Identifier
Identifier
Values
[1] => 0
[1,2] => 0
[2,1] => 1
[1,2,3] => 0
[1,3,2] => 1
[2,1,3] => 1
[2,3,1] => 3
[3,1,2] => 3
[3,2,1] => 4
[1,2,3,4] => 0
[1,2,4,3] => 1
[1,3,2,4] => 1
[1,3,4,2] => 3
[1,4,2,3] => 3
[1,4,3,2] => 4
[2,1,3,4] => 1
[2,1,4,3] => 2
[2,3,1,4] => 3
[2,3,4,1] => 6
[2,4,1,3] => 5
[2,4,3,1] => 7
[3,1,2,4] => 3
[3,1,4,2] => 5
[3,2,1,4] => 4
[3,2,4,1] => 7
[3,4,1,2] => 6
[3,4,2,1] => 7
[4,1,2,3] => 6
[4,1,3,2] => 7
[4,2,1,3] => 7
[4,2,3,1] => 9
[4,3,1,2] => 7
[4,3,2,1] => 8
[1,2,3,4,5] => 0
[1,2,3,5,4] => 1
[1,2,4,3,5] => 1
[1,2,4,5,3] => 3
[1,2,5,3,4] => 3
[1,2,5,4,3] => 4
[1,3,2,4,5] => 1
[1,3,2,5,4] => 2
[1,3,4,2,5] => 3
[1,3,4,5,2] => 6
[1,3,5,2,4] => 5
[1,3,5,4,2] => 7
[1,4,2,3,5] => 3
[1,4,2,5,3] => 5
[1,4,3,2,5] => 4
[1,4,3,5,2] => 7
[1,4,5,2,3] => 6
[1,4,5,3,2] => 7
[1,5,2,3,4] => 6
[1,5,2,4,3] => 7
[1,5,3,2,4] => 7
[1,5,3,4,2] => 9
[1,5,4,2,3] => 7
[1,5,4,3,2] => 8
[2,1,3,4,5] => 1
[2,1,3,5,4] => 2
[2,1,4,3,5] => 2
[2,1,4,5,3] => 4
[2,1,5,3,4] => 4
[2,1,5,4,3] => 5
[2,3,1,4,5] => 3
[2,3,1,5,4] => 4
[2,3,4,1,5] => 6
[2,3,4,5,1] => 10
[2,3,5,1,4] => 8
[2,3,5,4,1] => 11
[2,4,1,3,5] => 5
[2,4,1,5,3] => 7
[2,4,3,1,5] => 7
[2,4,3,5,1] => 11
[2,4,5,1,3] => 9
[2,4,5,3,1] => 11
[2,5,1,3,4] => 8
[2,5,1,4,3] => 9
[2,5,3,1,4] => 10
[2,5,3,4,1] => 13
[2,5,4,1,3] => 10
[2,5,4,3,1] => 12
[3,1,2,4,5] => 3
[3,1,2,5,4] => 4
[3,1,4,2,5] => 5
[3,1,4,5,2] => 8
[3,1,5,2,4] => 7
[3,1,5,4,2] => 9
[3,2,1,4,5] => 4
[3,2,1,5,4] => 5
[3,2,4,1,5] => 7
[3,2,4,5,1] => 11
[3,2,5,1,4] => 9
[3,2,5,4,1] => 12
[3,4,1,2,5] => 6
[3,4,1,5,2] => 9
[3,4,2,1,5] => 7
[3,4,2,5,1] => 11
[3,4,5,1,2] => 9
[3,4,5,2,1] => 10
[3,5,1,2,4] => 9
[3,5,1,4,2] => 11
[3,5,2,1,4] => 10
[3,5,2,4,1] => 13
[3,5,4,1,2] => 10
[3,5,4,2,1] => 11
[4,1,2,3,5] => 6
[4,1,2,5,3] => 8
[4,1,3,2,5] => 7
[4,1,3,5,2] => 10
[4,1,5,2,3] => 9
[4,1,5,3,2] => 10
[4,2,1,3,5] => 7
[4,2,1,5,3] => 9
[4,2,3,1,5] => 9
[4,2,3,5,1] => 13
[4,2,5,1,3] => 11
[4,2,5,3,1] => 13
[4,3,1,2,5] => 7
[4,3,1,5,2] => 10
[4,3,2,1,5] => 8
[4,3,2,5,1] => 12
[4,3,5,1,2] => 10
[4,3,5,2,1] => 11
[4,5,1,2,3] => 9
[4,5,1,3,2] => 10
[4,5,2,1,3] => 10
[4,5,2,3,1] => 12
[4,5,3,1,2] => 10
[4,5,3,2,1] => 11
[5,1,2,3,4] => 10
[5,1,2,4,3] => 11
[5,1,3,2,4] => 11
[5,1,3,4,2] => 13
[5,1,4,2,3] => 11
[5,1,4,3,2] => 12
[5,2,1,3,4] => 11
[5,2,1,4,3] => 12
[5,2,3,1,4] => 13
[5,2,3,4,1] => 16
[5,2,4,1,3] => 13
[5,2,4,3,1] => 15
[5,3,1,2,4] => 11
[5,3,1,4,2] => 13
[5,3,2,1,4] => 12
[5,3,2,4,1] => 15
[5,3,4,1,2] => 12
[5,3,4,2,1] => 13
[5,4,1,2,3] => 10
[5,4,1,3,2] => 11
[5,4,2,1,3] => 11
[5,4,2,3,1] => 13
[5,4,3,1,2] => 11
[5,4,3,2,1] => 12
[1,2,3,4,5,6] => 0
[1,2,3,4,6,5] => 1
[1,2,3,5,4,6] => 1
[1,2,3,5,6,4] => 3
[1,2,3,6,4,5] => 3
[1,2,3,6,5,4] => 4
[1,2,4,3,5,6] => 1
[1,2,4,3,6,5] => 2
[1,2,4,5,3,6] => 3
[1,2,4,5,6,3] => 6
[1,2,4,6,3,5] => 5
[1,2,4,6,5,3] => 7
[1,2,5,3,4,6] => 3
[1,2,5,3,6,4] => 5
[1,2,5,4,3,6] => 4
[1,2,5,4,6,3] => 7
[1,2,5,6,3,4] => 6
[1,2,5,6,4,3] => 7
[1,2,6,3,4,5] => 6
[1,2,6,3,5,4] => 7
[1,2,6,4,3,5] => 7
[1,2,6,4,5,3] => 9
[1,2,6,5,3,4] => 7
[1,2,6,5,4,3] => 8
[1,3,2,4,5,6] => 1
[1,3,2,4,6,5] => 2
[1,3,2,5,4,6] => 2
