edit this statistic or download as text // json
Identifier
Values
[1] => 1
[1,2] => 3
[2,1] => 1
[1,2,3] => 6
[1,3,2] => 3
[2,1,3] => 4
[2,3,1] => 3
[3,1,2] => 1
[3,2,1] => 1
[1,2,3,4] => 10
[1,2,4,3] => 6
[1,3,2,4] => 7
[1,3,4,2] => 6
[1,4,2,3] => 3
[1,4,3,2] => 3
[2,1,3,4] => 8
[2,1,4,3] => 4
[2,3,1,4] => 7
[2,3,4,1] => 6
[2,4,1,3] => 3
[2,4,3,1] => 3
[3,1,2,4] => 5
[3,1,4,2] => 4
[3,2,1,4] => 5
[3,2,4,1] => 4
[3,4,1,2] => 3
[3,4,2,1] => 3
[4,1,2,3] => 1
[4,1,3,2] => 1
[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] => 15
[1,2,3,5,4] => 10
[1,2,4,3,5] => 11
[1,2,4,5,3] => 10
[1,2,5,3,4] => 6
[1,2,5,4,3] => 6
[1,3,2,4,5] => 12
[1,3,2,5,4] => 7
[1,3,4,2,5] => 11
[1,3,4,5,2] => 10
[1,3,5,2,4] => 6
[1,3,5,4,2] => 6
[1,4,2,3,5] => 8
[1,4,2,5,3] => 7
[1,4,3,2,5] => 8
[1,4,3,5,2] => 7
[1,4,5,2,3] => 6
[1,4,5,3,2] => 6
[1,5,2,3,4] => 3
[1,5,2,4,3] => 3
[1,5,3,2,4] => 3
[1,5,3,4,2] => 3
[1,5,4,2,3] => 3
[1,5,4,3,2] => 3
[2,1,3,4,5] => 13
[2,1,3,5,4] => 8
[2,1,4,3,5] => 9
[2,1,4,5,3] => 8
[2,1,5,3,4] => 4
[2,1,5,4,3] => 4
[2,3,1,4,5] => 12
[2,3,1,5,4] => 7
[2,3,4,1,5] => 11
[2,3,4,5,1] => 10
[2,3,5,1,4] => 6
[2,3,5,4,1] => 6
[2,4,1,3,5] => 8
[2,4,1,5,3] => 7
[2,4,3,1,5] => 8
[2,4,3,5,1] => 7
[2,4,5,1,3] => 6
[2,4,5,3,1] => 6
[2,5,1,3,4] => 3
[2,5,1,4,3] => 3
[2,5,3,1,4] => 3
[2,5,3,4,1] => 3
[2,5,4,1,3] => 3
[2,5,4,3,1] => 3
[3,1,2,4,5] => 10
[3,1,2,5,4] => 5
[3,1,4,2,5] => 9
[3,1,4,5,2] => 8
[3,1,5,2,4] => 4
[3,1,5,4,2] => 4
[3,2,1,4,5] => 10
[3,2,1,5,4] => 5
[3,2,4,1,5] => 9
[3,2,4,5,1] => 8
[3,2,5,1,4] => 4
[3,2,5,4,1] => 4
[3,4,1,2,5] => 8
[3,4,1,5,2] => 7
[3,4,2,1,5] => 8
[3,4,2,5,1] => 7
[3,4,5,1,2] => 6
[3,4,5,2,1] => 6
[3,5,1,2,4] => 3
[3,5,1,4,2] => 3
>>> Load all 1201 entries. <<<
[3,5,2,1,4] => 3
[3,5,2,4,1] => 3
[3,5,4,1,2] => 3
[3,5,4,2,1] => 3
[4,1,2,3,5] => 6
[4,1,2,5,3] => 5
[4,1,3,2,5] => 6
[4,1,3,5,2] => 5
[4,1,5,2,3] => 4
[4,1,5,3,2] => 4
[4,2,1,3,5] => 6
[4,2,1,5,3] => 5
[4,2,3,1,5] => 6
[4,2,3,5,1] => 5
[4,2,5,1,3] => 4
[4,2,5,3,1] => 4
[4,3,1,2,5] => 6
[4,3,1,5,2] => 5
[4,3,2,1,5] => 6
[4,3,2,5,1] => 5
[4,3,5,1,2] => 4
[4,3,5,2,1] => 4
[4,5,1,2,3] => 3
[4,5,1,3,2] => 3
[4,5,2,1,3] => 3
[4,5,2,3,1] => 3
[4,5,3,1,2] => 3
[4,5,3,2,1] => 3
[5,1,2,3,4] => 1
[5,1,2,4,3] => 1
[5,1,3,2,4] => 1
[5,1,3,4,2] => 1
[5,1,4,2,3] => 1
[5,1,4,3,2] => 1
[5,2,1,3,4] => 1
[5,2,1,4,3] => 1
[5,2,3,1,4] => 1
[5,2,3,4,1] => 1
[5,2,4,1,3] => 1
[5,2,4,3,1] => 1
[5,3,1,2,4] => 1
[5,3,1,4,2] => 1
[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] => 1
[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] => 21
[1,2,3,4,6,5] => 15
[1,2,3,5,4,6] => 16
[1,2,3,5,6,4] => 15
[1,2,3,6,4,5] => 10
[1,2,3,6,5,4] => 10
[1,2,4,3,5,6] => 17
[1,2,4,3,6,5] => 11
[1,2,4,5,3,6] => 16
[1,2,4,5,6,3] => 15
[1,2,4,6,3,5] => 10
[1,2,4,6,5,3] => 10
[1,2,5,3,4,6] => 12
[1,2,5,3,6,4] => 11
[1,2,5,4,3,6] => 12
[1,2,5,4,6,3] => 11
[1,2,5,6,3,4] => 10
[1,2,5,6,4,3] => 10
[1,2,6,3,4,5] => 6
[1,2,6,3,5,4] => 6
[1,2,6,4,3,5] => 6
[1,2,6,4,5,3] => 6
[1,2,6,5,3,4] => 6
[1,2,6,5,4,3] => 6
