Identifier
Values
[1] => [1,0] => [1,0] => [1,0] => 0
[1,2] => [1,0,1,0] => [1,1,0,0] => [1,1,0,0] => 0
[2,1] => [1,1,0,0] => [1,0,1,0] => [1,0,1,0] => 1
[1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => [1,1,1,0,0,0] => 0
[1,3,2] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 2
[2,1,3] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 1
[2,3,1] => [1,1,0,1,0,0] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 2
[1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0] => 0
[1,2,4,3] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0] => 3
[1,3,2,4] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => 2
[2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0] => 1
[2,1,4,3] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => [1,1,1,0,1,0,0,0] => 3
[2,4,1,3] => [1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,0] => 2
[2,4,3,1] => [1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,0] => 2
[3,1,4,2] => [1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 4
[3,2,4,1] => [1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 4
[3,4,1,2] => [1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,0] => 3
[3,4,2,1] => [1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,0] => 3
[1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0] => 4
[1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0] => 2
[1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 4
[1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[1,4,3,5,2] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[1,4,5,2,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0] => 5
[1,4,5,3,2] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0] => 5
[2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 4
[2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[2,4,1,3,5] => [1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0] => 4
[2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0] => 4
[2,4,5,1,3] => [1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[2,4,5,3,1] => [1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[3,1,2,5,4] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 6
[3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 6
[3,4,1,2,5] => [1,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0] => 5
[3,4,1,5,2] => [1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 6
[3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0] => 5
[3,4,2,5,1] => [1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 6
[3,4,5,1,2] => [1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[3,4,5,2,1] => [1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,2,3,4,6,5] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 5
[1,2,3,5,4,6] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[1,2,4,5,3,6] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 3
[1,2,5,3,6,4] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 5
[1,2,5,4,6,3] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 5
[1,2,5,6,3,4] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 7
[1,2,5,6,4,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 7
[1,3,2,4,5,6] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,3,2,5,4,6] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => 6
[1,3,4,2,5,6] => [1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 5
[1,3,4,5,2,6] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 5
[1,3,5,2,4,6] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 4
[1,3,5,4,2,6] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 4
[1,4,2,3,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 5
[1,4,2,5,3,6] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 6
[1,4,3,2,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 5
[1,4,3,5,2,6] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 6
[1,4,5,2,3,6] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,4,5,2,6,3] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,4,5,3,2,6] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,4,5,3,6,2] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,4,5,6,2,3] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => 6
[1,4,5,6,3,2] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => 6
[2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[2,1,3,4,6,5] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 5
[2,1,3,6,4,5] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 4
[2,1,3,6,5,4] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 4
[2,1,5,3,4,6] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => 7
[2,1,5,4,3,6] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => 7
[2,1,5,6,3,4] => [1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,1,5,6,4,3] => [1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,4,1,3,5,6] => [1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 6
[2,4,3,1,5,6] => [1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 6
[2,4,5,1,3,6] => [1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 5
[2,4,5,3,1,6] => [1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 5
[2,4,5,6,1,3] => [1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,4,5,6,3,1] => [1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[3,1,2,4,6,5] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 8
[3,2,1,4,6,5] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 8
[3,4,1,2,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 7
[3,4,1,2,6,5] => [1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 9
[3,4,2,1,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 7
[3,4,2,1,6,5] => [1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 9
[3,4,5,1,2,6] => [1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 7
[3,4,5,1,6,2] => [1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 8
[3,4,5,2,1,6] => [1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 7
[3,4,5,2,6,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 8
[3,4,5,6,1,2] => [1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 5
[3,4,5,6,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 5
[5,6,1,2,3,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 8
[5,6,1,2,4,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 8
[5,6,1,3,2,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 8
[5,6,1,3,4,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 8
[5,6,1,4,2,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 8
[5,6,1,4,3,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 8
[5,6,2,1,3,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 8
>>> Load all 358 entries. <<<
[5,6,2,1,4,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 8
