Identifier
Identifier
Values
[1,2] => 2
[2,1] => 1
[1,2,3] => 5
[1,3,2] => 3
[2,1,3] => 2
[2,3,1] => 3
[3,1,2] => 2
[3,2,1] => 1
[1,2,3,4] => 14
[1,2,4,3] => 9
[1,3,2,4] => 7
[1,3,4,2] => 9
[1,4,2,3] => 7
[1,4,3,2] => 4
[2,1,3,4] => 5
[2,1,4,3] => 3
[2,3,1,4] => 7
[2,3,4,1] => 9
[2,4,1,3] => 7
[2,4,3,1] => 4
[3,1,2,4] => 5
[3,1,4,2] => 3
[3,2,1,4] => 2
[3,2,4,1] => 3
[3,4,1,2] => 7
[3,4,2,1] => 4
[4,1,2,3] => 5
[4,1,3,2] => 3
[4,2,1,3] => 2
[4,2,3,1] => 3
[4,3,1,2] => 2
[4,3,2,1] => 1
[1,2,3,4,5] => 42
[1,2,3,5,4] => 28
[1,2,4,3,5] => 23
[1,2,4,5,3] => 28
[1,2,5,3,4] => 23
[1,2,5,4,3] => 14
[1,3,2,4,5] => 19
[1,3,2,5,4] => 12
[1,3,4,2,5] => 23
[1,3,4,5,2] => 28
[1,3,5,2,4] => 23
[1,3,5,4,2] => 14
[1,4,2,3,5] => 19
[1,4,2,5,3] => 12
[1,4,3,2,5] => 9
[1,4,3,5,2] => 12
[1,4,5,2,3] => 23
[1,4,5,3,2] => 14
[1,5,2,3,4] => 19
[1,5,2,4,3] => 12
[1,5,3,2,4] => 9
[1,5,3,4,2] => 12
[1,5,4,2,3] => 9
[1,5,4,3,2] => 5
[2,1,3,4,5] => 14
[2,1,3,5,4] => 9
[2,1,4,3,5] => 7
[2,1,4,5,3] => 9
[2,1,5,3,4] => 7
[2,1,5,4,3] => 4
[2,3,1,4,5] => 19
[2,3,1,5,4] => 12
[2,3,4,1,5] => 23
[2,3,4,5,1] => 28
[2,3,5,1,4] => 23
[2,3,5,4,1] => 14
[2,4,1,3,5] => 19
[2,4,1,5,3] => 12
[2,4,3,1,5] => 9
[2,4,3,5,1] => 12
[2,4,5,1,3] => 23
[2,4,5,3,1] => 14
[2,5,1,3,4] => 19
[2,5,1,4,3] => 12
[2,5,3,1,4] => 9
[2,5,3,4,1] => 12
[2,5,4,1,3] => 9
[2,5,4,3,1] => 5
[3,1,2,4,5] => 14
[3,1,2,5,4] => 9
[3,1,4,2,5] => 7
[3,1,4,5,2] => 9
[3,1,5,2,4] => 7
[3,1,5,4,2] => 4
[3,2,1,4,5] => 5
[3,2,1,5,4] => 3
[3,2,4,1,5] => 7
[3,2,4,5,1] => 9
[3,2,5,1,4] => 7
[3,2,5,4,1] => 4
[3,4,1,2,5] => 19
[3,4,1,5,2] => 12
[3,4,2,1,5] => 9
[3,4,2,5,1] => 12
[3,4,5,1,2] => 23
[3,4,5,2,1] => 14
[3,5,1,2,4] => 19
[3,5,1,4,2] => 12
[3,5,2,1,4] => 9
[3,5,2,4,1] => 12
[3,5,4,1,2] => 9
[3,5,4,2,1] => 5
[4,1,2,3,5] => 14
[4,1,2,5,3] => 9
[4,1,3,2,5] => 7
[4,1,3,5,2] => 9
[4,1,5,2,3] => 7
[4,1,5,3,2] => 4
[4,2,1,3,5] => 5
[4,2,1,5,3] => 3
[4,2,3,1,5] => 7
[4,2,3,5,1] => 9
[4,2,5,1,3] => 7
[4,2,5,3,1] => 4
[4,3,1,2,5] => 5
[4,3,1,5,2] => 3
[4,3,2,1,5] => 2
[4,3,2,5,1] => 3
[4,3,5,1,2] => 7
[4,3,5,2,1] => 4
[4,5,1,2,3] => 19
[4,5,1,3,2] => 12
[4,5,2,1,3] => 9
[4,5,2,3,1] => 12
[4,5,3,1,2] => 9
[4,5,3,2,1] => 5
[5,1,2,3,4] => 14
[5,1,2,4,3] => 9
[5,1,3,2,4] => 7
[5,1,3,4,2] => 9
[5,1,4,2,3] => 7
[5,1,4,3,2] => 4
[5,2,1,3,4] => 5
[5,2,1,4,3] => 3
[5,2,3,1,4] => 7
[5,2,3,4,1] => 9
[5,2,4,1,3] => 7
[5,2,4,3,1] => 4
[5,3,1,2,4] => 5
[5,3,1,4,2] => 3
[5,3,2,1,4] => 2
[5,3,2,4,1] => 3
[5,3,4,1,2] => 7
[5,3,4,2,1] => 4
[5,4,1,2,3] => 5
[5,4,1,3,2] => 3
[5,4,2,1,3] => 2
[5,4,2,3,1] => 3
[5,4,3,1,2] => 2
[5,4,3,2,1] => 1
[1,2,3,4,5,6] => 132
[1,2,3,4,6,5] => 90
[1,2,3,5,4,6] => 76
[1,2,3,5,6,4] => 90
[1,2,3,6,4,5] => 76
[1,2,3,6,5,4] => 48
[1,2,4,3,5,6] => 66
[1,2,4,3,6,5] => 43
[1,2,4,5,3,6] => 76
[1,2,4,5,6,3] => 90
[1,2,4,6,3,5] => 76
[1,2,4,6,5,3] => 48
[1,2,5,3,4,6] => 66
[1,2,5,3,6,4] => 43
[1,2,5,4,3,6] => 34
[1,2,5,4,6,3] => 43
[1,2,5,6,3,4] => 76
[1,2,5,6,4,3] => 48
[1,2,6,3,4,5] => 66
[1,2,6,3,5,4] => 43
[1,2,6,4,3,5] => 34
[1,2,6,4,5,3] => 43
[1,2,6,5,3,4] => 34
[1,2,6,5,4,3] => 20
[1,3,2,4,5,6] => 56
[1,3,2,4,6,5] => 37
[1,3,2,5,4,6] => 30