[1,3,2,4,5,6] => 18
[1,3,2,4,6,5] => 12
[1,3,2,5,4,6] => 13
[1,3,2,5,6,4] => 12
[1,3,2,6,4,5] => 7
[1,3,2,6,5,4] => 7
[1,3,4,2,5,6] => 17
[1,3,4,2,6,5] => 11
[1,3,4,5,2,6] => 16
[1,3,4,5,6,2] => 15
[1,3,4,6,2,5] => 10
[1,3,4,6,5,2] => 10
[1,3,5,2,4,6] => 12
[1,3,5,2,6,4] => 11
[1,3,5,4,2,6] => 12
[1,3,5,4,6,2] => 11
[1,3,5,6,2,4] => 10
[1,3,5,6,4,2] => 10
[1,3,6,2,4,5] => 6
[1,3,6,2,5,4] => 6
[1,3,6,4,2,5] => 6
[1,3,6,4,5,2] => 6
[1,3,6,5,2,4] => 6
[1,3,6,5,4,2] => 6
[1,4,2,3,5,6] => 14
[1,4,2,3,6,5] => 8
[1,4,2,5,3,6] => 13
[1,4,2,5,6,3] => 12
[1,4,2,6,3,5] => 7
[1,4,2,6,5,3] => 7
[1,4,3,2,5,6] => 14
[1,4,3,2,6,5] => 8
[1,4,3,5,2,6] => 13
[1,4,3,5,6,2] => 12
[1,4,3,6,2,5] => 7
[1,4,3,6,5,2] => 7
[1,4,5,2,3,6] => 12
[1,4,5,2,6,3] => 11
[1,4,5,3,2,6] => 12
[1,4,5,3,6,2] => 11
[1,4,5,6,2,3] => 10
[1,4,5,6,3,2] => 10
[1,4,6,2,3,5] => 6
[1,4,6,2,5,3] => 6
[1,4,6,3,2,5] => 6
[1,4,6,3,5,2] => 6
[1,4,6,5,2,3] => 6
[1,4,6,5,3,2] => 6
[1,5,2,3,4,6] => 9
[1,5,2,3,6,4] => 8
[1,5,2,4,3,6] => 9
[1,5,2,4,6,3] => 8
[1,5,2,6,3,4] => 7
[1,5,2,6,4,3] => 7
[1,5,3,2,4,6] => 9
[1,5,3,2,6,4] => 8
[1,5,3,4,2,6] => 9
[1,5,3,4,6,2] => 8
[1,5,3,6,2,4] => 7
[1,5,3,6,4,2] => 7
[1,5,4,2,3,6] => 9
[1,5,4,2,6,3] => 8
[1,5,4,3,2,6] => 9
[1,5,4,3,6,2] => 8
[1,5,4,6,2,3] => 7
[1,5,4,6,3,2] => 7
[1,5,6,2,3,4] => 6
[1,5,6,2,4,3] => 6
[1,5,6,3,2,4] => 6
[1,5,6,3,4,2] => 6
[1,5,6,4,2,3] => 6
[1,5,6,4,3,2] => 6
[1,6,2,3,4,5] => 3
[1,6,2,3,5,4] => 3
[1,6,2,4,3,5] => 3
[1,6,2,4,5,3] => 3
[1,6,2,5,3,4] => 3
[1,6,2,5,4,3] => 3
[1,6,3,2,4,5] => 3
[1,6,3,2,5,4] => 3
[1,6,3,4,2,5] => 3
[1,6,3,4,5,2] => 3
[1,6,3,5,2,4] => 3
[1,6,3,5,4,2] => 3
[1,6,4,2,3,5] => 3
[1,6,4,2,5,3] => 3
[1,6,4,3,2,5] => 3
[1,6,4,3,5,2] => 3
[1,6,4,5,2,3] => 3
[1,6,4,5,3,2] => 3
[1,6,5,2,3,4] => 3
[1,6,5,2,4,3] => 3
[1,6,5,3,2,4] => 3
[1,6,5,3,4,2] => 3
[1,6,5,4,2,3] => 3
[1,6,5,4,3,2] => 3
[2,1,3,4,5,6] => 19
[2,1,3,4,6,5] => 13
[2,1,3,5,4,6] => 14
[2,1,3,5,6,4] => 13
[2,1,3,6,4,5] => 8
[2,1,3,6,5,4] => 8
[2,1,4,3,5,6] => 15
[2,1,4,3,6,5] => 9
[2,1,4,5,3,6] => 14
[2,1,4,5,6,3] => 13
[2,1,4,6,3,5] => 8
[2,1,4,6,5,3] => 8
[2,1,5,3,4,6] => 10
[2,1,5,3,6,4] => 9
[2,1,5,4,3,6] => 10
[2,1,5,4,6,3] => 9
[2,1,5,6,3,4] => 8
[2,1,5,6,4,3] => 8
[2,1,6,3,4,5] => 4
[2,1,6,3,5,4] => 4
[2,1,6,4,3,5] => 4
[2,1,6,4,5,3] => 4
[2,1,6,5,3,4] => 4
[2,1,6,5,4,3] => 4
[2,3,1,4,5,6] => 18
[2,3,1,4,6,5] => 12
[2,3,1,5,4,6] => 13
[2,3,1,5,6,4] => 12
[2,3,1,6,4,5] => 7
[2,3,1,6,5,4] => 7
[2,3,4,1,5,6] => 17
[2,3,4,1,6,5] => 11
[2,3,4,5,1,6] => 16
[2,3,4,5,6,1] => 15
[2,3,4,6,1,5] => 10
[2,3,4,6,5,1] => 10
[2,3,5,1,4,6] => 12
[2,3,5,1,6,4] => 11
[2,3,5,4,1,6] => 12
[2,3,5,4,6,1] => 11
[2,3,5,6,1,4] => 10
[2,3,5,6,4,1] => 10
[2,3,6,1,4,5] => 6
[2,3,6,1,5,4] => 6
[2,3,6,4,1,5] => 6
[2,3,6,4,5,1] => 6
[2,3,6,5,1,4] => 6
[2,3,6,5,4,1] => 6
[2,4,1,3,5,6] => 14
[2,4,1,3,6,5] => 8
[2,4,1,5,3,6] => 13
[2,4,1,5,6,3] => 12
[2,4,1,6,3,5] => 7
[2,4,1,6,5,3] => 7
[2,4,3,1,5,6] => 14
[2,4,3,1,6,5] => 8
[2,4,3,5,1,6] => 13
[2,4,3,5,6,1] => 12
[2,4,3,6,1,5] => 7
[2,4,3,6,5,1] => 7