[1,3,2,5,6,4] => 4
[1,3,2,6,4,5] => 4
[1,3,2,6,5,4] => 5
[1,3,4,2,5,6] => 3
[1,3,4,2,6,5] => 4
[1,3,4,5,2,6] => 6
[1,3,4,5,6,2] => 10
[1,3,4,6,2,5] => 8
[1,3,4,6,5,2] => 11
[1,3,5,2,4,6] => 5
[1,3,5,2,6,4] => 7
[1,3,5,4,2,6] => 7
[1,3,5,4,6,2] => 11
[1,3,5,6,2,4] => 9
[1,3,5,6,4,2] => 11
[1,3,6,2,4,5] => 8
[1,3,6,2,5,4] => 9
[1,3,6,4,2,5] => 10
[1,3,6,4,5,2] => 13
[1,3,6,5,2,4] => 10
[1,3,6,5,4,2] => 12
[1,4,2,3,5,6] => 3
[1,4,2,3,6,5] => 4
[1,4,2,5,3,6] => 5
[1,4,2,5,6,3] => 8
[1,4,2,6,3,5] => 7
[1,4,2,6,5,3] => 9
[1,4,3,2,5,6] => 4
[1,4,3,2,6,5] => 5
[1,4,3,5,2,6] => 7
[1,4,3,5,6,2] => 11
[1,4,3,6,2,5] => 9
[1,4,3,6,5,2] => 12
[1,4,5,2,3,6] => 6
[1,4,5,2,6,3] => 9
[1,4,5,3,2,6] => 7
[1,4,5,3,6,2] => 11
[1,4,5,6,2,3] => 9
[1,4,5,6,3,2] => 10
[1,4,6,2,3,5] => 9
[1,4,6,2,5,3] => 11
[1,4,6,3,2,5] => 10
[1,4,6,3,5,2] => 13
[1,4,6,5,2,3] => 10
[1,4,6,5,3,2] => 11
[1,5,2,3,4,6] => 6
[1,5,2,3,6,4] => 8
[1,5,2,4,3,6] => 7
[1,5,2,4,6,3] => 10
[1,5,2,6,3,4] => 9
[1,5,2,6,4,3] => 10
[1,5,3,2,4,6] => 7
[1,5,3,2,6,4] => 9
[1,5,3,4,2,6] => 9
[1,5,3,4,6,2] => 13
[1,5,3,6,2,4] => 11
[1,5,3,6,4,2] => 13
[1,5,4,2,3,6] => 7
[1,5,4,2,6,3] => 10
[1,5,4,3,2,6] => 8
[1,5,4,3,6,2] => 12
[1,5,4,6,2,3] => 10
[1,5,4,6,3,2] => 11
[1,5,6,2,3,4] => 9
[1,5,6,2,4,3] => 10
[1,5,6,3,2,4] => 10
[1,5,6,3,4,2] => 12
[1,5,6,4,2,3] => 10
[1,5,6,4,3,2] => 11
[1,6,2,3,4,5] => 10
[1,6,2,3,5,4] => 11
[1,6,2,4,3,5] => 11
[1,6,2,4,5,3] => 13
[1,6,2,5,3,4] => 11
[1,6,2,5,4,3] => 12
[1,6,3,2,4,5] => 11
[1,6,3,2,5,4] => 12
[1,6,3,4,2,5] => 13
[1,6,3,4,5,2] => 16
[1,6,3,5,2,4] => 13
[1,6,3,5,4,2] => 15
[1,6,4,2,3,5] => 11
[1,6,4,2,5,3] => 13
[1,6,4,3,2,5] => 12
[1,6,4,3,5,2] => 15
[1,6,4,5,2,3] => 12
[1,6,4,5,3,2] => 13
[1,6,5,2,3,4] => 10
[1,6,5,2,4,3] => 11
[1,6,5,3,2,4] => 11
[1,6,5,3,4,2] => 13
[1,6,5,4,2,3] => 11
[1,6,5,4,3,2] => 12
[2,1,3,4,5,6] => 1
[2,1,3,4,6,5] => 2
[2,1,3,5,4,6] => 2
[2,1,3,5,6,4] => 4
[2,1,3,6,4,5] => 4
[2,1,3,6,5,4] => 5
[2,1,4,3,5,6] => 2
[2,1,4,3,6,5] => 3
[2,1,4,5,3,6] => 4
[2,1,4,5,6,3] => 7
[2,1,4,6,3,5] => 6
[2,1,4,6,5,3] => 8
[2,1,5,3,4,6] => 4
[2,1,5,3,6,4] => 6
[2,1,5,4,3,6] => 5
[2,1,5,4,6,3] => 8
[2,1,5,6,3,4] => 7
[2,1,5,6,4,3] => 8
[2,1,6,3,4,5] => 7
[2,1,6,3,5,4] => 8
[2,1,6,4,3,5] => 8
[2,1,6,4,5,3] => 10
[2,1,6,5,3,4] => 8
[2,1,6,5,4,3] => 9
[2,3,1,4,5,6] => 3
[2,3,1,4,6,5] => 4
[2,3,1,5,4,6] => 4
[2,3,1,5,6,4] => 6
[2,3,1,6,4,5] => 6
[2,3,1,6,5,4] => 7
[2,3,4,1,5,6] => 6
[2,3,4,1,6,5] => 7
[2,3,4,5,1,6] => 10
[2,3,4,5,6,1] => 15
[2,3,4,6,1,5] => 12
[2,3,4,6,5,1] => 16
[2,3,5,1,4,6] => 8
[2,3,5,1,6,4] => 10
[2,3,5,4,1,6] => 11
[2,3,5,4,6,1] => 16
[2,3,5,6,1,4] => 13
[2,3,5,6,4,1] => 16
[2,3,6,1,4,5] => 11
[2,3,6,1,5,4] => 12
[2,3,6,4,1,5] => 14
[2,3,6,4,5,1] => 18
[2,3,6,5,1,4] => 14
[2,3,6,5,4,1] => 17
[2,4,1,3,5,6] => 5
[2,4,1,3,6,5] => 6
[2,4,1,5,3,6] => 7
[2,4,1,5,6,3] => 10
[2,4,1,6,3,5] => 9
[2,4,1,6,5,3] => 11
[2,4,3,1,5,6] => 7
[2,4,3,1,6,5] => 8
[2,4,3,5,1,6] => 11
[2,4,3,5,6,1] => 16
[2,4,3,6,1,5] => 13
[2,4,3,6,5,1] => 17
[2,4,5,1,3,6] => 9
[2,4,5,1,6,3] => 12
[2,4,5,3,1,6] => 11
[2,4,5,3,6,1] => 16
[2,4,5,6,1,3] => 13
[2,4,5,6,3,1] => 15
[2,4,6,1,3,5] => 12
