[2,4,3,1,5,6,7] => 2
[2,4,3,1,5,7,6] => 28
[2,4,3,1,6,5,7] => 26
[2,4,3,1,6,7,5] => 77
[2,4,3,1,7,5,6] => 77
[2,4,3,1,7,6,5] => 463
[2,4,3,5,1,6,7] => 2
[2,4,3,5,1,7,6] => 30
[2,4,3,5,6,1,7] => 2
[2,4,3,5,6,7,1] => 2
[2,4,3,5,7,1,6] => 15
[2,4,3,5,7,6,1] => 15
[2,4,3,6,1,5,7] => 13
[2,4,3,6,1,7,5] => 64
[2,4,3,6,5,1,7] => 13
[2,4,3,6,5,7,1] => 13
[2,4,3,6,7,1,5] => 32
[2,4,3,6,7,5,1] => 32
[2,4,3,7,1,5,6] => 32
[2,4,3,7,1,6,5] => 242
[2,4,3,7,5,1,6] => 32
[2,4,3,7,5,6,1] => 32
[2,4,3,7,6,1,5] => 121
[2,4,3,7,6,5,1] => 121
[2,4,5,1,3,6,7] => 3
[2,4,5,1,3,7,6] => 41
[2,4,5,1,6,3,7] => 8
[2,4,5,1,6,7,3] => 14
[2,4,5,1,7,3,6] => 45
[2,4,5,1,7,6,3] => 91
[2,4,5,3,1,6,7] => 3
[2,4,5,3,1,7,6] => 52
[2,4,5,3,6,1,7] => 3
[2,4,5,3,6,7,1] => 3
[2,4,5,3,7,1,6] => 26
[2,4,5,3,7,6,1] => 26
[2,4,5,6,1,3,7] => 4
[2,4,5,6,1,7,3] => 10
[2,4,5,6,3,1,7] => 4
[2,4,5,6,3,7,1] => 4
[2,4,5,6,7,1,3] => 5
[2,4,5,6,7,3,1] => 5
[2,4,5,7,1,3,6] => 15
[2,4,5,7,1,6,3] => 38
[2,4,5,7,3,1,6] => 15
[2,4,5,7,3,6,1] => 15
[2,4,5,7,6,1,3] => 19
[2,4,5,7,6,3,1] => 19
[2,4,6,1,3,5,7] => 8
[2,4,6,1,3,7,5] => 54
[2,4,6,1,5,3,7] => 22
[2,4,6,1,5,7,3] => 39
[2,4,6,1,7,3,5] => 60
[2,4,6,1,7,5,3] => 124
[2,4,6,3,1,5,7] => 8
[2,4,6,3,1,7,5] => 68
[2,4,6,3,5,1,7] => 8
[2,4,6,3,5,7,1] => 8
[2,4,6,3,7,1,5] => 34
[2,4,6,3,7,5,1] => 34
[2,4,6,5,1,3,7] => 11
[2,4,6,5,1,7,3] => 28
[2,4,6,5,3,1,7] => 11
[2,4,6,5,3,7,1] => 11
[2,4,6,5,7,1,3] => 14
[2,4,6,5,7,3,1] => 14
[2,4,6,7,1,3,5] => 20
[2,4,6,7,1,5,3] => 52
[2,4,6,7,3,1,5] => 20
[2,4,6,7,3,5,1] => 20
[2,4,6,7,5,1,3] => 26
[2,4,6,7,5,3,1] => 26
[2,4,7,1,3,5,6] => 15
[2,4,7,1,3,6,5] => 118
[2,4,7,1,5,3,6] => 42
[2,4,7,1,5,6,3] => 75
[2,4,7,1,6,3,5] => 132
[2,4,7,1,6,5,3] => 276
[2,4,7,3,1,5,6] => 15
[2,4,7,3,1,6,5] => 148
[2,4,7,3,5,1,6] => 15
[2,4,7,3,5,6,1] => 15
[2,4,7,3,6,1,5] => 74
[2,4,7,3,6,5,1] => 74
[2,4,7,5,1,3,6] => 21
[2,4,7,5,1,6,3] => 54
[2,4,7,5,3,1,6] => 21
[2,4,7,5,3,6,1] => 21
[2,4,7,5,6,1,3] => 27
[2,4,7,5,6,3,1] => 27
[2,4,7,6,1,3,5] => 44
[2,4,7,6,1,5,3] => 116
[2,4,7,6,3,1,5] => 44
[2,4,7,6,3,5,1] => 44
[2,4,7,6,5,1,3] => 58
[2,4,7,6,5,3,1] => 58
[2,5,1,3,4,6,7] => 3
[2,5,1,3,4,7,6] => 38
[2,5,1,3,6,4,7] => 13
[2,5,1,3,6,7,4] => 32
[2,5,1,3,7,4,6] => 73
[2,5,1,3,7,6,4] => 220
[2,5,1,4,3,6,7] => 10
[2,5,1,4,3,7,6] => 213
[2,5,1,4,6,3,7] => 19
[2,5,1,4,6,7,3] => 30
[2,5,1,4,7,3,6] => 147
[2,5,1,4,7,6,3] => 249
[2,5,1,6,3,4,7] => 17
[2,5,1,6,3,7,4] => 57
[2,5,1,6,4,3,7] => 40
[2,5,1,6,4,7,3] => 69
[2,5,1,6,7,3,4] => 52
[2,5,1,6,7,4,3] => 101
[2,5,1,7,3,4,6] => 57
[2,5,1,7,3,6,4] => 204
[2,5,1,7,4,3,6] => 147
[2,5,1,7,4,6,3] => 261
[2,5,1,7,6,3,4] => 208
[2,5,1,7,6,4,3] => 430
[2,5,3,1,4,6,7] => 3
[2,5,3,1,4,7,6] => 45
[2,5,3,1,6,4,7] => 16
[2,5,3,1,6,7,4] => 38
[2,5,3,1,7,4,6] => 87
[2,5,3,1,7,6,4] => 300
[2,5,3,4,1,6,7] => 3
[2,5,3,4,1,7,6] => 52
[2,5,3,4,6,1,7] => 3
[2,5,3,4,6,7,1] => 3
[2,5,3,4,7,1,6] => 26
[2,5,3,4,7,6,1] => 26
[2,5,3,6,1,4,7] => 8
[2,5,3,6,1,7,4] => 30
[2,5,3,6,4,1,7] => 8
[2,5,3,6,4,7,1] => 8
[2,5,3,6,7,1,4] => 15
[2,5,3,6,7,4,1] => 15
[2,5,3,7,1,4,6] => 34
[2,5,3,7,1,6,4] => 148
[2,5,3,7,4,1,6] => 34
[2,5,3,7,4,6,1] => 34
[2,5,3,7,6,1,4] => 74
[2,5,3,7,6,4,1] => 74
[2,5,4,1,3,6,7] => 5
[2,5,4,1,3,7,6] => 107
[2,5,4,1,6,3,7] => 14
[2,5,4,1,6,7,3] => 25
[2,5,4,1,7,3,6] => 120
[2,5,4,1,7,6,3] => 252
[2,5,4,3,1,6,7] => 5
[2,5,4,3,1,7,6] => 134