[1,3,2,5,6,4] => 37
[1,3,2,6,4,5] => 30
[1,3,2,6,5,4] => 18
[1,3,4,2,5,6] => 66
[1,3,4,2,6,5] => 43
[1,3,4,5,2,6] => 76
[1,3,4,5,6,2] => 90
[1,3,4,6,2,5] => 76
[1,3,4,6,5,2] => 48
[1,3,5,2,4,6] => 66
[1,3,5,2,6,4] => 43
[1,3,5,4,2,6] => 34
[1,3,5,4,6,2] => 43
[1,3,5,6,2,4] => 76
[1,3,5,6,4,2] => 48
[1,3,6,2,4,5] => 66
[1,3,6,2,5,4] => 43
[1,3,6,4,2,5] => 34
[1,3,6,4,5,2] => 43
[1,3,6,5,2,4] => 34
[1,3,6,5,4,2] => 20
[1,4,2,3,5,6] => 56
[1,4,2,3,6,5] => 37
[1,4,2,5,3,6] => 30
[1,4,2,5,6,3] => 37
[1,4,2,6,3,5] => 30
[1,4,2,6,5,3] => 18
[1,4,3,2,5,6] => 24
[1,4,3,2,6,5] => 15
[1,4,3,5,2,6] => 30
[1,4,3,5,6,2] => 37
[1,4,3,6,2,5] => 30
[1,4,3,6,5,2] => 18
[1,4,5,2,3,6] => 66
[1,4,5,2,6,3] => 43
[1,4,5,3,2,6] => 34
[1,4,5,3,6,2] => 43
[1,4,5,6,2,3] => 76
[1,4,5,6,3,2] => 48
[1,4,6,2,3,5] => 66
[1,4,6,2,5,3] => 43
[1,4,6,3,2,5] => 34
[1,4,6,3,5,2] => 43
[1,4,6,5,2,3] => 34
[1,4,6,5,3,2] => 20
[1,5,2,3,4,6] => 56
[1,5,2,3,6,4] => 37
[1,5,2,4,3,6] => 30
[1,5,2,4,6,3] => 37
[1,5,2,6,3,4] => 30
[1,5,2,6,4,3] => 18
[1,5,3,2,4,6] => 24
[1,5,3,2,6,4] => 15
[1,5,3,4,2,6] => 30
[1,5,3,4,6,2] => 37
[1,5,3,6,2,4] => 30
[1,5,3,6,4,2] => 18
[1,5,4,2,3,6] => 24
[1,5,4,2,6,3] => 15
[1,5,4,3,2,6] => 11
[1,5,4,3,6,2] => 15
[1,5,4,6,2,3] => 30
[1,5,4,6,3,2] => 18
[1,5,6,2,3,4] => 66
[1,5,6,2,4,3] => 43
[1,5,6,3,2,4] => 34
[1,5,6,3,4,2] => 43
[1,5,6,4,2,3] => 34
[1,5,6,4,3,2] => 20
[1,6,2,3,4,5] => 56
[1,6,2,3,5,4] => 37
[1,6,2,4,3,5] => 30
[1,6,2,4,5,3] => 37
[1,6,2,5,3,4] => 30
[1,6,2,5,4,3] => 18
[1,6,3,2,4,5] => 24
[1,6,3,2,5,4] => 15
[1,6,3,4,2,5] => 30
[1,6,3,4,5,2] => 37
[1,6,3,5,2,4] => 30
[1,6,3,5,4,2] => 18
[1,6,4,2,3,5] => 24
[1,6,4,2,5,3] => 15
[1,6,4,3,2,5] => 11
[1,6,4,3,5,2] => 15
[1,6,4,5,2,3] => 30
[1,6,4,5,3,2] => 18
[1,6,5,2,3,4] => 24
[1,6,5,2,4,3] => 15
[1,6,5,3,2,4] => 11
[1,6,5,3,4,2] => 15
[1,6,5,4,2,3] => 11
[1,6,5,4,3,2] => 6
[2,1,3,4,5,6] => 42
[2,1,3,4,6,5] => 28
[2,1,3,5,4,6] => 23
[2,1,3,5,6,4] => 28
[2,1,3,6,4,5] => 23
[2,1,3,6,5,4] => 14
[2,1,4,3,5,6] => 19
[2,1,4,3,6,5] => 12
[2,1,4,5,3,6] => 23
[2,1,4,5,6,3] => 28
[2,1,4,6,3,5] => 23
[2,1,4,6,5,3] => 14
[2,1,5,3,4,6] => 19
[2,1,5,3,6,4] => 12
[2,1,5,4,3,6] => 9
[2,1,5,4,6,3] => 12
[2,1,5,6,3,4] => 23
[2,1,5,6,4,3] => 14
[2,1,6,3,4,5] => 19
[2,1,6,3,5,4] => 12
[2,1,6,4,3,5] => 9
[2,1,6,4,5,3] => 12
[2,1,6,5,3,4] => 9
[2,1,6,5,4,3] => 5
[2,3,1,4,5,6] => 56
[2,3,1,4,6,5] => 37
[2,3,1,5,4,6] => 30
[2,3,1,5,6,4] => 37
[2,3,1,6,4,5] => 30
[2,3,1,6,5,4] => 18
[2,3,4,1,5,6] => 66
[2,3,4,1,6,5] => 43
[2,3,4,5,1,6] => 76
[2,3,4,5,6,1] => 90
[2,3,4,6,1,5] => 76
[2,3,4,6,5,1] => 48
[2,3,5,1,4,6] => 66
[2,3,5,1,6,4] => 43
[2,3,5,4,1,6] => 34
[2,3,5,4,6,1] => 43
[2,3,5,6,1,4] => 76
[2,3,5,6,4,1] => 48
[2,3,6,1,4,5] => 66
[2,3,6,1,5,4] => 43
[2,3,6,4,1,5] => 34
[2,3,6,4,5,1] => 43
[2,3,6,5,1,4] => 34
[2,3,6,5,4,1] => 20
[2,4,1,3,5,6] => 56
[2,4,1,3,6,5] => 37
[2,4,1,5,3,6] => 30
[2,4,1,5,6,3] => 37
[2,4,1,6,3,5] => 30
[2,4,1,6,5,3] => 18
[2,4,3,1,5,6] => 24
[2,4,3,1,6,5] => 15
[2,4,3,5,1,6] => 30
[2,4,3,5,6,1] => 37
[2,4,3,6,1,5] => 30
[2,4,3,6,5,1] => 18
[2,4,5,1,3,6] => 66
[2,4,5,1,6,3] => 43
[2,4,5,3,1,6] => 34
