Identifier
-
Mp00127:
Permutations
—left-to-right-maxima to Dyck path⟶
Dyck paths
St001504: Dyck paths ⟶ ℤ
Values
[1] => [1,0] => 2
[1,2] => [1,0,1,0] => 2
[2,1] => [1,1,0,0] => 3
[1,2,3] => [1,0,1,0,1,0] => 2
[1,3,2] => [1,0,1,1,0,0] => 4
[2,1,3] => [1,1,0,0,1,0] => 3
[2,3,1] => [1,1,0,1,0,0] => 3
[3,1,2] => [1,1,1,0,0,0] => 4
[3,2,1] => [1,1,1,0,0,0] => 4
[1,2,3,4] => [1,0,1,0,1,0,1,0] => 2
[1,2,4,3] => [1,0,1,0,1,1,0,0] => 4
[1,3,2,4] => [1,0,1,1,0,0,1,0] => 4
[1,3,4,2] => [1,0,1,1,0,1,0,0] => 4
[1,4,2,3] => [1,0,1,1,1,0,0,0] => 5
[1,4,3,2] => [1,0,1,1,1,0,0,0] => 5
[2,1,3,4] => [1,1,0,0,1,0,1,0] => 3
[2,1,4,3] => [1,1,0,0,1,1,0,0] => 5
[2,3,1,4] => [1,1,0,1,0,0,1,0] => 3
[2,3,4,1] => [1,1,0,1,0,1,0,0] => 3
[2,4,1,3] => [1,1,0,1,1,0,0,0] => 5
[2,4,3,1] => [1,1,0,1,1,0,0,0] => 5
[3,1,2,4] => [1,1,1,0,0,0,1,0] => 4
[3,1,4,2] => [1,1,1,0,0,1,0,0] => 4
[3,2,1,4] => [1,1,1,0,0,0,1,0] => 4
[3,2,4,1] => [1,1,1,0,0,1,0,0] => 4
[3,4,1,2] => [1,1,1,0,1,0,0,0] => 4
[3,4,2,1] => [1,1,1,0,1,0,0,0] => 4
[4,1,2,3] => [1,1,1,1,0,0,0,0] => 5
[4,1,3,2] => [1,1,1,1,0,0,0,0] => 5
[4,2,1,3] => [1,1,1,1,0,0,0,0] => 5
[4,2,3,1] => [1,1,1,1,0,0,0,0] => 5
[4,3,1,2] => [1,1,1,1,0,0,0,0] => 5
[4,3,2,1] => [1,1,1,1,0,0,0,0] => 5
[1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => 2
[1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0] => 4
[1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0] => 4
[1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0] => 5
[1,2,5,4,3] => [1,0,1,0,1,1,1,0,0,0] => 5
[1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0] => 4
[1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => 6
[1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0] => 4
[1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,3,5,2,4] => [1,0,1,1,0,1,1,0,0,0] => 6
[1,3,5,4,2] => [1,0,1,1,0,1,1,0,0,0] => 6
[1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0] => 5
[1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0] => 5
[1,4,3,2,5] => [1,0,1,1,1,0,0,0,1,0] => 5
[1,4,3,5,2] => [1,0,1,1,1,0,0,1,0,0] => 5
[1,4,5,2,3] => [1,0,1,1,1,0,1,0,0,0] => 5
[1,4,5,3,2] => [1,0,1,1,1,0,1,0,0,0] => 5
[1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0] => 6
[1,5,2,4,3] => [1,0,1,1,1,1,0,0,0,0] => 6
[1,5,3,2,4] => [1,0,1,1,1,1,0,0,0,0] => 6
[1,5,3,4,2] => [1,0,1,1,1,1,0,0,0,0] => 6
[1,5,4,2,3] => [1,0,1,1,1,1,0,0,0,0] => 6
[1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => 6
[2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => 3
[2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0] => 5
[2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => 5
[2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0] => 5
[2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0] => 6
[2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0] => 6
[2,3,1,4,5] => [1,1,0,1,0,0,1,0,1,0] => 3
[2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0] => 5
[2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0] => 3
[2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => 3
[2,3,5,1,4] => [1,1,0,1,0,1,1,0,0,0] => 5
[2,3,5,4,1] => [1,1,0,1,0,1,1,0,0,0] => 5
[2,4,1,3,5] => [1,1,0,1,1,0,0,0,1,0] => 5
[2,4,1,5,3] => [1,1,0,1,1,0,0,1,0,0] => 5
[2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0] => 5
[2,4,3,5,1] => [1,1,0,1,1,0,0,1,0,0] => 5
[2,4,5,1,3] => [1,1,0,1,1,0,1,0,0,0] => 5
[2,4,5,3,1] => [1,1,0,1,1,0,1,0,0,0] => 5
[2,5,1,3,4] => [1,1,0,1,1,1,0,0,0,0] => 6
[2,5,1,4,3] => [1,1,0,1,1,1,0,0,0,0] => 6
[2,5,3,1,4] => [1,1,0,1,1,1,0,0,0,0] => 6
[2,5,3,4,1] => [1,1,0,1,1,1,0,0,0,0] => 6
[2,5,4,1,3] => [1,1,0,1,1,1,0,0,0,0] => 6
[2,5,4,3,1] => [1,1,0,1,1,1,0,0,0,0] => 6
[3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0] => 4
[3,1,2,5,4] => [1,1,1,0,0,0,1,1,0,0] => 6
[3,1,4,2,5] => [1,1,1,0,0,1,0,0,1,0] => 4
[3,1,4,5,2] => [1,1,1,0,0,1,0,1,0,0] => 4
[3,1,5,2,4] => [1,1,1,0,0,1,1,0,0,0] => 6
[3,1,5,4,2] => [1,1,1,0,0,1,1,0,0,0] => 6
[3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => 4
[3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 6
[3,2,4,1,5] => [1,1,1,0,0,1,0,0,1,0] => 4
[3,2,4,5,1] => [1,1,1,0,0,1,0,1,0,0] => 4
[3,2,5,1,4] => [1,1,1,0,0,1,1,0,0,0] => 6
[3,2,5,4,1] => [1,1,1,0,0,1,1,0,0,0] => 6
[3,4,1,2,5] => [1,1,1,0,1,0,0,0,1,0] => 4
[3,4,1,5,2] => [1,1,1,0,1,0,0,1,0,0] => 4
[3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0] => 4
[3,4,2,5,1] => [1,1,1,0,1,0,0,1,0,0] => 4
[3,4,5,1,2] => [1,1,1,0,1,0,1,0,0,0] => 4
[3,4,5,2,1] => [1,1,1,0,1,0,1,0,0,0] => 4
[3,5,1,2,4] => [1,1,1,0,1,1,0,0,0,0] => 6
[3,5,1,4,2] => [1,1,1,0,1,1,0,0,0,0] => 6
>>> Load all 5913 entries. <<<[3,5,2,1,4] => [1,1,1,0,1,1,0,0,0,0] => 6
[3,5,2,4,1] => [1,1,1,0,1,1,0,0,0,0] => 6
[3,5,4,1,2] => [1,1,1,0,1,1,0,0,0,0] => 6
[3,5,4,2,1] => [1,1,1,0,1,1,0,0,0,0] => 6
[4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0] => 5
[4,1,2,5,3] => [1,1,1,1,0,0,0,1,0,0] => 5
[4,1,3,2,5] => [1,1,1,1,0,0,0,0,1,0] => 5
[4,1,3,5,2] => [1,1,1,1,0,0,0,1,0,0] => 5
[4,1,5,2,3] => [1,1,1,1,0,0,1,0,0,0] => 5
[4,1,5,3,2] => [1,1,1,1,0,0,1,0,0,0] => 5
[4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0] => 5
[4,2,1,5,3] => [1,1,1,1,0,0,0,1,0,0] => 5
[4,2,3,1,5] => [1,1,1,1,0,0,0,0,1,0] => 5
[4,2,3,5,1] => [1,1,1,1,0,0,0,1,0,0] => 5
[4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0] => 5
[4,2,5,3,1] => [1,1,1,1,0,0,1,0,0,0] => 5
[4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0] => 5
[4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0] => 5
[4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 5
[4,3,2,5,1] => [1,1,1,1,0,0,0,1,0,0] => 5
[4,3,5,1,2] => [1,1,1,1,0,0,1,0,0,0] => 5
[4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0] => 5
[4,5,1,2,3] => [1,1,1,1,0,1,0,0,0,0] => 5
[4,5,1,3,2] => [1,1,1,1,0,1,0,0,0,0] => 5
[4,5,2,1,3] => [1,1,1,1,0,1,0,0,0,0] => 5
[4,5,2,3,1] => [1,1,1,1,0,1,0,0,0,0] => 5
[4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0] => 5
[4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0] => 5
[5,1,2,3,4] => [1,1,1,1,1,0,0,0,0,0] => 6
[5,1,2,4,3] => [1,1,1,1,1,0,0,0,0,0] => 6
[5,1,3,2,4] => [1,1,1,1,1,0,0,0,0,0] => 6
[5,1,3,4,2] => [1,1,1,1,1,0,0,0,0,0] => 6
[5,1,4,2,3] => [1,1,1,1,1,0,0,0,0,0] => 6
[5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0] => 6
[5,2,1,3,4] => [1,1,1,1,1,0,0,0,0,0] => 6
[5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0] => 6
[5,2,3,1,4] => [1,1,1,1,1,0,0,0,0,0] => 6
[5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0] => 6
[5,2,4,1,3] => [1,1,1,1,1,0,0,0,0,0] => 6
[5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0] => 6
[5,3,1,2,4] => [1,1,1,1,1,0,0,0,0,0] => 6
[5,3,1,4,2] => [1,1,1,1,1,0,0,0,0,0] => 6
[5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0] => 6
[5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0] => 6
[5,3,4,1,2] => [1,1,1,1,1,0,0,0,0,0] => 6
[5,3,4,2,1] => [1,1,1,1,1,0,0,0,0,0] => 6
[5,4,1,2,3] => [1,1,1,1,1,0,0,0,0,0] => 6
[5,4,1,3,2] => [1,1,1,1,1,0,0,0,0,0] => 6
[5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0] => 6
[5,4,2,3,1] => [1,1,1,1,1,0,0,0,0,0] => 6
[5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0] => 6
[5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => 6
[1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,2,3,4,6,5] => [1,0,1,0,1,0,1,0,1,1,0,0] => 4
[1,2,3,5,4,6] => [1,0,1,0,1,0,1,1,0,0,1,0] => 4
[1,2,3,5,6,4] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,2,3,6,4,5] => [1,0,1,0,1,0,1,1,1,0,0,0] => 5
[1,2,3,6,5,4] => [1,0,1,0,1,0,1,1,1,0,0,0] => 5
[1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0] => 4
[1,2,4,3,6,5] => [1,0,1,0,1,1,0,0,1,1,0,0] => 6
[1,2,4,5,3,6] => [1,0,1,0,1,1,0,1,0,0,1,0] => 4
[1,2,4,5,6,3] => [1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,2,4,6,3,5] => [1,0,1,0,1,1,0,1,1,0,0,0] => 6
[1,2,4,6,5,3] => [1,0,1,0,1,1,0,1,1,0,0,0] => 6
[1,2,5,3,4,6] => [1,0,1,0,1,1,1,0,0,0,1,0] => 5
[1,2,5,3,6,4] => [1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,2,5,4,3,6] => [1,0,1,0,1,1,1,0,0,0,1,0] => 5
[1,2,5,4,6,3] => [1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,2,5,6,3,4] => [1,0,1,0,1,1,1,0,1,0,0,0] => 5
[1,2,5,6,4,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 5
[1,2,6,3,4,5] => [1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,2,6,3,5,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,2,6,4,3,5] => [1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,2,6,4,5,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,2,6,5,3,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,2,6,5,4,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,3,2,4,5,6] => [1,0,1,1,0,0,1,0,1,0,1,0] => 4
[1,3,2,4,6,5] => [1,0,1,1,0,0,1,0,1,1,0,0] => 6
[1,3,2,5,4,6] => [1,0,1,1,0,0,1,1,0,0,1,0] => 6
[1,3,2,5,6,4] => [1,0,1,1,0,0,1,1,0,1,0,0] => 6
[1,3,2,6,4,5] => [1,0,1,1,0,0,1,1,1,0,0,0] => 7
[1,3,2,6,5,4] => [1,0,1,1,0,0,1,1,1,0,0,0] => 7
[1,3,4,2,5,6] => [1,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,3,4,2,6,5] => [1,0,1,1,0,1,0,0,1,1,0,0] => 6
[1,3,4,5,2,6] => [1,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,3,4,5,6,2] => [1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,3,4,6,2,5] => [1,0,1,1,0,1,0,1,1,0,0,0] => 6
[1,3,4,6,5,2] => [1,0,1,1,0,1,0,1,1,0,0,0] => 6
[1,3,5,2,4,6] => [1,0,1,1,0,1,1,0,0,0,1,0] => 6
[1,3,5,2,6,4] => [1,0,1,1,0,1,1,0,0,1,0,0] => 6
[1,3,5,4,2,6] => [1,0,1,1,0,1,1,0,0,0,1,0] => 6
[1,3,5,4,6,2] => [1,0,1,1,0,1,1,0,0,1,0,0] => 6
[1,3,5,6,2,4] => [1,0,1,1,0,1,1,0,1,0,0,0] => 6
[1,3,5,6,4,2] => [1,0,1,1,0,1,1,0,1,0,0,0] => 6
[1,3,6,2,4,5] => [1,0,1,1,0,1,1,1,0,0,0,0] => 7
[1,3,6,2,5,4] => [1,0,1,1,0,1,1,1,0,0,0,0] => 7
[1,3,6,4,2,5] => [1,0,1,1,0,1,1,1,0,0,0,0] => 7
[1,3,6,4,5,2] => [1,0,1,1,0,1,1,1,0,0,0,0] => 7
[1,3,6,5,2,4] => [1,0,1,1,0,1,1,1,0,0,0,0] => 7
[1,3,6,5,4,2] => [1,0,1,1,0,1,1,1,0,0,0,0] => 7
[1,4,2,3,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0] => 5
[1,4,2,3,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0] => 7
[1,4,2,5,3,6] => [1,0,1,1,1,0,0,1,0,0,1,0] => 5
[1,4,2,5,6,3] => [1,0,1,1,1,0,0,1,0,1,0,0] => 5
[1,4,2,6,3,5] => [1,0,1,1,1,0,0,1,1,0,0,0] => 7
[1,4,2,6,5,3] => [1,0,1,1,1,0,0,1,1,0,0,0] => 7
[1,4,3,2,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0] => 5
[1,4,3,2,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0] => 7
[1,4,3,5,2,6] => [1,0,1,1,1,0,0,1,0,0,1,0] => 5
[1,4,3,5,6,2] => [1,0,1,1,1,0,0,1,0,1,0,0] => 5
[1,4,3,6,2,5] => [1,0,1,1,1,0,0,1,1,0,0,0] => 7
[1,4,3,6,5,2] => [1,0,1,1,1,0,0,1,1,0,0,0] => 7
[1,4,5,2,3,6] => [1,0,1,1,1,0,1,0,0,0,1,0] => 5
[1,4,5,2,6,3] => [1,0,1,1,1,0,1,0,0,1,0,0] => 5
[1,4,5,3,2,6] => [1,0,1,1,1,0,1,0,0,0,1,0] => 5
[1,4,5,3,6,2] => [1,0,1,1,1,0,1,0,0,1,0,0] => 5
[1,4,5,6,2,3] => [1,0,1,1,1,0,1,0,1,0,0,0] => 5
[1,4,5,6,3,2] => [1,0,1,1,1,0,1,0,1,0,0,0] => 5
[1,4,6,2,3,5] => [1,0,1,1,1,0,1,1,0,0,0,0] => 7
[1,4,6,2,5,3] => [1,0,1,1,1,0,1,1,0,0,0,0] => 7
[1,4,6,3,2,5] => [1,0,1,1,1,0,1,1,0,0,0,0] => 7
[1,4,6,3,5,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 7
[1,4,6,5,2,3] => [1,0,1,1,1,0,1,1,0,0,0,0] => 7
[1,4,6,5,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 7
[1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => 6
[1,5,2,3,6,4] => [1,0,1,1,1,1,0,0,0,1,0,0] => 6
[1,5,2,4,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => 6
[1,5,2,4,6,3] => [1,0,1,1,1,1,0,0,0,1,0,0] => 6
[1,5,2,6,3,4] => [1,0,1,1,1,1,0,0,1,0,0,0] => 6
[1,5,2,6,4,3] => [1,0,1,1,1,1,0,0,1,0,0,0] => 6
[1,5,3,2,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => 6
[1,5,3,2,6,4] => [1,0,1,1,1,1,0,0,0,1,0,0] => 6
[1,5,3,4,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => 6
[1,5,3,4,6,2] => [1,0,1,1,1,1,0,0,0,1,0,0] => 6
[1,5,3,6,2,4] => [1,0,1,1,1,1,0,0,1,0,0,0] => 6
[1,5,3,6,4,2] => [1,0,1,1,1,1,0,0,1,0,0,0] => 6
[1,5,4,2,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => 6
[1,5,4,2,6,3] => [1,0,1,1,1,1,0,0,0,1,0,0] => 6
[1,5,4,3,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => 6
[1,5,4,3,6,2] => [1,0,1,1,1,1,0,0,0,1,0,0] => 6
[1,5,4,6,2,3] => [1,0,1,1,1,1,0,0,1,0,0,0] => 6
[1,5,4,6,3,2] => [1,0,1,1,1,1,0,0,1,0,0,0] => 6
[1,5,6,2,3,4] => [1,0,1,1,1,1,0,1,0,0,0,0] => 6
[1,5,6,2,4,3] => [1,0,1,1,1,1,0,1,0,0,0,0] => 6
[1,5,6,3,2,4] => [1,0,1,1,1,1,0,1,0,0,0,0] => 6
[1,5,6,3,4,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 6
[1,5,6,4,2,3] => [1,0,1,1,1,1,0,1,0,0,0,0] => 6
[1,5,6,4,3,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 6
[1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,6,2,3,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,6,2,4,3,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,6,2,4,5,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,6,2,5,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,6,2,5,4,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,6,3,2,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,6,3,2,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,6,3,4,2,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,6,3,4,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,6,3,5,2,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,6,3,5,4,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,6,4,2,3,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,6,4,2,5,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,6,4,3,2,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,6,4,3,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,6,4,5,2,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,6,4,5,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,6,5,2,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,6,5,2,4,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,6,5,3,2,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,6,5,3,4,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,6,5,4,2,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 7
[2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => 3
[2,1,3,4,6,5] => [1,1,0,0,1,0,1,0,1,1,0,0] => 5
[2,1,3,5,4,6] => [1,1,0,0,1,0,1,1,0,0,1,0] => 5