[2,5,4,3,6,1,7] => 5
[2,5,4,3,6,7,1] => 5
[2,5,4,3,7,1,6] => 67
[2,5,4,3,7,6,1] => 67
[2,5,4,6,1,3,7] => 7
[2,5,4,6,1,7,3] => 18
[2,5,4,6,3,1,7] => 7
[2,5,4,6,3,7,1] => 7
[2,5,4,6,7,1,3] => 9
[2,5,4,6,7,3,1] => 9
[2,5,4,7,1,3,6] => 40
[2,5,4,7,1,6,3] => 106
[2,5,4,7,3,1,6] => 40
[2,5,4,7,3,6,1] => 40
[2,5,4,7,6,1,3] => 53
[2,5,4,7,6,3,1] => 53
[2,5,6,1,3,4,7] => 6
[2,5,6,1,3,7,4] => 24
[2,5,6,1,4,3,7] => 18
[2,5,6,1,4,7,3] => 33
[2,5,6,1,7,3,4] => 29
[2,5,6,1,7,4,3] => 64
[2,5,6,3,1,4,7] => 6
[2,5,6,3,1,7,4] => 30
[2,5,6,3,4,1,7] => 6
[2,5,6,3,4,7,1] => 6
[2,5,6,3,7,1,4] => 15
[2,5,6,3,7,4,1] => 15
[2,5,6,4,1,3,7] => 9
[2,5,6,4,1,7,3] => 24
[2,5,6,4,3,1,7] => 9
[2,5,6,4,3,7,1] => 9
[2,5,6,4,7,1,3] => 12
[2,5,6,4,7,3,1] => 12
[2,5,6,7,1,3,4] => 10
[2,5,6,7,1,4,3] => 28
[2,5,6,7,3,1,4] => 10
[2,5,6,7,3,4,1] => 10
[2,5,6,7,4,1,3] => 14
[2,5,6,7,4,3,1] => 14
[2,5,7,1,3,4,6] => 15
[2,5,7,1,3,6,4] => 61
[2,5,7,1,4,3,6] => 46
[2,5,7,1,4,6,3] => 85
[2,5,7,1,6,3,4] => 75
[2,5,7,1,6,4,3] => 168
[2,5,7,3,1,4,6] => 15
[2,5,7,3,1,6,4] => 76
[2,5,7,3,4,1,6] => 15
[2,5,7,3,4,6,1] => 15
[2,5,7,3,6,1,4] => 38
[2,5,7,3,6,4,1] => 38
[2,5,7,4,1,3,6] => 23
[2,5,7,4,1,6,3] => 62
[2,5,7,4,3,1,6] => 23
[2,5,7,4,3,6,1] => 23
[2,5,7,4,6,1,3] => 31
[2,5,7,4,6,3,1] => 31
[2,5,7,6,1,3,4] => 26
[2,5,7,6,1,4,3] => 74
[2,5,7,6,3,1,4] => 26
[2,5,7,6,3,4,1] => 26
[2,5,7,6,4,1,3] => 37
[2,5,7,6,4,3,1] => 37
[2,6,1,3,4,5,7] => 4
[2,6,1,3,4,7,5] => 22
[2,6,1,3,5,4,7] => 18
[2,6,1,3,5,7,4] => 45
[2,6,1,3,7,4,5] => 43
[2,6,1,3,7,5,4] => 131
[2,6,1,4,3,5,7] => 14
[2,6,1,4,3,7,5] => 127
[2,6,1,4,5,3,7] => 27
[2,6,1,4,5,7,3] => 43
[2,6,1,4,7,3,5] => 88
[2,6,1,4,7,5,3] => 150
[2,6,1,5,3,4,7] => 25
[2,6,1,5,3,7,4] => 86
[2,6,1,5,4,3,7] => 61
[2,6,1,5,4,7,3] => 107
[2,6,1,5,7,3,4] => 81
[2,6,1,5,7,4,3] => 161
[2,6,1,7,3,4,5] => 36
[2,6,1,7,3,5,4] => 132
[2,6,1,7,4,3,5] => 96
[2,6,1,7,4,5,3] => 173
[2,6,1,7,5,3,4] => 141
[2,6,1,7,5,4,3] => 300
[2,6,3,1,4,5,7] => 4
[2,6,3,1,4,7,5] => 26
[2,6,3,1,5,4,7] => 22
[2,6,3,1,5,7,4] => 53
[2,6,3,1,7,4,5] => 51
[2,6,3,1,7,5,4] => 178
[2,6,3,4,1,5,7] => 4
[2,6,3,4,1,7,5] => 30
[2,6,3,4,5,1,7] => 4
[2,6,3,4,5,7,1] => 4
[2,6,3,4,7,1,5] => 15
[2,6,3,4,7,5,1] => 15
[2,6,3,5,1,4,7] => 11
[2,6,3,5,1,7,4] => 42
[2,6,3,5,4,1,7] => 11
[2,6,3,5,4,7,1] => 11
[2,6,3,5,7,1,4] => 21
[2,6,3,5,7,4,1] => 21
[2,6,3,7,1,4,5] => 20
[2,6,3,7,1,5,4] => 88
[2,6,3,7,4,1,5] => 20
[2,6,3,7,4,5,1] => 20
[2,6,3,7,5,1,4] => 44
[2,6,3,7,5,4,1] => 44
[2,6,4,1,3,5,7] => 7
[2,6,4,1,3,7,5] => 64
[2,6,4,1,5,3,7] => 20
[2,6,4,1,5,7,3] => 36
[2,6,4,1,7,3,5] => 72
[2,6,4,1,7,5,3] => 152
[2,6,4,3,1,5,7] => 7
[2,6,4,3,1,7,5] => 80
[2,6,4,3,5,1,7] => 7
[2,6,4,3,5,7,1] => 7
[2,6,4,3,7,1,5] => 40
[2,6,4,3,7,5,1] => 40
[2,6,4,5,1,3,7] => 10
[2,6,4,5,1,7,3] => 26
[2,6,4,5,3,1,7] => 10
[2,6,4,5,3,7,1] => 10
[2,6,4,5,7,1,3] => 13
[2,6,4,5,7,3,1] => 13
[2,6,4,7,1,3,5] => 24
[2,6,4,7,1,5,3] => 64
[2,6,4,7,3,1,5] => 24
[2,6,4,7,3,5,1] => 24
[2,6,4,7,5,1,3] => 32
[2,6,4,7,5,3,1] => 32
[2,6,5,1,3,4,7] => 9
[2,6,5,1,3,7,4] => 37
[2,6,5,1,4,3,7] => 28
[2,6,5,1,4,7,3] => 52
[2,6,5,1,7,3,4] => 46
[2,6,5,1,7,4,3] => 104
[2,6,5,3,1,4,7] => 9
[2,6,5,3,1,7,4] => 46
[2,6,5,3,4,1,7] => 9
[2,6,5,3,4,7,1] => 9
[2,6,5,3,7,1,4] => 23
[2,6,5,3,7,4,1] => 23
[2,6,5,4,1,3,7] => 14
[2,6,5,4,1,7,3] => 38
[2,6,5,4,3,1,7] => 14
[2,6,5,4,3,7,1] => 14
[2,6,5,4,7,1,3] => 19