[2,4,5,3,6,1] => 43
[2,4,5,6,1,3] => 76
[2,4,5,6,3,1] => 48
[2,4,6,1,3,5] => 66
[2,4,6,1,5,3] => 43
[2,4,6,3,1,5] => 34
[2,4,6,3,5,1] => 43
[2,4,6,5,1,3] => 34
[2,4,6,5,3,1] => 20
[2,5,1,3,4,6] => 56
[2,5,1,3,6,4] => 37
[2,5,1,4,3,6] => 30
[2,5,1,4,6,3] => 37
[2,5,1,6,3,4] => 30
[2,5,1,6,4,3] => 18
[2,5,3,1,4,6] => 24
[2,5,3,1,6,4] => 15
[2,5,3,4,1,6] => 30
[2,5,3,4,6,1] => 37
[2,5,3,6,1,4] => 30
[2,5,3,6,4,1] => 18
[2,5,4,1,3,6] => 24
[2,5,4,1,6,3] => 15
[2,5,4,3,1,6] => 11
[2,5,4,3,6,1] => 15
[2,5,4,6,1,3] => 30
[2,5,4,6,3,1] => 18
[2,5,6,1,3,4] => 66
[2,5,6,1,4,3] => 43
[2,5,6,3,1,4] => 34
[2,5,6,3,4,1] => 43
[2,5,6,4,1,3] => 34
[2,5,6,4,3,1] => 20
[2,6,1,3,4,5] => 56
[2,6,1,3,5,4] => 37
[2,6,1,4,3,5] => 30
[2,6,1,4,5,3] => 37
[2,6,1,5,3,4] => 30
[2,6,1,5,4,3] => 18
[2,6,3,1,4,5] => 24
[2,6,3,1,5,4] => 15
[2,6,3,4,1,5] => 30
[2,6,3,4,5,1] => 37
[2,6,3,5,1,4] => 30
[2,6,3,5,4,1] => 18
[2,6,4,1,3,5] => 24
[2,6,4,1,5,3] => 15
[2,6,4,3,1,5] => 11
[2,6,4,3,5,1] => 15
[2,6,4,5,1,3] => 30
[2,6,4,5,3,1] => 18
[2,6,5,1,3,4] => 24
[2,6,5,1,4,3] => 15
[2,6,5,3,1,4] => 11
[2,6,5,3,4,1] => 15
[2,6,5,4,1,3] => 11
[2,6,5,4,3,1] => 6
[3,1,2,4,5,6] => 42
[3,1,2,4,6,5] => 28
[3,1,2,5,4,6] => 23
[3,1,2,5,6,4] => 28
[3,1,2,6,4,5] => 23
[3,1,2,6,5,4] => 14
[3,1,4,2,5,6] => 19
[3,1,4,2,6,5] => 12
[3,1,4,5,2,6] => 23
[3,1,4,5,6,2] => 28
[3,1,4,6,2,5] => 23
[3,1,4,6,5,2] => 14
[3,1,5,2,4,6] => 19
[3,1,5,2,6,4] => 12
[3,1,5,4,2,6] => 9
[3,1,5,4,6,2] => 12
[3,1,5,6,2,4] => 23
[3,1,5,6,4,2] => 14
[3,1,6,2,4,5] => 19
[3,1,6,2,5,4] => 12
[3,1,6,4,2,5] => 9
[3,1,6,4,5,2] => 12
[3,1,6,5,2,4] => 9
[3,1,6,5,4,2] => 5
[3,2,1,4,5,6] => 14
[3,2,1,4,6,5] => 9
[3,2,1,5,4,6] => 7
[3,2,1,5,6,4] => 9
[3,2,1,6,4,5] => 7
[3,2,1,6,5,4] => 4
[3,2,4,1,5,6] => 19
[3,2,4,1,6,5] => 12
[3,2,4,5,1,6] => 23
[3,2,4,5,6,1] => 28
[3,2,4,6,1,5] => 23
[3,2,4,6,5,1] => 14
[3,2,5,1,4,6] => 19
[3,2,5,1,6,4] => 12
[3,2,5,4,1,6] => 9
[3,2,5,4,6,1] => 12
[3,2,5,6,1,4] => 23
[3,2,5,6,4,1] => 14
[3,2,6,1,4,5] => 19
[3,2,6,1,5,4] => 12
[3,2,6,4,1,5] => 9
[3,2,6,4,5,1] => 12
[3,2,6,5,1,4] => 9
[3,2,6,5,4,1] => 5
[3,4,1,2,5,6] => 56
[3,4,1,2,6,5] => 37
[3,4,1,5,2,6] => 30
[3,4,1,5,6,2] => 37
[3,4,1,6,2,5] => 30
[3,4,1,6,5,2] => 18
[3,4,2,1,5,6] => 24
[3,4,2,1,6,5] => 15
[3,4,2,5,1,6] => 30
[3,4,2,5,6,1] => 37
[3,4,2,6,1,5] => 30
[3,4,2,6,5,1] => 18
[3,4,5,1,2,6] => 66
[3,4,5,1,6,2] => 43
[3,4,5,2,1,6] => 34
[3,4,5,2,6,1] => 43
[3,4,5,6,1,2] => 76
[3,4,5,6,2,1] => 48
[3,4,6,1,2,5] => 66
[3,4,6,1,5,2] => 43
[3,4,6,2,1,5] => 34
[3,4,6,2,5,1] => 43
[3,4,6,5,1,2] => 34
[3,4,6,5,2,1] => 20
[3,5,1,2,4,6] => 56
[3,5,1,2,6,4] => 37
[3,5,1,4,2,6] => 30
[3,5,1,4,6,2] => 37
[3,5,1,6,2,4] => 30
[3,5,1,6,4,2] => 18
[3,5,2,1,4,6] => 24
[3,5,2,1,6,4] => 15
[3,5,2,4,1,6] => 30
[3,5,2,4,6,1] => 37
[3,5,2,6,1,4] => 30
[3,5,2,6,4,1] => 18
[3,5,4,1,2,6] => 24
[3,5,4,1,6,2] => 15
[3,5,4,2,1,6] => 11
[3,5,4,2,6,1] => 15
[3,5,4,6,1,2] => 30
[3,5,4,6,2,1] => 18
[3,5,6,1,2,4] => 66
[3,5,6,1,4,2] => 43
[3,5,6,2,1,4] => 34
[3,5,6,2,4,1] => 43
[3,5,6,4,1,2] => 34
[3,5,6,4,2,1] => 20
[3,6,1,2,4,5] => 56
[3,6,1,2,5,4] => 37
[3,6,1,4,2,5] => 30