[2,1,3,5,6,4] => [1,1,0,0,1,0,1,1,0,1,0,0] => 5
[2,1,3,6,4,5] => [1,1,0,0,1,0,1,1,1,0,0,0] => 6
[2,1,3,6,5,4] => [1,1,0,0,1,0,1,1,1,0,0,0] => 6
[2,1,4,3,5,6] => [1,1,0,0,1,1,0,0,1,0,1,0] => 5
[2,1,4,3,6,5] => [1,1,0,0,1,1,0,0,1,1,0,0] => 7
[2,1,4,5,3,6] => [1,1,0,0,1,1,0,1,0,0,1,0] => 5
[2,1,4,5,6,3] => [1,1,0,0,1,1,0,1,0,1,0,0] => 5
[2,1,4,6,3,5] => [1,1,0,0,1,1,0,1,1,0,0,0] => 7
[2,1,4,6,5,3] => [1,1,0,0,1,1,0,1,1,0,0,0] => 7
[2,1,5,3,4,6] => [1,1,0,0,1,1,1,0,0,0,1,0] => 6
[2,1,5,3,6,4] => [1,1,0,0,1,1,1,0,0,1,0,0] => 6
[2,1,5,4,3,6] => [1,1,0,0,1,1,1,0,0,0,1,0] => 6
[2,1,5,4,6,3] => [1,1,0,0,1,1,1,0,0,1,0,0] => 6
[2,1,5,6,3,4] => [1,1,0,0,1,1,1,0,1,0,0,0] => 6
[2,1,5,6,4,3] => [1,1,0,0,1,1,1,0,1,0,0,0] => 6
[2,1,6,3,4,5] => [1,1,0,0,1,1,1,1,0,0,0,0] => 7
[2,1,6,3,5,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 7
[2,1,6,4,3,5] => [1,1,0,0,1,1,1,1,0,0,0,0] => 7
[2,1,6,4,5,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => 7
[2,1,6,5,3,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 7
[2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => 7
[2,3,1,4,5,6] => [1,1,0,1,0,0,1,0,1,0,1,0] => 3
[2,3,1,4,6,5] => [1,1,0,1,0,0,1,0,1,1,0,0] => 5
[2,3,1,5,4,6] => [1,1,0,1,0,0,1,1,0,0,1,0] => 5
[2,3,1,5,6,4] => [1,1,0,1,0,0,1,1,0,1,0,0] => 5
[2,3,1,6,4,5] => [1,1,0,1,0,0,1,1,1,0,0,0] => 6
[2,3,1,6,5,4] => [1,1,0,1,0,0,1,1,1,0,0,0] => 6
[2,3,4,1,5,6] => [1,1,0,1,0,1,0,0,1,0,1,0] => 3
[2,3,4,1,6,5] => [1,1,0,1,0,1,0,0,1,1,0,0] => 5
[2,3,4,5,1,6] => [1,1,0,1,0,1,0,1,0,0,1,0] => 3
[2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 3
[2,3,4,6,1,5] => [1,1,0,1,0,1,0,1,1,0,0,0] => 5
[2,3,4,6,5,1] => [1,1,0,1,0,1,0,1,1,0,0,0] => 5
[2,3,5,1,4,6] => [1,1,0,1,0,1,1,0,0,0,1,0] => 5
[2,3,5,1,6,4] => [1,1,0,1,0,1,1,0,0,1,0,0] => 5
[2,3,5,4,1,6] => [1,1,0,1,0,1,1,0,0,0,1,0] => 5
[2,3,5,4,6,1] => [1,1,0,1,0,1,1,0,0,1,0,0] => 5
[2,3,5,6,1,4] => [1,1,0,1,0,1,1,0,1,0,0,0] => 5
[2,3,5,6,4,1] => [1,1,0,1,0,1,1,0,1,0,0,0] => 5
[2,3,6,1,4,5] => [1,1,0,1,0,1,1,1,0,0,0,0] => 6
[2,3,6,1,5,4] => [1,1,0,1,0,1,1,1,0,0,0,0] => 6
[2,3,6,4,1,5] => [1,1,0,1,0,1,1,1,0,0,0,0] => 6
[2,3,6,4,5,1] => [1,1,0,1,0,1,1,1,0,0,0,0] => 6
[2,3,6,5,1,4] => [1,1,0,1,0,1,1,1,0,0,0,0] => 6
[2,3,6,5,4,1] => [1,1,0,1,0,1,1,1,0,0,0,0] => 6
[2,4,1,3,5,6] => [1,1,0,1,1,0,0,0,1,0,1,0] => 5
[2,4,1,3,6,5] => [1,1,0,1,1,0,0,0,1,1,0,0] => 7
[2,4,1,5,3,6] => [1,1,0,1,1,0,0,1,0,0,1,0] => 5
[2,4,1,5,6,3] => [1,1,0,1,1,0,0,1,0,1,0,0] => 5
[2,4,1,6,3,5] => [1,1,0,1,1,0,0,1,1,0,0,0] => 7
[2,4,1,6,5,3] => [1,1,0,1,1,0,0,1,1,0,0,0] => 7
[2,4,3,1,5,6] => [1,1,0,1,1,0,0,0,1,0,1,0] => 5
[2,4,3,1,6,5] => [1,1,0,1,1,0,0,0,1,1,0,0] => 7
[2,4,3,5,1,6] => [1,1,0,1,1,0,0,1,0,0,1,0] => 5
[2,4,3,5,6,1] => [1,1,0,1,1,0,0,1,0,1,0,0] => 5
[2,4,3,6,1,5] => [1,1,0,1,1,0,0,1,1,0,0,0] => 7
[2,4,3,6,5,1] => [1,1,0,1,1,0,0,1,1,0,0,0] => 7
[2,4,5,1,3,6] => [1,1,0,1,1,0,1,0,0,0,1,0] => 5
[2,4,5,1,6,3] => [1,1,0,1,1,0,1,0,0,1,0,0] => 5
[2,4,5,3,1,6] => [1,1,0,1,1,0,1,0,0,0,1,0] => 5
[2,4,5,3,6,1] => [1,1,0,1,1,0,1,0,0,1,0,0] => 5
[2,4,5,6,1,3] => [1,1,0,1,1,0,1,0,1,0,0,0] => 5
[2,4,5,6,3,1] => [1,1,0,1,1,0,1,0,1,0,0,0] => 5
[2,4,6,1,3,5] => [1,1,0,1,1,0,1,1,0,0,0,0] => 7
[2,4,6,1,5,3] => [1,1,0,1,1,0,1,1,0,0,0,0] => 7
[2,4,6,3,1,5] => [1,1,0,1,1,0,1,1,0,0,0,0] => 7
[2,4,6,3,5,1] => [1,1,0,1,1,0,1,1,0,0,0,0] => 7
[2,4,6,5,1,3] => [1,1,0,1,1,0,1,1,0,0,0,0] => 7
[2,4,6,5,3,1] => [1,1,0,1,1,0,1,1,0,0,0,0] => 7
[2,5,1,3,4,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
[2,5,1,3,6,4] => [1,1,0,1,1,1,0,0,0,1,0,0] => 6
[2,5,1,4,3,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
[2,5,1,4,6,3] => [1,1,0,1,1,1,0,0,0,1,0,0] => 6
[2,5,1,6,3,4] => [1,1,0,1,1,1,0,0,1,0,0,0] => 6
[2,5,1,6,4,3] => [1,1,0,1,1,1,0,0,1,0,0,0] => 6
[2,5,3,1,4,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
[2,5,3,1,6,4] => [1,1,0,1,1,1,0,0,0,1,0,0] => 6
[2,5,3,4,1,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
[2,5,3,4,6,1] => [1,1,0,1,1,1,0,0,0,1,0,0] => 6
[2,5,3,6,1,4] => [1,1,0,1,1,1,0,0,1,0,0,0] => 6
[2,5,3,6,4,1] => [1,1,0,1,1,1,0,0,1,0,0,0] => 6
[2,5,4,1,3,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
[2,5,4,1,6,3] => [1,1,0,1,1,1,0,0,0,1,0,0] => 6
[2,5,4,3,1,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
[2,5,4,3,6,1] => [1,1,0,1,1,1,0,0,0,1,0,0] => 6
[2,5,4,6,1,3] => [1,1,0,1,1,1,0,0,1,0,0,0] => 6
[2,5,4,6,3,1] => [1,1,0,1,1,1,0,0,1,0,0,0] => 6
[2,5,6,1,3,4] => [1,1,0,1,1,1,0,1,0,0,0,0] => 6
[2,5,6,1,4,3] => [1,1,0,1,1,1,0,1,0,0,0,0] => 6
[2,5,6,3,1,4] => [1,1,0,1,1,1,0,1,0,0,0,0] => 6
[2,5,6,3,4,1] => [1,1,0,1,1,1,0,1,0,0,0,0] => 6
[2,5,6,4,1,3] => [1,1,0,1,1,1,0,1,0,0,0,0] => 6
[2,5,6,4,3,1] => [1,1,0,1,1,1,0,1,0,0,0,0] => 6
[2,6,1,3,4,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => 7
[2,6,1,3,5,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => 7
[2,6,1,4,3,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => 7
[2,6,1,4,5,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => 7
[2,6,1,5,3,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => 7
[2,6,1,5,4,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => 7
[2,6,3,1,4,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => 7
[2,6,3,1,5,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => 7
[2,6,3,4,1,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => 7
[2,6,3,4,5,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 7
[2,6,3,5,1,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => 7
[2,6,3,5,4,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 7
[2,6,4,1,3,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => 7
[2,6,4,1,5,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => 7
[2,6,4,3,1,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => 7
[2,6,4,3,5,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 7
[2,6,4,5,1,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => 7
[2,6,4,5,3,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 7
[2,6,5,1,3,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => 7
[2,6,5,1,4,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => 7
[2,6,5,3,1,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => 7
[2,6,5,3,4,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 7
[2,6,5,4,1,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => 7
[2,6,5,4,3,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 7
[3,1,2,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0] => 4
[3,1,2,4,6,5] => [1,1,1,0,0,0,1,0,1,1,0,0] => 6
[3,1,2,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0] => 6
[3,1,2,5,6,4] => [1,1,1,0,0,0,1,1,0,1,0,0] => 6
[3,1,2,6,4,5] => [1,1,1,0,0,0,1,1,1,0,0,0] => 7
[3,1,2,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 7
[3,1,4,2,5,6] => [1,1,1,0,0,1,0,0,1,0,1,0] => 4
[3,1,4,2,6,5] => [1,1,1,0,0,1,0,0,1,1,0,0] => 6
[3,1,4,5,2,6] => [1,1,1,0,0,1,0,1,0,0,1,0] => 4
[3,1,4,5,6,2] => [1,1,1,0,0,1,0,1,0,1,0,0] => 4
[3,1,4,6,2,5] => [1,1,1,0,0,1,0,1,1,0,0,0] => 6
[3,1,4,6,5,2] => [1,1,1,0,0,1,0,1,1,0,0,0] => 6
[3,1,5,2,4,6] => [1,1,1,0,0,1,1,0,0,0,1,0] => 6
[3,1,5,2,6,4] => [1,1,1,0,0,1,1,0,0,1,0,0] => 6
[3,1,5,4,2,6] => [1,1,1,0,0,1,1,0,0,0,1,0] => 6
[3,1,5,4,6,2] => [1,1,1,0,0,1,1,0,0,1,0,0] => 6
[3,1,5,6,2,4] => [1,1,1,0,0,1,1,0,1,0,0,0] => 6
[3,1,5,6,4,2] => [1,1,1,0,0,1,1,0,1,0,0,0] => 6
[3,1,6,2,4,5] => [1,1,1,0,0,1,1,1,0,0,0,0] => 7
[3,1,6,2,5,4] => [1,1,1,0,0,1,1,1,0,0,0,0] => 7
[3,1,6,4,2,5] => [1,1,1,0,0,1,1,1,0,0,0,0] => 7
[3,1,6,4,5,2] => [1,1,1,0,0,1,1,1,0,0,0,0] => 7
[3,1,6,5,2,4] => [1,1,1,0,0,1,1,1,0,0,0,0] => 7
[3,1,6,5,4,2] => [1,1,1,0,0,1,1,1,0,0,0,0] => 7
[3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0] => 4
[3,2,1,4,6,5] => [1,1,1,0,0,0,1,0,1,1,0,0] => 6
[3,2,1,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0] => 6
[3,2,1,5,6,4] => [1,1,1,0,0,0,1,1,0,1,0,0] => 6
[3,2,1,6,4,5] => [1,1,1,0,0,0,1,1,1,0,0,0] => 7
[3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 7
[3,2,4,1,5,6] => [1,1,1,0,0,1,0,0,1,0,1,0] => 4
[3,2,4,1,6,5] => [1,1,1,0,0,1,0,0,1,1,0,0] => 6
[3,2,4,5,1,6] => [1,1,1,0,0,1,0,1,0,0,1,0] => 4
[3,2,4,5,6,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 4
[3,2,4,6,1,5] => [1,1,1,0,0,1,0,1,1,0,0,0] => 6
[3,2,4,6,5,1] => [1,1,1,0,0,1,0,1,1,0,0,0] => 6
[3,2,5,1,4,6] => [1,1,1,0,0,1,1,0,0,0,1,0] => 6
[3,2,5,1,6,4] => [1,1,1,0,0,1,1,0,0,1,0,0] => 6
[3,2,5,4,1,6] => [1,1,1,0,0,1,1,0,0,0,1,0] => 6
[3,2,5,4,6,1] => [1,1,1,0,0,1,1,0,0,1,0,0] => 6
[3,2,5,6,1,4] => [1,1,1,0,0,1,1,0,1,0,0,0] => 6
[3,2,5,6,4,1] => [1,1,1,0,0,1,1,0,1,0,0,0] => 6
[3,2,6,1,4,5] => [1,1,1,0,0,1,1,1,0,0,0,0] => 7
[3,2,6,1,5,4] => [1,1,1,0,0,1,1,1,0,0,0,0] => 7
[3,2,6,4,1,5] => [1,1,1,0,0,1,1,1,0,0,0,0] => 7
[3,2,6,4,5,1] => [1,1,1,0,0,1,1,1,0,0,0,0] => 7
[3,2,6,5,1,4] => [1,1,1,0,0,1,1,1,0,0,0,0] => 7
[3,2,6,5,4,1] => [1,1,1,0,0,1,1,1,0,0,0,0] => 7
[3,4,1,2,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0] => 4
[3,4,1,2,6,5] => [1,1,1,0,1,0,0,0,1,1,0,0] => 6
[3,4,1,5,2,6] => [1,1,1,0,1,0,0,1,0,0,1,0] => 4
[3,4,1,5,6,2] => [1,1,1,0,1,0,0,1,0,1,0,0] => 4
[3,4,1,6,2,5] => [1,1,1,0,1,0,0,1,1,0,0,0] => 6
[3,4,1,6,5,2] => [1,1,1,0,1,0,0,1,1,0,0,0] => 6
[3,4,2,1,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0] => 4
[3,4,2,1,6,5] => [1,1,1,0,1,0,0,0,1,1,0,0] => 6
[3,4,2,5,1,6] => [1,1,1,0,1,0,0,1,0,0,1,0] => 4
[3,4,2,5,6,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 4
[3,4,2,6,1,5] => [1,1,1,0,1,0,0,1,1,0,0,0] => 6
[3,4,2,6,5,1] => [1,1,1,0,1,0,0,1,1,0,0,0] => 6
[3,4,5,1,2,6] => [1,1,1,0,1,0,1,0,0,0,1,0] => 4
[3,4,5,1,6,2] => [1,1,1,0,1,0,1,0,0,1,0,0] => 4
[3,4,5,2,1,6] => [1,1,1,0,1,0,1,0,0,0,1,0] => 4
[3,4,5,2,6,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 4
[3,4,5,6,1,2] => [1,1,1,0,1,0,1,0,1,0,0,0] => 4
[3,4,5,6,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0] => 4
[3,4,6,1,2,5] => [1,1,1,0,1,0,1,1,0,0,0,0] => 6
[3,4,6,1,5,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 6
[3,4,6,2,1,5] => [1,1,1,0,1,0,1,1,0,0,0,0] => 6
[3,4,6,2,5,1] => [1,1,1,0,1,0,1,1,0,0,0,0] => 6
[3,4,6,5,1,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 6
[3,4,6,5,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0] => 6
[3,5,1,2,4,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => 6
[3,5,1,2,6,4] => [1,1,1,0,1,1,0,0,0,1,0,0] => 6
[3,5,1,4,2,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => 6
[3,5,1,4,6,2] => [1,1,1,0,1,1,0,0,0,1,0,0] => 6
[3,5,1,6,2,4] => [1,1,1,0,1,1,0,0,1,0,0,0] => 6
[3,5,1,6,4,2] => [1,1,1,0,1,1,0,0,1,0,0,0] => 6
[3,5,2,1,4,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => 6
[3,5,2,1,6,4] => [1,1,1,0,1,1,0,0,0,1,0,0] => 6
[3,5,2,4,1,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => 6
[3,5,2,4,6,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 6
[3,5,2,6,1,4] => [1,1,1,0,1,1,0,0,1,0,0,0] => 6
[3,5,2,6,4,1] => [1,1,1,0,1,1,0,0,1,0,0,0] => 6
[3,5,4,1,2,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => 6
[3,5,4,1,6,2] => [1,1,1,0,1,1,0,0,0,1,0,0] => 6
[3,5,4,2,1,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => 6
[3,5,4,2,6,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 6
[3,5,4,6,1,2] => [1,1,1,0,1,1,0,0,1,0,0,0] => 6
[3,5,4,6,2,1] => [1,1,1,0,1,1,0,0,1,0,0,0] => 6
[3,5,6,1,2,4] => [1,1,1,0,1,1,0,1,0,0,0,0] => 6
[3,5,6,1,4,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 6
[3,5,6,2,1,4] => [1,1,1,0,1,1,0,1,0,0,0,0] => 6
[3,5,6,2,4,1] => [1,1,1,0,1,1,0,1,0,0,0,0] => 6
[3,5,6,4,1,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 6
[3,5,6,4,2,1] => [1,1,1,0,1,1,0,1,0,0,0,0] => 6
[3,6,1,2,4,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => 7
[3,6,1,2,5,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => 7
[3,6,1,4,2,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => 7
[3,6,1,4,5,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 7
[3,6,1,5,2,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => 7
[3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 7
[3,6,2,1,4,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => 7
[3,6,2,1,5,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => 7
[3,6,2,4,1,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => 7
[3,6,2,4,5,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 7
[3,6,2,5,1,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => 7
[3,6,2,5,4,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 7
[3,6,4,1,2,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => 7
[3,6,4,1,5,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 7
[3,6,4,2,1,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => 7
[3,6,4,2,5,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 7
[3,6,4,5,1,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 7
[3,6,4,5,2,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 7
[3,6,5,1,2,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => 7
[3,6,5,1,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 7
[3,6,5,2,1,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => 7
[3,6,5,2,4,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 7
[3,6,5,4,1,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 7
[3,6,5,4,2,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 7
[4,1,2,3,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 5
[4,1,2,3,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 7
[4,1,2,5,3,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => 5
[4,1,2,5,6,3] => [1,1,1,1,0,0,0,1,0,1,0,0] => 5
[4,1,2,6,3,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 7
[4,1,2,6,5,3] => [1,1,1,1,0,0,0,1,1,0,0,0] => 7
[4,1,3,2,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 5
[4,1,3,2,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 7
[4,1,3,5,2,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => 5
[4,1,3,5,6,2] => [1,1,1,1,0,0,0,1,0,1,0,0] => 5
[4,1,3,6,2,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 7
[4,1,3,6,5,2] => [1,1,1,1,0,0,0,1,1,0,0,0] => 7
[4,1,5,2,3,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => 5