[2,6,5,4,7,3,1] => 19
[2,6,5,7,1,3,4] => 16
[2,6,5,7,1,4,3] => 46
[2,6,5,7,3,1,4] => 16
[2,6,5,7,3,4,1] => 16
[2,6,5,7,4,1,3] => 23
[2,6,5,7,4,3,1] => 23
[2,6,7,1,3,4,5] => 10
[2,6,7,1,3,5,4] => 42
[2,6,7,1,4,3,5] => 32
[2,6,7,1,4,5,3] => 60
[2,6,7,1,5,3,4] => 54
[2,6,7,1,5,4,3] => 125
[2,6,7,3,1,4,5] => 10
[2,6,7,3,1,5,4] => 52
[2,6,7,3,4,1,5] => 10
[2,6,7,3,4,5,1] => 10
[2,6,7,3,5,1,4] => 26
[2,6,7,3,5,4,1] => 26
[2,6,7,4,1,3,5] => 16
[2,6,7,4,1,5,3] => 44
[2,6,7,4,3,1,5] => 16
[2,6,7,4,3,5,1] => 16
[2,6,7,4,5,1,3] => 22
[2,6,7,4,5,3,1] => 22
[2,6,7,5,1,3,4] => 19
[2,6,7,5,1,4,3] => 56
[2,6,7,5,3,1,4] => 19
[2,6,7,5,3,4,1] => 19
[2,6,7,5,4,1,3] => 28
[2,6,7,5,4,3,1] => 28
[2,7,1,3,4,5,6] => 5
[2,7,1,3,4,6,5] => 28
[2,7,1,3,5,4,6] => 23
[2,7,1,3,5,6,4] => 58
[2,7,1,3,6,4,5] => 56
[2,7,1,3,6,5,4] => 173
[2,7,1,4,3,5,6] => 18
[2,7,1,4,3,6,5] => 168
[2,7,1,4,5,3,6] => 35
[2,7,1,4,5,6,3] => 56
[2,7,1,4,6,3,5] => 117
[2,7,1,4,6,5,3] => 201
[2,7,1,5,3,4,6] => 33
[2,7,1,5,3,6,4] => 115
[2,7,1,5,4,3,6] => 82
[2,7,1,5,4,6,3] => 145
[2,7,1,5,6,3,4] => 110
[2,7,1,5,6,4,3] => 221
[2,7,1,6,3,4,5] => 49
[2,7,1,6,3,5,4] => 183
[2,7,1,6,4,3,5] => 134
[2,7,1,6,4,5,3] => 244
[2,7,1,6,5,3,4] => 201
[2,7,1,6,5,4,3] => 435
[2,7,3,1,4,5,6] => 5
[2,7,3,1,4,6,5] => 33
[2,7,3,1,5,4,6] => 28
[2,7,3,1,5,6,4] => 68
[2,7,3,1,6,4,5] => 66
[2,7,3,1,6,5,4] => 234
[2,7,3,4,1,5,6] => 5
[2,7,3,4,1,6,5] => 38
[2,7,3,4,5,1,6] => 5
[2,7,3,4,5,6,1] => 5
[2,7,3,4,6,1,5] => 19
[2,7,3,4,6,5,1] => 19
[2,7,3,5,1,4,6] => 14
[2,7,3,5,1,6,4] => 54
[2,7,3,5,4,1,6] => 14
[2,7,3,5,4,6,1] => 14
[2,7,3,5,6,1,4] => 27
[2,7,3,5,6,4,1] => 27
[2,7,3,6,1,4,5] => 26
[2,7,3,6,1,5,4] => 116
[2,7,3,6,4,1,5] => 26
[2,7,3,6,4,5,1] => 26
[2,7,3,6,5,1,4] => 58
[2,7,3,6,5,4,1] => 58
[2,7,4,1,3,5,6] => 9
[2,7,4,1,3,6,5] => 85
[2,7,4,1,5,3,6] => 26
[2,7,4,1,5,6,3] => 47
[2,7,4,1,6,3,5] => 96
[2,7,4,1,6,5,3] => 204
[2,7,4,3,1,5,6] => 9
[2,7,4,3,1,6,5] => 106
[2,7,4,3,5,1,6] => 9
[2,7,4,3,5,6,1] => 9
[2,7,4,3,6,1,5] => 53
[2,7,4,3,6,5,1] => 53
[2,7,4,5,1,3,6] => 13
[2,7,4,5,1,6,3] => 34
[2,7,4,5,3,1,6] => 13
[2,7,4,5,3,6,1] => 13
[2,7,4,5,6,1,3] => 17
[2,7,4,5,6,3,1] => 17
[2,7,4,6,1,3,5] => 32
[2,7,4,6,1,5,3] => 86
[2,7,4,6,3,1,5] => 32
[2,7,4,6,3,5,1] => 32
[2,7,4,6,5,1,3] => 43
[2,7,4,6,5,3,1] => 43
[2,7,5,1,3,4,6] => 12
[2,7,5,1,3,6,4] => 50
[2,7,5,1,4,3,6] => 38
[2,7,5,1,4,6,3] => 71
[2,7,5,1,6,3,4] => 63
[2,7,5,1,6,4,3] => 144
[2,7,5,3,1,4,6] => 12
[2,7,5,3,1,6,4] => 62
[2,7,5,3,4,1,6] => 12
[2,7,5,3,4,6,1] => 12
[2,7,5,3,6,1,4] => 31
[2,7,5,3,6,4,1] => 31
[2,7,5,4,1,3,6] => 19
[2,7,5,4,1,6,3] => 52
[2,7,5,4,3,1,6] => 19
[2,7,5,4,3,6,1] => 19
[2,7,5,4,6,1,3] => 26
[2,7,5,4,6,3,1] => 26
[2,7,5,6,1,3,4] => 22
[2,7,5,6,1,4,3] => 64
[2,7,5,6,3,1,4] => 22
[2,7,5,6,3,4,1] => 22
[2,7,5,6,4,1,3] => 32
[2,7,5,6,4,3,1] => 32
[2,7,6,1,3,4,5] => 14
[2,7,6,1,3,5,4] => 60
[2,7,6,1,4,3,5] => 46
[2,7,6,1,4,5,3] => 87
[2,7,6,1,5,3,4] => 79
[2,7,6,1,5,4,3] => 186
[2,7,6,3,1,4,5] => 14
[2,7,6,3,1,5,4] => 74
[2,7,6,3,4,1,5] => 14
[2,7,6,3,4,5,1] => 14
[2,7,6,3,5,1,4] => 37
[2,7,6,3,5,4,1] => 37
[2,7,6,4,1,3,5] => 23
[2,7,6,4,1,5,3] => 64
[2,7,6,4,3,1,5] => 23
[2,7,6,4,3,5,1] => 23
[2,7,6,4,5,1,3] => 32
[2,7,6,4,5,3,1] => 32
[2,7,6,5,1,3,4] => 28
[2,7,6,5,1,4,3] => 84
[2,7,6,5,3,1,4] => 28
[2,7,6,5,3,4,1] => 28
[2,7,6,5,4,1,3] => 42
[2,7,6,5,4,3,1] => 42
[3,1,2,4,5,6,7] => 1