[3,6,1,4,5,2] => 37
[3,6,1,5,2,4] => 30
[3,6,1,5,4,2] => 18
[3,6,2,1,4,5] => 24
[3,6,2,1,5,4] => 15
[3,6,2,4,1,5] => 30
[3,6,2,4,5,1] => 37
[3,6,2,5,1,4] => 30
[3,6,2,5,4,1] => 18
[3,6,4,1,2,5] => 24
[3,6,4,1,5,2] => 15
[3,6,4,2,1,5] => 11
[3,6,4,2,5,1] => 15
[3,6,4,5,1,2] => 30
[3,6,4,5,2,1] => 18
[3,6,5,1,2,4] => 24
[3,6,5,1,4,2] => 15
[3,6,5,2,1,4] => 11
[3,6,5,2,4,1] => 15
[3,6,5,4,1,2] => 11
[3,6,5,4,2,1] => 6
[4,1,2,3,5,6] => 42
[4,1,2,3,6,5] => 28
[4,1,2,5,3,6] => 23
[4,1,2,5,6,3] => 28
[4,1,2,6,3,5] => 23
[4,1,2,6,5,3] => 14
[4,1,3,2,5,6] => 19
[4,1,3,2,6,5] => 12
[4,1,3,5,2,6] => 23
[4,1,3,5,6,2] => 28
[4,1,3,6,2,5] => 23
[4,1,3,6,5,2] => 14
[4,1,5,2,3,6] => 19
[4,1,5,2,6,3] => 12
[4,1,5,3,2,6] => 9
[4,1,5,3,6,2] => 12
[4,1,5,6,2,3] => 23
[4,1,5,6,3,2] => 14
[4,1,6,2,3,5] => 19
[4,1,6,2,5,3] => 12
[4,1,6,3,2,5] => 9
[4,1,6,3,5,2] => 12
[4,1,6,5,2,3] => 9
[4,1,6,5,3,2] => 5
[4,2,1,3,5,6] => 14
[4,2,1,3,6,5] => 9
[4,2,1,5,3,6] => 7
[4,2,1,5,6,3] => 9
[4,2,1,6,3,5] => 7
[4,2,1,6,5,3] => 4
[4,2,3,1,5,6] => 19
[4,2,3,1,6,5] => 12
[4,2,3,5,1,6] => 23
[4,2,3,5,6,1] => 28
[4,2,3,6,1,5] => 23
[4,2,3,6,5,1] => 14
[4,2,5,1,3,6] => 19
[4,2,5,1,6,3] => 12
[4,2,5,3,1,6] => 9
[4,2,5,3,6,1] => 12
[4,2,5,6,1,3] => 23
[4,2,5,6,3,1] => 14
[4,2,6,1,3,5] => 19
[4,2,6,1,5,3] => 12
[4,2,6,3,1,5] => 9
[4,2,6,3,5,1] => 12
[4,2,6,5,1,3] => 9
[4,2,6,5,3,1] => 5
[4,3,1,2,5,6] => 14
[4,3,1,2,6,5] => 9
[4,3,1,5,2,6] => 7
[4,3,1,5,6,2] => 9
[4,3,1,6,2,5] => 7
[4,3,1,6,5,2] => 4
[4,3,2,1,5,6] => 5
[4,3,2,1,6,5] => 3
[4,3,2,5,1,6] => 7
[4,3,2,5,6,1] => 9
[4,3,2,6,1,5] => 7
[4,3,2,6,5,1] => 4
[4,3,5,1,2,6] => 19
[4,3,5,1,6,2] => 12
[4,3,5,2,1,6] => 9
[4,3,5,2,6,1] => 12
[4,3,5,6,1,2] => 23
[4,3,5,6,2,1] => 14
[4,3,6,1,2,5] => 19
[4,3,6,1,5,2] => 12
[4,3,6,2,1,5] => 9
[4,3,6,2,5,1] => 12
[4,3,6,5,1,2] => 9
[4,3,6,5,2,1] => 5
[4,5,1,2,3,6] => 56
[4,5,1,2,6,3] => 37
[4,5,1,3,2,6] => 30
[4,5,1,3,6,2] => 37
[4,5,1,6,2,3] => 30
[4,5,1,6,3,2] => 18
[4,5,2,1,3,6] => 24
[4,5,2,1,6,3] => 15
[4,5,2,3,1,6] => 30
[4,5,2,3,6,1] => 37
[4,5,2,6,1,3] => 30
[4,5,2,6,3,1] => 18
[4,5,3,1,2,6] => 24
[4,5,3,1,6,2] => 15
[4,5,3,2,1,6] => 11
[4,5,3,2,6,1] => 15
[4,5,3,6,1,2] => 30
[4,5,3,6,2,1] => 18
[4,5,6,1,2,3] => 66
[4,5,6,1,3,2] => 43
[4,5,6,2,1,3] => 34
[4,5,6,2,3,1] => 43
[4,5,6,3,1,2] => 34
[4,5,6,3,2,1] => 20
[4,6,1,2,3,5] => 56
[4,6,1,2,5,3] => 37
[4,6,1,3,2,5] => 30
[4,6,1,3,5,2] => 37
[4,6,1,5,2,3] => 30
[4,6,1,5,3,2] => 18
[4,6,2,1,3,5] => 24
[4,6,2,1,5,3] => 15
[4,6,2,3,1,5] => 30
[4,6,2,3,5,1] => 37
[4,6,2,5,1,3] => 30
[4,6,2,5,3,1] => 18
[4,6,3,1,2,5] => 24
[4,6,3,1,5,2] => 15
[4,6,3,2,1,5] => 11
[4,6,3,2,5,1] => 15
[4,6,3,5,1,2] => 30
[4,6,3,5,2,1] => 18
[4,6,5,1,2,3] => 24
[4,6,5,1,3,2] => 15
[4,6,5,2,1,3] => 11
[4,6,5,2,3,1] => 15
[4,6,5,3,1,2] => 11
[4,6,5,3,2,1] => 6
[5,1,2,3,4,6] => 42
[5,1,2,3,6,4] => 28
[5,1,2,4,3,6] => 23
[5,1,2,4,6,3] => 28
[5,1,2,6,3,4] => 23
[5,1,2,6,4,3] => 14
[5,1,3,2,4,6] => 19
[5,1,3,2,6,4] => 12
[5,1,3,4,2,6] => 23
[5,1,3,4,6,2] => 28
[5,1,3,6,2,4] => 23
[5,1,3,6,4,2] => 14
[5,1,4,2,3,6] => 19
[5,1,4,2,6,3] => 12
[5,1,4,3,2,6] => 9
[5,1,4,3,6,2] => 12
[5,1,4,6,2,3] => 23
