edit this statistic or download as text // json
Identifier
Values
[1] => 0
[1,2] => 0
[2,1] => 0
[1,2,3] => 0
[1,3,2] => 1
[2,1,3] => 1
[2,3,1] => 1
[3,1,2] => 1
[3,2,1] => 0
[1,2,3,4] => 0
[1,2,4,3] => 3
[1,3,2,4] => 2
[1,3,4,2] => 3
[1,4,2,3] => 3
[1,4,3,2] => 1
[2,1,3,4] => 3
[2,1,4,3] => 2
[2,3,1,4] => 3
[2,3,4,1] => 1
[2,4,1,3] => 4
[2,4,3,1] => 3
[3,1,2,4] => 3
[3,1,4,2] => 4
[3,2,1,4] => 1
[3,2,4,1] => 3
[3,4,1,2] => 2
[3,4,2,1] => 3
[4,1,2,3] => 1
[4,1,3,2] => 3
[4,2,1,3] => 3
[4,2,3,1] => 2
[4,3,1,2] => 3
[4,3,2,1] => 0
[1,2,3,4,5] => 0
[1,2,3,5,4] => 6
[1,2,4,3,5] => 5
[1,2,4,5,3] => 7
[1,2,5,3,4] => 7
[1,2,5,4,3] => 3
[1,3,2,4,5] => 5
[1,3,2,5,4] => 6
[1,3,4,2,5] => 6
[1,3,4,5,2] => 5
[1,3,5,2,4] => 9
[1,3,5,4,2] => 7
[1,4,2,3,5] => 6
[1,4,2,5,3] => 9
[1,4,3,2,5] => 2
[1,4,3,5,2] => 7
[1,4,5,2,3] => 4
[1,4,5,3,2] => 6
[1,5,2,3,4] => 5
[1,5,2,4,3] => 7
[1,5,3,2,4] => 7
[1,5,3,4,2] => 6
[1,5,4,2,3] => 6
[1,5,4,3,2] => 3
[2,1,3,4,5] => 6
[2,1,3,5,4] => 7
[2,1,4,3,5] => 6
[2,1,4,5,3] => 6
[2,1,5,3,4] => 6
[2,1,5,4,3] => 5
[2,3,1,4,5] => 7
[2,3,1,5,4] => 6
[2,3,4,1,5] => 5
[2,3,4,5,1] => 3
[2,3,5,1,4] => 7
[2,3,5,4,1] => 6
[2,4,1,3,5] => 9
[2,4,1,5,3] => 8
[2,4,3,1,5] => 7
[2,4,3,5,1] => 6
[2,4,5,1,3] => 7
[2,4,5,3,1] => 7
[2,5,1,3,4] => 7
[2,5,1,4,3] => 7
[2,5,3,1,4] => 9
[2,5,3,4,1] => 7
[2,5,4,1,3] => 7
[2,5,4,3,1] => 5
[3,1,2,4,5] => 7
[3,1,2,5,4] => 6
[3,1,4,2,5] => 9
[3,1,4,5,2] => 7
[3,1,5,2,4] => 8
[3,1,5,4,2] => 7
[3,2,1,4,5] => 3
[3,2,1,5,4] => 5
[3,2,4,1,5] => 7
[3,2,4,5,1] => 6
[3,2,5,1,4] => 7
[3,2,5,4,1] => 4
[3,4,1,2,5] => 4
[3,4,1,5,2] => 7
[3,4,2,1,5] => 6
[3,4,2,5,1] => 7
[3,4,5,1,2] => 5
[3,4,5,2,1] => 3
[3,5,1,2,4] => 7
[3,5,1,4,2] => 8
>>> Load all 1200 entries. <<<
[3,5,2,1,4] => 7
[3,5,2,4,1] => 9
[3,5,4,1,2] => 6
[3,5,4,2,1] => 7
[4,1,2,3,5] => 5
[4,1,2,5,3] => 7
[4,1,3,2,5] => 7
[4,1,3,5,2] => 9
[4,1,5,2,3] => 7
[4,1,5,3,2] => 7
[4,2,1,3,5] => 7
[4,2,1,5,3] => 7
[4,2,3,1,5] => 6
[4,2,3,5,1] => 7
[4,2,5,1,3] => 8
[4,2,5,3,1] => 9
[4,3,1,2,5] => 6
[4,3,1,5,2] => 7
[4,3,2,1,5] => 3
[4,3,2,5,1] => 5
[4,3,5,1,2] => 6
[4,3,5,2,1] => 7
[4,5,1,2,3] => 5
[4,5,1,3,2] => 6
[4,5,2,1,3] => 6
[4,5,2,3,1] => 6
[4,5,3,1,2] => 7
[4,5,3,2,1] => 6
[5,1,2,3,4] => 3
[5,1,2,4,3] => 6
[5,1,3,2,4] => 6
[5,1,3,4,2] => 7
[5,1,4,2,3] => 7
[5,1,4,3,2] => 5
[5,2,1,3,4] => 6
[5,2,1,4,3] => 4
[5,2,3,1,4] => 7
[5,2,3,4,1] => 2
[5,2,4,1,3] => 9
[5,2,4,3,1] => 6
[5,3,1,2,4] => 7
[5,3,1,4,2] => 9
[5,3,2,1,4] => 5
[5,3,2,4,1] => 6
[5,3,4,1,2] => 6
[5,3,4,2,1] => 5
[5,4,1,2,3] => 3
[5,4,1,3,2] => 7
[5,4,2,1,3] => 7
[5,4,2,3,1] => 5
[5,4,3,1,2] => 6
[5,4,3,2,1] => 0
[1,2,3,4,5,6] => 0
[1,2,3,4,6,5] => 11
[1,2,3,5,4,6] => 9
[1,2,3,5,6,4] => 13
[1,2,3,6,4,5] => 13
[1,2,3,6,5,4] => 6
[1,2,4,3,5,6] => 10
[1,2,4,3,6,5] => 14
[1,2,4,5,3,6] => 12
[1,2,4,5,6,3] => 13
[1,2,4,6,3,5] => 17
[1,2,4,6,5,3] => 14
[1,2,5,3,4,6] => 12
[1,2,5,3,6,4] => 17
[1,2,5,4,3,6] => 5
[1,2,5,4,6,3] => 14
[1,2,5,6,3,4] => 8
[1,2,5,6,4,3] => 12
[1,2,6,3,4,5] => 13
[1,2,6,3,5,4] => 14
[1,2,6,4,3,5] => 14
[1,2,6,4,5,3] => 12
[1,2,6,5,3,4] => 12
[1,2,6,5,4,3] => 9
[1,3,2,4,5,6] => 9
[1,3,2,4,6,5] => 14
[1,3,2,5,4,6] => 11
[1,3,2,5,6,4] => 13