[3,1,2,4,5,7,6] => 8
[3,1,2,4,6,5,7] => 7
[3,1,2,4,6,7,5] => 22
[3,1,2,4,7,5,6] => 22
[3,1,2,4,7,6,5] => 93
[3,1,2,5,4,6,7] => 6
[3,1,2,5,4,7,6] => 92
[3,1,2,5,6,4,7] => 15
[3,1,2,5,6,7,4] => 29
[3,1,2,5,7,4,6] => 71
[3,1,2,5,7,6,4] => 153
[3,1,2,6,4,5,7] => 15
[3,1,2,6,4,7,5] => 71
[3,1,2,6,5,4,7] => 56
[3,1,2,6,5,7,4] => 124
[3,1,2,6,7,4,5] => 87
[3,1,2,6,7,5,4] => 235
[3,1,2,7,4,5,6] => 29
[3,1,2,7,4,6,5] => 154
[3,1,2,7,5,4,6] => 125
[3,1,2,7,5,6,4] => 287
[3,1,2,7,6,4,5] => 232
[3,1,2,7,6,5,4] => 709
[3,1,4,2,5,6,7] => 2
[3,1,4,2,5,7,6] => 23
[3,1,4,2,6,5,7] => 21
[3,1,4,2,6,7,5] => 63
[3,1,4,2,7,5,6] => 64
[3,1,4,2,7,6,5] => 346
[3,1,4,5,2,6,7] => 3
[3,1,4,5,2,7,6] => 38
[3,1,4,5,6,2,7] => 4
[3,1,4,5,6,7,2] => 5
[3,1,4,5,7,2,6] => 22
[3,1,4,5,7,6,2] => 28
[3,1,4,6,2,5,7] => 13
[3,1,4,6,2,7,5] => 73
[3,1,4,6,5,2,7] => 18
[3,1,4,6,5,7,2] => 23
[3,1,4,6,7,2,5] => 43
[3,1,4,6,7,5,2] => 56
[3,1,4,7,2,5,6] => 32
[3,1,4,7,2,6,5] => 220
[3,1,4,7,5,2,6] => 45
[3,1,4,7,5,6,2] => 58
[3,1,4,7,6,2,5] => 131
[3,1,4,7,6,5,2] => 173
[3,1,5,2,4,6,7] => 6
[3,1,5,2,4,7,6] => 93
[3,1,5,2,6,4,7] => 24
[3,1,5,2,6,7,4] => 53
[3,1,5,2,7,4,6] => 133
[3,1,5,2,7,6,4] => 378
[3,1,5,4,2,6,7] => 10
[3,1,5,4,2,7,6] => 213
[3,1,5,4,6,2,7] => 14
[3,1,5,4,6,7,2] => 18
[3,1,5,4,7,2,6] => 127
[3,1,5,4,7,6,2] => 168
[3,1,5,6,2,4,7] => 17
[3,1,5,6,2,7,4] => 57
[3,1,5,6,4,2,7] => 25
[3,1,5,6,4,7,2] => 33
[3,1,5,6,7,2,4] => 36
[3,1,5,6,7,4,2] => 49
[3,1,5,7,2,4,6] => 57
[3,1,5,7,2,6,4] => 204
[3,1,5,7,4,2,6] => 86
[3,1,5,7,4,6,2] => 115
[3,1,5,7,6,2,4] => 132
[3,1,5,7,6,4,2] => 183
[3,1,6,2,4,5,7] => 11
[3,1,6,2,4,7,5] => 63
[3,1,6,2,5,4,7] => 52
[3,1,6,2,5,7,4] => 121
[3,1,6,2,7,4,5] => 103
[3,1,6,2,7,5,4] => 323
[3,1,6,4,2,5,7] => 19
[3,1,6,4,2,7,5] => 147
[3,1,6,4,5,2,7] => 27
[3,1,6,4,5,7,2] => 35
[3,1,6,4,7,2,5] => 88
[3,1,6,4,7,5,2] => 117
[3,1,6,5,2,4,7] => 40
[3,1,6,5,2,7,4] => 147
[3,1,6,5,4,2,7] => 61
[3,1,6,5,4,7,2] => 82
[3,1,6,5,7,2,4] => 96
[3,1,6,5,7,4,2] => 134
[3,1,6,7,2,4,5] => 52
[3,1,6,7,2,5,4] => 208
[3,1,6,7,4,2,5] => 81
[3,1,6,7,4,5,2] => 110
[3,1,6,7,5,2,4] => 141
[3,1,6,7,5,4,2] => 201
[3,1,7,2,4,5,6] => 17
[3,1,7,2,4,6,5] => 103
[3,1,7,2,5,4,6] => 86
[3,1,7,2,5,6,4] => 204
[3,1,7,2,6,4,5] => 183
[3,1,7,2,6,5,4] => 609
[3,1,7,4,2,5,6] => 30
[3,1,7,4,2,6,5] => 249
[3,1,7,4,5,2,6] => 43
[3,1,7,4,5,6,2] => 56
[3,1,7,4,6,2,5] => 150
[3,1,7,4,6,5,2] => 201
[3,1,7,5,2,4,6] => 69
[3,1,7,5,2,6,4] => 261
[3,1,7,5,4,2,6] => 107
[3,1,7,5,4,6,2] => 145
[3,1,7,5,6,2,4] => 173
[3,1,7,5,6,4,2] => 244
[3,1,7,6,2,4,5] => 101
[3,1,7,6,2,5,4] => 430
[3,1,7,6,4,2,5] => 161
[3,1,7,6,4,5,2] => 221
[3,1,7,6,5,2,4] => 300
[3,1,7,6,5,4,2] => 435
[3,2,1,4,5,6,7] => 1
[3,2,1,4,5,7,6] => 10
[3,2,1,4,6,5,7] => 9
[3,2,1,4,6,7,5] => 29
[3,2,1,4,7,5,6] => 29
[3,2,1,4,7,6,5] => 131
[3,2,1,5,4,6,7] => 8
[3,2,1,5,4,7,6] => 130
[3,2,1,5,6,4,7] => 20
[3,2,1,5,6,7,4] => 38
[3,2,1,5,7,4,6] => 102
[3,2,1,5,7,6,4] => 222
[3,2,1,6,4,5,7] => 20
[3,2,1,6,4,7,5] => 102
[3,2,1,6,5,4,7] => 82
[3,2,1,6,5,7,4] => 184
[3,2,1,6,7,4,5] => 126
[3,2,1,6,7,5,4] => 345
[3,2,1,7,4,5,6] => 38
[3,2,1,7,4,6,5] => 222
[3,2,1,7,5,4,6] => 184
[3,2,1,7,5,6,4] => 428
[3,2,1,7,6,4,5] => 345
[3,2,1,7,6,5,4] => 1101
[3,2,4,1,5,6,7] => 1
[3,2,4,1,5,7,6] => 11
[3,2,4,1,6,5,7] => 10
[3,2,4,1,6,7,5] => 31
[3,2,4,1,7,5,6] => 31
[3,2,4,1,7,6,5] => 165