[5,1,4,6,3,2] => 14
[5,1,6,2,3,4] => 19
[5,1,6,2,4,3] => 12
[5,1,6,3,2,4] => 9
[5,1,6,3,4,2] => 12
[5,1,6,4,2,3] => 9
[5,1,6,4,3,2] => 5
[5,2,1,3,4,6] => 14
[5,2,1,3,6,4] => 9
[5,2,1,4,3,6] => 7
[5,2,1,4,6,3] => 9
[5,2,1,6,3,4] => 7
[5,2,1,6,4,3] => 4
[5,2,3,1,4,6] => 19
[5,2,3,1,6,4] => 12
[5,2,3,4,1,6] => 23
[5,2,3,4,6,1] => 28
[5,2,3,6,1,4] => 23
[5,2,3,6,4,1] => 14
[5,2,4,1,3,6] => 19
[5,2,4,1,6,3] => 12
[5,2,4,3,1,6] => 9
[5,2,4,3,6,1] => 12
[5,2,4,6,1,3] => 23
[5,2,4,6,3,1] => 14
[5,2,6,1,3,4] => 19
[5,2,6,1,4,3] => 12
[5,2,6,3,1,4] => 9
[5,2,6,3,4,1] => 12
[5,2,6,4,1,3] => 9
[5,2,6,4,3,1] => 5
[5,3,1,2,4,6] => 14
[5,3,1,2,6,4] => 9
[5,3,1,4,2,6] => 7
[5,3,1,4,6,2] => 9
[5,3,1,6,2,4] => 7
[5,3,1,6,4,2] => 4
[5,3,2,1,4,6] => 5
[5,3,2,1,6,4] => 3
[5,3,2,4,1,6] => 7
[5,3,2,4,6,1] => 9
[5,3,2,6,1,4] => 7
[5,3,2,6,4,1] => 4
[5,3,4,1,2,6] => 19
[5,3,4,1,6,2] => 12
[5,3,4,2,1,6] => 9
[5,3,4,2,6,1] => 12
[5,3,4,6,1,2] => 23
[5,3,4,6,2,1] => 14
[5,3,6,1,2,4] => 19
[5,3,6,1,4,2] => 12
[5,3,6,2,1,4] => 9
[5,3,6,2,4,1] => 12
[5,3,6,4,1,2] => 9
[5,3,6,4,2,1] => 5
[5,4,1,2,3,6] => 14
[5,4,1,2,6,3] => 9
[5,4,1,3,2,6] => 7
[5,4,1,3,6,2] => 9
[5,4,1,6,2,3] => 7
[5,4,1,6,3,2] => 4
[5,4,2,1,3,6] => 5
[5,4,2,1,6,3] => 3
[5,4,2,3,1,6] => 7
[5,4,2,3,6,1] => 9
[5,4,2,6,1,3] => 7
[5,4,2,6,3,1] => 4
[5,4,3,1,2,6] => 5
[5,4,3,1,6,2] => 3
[5,4,3,2,1,6] => 2
[5,4,3,2,6,1] => 3
[5,4,3,6,1,2] => 7
[5,4,3,6,2,1] => 4
[5,4,6,1,2,3] => 19
[5,4,6,1,3,2] => 12
[5,4,6,2,1,3] => 9
[5,4,6,2,3,1] => 12
[5,4,6,3,1,2] => 9
[5,4,6,3,2,1] => 5
[5,6,1,2,3,4] => 56
[5,6,1,2,4,3] => 37
[5,6,1,3,2,4] => 30
[5,6,1,3,4,2] => 37
[5,6,1,4,2,3] => 30
[5,6,1,4,3,2] => 18
[5,6,2,1,3,4] => 24
[5,6,2,1,4,3] => 15
[5,6,2,3,1,4] => 30
[5,6,2,3,4,1] => 37
[5,6,2,4,1,3] => 30
[5,6,2,4,3,1] => 18
[5,6,3,1,2,4] => 24
[5,6,3,1,4,2] => 15
[5,6,3,2,1,4] => 11
[5,6,3,2,4,1] => 15
[5,6,3,4,1,2] => 30
[5,6,3,4,2,1] => 18
[5,6,4,1,2,3] => 24
[5,6,4,1,3,2] => 15
[5,6,4,2,1,3] => 11
[5,6,4,2,3,1] => 15
[5,6,4,3,1,2] => 11
[5,6,4,3,2,1] => 6
[6,1,2,3,4,5] => 42
[6,1,2,3,5,4] => 28
[6,1,2,4,3,5] => 23
[6,1,2,4,5,3] => 28
[6,1,2,5,3,4] => 23
[6,1,2,5,4,3] => 14
[6,1,3,2,4,5] => 19
[6,1,3,2,5,4] => 12
[6,1,3,4,2,5] => 23
[6,1,3,4,5,2] => 28
[6,1,3,5,2,4] => 23
[6,1,3,5,4,2] => 14
[6,1,4,2,3,5] => 19
[6,1,4,2,5,3] => 12
[6,1,4,3,2,5] => 9
[6,1,4,3,5,2] => 12
[6,1,4,5,2,3] => 23
[6,1,4,5,3,2] => 14
[6,1,5,2,3,4] => 19
[6,1,5,2,4,3] => 12
[6,1,5,3,2,4] => 9
[6,1,5,3,4,2] => 12
[6,1,5,4,2,3] => 9
[6,1,5,4,3,2] => 5
[6,2,1,3,4,5] => 14
[6,2,1,3,5,4] => 9
[6,2,1,4,3,5] => 7
[6,2,1,4,5,3] => 9
[6,2,1,5,3,4] => 7
[6,2,1,5,4,3] => 4
[6,2,3,1,4,5] => 19
[6,2,3,1,5,4] => 12
[6,2,3,4,1,5] => 23
[6,2,3,4,5,1] => 28
[6,2,3,5,1,4] => 23
[6,2,3,5,4,1] => 14
[6,2,4,1,3,5] => 19
[6,2,4,1,5,3] => 12
[6,2,4,3,1,5] => 9
[6,2,4,3,5,1] => 12
[6,2,4,5,1,3] => 23
[6,2,4,5,3,1] => 14
[6,2,5,1,3,4] => 19
[6,2,5,1,4,3] => 12
[6,2,5,3,1,4] => 9
[6,2,5,3,4,1] => 12
[6,2,5,4,1,3] => 9
[6,2,5,4,3,1] => 5
[6,3,1,2,4,5] => 14
[6,3,1,2,5,4] => 9
[6,3,1,4,2,5] => 7
[6,3,1,4,5,2] => 9
[6,3,1,5,2,4] => 7
[6,3,1,5,4,2] => 4
[6,3,2,1,4,5] => 5
[6,3,2,1,5,4] => 3