[4,1,5,2,6,3] => [1,1,1,1,0,0,1,0,0,1,0,0] => 5
[4,1,5,3,2,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => 5
[4,1,5,3,6,2] => [1,1,1,1,0,0,1,0,0,1,0,0] => 5
[4,1,5,6,2,3] => [1,1,1,1,0,0,1,0,1,0,0,0] => 5
[4,1,5,6,3,2] => [1,1,1,1,0,0,1,0,1,0,0,0] => 5
[4,1,6,2,3,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => 7
[4,1,6,2,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => 7
[4,1,6,3,2,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => 7
[4,1,6,3,5,2] => [1,1,1,1,0,0,1,1,0,0,0,0] => 7
[4,1,6,5,2,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => 7
[4,1,6,5,3,2] => [1,1,1,1,0,0,1,1,0,0,0,0] => 7
[4,2,1,3,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 5
[4,2,1,3,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 7
[4,2,1,5,3,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => 5
[4,2,1,5,6,3] => [1,1,1,1,0,0,0,1,0,1,0,0] => 5
[4,2,1,6,3,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 7
[4,2,1,6,5,3] => [1,1,1,1,0,0,0,1,1,0,0,0] => 7
[4,2,3,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 5
[4,2,3,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 7
[4,2,3,5,1,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => 5
[4,2,3,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 5
[4,2,3,6,1,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 7
[4,2,3,6,5,1] => [1,1,1,1,0,0,0,1,1,0,0,0] => 7
[4,2,5,1,3,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => 5
[4,2,5,1,6,3] => [1,1,1,1,0,0,1,0,0,1,0,0] => 5
[4,2,5,3,1,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => 5
[4,2,5,3,6,1] => [1,1,1,1,0,0,1,0,0,1,0,0] => 5
[4,2,5,6,1,3] => [1,1,1,1,0,0,1,0,1,0,0,0] => 5
[4,2,5,6,3,1] => [1,1,1,1,0,0,1,0,1,0,0,0] => 5
[4,2,6,1,3,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => 7
[4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => 7
[4,2,6,3,1,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => 7
[4,2,6,3,5,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => 7
[4,2,6,5,1,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => 7
[4,2,6,5,3,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => 7
[4,3,1,2,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 5
[4,3,1,2,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 7
[4,3,1,5,2,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => 5
[4,3,1,5,6,2] => [1,1,1,1,0,0,0,1,0,1,0,0] => 5
[4,3,1,6,2,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 7
[4,3,1,6,5,2] => [1,1,1,1,0,0,0,1,1,0,0,0] => 7
[4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 5
[4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 7
[4,3,2,5,1,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => 5
[4,3,2,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 5
[4,3,2,6,1,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 7
[4,3,2,6,5,1] => [1,1,1,1,0,0,0,1,1,0,0,0] => 7
[4,3,5,1,2,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => 5
[4,3,5,1,6,2] => [1,1,1,1,0,0,1,0,0,1,0,0] => 5
[4,3,5,2,1,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => 5
[4,3,5,2,6,1] => [1,1,1,1,0,0,1,0,0,1,0,0] => 5
[4,3,5,6,1,2] => [1,1,1,1,0,0,1,0,1,0,0,0] => 5
[4,3,5,6,2,1] => [1,1,1,1,0,0,1,0,1,0,0,0] => 5
[4,3,6,1,2,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => 7
[4,3,6,1,5,2] => [1,1,1,1,0,0,1,1,0,0,0,0] => 7
[4,3,6,2,1,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => 7
[4,3,6,2,5,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => 7
[4,3,6,5,1,2] => [1,1,1,1,0,0,1,1,0,0,0,0] => 7
[4,3,6,5,2,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => 7
[4,5,1,2,3,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => 5
[4,5,1,2,6,3] => [1,1,1,1,0,1,0,0,0,1,0,0] => 5
[4,5,1,3,2,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => 5
[4,5,1,3,6,2] => [1,1,1,1,0,1,0,0,0,1,0,0] => 5
[4,5,1,6,2,3] => [1,1,1,1,0,1,0,0,1,0,0,0] => 5
[4,5,1,6,3,2] => [1,1,1,1,0,1,0,0,1,0,0,0] => 5
[4,5,2,1,3,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => 5
[4,5,2,1,6,3] => [1,1,1,1,0,1,0,0,0,1,0,0] => 5
[4,5,2,3,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => 5
[4,5,2,3,6,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 5
[4,5,2,6,1,3] => [1,1,1,1,0,1,0,0,1,0,0,0] => 5
[4,5,2,6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0] => 5
[4,5,3,1,2,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => 5
[4,5,3,1,6,2] => [1,1,1,1,0,1,0,0,0,1,0,0] => 5
[4,5,3,2,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => 5
[4,5,3,2,6,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 5
[4,5,3,6,1,2] => [1,1,1,1,0,1,0,0,1,0,0,0] => 5
[4,5,3,6,2,1] => [1,1,1,1,0,1,0,0,1,0,0,0] => 5
[4,5,6,1,2,3] => [1,1,1,1,0,1,0,1,0,0,0,0] => 5
[4,5,6,1,3,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 5
[4,5,6,2,1,3] => [1,1,1,1,0,1,0,1,0,0,0,0] => 5
[4,5,6,2,3,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => 5
[4,5,6,3,1,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 5
[4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => 5
[4,6,1,2,3,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => 7
[4,6,1,2,5,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => 7
[4,6,1,3,2,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => 7
[4,6,1,3,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 7
[4,6,1,5,2,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => 7
[4,6,1,5,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 7
[4,6,2,1,3,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => 7
[4,6,2,1,5,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => 7
[4,6,2,3,1,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => 7
[4,6,2,3,5,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 7
[4,6,2,5,1,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => 7
[4,6,2,5,3,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 7
[4,6,3,1,2,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => 7
[4,6,3,1,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 7
[4,6,3,2,1,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => 7
[4,6,3,2,5,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 7
[4,6,3,5,1,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 7
[4,6,3,5,2,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 7
[4,6,5,1,2,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => 7
[4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 7
[4,6,5,2,1,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => 7
[4,6,5,2,3,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 7
[4,6,5,3,1,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 7
[4,6,5,3,2,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 7
[5,1,2,3,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[5,1,2,3,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => 6
[5,1,2,4,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[5,1,2,4,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => 6
[5,1,2,6,3,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => 6
[5,1,2,6,4,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => 6
[5,1,3,2,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[5,1,3,2,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => 6
[5,1,3,4,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[5,1,3,4,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => 6
[5,1,3,6,2,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => 6
[5,1,3,6,4,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => 6
[5,1,4,2,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[5,1,4,2,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => 6
[5,1,4,3,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[5,1,4,3,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => 6
[5,1,4,6,2,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => 6
[5,1,4,6,3,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => 6
[5,1,6,2,3,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => 6
[5,1,6,2,4,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => 6
[5,1,6,3,2,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => 6
[5,1,6,3,4,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 6
[5,1,6,4,2,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => 6
[5,1,6,4,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 6
[5,2,1,3,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[5,2,1,3,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => 6
[5,2,1,4,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[5,2,1,4,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => 6
[5,2,1,6,3,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => 6
[5,2,1,6,4,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => 6
[5,2,3,1,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[5,2,3,1,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => 6
[5,2,3,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[5,2,3,4,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 6
[5,2,3,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => 6
[5,2,3,6,4,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 6
[5,2,4,1,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[5,2,4,1,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => 6
[5,2,4,3,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[5,2,4,3,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 6
[5,2,4,6,1,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => 6
[5,2,4,6,3,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 6
[5,2,6,1,3,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => 6
[5,2,6,1,4,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => 6
[5,2,6,3,1,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => 6
[5,2,6,3,4,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 6
[5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => 6
[5,2,6,4,3,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 6
[5,3,1,2,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[5,3,1,2,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => 6
[5,3,1,4,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[5,3,1,4,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => 6
[5,3,1,6,2,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => 6
[5,3,1,6,4,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => 6
[5,3,2,1,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[5,3,2,1,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => 6
[5,3,2,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[5,3,2,4,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 6
[5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => 6
[5,3,2,6,4,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 6
[5,3,4,1,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[5,3,4,1,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => 6
[5,3,4,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[5,3,4,2,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 6
[5,3,4,6,1,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => 6
[5,3,4,6,2,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 6
[5,3,6,1,2,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => 6
[5,3,6,1,4,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 6
[5,3,6,2,1,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => 6
[5,3,6,2,4,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 6
[5,3,6,4,1,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 6
[5,3,6,4,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 6
[5,4,1,2,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[5,4,1,2,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => 6
[5,4,1,3,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[5,4,1,3,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => 6
[5,4,1,6,2,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => 6
[5,4,1,6,3,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => 6
[5,4,2,1,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[5,4,2,1,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => 6
[5,4,2,3,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[5,4,2,3,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 6
[5,4,2,6,1,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => 6
[5,4,2,6,3,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 6
[5,4,3,1,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[5,4,3,1,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => 6
[5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[5,4,3,2,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 6
[5,4,3,6,1,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => 6
[5,4,3,6,2,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 6
[5,4,6,1,2,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => 6
[5,4,6,1,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 6
[5,4,6,2,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => 6
[5,4,6,2,3,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 6
[5,4,6,3,1,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 6
[5,4,6,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 6
[5,6,1,2,3,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 6
[5,6,1,2,4,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => 6
[5,6,1,3,2,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 6
[5,6,1,3,4,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 6
[5,6,1,4,2,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => 6
[5,6,1,4,3,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 6
[5,6,2,1,3,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 6
[5,6,2,1,4,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => 6
[5,6,2,3,1,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 6
[5,6,2,3,4,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 6
[5,6,2,4,1,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => 6
[5,6,2,4,3,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 6
[5,6,3,1,2,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 6
[5,6,3,1,4,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 6
[5,6,3,2,1,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 6