[3,2,4,5,1,6,7] => 1
[3,2,4,5,1,7,6] => 12
[3,2,4,5,6,1,7] => 1
[3,2,4,5,6,7,1] => 1
[3,2,4,5,7,1,6] => 6
[3,2,4,5,7,6,1] => 6
[3,2,4,6,1,5,7] => 5
[3,2,4,6,1,7,5] => 26
[3,2,4,6,5,1,7] => 5
[3,2,4,6,5,7,1] => 5
[3,2,4,6,7,1,5] => 13
[3,2,4,6,7,5,1] => 13
[3,2,4,7,1,5,6] => 13
[3,2,4,7,1,6,5] => 84
[3,2,4,7,5,1,6] => 13
[3,2,4,7,5,6,1] => 13
[3,2,4,7,6,1,5] => 42
[3,2,4,7,6,5,1] => 42
[3,2,5,1,4,6,7] => 4
[3,2,5,1,4,7,6] => 70
[3,2,5,1,6,4,7] => 16
[3,2,5,1,6,7,4] => 34
[3,2,5,1,7,4,6] => 87
[3,2,5,1,7,6,4] => 233
[3,2,5,4,1,6,7] => 4
[3,2,5,4,1,7,6] => 82
[3,2,5,4,6,1,7] => 4
[3,2,5,4,6,7,1] => 4
[3,2,5,4,7,1,6] => 41
[3,2,5,4,7,6,1] => 41
[3,2,5,6,1,4,7] => 8
[3,2,5,6,1,7,4] => 26
[3,2,5,6,4,1,7] => 8
[3,2,5,6,4,7,1] => 8
[3,2,5,6,7,1,4] => 13
[3,2,5,6,7,4,1] => 13
[3,2,5,7,1,4,6] => 29
[3,2,5,7,1,6,4] => 102
[3,2,5,7,4,1,6] => 29
[3,2,5,7,4,6,1] => 29
[3,2,5,7,6,1,4] => 51
[3,2,5,7,6,4,1] => 51
[3,2,6,1,4,5,7] => 8
[3,2,6,1,4,7,5] => 50
[3,2,6,1,5,4,7] => 42
[3,2,6,1,5,7,4] => 97
[3,2,6,1,7,4,5] => 79
[3,2,6,1,7,5,4] => 251
[3,2,6,4,1,5,7] => 8
[3,2,6,4,1,7,5] => 58
[3,2,6,4,5,1,7] => 8
[3,2,6,4,5,7,1] => 8
[3,2,6,4,7,1,5] => 29
[3,2,6,4,7,5,1] => 29
[3,2,6,5,1,4,7] => 21
[3,2,6,5,1,7,4] => 76
[3,2,6,5,4,1,7] => 21
[3,2,6,5,4,7,1] => 21
[3,2,6,5,7,1,4] => 38
[3,2,6,5,7,4,1] => 38
[3,2,6,7,1,4,5] => 29
[3,2,6,7,1,5,4] => 120
[3,2,6,7,4,1,5] => 29
[3,2,6,7,4,5,1] => 29
[3,2,6,7,5,1,4] => 60
[3,2,6,7,5,4,1] => 60
[3,2,7,1,4,5,6] => 13
[3,2,7,1,4,6,5] => 89
[3,2,7,1,5,4,6] => 76
[3,2,7,1,5,6,4] => 180
[3,2,7,1,6,4,5] => 158
[3,2,7,1,6,5,4] => 549
[3,2,7,4,1,5,6] => 13
[3,2,7,4,1,6,5] => 102
[3,2,7,4,5,1,6] => 13
[3,2,7,4,5,6,1] => 13
[3,2,7,4,6,1,5] => 51
[3,2,7,4,6,5,1] => 51
[3,2,7,5,1,4,6] => 38
[3,2,7,5,1,6,4] => 142
[3,2,7,5,4,1,6] => 38
[3,2,7,5,4,6,1] => 38
[3,2,7,5,6,1,4] => 71
[3,2,7,5,6,4,1] => 71
[3,2,7,6,1,4,5] => 60
[3,2,7,6,1,5,4] => 270
[3,2,7,6,4,1,5] => 60
[3,2,7,6,4,5,1] => 60
[3,2,7,6,5,1,4] => 135
[3,2,7,6,5,4,1] => 135
[3,4,1,2,5,6,7] => 1
[3,4,1,2,5,7,6] => 10
[3,4,1,2,6,5,7] => 9
[3,4,1,2,6,7,5] => 27
[3,4,1,2,7,5,6] => 27
[3,4,1,2,7,6,5] => 148
[3,4,1,5,2,6,7] => 2
[3,4,1,5,2,7,6] => 29
[3,4,1,5,6,2,7] => 3
[3,4,1,5,6,7,2] => 4
[3,4,1,5,7,2,6] => 18
[3,4,1,5,7,6,2] => 25
[3,4,1,6,2,5,7] => 9
[3,4,1,6,2,7,5] => 48
[3,4,1,6,5,2,7] => 15
[3,4,1,6,5,7,2] => 21
[3,4,1,6,7,2,5] => 33
[3,4,1,6,7,5,2] => 48
[3,4,1,7,2,5,6] => 21
[3,4,1,7,2,6,5] => 145
[3,4,1,7,5,2,6] => 36
[3,4,1,7,5,6,2] => 51
[3,4,1,7,6,2,5] => 109
[3,4,1,7,6,5,2] => 165
[3,4,2,1,5,6,7] => 1
[3,4,2,1,5,7,6] => 13
[3,4,2,1,6,5,7] => 12
[3,4,2,1,6,7,5] => 36
[3,4,2,1,7,5,6] => 36
[3,4,2,1,7,6,5] => 213
[3,4,2,5,1,6,7] => 1
[3,4,2,5,1,7,6] => 14
[3,4,2,5,6,1,7] => 1
[3,4,2,5,6,7,1] => 1
[3,4,2,5,7,1,6] => 7
[3,4,2,5,7,6,1] => 7
[3,4,2,6,1,5,7] => 6
[3,4,2,6,1,7,5] => 30
[3,4,2,6,5,1,7] => 6
[3,4,2,6,5,7,1] => 6
[3,4,2,6,7,1,5] => 15
[3,4,2,6,7,5,1] => 15
[3,4,2,7,1,5,6] => 15
[3,4,2,7,1,6,5] => 112
[3,4,2,7,5,1,6] => 15
[3,4,2,7,5,6,1] => 15
[3,4,2,7,6,1,5] => 56
[3,4,2,7,6,5,1] => 56
[3,4,5,1,2,6,7] => 1
[3,4,5,1,2,7,6] => 12
[3,4,5,1,6,2,7] => 2
[3,4,5,1,6,7,2] => 3
[3,4,5,1,7,2,6] => 12
[3,4,5,1,7,6,2] => 20
[3,4,5,2,1,6,7] => 1
[3,4,5,2,1,7,6] => 16
[3,4,5,2,6,1,7] => 1
[3,4,5,2,6,7,1] => 1
[3,4,5,2,7,1,6] => 8
[3,4,5,2,7,6,1] => 8
[3,4,5,6,1,2,7] => 1
[3,4,5,6,1,7,2] => 2
[3,4,5,6,2,1,7] => 1
[3,4,5,6,2,7,1] => 1