[6,3,2,4,1,5] => 7
[6,3,2,4,5,1] => 9
[6,3,2,5,1,4] => 7
[6,3,2,5,4,1] => 4
[6,3,4,1,2,5] => 19
[6,3,4,1,5,2] => 12
[6,3,4,2,1,5] => 9
[6,3,4,2,5,1] => 12
[6,3,4,5,1,2] => 23
[6,3,4,5,2,1] => 14
[6,3,5,1,2,4] => 19
[6,3,5,1,4,2] => 12
[6,3,5,2,1,4] => 9
[6,3,5,2,4,1] => 12
[6,3,5,4,1,2] => 9
[6,3,5,4,2,1] => 5
[6,4,1,2,3,5] => 14
[6,4,1,2,5,3] => 9
[6,4,1,3,2,5] => 7
[6,4,1,3,5,2] => 9
[6,4,1,5,2,3] => 7
[6,4,1,5,3,2] => 4
[6,4,2,1,3,5] => 5
[6,4,2,1,5,3] => 3
[6,4,2,3,1,5] => 7
[6,4,2,3,5,1] => 9
[6,4,2,5,1,3] => 7
[6,4,2,5,3,1] => 4
[6,4,3,1,2,5] => 5
[6,4,3,1,5,2] => 3
[6,4,3,2,1,5] => 2
[6,4,3,2,5,1] => 3
[6,4,3,5,1,2] => 7
[6,4,3,5,2,1] => 4
[6,4,5,1,2,3] => 19
[6,4,5,1,3,2] => 12
[6,4,5,2,1,3] => 9
[6,4,5,2,3,1] => 12
[6,4,5,3,1,2] => 9
[6,4,5,3,2,1] => 5
[6,5,1,2,3,4] => 14
[6,5,1,2,4,3] => 9
[6,5,1,3,2,4] => 7
[6,5,1,3,4,2] => 9
[6,5,1,4,2,3] => 7
[6,5,1,4,3,2] => 4
[6,5,2,1,3,4] => 5
[6,5,2,1,4,3] => 3
[6,5,2,3,1,4] => 7
[6,5,2,3,4,1] => 9
[6,5,2,4,1,3] => 7
[6,5,2,4,3,1] => 4
[6,5,3,1,2,4] => 5
[6,5,3,1,4,2] => 3
[6,5,3,2,1,4] => 2
[6,5,3,2,4,1] => 3
[6,5,3,4,1,2] => 7
[6,5,3,4,2,1] => 4
[6,5,4,1,2,3] => 5
[6,5,4,1,3,2] => 3
[6,5,4,2,1,3] => 2
[6,5,4,2,3,1] => 3
[6,5,4,3,1,2] => 2
[6,5,4,3,2,1] => 1
[1,2,3,4,5,6,7] => 429
[1,2,3,4,5,7,6] => 297
[1,2,3,4,6,5,7] => 255
[1,2,3,4,6,7,5] => 297
[1,2,3,4,7,5,6] => 255
[1,2,3,4,7,6,5] => 165
[1,2,3,5,4,6,7] => 227
[1,2,3,5,4,7,6] => 151
[1,2,3,5,6,4,7] => 255
[1,2,3,5,6,7,4] => 297
[1,2,3,5,7,4,6] => 255
[1,2,3,5,7,6,4] => 165
[1,2,3,6,4,5,7] => 227
[1,2,3,6,4,7,5] => 151
[1,2,3,6,5,4,7] => 123
[1,2,3,6,5,7,4] => 151
[1,2,3,6,7,4,5] => 255
[1,2,3,6,7,5,4] => 165
[1,2,3,7,4,5,6] => 227
[1,2,3,7,4,6,5] => 151
[1,2,3,7,5,4,6] => 123
[1,2,3,7,5,6,4] => 151
[1,2,3,7,6,4,5] => 123
[1,2,3,7,6,5,4] => 75
[1,2,4,3,5,6,7] => 202
[1,2,4,3,5,7,6] => 136
[1,2,4,3,6,5,7] => 113
[1,2,4,3,6,7,5] => 136
[1,2,4,3,7,5,6] => 113
[1,2,4,3,7,6,5] => 70
[1,2,4,5,3,6,7] => 227
[1,2,4,5,3,7,6] => 151
[1,2,4,5,6,3,7] => 255
[1,2,4,5,6,7,3] => 297
[1,2,4,5,7,3,6] => 255
[1,2,4,5,7,6,3] => 165
[1,2,4,6,3,5,7] => 227
[1,2,4,6,3,7,5] => 151
[1,2,4,6,5,3,7] => 123
[1,2,4,6,5,7,3] => 151
[1,2,4,6,7,3,5] => 255
[1,2,4,6,7,5,3] => 165
[1,2,4,7,3,5,6] => 227
[1,2,4,7,3,6,5] => 151
[1,2,4,7,5,3,6] => 123
[1,2,4,7,5,6,3] => 151
[1,2,4,7,6,3,5] => 123
[1,2,4,7,6,5,3] => 75
[1,2,5,3,4,6,7] => 202
[1,2,5,3,4,7,6] => 136
[1,2,5,3,6,4,7] => 113
[1,2,5,3,6,7,4] => 136
[1,2,5,3,7,4,6] => 113
[1,2,5,3,7,6,4] => 70
[1,2,5,4,3,6,7] => 95
[1,2,5,4,3,7,6] => 61
[1,2,5,4,6,3,7] => 113
[1,2,5,4,6,7,3] => 136
[1,2,5,4,7,3,6] => 113
[1,2,5,4,7,6,3] => 70
[1,2,5,6,3,4,7] => 227
[1,2,5,6,3,7,4] => 151
[1,2,5,6,4,3,7] => 123
[1,2,5,6,4,7,3] => 151
[1,2,5,6,7,3,4] => 255
[1,2,5,6,7,4,3] => 165
[1,2,5,7,3,4,6] => 227
[1,2,5,7,3,6,4] => 151
[1,2,5,7,4,3,6] => 123
[1,2,5,7,4,6,3] => 151
[1,2,5,7,6,3,4] => 123
[1,2,5,7,6,4,3] => 75
[1,2,6,3,4,5,7] => 202
[1,2,6,3,4,7,5] => 136
[1,2,6,3,5,4,7] => 113
[1,2,6,3,5,7,4] => 136
[1,2,6,3,7,4,5] => 113
[1,2,6,3,7,5,4] => 70
[1,2,6,4,3,5,7] => 95
[1,2,6,4,3,7,5] => 61
[1,2,6,4,5,3,7] => 113
[1,2,6,4,5,7,3] => 136