[2,4,5,1,3,6] => 12
[2,4,5,1,6,3] => 11
[2,4,5,3,1,6] => 12
[2,4,5,3,6,1] => 11
[2,4,5,6,1,3] => 10
[2,4,5,6,3,1] => 10
[2,4,6,1,3,5] => 6
[2,4,6,1,5,3] => 6
[2,4,6,3,1,5] => 6
[2,4,6,3,5,1] => 6
[2,4,6,5,1,3] => 6
[2,4,6,5,3,1] => 6
[2,5,1,3,4,6] => 9
[2,5,1,3,6,4] => 8
[2,5,1,4,3,6] => 9
[2,5,1,4,6,3] => 8
[2,5,1,6,3,4] => 7
[2,5,1,6,4,3] => 7
[2,5,3,1,4,6] => 9
[2,5,3,1,6,4] => 8
[2,5,3,4,1,6] => 9
[2,5,3,4,6,1] => 8
[2,5,3,6,1,4] => 7
[2,5,3,6,4,1] => 7
[2,5,4,1,3,6] => 9
[2,5,4,1,6,3] => 8
[2,5,4,3,1,6] => 9
[2,5,4,3,6,1] => 8
[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] => 6
[2,5,6,3,1,4] => 6
[2,5,6,3,4,1] => 6
[2,5,6,4,1,3] => 6
[2,5,6,4,3,1] => 6
[2,6,1,3,4,5] => 3
[2,6,1,3,5,4] => 3
[2,6,1,4,3,5] => 3
[2,6,1,4,5,3] => 3
[2,6,1,5,3,4] => 3
[2,6,1,5,4,3] => 3
[2,6,3,1,4,5] => 3
[2,6,3,1,5,4] => 3
[2,6,3,4,1,5] => 3
[2,6,3,4,5,1] => 3
[2,6,3,5,1,4] => 3
[2,6,3,5,4,1] => 3
[2,6,4,1,3,5] => 3
[2,6,4,1,5,3] => 3
[2,6,4,3,1,5] => 3
[2,6,4,3,5,1] => 3
[2,6,4,5,1,3] => 3
[2,6,4,5,3,1] => 3
[2,6,5,1,3,4] => 3
[2,6,5,1,4,3] => 3
[2,6,5,3,1,4] => 3
[2,6,5,3,4,1] => 3
[2,6,5,4,1,3] => 3
[2,6,5,4,3,1] => 3
[3,1,2,4,5,6] => 16
[3,1,2,4,6,5] => 10
[3,1,2,5,4,6] => 11
[3,1,2,5,6,4] => 10
[3,1,2,6,4,5] => 5
[3,1,2,6,5,4] => 5
[3,1,4,2,5,6] => 15
[3,1,4,2,6,5] => 9
[3,1,4,5,2,6] => 14
[3,1,4,5,6,2] => 13
[3,1,4,6,2,5] => 8
[3,1,4,6,5,2] => 8
[3,1,5,2,4,6] => 10
[3,1,5,2,6,4] => 9
[3,1,5,4,2,6] => 10
[3,1,5,4,6,2] => 9
[3,1,5,6,2,4] => 8
[3,1,5,6,4,2] => 8
[3,1,6,2,4,5] => 4
[3,1,6,2,5,4] => 4
[3,1,6,4,2,5] => 4
[3,1,6,4,5,2] => 4
[3,1,6,5,2,4] => 4
[3,1,6,5,4,2] => 4
[3,2,1,4,5,6] => 16
[3,2,1,4,6,5] => 10
[3,2,1,5,4,6] => 11
[3,2,1,5,6,4] => 10
[3,2,1,6,4,5] => 5
[3,2,1,6,5,4] => 5
[3,2,4,1,5,6] => 15
[3,2,4,1,6,5] => 9
[3,2,4,5,1,6] => 14
[3,2,4,5,6,1] => 13
[3,2,4,6,1,5] => 8
[3,2,4,6,5,1] => 8
[3,2,5,1,4,6] => 10
[3,2,5,1,6,4] => 9
[3,2,5,4,1,6] => 10
[3,2,5,4,6,1] => 9
[3,2,5,6,1,4] => 8
[3,2,5,6,4,1] => 8
[3,2,6,1,4,5] => 4
[3,2,6,1,5,4] => 4
[3,2,6,4,1,5] => 4
[3,2,6,4,5,1] => 4
[3,2,6,5,1,4] => 4
[3,2,6,5,4,1] => 4
[3,4,1,2,5,6] => 14
[3,4,1,2,6,5] => 8
[3,4,1,5,2,6] => 13
[3,4,1,5,6,2] => 12
[3,4,1,6,2,5] => 7
[3,4,1,6,5,2] => 7
[3,4,2,1,5,6] => 14
[3,4,2,1,6,5] => 8
[3,4,2,5,1,6] => 13
[3,4,2,5,6,1] => 12
[3,4,2,6,1,5] => 7
[3,4,2,6,5,1] => 7
[3,4,5,1,2,6] => 12
[3,4,5,1,6,2] => 11
[3,4,5,2,1,6] => 12
[3,4,5,2,6,1] => 11
[3,4,5,6,1,2] => 10
[3,4,5,6,2,1] => 10
[3,4,6,1,2,5] => 6
[3,4,6,1,5,2] => 6
[3,4,6,2,1,5] => 6
[3,4,6,2,5,1] => 6
[3,4,6,5,1,2] => 6
[3,4,6,5,2,1] => 6
[3,5,1,2,4,6] => 9
[3,5,1,2,6,4] => 8
[3,5,1,4,2,6] => 9
[3,5,1,4,6,2] => 8
[3,5,1,6,2,4] => 7
[3,5,1,6,4,2] => 7
[3,5,2,1,4,6] => 9
[3,5,2,1,6,4] => 8
[3,5,2,4,1,6] => 9
[3,5,2,4,6,1] => 8
[3,5,2,6,1,4] => 7
[3,5,2,6,4,1] => 7
[3,5,4,1,2,6] => 9
[3,5,4,1,6,2] => 8
[3,5,4,2,1,6] => 9
[3,5,4,2,6,1] => 8
[3,5,4,6,1,2] => 7
[3,5,4,6,2,1] => 7
[3,5,6,1,2,4] => 6
[3,5,6,1,4,2] => 6
[3,5,6,2,1,4] => 6
[3,5,6,2,4,1] => 6
[3,5,6,4,1,2] => 6
[3,5,6,4,2,1] => 6
[3,6,1,2,4,5] => 3
[3,6,1,2,5,4] => 3