[5,6,3,2,4,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 6
[5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 6
[5,6,3,4,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 6
[5,6,4,1,2,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => 6
[5,6,4,1,3,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 6
[5,6,4,2,1,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => 6
[5,6,4,2,3,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 6
[5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 6
[5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 6
[6,1,2,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,1,2,3,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,1,2,4,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,1,2,4,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,1,2,5,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,1,2,5,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,1,3,2,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,1,3,2,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,1,3,4,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,1,3,4,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,1,3,5,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,1,3,5,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,1,4,2,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,1,4,2,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,1,4,3,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,1,4,3,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,1,4,5,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,1,4,5,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,1,5,2,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,1,5,2,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,1,5,3,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,1,5,3,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,1,5,4,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,1,5,4,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,2,1,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,2,1,3,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,2,1,4,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,2,1,4,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,2,1,5,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,2,1,5,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,2,3,1,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,2,3,1,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,2,3,4,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,2,3,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,2,3,5,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,2,3,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,2,4,1,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,2,4,1,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,2,4,3,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,2,4,3,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,2,4,5,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,2,4,5,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,2,5,1,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,2,5,1,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,2,5,3,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,2,5,3,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,2,5,4,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,3,1,2,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,3,1,2,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,3,1,4,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,3,1,4,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,3,1,5,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,3,1,5,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,3,2,1,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,3,2,1,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,3,2,4,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,3,2,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,3,2,5,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,3,2,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,3,4,1,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,3,4,1,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,3,4,2,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,3,4,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,3,4,5,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,3,4,5,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,3,5,1,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,3,5,1,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,3,5,2,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,3,5,2,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,3,5,4,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,3,5,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,4,1,2,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,4,1,2,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,4,1,3,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,4,1,3,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,4,1,5,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,4,1,5,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,4,2,1,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,4,2,1,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,4,2,3,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,4,2,3,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,4,2,5,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,4,2,5,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,4,3,1,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,4,3,1,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,4,3,2,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,4,3,5,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,4,3,5,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,4,5,1,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,4,5,1,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,4,5,2,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,4,5,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,4,5,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,4,5,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,5,1,2,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,5,1,2,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,5,1,3,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,5,1,3,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,5,1,4,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,5,1,4,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,5,2,1,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,5,2,1,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,5,2,3,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,5,2,3,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,5,2,4,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,5,2,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,5,3,1,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,5,3,1,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,5,3,2,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,5,3,2,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,5,3,4,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,5,4,1,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,5,4,1,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,5,4,2,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,5,4,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,5,4,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7
[1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,2,3,4,5,7,6] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 4
[1,2,3,4,6,5,7] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 4
[1,2,3,4,6,7,5] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,2,3,4,7,5,6] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 5
[1,2,3,4,7,6,5] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 5
[1,2,3,5,4,6,7] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 4
[1,2,3,5,4,7,6] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 6
[1,2,3,5,6,4,7] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 4
[1,2,3,5,6,7,4] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,2,3,5,7,4,6] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 6
[1,2,3,5,7,6,4] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 6
[1,2,3,6,4,5,7] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 5
[1,2,3,6,4,7,5] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,2,3,6,5,4,7] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 5
[1,2,3,6,5,7,4] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,2,3,6,7,4,5] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 5
[1,2,3,6,7,5,4] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 5
[1,2,3,7,4,5,6] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,2,3,7,4,6,5] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,2,3,7,5,4,6] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,2,3,7,5,6,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,2,3,7,6,4,5] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,2,3,7,6,5,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,2,4,3,5,6,7] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4
[1,2,4,3,5,7,6] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 6
[1,2,4,3,6,5,7] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 6
[1,2,4,3,6,7,5] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 6
[1,2,4,3,7,5,6] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 7
[1,2,4,3,7,6,5] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 7
[1,2,4,5,3,6,7] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,2,4,5,3,7,6] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 6
[1,2,4,5,6,3,7] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,2,4,5,6,7,3] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,2,4,5,7,3,6] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 6
[1,2,4,5,7,6,3] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 6
[1,2,4,6,3,5,7] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 6
[1,2,4,6,3,7,5] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 6
[1,2,4,6,5,3,7] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 6
[1,2,4,6,5,7,3] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 6
[1,2,4,6,7,3,5] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 6
[1,2,4,6,7,5,3] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 6
[1,2,4,7,3,5,6] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 7
[1,2,4,7,3,6,5] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 7
[1,2,4,7,5,3,6] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 7
[1,2,4,7,5,6,3] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 7
[1,2,4,7,6,3,5] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 7
[1,2,4,7,6,5,3] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 7
[1,2,5,3,4,6,7] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 5
[1,2,5,3,4,7,6] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 7
[1,2,5,3,6,4,7] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 5
[1,2,5,3,6,7,4] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 5
[1,2,5,3,7,4,6] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 7
[1,2,5,3,7,6,4] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 7
[1,2,5,4,3,6,7] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 5
[1,2,5,4,3,7,6] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 7
[1,2,5,4,6,3,7] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 5
[1,2,5,4,6,7,3] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 5
[1,2,5,4,7,3,6] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 7
[1,2,5,4,7,6,3] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 7
[1,2,5,6,3,4,7] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 5
[1,2,5,6,3,7,4] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 5
[1,2,5,6,4,3,7] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 5
[1,2,5,6,4,7,3] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 5
[1,2,5,6,7,3,4] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 5
[1,2,5,6,7,4,3] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 5
[1,2,5,7,3,4,6] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 7
[1,2,5,7,3,6,4] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 7
[1,2,5,7,4,3,6] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 7
[1,2,5,7,4,6,3] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 7
[1,2,5,7,6,3,4] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 7
[1,2,5,7,6,4,3] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 7
[1,2,6,3,4,5,7] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 6
[1,2,6,3,4,7,5] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 6
[1,2,6,3,5,4,7] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 6
[1,2,6,3,5,7,4] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 6
[1,2,6,3,7,4,5] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 6
[1,2,6,3,7,5,4] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 6
[1,2,6,4,3,5,7] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 6
[1,2,6,4,3,7,5] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 6
[1,2,6,4,5,3,7] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 6
[1,2,6,4,5,7,3] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 6
[1,2,6,4,7,3,5] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 6
[1,2,6,4,7,5,3] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 6
[1,2,6,5,3,4,7] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 6
[1,2,6,5,3,7,4] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 6
[1,2,6,5,4,3,7] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 6
[1,2,6,5,4,7,3] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 6
[1,2,6,5,7,3,4] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 6
[1,2,6,5,7,4,3] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 6