[2,4,6,1,5,3] => 14
[2,4,6,3,1,5] => 14
[2,4,6,3,5,1] => 18
[2,4,6,5,1,3] => 14
[2,4,6,5,3,1] => 16
[2,5,1,3,4,6] => 8
[2,5,1,3,6,4] => 10
[2,5,1,4,3,6] => 9
[2,5,1,4,6,3] => 12
[2,5,1,6,3,4] => 11
[2,5,1,6,4,3] => 12
[2,5,3,1,4,6] => 10
[2,5,3,1,6,4] => 12
[2,5,3,4,1,6] => 13
[2,5,3,4,6,1] => 18
[2,5,3,6,1,4] => 15
[2,5,3,6,4,1] => 18
[2,5,4,1,3,6] => 10
[2,5,4,1,6,3] => 13
[2,5,4,3,1,6] => 12
[2,5,4,3,6,1] => 17
[2,5,4,6,1,3] => 14
[2,5,4,6,3,1] => 16
[2,5,6,1,3,4] => 12
[2,5,6,1,4,3] => 13
[2,5,6,3,1,4] => 14
[2,5,6,3,4,1] => 17
[2,5,6,4,1,3] => 14
[2,5,6,4,3,1] => 16
[2,6,1,3,4,5] => 12
[2,6,1,3,5,4] => 13
[2,6,1,4,3,5] => 13
[2,6,1,4,5,3] => 15
[2,6,1,5,3,4] => 13
[2,6,1,5,4,3] => 14
[2,6,3,1,4,5] => 14
[2,6,3,1,5,4] => 15
[2,6,3,4,1,5] => 17
[2,6,3,4,5,1] => 21
[2,6,3,5,1,4] => 17
[2,6,3,5,4,1] => 20
[2,6,4,1,3,5] => 14
[2,6,4,1,5,3] => 16
[2,6,4,3,1,5] => 16
[2,6,4,3,5,1] => 20
[2,6,4,5,1,3] => 16
[2,6,4,5,3,1] => 18
[2,6,5,1,3,4] => 13
[2,6,5,1,4,3] => 14
[2,6,5,3,1,4] => 15
[2,6,5,3,4,1] => 18
[2,6,5,4,1,3] => 15
[2,6,5,4,3,1] => 17
[3,1,2,4,5,6] => 3
[3,1,2,4,6,5] => 4
[3,1,2,5,4,6] => 4
[3,1,2,5,6,4] => 6
[3,1,2,6,4,5] => 6
[3,1,2,6,5,4] => 7
[3,1,4,2,5,6] => 5
[3,1,4,2,6,5] => 6
[3,1,4,5,2,6] => 8
[3,1,4,5,6,2] => 12
[3,1,4,6,2,5] => 10
[3,1,4,6,5,2] => 13
[3,1,5,2,4,6] => 7
[3,1,5,2,6,4] => 9
[3,1,5,4,2,6] => 9
[3,1,5,4,6,2] => 13
[3,1,5,6,2,4] => 11
[3,1,5,6,4,2] => 13
[3,1,6,2,4,5] => 10
[3,1,6,2,5,4] => 11
[3,1,6,4,2,5] => 12
[3,1,6,4,5,2] => 15
[3,1,6,5,2,4] => 12
[3,1,6,5,4,2] => 14
[3,2,1,4,5,6] => 4
[3,2,1,4,6,5] => 5
[3,2,1,5,4,6] => 5
[3,2,1,5,6,4] => 7
[3,2,1,6,4,5] => 7
[3,2,1,6,5,4] => 8
[3,2,4,1,5,6] => 7
[3,2,4,1,6,5] => 8
[3,2,4,5,1,6] => 11
[3,2,4,5,6,1] => 16
[3,2,4,6,1,5] => 13
[3,2,4,6,5,1] => 17
[3,2,5,1,4,6] => 9
[3,2,5,1,6,4] => 11
[3,2,5,4,1,6] => 12
[3,2,5,4,6,1] => 17
[3,2,5,6,1,4] => 14
[3,2,5,6,4,1] => 17
[3,2,6,1,4,5] => 12
[3,2,6,1,5,4] => 13
[3,2,6,4,1,5] => 15
[3,2,6,4,5,1] => 19
[3,2,6,5,1,4] => 15
[3,2,6,5,4,1] => 18
[3,4,1,2,5,6] => 6
[3,4,1,2,6,5] => 7
[3,4,1,5,2,6] => 9
[3,4,1,5,6,2] => 13
[3,4,1,6,2,5] => 11
[3,4,1,6,5,2] => 14
[3,4,2,1,5,6] => 7
[3,4,2,1,6,5] => 8
[3,4,2,5,1,6] => 11
[3,4,2,5,6,1] => 16
[3,4,2,6,1,5] => 13
[3,4,2,6,5,1] => 17
[3,4,5,1,2,6] => 9
[3,4,5,1,6,2] => 13
[3,4,5,2,1,6] => 10
[3,4,5,2,6,1] => 15
[3,4,5,6,1,2] => 12
[3,4,5,6,2,1] => 13
[3,4,6,1,2,5] => 12
[3,4,6,1,5,2] => 15
[3,4,6,2,1,5] => 13
[3,4,6,2,5,1] => 17
[3,4,6,5,1,2] => 13
[3,4,6,5,2,1] => 14
[3,5,1,2,4,6] => 9
[3,5,1,2,6,4] => 11
[3,5,1,4,2,6] => 11
[3,5,1,4,6,2] => 15
[3,5,1,6,2,4] => 13
[3,5,1,6,4,2] => 15
[3,5,2,1,4,6] => 10
[3,5,2,1,6,4] => 12
[3,5,2,4,1,6] => 13
[3,5,2,4,6,1] => 18
[3,5,2,6,1,4] => 15
[3,5,2,6,4,1] => 18
[3,5,4,1,2,6] => 10
[3,5,4,1,6,2] => 14
[3,5,4,2,1,6] => 11
[3,5,4,2,6,1] => 16
[3,5,4,6,1,2] => 13
[3,5,4,6,2,1] => 14
[3,5,6,1,2,4] => 12
[3,5,6,1,4,2] => 14
[3,5,6,2,1,4] => 13
[3,5,6,2,4,1] => 16
[3,5,6,4,1,2] => 13
[3,5,6,4,2,1] => 14
[3,6,1,2,4,5] => 13
[3,6,1,2,5,4] => 14
[3,6,1,4,2,5] => 15
[3,6,1,4,5,2] => 18
[3,6,1,5,2,4] => 15
[3,6,1,5,4,2] => 17
[3,6,2,1,4,5] => 14
[3,6,2,1,5,4] => 15