[3,6,1,4,2,5] => 3
[3,6,1,4,5,2] => 3
[3,6,1,5,2,4] => 3
[3,6,1,5,4,2] => 3
[3,6,2,1,4,5] => 3
[3,6,2,1,5,4] => 3
[3,6,2,4,1,5] => 3
[3,6,2,4,5,1] => 3
[3,6,2,5,1,4] => 3
[3,6,2,5,4,1] => 3
[3,6,4,1,2,5] => 3
[3,6,4,1,5,2] => 3
[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] => 3
[3,6,5,1,4,2] => 3
[3,6,5,2,1,4] => 3
[3,6,5,2,4,1] => 3
[3,6,5,4,1,2] => 3
[3,6,5,4,2,1] => 3
[4,1,2,3,5,6] => 12
[4,1,2,3,6,5] => 6
[4,1,2,5,3,6] => 11
[4,1,2,5,6,3] => 10
[4,1,2,6,3,5] => 5
[4,1,2,6,5,3] => 5
[4,1,3,2,5,6] => 12
[4,1,3,2,6,5] => 6
[4,1,3,5,2,6] => 11
[4,1,3,5,6,2] => 10
[4,1,3,6,2,5] => 5
[4,1,3,6,5,2] => 5
[4,1,5,2,3,6] => 10
[4,1,5,2,6,3] => 9
[4,1,5,3,2,6] => 10
[4,1,5,3,6,2] => 9
[4,1,5,6,2,3] => 8
[4,1,5,6,3,2] => 8
[4,1,6,2,3,5] => 4
[4,1,6,2,5,3] => 4
[4,1,6,3,2,5] => 4
[4,1,6,3,5,2] => 4
[4,1,6,5,2,3] => 4
[4,1,6,5,3,2] => 4
[4,2,1,3,5,6] => 12
[4,2,1,3,6,5] => 6
[4,2,1,5,3,6] => 11
[4,2,1,5,6,3] => 10
[4,2,1,6,3,5] => 5
[4,2,1,6,5,3] => 5
[4,2,3,1,5,6] => 12
[4,2,3,1,6,5] => 6
[4,2,3,5,1,6] => 11
[4,2,3,5,6,1] => 10
[4,2,3,6,1,5] => 5
[4,2,3,6,5,1] => 5
[4,2,5,1,3,6] => 10
[4,2,5,1,6,3] => 9
[4,2,5,3,1,6] => 10
[4,2,5,3,6,1] => 9
[4,2,5,6,1,3] => 8
[4,2,5,6,3,1] => 8
[4,2,6,1,3,5] => 4
[4,2,6,1,5,3] => 4
[4,2,6,3,1,5] => 4
[4,2,6,3,5,1] => 4
[4,2,6,5,1,3] => 4
[4,2,6,5,3,1] => 4
[4,3,1,2,5,6] => 12
[4,3,1,2,6,5] => 6
[4,3,1,5,2,6] => 11
[4,3,1,5,6,2] => 10
[4,3,1,6,2,5] => 5
[4,3,1,6,5,2] => 5
[4,3,2,1,5,6] => 12
[4,3,2,1,6,5] => 6
[4,3,2,5,1,6] => 11
[4,3,2,5,6,1] => 10
[4,3,2,6,1,5] => 5
[4,3,2,6,5,1] => 5
[4,3,5,1,2,6] => 10
[4,3,5,1,6,2] => 9
[4,3,5,2,1,6] => 10
[4,3,5,2,6,1] => 9
[4,3,5,6,1,2] => 8
[4,3,5,6,2,1] => 8
[4,3,6,1,2,5] => 4
[4,3,6,1,5,2] => 4
[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] => 9
[4,5,1,2,6,3] => 8
[4,5,1,3,2,6] => 9
[4,5,1,3,6,2] => 8
[4,5,1,6,2,3] => 7
[4,5,1,6,3,2] => 7
[4,5,2,1,3,6] => 9
[4,5,2,1,6,3] => 8
[4,5,2,3,1,6] => 9
[4,5,2,3,6,1] => 8
[4,5,2,6,1,3] => 7
[4,5,2,6,3,1] => 7
[4,5,3,1,2,6] => 9
[4,5,3,1,6,2] => 8
[4,5,3,2,1,6] => 9
[4,5,3,2,6,1] => 8
[4,5,3,6,1,2] => 7
[4,5,3,6,2,1] => 7
[4,5,6,1,2,3] => 6
[4,5,6,1,3,2] => 6
[4,5,6,2,1,3] => 6
[4,5,6,2,3,1] => 6
[4,5,6,3,1,2] => 6
[4,5,6,3,2,1] => 6
[4,6,1,2,3,5] => 3
[4,6,1,2,5,3] => 3
[4,6,1,3,2,5] => 3
[4,6,1,3,5,2] => 3
[4,6,1,5,2,3] => 3
[4,6,1,5,3,2] => 3
[4,6,2,1,3,5] => 3
[4,6,2,1,5,3] => 3
[4,6,2,3,1,5] => 3
[4,6,2,3,5,1] => 3
[4,6,2,5,1,3] => 3
[4,6,2,5,3,1] => 3
[4,6,3,1,2,5] => 3
[4,6,3,1,5,2] => 3
[4,6,3,2,1,5] => 3
[4,6,3,2,5,1] => 3
[4,6,3,5,1,2] => 3
[4,6,3,5,2,1] => 3
[4,6,5,1,2,3] => 3
[4,6,5,1,3,2] => 3
[4,6,5,2,1,3] => 3
[4,6,5,2,3,1] => 3
[4,6,5,3,1,2] => 3
[4,6,5,3,2,1] => 3
[5,1,2,3,4,6] => 7
[5,1,2,3,6,4] => 6
[5,1,2,4,3,6] => 7
[5,1,2,4,6,3] => 6
[5,1,2,6,3,4] => 5
[5,1,2,6,4,3] => 5
[5,1,3,2,4,6] => 7
[5,1,3,2,6,4] => 6
[5,1,3,4,2,6] => 7
[5,1,3,4,6,2] => 6
[5,1,3,6,2,4] => 5
[5,1,3,6,4,2] => 5
[5,1,4,2,3,6] => 7
[5,1,4,2,6,3] => 6
[5,1,4,3,2,6] => 7
[5,1,4,3,6,2] => 6
[5,1,4,6,2,3] => 5
[5,1,4,6,3,2] => 5
[5,1,6,2,3,4] => 4