[1,2,6,7,3,4,5] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 6
[1,2,6,7,3,5,4] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 6
[1,2,6,7,4,3,5] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 6
[1,2,6,7,4,5,3] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 6
[1,2,6,7,5,3,4] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 6
[1,2,6,7,5,4,3] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 6
[1,2,7,3,4,5,6] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,2,7,3,4,6,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,2,7,3,5,4,6] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,2,7,3,5,6,4] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,2,7,3,6,4,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,2,7,3,6,5,4] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,2,7,4,3,5,6] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,2,7,4,3,6,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,2,7,4,5,3,6] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,2,7,4,5,6,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,2,7,4,6,3,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,2,7,4,6,5,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,2,7,5,3,4,6] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,2,7,5,3,6,4] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,2,7,5,4,3,6] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,2,7,5,4,6,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,2,7,5,6,3,4] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,2,7,5,6,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,2,7,6,3,4,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,2,7,6,3,5,4] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,2,7,6,4,3,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,2,7,6,4,5,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,2,7,6,5,3,4] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,3,2,4,5,6,7] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 4
[1,3,2,4,5,7,6] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 6
[1,3,2,4,6,5,7] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 6
[1,3,2,4,6,7,5] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 6
[1,3,2,4,7,5,6] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 7
[1,3,2,4,7,6,5] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 7
[1,3,2,5,4,6,7] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 6
[1,3,2,5,4,7,6] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 8
[1,3,2,5,6,4,7] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 6
[1,3,2,5,6,7,4] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 6
[1,3,2,5,7,4,6] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 8
[1,3,2,5,7,6,4] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 8
[1,3,2,6,4,5,7] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 7
[1,3,2,6,4,7,5] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 7
[1,3,2,6,5,4,7] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 7
[1,3,2,6,5,7,4] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 7
[1,3,2,6,7,4,5] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 7
[1,3,2,6,7,5,4] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 7
[1,3,2,7,4,5,6] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 8
[1,3,2,7,4,6,5] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 8
[1,3,2,7,5,4,6] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 8
[1,3,2,7,5,6,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 8
[1,3,2,7,6,4,5] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 8
[1,3,2,7,6,5,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 8
[1,3,4,2,5,6,7] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 4
[1,3,4,2,5,7,6] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 6
[1,3,4,2,6,5,7] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 6
[1,3,4,2,6,7,5] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 6
[1,3,4,2,7,5,6] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 7
[1,3,4,2,7,6,5] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 7
[1,3,4,5,2,6,7] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,3,4,5,2,7,6] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 6
[1,3,4,5,6,2,7] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 4
[1,3,4,5,6,7,2] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 4
[1,3,4,5,7,2,6] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 6
[1,3,4,5,7,6,2] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 6
[1,3,4,6,2,5,7] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 6
[1,3,4,6,2,7,5] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 6
[1,3,4,6,5,2,7] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 6
[1,3,4,6,5,7,2] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 6
[1,3,4,6,7,2,5] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 6
[1,3,4,6,7,5,2] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 6
[1,3,4,7,2,5,6] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 7
[1,3,4,7,2,6,5] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 7
[1,3,4,7,5,2,6] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 7
[1,3,4,7,5,6,2] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 7
[1,3,4,7,6,2,5] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 7
[1,3,4,7,6,5,2] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 7
[1,3,5,2,4,6,7] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 6
[1,3,5,2,4,7,6] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 8
[1,3,5,2,6,4,7] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 6
[1,3,5,2,6,7,4] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 6
[1,3,5,2,7,4,6] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 8
[1,3,5,2,7,6,4] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 8
[1,3,5,4,2,6,7] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 6
[1,3,5,4,2,7,6] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 8
[1,3,5,4,6,2,7] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 6
[1,3,5,4,6,7,2] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 6
[1,3,5,4,7,2,6] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 8
[1,3,5,4,7,6,2] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 8
[1,3,5,6,2,4,7] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 6
[1,3,5,6,2,7,4] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 6
[1,3,5,6,4,2,7] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 6
[1,3,5,6,4,7,2] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 6
[1,3,5,6,7,2,4] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 6
[1,3,5,6,7,4,2] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 6
[1,3,5,7,2,4,6] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 8
[1,3,5,7,2,6,4] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 8
[1,3,5,7,4,2,6] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 8
[1,3,5,7,4,6,2] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 8
[1,3,5,7,6,2,4] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 8
[1,3,5,7,6,4,2] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 8
[1,3,6,2,4,5,7] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 7
[1,3,6,2,4,7,5] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 7
[1,3,6,2,5,4,7] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 7
[1,3,6,2,5,7,4] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 7
[1,3,6,2,7,4,5] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 7
[1,3,6,2,7,5,4] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 7
[1,3,6,4,2,5,7] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 7
[1,3,6,4,2,7,5] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 7
[1,3,6,4,5,2,7] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 7
[1,3,6,4,5,7,2] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 7
[1,3,6,4,7,2,5] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 7
[1,3,6,4,7,5,2] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 7
[1,3,6,5,2,4,7] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 7
[1,3,6,5,2,7,4] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 7
[1,3,6,5,4,2,7] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 7
[1,3,6,5,4,7,2] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 7
[1,3,6,5,7,2,4] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 7
[1,3,6,5,7,4,2] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 7
[1,3,6,7,2,4,5] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 7
[1,3,6,7,2,5,4] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 7
[1,3,6,7,4,2,5] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 7
[1,3,6,7,4,5,2] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 7
[1,3,6,7,5,2,4] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 7
[1,3,6,7,5,4,2] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 7
[1,3,7,2,4,5,6] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 8
[1,3,7,2,4,6,5] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 8
[1,3,7,2,5,4,6] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 8
[1,3,7,2,5,6,4] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 8
[1,3,7,2,6,4,5] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 8
[1,3,7,2,6,5,4] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 8
[1,3,7,4,2,5,6] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 8
[1,3,7,4,2,6,5] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 8
[1,3,7,4,5,2,6] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 8
[1,3,7,4,5,6,2] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 8
[1,3,7,4,6,2,5] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 8
[1,3,7,4,6,5,2] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 8
[1,3,7,5,2,4,6] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 8
[1,3,7,5,2,6,4] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 8
[1,3,7,5,4,2,6] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 8
[1,3,7,5,4,6,2] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 8
[1,3,7,5,6,2,4] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 8
[1,3,7,5,6,4,2] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 8
[1,3,7,6,2,4,5] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 8
[1,3,7,6,2,5,4] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 8
[1,3,7,6,4,2,5] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 8
[1,3,7,6,4,5,2] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 8
[1,3,7,6,5,2,4] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 8
[1,3,7,6,5,4,2] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 8
[1,4,2,3,5,6,7] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 5
[1,4,2,3,5,7,6] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 7
[1,4,2,3,6,5,7] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 7
[1,4,2,3,6,7,5] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 7
[1,4,2,3,7,5,6] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 8
[1,4,2,3,7,6,5] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 8
[1,4,2,5,3,6,7] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 5
[1,4,2,5,3,7,6] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 7
[1,4,2,5,6,3,7] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 5
[1,4,2,5,6,7,3] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 5
[1,4,2,5,7,3,6] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 7
[1,4,2,5,7,6,3] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 7
[1,4,2,6,3,5,7] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 7
[1,4,2,6,3,7,5] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 7
[1,4,2,6,5,3,7] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 7
[1,4,2,6,5,7,3] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 7
[1,4,2,6,7,3,5] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 7
[1,4,2,6,7,5,3] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 7
[1,4,2,7,3,5,6] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 8
[1,4,2,7,3,6,5] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 8
[1,4,2,7,5,3,6] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 8
[1,4,2,7,5,6,3] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 8
[1,4,2,7,6,3,5] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 8
[1,4,2,7,6,5,3] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 8
[1,4,3,2,5,6,7] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 5
[1,4,3,2,5,7,6] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 7
[1,4,3,2,6,5,7] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 7
[1,4,3,2,6,7,5] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 7
[1,4,3,2,7,5,6] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 8
[1,4,3,2,7,6,5] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 8
[1,4,3,5,2,6,7] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 5
[1,4,3,5,2,7,6] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 7
[1,4,3,5,6,2,7] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 5
[1,4,3,5,6,7,2] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 5
[1,4,3,5,7,2,6] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 7
[1,4,3,5,7,6,2] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 7
[1,4,3,6,2,5,7] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 7
[1,4,3,6,2,7,5] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 7
[1,4,3,6,5,2,7] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 7
[1,4,3,6,5,7,2] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 7
[1,4,3,6,7,2,5] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 7
[1,4,3,6,7,5,2] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 7
[1,4,3,7,2,5,6] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 8
[1,4,3,7,2,6,5] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 8
[1,4,3,7,5,2,6] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 8
[1,4,3,7,5,6,2] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 8
[1,4,3,7,6,2,5] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 8
[1,4,3,7,6,5,2] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 8