[1,3,2,6,4,5] => 13
[1,3,2,6,5,4] => 10
[1,3,4,2,5,6] => 12
[1,3,4,2,6,5] => 14
[1,3,4,5,2,6] => 10
[1,3,4,5,6,2] => 10
[1,3,4,6,2,5] => 15
[1,3,4,6,5,2] => 13
[1,3,5,2,4,6] => 17
[1,3,5,2,6,4] => 17
[1,3,5,4,2,6] => 13
[1,3,5,4,6,2] => 14
[1,3,5,6,2,4] => 14
[1,3,5,6,4,2] => 15
[1,3,6,2,4,5] => 16
[1,3,6,2,5,4] => 14
[1,3,6,4,2,5] => 18
[1,3,6,4,5,2] => 14
[1,3,6,5,2,4] => 14
[1,3,6,5,4,2] => 12
[1,4,2,3,5,6] => 12
[1,4,2,3,6,5] => 14
[1,4,2,5,3,6] => 17
[1,4,2,5,6,3] => 16
[1,4,2,6,3,5] => 17
[1,4,2,6,5,3] => 14
[1,4,3,2,5,6] => 5
[1,4,3,2,6,5] => 11
[1,4,3,5,2,6] => 13
[1,4,3,5,6,2] => 13
[1,4,3,6,2,5] => 15
[1,4,3,6,5,2] => 9
[1,4,5,2,3,6] => 7
[1,4,5,2,6,3] => 14
[1,4,5,3,2,6] => 10
[1,4,5,3,6,2] => 14
[1,4,5,6,2,3] => 10
[1,4,5,6,3,2] => 7
[1,4,6,2,3,5] => 14
[1,4,6,2,5,3] => 15
[1,4,6,3,2,5] => 15
[1,4,6,3,5,2] => 17
[1,4,6,5,2,3] => 13
[1,4,6,5,3,2] => 14
[1,5,2,3,4,6] => 10
[1,5,2,3,6,4] => 15
[1,5,2,4,3,6] => 13
[1,5,2,4,6,3] => 18
[1,5,2,6,3,4] => 14
[1,5,2,6,4,3] => 14
[1,5,3,2,4,6] => 13
[1,5,3,2,6,4] => 15
[1,5,3,4,2,6] => 12
[1,5,3,4,6,2] => 15
[1,5,3,6,2,4] => 16
[1,5,3,6,4,2] => 17
[1,5,4,2,3,6] => 10
[1,5,4,2,6,3] => 15
[1,5,4,3,2,6] => 6
[1,5,4,3,6,2] => 12
[1,5,4,6,2,3] => 12
[1,5,4,6,3,2] => 13
[1,5,6,2,3,4] => 10
[1,5,6,2,4,3] => 13
[1,5,6,3,2,4] => 12
[1,5,6,3,4,2] => 13
[1,5,6,4,2,3] => 14
[1,5,6,4,3,2] => 12
[1,6,2,3,4,5] => 10
[1,6,2,3,5,4] => 13
[1,6,2,4,3,5] => 14
[1,6,2,4,5,3] => 14
[1,6,2,5,3,4] => 15
[1,6,2,5,4,3] => 12
[1,6,3,2,4,5] => 13
[1,6,3,2,5,4] => 9
[1,6,3,4,2,5] => 15
[1,6,3,4,5,2] => 7
[1,6,3,5,2,4] => 17
[1,6,3,5,4,2] => 13
[1,6,4,2,3,5] => 14
[1,6,4,2,5,3] => 17
[1,6,4,3,2,5] => 12
[1,6,4,3,5,2] => 14
[1,6,4,5,2,3] => 13
[1,6,4,5,3,2] => 12
[1,6,5,2,3,4] => 7
[1,6,5,2,4,3] => 14
[1,6,5,3,2,4] => 13
[1,6,5,3,4,2] => 12
[1,6,5,4,2,3] => 12
[1,6,5,4,3,2] => 4
[2,1,3,4,5,6] => 11
[2,1,3,4,6,5] => 15
[2,1,3,5,4,6] => 14
[2,1,3,5,6,4] => 15
[2,1,3,6,4,5] => 15
[2,1,3,6,5,4] => 12
[2,1,4,3,5,6] => 14
[2,1,4,3,6,5] => 11
[2,1,4,5,3,6] => 14
[2,1,4,5,6,3] => 9
[2,1,4,6,3,5] => 16
[2,1,4,6,5,3] => 14
[2,1,5,3,4,6] => 14
[2,1,5,3,6,4] => 16
[2,1,5,4,3,6] => 11
[2,1,5,4,6,3] => 14
[2,1,5,6,3,4] => 13
[2,1,5,6,4,3] => 14
[2,1,6,3,4,5] => 9
[2,1,6,3,5,4] => 14
[2,1,6,4,3,5] => 14
[2,1,6,4,5,3] => 13
[2,1,6,5,3,4] => 14
[2,1,6,5,4,3] => 8
[2,3,1,4,5,6] => 13
[2,3,1,4,6,5] => 15
[2,3,1,5,4,6] => 13
[2,3,1,5,6,4] => 14
[2,3,1,6,4,5] => 13
[2,3,1,6,5,4] => 12
[2,3,4,1,5,6] => 13
[2,3,4,1,6,5] => 9
[2,3,4,5,1,6] => 10
[2,3,4,5,6,1] => 4
[2,3,4,6,1,5] => 14
[2,3,4,6,5,1] => 12
[2,3,5,1,4,6] => 16
[2,3,5,1,6,4] => 16
[2,3,5,4,1,6] => 13
[2,3,5,4,6,1] => 12
[2,3,5,6,1,4] => 15
[2,3,5,6,4,1] => 14
[2,3,6,1,4,5] => 9
[2,3,6,1,5,4] => 13
[2,3,6,4,1,5] => 16
[2,3,6,4,5,1] => 13
[2,3,6,5,1,4] => 14
[2,3,6,5,4,1] => 7
[2,4,1,3,5,6] => 17
[2,4,1,3,6,5] => 16
[2,4,1,5,3,6] => 17
[2,4,1,5,6,3] => 16
[2,4,1,6,3,5] => 15
[2,4,1,6,5,3] => 15
[2,4,3,1,5,6] => 14
[2,4,3,1,6,5] => 14
[2,4,3,5,1,6] => 14
[2,4,3,5,6,1] => 12
[2,4,3,6,1,5] => 15
[2,4,3,6,5,1] => 13
[2,4,5,1,3,6] => 14
[2,4,5,1,6,3] => 15
[2,4,5,3,1,6] => 14
[2,4,5,3,6,1] => 13
[2,4,5,6,1,3] => 14
[2,4,5,6,3,1] => 12
[2,4,6,1,3,5] => 15