[5,1,6,2,4,3] => 4
[5,1,6,3,2,4] => 4
[5,1,6,3,4,2] => 4
[5,1,6,4,2,3] => 4
[5,1,6,4,3,2] => 4
[5,2,1,3,4,6] => 7
[5,2,1,3,6,4] => 6
[5,2,1,4,3,6] => 7
[5,2,1,4,6,3] => 6
[5,2,1,6,3,4] => 5
[5,2,1,6,4,3] => 5
[5,2,3,1,4,6] => 7
[5,2,3,1,6,4] => 6
[5,2,3,4,1,6] => 7
[5,2,3,4,6,1] => 6
[5,2,3,6,1,4] => 5
[5,2,3,6,4,1] => 5
[5,2,4,1,3,6] => 7
[5,2,4,1,6,3] => 6
[5,2,4,3,1,6] => 7
[5,2,4,3,6,1] => 6
[5,2,4,6,1,3] => 5
[5,2,4,6,3,1] => 5
[5,2,6,1,3,4] => 4
[5,2,6,1,4,3] => 4
[5,2,6,3,1,4] => 4
[5,2,6,3,4,1] => 4
[5,2,6,4,1,3] => 4
[5,2,6,4,3,1] => 4
[5,3,1,2,4,6] => 7
[5,3,1,2,6,4] => 6
[5,3,1,4,2,6] => 7
[5,3,1,4,6,2] => 6
[5,3,1,6,2,4] => 5
[5,3,1,6,4,2] => 5
[5,3,2,1,4,6] => 7
[5,3,2,1,6,4] => 6
[5,3,2,4,1,6] => 7
[5,3,2,4,6,1] => 6
[5,3,2,6,1,4] => 5
[5,3,2,6,4,1] => 5
[5,3,4,1,2,6] => 7
[5,3,4,1,6,2] => 6
[5,3,4,2,1,6] => 7
[5,3,4,2,6,1] => 6
[5,3,4,6,1,2] => 5
[5,3,4,6,2,1] => 5
[5,3,6,1,2,4] => 4
[5,3,6,1,4,2] => 4
[5,3,6,2,1,4] => 4
[5,3,6,2,4,1] => 4
[5,3,6,4,1,2] => 4
[5,3,6,4,2,1] => 4
[5,4,1,2,3,6] => 7
[5,4,1,2,6,3] => 6
[5,4,1,3,2,6] => 7
[5,4,1,3,6,2] => 6
[5,4,1,6,2,3] => 5
[5,4,1,6,3,2] => 5
[5,4,2,1,3,6] => 7
[5,4,2,1,6,3] => 6
[5,4,2,3,1,6] => 7
[5,4,2,3,6,1] => 6
[5,4,2,6,1,3] => 5
[5,4,2,6,3,1] => 5
[5,4,3,1,2,6] => 7
[5,4,3,1,6,2] => 6
[5,4,3,2,1,6] => 7
[5,4,3,2,6,1] => 6
[5,4,3,6,1,2] => 5
[5,4,3,6,2,1] => 5
[5,4,6,1,2,3] => 4
[5,4,6,1,3,2] => 4
[5,4,6,2,1,3] => 4
[5,4,6,2,3,1] => 4
[5,4,6,3,1,2] => 4
[5,4,6,3,2,1] => 4
[5,6,1,2,3,4] => 3
[5,6,1,2,4,3] => 3
[5,6,1,3,2,4] => 3
[5,6,1,3,4,2] => 3
[5,6,1,4,2,3] => 3
[5,6,1,4,3,2] => 3
[5,6,2,1,3,4] => 3
[5,6,2,1,4,3] => 3
[5,6,2,3,1,4] => 3
[5,6,2,3,4,1] => 3
[5,6,2,4,1,3] => 3
[5,6,2,4,3,1] => 3
[5,6,3,1,2,4] => 3
[5,6,3,1,4,2] => 3
[5,6,3,2,1,4] => 3
[5,6,3,2,4,1] => 3
[5,6,3,4,1,2] => 3
[5,6,3,4,2,1] => 3
[5,6,4,1,2,3] => 3
[5,6,4,1,3,2] => 3
[5,6,4,2,1,3] => 3
[5,6,4,2,3,1] => 3
[5,6,4,3,1,2] => 3
[5,6,4,3,2,1] => 3
[6,1,2,3,4,5] => 1
[6,1,2,3,5,4] => 1
[6,1,2,4,3,5] => 1
[6,1,2,4,5,3] => 1
[6,1,2,5,3,4] => 1
[6,1,2,5,4,3] => 1
[6,1,3,2,4,5] => 1
[6,1,3,2,5,4] => 1
[6,1,3,4,2,5] => 1
[6,1,3,4,5,2] => 1
[6,1,3,5,2,4] => 1
[6,1,3,5,4,2] => 1
[6,1,4,2,3,5] => 1
[6,1,4,2,5,3] => 1
[6,1,4,3,2,5] => 1
[6,1,4,3,5,2] => 1
[6,1,4,5,2,3] => 1
[6,1,4,5,3,2] => 1
[6,1,5,2,3,4] => 1
[6,1,5,2,4,3] => 1
[6,1,5,3,2,4] => 1
[6,1,5,3,4,2] => 1
[6,1,5,4,2,3] => 1
[6,1,5,4,3,2] => 1
[6,2,1,3,4,5] => 1
[6,2,1,3,5,4] => 1
[6,2,1,4,3,5] => 1
[6,2,1,4,5,3] => 1
[6,2,1,5,3,4] => 1
[6,2,1,5,4,3] => 1
[6,2,3,1,4,5] => 1
[6,2,3,1,5,4] => 1
[6,2,3,4,1,5] => 1
[6,2,3,4,5,1] => 1
[6,2,3,5,1,4] => 1
[6,2,3,5,4,1] => 1
[6,2,4,1,3,5] => 1
[6,2,4,1,5,3] => 1
[6,2,4,3,1,5] => 1
[6,2,4,3,5,1] => 1
[6,2,4,5,1,3] => 1
[6,2,4,5,3,1] => 1
[6,2,5,1,3,4] => 1
[6,2,5,1,4,3] => 1
[6,2,5,3,1,4] => 1
[6,2,5,3,4,1] => 1
[6,2,5,4,1,3] => 1
[6,2,5,4,3,1] => 1
[6,3,1,2,4,5] => 1
[6,3,1,2,5,4] => 1
[6,3,1,4,2,5] => 1
[6,3,1,4,5,2] => 1
[6,3,1,5,2,4] => 1
[6,3,1,5,4,2] => 1
[6,3,2,1,4,5] => 1
[6,3,2,1,5,4] => 1
[6,3,2,4,1,5] => 1