[1,4,5,2,3,6,7] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 5
[1,4,5,2,3,7,6] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 7
[1,4,5,2,6,3,7] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 5
[1,4,5,2,6,7,3] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 5
[1,4,5,2,7,3,6] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 7
[1,4,5,2,7,6,3] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 7
[1,4,5,3,2,6,7] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 5
[1,4,5,3,2,7,6] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 7
[1,4,5,3,6,2,7] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 5
[1,4,5,3,6,7,2] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 5
[1,4,5,3,7,2,6] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 7
[1,4,5,3,7,6,2] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 7
[1,4,5,6,2,3,7] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 5
[1,4,5,6,2,7,3] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 5
[1,4,5,6,3,2,7] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 5
[1,4,5,6,3,7,2] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 5
[1,4,5,6,7,2,3] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 5
[1,4,5,6,7,3,2] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 5
[1,4,5,7,2,3,6] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 7
[1,4,5,7,2,6,3] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 7
[1,4,5,7,3,2,6] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 7
[1,4,5,7,3,6,2] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 7
[1,4,5,7,6,2,3] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 7
[1,4,5,7,6,3,2] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 7
[1,4,6,2,3,5,7] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 7
[1,4,6,2,3,7,5] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 7
[1,4,6,2,5,3,7] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 7
[1,4,6,2,5,7,3] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 7
[1,4,6,2,7,3,5] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 7
[1,4,6,2,7,5,3] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 7
[1,4,6,3,2,5,7] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 7
[1,4,6,3,2,7,5] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 7
[1,4,6,3,5,2,7] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 7
[1,4,6,3,5,7,2] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 7
[1,4,6,3,7,2,5] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 7
[1,4,6,3,7,5,2] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 7
[1,4,6,5,2,3,7] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 7
[1,4,6,5,2,7,3] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 7
[1,4,6,5,3,2,7] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 7
[1,4,6,5,3,7,2] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 7
[1,4,6,5,7,2,3] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 7
[1,4,6,5,7,3,2] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 7
[1,4,6,7,2,3,5] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 7
[1,4,6,7,2,5,3] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 7
[1,4,6,7,3,2,5] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 7
[1,4,6,7,3,5,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 7
[1,4,6,7,5,2,3] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 7
[1,4,6,7,5,3,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 7
[1,4,7,2,3,5,6] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 8
[1,4,7,2,3,6,5] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 8
[1,4,7,2,5,3,6] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 8
[1,4,7,2,5,6,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 8
[1,4,7,2,6,3,5] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 8
[1,4,7,2,6,5,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 8
[1,4,7,3,2,5,6] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 8
[1,4,7,3,2,6,5] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 8
[1,4,7,3,5,2,6] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 8
[1,4,7,3,5,6,2] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 8
[1,4,7,3,6,2,5] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 8
[1,4,7,3,6,5,2] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 8
[1,4,7,5,2,3,6] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 8
[1,4,7,5,2,6,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 8
[1,4,7,5,3,2,6] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 8
[1,4,7,5,3,6,2] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 8
[1,4,7,5,6,2,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 8
[1,4,7,5,6,3,2] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 8
[1,4,7,6,2,3,5] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 8
[1,4,7,6,2,5,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 8
[1,4,7,6,3,2,5] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 8
[1,4,7,6,3,5,2] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 8
[1,4,7,6,5,2,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 8
[1,4,7,6,5,3,2] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 8
[1,5,2,3,4,6,7] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 6
[1,5,2,3,4,7,6] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 8
[1,5,2,3,6,4,7] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 6
[1,5,2,3,6,7,4] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 6
[1,5,2,3,7,4,6] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 8
[1,5,2,3,7,6,4] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 8
[1,5,2,4,3,6,7] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 6
[1,5,2,4,3,7,6] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 8
[1,5,2,4,6,3,7] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 6
[1,5,2,4,6,7,3] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 6
[1,5,2,4,7,3,6] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 8
[1,5,2,4,7,6,3] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 8
[1,5,2,6,3,4,7] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 6
[1,5,2,6,3,7,4] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 6
[1,5,2,6,4,3,7] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 6
[1,5,2,6,4,7,3] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 6
[1,5,2,6,7,3,4] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 6
[1,5,2,6,7,4,3] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 6
[1,5,2,7,3,4,6] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 8
[1,5,2,7,3,6,4] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 8
[1,5,2,7,4,3,6] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 8
[1,5,2,7,4,6,3] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 8
[1,5,2,7,6,3,4] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 8
[1,5,2,7,6,4,3] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 8
[1,5,3,2,4,6,7] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 6
[1,5,3,2,4,7,6] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 8
[1,5,3,2,6,4,7] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 6
[1,5,3,2,6,7,4] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 6
[1,5,3,2,7,4,6] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 8
[1,5,3,2,7,6,4] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 8
[1,5,3,4,2,6,7] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 6
[1,5,3,4,2,7,6] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 8
[1,5,3,4,6,2,7] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 6
[1,5,3,4,6,7,2] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 6
[1,5,3,4,7,2,6] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 8
[1,5,3,4,7,6,2] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 8
[1,5,3,6,2,4,7] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 6
[1,5,3,6,2,7,4] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 6
[1,5,3,6,4,2,7] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 6
[1,5,3,6,4,7,2] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 6
[1,5,3,6,7,2,4] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 6
[1,5,3,6,7,4,2] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 6
[1,5,3,7,2,4,6] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 8
[1,5,3,7,2,6,4] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 8
[1,5,3,7,4,2,6] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 8
[1,5,3,7,4,6,2] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 8
[1,5,3,7,6,2,4] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 8
[1,5,3,7,6,4,2] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 8
[1,5,4,2,3,6,7] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 6
[1,5,4,2,3,7,6] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 8
[1,5,4,2,6,3,7] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 6
[1,5,4,2,6,7,3] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 6
[1,5,4,2,7,3,6] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 8
[1,5,4,2,7,6,3] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 8
[1,5,4,3,2,6,7] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 6
[1,5,4,3,2,7,6] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 8
[1,5,4,3,6,2,7] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 6
[1,5,4,3,6,7,2] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 6
[1,5,4,3,7,2,6] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 8
[1,5,4,3,7,6,2] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 8
[1,5,4,6,2,3,7] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 6
[1,5,4,6,2,7,3] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 6
[1,5,4,6,3,2,7] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 6
[1,5,4,6,3,7,2] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 6
[1,5,4,6,7,2,3] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 6
[1,5,4,6,7,3,2] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 6
[1,5,4,7,2,3,6] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 8
[1,5,4,7,2,6,3] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 8
[1,5,4,7,3,2,6] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 8
[1,5,4,7,3,6,2] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 8
[1,5,4,7,6,2,3] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 8
[1,5,4,7,6,3,2] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 8
[1,5,6,2,3,4,7] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 6
[1,5,6,2,3,7,4] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 6
[1,5,6,2,4,3,7] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 6
[1,5,6,2,4,7,3] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 6
[1,5,6,2,7,3,4] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 6
[1,5,6,2,7,4,3] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 6
[1,5,6,3,2,4,7] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 6
[1,5,6,3,2,7,4] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 6
[1,5,6,3,4,2,7] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 6
[1,5,6,3,4,7,2] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 6
[1,5,6,3,7,2,4] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 6
[1,5,6,3,7,4,2] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 6
[1,5,6,4,2,3,7] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 6
[1,5,6,4,2,7,3] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 6
[1,5,6,4,3,2,7] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 6
[1,5,6,4,3,7,2] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 6
[1,5,6,4,7,2,3] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 6
[1,5,6,4,7,3,2] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 6
[1,5,6,7,2,3,4] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 6
[1,5,6,7,2,4,3] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 6
[1,5,6,7,3,2,4] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 6
[1,5,6,7,3,4,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 6
[1,5,6,7,4,2,3] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 6
[1,5,6,7,4,3,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 6
[1,5,7,2,3,4,6] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 8
[1,5,7,2,3,6,4] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 8
[1,5,7,2,4,3,6] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 8
[1,5,7,2,4,6,3] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 8
[1,5,7,2,6,3,4] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 8
[1,5,7,2,6,4,3] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 8
[1,5,7,3,2,4,6] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 8
[1,5,7,3,2,6,4] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 8
[1,5,7,3,4,2,6] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 8
[1,5,7,3,4,6,2] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 8
[1,5,7,3,6,2,4] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 8
[1,5,7,3,6,4,2] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 8
[1,5,7,4,2,3,6] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 8
[1,5,7,4,2,6,3] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 8
[1,5,7,4,3,2,6] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 8
[1,5,7,4,3,6,2] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 8
[1,5,7,4,6,2,3] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 8
[1,5,7,4,6,3,2] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 8
[1,5,7,6,2,3,4] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 8
[1,5,7,6,2,4,3] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 8
[1,5,7,6,3,2,4] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 8
[1,5,7,6,3,4,2] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 8
[1,5,7,6,4,2,3] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 8
[1,5,7,6,4,3,2] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 8
[1,6,2,3,4,5,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[1,6,2,3,4,7,5] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 7
[1,6,2,3,5,4,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[1,6,2,3,5,7,4] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 7