[2,4,6,1,5,3] => 16
[2,4,6,3,1,5] => 17
[2,4,6,3,5,1] => 17
[2,4,6,5,1,3] => 16
[2,4,6,5,3,1] => 15
[2,5,1,3,4,6] => 15
[2,5,1,3,6,4] => 15
[2,5,1,4,3,6] => 15
[2,5,1,4,6,3] => 16
[2,5,1,6,3,4] => 14
[2,5,1,6,4,3] => 15
[2,5,3,1,4,6] => 18
[2,5,3,1,6,4] => 16
[2,5,3,4,1,6] => 15
[2,5,3,4,6,1] => 14
[2,5,3,6,1,4] => 16
[2,5,3,6,4,1] => 17
[2,5,4,1,3,6] => 15
[2,5,4,1,6,3] => 10
[2,5,4,3,1,6] => 12
[2,5,4,3,6,1] => 7
[2,5,4,6,1,3] => 14
[2,5,4,6,3,1] => 14
[2,5,6,1,3,4] => 13
[2,5,6,1,4,3] => 10
[2,5,6,3,1,4] => 14
[2,5,6,3,4,1] => 9
[2,5,6,4,1,3] => 15
[2,5,6,4,3,1] => 13
[2,6,1,3,4,5] => 14
[2,6,1,3,5,4] => 15
[2,6,1,4,3,5] => 15
[2,6,1,4,5,3] => 14
[2,6,1,5,3,4] => 16
[2,6,1,5,4,3] => 14
[2,6,3,1,4,5] => 16
[2,6,3,1,5,4] => 14
[2,6,3,4,1,5] => 17
[2,6,3,4,5,1] => 12
[2,6,3,5,1,4] => 17
[2,6,3,5,4,1] => 14
[2,6,4,1,3,5] => 17
[2,6,4,1,5,3] => 16
[2,6,4,3,1,5] => 17
[2,6,4,3,5,1] => 15
[2,6,4,5,1,3] => 15
[2,6,4,5,3,1] => 14
[2,6,5,1,3,4] => 14
[2,6,5,1,4,3] => 15
[2,6,5,3,1,4] => 16
[2,6,5,3,4,1] => 13
[2,6,5,4,1,3] => 14
[2,6,5,4,3,1] => 10
[3,1,2,4,5,6] => 13
[3,1,2,4,6,5] => 15
[3,1,2,5,4,6] => 13
[3,1,2,5,6,4] => 13
[3,1,2,6,4,5] => 14
[3,1,2,6,5,4] => 12
[3,1,4,2,5,6] => 17
[3,1,4,2,6,5] => 16
[3,1,4,5,2,6] => 15
[3,1,4,5,6,2] => 14
[3,1,4,6,2,5] => 15
[3,1,4,6,5,2] => 15
[3,1,5,2,4,6] => 17
[3,1,5,2,6,4] => 15
[3,1,5,4,2,6] => 15
[3,1,5,4,6,2] => 15
[3,1,5,6,2,4] => 14
[3,1,5,6,4,2] => 16
[3,1,6,2,4,5] => 16
[3,1,6,2,5,4] => 15
[3,1,6,4,2,5] => 16
[3,1,6,4,5,2] => 14
[3,1,6,5,2,4] => 15
[3,1,6,5,4,2] => 14
[3,2,1,4,5,6] => 6
[3,2,1,4,6,5] => 12
[3,2,1,5,4,6] => 10
[3,2,1,5,6,4] => 12
[3,2,1,6,4,5] => 12
[3,2,1,6,5,4] => 8
[3,2,4,1,5,6] => 14
[3,2,4,1,6,5] => 14
[3,2,4,5,1,6] => 13
[3,2,4,5,6,1] => 12
[3,2,4,6,1,5] => 15
[3,2,4,6,5,1] => 14
[3,2,5,1,4,6] => 14
[3,2,5,1,6,4] => 15
[3,2,5,4,1,6] => 9
[3,2,5,4,6,1] => 13
[3,2,5,6,1,4] => 10
[3,2,5,6,4,1] => 13
[3,2,6,1,4,5] => 13
[3,2,6,1,5,4] => 14
[3,2,6,4,1,5] => 14
[3,2,6,4,5,1] => 12
[3,2,6,5,1,4] => 13
[3,2,6,5,4,1] => 10
[3,4,1,2,5,6] => 8
[3,4,1,2,6,5] => 13
[3,4,1,5,2,6] => 14
[3,4,1,5,6,2] => 15
[3,4,1,6,2,5] => 14
[3,4,1,6,5,2] => 10
[3,4,2,1,5,6] => 12
[3,4,2,1,6,5] => 14
[3,4,2,5,1,6] => 15
[3,4,2,5,6,1] => 14
[3,4,2,6,1,5] => 16
[3,4,2,6,5,1] => 13
[3,4,5,1,2,6] => 10
[3,4,5,1,6,2] => 14
[3,4,5,2,1,6] => 7
[3,4,5,2,6,1] => 12
[3,4,5,6,1,2] => 8
[3,4,5,6,2,1] => 9
[3,4,6,1,2,5] => 13
[3,4,6,1,5,2] => 15
[3,4,6,2,1,5] => 14
[3,4,6,2,5,1] => 14
[3,4,6,5,1,2] => 14
[3,4,6,5,2,1] => 12
[3,5,1,2,4,6] => 14
[3,5,1,2,6,4] => 14
[3,5,1,4,2,6] => 16
[3,5,1,4,6,2] => 16
[3,5,1,6,2,4] => 16
[3,5,1,6,4,2] => 16
[3,5,2,1,4,6] => 14
[3,5,2,1,6,4] => 15
[3,5,2,4,1,6] => 17
[3,5,2,4,6,1] => 17
[3,5,2,6,1,4] => 16
[3,5,2,6,4,1] => 15
[3,5,4,1,2,6] => 12
[3,5,4,1,6,2] => 14
[3,5,4,2,1,6] => 13
[3,5,4,2,6,1] => 14
[3,5,4,6,1,2] => 13
[3,5,4,6,2,1] => 12
[3,5,6,1,2,4] => 14
[3,5,6,1,4,2] => 15
[3,5,6,2,1,4] => 13
[3,5,6,2,4,1] => 14
[3,5,6,4,1,2] => 14
[3,5,6,4,2,1] => 14
[3,6,1,2,4,5] => 15
[3,6,1,2,5,4] => 10
[3,6,1,4,2,5] => 16
[3,6,1,4,5,2] => 10
[3,6,1,5,2,4] => 16
[3,6,1,5,4,2] => 15
[3,6,2,1,4,5] => 14
[3,6,2,1,5,4] => 13
[3,6,2,4,1,5] => 17
[3,6,2,4,5,1] => 15