[6,3,2,4,5,1] => 1
[6,3,2,5,1,4] => 1
[6,3,2,5,4,1] => 1
[6,3,4,1,2,5] => 1
[6,3,4,1,5,2] => 1
[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] => 1
[6,3,5,1,4,2] => 1
[6,3,5,2,1,4] => 1
[6,3,5,2,4,1] => 1
[6,3,5,4,1,2] => 1
[6,3,5,4,2,1] => 1
[6,4,1,2,3,5] => 1
[6,4,1,2,5,3] => 1
[6,4,1,3,2,5] => 1
[6,4,1,3,5,2] => 1
[6,4,1,5,2,3] => 1
[6,4,1,5,3,2] => 1
[6,4,2,1,3,5] => 1
[6,4,2,1,5,3] => 1
[6,4,2,3,1,5] => 1
[6,4,2,3,5,1] => 1
[6,4,2,5,1,3] => 1
[6,4,2,5,3,1] => 1
[6,4,3,1,2,5] => 1
[6,4,3,1,5,2] => 1
[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] => 1
[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] => 1
[6,5,1,3,2,4] => 1
[6,5,1,3,4,2] => 1
[6,5,1,4,2,3] => 1
[6,5,1,4,3,2] => 1
[6,5,2,1,3,4] => 1
[6,5,2,1,4,3] => 1
[6,5,2,3,1,4] => 1
[6,5,2,3,4,1] => 1
[6,5,2,4,1,3] => 1
[6,5,2,4,3,1] => 1
[6,5,3,1,2,4] => 1
[6,5,3,1,4,2] => 1
[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] => 1
[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] => 28
[1,2,3,4,5,7,6] => 21
[1,2,3,4,6,5,7] => 22
[1,2,3,4,6,7,5] => 21
[1,2,3,4,7,5,6] => 15
[1,2,3,4,7,6,5] => 15
[1,2,3,5,4,6,7] => 23
[1,2,3,5,4,7,6] => 16
[1,2,3,5,6,4,7] => 22
[1,2,3,5,6,7,4] => 21
[1,2,3,5,7,4,6] => 15
[1,2,3,5,7,6,4] => 15
[1,2,3,6,4,5,7] => 17
[1,2,3,6,4,7,5] => 16
[1,2,3,6,5,4,7] => 17
[1,2,3,6,5,7,4] => 16
[1,2,3,6,7,4,5] => 15
[1,2,3,6,7,5,4] => 15
[1,2,3,7,4,5,6] => 10
[1,2,3,7,4,6,5] => 10
[1,2,3,7,5,4,6] => 10
[1,2,3,7,5,6,4] => 10
[1,2,3,7,6,4,5] => 10
[1,2,3,7,6,5,4] => 10
[1,2,4,3,5,6,7] => 24
[1,2,4,3,5,7,6] => 17
[1,2,4,3,6,5,7] => 18
[1,2,4,3,6,7,5] => 17
[1,2,4,3,7,5,6] => 11
[1,2,4,3,7,6,5] => 11
[1,2,4,5,3,6,7] => 23
[1,2,4,5,3,7,6] => 16
[1,2,4,5,6,3,7] => 22
[1,2,4,5,6,7,3] => 21
[1,2,4,5,7,3,6] => 15
[1,2,4,5,7,6,3] => 15
[1,2,4,6,3,5,7] => 17
[1,2,4,6,3,7,5] => 16
[1,2,4,6,5,3,7] => 17
[1,2,4,6,5,7,3] => 16
[1,2,4,6,7,3,5] => 15
[1,2,4,6,7,5,3] => 15
[1,2,4,7,3,5,6] => 10
[1,2,4,7,3,6,5] => 10
[1,2,4,7,5,3,6] => 10
[1,2,4,7,5,6,3] => 10
[1,2,4,7,6,3,5] => 10
[1,2,4,7,6,5,3] => 10
[1,2,5,3,4,6,7] => 19
[1,2,5,3,4,7,6] => 12
[1,2,5,3,6,4,7] => 18
[1,2,5,3,6,7,4] => 17
[1,2,5,3,7,4,6] => 11
[1,2,5,3,7,6,4] => 11
[1,2,5,4,3,6,7] => 19
[1,2,5,4,3,7,6] => 12
[1,2,5,4,6,3,7] => 18
[1,2,5,4,6,7,3] => 17
[1,2,5,4,7,3,6] => 11
[1,2,5,4,7,6,3] => 11
[1,2,5,6,3,4,7] => 17
[1,2,5,6,3,7,4] => 16
[1,2,5,6,4,3,7] => 17
[1,2,5,6,4,7,3] => 16
[1,2,5,6,7,3,4] => 15
[1,2,5,6,7,4,3] => 15
[1,2,5,7,3,4,6] => 10
[1,2,5,7,3,6,4] => 10
[1,2,5,7,4,3,6] => 10
[1,2,5,7,4,6,3] => 10
[1,2,5,7,6,3,4] => 10
[1,2,5,7,6,4,3] => 10
[1,2,6,3,4,5,7] => 13
[1,2,6,3,4,7,5] => 12
[1,2,6,3,5,4,7] => 13
[1,2,6,3,5,7,4] => 12
[1,2,6,3,7,4,5] => 11
[1,2,6,3,7,5,4] => 11
[1,2,6,4,3,5,7] => 13
[1,2,6,4,3,7,5] => 12
[1,2,6,4,5,3,7] => 13
[1,2,6,4,5,7,3] => 12
[1,2,6,4,7,3,5] => 11
[1,2,6,4,7,5,3] => 11
[1,2,6,5,3,4,7] => 13
[1,2,6,5,3,7,4] => 12
[1,2,6,5,4,3,7] => 13
[1,2,6,5,4,7,3] => 12
[1,2,6,5,7,3,4] => 11
[1,2,6,5,7,4,3] => 11
[1,2,6,7,3,4,5] => 10
[1,2,6,7,3,5,4] => 10
[1,2,6,7,4,3,5] => 10