[1,6,2,3,7,4,5] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 7
[1,6,2,3,7,5,4] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 7
[1,6,2,4,3,5,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[1,6,2,4,3,7,5] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 7
[1,6,2,4,5,3,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[1,6,2,4,5,7,3] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 7
[1,6,2,4,7,3,5] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 7
[1,6,2,4,7,5,3] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 7
[1,6,2,5,3,4,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[1,6,2,5,3,7,4] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 7
[1,6,2,5,4,3,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[1,6,2,5,4,7,3] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 7
[1,6,2,5,7,3,4] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 7
[1,6,2,5,7,4,3] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 7
[1,6,2,7,3,4,5] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 7
[1,6,2,7,3,5,4] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 7
[1,6,2,7,4,3,5] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 7
[1,6,2,7,4,5,3] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 7
[1,6,2,7,5,3,4] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 7
[1,6,2,7,5,4,3] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 7
[1,6,3,2,4,5,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[1,6,3,2,4,7,5] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 7
[1,6,3,2,5,4,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[1,6,3,2,5,7,4] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 7
[1,6,3,2,7,4,5] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 7
[1,6,3,2,7,5,4] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 7
[1,6,3,4,2,5,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[1,6,3,4,2,7,5] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 7
[1,6,3,4,5,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[1,6,3,4,5,7,2] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 7
[1,6,3,4,7,2,5] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 7
[1,6,3,4,7,5,2] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 7
[1,6,3,5,2,4,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[1,6,3,5,2,7,4] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 7
[1,6,3,5,4,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[1,6,3,5,4,7,2] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 7
[1,6,3,5,7,2,4] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 7
[1,6,3,5,7,4,2] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 7
[1,6,3,7,2,4,5] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 7
[1,6,3,7,2,5,4] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 7
[1,6,3,7,4,2,5] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 7
[1,6,3,7,4,5,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 7
[1,6,3,7,5,2,4] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 7
[1,6,3,7,5,4,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 7
[1,6,4,2,3,5,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[1,6,4,2,3,7,5] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 7
[1,6,4,2,5,3,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[1,6,4,2,5,7,3] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 7
[1,6,4,2,7,3,5] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 7
[1,6,4,2,7,5,3] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 7
[1,6,4,3,2,5,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[1,6,4,3,2,7,5] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 7
[1,6,4,3,5,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[1,6,4,3,5,7,2] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 7
[1,6,4,3,7,2,5] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 7
[1,6,4,3,7,5,2] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 7
[1,6,4,5,2,3,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[1,6,4,5,2,7,3] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 7
[1,6,4,5,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[1,6,4,5,3,7,2] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 7
[1,6,4,5,7,2,3] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 7
[1,6,4,5,7,3,2] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 7
[1,6,4,7,2,3,5] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 7
[1,6,4,7,2,5,3] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 7
[1,6,4,7,3,2,5] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 7
[1,6,4,7,3,5,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 7
[1,6,4,7,5,2,3] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 7
[1,6,4,7,5,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 7
[1,6,5,2,3,4,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[1,6,5,2,3,7,4] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 7
[1,6,5,2,4,3,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[1,6,5,2,4,7,3] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 7
[1,6,5,2,7,3,4] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 7
[1,6,5,2,7,4,3] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 7
[1,6,5,3,2,4,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[1,6,5,3,2,7,4] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 7
[1,6,5,3,4,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[1,6,5,3,4,7,2] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 7
[1,6,5,3,7,2,4] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 7
[1,6,5,3,7,4,2] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 7
[1,6,5,4,2,3,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[1,6,5,4,2,7,3] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 7
[1,6,5,4,3,2,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[1,6,5,4,3,7,2] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 7
[1,6,5,4,7,2,3] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 7
[1,6,5,4,7,3,2] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 7
[1,6,5,7,2,3,4] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 7
[1,6,5,7,2,4,3] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 7
[1,6,5,7,3,2,4] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 7
[1,6,5,7,3,4,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 7
[1,6,5,7,4,2,3] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 7
[1,6,5,7,4,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 7
[1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 7
[1,6,7,2,3,5,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 7
[1,6,7,2,4,3,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 7
[1,6,7,2,4,5,3] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 7
[1,6,7,2,5,3,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 7
[1,6,7,2,5,4,3] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 7
[1,6,7,3,2,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 7
[1,6,7,3,2,5,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 7
[1,6,7,3,4,2,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 7
[1,6,7,3,4,5,2] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 7
[1,6,7,3,5,2,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 7
[1,6,7,3,5,4,2] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 7
[1,6,7,4,2,3,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 7
[1,6,7,4,2,5,3] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 7
[1,6,7,4,3,2,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 7
[1,6,7,4,3,5,2] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 7
[1,6,7,4,5,2,3] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 7
[1,6,7,4,5,3,2] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 7
[1,6,7,5,2,3,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 7
[1,6,7,5,2,4,3] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 7
[1,6,7,5,3,2,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 7
[1,6,7,5,3,4,2] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 7
[1,6,7,5,4,2,3] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 7
[1,6,7,5,4,3,2] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 7
[1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,2,3,5,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,2,3,6,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,2,4,3,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,2,4,5,3,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,2,4,5,6,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,2,4,6,3,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,2,4,6,5,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,2,5,3,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,2,5,4,3,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,2,5,4,6,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,2,5,6,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,2,5,6,4,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,2,6,3,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,2,6,4,3,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,2,6,4,5,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,2,6,5,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,2,6,5,4,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,3,2,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,3,2,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,3,2,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,3,2,5,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,3,2,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,3,2,6,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,3,4,2,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,3,4,2,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,3,4,5,2,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,3,4,5,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,3,4,6,2,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,3,4,6,5,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,3,5,2,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,3,5,2,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,3,5,4,2,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,3,5,4,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,3,5,6,2,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,3,5,6,4,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,3,6,2,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,3,6,2,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,3,6,4,2,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,3,6,4,5,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,3,6,5,2,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,3,6,5,4,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,4,2,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,4,2,3,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,4,2,5,3,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,4,2,5,6,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,4,2,6,3,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,4,2,6,5,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,4,3,2,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,4,3,2,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,4,3,5,2,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,4,3,5,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,4,3,6,2,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,4,3,6,5,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,4,5,2,3,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,4,5,2,6,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,4,5,3,2,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,4,5,3,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,4,5,6,2,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,4,5,6,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,4,6,2,3,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,4,6,2,5,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,4,6,3,2,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,4,6,3,5,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,4,6,5,2,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,4,6,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,5,2,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,5,2,3,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,5,2,4,3,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,5,2,4,6,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,5,2,6,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,5,2,6,4,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,5,3,2,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,5,3,2,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,5,3,4,2,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,5,3,4,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,5,3,6,2,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,5,3,6,4,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,5,4,2,3,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,5,4,2,6,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,5,4,3,2,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,5,4,3,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,5,4,6,2,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,5,4,6,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,5,6,2,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,5,6,2,4,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,5,6,3,2,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,5,6,3,4,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,5,6,4,2,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,5,6,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,6,2,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,6,2,3,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,6,2,4,3,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,6,2,4,5,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,6,2,5,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,6,2,5,4,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,6,3,2,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,6,3,2,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,6,3,4,2,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,6,3,4,5,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,6,3,5,2,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,6,3,5,4,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,6,4,2,3,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,6,4,2,5,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,6,4,3,2,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,6,4,3,5,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,6,4,5,2,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,6,5,2,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,6,5,2,4,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,6,5,3,2,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,6,5,3,4,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,6,5,4,2,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,1,3,4,5,6,7] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 3