[3,6,2,4,1,5] => 17
[3,6,2,4,5,1] => 21
[3,6,2,5,1,4] => 17
[3,6,2,5,4,1] => 20
[3,6,4,1,2,5] => 14
[3,6,4,1,5,2] => 17
[3,6,4,2,1,5] => 15
[3,6,4,2,5,1] => 19
[3,6,4,5,1,2] => 15
[3,6,4,5,2,1] => 16
[3,6,5,1,2,4] => 13
[3,6,5,1,4,2] => 15
[3,6,5,2,1,4] => 14
[3,6,5,2,4,1] => 17
[3,6,5,4,1,2] => 14
[3,6,5,4,2,1] => 15
[4,1,2,3,5,6] => 6
[4,1,2,3,6,5] => 7
[4,1,2,5,3,6] => 8
[4,1,2,5,6,3] => 11
[4,1,2,6,3,5] => 10
[4,1,2,6,5,3] => 12
[4,1,3,2,5,6] => 7
[4,1,3,2,6,5] => 8
[4,1,3,5,2,6] => 10
[4,1,3,5,6,2] => 14
[4,1,3,6,2,5] => 12
[4,1,3,6,5,2] => 15
[4,1,5,2,3,6] => 9
[4,1,5,2,6,3] => 12
[4,1,5,3,2,6] => 10
[4,1,5,3,6,2] => 14
[4,1,5,6,2,3] => 12
[4,1,5,6,3,2] => 13
[4,1,6,2,3,5] => 12
[4,1,6,2,5,3] => 14
[4,1,6,3,2,5] => 13
[4,1,6,3,5,2] => 16
[4,1,6,5,2,3] => 13
[4,1,6,5,3,2] => 14
[4,2,1,3,5,6] => 7
[4,2,1,3,6,5] => 8
[4,2,1,5,3,6] => 9
[4,2,1,5,6,3] => 12
[4,2,1,6,3,5] => 11
[4,2,1,6,5,3] => 13
[4,2,3,1,5,6] => 9
[4,2,3,1,6,5] => 10
[4,2,3,5,1,6] => 13
[4,2,3,5,6,1] => 18
[4,2,3,6,1,5] => 15
[4,2,3,6,5,1] => 19
[4,2,5,1,3,6] => 11
[4,2,5,1,6,3] => 14
[4,2,5,3,1,6] => 13
[4,2,5,3,6,1] => 18
[4,2,5,6,1,3] => 15
[4,2,5,6,3,1] => 17
[4,2,6,1,3,5] => 14
[4,2,6,1,5,3] => 16
[4,2,6,3,1,5] => 16
[4,2,6,3,5,1] => 20
[4,2,6,5,1,3] => 16
[4,2,6,5,3,1] => 18
[4,3,1,2,5,6] => 7
[4,3,1,2,6,5] => 8
[4,3,1,5,2,6] => 10
[4,3,1,5,6,2] => 14
[4,3,1,6,2,5] => 12
[4,3,1,6,5,2] => 15
[4,3,2,1,5,6] => 8
[4,3,2,1,6,5] => 9
[4,3,2,5,1,6] => 12
[4,3,2,5,6,1] => 17
[4,3,2,6,1,5] => 14
[4,3,2,6,5,1] => 18
[4,3,5,1,2,6] => 10
[4,3,5,1,6,2] => 14
[4,3,5,2,1,6] => 11
[4,3,5,2,6,1] => 16
[4,3,5,6,1,2] => 13
[4,3,5,6,2,1] => 14
[4,3,6,1,2,5] => 13
[4,3,6,1,5,2] => 16
[4,3,6,2,1,5] => 14
[4,3,6,2,5,1] => 18
[4,3,6,5,1,2] => 14
[4,3,6,5,2,1] => 15
[4,5,1,2,3,6] => 9
[4,5,1,2,6,3] => 12
[4,5,1,3,2,6] => 10
[4,5,1,3,6,2] => 14
[4,5,1,6,2,3] => 12
[4,5,1,6,3,2] => 13
[4,5,2,1,3,6] => 10
[4,5,2,1,6,3] => 13
[4,5,2,3,1,6] => 12
[4,5,2,3,6,1] => 17
[4,5,2,6,1,3] => 14
[4,5,2,6,3,1] => 16
[4,5,3,1,2,6] => 10
[4,5,3,1,6,2] => 14
[4,5,3,2,1,6] => 11
[4,5,3,2,6,1] => 16
[4,5,3,6,1,2] => 13
[4,5,3,6,2,1] => 14
[4,5,6,1,2,3] => 12
[4,5,6,1,3,2] => 13
[4,5,6,2,1,3] => 13
[4,5,6,2,3,1] => 15
[4,5,6,3,1,2] => 13
[4,5,6,3,2,1] => 14
[4,6,1,2,3,5] => 13
[4,6,1,2,5,3] => 15
[4,6,1,3,2,5] => 14
[4,6,1,3,5,2] => 17
[4,6,1,5,2,3] => 14
[4,6,1,5,3,2] => 15
[4,6,2,1,3,5] => 14
[4,6,2,1,5,3] => 16
[4,6,2,3,1,5] => 16
[4,6,2,3,5,1] => 20
[4,6,2,5,1,3] => 16
[4,6,2,5,3,1] => 18
[4,6,3,1,2,5] => 14
[4,6,3,1,5,2] => 17
[4,6,3,2,1,5] => 15
[4,6,3,2,5,1] => 19
[4,6,3,5,1,2] => 15
[4,6,3,5,2,1] => 16
[4,6,5,1,2,3] => 13
[4,6,5,1,3,2] => 14
[4,6,5,2,1,3] => 14
[4,6,5,2,3,1] => 16
[4,6,5,3,1,2] => 14
[4,6,5,3,2,1] => 15
[5,1,2,3,4,6] => 10
[5,1,2,3,6,4] => 12
[5,1,2,4,3,6] => 11
[5,1,2,4,6,3] => 14
[5,1,2,6,3,4] => 13
[5,1,2,6,4,3] => 14
[5,1,3,2,4,6] => 11
[5,1,3,2,6,4] => 13
[5,1,3,4,2,6] => 13
[5,1,3,4,6,2] => 17
[5,1,3,6,2,4] => 15
[5,1,3,6,4,2] => 17
[5,1,4,2,3,6] => 11
[5,1,4,2,6,3] => 14
[5,1,4,3,2,6] => 12
[5,1,4,3,6,2] => 16
[5,1,4,6,2,3] => 14
[5,1,4,6,3,2] => 15
[5,1,6,2,3,4] => 13
[5,1,6,2,4,3] => 14
[5,1,6,3,2,4] => 14