[1,2,6,7,4,5,3] => 10
[1,2,6,7,5,3,4] => 10
[1,2,6,7,5,4,3] => 10
[1,2,7,3,4,5,6] => 6
[1,2,7,3,4,6,5] => 6
[1,2,7,3,5,4,6] => 6
[1,2,7,3,5,6,4] => 6
[1,2,7,3,6,4,5] => 6
[1,2,7,3,6,5,4] => 6
[1,2,7,4,3,5,6] => 6
[1,2,7,4,3,6,5] => 6
[1,2,7,4,5,3,6] => 6
[1,2,7,4,5,6,3] => 6
[1,2,7,4,6,3,5] => 6
[1,2,7,4,6,5,3] => 6
[1,2,7,5,3,4,6] => 6
[1,2,7,5,3,6,4] => 6
[1,2,7,5,4,3,6] => 6
[1,2,7,5,4,6,3] => 6
[1,2,7,5,6,3,4] => 6
[1,2,7,5,6,4,3] => 6
[1,2,7,6,3,4,5] => 6
[1,2,7,6,3,5,4] => 6
[1,2,7,6,4,3,5] => 6
[1,2,7,6,4,5,3] => 6
[1,2,7,6,5,3,4] => 6
[1,2,7,6,5,4,3] => 6
[1,3,2,4,5,6,7] => 25
[1,3,2,4,5,7,6] => 18
[1,3,2,4,6,5,7] => 19
[1,3,2,4,6,7,5] => 18
[1,3,2,4,7,5,6] => 12
[1,3,2,4,7,6,5] => 12
[1,3,2,5,4,6,7] => 20
[1,3,2,5,4,7,6] => 13
[1,3,2,5,6,4,7] => 19
[1,3,2,5,6,7,4] => 18
[1,3,2,5,7,4,6] => 12
[1,3,2,5,7,6,4] => 12
[1,3,2,6,4,5,7] => 14
[1,3,2,6,4,7,5] => 13
[1,3,2,6,5,4,7] => 14
[1,3,2,6,5,7,4] => 13
[1,3,2,6,7,4,5] => 12
[1,3,2,6,7,5,4] => 12
[1,3,2,7,4,5,6] => 7
[1,3,2,7,4,6,5] => 7
[1,3,2,7,5,4,6] => 7
[1,3,2,7,5,6,4] => 7
[1,3,2,7,6,4,5] => 7
[1,3,2,7,6,5,4] => 7
[1,3,4,2,5,6,7] => 24
[1,3,4,2,5,7,6] => 17
[1,3,4,2,6,5,7] => 18
[1,3,4,2,6,7,5] => 17
[1,3,4,2,7,5,6] => 11
[1,3,4,2,7,6,5] => 11
[1,3,4,5,2,6,7] => 23
[1,3,4,5,2,7,6] => 16
[1,3,4,5,6,2,7] => 22
[1,3,4,5,6,7,2] => 21
[1,3,4,5,7,2,6] => 15
[1,3,4,5,7,6,2] => 15
[1,3,4,6,2,5,7] => 17
[1,3,4,6,2,7,5] => 16
[1,3,4,6,5,2,7] => 17
[1,3,4,6,5,7,2] => 16
[1,3,4,6,7,2,5] => 15
[1,3,4,6,7,5,2] => 15
[1,3,4,7,2,5,6] => 10
[1,3,4,7,2,6,5] => 10
[1,3,4,7,5,2,6] => 10
[1,3,4,7,5,6,2] => 10
[1,3,4,7,6,2,5] => 10
[1,3,4,7,6,5,2] => 10
[1,3,5,2,4,6,7] => 19
[1,3,5,2,4,7,6] => 12
[1,3,5,2,6,4,7] => 18
[1,3,5,2,6,7,4] => 17
[1,3,5,2,7,4,6] => 11
[1,3,5,2,7,6,4] => 11
[1,3,5,4,2,6,7] => 19
[1,3,5,4,2,7,6] => 12
[1,3,5,4,6,2,7] => 18
[1,3,5,4,6,7,2] => 17
[1,3,5,4,7,2,6] => 11
[1,3,5,4,7,6,2] => 11
[1,3,5,6,2,4,7] => 17
[1,3,5,6,2,7,4] => 16
[1,3,5,6,4,2,7] => 17
[1,3,5,6,4,7,2] => 16
[1,3,5,6,7,2,4] => 15
[1,3,5,6,7,4,2] => 15
[1,3,5,7,2,4,6] => 10
[1,3,5,7,2,6,4] => 10
[1,3,5,7,4,2,6] => 10
[1,3,5,7,4,6,2] => 10
[1,3,5,7,6,2,4] => 10
[1,3,5,7,6,4,2] => 10
[1,3,6,2,4,5,7] => 13
[1,3,6,2,4,7,5] => 12
[1,3,6,2,5,4,7] => 13
[1,3,6,2,5,7,4] => 12
[1,3,6,2,7,4,5] => 11
[1,3,6,2,7,5,4] => 11
[1,3,6,4,2,5,7] => 13
[1,3,6,4,2,7,5] => 12
[1,3,6,4,5,2,7] => 13
[1,3,6,4,5,7,2] => 12
[1,3,6,4,7,2,5] => 11
[1,3,6,4,7,5,2] => 11
[1,3,6,5,2,4,7] => 13
[1,3,6,5,2,7,4] => 12
[1,3,6,5,4,2,7] => 13
[1,3,6,5,4,7,2] => 12
[1,3,6,5,7,2,4] => 11
[1,3,6,5,7,4,2] => 11
[1,3,6,7,2,4,5] => 10
[1,3,6,7,2,5,4] => 10
[1,3,6,7,4,2,5] => 10
[1,3,6,7,4,5,2] => 10
[1,3,6,7,5,2,4] => 10
[1,3,6,7,5,4,2] => 10
[1,3,7,2,4,5,6] => 6
[1,3,7,2,4,6,5] => 6
[1,3,7,2,5,4,6] => 6
[1,3,7,2,5,6,4] => 6
[1,3,7,2,6,4,5] => 6
[1,3,7,2,6,5,4] => 6
[1,3,7,4,2,5,6] => 6
[1,3,7,4,2,6,5] => 6
[1,3,7,4,5,2,6] => 6
[1,3,7,4,5,6,2] => 6
[1,3,7,4,6,2,5] => 6
[1,3,7,4,6,5,2] => 6
[1,3,7,5,2,4,6] => 6
[1,3,7,5,2,6,4] => 6
[1,3,7,5,4,2,6] => 6
[1,3,7,5,4,6,2] => 6
[1,3,7,5,6,2,4] => 6