[3,6,2,5,1,4] => 15
[3,6,2,5,4,1] => 14
[3,6,4,1,2,5] => 14
[3,6,4,1,5,2] => 16
[3,6,4,2,1,5] => 16
[3,6,4,2,5,1] => 18
[3,6,4,5,1,2] => 14
[3,6,4,5,2,1] => 14
[3,6,5,1,2,4] => 13
[3,6,5,1,4,2] => 16
[3,6,5,2,1,4] => 9
[3,6,5,2,4,1] => 16
[3,6,5,4,1,2] => 9
[3,6,5,4,2,1] => 13
[4,1,2,3,5,6] => 13
[4,1,2,3,6,5] => 9
[4,1,2,5,3,6] => 16
[4,1,2,5,6,3] => 9
[4,1,2,6,3,5] => 16
[4,1,2,6,5,3] => 13
[4,1,3,2,5,6] => 14
[4,1,3,2,6,5] => 14
[4,1,3,5,2,6] => 18
[4,1,3,5,6,2] => 16
[4,1,3,6,2,5] => 16
[4,1,3,6,5,2] => 14
[4,1,5,2,3,6] => 14
[4,1,5,2,6,3] => 15
[4,1,5,3,2,6] => 15
[4,1,5,3,6,2] => 17
[4,1,5,6,2,3] => 13
[4,1,5,6,3,2] => 14
[4,1,6,2,3,5] => 15
[4,1,6,2,5,3] => 16
[4,1,6,3,2,5] => 10
[4,1,6,3,5,2] => 16
[4,1,6,5,2,3] => 10
[4,1,6,5,3,2] => 15
[4,2,1,3,5,6] => 14
[4,2,1,3,6,5] => 14
[4,2,1,5,3,6] => 14
[4,2,1,5,6,3] => 13
[4,2,1,6,3,5] => 15
[4,2,1,6,5,3] => 14
[4,2,3,1,5,6] => 12
[4,2,3,1,6,5] => 13
[4,2,3,5,1,6] => 14
[4,2,3,5,6,1] => 13
[4,2,3,6,1,5] => 14
[4,2,3,6,5,1] => 12
[4,2,5,1,3,6] => 15
[4,2,5,1,6,3] => 16
[4,2,5,3,1,6] => 17
[4,2,5,3,6,1] => 17
[4,2,5,6,1,3] => 15
[4,2,5,6,3,1] => 14
[4,2,6,1,3,5] => 16
[4,2,6,1,5,3] => 16
[4,2,6,3,1,5] => 16
[4,2,6,3,5,1] => 16
[4,2,6,5,1,3] => 14
[4,2,6,5,3,1] => 14
[4,3,1,2,5,6] => 12
[4,3,1,2,6,5] => 14
[4,3,1,5,2,6] => 14
[4,3,1,5,6,2] => 14
[4,3,1,6,2,5] => 15
[4,3,1,6,5,2] => 13
[4,3,2,1,5,6] => 9
[4,3,2,1,6,5] => 8
[4,3,2,5,1,6] => 12
[4,3,2,5,6,1] => 7
[4,3,2,6,1,5] => 14
[4,3,2,6,5,1] => 10
[4,3,5,1,2,6] => 13
[4,3,5,1,6,2] => 16
[4,3,5,2,1,6] => 14
[4,3,5,2,6,1] => 15
[4,3,5,6,1,2] => 14
[4,3,5,6,2,1] => 12
[4,3,6,1,2,5] => 10
[4,3,6,1,5,2] => 14
[4,3,6,2,1,5] => 15
[4,3,6,2,5,1] => 14
[4,3,6,5,1,2] => 13
[4,3,6,5,2,1] => 8
[4,5,1,2,3,6] => 10
[4,5,1,2,6,3] => 13
[4,5,1,3,2,6] => 12
[4,5,1,3,6,2] => 14
[4,5,1,6,2,3] => 14
[4,5,1,6,3,2] => 13
[4,5,2,1,3,6] => 13
[4,5,2,1,6,3] => 10
[4,5,2,3,1,6] => 13
[4,5,2,3,6,1] => 9
[4,5,2,6,1,3] => 15
[4,5,2,6,3,1] => 14
[4,5,3,1,2,6] => 14
[4,5,3,1,6,2] => 15
[4,5,3,2,1,6] => 12
[4,5,3,2,6,1] => 13
[4,5,3,6,1,2] => 14
[4,5,3,6,2,1] => 14
[4,5,6,1,2,3] => 8
[4,5,6,1,3,2] => 12
[4,5,6,2,1,3] => 12
[4,5,6,2,3,1] => 10
[4,5,6,3,1,2] => 12
[4,5,6,3,2,1] => 6
[4,6,1,2,3,5] => 14
[4,6,1,2,5,3] => 15
[4,6,1,3,2,5] => 14
[4,6,1,3,5,2] => 16
[4,6,1,5,2,3] => 15
[4,6,1,5,3,2] => 16
[4,6,2,1,3,5] => 16
[4,6,2,1,5,3] => 14
[4,6,2,3,1,5] => 15
[4,6,2,3,5,1] => 15
[4,6,2,5,1,3] => 15
[4,6,2,5,3,1] => 17
[4,6,3,1,2,5] => 15
[4,6,3,1,5,2] => 15
[4,6,3,2,1,5] => 14
[4,6,3,2,5,1] => 15
[4,6,3,5,1,2] => 16
[4,6,3,5,2,1] => 17
[4,6,5,1,2,3] => 12
[4,6,5,1,3,2] => 14
[4,6,5,2,1,3] => 13
[4,6,5,2,3,1] => 13
[4,6,5,3,1,2] => 15
[4,6,5,3,2,1] => 13
[5,1,2,3,4,6] => 10
[5,1,2,3,6,4] => 14
[5,1,2,4,3,6] => 13
[5,1,2,4,6,3] => 16
[5,1,2,6,3,4] => 15
[5,1,2,6,4,3] => 14
[5,1,3,2,4,6] => 14
[5,1,3,2,6,4] => 15
[5,1,3,4,2,6] => 15
[5,1,3,4,6,2] => 17
[5,1,3,6,2,4] => 16
[5,1,3,6,4,2] => 17
[5,1,4,2,3,6] => 14
[5,1,4,2,6,3] => 17
[5,1,4,3,2,6] => 12
[5,1,4,3,6,2] => 17
[5,1,4,6,2,3] => 14
[5,1,4,6,3,2] => 16
[5,1,6,2,3,4] => 14
[5,1,6,2,4,3] => 16
[5,1,6,3,2,4] => 14
[5,1,6,3,4,2] => 15
[5,1,6,4,2,3] => 15
[5,1,6,4,3,2] => 14
[5,2,1,3,4,6] => 13