[5,1,6,3,4,2] => 16
[5,1,6,4,2,3] => 14
[5,1,6,4,3,2] => 15
[5,2,1,3,4,6] => 11
[5,2,1,3,6,4] => 13
[5,2,1,4,3,6] => 12
[5,2,1,4,6,3] => 15
[5,2,1,6,3,4] => 14
[5,2,1,6,4,3] => 15
[5,2,3,1,4,6] => 13
[5,2,3,1,6,4] => 15
[5,2,3,4,1,6] => 16
[5,2,3,4,6,1] => 21
[5,2,3,6,1,4] => 18
[5,2,3,6,4,1] => 21
[5,2,4,1,3,6] => 13
[5,2,4,1,6,3] => 16
[5,2,4,3,1,6] => 15
[5,2,4,3,6,1] => 20
[5,2,4,6,1,3] => 17
[5,2,4,6,3,1] => 19
[5,2,6,1,3,4] => 15
[5,2,6,1,4,3] => 16
[5,2,6,3,1,4] => 17
[5,2,6,3,4,1] => 20
[5,2,6,4,1,3] => 17
[5,2,6,4,3,1] => 19
[5,3,1,2,4,6] => 11
[5,3,1,2,6,4] => 13
[5,3,1,4,2,6] => 13
[5,3,1,4,6,2] => 17
[5,3,1,6,2,4] => 15
[5,3,1,6,4,2] => 17
[5,3,2,1,4,6] => 12
[5,3,2,1,6,4] => 14
[5,3,2,4,1,6] => 15
[5,3,2,4,6,1] => 20
[5,3,2,6,1,4] => 17
[5,3,2,6,4,1] => 20
[5,3,4,1,2,6] => 12
[5,3,4,1,6,2] => 16
[5,3,4,2,1,6] => 13
[5,3,4,2,6,1] => 18
[5,3,4,6,1,2] => 15
[5,3,4,6,2,1] => 16
[5,3,6,1,2,4] => 14
[5,3,6,1,4,2] => 16
[5,3,6,2,1,4] => 15
[5,3,6,2,4,1] => 18
[5,3,6,4,1,2] => 15
[5,3,6,4,2,1] => 16
[5,4,1,2,3,6] => 10
[5,4,1,2,6,3] => 13
[5,4,1,3,2,6] => 11
[5,4,1,3,6,2] => 15
[5,4,1,6,2,3] => 13
[5,4,1,6,3,2] => 14
[5,4,2,1,3,6] => 11
[5,4,2,1,6,3] => 14
[5,4,2,3,1,6] => 13
[5,4,2,3,6,1] => 18
[5,4,2,6,1,3] => 15
[5,4,2,6,3,1] => 17
[5,4,3,1,2,6] => 11
[5,4,3,1,6,2] => 15
[5,4,3,2,1,6] => 12
[5,4,3,2,6,1] => 17
[5,4,3,6,1,2] => 14
[5,4,3,6,2,1] => 15
[5,4,6,1,2,3] => 13
[5,4,6,1,3,2] => 14
[5,4,6,2,1,3] => 14
[5,4,6,2,3,1] => 16
[5,4,6,3,1,2] => 14
[5,4,6,3,2,1] => 15
[5,6,1,2,3,4] => 12
[5,6,1,2,4,3] => 13
[5,6,1,3,2,4] => 13
[5,6,1,3,4,2] => 15
[5,6,1,4,2,3] => 13
[5,6,1,4,3,2] => 14
[5,6,2,1,3,4] => 13
[5,6,2,1,4,3] => 14
[5,6,2,3,1,4] => 15
[5,6,2,3,4,1] => 18
[5,6,2,4,1,3] => 15
[5,6,2,4,3,1] => 17
[5,6,3,1,2,4] => 13
[5,6,3,1,4,2] => 15
[5,6,3,2,1,4] => 14
[5,6,3,2,4,1] => 17
[5,6,3,4,1,2] => 14
[5,6,3,4,2,1] => 15
[5,6,4,1,2,3] => 13
[5,6,4,1,3,2] => 14
[5,6,4,2,1,3] => 14
[5,6,4,2,3,1] => 16
[5,6,4,3,1,2] => 14
[5,6,4,3,2,1] => 15
[6,1,2,3,4,5] => 15
[6,1,2,3,5,4] => 16
[6,1,2,4,3,5] => 16
[6,1,2,4,5,3] => 18
[6,1,2,5,3,4] => 16
[6,1,2,5,4,3] => 17
[6,1,3,2,4,5] => 16
[6,1,3,2,5,4] => 17
[6,1,3,4,2,5] => 18
[6,1,3,4,5,2] => 21
[6,1,3,5,2,4] => 18
[6,1,3,5,4,2] => 20
[6,1,4,2,3,5] => 16
[6,1,4,2,5,3] => 18
[6,1,4,3,2,5] => 17
[6,1,4,3,5,2] => 20
[6,1,4,5,2,3] => 17
[6,1,4,5,3,2] => 18
[6,1,5,2,3,4] => 15
[6,1,5,2,4,3] => 16
[6,1,5,3,2,4] => 16
[6,1,5,3,4,2] => 18
[6,1,5,4,2,3] => 16
[6,1,5,4,3,2] => 17
[6,2,1,3,4,5] => 16
[6,2,1,3,5,4] => 17
[6,2,1,4,3,5] => 17
[6,2,1,4,5,3] => 19
[6,2,1,5,3,4] => 17
[6,2,1,5,4,3] => 18
[6,2,3,1,4,5] => 18
[6,2,3,1,5,4] => 19
[6,2,3,4,1,5] => 21
[6,2,3,4,5,1] => 25
[6,2,3,5,1,4] => 21
[6,2,3,5,4,1] => 24
[6,2,4,1,3,5] => 18
[6,2,4,1,5,3] => 20
[6,2,4,3,1,5] => 20
[6,2,4,3,5,1] => 24
[6,2,4,5,1,3] => 20
[6,2,4,5,3,1] => 22
[6,2,5,1,3,4] => 17
[6,2,5,1,4,3] => 18
[6,2,5,3,1,4] => 19
[6,2,5,3,4,1] => 22
[6,2,5,4,1,3] => 19
[6,2,5,4,3,1] => 21
[6,3,1,2,4,5] => 16
[6,3,1,2,5,4] => 17
[6,3,1,4,2,5] => 18
[6,3,1,4,5,2] => 21
[6,3,1,5,2,4] => 18
[6,3,1,5,4,2] => 20
[6,3,2,1,4,5] => 17
[6,3,2,1,5,4] => 18