[1,3,7,5,6,4,2] => 6
[1,3,7,6,2,4,5] => 6
[1,3,7,6,2,5,4] => 6
[1,3,7,6,4,2,5] => 6
[1,3,7,6,4,5,2] => 6
[1,3,7,6,5,2,4] => 6
[1,3,7,6,5,4,2] => 6
[1,4,2,3,5,6,7] => 21
[1,4,2,3,5,7,6] => 14
[1,4,2,3,6,5,7] => 15
[1,4,2,3,6,7,5] => 14
[1,4,2,3,7,5,6] => 8
[1,4,2,3,7,6,5] => 8
[1,4,2,5,3,6,7] => 20
[1,4,2,5,3,7,6] => 13
[1,4,2,5,6,3,7] => 19
[1,4,2,5,6,7,3] => 18
[1,4,2,5,7,3,6] => 12
[1,4,2,5,7,6,3] => 12
[1,4,2,6,3,5,7] => 14
[1,4,2,6,3,7,5] => 13
[1,4,2,6,5,3,7] => 14
[1,4,2,6,5,7,3] => 13
[1,4,2,6,7,3,5] => 12
[1,4,2,6,7,5,3] => 12
[1,4,2,7,3,5,6] => 7
[1,4,2,7,3,6,5] => 7
[1,4,2,7,5,3,6] => 7
[1,4,2,7,5,6,3] => 7
[1,4,2,7,6,3,5] => 7
[1,4,2,7,6,5,3] => 7
[1,4,3,2,5,6,7] => 21
[1,4,3,2,5,7,6] => 14
[1,4,3,2,6,5,7] => 15
[1,4,3,2,6,7,5] => 14
[1,4,3,2,7,5,6] => 8
[1,4,3,2,7,6,5] => 8
[1,4,3,5,2,6,7] => 20
[1,4,3,5,2,7,6] => 13
[1,4,3,5,6,2,7] => 19
[1,4,3,5,6,7,2] => 18
[1,4,3,5,7,2,6] => 12
[1,4,3,5,7,6,2] => 12
[1,4,3,6,2,5,7] => 14
[1,4,3,6,2,7,5] => 13
[1,4,3,6,5,2,7] => 14
[1,4,3,6,5,7,2] => 13
[1,4,3,6,7,2,5] => 12
[1,4,3,6,7,5,2] => 12
[1,4,3,7,2,5,6] => 7
[1,4,3,7,2,6,5] => 7
[1,4,3,7,5,2,6] => 7
[1,4,3,7,5,6,2] => 7
[1,4,3,7,6,2,5] => 7
[1,4,3,7,6,5,2] => 7
[1,4,5,2,3,6,7] => 19
[1,4,5,2,3,7,6] => 12
[1,4,5,2,6,3,7] => 18
[1,4,5,2,6,7,3] => 17
[1,4,5,2,7,3,6] => 11
[1,4,5,2,7,6,3] => 11
[1,4,5,3,2,6,7] => 19
[1,4,5,3,2,7,6] => 12
[1,4,5,3,6,2,7] => 18
[1,4,5,3,6,7,2] => 17
[1,4,5,3,7,2,6] => 11
[1,4,5,3,7,6,2] => 11
[1,4,5,6,2,3,7] => 17
[1,4,5,6,2,7,3] => 16
[1,4,5,6,3,2,7] => 17
[1,4,5,6,3,7,2] => 16
[1,4,5,6,7,2,3] => 15
[1,4,5,6,7,3,2] => 15
[1,4,5,7,2,3,6] => 10
[1,4,5,7,2,6,3] => 10
[1,4,5,7,3,2,6] => 10
[1,4,5,7,3,6,2] => 10
[1,4,5,7,6,2,3] => 10
[1,4,5,7,6,3,2] => 10
[1,4,6,2,3,5,7] => 13
[1,4,6,2,3,7,5] => 12
[1,4,6,2,5,3,7] => 13
[1,4,6,2,5,7,3] => 12
[1,4,6,2,7,3,5] => 11
[1,4,6,2,7,5,3] => 11
[1,4,6,3,2,5,7] => 13
[1,4,6,3,2,7,5] => 12
[1,4,6,3,5,2,7] => 13
[1,4,6,3,5,7,2] => 12
[1,4,6,3,7,2,5] => 11
[1,4,6,3,7,5,2] => 11
[1,4,6,5,2,3,7] => 13
[1,4,6,5,2,7,3] => 12
[1,4,6,5,3,2,7] => 13
[1,4,6,5,3,7,2] => 12
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Description
The sum of the positions of the left to right maxima of a permutation.
The generating function for this statistic is $$\sum_{\pi\in\mathfrak S_n} q^{slrmax(pi)} = \prod_{k=1}^n (q^k+k-1),$$
see [prop. 2.6., 1].
References
[1] Kortchemski, I. Asymptotic behavior of permutation records arXiv:0804.0446
[2] Triangle read by rows: T(n,k) is the number of permutations of [n] for which the sum of the positions of the left-to-right maxima is k (1<=k<=n(n+1)/2). OEIS:A143946
Code
def statistic(pi):
    """
    sage: r=5; factor(sum(x^statistic(pi) for pi in Permutations(r)))
    (x^5 + 4)*(x^4 + 3)*(x^3 + 2)*(x^2 + 1)*x
    """
    pi = list(pi)
    i = 0
    res = 0
    for j in range(len(pi)):
        if pi[j] > i:
            i = pi[j] 
            res += j+1
    return res
Created
Apr 08, 2017 at 21:39 by Martin Rubey
Updated
May 03, 2019 at 12:57 by Henning Ulfarsson