[5,6,2,3,1,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 8
[5,6,2,3,4,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 8
[5,6,2,4,1,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 8
[5,6,2,4,3,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 8
[5,6,3,1,2,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 8
[5,6,3,1,4,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 8
[5,6,3,2,1,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 8
[5,6,3,2,4,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 8
[5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 8
[5,6,3,4,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 8
[5,6,4,1,2,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 8
[5,6,4,1,3,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 8
[5,6,4,2,1,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 8
[5,6,4,2,3,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 8
[5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 8
[5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 8
[1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,2,3,4,5,7,6] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
[1,2,3,4,6,5,7] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 5
[1,2,3,5,4,6,7] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
[1,2,3,5,6,4,7] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 5
[1,2,3,6,4,7,5] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 7
[1,2,3,6,5,7,4] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 7
[1,2,3,6,7,4,5] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 9
[1,2,3,6,7,5,4] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 9
[1,2,4,3,5,6,7] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 3
[1,2,4,3,6,5,7] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 5
[1,2,4,5,3,6,7] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 6
[1,2,4,6,3,5,7] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 3
[1,2,4,6,5,3,7] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 3
[1,2,5,3,4,7,6] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 4
[1,2,5,3,6,4,7] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 4
[1,2,5,4,3,7,6] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 4
[1,2,5,4,6,3,7] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 4
[1,2,5,6,3,4,7] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 7
[1,2,5,6,3,7,4] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 6
[1,2,5,6,4,3,7] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 7
[1,2,5,6,4,7,3] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 6
[1,2,5,6,7,3,4] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 8
[1,2,5,6,7,4,3] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 8
[1,3,2,4,5,6,7] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[1,3,2,4,6,5,7] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[1,3,2,5,4,6,7] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 9
[1,3,2,6,4,5,7] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 6
[1,3,2,6,5,4,7] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 6
[1,3,4,2,5,6,7] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 7
[1,3,4,6,2,5,7] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 7
[1,3,4,6,5,2,7] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 7
[1,3,5,2,4,6,7] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 6
[1,3,5,2,6,4,7] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 8
[1,3,5,4,2,6,7] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 6
[1,3,5,4,6,2,7] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 8
[1,3,5,6,2,4,7] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 4
[1,3,5,6,4,2,7] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 4
[1,3,6,2,4,5,7] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 6
[1,3,6,2,5,4,7] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 6
[1,3,6,4,2,5,7] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 6
[1,3,6,4,5,2,7] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 6
[1,3,6,5,2,4,7] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 6
[1,3,6,5,4,2,7] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 6
[1,4,2,3,5,7,6] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 7
[1,4,2,3,6,5,7] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 9
[1,4,2,5,3,6,7] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 6
[1,4,2,5,6,3,7] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 7
[1,4,3,2,5,7,6] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 7
[1,4,3,2,6,5,7] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 9
[1,4,3,5,2,6,7] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 6
[1,4,3,5,6,2,7] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 7
[1,4,5,2,3,6,7] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 6
[1,4,5,2,3,7,6] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 7
[1,4,5,2,6,3,7] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[1,4,5,3,2,6,7] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 6
[1,4,5,3,2,7,6] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 7
[1,4,5,3,6,2,7] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[1,4,5,6,2,3,7] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 5
[1,4,5,6,2,7,3] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 5
[1,4,5,6,3,2,7] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 5
[1,4,5,6,3,7,2] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 5
[1,4,5,6,7,2,3] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 7
[1,4,5,6,7,3,2] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 7
[1,5,2,3,4,7,6] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 6
[1,5,2,3,6,4,7] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 6
[1,5,2,4,3,7,6] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 6
[1,5,2,4,6,3,7] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 6
[1,5,3,2,4,7,6] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 6
[1,5,3,2,6,4,7] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 6
[1,5,3,4,2,7,6] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 6
[1,5,3,4,6,2,7] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 6
[1,5,4,2,3,7,6] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 6
[1,5,4,2,6,3,7] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 6
[1,5,4,3,2,7,6] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 6
[1,5,4,3,6,2,7] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 6
[1,6,2,3,4,7,5] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 8
[1,6,2,3,5,7,4] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 8