[6,3,2,4,1,5] => 20
[6,3,2,4,5,1] => 24
[6,3,2,5,1,4] => 20
[6,3,2,5,4,1] => 23
[6,3,4,1,2,5] => 17
[6,3,4,1,5,2] => 20
[6,3,4,2,1,5] => 18
[6,3,4,2,5,1] => 22
[6,3,4,5,1,2] => 18
[6,3,4,5,2,1] => 19
[6,3,5,1,2,4] => 16
[6,3,5,1,4,2] => 18
[6,3,5,2,1,4] => 17
[6,3,5,2,4,1] => 20
[6,3,5,4,1,2] => 17
[6,3,5,4,2,1] => 18
[6,4,1,2,3,5] => 15
[6,4,1,2,5,3] => 17
[6,4,1,3,2,5] => 16
[6,4,1,3,5,2] => 19
[6,4,1,5,2,3] => 16
[6,4,1,5,3,2] => 17
[6,4,2,1,3,5] => 16
[6,4,2,1,5,3] => 18
[6,4,2,3,1,5] => 18
[6,4,2,3,5,1] => 22
[6,4,2,5,1,3] => 18
[6,4,2,5,3,1] => 20
[6,4,3,1,2,5] => 16
[6,4,3,1,5,2] => 19
[6,4,3,2,1,5] => 17
[6,4,3,2,5,1] => 21
[6,4,3,5,1,2] => 17
[6,4,3,5,2,1] => 18
[6,4,5,1,2,3] => 15
[6,4,5,1,3,2] => 16
[6,4,5,2,1,3] => 16
[6,4,5,2,3,1] => 18
[6,4,5,3,1,2] => 16
[6,4,5,3,2,1] => 17
[6,5,1,2,3,4] => 13
[6,5,1,2,4,3] => 14
[6,5,1,3,2,4] => 14
[6,5,1,3,4,2] => 16
[6,5,1,4,2,3] => 14
[6,5,1,4,3,2] => 15
[6,5,2,1,3,4] => 14
[6,5,2,1,4,3] => 15
[6,5,2,3,1,4] => 16
[6,5,2,3,4,1] => 19
[6,5,2,4,1,3] => 16
[6,5,2,4,3,1] => 18
[6,5,3,1,2,4] => 14
[6,5,3,1,4,2] => 16
[6,5,3,2,1,4] => 15
[6,5,3,2,4,1] => 18
[6,5,3,4,1,2] => 15
[6,5,3,4,2,1] => 16
[6,5,4,1,2,3] => 14
[6,5,4,1,3,2] => 15
[6,5,4,2,1,3] => 15
[6,5,4,2,3,1] => 17
[6,5,4,3,1,2] => 15
[6,5,4,3,2,1] => 16
[1,2,3,4,5,6,7] => 0
[1,2,3,4,5,7,6] => 1
[1,2,3,4,6,5,7] => 1
[1,2,3,4,6,7,5] => 3
[1,2,3,4,7,5,6] => 3
[1,2,3,4,7,6,5] => 4
[1,2,3,5,4,6,7] => 1
[1,2,3,5,4,7,6] => 2
[1,2,3,5,6,4,7] => 3
[1,2,3,5,6,7,4] => 6
[1,2,3,5,7,4,6] => 5
[1,2,3,5,7,6,4] => 7
[1,2,3,6,4,5,7] => 3
[1,2,3,6,4,7,5] => 5
[1,2,3,6,5,4,7] => 4
[1,2,3,6,5,7,4] => 7
[1,2,3,6,7,4,5] => 6
[1,2,3,6,7,5,4] => 7
[1,2,3,7,4,5,6] => 6
[1,2,3,7,4,6,5] => 7
[1,2,3,7,5,4,6] => 7
[1,2,3,7,5,6,4] => 9
[1,2,3,7,6,4,5] => 7
[1,2,3,7,6,5,4] => 8
[1,2,4,3,5,6,7] => 1
[1,2,4,3,5,7,6] => 2
[1,2,4,3,6,5,7] => 2
[1,2,4,3,6,7,5] => 4
[1,2,4,3,7,5,6] => 4
[1,2,4,3,7,6,5] => 5
[1,2,4,5,3,6,7] => 3
[1,2,4,5,3,7,6] => 4
[1,2,4,5,6,3,7] => 6
[1,2,4,5,6,7,3] => 10
[1,2,4,5,7,3,6] => 8
[1,2,4,5,7,6,3] => 11
[1,2,4,6,3,5,7] => 5
[1,2,4,6,3,7,5] => 7
[1,2,4,6,5,3,7] => 7
[1,2,4,6,5,7,3] => 11
[1,2,4,6,7,3,5] => 9
[1,2,4,6,7,5,3] => 11
[1,2,4,7,3,5,6] => 8
[1,2,4,7,3,6,5] => 9
[1,2,4,7,5,3,6] => 10
[1,2,4,7,5,6,3] => 13
[1,2,4,7,6,3,5] => 10
[1,2,4,7,6,5,3] => 12
[1,2,5,3,4,6,7] => 3
[1,2,5,3,4,7,6] => 4
[1,2,5,3,6,4,7] => 5
[1,2,5,3,6,7,4] => 8
[1,2,5,3,7,4,6] => 7
[1,2,5,3,7,6,4] => 9
[1,2,5,4,3,6,7] => 4
[1,2,5,4,3,7,6] => 5
[1,2,5,4,6,3,7] => 7
[1,2,5,4,6,7,3] => 11
[1,2,5,4,7,3,6] => 9
[1,2,5,4,7,6,3] => 12
[1,2,5,6,3,4,7] => 6
[1,2,5,6,3,7,4] => 9
[1,2,5,6,4,3,7] => 7
[1,2,5,6,4,7,3] => 11
[1,2,5,6,7,3,4] => 9
[1,2,5,6,7,4,3] => 10
[1,2,5,7,3,4,6] => 9
[1,2,5,7,3,6,4] => 11
[1,2,5,7,4,3,6] => 10
[1,2,5,7,4,6,3] => 13
[1,2,5,7,6,3,4] => 10
[1,2,5,7,6,4,3] => 11
[1,2,6,3,4,5,7] => 6
[1,2,6,3,4,7,5] => 8
[1,2,6,3,5,4,7] => 7
[1,2,6,3,5,7,4] => 10
[1,2,6,3,7,4,5] => 9
[1,2,6,3,7,5,4] => 10
[1,2,6,4,3,5,7] => 7
[1,2,6,4,3,7,5] => 9
[1,2,6,4,5,3,7] => 9
[1,2,6,4,5,7,3] => 13
[1,2,6,4,7,3,5] => 11
[1,2,6,4,7,5,3] => 13
[1,2,6,5,3,4,7] => 7
[1,2,6,5,3,7,4] => 10