[5,2,1,3,6,4] => 15
[5,2,1,4,3,6] => 9
[5,2,1,4,6,3] => 14
[5,2,1,6,3,4] => 10
[5,2,1,6,4,3] => 13
[5,2,3,1,4,6] => 14
[5,2,3,1,6,4] => 14
[5,2,3,4,1,6] => 7
[5,2,3,4,6,1] => 12
[5,2,3,6,1,4] => 10
[5,2,3,6,4,1] => 15
[5,2,4,1,3,6] => 17
[5,2,4,1,6,3] => 16
[5,2,4,3,1,6] => 14
[5,2,4,3,6,1] => 15
[5,2,4,6,1,3] => 16
[5,2,4,6,3,1] => 18
[5,2,6,1,3,4] => 15
[5,2,6,1,4,3] => 14
[5,2,6,3,1,4] => 16
[5,2,6,3,4,1] => 15
[5,2,6,4,1,3] => 15
[5,2,6,4,3,1] => 15
[5,3,1,2,4,6] => 15
[5,3,1,2,6,4] => 16
[5,3,1,4,2,6] => 17
[5,3,1,4,6,2] => 17
[5,3,1,6,2,4] => 16
[5,3,1,6,4,2] => 15
[5,3,2,1,4,6] => 12
[5,3,2,1,6,4] => 14
[5,3,2,4,1,6] => 13
[5,3,2,4,6,1] => 14
[5,3,2,6,1,4] => 15
[5,3,2,6,4,1] => 14
[5,3,4,1,2,6] => 13
[5,3,4,1,6,2] => 15
[5,3,4,2,1,6] => 12
[5,3,4,2,6,1] => 14
[5,3,4,6,1,2] => 14
[5,3,4,6,2,1] => 14
[5,3,6,1,2,4] => 15
[5,3,6,1,4,2] => 15
[5,3,6,2,1,4] => 16
[5,3,6,2,4,1] => 17
[5,3,6,4,1,2] => 16
[5,3,6,4,2,1] => 17
[5,4,1,2,3,6] => 7
[5,4,1,2,6,3] => 14
[5,4,1,3,2,6] => 13
[5,4,1,3,6,2] => 16
[5,4,1,6,2,3] => 13
[5,4,1,6,3,2] => 9
[5,4,2,1,3,6] => 14
[5,4,2,1,6,3] => 15
[5,4,2,3,1,6] => 12
[5,4,2,3,6,1] => 13
[5,4,2,6,1,3] => 16
[5,4,2,6,3,1] => 16
[5,4,3,1,2,6] => 12
[5,4,3,1,6,2] => 14
[5,4,3,2,1,6] => 4
[5,4,3,2,6,1] => 10
[5,4,3,6,1,2] => 9
[5,4,3,6,2,1] => 13
[5,4,6,1,2,3] => 12
[5,4,6,1,3,2] => 13
[5,4,6,2,1,3] => 14
[5,4,6,2,3,1] => 13
[5,4,6,3,1,2] => 15
[5,4,6,3,2,1] => 13
[5,6,1,2,3,4] => 8
[5,6,1,2,4,3] => 14
[5,6,1,3,2,4] => 13
[5,6,1,3,4,2] => 14
[5,6,1,4,2,3] => 14
[5,6,1,4,3,2] => 9
[5,6,2,1,3,4] => 14
[5,6,2,1,4,3] => 13
[5,6,2,3,1,4] => 14
[5,6,2,3,4,1] => 11
[5,6,2,4,1,3] => 16
[5,6,2,4,3,1] => 14
[5,6,3,1,2,4] => 14
[5,6,3,1,4,2] => 16
[5,6,3,2,1,4] => 9
[5,6,3,2,4,1] => 14
[5,6,3,4,1,2] => 11
[5,6,3,4,2,1] => 14
[5,6,4,1,2,3] => 12
[5,6,4,1,3,2] => 15
[5,6,4,2,1,3] => 15
[5,6,4,2,3,1] => 14
[5,6,4,3,1,2] => 15
[5,6,4,3,2,1] => 11
[6,1,2,3,4,5] => 4
[6,1,2,3,5,4] => 12
[6,1,2,4,3,5] => 12
[6,1,2,4,5,3] => 13
[6,1,2,5,3,4] => 14
[6,1,2,5,4,3] => 7
[6,1,3,2,4,5] => 12
[6,1,3,2,5,4] => 13
[6,1,3,4,2,5] => 14
[6,1,3,4,5,2] => 12
[6,1,3,5,2,4] => 17
[6,1,3,5,4,2] => 14
[6,1,4,2,3,5] => 13
[6,1,4,2,5,3] => 17
[6,1,4,3,2,5] => 7
[6,1,4,3,5,2] => 15
[6,1,4,5,2,3] => 9
[6,1,4,5,3,2] => 13
[6,1,5,2,3,4] => 12
[6,1,5,2,4,3] => 15
[6,1,5,3,2,4] => 14
[6,1,5,3,4,2] => 14
[6,1,5,4,2,3] => 13
[6,1,5,4,3,2] => 10
[6,2,1,3,4,5] => 12
[6,2,1,3,5,4] => 14
[6,2,1,4,3,5] => 13
[6,2,1,4,5,3] => 12
[6,2,1,5,3,4] => 13
[6,2,1,5,4,3] => 10
[6,2,3,1,4,5] => 13
[6,2,3,1,5,4] => 12
[6,2,3,4,1,5] => 12
[6,2,3,4,5,1] => 6
[6,2,3,5,1,4] => 15
[6,2,3,5,4,1] => 10
[6,2,4,1,3,5] => 17
[6,2,4,1,5,3] => 16
[6,2,4,3,1,5] => 15
[6,2,4,3,5,1] => 12
[6,2,4,5,1,3] => 15
[6,2,4,5,3,1] => 13
[6,2,5,1,3,4] => 14
[6,2,5,1,4,3] => 14
[6,2,5,3,1,4] => 18
[6,2,5,3,4,1] => 13
[6,2,5,4,1,3] => 15
[6,2,5,4,3,1] => 10
[6,3,1,2,4,5] => 14
[6,3,1,2,5,4] => 13
[6,3,1,4,2,5] => 17
[6,3,1,4,5,2] => 15
[6,3,1,5,2,4] => 15
[6,3,1,5,4,2] => 14
[6,3,2,1,4,5] => 7
[6,3,2,1,5,4] => 10
[6,3,2,4,1,5] => 14
[6,3,2,4,5,1] => 10
[6,3,2,5,1,4] => 14
[6,3,2,5,4,1] => 7
[6,3,4,1,2,5] => 9
[6,3,4,1,5,2] => 15
[6,3,4,2,1,5] => 13
[6,3,4,2,5,1] => 13