[1,6,2,4,3,7,5] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 8
[1,6,2,4,5,7,3] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 8
[1,6,2,5,3,7,4] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 8
[1,6,2,5,4,7,3] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 8
[1,6,3,2,4,7,5] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 8
[1,6,3,2,5,7,4] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 8
[1,6,3,4,2,7,5] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 8
[1,6,3,4,5,7,2] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 8
[1,6,3,5,2,7,4] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 8
[1,6,3,5,4,7,2] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 8
[1,6,4,2,3,7,5] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 8
[1,6,4,2,5,7,3] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 8
[1,6,4,3,2,7,5] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 8
[1,6,4,3,5,7,2] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 8
[1,6,4,5,2,7,3] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 8
[1,6,4,5,3,7,2] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 8
[1,6,5,2,3,7,4] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 8
[1,6,5,2,4,7,3] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 8
[1,6,5,3,2,7,4] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 8
[1,6,5,3,4,7,2] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 8
[1,6,5,4,2,7,3] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 8
[1,6,5,4,3,7,2] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 8
[2,1,3,4,5,6,7] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[2,1,3,4,5,7,6] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 6
[2,1,3,4,7,5,6] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 5
[2,1,3,4,7,6,5] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 5
[2,1,3,6,4,5,7] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 10
[2,1,3,6,5,4,7] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 10
[2,1,3,6,7,4,5] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 4
[2,1,3,6,7,5,4] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 4
[2,1,5,3,4,6,7] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 5
[2,1,5,4,3,6,7] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 5
[2,1,5,6,3,4,7] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 8
[2,1,5,6,4,3,7] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 8
[2,1,5,6,7,3,4] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[2,1,5,6,7,4,3] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[2,1,6,3,4,5,7] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
[2,1,6,3,5,4,7] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
[2,1,6,4,3,5,7] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
[2,1,6,4,5,3,7] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
[2,1,6,5,3,4,7] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
[2,1,6,5,4,3,7] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
[2,4,1,3,5,6,7] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 8
[2,4,3,1,5,6,7] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 8
[2,4,5,1,3,6,7] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 8
[2,4,5,3,1,6,7] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 8
[2,4,5,6,1,3,7] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 6
[2,4,5,6,3,1,7] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 6
[2,4,5,6,7,1,3] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,4,5,6,7,3,1] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,6,1,3,4,5,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 10
[2,6,1,3,5,4,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 10
[2,6,1,4,3,5,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 10
[2,6,1,4,5,3,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 10
[2,6,1,5,3,4,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 10
[2,6,1,5,4,3,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 10
[2,6,3,1,4,5,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 10
[2,6,3,1,5,4,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 10
[2,6,3,4,1,5,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 10
[2,6,3,4,5,1,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 10
[2,6,3,5,1,4,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 10
[2,6,3,5,4,1,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 10
[2,6,4,1,3,5,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 10
[2,6,4,1,5,3,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 10
[2,6,4,3,1,5,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 10
[2,6,4,3,5,1,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 10
[2,6,4,5,1,3,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 10
[2,6,4,5,3,1,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 10
[2,6,5,1,3,4,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 10
[2,6,5,1,4,3,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 10
[2,6,5,3,1,4,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 10
[2,6,5,3,4,1,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 10
[2,6,5,4,1,3,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 10
[2,6,5,4,3,1,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 10
[3,1,2,4,5,7,6] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 10
[3,2,1,4,5,7,6] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 10
[3,4,1,2,5,6,7] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 9
[3,4,1,2,5,7,6] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 12
[3,4,2,1,5,6,7] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 9
[3,4,2,1,5,7,6] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 12
[3,4,5,1,2,6,7] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 10
[3,4,5,1,2,7,6] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 12
[3,4,5,2,1,6,7] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 10
[3,4,5,2,1,7,6] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 12
[3,4,5,6,1,2,7] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 9
[3,4,5,6,1,7,2] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 10
[3,4,5,6,2,1,7] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 9
[3,4,5,6,2,7,1] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 10
[3,4,5,6,7,1,2] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 6
[3,4,5,6,7,2,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 6
[3,6,7,1,2,4,5] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 11
[3,6,7,1,2,5,4] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 11
[3,6,7,1,4,2,5] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 11
[3,6,7,1,4,5,2] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 11