[1,2,6,5,4,3,7] => 8
[1,2,6,5,4,7,3] => 12
[1,2,6,5,7,3,4] => 10
[1,2,6,5,7,4,3] => 11
[1,2,6,7,3,4,5] => 9
[1,2,6,7,3,5,4] => 10
[1,2,6,7,4,3,5] => 10
[1,2,6,7,4,5,3] => 12
[1,2,6,7,5,3,4] => 10
[1,2,6,7,5,4,3] => 11
[1,2,7,3,4,5,6] => 10
[1,2,7,3,4,6,5] => 11
[1,2,7,3,5,4,6] => 11
[1,2,7,3,5,6,4] => 13
[1,2,7,3,6,4,5] => 11
[1,2,7,3,6,5,4] => 12
[1,2,7,4,3,5,6] => 11
[1,2,7,4,3,6,5] => 12
[1,2,7,4,5,3,6] => 13
[1,2,7,4,5,6,3] => 16
[1,2,7,4,6,3,5] => 13
[1,2,7,4,6,5,3] => 15
[1,2,7,5,3,4,6] => 11
[1,2,7,5,3,6,4] => 13
[1,2,7,5,4,3,6] => 12
[1,2,7,5,4,6,3] => 15
[1,2,7,5,6,3,4] => 12
[1,2,7,5,6,4,3] => 13
[1,2,7,6,3,4,5] => 10
[1,2,7,6,3,5,4] => 11
[1,2,7,6,4,3,5] => 11
[1,2,7,6,4,5,3] => 13
[1,2,7,6,5,3,4] => 11
[1,2,7,6,5,4,3] => 12
[1,3,2,4,5,6,7] => 1
[1,3,2,4,5,7,6] => 2
[1,3,2,4,6,5,7] => 2
[1,3,2,4,6,7,5] => 4
[1,3,2,4,7,5,6] => 4
[1,3,2,4,7,6,5] => 5
[1,3,2,5,4,6,7] => 2
[1,3,2,5,4,7,6] => 3
[1,3,2,5,6,4,7] => 4
[1,3,2,5,6,7,4] => 7
[1,3,2,5,7,4,6] => 6
[1,3,2,5,7,6,4] => 8
[1,3,2,6,4,5,7] => 4
[1,3,2,6,4,7,5] => 6
[1,3,2,6,5,4,7] => 5
[1,3,2,6,5,7,4] => 8
[1,3,2,6,7,4,5] => 7
[1,3,2,6,7,5,4] => 8
[1,3,2,7,4,5,6] => 7
[1,3,2,7,4,6,5] => 8
[1,3,2,7,5,4,6] => 8
[1,3,2,7,5,6,4] => 10
[1,3,2,7,6,4,5] => 8
[1,3,2,7,6,5,4] => 9
[1,3,4,2,5,6,7] => 3
[1,3,4,2,5,7,6] => 4
[1,3,4,2,6,5,7] => 4
[1,3,4,2,6,7,5] => 6
[1,3,4,2,7,5,6] => 6
[1,3,4,2,7,6,5] => 7
[1,3,4,5,2,6,7] => 6
[1,3,4,5,2,7,6] => 7
[1,3,4,5,6,2,7] => 10
[1,3,4,5,6,7,2] => 15
[1,3,4,5,7,2,6] => 12
[1,3,4,5,7,6,2] => 16
[1,3,4,6,2,5,7] => 8
[1,3,4,6,2,7,5] => 10
[1,3,4,6,5,2,7] => 11
[1,3,4,6,5,7,2] => 16
[1,3,4,6,7,2,5] => 13
[1,3,4,6,7,5,2] => 16
[1,3,4,7,2,5,6] => 11
[1,3,4,7,2,6,5] => 12
[1,3,4,7,5,2,6] => 14
[1,3,4,7,5,6,2] => 18
[1,3,4,7,6,2,5] => 14
[1,3,4,7,6,5,2] => 17
[1,3,5,2,4,6,7] => 5
[1,3,5,2,4,7,6] => 6
[1,3,5,2,6,4,7] => 7
[1,3,5,2,6,7,4] => 10
[1,3,5,2,7,4,6] => 9
[1,3,5,2,7,6,4] => 11
[1,3,5,4,2,6,7] => 7
[1,3,5,4,2,7,6] => 8
[1,3,5,4,6,2,7] => 11
[1,3,5,4,6,7,2] => 16
[1,3,5,4,7,2,6] => 13
[1,3,5,4,7,6,2] => 17
[1,3,5,6,2,4,7] => 9
[1,3,5,6,2,7,4] => 12
[1,3,5,6,4,2,7] => 11
[1,3,5,6,4,7,2] => 16
[1,3,5,6,7,2,4] => 13
[1,3,5,6,7,4,2] => 15
[1,3,5,7,2,4,6] => 12
[1,3,5,7,2,6,4] => 14
[1,3,5,7,4,2,6] => 14
[1,3,5,7,4,6,2] => 18
[1,3,5,7,6,2,4] => 14
[1,3,5,7,6,4,2] => 16
[1,3,6,2,4,5,7] => 8
[1,3,6,2,4,7,5] => 10
[1,3,6,2,5,4,7] => 9
[1,3,6,2,5,7,4] => 12
[1,3,6,2,7,4,5] => 11
[1,3,6,2,7,5,4] => 12
[1,3,6,4,2,5,7] => 10
[1,3,6,4,2,7,5] => 12
[1,3,6,4,5,2,7] => 13
[1,3,6,4,5,7,2] => 18
[1,3,6,4,7,2,5] => 15
[1,3,6,4,7,5,2] => 18
[1,3,6,5,2,4,7] => 10
[1,3,6,5,2,7,4] => 13
[1,3,6,5,4,2,7] => 12
[1,3,6,5,4,7,2] => 17
[1,3,6,5,7,2,4] => 14
[1,3,6,5,7,4,2] => 16
[1,3,6,7,2,4,5] => 12
[1,3,6,7,2,5,4] => 13
[1,3,6,7,4,2,5] => 14
[1,3,6,7,4,5,2] => 17
[1,3,6,7,5,2,4] => 14
[1,3,6,7,5,4,2] => 16
[1,3,7,2,4,5,6] => 12
[1,3,7,2,4,6,5] => 13
[1,3,7,2,5,4,6] => 13
[1,3,7,2,5,6,4] => 15
[1,3,7,2,6,4,5] => 13
[1,3,7,2,6,5,4] => 14
[1,3,7,4,2,5,6] => 14
[1,3,7,4,2,6,5] => 15
[1,3,7,4,5,2,6] => 17
[1,3,7,4,5,6,2] => 21
[1,3,7,4,6,2,5] => 17
[1,3,7,4,6,5,2] => 20
[1,3,7,5,2,4,6] => 14
[1,3,7,5,2,6,4] => 16