[6,3,4,5,1,2] => 11
[6,3,4,5,2,1] => 5
[6,3,5,1,2,4] => 14
[6,3,5,1,4,2] => 17
[6,3,5,2,1,4] => 16
[6,3,5,2,4,1] => 17
[6,3,5,4,1,2] => 14
[6,3,5,4,2,1] => 12
[6,4,1,2,3,5] => 12
[6,4,1,2,5,3] => 14
[6,4,1,3,2,5] => 14
[6,4,1,3,5,2] => 18
[6,4,1,5,2,3] => 14
[6,4,1,5,3,2] => 16
[6,4,2,1,3,5] => 15
[6,4,2,1,5,3] => 14
[6,4,2,3,1,5] => 14
[6,4,2,3,5,1] => 13
[6,4,2,5,1,3] => 17
[6,4,2,5,3,1] => 17
[6,4,3,1,2,5] => 13
[6,4,3,1,5,2] => 15
[6,4,3,2,1,5] => 10
[6,4,3,2,5,1] => 10
[6,4,3,5,1,2] => 14
[6,4,3,5,2,1] => 12
[6,4,5,1,2,3] => 10
[6,4,5,1,3,2] => 13
[6,4,5,2,1,3] => 13
[6,4,5,2,3,1] => 11
[6,4,5,3,1,2] => 14
[6,4,5,3,2,1] => 9
[6,5,1,2,3,4] => 9
[6,5,1,2,4,3] => 12
[6,5,1,3,2,4] => 12
[6,5,1,3,4,2] => 14
[6,5,1,4,2,3] => 14
[6,5,1,4,3,2] => 13
[6,5,2,1,3,4] => 12
[6,5,2,1,4,3] => 8
[6,5,2,3,1,4] => 14
[6,5,2,3,4,1] => 5
[6,5,2,4,1,3] => 17
[6,5,2,4,3,1] => 12
[6,5,3,1,2,4] => 14
[6,5,3,1,4,2] => 17
[6,5,3,2,1,4] => 13
[6,5,3,2,4,1] => 12
[6,5,3,4,1,2] => 14
[6,5,3,4,2,1] => 10
[6,5,4,1,2,3] => 6
[6,5,4,1,3,2] => 13
[6,5,4,2,1,3] => 13
[6,5,4,2,3,1] => 9
[6,5,4,3,1,2] => 11
[6,5,4,3,2,1] => 0
[1,2,3,4,5,6,7] => 0
[1,2,3,4,5,7,6] => 19
[1,2,3,4,6,5,7] => 16
[1,2,3,4,6,7,5] => 23
[1,2,3,4,7,5,6] => 23
[1,2,3,4,7,6,5] => 11
[1,2,3,5,4,6,7] => 17
[1,2,3,5,4,7,6] => 26
[1,2,3,5,6,4,7] => 21
[1,2,3,5,6,7,4] => 25
[1,2,3,5,7,4,6] => 30
[1,2,3,5,7,6,4] => 25
[1,2,3,6,4,5,7] => 21
[1,2,3,6,4,7,5] => 30
[1,2,3,6,5,4,7] => 9
[1,2,3,6,5,7,4] => 25
[1,2,3,6,7,4,5] => 14
[1,2,3,6,7,5,4] => 21
[1,2,3,7,4,5,6] => 25
[1,2,3,7,4,6,5] => 25
[1,2,3,7,5,4,6] => 25
[1,2,3,7,5,6,4] => 22
[1,2,3,7,6,4,5] => 21
[1,2,3,7,6,5,4] => 18
[1,2,4,3,5,6,7] => 17
[1,2,4,3,5,7,6] => 27
[1,2,4,3,6,5,7] => 23
[1,2,4,3,6,7,5] => 27
[1,2,4,3,7,5,6] => 27
[1,2,4,3,7,6,5] => 21
[1,2,4,5,3,6,7] => 22
[1,2,4,5,3,7,6] => 28
[1,2,4,5,6,3,7] => 22
[1,2,4,5,6,7,3] => 24
[1,2,4,5,7,3,6] => 30
[1,2,4,5,7,6,3] => 26
[1,2,4,6,3,5,7] => 30
[1,2,4,6,3,7,5] => 32
[1,2,4,6,5,3,7] => 24
[1,2,4,6,5,7,3] => 28
[1,2,4,6,7,3,5] => 26
[1,2,4,6,7,5,3] => 28
[1,2,4,7,3,5,6] => 31
[1,2,4,7,3,6,5] => 27
[1,2,4,7,5,3,6] => 33
[1,2,4,7,5,6,3] => 27
[1,2,4,7,6,3,5] => 27
[1,2,4,7,6,5,3] => 25
[1,2,5,3,4,6,7] => 22
[1,2,5,3,4,7,6] => 28
[1,2,5,3,6,4,7] => 30
[1,2,5,3,6,7,4] => 31
[1,2,5,3,7,4,6] => 32
[1,2,5,3,7,6,4] => 27
[1,2,5,4,3,6,7] => 10
[1,2,5,4,3,7,6] => 22
[1,2,5,4,6,3,7] => 24
[1,2,5,4,6,7,3] => 26
[1,2,5,4,7,3,6] => 28
[1,2,5,4,7,6,3] => 18
[1,2,5,6,3,4,7] => 13
[1,2,5,6,3,7,4] => 26
[1,2,5,6,4,3,7] => 19
[1,2,5,6,4,7,3] => 27
[1,2,5,6,7,3,4] => 20
[1,2,5,6,7,4,3] => 15
[1,2,5,7,3,4,6] => 26
[1,2,5,7,3,6,4] => 27
[1,2,5,7,4,3,6] => 28
[1,2,5,7,4,6,3] => 30
[1,2,5,7,6,3,4] => 25
[1,2,5,7,6,4,3] => 26
[1,2,6,3,4,5,7] => 22
[1,2,6,3,4,7,5] => 30
[1,2,6,3,5,4,7] => 24
[1,2,6,3,5,7,4] => 33
[1,2,6,3,7,4,5] => 26
[1,2,6,3,7,5,4] => 27
[1,2,6,4,3,5,7] => 24
[1,2,6,4,3,7,5] => 28
[1,2,6,4,5,3,7] => 22
[1,2,6,4,5,7,3] => 28
[1,2,6,4,7,3,5] => 28
[1,2,6,4,7,5,3] => 30
[1,2,6,5,3,4,7] => 19
[1,2,6,5,3,7,4] => 28
[1,2,6,5,4,3,7] => 15
[1,2,6,5,4,7,3] => 25
[1,2,6,5,7,3,4] => 24
[1,2,6,5,7,4,3] => 25
[1,2,6,7,3,4,5] => 20
[1,2,6,7,3,5,4] => 25
[1,2,6,7,4,3,5] => 24