[3,6,7,1,5,2,4] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 11
[3,6,7,1,5,4,2] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 11
[3,6,7,2,1,4,5] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 11
[3,6,7,2,1,5,4] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 11
[3,6,7,2,4,1,5] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 11
[3,6,7,2,4,5,1] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 11
[3,6,7,2,5,1,4] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 11
[3,6,7,2,5,4,1] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 11
[3,6,7,4,1,2,5] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 11
[3,6,7,4,1,5,2] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 11
[3,6,7,4,2,1,5] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 11
[3,6,7,4,2,5,1] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 11
[3,6,7,4,5,1,2] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 11
[3,6,7,4,5,2,1] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 11
[3,6,7,5,1,2,4] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 11
[3,6,7,5,1,4,2] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 11
[3,6,7,5,2,1,4] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 11
[3,6,7,5,2,4,1] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 11
[3,6,7,5,4,1,2] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 11
[3,6,7,5,4,2,1] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 11
[5,6,1,2,7,3,4] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 11
[5,6,1,2,7,4,3] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 11
[5,6,1,3,7,2,4] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 11
[5,6,1,3,7,4,2] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 11
[5,6,1,4,7,2,3] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 11
[5,6,1,4,7,3,2] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 11
[5,6,2,1,7,3,4] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 11
[5,6,2,1,7,4,3] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 11
[5,6,2,3,7,1,4] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 11
[5,6,2,3,7,4,1] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 11
[5,6,2,4,7,1,3] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 11
[5,6,2,4,7,3,1] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 11
[5,6,3,1,7,2,4] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 11
[5,6,3,1,7,4,2] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 11
[5,6,3,2,7,1,4] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 11
[5,6,3,2,7,4,1] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 11
[5,6,3,4,7,1,2] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 11
[5,6,3,4,7,2,1] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 11
[5,6,4,1,7,2,3] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 11
[5,6,4,1,7,3,2] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 11
[5,6,4,2,7,1,3] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 11
[5,6,4,2,7,3,1] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 11
[5,6,4,3,7,1,2] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 11
[5,6,4,3,7,2,1] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 11
[5,6,7,1,2,3,4] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 10
[5,6,7,1,2,4,3] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 10
[5,6,7,1,3,2,4] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 10
[5,6,7,1,3,4,2] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 10
[5,6,7,1,4,2,3] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 10
[5,6,7,1,4,3,2] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 10
[5,6,7,2,1,3,4] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 10
[5,6,7,2,1,4,3] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 10
[5,6,7,2,3,1,4] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 10
[5,6,7,2,3,4,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 10
[5,6,7,2,4,1,3] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 10
[5,6,7,2,4,3,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 10
[5,6,7,3,1,2,4] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 10
[5,6,7,3,1,4,2] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 10
[5,6,7,3,2,1,4] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 10
[5,6,7,3,2,4,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 10
[5,6,7,3,4,1,2] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 10
[5,6,7,3,4,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 10
[5,6,7,4,1,2,3] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 10
[5,6,7,4,1,3,2] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 10
[5,6,7,4,2,1,3] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 10
[5,6,7,4,2,3,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 10
[5,6,7,4,3,1,2] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 10
[5,6,7,4,3,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 10
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
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Map
Barnabei-Castronuovo involution
Description
The Barnabei-Castronuovo Schützenberger involution on Dyck paths.
The image of a Dyck path is obtained by reversing the canonical decompositions of the two halves of the Dyck path. More precisely, let $D_1, 1, D_2, 1, \dots$ be the canonical decomposition of the first half, then the canonical decomposition of the first half of the image is $\dots, 1, D_2, 1, D_1$.
Map
Delest-Viennot-inverse
Description
Return the Dyck path obtained by applying the inverse of Delest-Viennot's bijection to the corresponding parallelogram polyomino.
Let $D$ be a Dyck path of semilength $n$. The parallelogram polyomino $\gamma(D)$ is defined as follows: let $\tilde D = d_0 d_1 \dots d_{2n+1}$ be the Dyck path obtained by prepending an up step and appending a down step to $D$. Then, the upper path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with even indices, and the lower path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with odd indices.
The Delest-Viennot bijection $\beta$ returns the parallelogram polyomino, whose column heights are the heights of the peaks of the Dyck path, and the intersection heights between columns are the heights of the valleys of the Dyck path.
This map returns the Dyck path $(\beta^{(-1)}\circ\gamma)(D)$.
Map
left-to-right-maxima to Dyck path
Description
The left-to-right maxima of a permutation as a Dyck path.
Let $(c_1, \dots, c_k)$ be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are $c_1, c_1+c_2, \dots, c_1+\dots+c_k$.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.