[3,4,5,6,7,1,2] => 1
[3,4,5,6,7,2,1] => 1
[3,4,5,7,1,2,6] => 4
[3,4,5,7,1,6,2] => 8
[3,4,5,7,2,1,6] => 4
[3,4,5,7,2,6,1] => 4
[3,4,5,7,6,1,2] => 4
[3,4,5,7,6,2,1] => 4
[3,4,6,1,2,5,7] => 3
[3,4,6,1,2,7,5] => 18
[3,4,6,1,5,2,7] => 6
[3,4,6,1,5,7,2] => 9
[3,4,6,1,7,2,5] => 18
[3,4,6,1,7,5,2] => 30
[3,4,6,2,1,5,7] => 3
[3,4,6,2,1,7,5] => 24
[3,4,6,2,5,1,7] => 3
[3,4,6,2,5,7,1] => 3
[3,4,6,2,7,1,5] => 12
[3,4,6,2,7,5,1] => 12
[3,4,6,5,1,2,7] => 3
[3,4,6,5,1,7,2] => 6
[3,4,6,5,2,1,7] => 3
[3,4,6,5,2,7,1] => 3
[3,4,6,5,7,1,2] => 3
[3,4,6,5,7,2,1] => 3
[3,4,6,7,1,2,5] => 6
[3,4,6,7,1,5,2] => 12
[3,4,6,7,2,1,5] => 6
[3,4,6,7,2,5,1] => 6
[3,4,6,7,5,1,2] => 6
[3,4,6,7,5,2,1] => 6
[3,4,7,1,2,5,6] => 6
[3,4,7,1,2,6,5] => 42
[3,4,7,1,5,2,6] => 12
[3,4,7,1,5,6,2] => 18
[3,4,7,1,6,2,5] => 42
[3,4,7,1,6,5,2] => 70
[3,4,7,2,1,5,6] => 6
[3,4,7,2,1,6,5] => 56
[3,4,7,2,5,1,6] => 6
[3,4,7,2,5,6,1] => 6
[3,4,7,2,6,1,5] => 28
[3,4,7,2,6,5,1] => 28
[3,4,7,5,1,2,6] => 6
[3,4,7,5,1,6,2] => 12
[3,4,7,5,2,1,6] => 6
[3,4,7,5,2,6,1] => 6
[3,4,7,5,6,1,2] => 6
[3,4,7,5,6,2,1] => 6
[3,4,7,6,1,2,5] => 14
[3,4,7,6,1,5,2] => 28
[3,4,7,6,2,1,5] => 14
[3,4,7,6,2,5,1] => 14
[3,4,7,6,5,1,2] => 14
[3,4,7,6,5,2,1] => 14
[3,5,1,2,4,6,7] => 2
[3,5,1,2,4,7,6] => 29
[3,5,1,2,6,4,7] => 9
[3,5,1,2,6,7,4] => 21
[3,5,1,2,7,4,6] => 48
[3,5,1,2,7,6,4] => 145
[3,5,1,4,2,6,7] => 4
[3,5,1,4,2,7,6] => 89
[3,5,1,4,6,2,7] => 6
[3,5,1,4,6,7,2] => 8
[3,5,1,4,7,2,6] => 55
[3,5,1,4,7,6,2] => 76
[3,5,1,6,2,4,7] => 9
[3,5,1,6,2,7,4] => 32
[3,5,1,6,4,2,7] => 15
[3,5,1,6,4,7,2] => 21
[3,5,1,6,7,2,4] => 23
[3,5,1,6,7,4,2] => 34
[3,5,1,7,2,4,6] => 32
[3,5,1,7,2,6,4] => 121
[3,5,1,7,4,2,6] => 56
[3,5,1,7,4,6,2] => 80
[3,5,1,7,6,2,4] => 96
[3,5,1,7,6,4,2] => 148
[3,5,2,1,4,6,7] => 2
[3,5,2,1,4,7,6] => 37
[3,5,2,1,6,4,7] => 12
[3,5,2,1,6,7,4] => 28
[3,5,2,1,7,4,6] => 64
[3,5,2,1,7,6,4] => 213
[3,5,2,4,1,6,7] => 2
[3,5,2,4,1,7,6] => 42
[3,5,2,4,6,1,7] => 2
[3,5,2,4,6,7,1] => 2
[3,5,2,4,7,1,6] => 21
[3,5,2,4,7,6,1] => 21
[3,5,2,6,1,4,7] => 6
[3,5,2,6,1,7,4] => 22
[3,5,2,6,4,1,7] => 6
[3,5,2,6,4,7,1] => 6
[3,5,2,6,7,1,4] => 11
[3,5,2,6,7,4,1] => 11
[3,5,2,7,1,4,6] => 24
[3,5,2,7,1,6,4] => 104
[3,5,2,7,4,1,6] => 24
[3,5,2,7,4,6,1] => 24
[3,5,2,7,6,1,4] => 52
[3,5,2,7,6,4,1] => 52
[3,5,4,1,2,6,7] => 2
[3,5,4,1,2,7,6] => 39
[3,5,4,1,6,2,7] => 4
[3,5,4,1,6,7,2] => 6
[3,5,4,1,7,2,6] => 39
[3,5,4,1,7,6,2] => 65
[3,5,4,2,1,6,7] => 2
[3,5,4,2,1,7,6] => 52
[3,5,4,2,6,1,7] => 2
[3,5,4,2,6,7,1] => 2
[3,5,4,2,7,1,6] => 26
[3,5,4,2,7,6,1] => 26
[3,5,4,6,1,2,7] => 2
[3,5,4,6,1,7,2] => 4
[3,5,4,6,2,1,7] => 2
[3,5,4,6,2,7,1] => 2
[3,5,4,6,7,1,2] => 2
[3,5,4,6,7,2,1] => 2
[3,5,4,7,1,2,6] => 13
[3,5,4,7,1,6,2] => 26
[3,5,4,7,2,1,6] => 13
[3,5,4,7,2,6,1] => 13
[3,5,4,7,6,1,2] => 13
[3,5,4,7,6,2,1] => 13
[3,5,6,1,2,4,7] => 3
[3,5,6,1,2,7,4] => 12
[3,5,6,1,4,2,7] => 6
[3,5,6,1,4,7,2] => 9
[3,5,6,1,7,2,4] => 12
[3,5,6,1,7,4,2] => 20
[3,5,6,2,1,4,7] => 3
[3,5,6,2,1,7,4] => 16
[3,5,6,2,4,1,7] => 3
[3,5,6,2,4,7,1] => 3
[3,5,6,2,7,1,4] => 8
[3,5,6,2,7,4,1] => 8
[3,5,6,4,1,2,7] => 3
[3,5,6,4,1,7,2] => 6
[3,5,6,4,2,1,7] => 3
[3,5,6,4,2,7,1] => 3
[3,5,6,4,7,1,2] => 3
[3,5,6,4,7,2,1] => 3
[3,5,6,7,1,2,4] => 4
[3,5,6,7,1,4,2] => 8
[3,5,6,7,2,1,4] => 4
[3,5,6,7,2,4,1] => 4
[3,5,6,7,4,1,2] => 4
[3,5,6,7,4,2,1] => 4
[3,5,7,1,2,4,6] => 8
[3,5,7,1,2,6,4] => 33
[3,5,7,1,4,2,6] => 16