[1,2,6,7,4,5,3] => 26
[1,2,6,7,5,3,4] => 27
[1,2,6,7,5,4,3] => 24
[1,2,7,3,4,5,6] => 24
[1,2,7,3,4,6,5] => 26
[1,2,7,3,5,4,6] => 28
[1,2,7,3,5,6,4] => 27
[1,2,7,3,6,4,5] => 28
[1,2,7,3,6,5,4] => 25
[1,2,7,4,3,5,6] => 26
[1,2,7,4,3,6,5] => 18
[1,2,7,4,5,3,6] => 28
[1,2,7,4,5,6,3] => 15
[1,2,7,4,6,3,5] => 30
[1,2,7,4,6,5,3] => 25
[1,2,7,5,3,4,6] => 27
[1,2,7,5,3,6,4] => 30
[1,2,7,5,4,3,6] => 25
[1,2,7,5,4,6,3] => 26
[1,2,7,5,6,3,4] => 26
[1,2,7,5,6,4,3] => 24
[1,2,7,6,3,4,5] => 15
[1,2,7,6,3,5,4] => 26
[1,2,7,6,4,3,5] => 25
[1,2,7,6,4,5,3] => 24
[1,2,7,6,5,3,4] => 24
[1,2,7,6,5,4,3] => 12
[1,3,2,4,5,6,7] => 16
[1,3,2,4,5,7,6] => 26
[1,3,2,4,6,5,7] => 25
[1,3,2,4,6,7,5] => 28
[1,3,2,4,7,5,6] => 28
[1,3,2,4,7,6,5] => 21
[1,3,2,5,4,6,7] => 23
[1,3,2,5,4,7,6] => 24
[1,3,2,5,6,4,7] => 25
[1,3,2,5,6,7,4] => 22
[1,3,2,5,7,4,6] => 31
[1,3,2,5,7,6,4] => 27
[1,3,2,6,4,5,7] => 25
[1,3,2,6,4,7,5] => 31
[1,3,2,6,5,4,7] => 18
[1,3,2,6,5,7,4] => 27
[1,3,2,6,7,4,5] => 22
[1,3,2,6,7,5,4] => 25
[1,3,2,7,4,5,6] => 22
[1,3,2,7,4,6,5] => 27
[1,3,2,7,5,4,6] => 27
[1,3,2,7,5,6,4] => 26
[1,3,2,7,6,4,5] => 25
[1,3,2,7,6,5,4] => 19
[1,3,4,2,5,6,7] => 21
[1,3,4,2,5,7,6] => 28
[1,3,4,2,6,5,7] => 25
[1,3,4,2,6,7,5] => 28
[1,3,4,2,7,5,6] => 27
[1,3,4,2,7,6,5] => 23
[1,3,4,5,2,6,7] => 22
[1,3,4,5,2,7,6] => 22
[1,3,4,5,6,2,7] => 20
[1,3,4,5,6,7,2] => 16
[1,3,4,5,7,2,6] => 29
[1,3,4,5,7,6,2] => 25
[1,3,4,6,2,5,7] => 29
[1,3,4,6,2,7,5] => 32
[1,3,4,6,5,2,7] => 23
[1,3,4,6,5,7,2] => 26
[1,3,4,6,7,2,5] => 27
[1,3,4,6,7,5,2] => 27
[1,3,4,7,2,5,6] => 23
[1,3,4,7,2,6,5] => 26
[1,3,4,7,5,2,6] => 31
[1,3,4,7,5,6,2] => 27
[1,3,4,7,6,2,5] => 26
[1,3,4,7,6,5,2] => 19
[1,3,5,2,4,6,7] => 30
[1,3,5,2,4,7,6] => 32
[1,3,5,2,6,4,7] => 31
[1,3,5,2,6,7,4] => 32
[1,3,5,2,7,4,6] => 31
[1,3,5,2,7,6,4] => 30
[1,3,5,4,2,6,7] => 24
[1,3,5,4,2,7,6] => 28
[1,3,5,4,6,2,7] => 26
[1,3,5,4,6,7,2] => 26
[1,3,5,4,7,2,6] => 30
[1,3,5,4,7,6,2] => 26
[1,3,5,6,2,4,7] => 25
[1,3,5,6,2,7,4] => 30
[1,3,5,6,4,2,7] => 26
[1,3,5,6,4,7,2] => 28
[1,3,5,6,7,2,4] => 28
[1,3,5,6,7,4,2] => 25
[1,3,5,7,2,4,6] => 29
[1,3,5,7,2,6,4] => 30
[1,3,5,7,4,2,6] => 32
[1,3,5,7,4,6,2] => 32
[1,3,5,7,6,2,4] => 30
[1,3,5,7,6,4,2] => 29
[1,3,6,2,4,5,7] => 29
[1,3,6,2,4,7,5] => 31
[1,3,6,2,5,4,7] => 26
[1,3,6,2,5,7,4] => 31
[1,3,6,2,7,4,5] => 26
[1,3,6,2,7,5,4] => 29
[1,3,6,4,2,5,7] => 33
[1,3,6,4,2,7,5] => 32
[1,3,6,4,5,2,7] => 26
[1,3,6,4,5,7,2] => 28
[1,3,6,4,7,2,5] => 29
[1,3,6,4,7,5,2] => 32
[1,3,6,5,2,4,7] => 27
[1,3,6,5,2,7,4] => 24
[1,3,6,5,4,2,7] => 23
[1,3,6,5,4,7,2] => 20
[1,3,6,5,7,2,4] => 29
[1,3,6,5,7,4,2] => 29
[1,3,6,7,2,4,5] => 25
[1,3,6,7,2,5,4] => 23
[1,3,6,7,4,2,5] => 27
[1,3,6,7,4,5,2] => 22
[1,3,6,7,5,2,4] => 30
[1,3,6,7,5,4,2] => 27
[1,3,7,2,4,5,6] => 30
[1,3,7,2,4,6,5] => 30
[1,3,7,2,5,4,6] => 30
[1,3,7,2,5,6,4] => 28
[1,3,7,2,6,4,5] => 30
[1,3,7,2,6,5,4] => 28
[1,3,7,4,2,5,6] => 32
[1,3,7,4,2,6,5] => 27
[1,3,7,4,5,2,6] => 32
[1,3,7,4,5,6,2] => 24
[1,3,7,4,6,2,5] => 31
[1,3,7,4,6,5,2] => 28
[1,3,7,5,2,4,6] => 32
[1,3,7,5,2,6,4] => 29
[1,3,7,5,4,2,6] => 32
[1,3,7,5,4,6,2] => 28
[1,3,7,5,6,2,4] => 29
[1,3,7,5,6,4,2] => 28
[1,3,7,6,2,4,5] => 26
[1,3,7,6,2,5,4] => 28
[1,3,7,6,4,2,5] => 30