[1,3,7,5,4,2,6] => 16
[1,3,7,5,4,6,2] => 20
[1,3,7,5,6,2,4] => 16
[1,3,7,5,6,4,2] => 18
[1,3,7,6,2,4,5] => 13
[1,3,7,6,2,5,4] => 14
[1,3,7,6,4,2,5] => 15
[1,3,7,6,4,5,2] => 18
[1,3,7,6,5,2,4] => 15
[1,3,7,6,5,4,2] => 17
[1,4,2,3,5,6,7] => 3
[1,4,2,3,5,7,6] => 4
[1,4,2,3,6,5,7] => 4
[1,4,2,3,6,7,5] => 6
[1,4,2,3,7,5,6] => 6
[1,4,2,3,7,6,5] => 7
[1,4,2,5,3,6,7] => 5
[1,4,2,5,3,7,6] => 6
[1,4,2,5,6,3,7] => 8
[1,4,2,5,6,7,3] => 12
[1,4,2,5,7,3,6] => 10
[1,4,2,5,7,6,3] => 13
[1,4,2,6,3,5,7] => 7
[1,4,2,6,3,7,5] => 9
[1,4,2,6,5,3,7] => 9
[1,4,2,6,5,7,3] => 13
[1,4,2,6,7,3,5] => 11
[1,4,2,6,7,5,3] => 13
[1,4,2,7,3,5,6] => 10
[1,4,2,7,3,6,5] => 11
[1,4,2,7,5,3,6] => 12
[1,4,2,7,5,6,3] => 15
[1,4,2,7,6,3,5] => 12
[1,4,2,7,6,5,3] => 14
[1,4,3,2,5,6,7] => 4
[1,4,3,2,5,7,6] => 5
[1,4,3,2,6,5,7] => 5
[1,4,3,2,6,7,5] => 7
[1,4,3,2,7,5,6] => 7
[1,4,3,2,7,6,5] => 8
[1,4,3,5,2,6,7] => 7
[1,4,3,5,2,7,6] => 8
[1,4,3,5,6,2,7] => 11
[1,4,3,5,6,7,2] => 16
[1,4,3,5,7,2,6] => 13
[1,4,3,5,7,6,2] => 17
[1,4,3,6,2,5,7] => 9
[1,4,3,6,2,7,5] => 11
[1,4,3,6,5,2,7] => 12
[1,4,3,6,5,7,2] => 17
[1,4,3,6,7,2,5] => 14
[1,4,3,6,7,5,2] => 17
[1,4,3,7,2,5,6] => 12
[1,4,3,7,2,6,5] => 13
[1,4,3,7,5,2,6] => 15
[1,4,3,7,5,6,2] => 19
[1,4,3,7,6,2,5] => 15
[1,4,3,7,6,5,2] => 18
[1,4,5,2,3,6,7] => 6
[1,4,5,2,3,7,6] => 7
[1,4,5,2,6,3,7] => 9
[1,4,5,2,6,7,3] => 13
[1,4,5,2,7,3,6] => 11
[1,4,5,2,7,6,3] => 14
[1,4,5,3,2,6,7] => 7
[1,4,5,3,2,7,6] => 8
[1,4,5,3,6,2,7] => 11
[1,4,5,3,6,7,2] => 16
[1,4,5,3,7,2,6] => 13
[1,4,5,3,7,6,2] => 17
[1,4,5,6,2,3,7] => 9
[1,4,5,6,2,7,3] => 13
[1,4,5,6,3,2,7] => 10
[1,4,5,6,3,7,2] => 15
[1,4,5,6,7,2,3] => 12
[1,4,5,6,7,3,2] => 13
[1,4,5,7,2,3,6] => 12
[1,4,5,7,2,6,3] => 15
[1,4,5,7,3,2,6] => 13
[1,4,5,7,3,6,2] => 17
[1,4,5,7,6,2,3] => 13
[1,4,5,7,6,3,2] => 14
[1,4,6,2,3,5,7] => 9
[1,4,6,2,3,7,5] => 11
[1,4,6,2,5,3,7] => 11
[1,4,6,2,5,7,3] => 15
[1,4,6,2,7,3,5] => 13
[1,4,6,2,7,5,3] => 15
[1,4,6,3,2,5,7] => 10
[1,4,6,3,2,7,5] => 12
[1,4,6,3,5,2,7] => 13
[1,4,6,3,5,7,2] => 18
[1,4,6,3,7,2,5] => 15
[1,4,6,3,7,5,2] => 18
[1,4,6,5,2,3,7] => 10
[1,4,6,5,2,7,3] => 14
[1,4,6,5,3,2,7] => 11
click to show generating function       
Description
Number of minimal entries in the Bruhat order matrix of a permutation.
Associate to a permutation $\sigma$ of length $n$ the $n \times n$ matrix with entries
$$r_{ij}(\sigma) = \left| \big\{ u \in \{1,\dots,i\} \mid \sigma(u) \leq j \big\}\right|.$$
For the identity permutation, one has $r_{ij} = \min\{i,j\}$, and $\sigma \leq \tau$ in the (strong) Bruhat order if and only if $r_{ij}(\tau) \leq r_{ij}(\sigma)$ for all $i,j$.
This statistic records the number of indices $i,j$ with $r_{ij} = \min\{i,j\}$.
Code
def B(sigma):        
    n = len(sigma)                                                                 
    return Matrix([[sum(1 for u in [1 .. i] if sigma(u) <= j) for i in [1 .. n]] for j in [1 .. n]])

def statistic(sigma):
    n = len(sigma)
    M = B(sigma)
    return sum(1 for i in range(n) for j in range(n) if M[i,j] == min(i,j))
Created
Jun 06, 2019 at 13:50 by Christian Stump
Updated
Jun 06, 2019 at 13:50 by Christian Stump