[3,5,7,1,4,6,2] => 24
[3,5,7,1,6,2,4] => 33
[3,5,7,1,6,4,2] => 55
[3,5,7,2,1,4,6] => 8
[3,5,7,2,1,6,4] => 44
[3,5,7,2,4,1,6] => 8
[3,5,7,2,4,6,1] => 8
[3,5,7,2,6,1,4] => 22
[3,5,7,2,6,4,1] => 22
[3,5,7,4,1,2,6] => 8
[3,5,7,4,1,6,2] => 16
[3,5,7,4,2,1,6] => 8
[3,5,7,4,2,6,1] => 8
[3,5,7,4,6,1,2] => 8
[3,5,7,4,6,2,1] => 8
[3,5,7,6,1,2,4] => 11
[3,5,7,6,1,4,2] => 22
[3,5,7,6,2,1,4] => 11
[3,5,7,6,2,4,1] => 11
[3,5,7,6,4,1,2] => 11
[3,5,7,6,4,2,1] => 11
[3,6,1,2,4,5,7] => 3
[3,6,1,2,4,7,5] => 18
[3,6,1,2,5,4,7] => 15
[3,6,1,2,5,7,4] => 36
[3,6,1,2,7,4,5] => 33
[3,6,1,2,7,5,4] => 109
[3,6,1,4,2,5,7] => 6
[3,6,1,4,2,7,5] => 55
[3,6,1,4,5,2,7] => 9
[3,6,1,4,5,7,2] => 12
[3,6,1,4,7,2,5] => 34
[3,6,1,4,7,5,2] => 47
[3,6,1,5,2,4,7] => 15
[3,6,1,5,2,7,4] => 56
[3,6,1,5,4,2,7] => 25
[3,6,1,5,4,7,2] => 35
[3,6,1,5,7,2,4] => 40
[3,6,1,5,7,4,2] => 59
[3,6,1,7,2,4,5] => 23
[3,6,1,7,2,5,4] => 96
[3,6,1,7,4,2,5] => 40
[3,6,1,7,4,5,2] => 57
[3,6,1,7,5,2,4] => 75
[3,6,1,7,5,4,2] => 115
[3,6,2,1,4,5,7] => 3
[3,6,2,1,4,7,5] => 23
[3,6,2,1,5,4,7] => 20
[3,6,2,1,5,7,4] => 48
[3,6,2,1,7,4,5] => 44
[3,6,2,1,7,5,4] => 160
[3,6,2,4,1,5,7] => 3
[3,6,2,4,1,7,5] => 26
[3,6,2,4,5,1,7] => 3
[3,6,2,4,5,7,1] => 3
[3,6,2,4,7,1,5] => 13
[3,6,2,4,7,5,1] => 13
[3,6,2,5,1,4,7] => 10
[3,6,2,5,1,7,4] => 38
[3,6,2,5,4,1,7] => 10
[3,6,2,5,4,7,1] => 10
[3,6,2,5,7,1,4] => 19
[3,6,2,5,7,4,1] => 19
[3,6,2,7,1,4,5] => 17
[3,6,2,7,1,5,4] => 80
[3,6,2,7,4,1,5] => 17
[3,6,2,7,4,5,1] => 17
[3,6,2,7,5,1,4] => 40
[3,6,2,7,5,4,1] => 40
[3,6,4,1,2,5,7] => 3
[3,6,4,1,2,7,5] => 24
[3,6,4,1,5,2,7] => 6
[3,6,4,1,5,7,2] => 9
[3,6,4,1,7,2,5] => 24
[3,6,4,1,7,5,2] => 40
[3,6,4,2,1,5,7] => 3
[3,6,4,2,1,7,5] => 32
[3,6,4,2,5,1,7] => 3
[3,6,4,2,5,7,1] => 3
[3,6,4,2,7,1,5] => 16
[3,6,4,2,7,5,1] => 16
[3,6,4,5,1,2,7] => 3
[3,6,4,5,1,7,2] => 6
[3,6,4,5,2,1,7] => 3
[3,6,4,5,2,7,1] => 3
[3,6,4,5,7,1,2] => 3
[3,6,4,5,7,2,1] => 3
[3,6,4,7,1,2,5] => 8
[3,6,4,7,1,5,2] => 16
[3,6,4,7,2,1,5] => 8
[3,6,4,7,2,5,1] => 8
[3,6,4,7,5,1,2] => 8
[3,6,4,7,5,2,1] => 8
[3,6,5,1,2,4,7] => 5
[3,6,5,1,2,7,4] => 21
[3,6,5,1,4,2,7] => 10
[3,6,5,1,4,7,2] => 15
[3,6,5,1,7,2,4] => 21
[3,6,5,1,7,4,2] => 35
[3,6,5,2,1,4,7] => 5
[3,6,5,2,1,7,4] => 28
[3,6,5,2,4,1,7] => 5
[3,6,5,2,4,7,1] => 5
[3,6,5,2,7,1,4] => 14
[3,6,5,2,7,4,1] => 14
[3,6,5,4,1,2,7] => 5
[3,6,5,4,1,7,2] => 10
[3,6,5,4,2,1,7] => 5
[3,6,5,4,2,7,1] => 5
[3,6,5,4,7,1,2] => 5
[3,6,5,4,7,2,1] => 5
[3,6,5,7,1,2,4] => 7
[3,6,5,7,1,4,2] => 14
[3,6,5,7,2,1,4] => 7
[3,6,5,7,2,4,1] => 7
[3,6,5,7,4,1,2] => 7
[3,6,5,7,4,2,1] => 7
[3,6,7,1,2,4,5] => 6
[3,6,7,1,2,5,4] => 27
[3,6,7,1,4,2,5] => 12
[3,6,7,1,4,5,2] => 18
[3,6,7,1,5,2,4] => 27
[3,6,7,1,5,4,2] => 45
[3,6,7,2,1,4,5] => 6
[3,6,7,2,1,5,4] => 36
[3,6,7,2,4,1,5] => 6
[3,6,7,2,4,5,1] => 6
[3,6,7,2,5,1,4] => 18
[3,6,7,2,5,4,1] => 18
[3,6,7,4,1,2,5] => 6
[3,6,7,4,1,5,2] => 12
[3,6,7,4,2,1,5] => 6
[3,6,7,4,2,5,1] => 6
[3,6,7,4,5,1,2] => 6
[3,6,7,4,5,2,1] => 6
[3,6,7,5,1,2,4] => 9
[3,6,7,5,1,4,2] => 18
[3,6,7,5,2,1,4] => 9
[3,6,7,5,2,4,1] => 9
[3,6,7,5,4,1,2] => 9
[3,6,7,5,4,2,1] => 9
[3,7,1,2,4,5,6] => 4
[3,7,1,2,4,6,5] => 25
[3,7,1,2,5,4,6] => 21
[3,7,1,2,5,6,4] => 51
[3,7,1,2,6,4,5] => 48
[3,7,1,2,6,5,4] => 165
[3,7,1,4,2,5,6] => 8
[3,7,1,4,2,6,5] => 76
[3,7,1,4,5,2,6] => 12
[3,7,1,4,5,6,2] => 16
[3,7,1,4,6,2,5] => 47
[3,7,1,4,6,5,2] => 65
[3,7,1,5,2,4,6] => 21
[3,7,1,5,2,6,4] => 80