[1,3,7,6,4,5,2] => 26
[1,3,7,6,5,2,4] => 28
[1,3,7,6,5,4,2] => 22
[1,4,2,3,5,6,7] => 21
[1,4,2,3,5,7,6] => 28
[1,4,2,3,6,5,7] => 25
[1,4,2,3,6,7,5] => 27
[1,4,2,3,7,5,6] => 28
[1,4,2,3,7,6,5] => 23
[1,4,2,5,3,6,7] => 30
[1,4,2,5,3,7,6] => 32
[1,4,2,5,6,3,7] => 29
[1,4,2,5,6,7,3] => 30
[1,4,2,5,7,3,6] => 31
[1,4,2,5,7,6,3] => 30
[1,4,2,6,3,5,7] => 31
[1,4,2,6,3,7,5] => 31
[1,4,2,6,5,3,7] => 26
[1,4,2,6,5,7,3] => 30
[1,4,2,6,7,3,5] => 26
[1,4,2,6,7,5,3] => 30
[1,4,2,7,3,5,6] => 32
[1,4,2,7,3,6,5] => 30
[1,4,2,7,5,3,6] => 31
[1,4,2,7,5,6,3] => 28
[1,4,2,7,6,3,5] => 29
[1,4,2,7,6,5,3] => 28
[1,4,3,2,5,6,7] => 9
[1,4,3,2,5,7,6] => 22
[1,4,3,2,6,5,7] => 18
[1,4,3,2,6,7,5] => 23
[1,4,3,2,7,5,6] => 23
[1,4,3,2,7,6,5] => 15
[1,4,3,5,2,6,7] => 24
[1,4,3,5,2,7,6] => 28
[1,4,3,5,6,2,7] => 23
[1,4,3,5,6,7,2] => 25
[1,4,3,5,7,2,6] => 29
[1,4,3,5,7,6,2] => 27
[1,4,3,6,2,5,7] => 26
[1,4,3,6,2,7,5] => 30
[1,4,3,6,5,2,7] => 16
[1,4,3,6,5,7,2] => 26
[1,4,3,6,7,2,5] => 19
[1,4,3,6,7,5,2] => 25
[1,4,3,7,2,5,6] => 27
[1,4,3,7,2,6,5] => 27
[1,4,3,7,5,2,6] => 27
[1,4,3,7,5,6,2] => 24
[1,4,3,7,6,2,5] => 24
[1,4,3,7,6,5,2] => 21
[1,4,5,2,3,6,7] => 13
[1,4,5,2,3,7,6] => 24
[1,4,5,2,6,3,7] => 25
[1,4,5,2,6,7,3] => 28
[1,4,5,2,7,3,6] => 27
[1,4,5,2,7,6,3] => 19
[1,4,5,3,2,6,7] => 19
[1,4,5,3,2,7,6] => 26
[1,4,5,3,6,2,7] => 26
[1,4,5,3,6,7,2] => 27
[1,4,5,3,7,2,6] => 30
[1,4,5,3,7,6,2] => 24
[1,4,5,6,2,3,7] => 17
[1,4,5,6,2,7,3] => 27
[1,4,5,6,3,2,7] => 12
[1,4,5,6,3,7,2] => 24
[1,4,5,6,7,2,3] => 15
[1,4,5,6,7,3,2] => 17
[1,4,5,7,2,3,6] => 25
[1,4,5,7,2,6,3] => 28
[1,4,5,7,3,2,6] => 26
[1,4,5,7,3,6,2] => 27
[1,4,5,7,6,2,3] => 25
[1,4,5,7,6,3,2] => 23
[1,4,6,2,3,5,7] => 25
[1,4,6,2,3,7,5] => 27
[1,4,6,2,5,3,7] => 28
[1,4,6,2,5,7,3] => 30
[1,4,6,2,7,3,5] => 29
[1,4,6,2,7,5,3] => 29
[1,4,6,3,2,5,7] => 27
[1,4,6,3,2,7,5] => 30
[1,4,6,3,5,2,7] => 30
[1,4,6,3,5,7,2] => 32
[1,4,6,3,7,2,5] => 30
[1,4,6,3,7,5,2] => 29
[1,4,6,5,2,3,7] => 23
[1,4,6,5,2,7,3] => 29
[1,4,6,5,3,2,7] => 23
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
click to show known generating functions       
Description
The number of alternating subsets such that applying the permutation does not yield an alternating subset.
A subset of $[n]=\{1,\dots,n\}$ is alternating if any two successive elements have different parity. This statistic records for each permutation $\pi\in\mathfrak S_n$ the number of alternating subsets $S\subseteq [n]$ such that $\pi(S)$ is not alternating.
Note that the number of alternating subsets of $[n]$ is $F(n+3)-1$, where $F(n)$ is the $n$-th Fibonacci number.
References
[1] Dawar, A. Counting sets whose alternation is preserved by a permutation MathOverflow:375868
Code
def is_alternating(S):
    return all(is_odd(s + t) for s, t in zip(S, S[1:]))

@cached_function
def alternating_subsets(n):
    return [S for S in Subsets(n) if (is_alternating(sorted(S)))]

def statistic(pi):
    pi = Permutation(pi)
    n = len(pi)
    good = 0
    for S in alternating_subsets(n):
        if not is_alternating(sorted(pi(s) for s in S)):
            good += 1
    return good
Created
Nov 07, 2020 at 18:04 by Martin Rubey
Updated
Nov 07, 2020 at 18:04 by Martin Rubey