[1,2,6,4,7,3,5] => 113
[1,2,6,4,7,5,3] => 70
[1,2,6,5,3,4,7] => 95
[1,2,6,5,3,7,4] => 61
[1,2,6,5,4,3,7] => 47
[1,2,6,5,4,7,3] => 61
[1,2,6,5,7,3,4] => 113
[1,2,6,5,7,4,3] => 70
[1,2,6,7,3,4,5] => 227
[1,2,6,7,3,5,4] => 151
[1,2,6,7,4,3,5] => 123
[1,2,6,7,4,5,3] => 151
[1,2,6,7,5,3,4] => 123
[1,2,6,7,5,4,3] => 75
[1,2,7,3,4,5,6] => 202
[1,2,7,3,4,6,5] => 136
[1,2,7,3,5,4,6] => 113
[1,2,7,3,5,6,4] => 136
[1,2,7,3,6,4,5] => 113
[1,2,7,3,6,5,4] => 70
[1,2,7,4,3,5,6] => 95
[1,2,7,4,3,6,5] => 61
[1,2,7,4,5,3,6] => 113
[1,2,7,4,5,6,3] => 136
[1,2,7,4,6,3,5] => 113
[1,2,7,4,6,5,3] => 70
[1,2,7,5,3,4,6] => 95
[1,2,7,5,3,6,4] => 61
[1,2,7,5,4,3,6] => 47
[1,2,7,5,4,6,3] => 61
[1,2,7,5,6,3,4] => 113
[1,2,7,5,6,4,3] => 70
[1,2,7,6,3,4,5] => 95
[1,2,7,6,3,5,4] => 61
[1,2,7,6,4,3,5] => 47
[1,2,7,6,4,5,3] => 61
[1,2,7,6,5,3,4] => 47
[1,2,7,6,5,4,3] => 27
[1,3,2,4,5,6,7] => 174
[1,3,2,4,5,7,6] => 118
[1,3,2,4,6,5,7] => 99
[1,3,2,4,6,7,5] => 118
[1,3,2,4,7,5,6] => 99
[1,3,2,4,7,6,5] => 62
[1,3,2,5,4,6,7] => 85
[1,3,2,5,4,7,6] => 55
[1,3,2,5,6,4,7] => 99
[1,3,2,5,6,7,4] => 118
[1,3,2,5,7,4,6] => 99
[1,3,2,5,7,6,4] => 62
[1,3,2,6,4,5,7] => 85
[1,3,2,6,4,7,5] => 55
[1,3,2,6,5,4,7] => 43
[1,3,2,6,5,7,4] => 55
[1,3,2,6,7,4,5] => 99
[1,3,2,6,7,5,4] => 62
[1,3,2,7,4,5,6] => 85
[1,3,2,7,4,6,5] => 55
[1,3,2,7,5,4,6] => 43
[1,3,2,7,5,6,4] => 55
[1,3,2,7,6,4,5] => 43
[1,3,2,7,6,5,4] => 25
[1,3,4,2,5,6,7] => 202
[1,3,4,2,5,7,6] => 136
[1,3,4,2,6,5,7] => 113
[1,3,4,2,6,7,5] => 136
[1,3,4,2,7,5,6] => 113
[1,3,4,2,7,6,5] => 70
[1,3,4,5,2,6,7] => 227
[1,3,4,5,2,7,6] => 151
[1,3,4,5,6,2,7] => 255
[1,3,4,5,6,7,2] => 297
[1,3,4,5,7,2,6] => 255
[1,3,4,5,7,6,2] => 165
[1,3,4,6,2,5,7] => 227
[1,3,4,6,2,7,5] => 151
[1,3,4,6,5,2,7] => 123
[1,3,4,6,5,7,2] => 151
[1,3,4,6,7,2,5] => 255
[1,3,4,6,7,5,2] => 165
[1,3,4,7,2,5,6] => 227
[1,3,4,7,2,6,5] => 151
[1,3,4,7,5,2,6] => 123
[1,3,4,7,5,6,2] => 151
[1,3,4,7,6,2,5] => 123
[1,3,4,7,6,5,2] => 75
[1,3,5,2,4,6,7] => 202
[1,3,5,2,4,7,6] => 136
[1,3,5,2,6,4,7] => 113
[1,3,5,2,6,7,4] => 136
[1,3,5,2,7,4,6] => 113
[1,3,5,2,7,6,4] => 70
[1,3,5,4,2,6,7] => 95
[1,3,5,4,2,7,6] => 61
[1,3,5,4,6,2,7] => 113
[1,3,5,4,6,7,2] => 136
[1,3,5,4,7,2,6] => 113
[1,3,5,4,7,6,2] => 70
[1,3,5,6,2,4,7] => 227
[1,3,5,6,2,7,4] => 151
[1,3,5,6,4,2,7] => 123
[1,3,5,6,4,7,2] => 151
[1,3,5,6,7,2,4] => 255
[1,3,5,6,7,4,2] => 165
[1,3,5,7,2,4,6] => 227
[1,3,5,7,2,6,4] => 151
[1,3,5,7,4,2,6] => 123
[1,3,5,7,4,6,2] => 151
[1,3,5,7,6,2,4] => 123
[1,3,5,7,6,4,2] => 75
[1,3,6,2,4,5,7] => 202
[1,3,6,2,4,7,5] => 136
[1,3,6,2,5,4,7] => 113
[1,3,6,2,5,7,4] => 136
[1,3,6,2,7,4,5] => 113
[1,3,6,2,7,5,4] => 70
[1,3,6,4,2,5,7] => 95
[1,3,6,4,2,7,5] => 61
[1,3,6,4,5,2,7] => 113
[1,3,6,4,5,7,2] => 136
[1,3,6,4,7,2,5] => 113
[1,3,6,4,7,5,2] => 70
[1,3,6,5,2,4,7] => 95
[1,3,6,5,2,7,4] => 61
[1,3,6,5,4,2,7] => 47
[1,3,6,5,4,7,2] => 61
[1,3,6,5,7,2,4] => 113
[1,3,6,5,7,4,2] => 70
[1,3,6,7,2,4,5] => 227
[1,3,6,7,2,5,4] => 151
[1,3,6,7,4,2,5] => 123
[1,3,6,7,4,5,2] => 151
[1,3,6,7,5,2,4] => 123
[1,3,6,7,5,4,2] => 75
[1,3,7,2,4,5,6] => 202
[1,3,7,2,4,6,5] => 136
[1,3,7,2,5,4,6] => 113
[1,3,7,2,5,6,4] => 136