[3,7,1,5,4,2,6] => 35
[3,7,1,5,4,6,2] => 49
[3,7,1,5,6,2,4] => 57
[3,7,1,5,6,4,2] => 84
[3,7,1,6,2,4,5] => 34
[3,7,1,6,2,5,4] => 148
[3,7,1,6,4,2,5] => 59
[3,7,1,6,4,5,2] => 84
[3,7,1,6,5,2,4] => 115
[3,7,1,6,5,4,2] => 176
[3,7,2,1,4,5,6] => 4
[3,7,2,1,4,6,5] => 32
[3,7,2,1,5,4,6] => 28
[3,7,2,1,5,6,4] => 68
[3,7,2,1,6,4,5] => 64
[3,7,2,1,6,5,4] => 242
[3,7,2,4,1,5,6] => 4
[3,7,2,4,1,6,5] => 36
[3,7,2,4,5,1,6] => 4
[3,7,2,4,5,6,1] => 4
[3,7,2,4,6,1,5] => 18
[3,7,2,4,6,5,1] => 18
[3,7,2,5,1,4,6] => 14
[3,7,2,5,1,6,4] => 54
[3,7,2,5,4,1,6] => 14
[3,7,2,5,4,6,1] => 14
[3,7,2,5,6,1,4] => 27
[3,7,2,5,6,4,1] => 27
[3,7,2,6,1,4,5] => 25
[3,7,2,6,1,5,4] => 122
[3,7,2,6,4,1,5] => 25
[3,7,2,6,4,5,1] => 25
[3,7,2,6,5,1,4] => 61
[3,7,2,6,5,4,1] => 61
[3,7,4,1,2,5,6] => 4
[3,7,4,1,2,6,5] => 33
[3,7,4,1,5,2,6] => 8
[3,7,4,1,5,6,2] => 12
[3,7,4,1,6,2,5] => 33
[3,7,4,1,6,5,2] => 55
[3,7,4,2,1,5,6] => 4
[3,7,4,2,1,6,5] => 44
[3,7,4,2,5,1,6] => 4
[3,7,4,2,5,6,1] => 4
[3,7,4,2,6,1,5] => 22
[3,7,4,2,6,5,1] => 22
[3,7,4,5,1,2,6] => 4
[3,7,4,5,1,6,2] => 8
[3,7,4,5,2,1,6] => 4
[3,7,4,5,2,6,1] => 4
[3,7,4,5,6,1,2] => 4
[3,7,4,5,6,2,1] => 4
[3,7,4,6,1,2,5] => 11
[3,7,4,6,1,5,2] => 22
[3,7,4,6,2,1,5] => 11
[3,7,4,6,2,5,1] => 11
[3,7,4,6,5,1,2] => 11
[3,7,4,6,5,2,1] => 11
[3,7,5,1,2,4,6] => 7
[3,7,5,1,2,6,4] => 30
[3,7,5,1,4,2,6] => 14
[3,7,5,1,4,6,2] => 21
[3,7,5,1,6,2,4] => 30
[3,7,5,1,6,4,2] => 50
[3,7,5,2,1,4,6] => 7
[3,7,5,2,1,6,4] => 40
[3,7,5,2,4,1,6] => 7
[3,7,5,2,4,6,1] => 7
[3,7,5,2,6,1,4] => 20
[3,7,5,2,6,4,1] => 20
[3,7,5,4,1,2,6] => 7
[3,7,5,4,1,6,2] => 14
[3,7,5,4,2,1,6] => 7
[3,7,5,4,2,6,1] => 7
[3,7,5,4,6,1,2] => 7
[3,7,5,4,6,2,1] => 7
[3,7,5,6,1,2,4] => 10
[3,7,5,6,1,4,2] => 20
[3,7,5,6,2,1,4] => 10
[3,7,5,6,2,4,1] => 10
[3,7,5,6,4,1,2] => 10
[3,7,5,6,4,2,1] => 10
[3,7,6,1,2,4,5] => 9
[3,7,6,1,2,5,4] => 42
[3,7,6,1,4,2,5] => 18
[3,7,6,1,4,5,2] => 27
[3,7,6,1,5,2,4] => 42
[3,7,6,1,5,4,2] => 70
[3,7,6,2,1,4,5] => 9
[3,7,6,2,1,5,4] => 56
[3,7,6,2,4,1,5] => 9
[3,7,6,2,4,5,1] => 9
[3,7,6,2,5,1,4] => 28
[3,7,6,2,5,4,1] => 28
[3,7,6,4,1,2,5] => 9
[3,7,6,4,1,5,2] => 18
[3,7,6,4,2,1,5] => 9
[3,7,6,4,2,5,1] => 9
[3,7,6,4,5,1,2] => 9
[3,7,6,4,5,2,1] => 9
[3,7,6,5,1,2,4] => 14
[3,7,6,5,1,4,2] => 28
[3,7,6,5,2,1,4] => 14
[3,7,6,5,2,4,1] => 14
[3,7,6,5,4,1,2] => 14
[3,7,6,5,4,2,1] => 14
[4,2,5,1,3,6,7] => 2
[4,3,2,1,5,6,7] => 1
[4,5,6,1,2,3,7] => 1
[5,2,6,7,1,3,4] => 6
[5,3,2,6,1,4,7] => 4
[5,4,3,2,1,6,7] => 1
[5,6,3,4,1,2,7] => 1
[6,4,3,2,7,1,5] => 8
[6,4,7,2,5,1,3] => 4
click to show generating function       
Description
The number of alternating sign matrices whose left key is the permutation.
The left key of an alternating sign matrix was defined by Lascoux
in [2] and is obtained by successively removing all the `-1`'s until what remains is a permutation matrix. This notion corresponds to the notion of left key for semistandard tableaux.
References
[1] Aval, J.-C. Keys and alternating sign matrices MathSciNet:2465402
[2] A. Lascoux. Chern and Yang through ice, http://phalanstere.univ-mlv.fr/~al/ARTICLES/ChernYang.ps.gz
Code
def statistic(self):
    count = 0
    for a in AlternatingSignMatrices(len(list(self))):
        if a.left_key_as_permutation() == self:
            count = count + 1
    return count
Created
Jun 11, 2013 at 20:43 by Jessica Striker
Updated
Apr 27, 2018 at 14:43 by Christian Stump