[1,3,7,2,6,4,5] => 113
[1,3,7,2,6,5,4] => 70
[1,3,7,4,2,5,6] => 95
[1,3,7,4,2,6,5] => 61
[1,3,7,4,5,2,6] => 113
[1,3,7,4,5,6,2] => 136
[1,3,7,4,6,2,5] => 113
[1,3,7,4,6,5,2] => 70
[1,3,7,5,2,4,6] => 95
[1,3,7,5,2,6,4] => 61
[1,3,7,5,4,2,6] => 47
[1,3,7,5,4,6,2] => 61
[1,3,7,5,6,2,4] => 113
[1,3,7,5,6,4,2] => 70
[1,3,7,6,2,4,5] => 95
[1,3,7,6,2,5,4] => 61
[1,3,7,6,4,2,5] => 47
[1,3,7,6,4,5,2] => 61
[1,3,7,6,5,2,4] => 47
[1,3,7,6,5,4,2] => 27
[1,4,2,3,5,6,7] => 174
[1,4,2,3,5,7,6] => 118
[1,4,2,3,6,5,7] => 99
[1,4,2,3,6,7,5] => 118
[1,4,2,3,7,5,6] => 99
[1,4,2,3,7,6,5] => 62
[1,4,2,5,3,6,7] => 85
[1,4,2,5,3,7,6] => 55
[1,4,2,5,6,3,7] => 99
[1,4,2,5,6,7,3] => 118
[1,4,2,5,7,3,6] => 99
[1,4,2,5,7,6,3] => 62
[1,4,2,6,3,5,7] => 85
[1,4,2,6,3,7,5] => 55
[1,4,2,6,5,3,7] => 43
[1,4,2,6,5,7,3] => 55
[1,4,2,6,7,3,5] => 99
[1,4,2,6,7,5,3] => 62
[1,4,2,7,3,5,6] => 85
[1,4,2,7,3,6,5] => 55
[1,4,2,7,5,3,6] => 43
[1,4,2,7,5,6,3] => 55
[1,4,2,7,6,3,5] => 43
[1,4,2,7,6,5,3] => 25
[1,4,3,2,5,6,7] => 70
[1,4,3,2,5,7,6] => 46
[1,4,3,2,6,5,7] => 37
[1,4,3,2,6,7,5] => 46
[1,4,3,2,7,5,6] => 37
[1,4,3,2,7,6,5] => 22
[1,4,3,5,2,6,7] => 85
[1,4,3,5,2,7,6] => 55
[1,4,3,5,6,2,7] => 99
[1,4,3,5,6,7,2] => 118
[1,4,3,5,7,2,6] => 99
[1,4,3,5,7,6,2] => 62
[1,4,3,6,2,5,7] => 85
[1,4,3,6,2,7,5] => 55
[1,4,3,6,5,2,7] => 43
[1,4,3,6,5,7,2] => 55
[1,4,3,6,7,2,5] => 99
[1,4,3,6,7,5,2] => 62
[1,4,3,7,2,5,6] => 85
[1,4,3,7,2,6,5] => 55
[1,4,3,7,5,2,6] => 43
[1,4,3,7,5,6,2] => 55
[1,4,3,7,6,2,5] => 43
[1,4,3,7,6,5,2] => 25
[1,4,5,2,3,6,7] => 202
[1,4,5,2,3,7,6] => 136
[1,4,5,2,6,3,7] => 113
[1,4,5,2,6,7,3] => 136
[1,4,5,2,7,3,6] => 113
[1,4,5,2,7,6,3] => 70
[1,4,5,3,2,6,7] => 95
[1,4,5,3,2,7,6] => 61
[1,4,5,3,6,2,7] => 113
[1,4,5,3,6,7,2] => 136
[1,4,5,3,7,2,6] => 113
[1,4,5,3,7,6,2] => 70
[1,4,5,6,2,3,7] => 227
[1,4,5,6,2,7,3] => 151
[1,4,5,6,3,2,7] => 123
[1,4,5,6,3,7,2] => 151
[1,4,5,6,7,2,3] => 255
[1,4,5,6,7,3,2] => 165
[1,4,5,7,2,3,6] => 227
[1,4,5,7,2,6,3] => 151
[1,4,5,7,3,2,6] => 123
[1,4,5,7,3,6,2] => 151
[1,4,5,7,6,2,3] => 123
[1,4,5,7,6,3,2] => 75
[1,4,6,2,3,5,7] => 202
[1,4,6,2,3,7,5] => 136
[1,4,6,2,5,3,7] => 113
[1,4,6,2,5,7,3] => 136
[1,4,6,2,7,3,5] => 113
[1,4,6,2,7,5,3] => 70
[1,4,6,3,2,5,7] => 95
[1,4,6,3,2,7,5] => 61
[1,4,6,3,5,2,7] => 113
[1,4,6,3,5,7,2] => 136
[1,4,6,3,7,2,5] => 113
[1,4,6,3,7,5,2] => 70
[1,4,6,5,2,3,7] => 95
[1,4,6,5,2,7,3] => 61
[1,4,6,5,3,2,7] => 47
[1,4,6,5,3,7,2] => 61
click to show generating function       
Description
The size of the preimage of the map 'to labelling permutation' from Parking functions to Permutations.
Code
def to_labelling_permutation(elt):
    from sage.combinat.words.word import Word
    return Word(elt).standard_permutation().inverse()

@cached_function
def preimages(level):
    print "computing preimages for level", level
    result = dict()
    for el in ParkingFunctions(level):
        image = to_labelling_permutation(el)
        result[image] = result.get(image, 0) + 1
    return result

def statistic(x):
    return preimages(x.size()).get(x, 0)

Created
Sep 11, 2015 at 22:08 by Martin Rubey
Updated
Sep 11, 2015 at 22:08 by Martin Rubey