[2,1,3,4,5,7,6] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 5
[2,1,3,4,6,5,7] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 5
[2,1,3,4,6,7,5] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 5
[2,1,3,4,7,5,6] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 6
[2,1,3,4,7,6,5] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 6
[2,1,3,5,4,6,7] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 5
[2,1,3,5,4,7,6] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 7
[2,1,3,5,6,4,7] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 5
[2,1,3,5,6,7,4] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 5
[2,1,3,5,7,4,6] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 7
[2,1,3,5,7,6,4] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 7
[2,1,3,6,4,5,7] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 6
[2,1,3,6,4,7,5] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 6
[2,1,3,6,5,4,7] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 6
[2,1,3,6,5,7,4] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 6
[2,1,3,6,7,4,5] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 6
[2,1,3,6,7,5,4] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 6
[2,1,3,7,4,5,6] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 7
[2,1,3,7,4,6,5] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 7
[2,1,3,7,5,4,6] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 7
[2,1,3,7,5,6,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 7
[2,1,3,7,6,4,5] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 7
[2,1,3,7,6,5,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 7
[2,1,4,3,5,6,7] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 5
[2,1,4,3,5,7,6] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 7
[2,1,4,3,6,5,7] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 7
[2,1,4,3,6,7,5] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 7
[2,1,4,3,7,5,6] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 8
[2,1,4,3,7,6,5] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 8
[2,1,4,5,3,6,7] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 5
[2,1,4,5,3,7,6] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 7
[2,1,4,5,6,3,7] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 5
[2,1,4,5,6,7,3] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 5
[2,1,4,5,7,3,6] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 7
[2,1,4,5,7,6,3] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 7
[2,1,4,6,3,5,7] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 7
[2,1,4,6,3,7,5] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 7
[2,1,4,6,5,3,7] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 7
[2,1,4,6,5,7,3] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 7
[2,1,4,6,7,3,5] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 7
[2,1,4,6,7,5,3] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 7
[2,1,4,7,3,5,6] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 8
[2,1,4,7,3,6,5] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 8
[2,1,4,7,5,3,6] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 8
[2,1,4,7,5,6,3] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 8
[2,1,4,7,6,3,5] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 8
[2,1,4,7,6,5,3] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 8
[2,1,5,3,4,6,7] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 6
[2,1,5,3,4,7,6] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 8
[2,1,5,3,6,4,7] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 6
[2,1,5,3,6,7,4] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 6
[2,1,5,3,7,4,6] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 8
[2,1,5,3,7,6,4] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 8
[2,1,5,4,3,6,7] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 6
[2,1,5,4,3,7,6] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 8
[2,1,5,4,6,3,7] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 6
[2,1,5,4,6,7,3] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 6
[2,1,5,4,7,3,6] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 8
[2,1,5,4,7,6,3] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 8
[2,1,5,6,3,4,7] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 6
[2,1,5,6,3,7,4] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 6
[2,1,5,6,4,3,7] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 6
[2,1,5,6,4,7,3] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 6
[2,1,5,6,7,3,4] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 6
[2,1,5,6,7,4,3] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 6
[2,1,5,7,3,4,6] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 8
[2,1,5,7,3,6,4] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 8
[2,1,5,7,4,3,6] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 8
[2,1,5,7,4,6,3] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 8
[2,1,5,7,6,3,4] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 8
[2,1,5,7,6,4,3] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 8
[2,1,6,3,4,5,7] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 7
[2,1,6,3,4,7,5] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 7
[2,1,6,3,5,4,7] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 7
[2,1,6,3,5,7,4] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 7
[2,1,6,3,7,4,5] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 7
[2,1,6,3,7,5,4] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 7
[2,1,6,4,3,5,7] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 7
[2,1,6,4,3,7,5] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 7
[2,1,6,4,5,3,7] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 7
[2,1,6,4,5,7,3] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 7
[2,1,6,4,7,3,5] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 7
[2,1,6,4,7,5,3] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 7
[2,1,6,5,3,4,7] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 7
[2,1,6,5,3,7,4] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 7
[2,1,6,5,4,3,7] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 7
[2,1,6,5,4,7,3] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 7
[2,1,6,5,7,3,4] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 7
[2,1,6,5,7,4,3] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 7
[2,1,6,7,3,4,5] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 7
[2,1,6,7,3,5,4] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 7
[2,1,6,7,4,3,5] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 7
[2,1,6,7,4,5,3] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 7
[2,1,6,7,5,3,4] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 7
[2,1,6,7,5,4,3] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 7
[2,1,7,3,4,5,6] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 8
[2,1,7,3,4,6,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 8
[2,1,7,3,5,4,6] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 8
[2,1,7,3,5,6,4] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 8
[2,1,7,3,6,4,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 8
[2,1,7,3,6,5,4] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 8
[2,1,7,4,3,5,6] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 8
[2,1,7,4,3,6,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 8
[2,1,7,4,5,3,6] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 8
[2,1,7,4,5,6,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 8
[2,1,7,4,6,3,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 8
[2,1,7,4,6,5,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 8
[2,1,7,5,3,4,6] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 8
[2,1,7,5,3,6,4] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 8
[2,1,7,5,4,3,6] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 8
[2,1,7,5,4,6,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 8
[2,1,7,5,6,3,4] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 8
[2,1,7,5,6,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 8
[2,1,7,6,3,4,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 8
[2,1,7,6,3,5,4] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 8
[2,1,7,6,4,3,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 8
[2,1,7,6,4,5,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 8
[2,1,7,6,5,3,4] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 8
[2,1,7,6,5,4,3] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 8
[2,3,1,4,5,6,7] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 3
[2,3,1,4,5,7,6] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 5
[2,3,1,4,6,5,7] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 5
[2,3,1,4,6,7,5] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 5
[2,3,1,4,7,5,6] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 6
[2,3,1,4,7,6,5] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 6
[2,3,1,5,4,6,7] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 5
[2,3,1,5,4,7,6] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 7
[2,3,1,5,6,4,7] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 5
[2,3,1,5,6,7,4] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 5
[2,3,1,5,7,4,6] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 7
[2,3,1,5,7,6,4] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 7
[2,3,1,6,4,5,7] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 6
[2,3,1,6,4,7,5] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 6
[2,3,1,6,5,4,7] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 6
[2,3,1,6,5,7,4] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 6
[2,3,1,6,7,4,5] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 6
[2,3,1,6,7,5,4] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 6
[2,3,1,7,4,5,6] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 7
[2,3,1,7,4,6,5] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 7
[2,3,1,7,5,4,6] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 7
[2,3,1,7,5,6,4] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 7
[2,3,1,7,6,4,5] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 7
[2,3,1,7,6,5,4] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 7
[2,3,4,1,5,6,7] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 3
[2,3,4,1,5,7,6] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 5
[2,3,4,1,6,5,7] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 5
[2,3,4,1,6,7,5] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 5
[2,3,4,1,7,5,6] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 6
[2,3,4,1,7,6,5] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 6
[2,3,4,5,1,6,7] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 3
[2,3,4,5,1,7,6] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 5
[2,3,4,5,6,1,7] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 3
[2,3,4,5,6,7,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 3
[2,3,4,5,7,1,6] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 5
[2,3,4,5,7,6,1] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 5
[2,3,4,6,1,5,7] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 5
[2,3,4,6,1,7,5] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 5
[2,3,4,6,5,1,7] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 5
[2,3,4,6,5,7,1] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 5
[2,3,4,6,7,1,5] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 5
[2,3,4,6,7,5,1] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 5
[2,3,4,7,1,5,6] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 6
[2,3,4,7,1,6,5] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 6
[2,3,4,7,5,1,6] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 6
[2,3,4,7,5,6,1] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 6
[2,3,4,7,6,1,5] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 6
[2,3,4,7,6,5,1] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 6
[2,3,5,1,4,6,7] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 5
[2,3,5,1,4,7,6] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 7
[2,3,5,1,6,4,7] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 5
[2,3,5,1,6,7,4] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 5
[2,3,5,1,7,4,6] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 7
[2,3,5,1,7,6,4] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 7
[2,3,5,4,1,6,7] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 5
[2,3,5,4,1,7,6] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 7
[2,3,5,4,6,1,7] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 5
[2,3,5,4,6,7,1] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 5
[2,3,5,4,7,1,6] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 7
[2,3,5,4,7,6,1] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 7
[2,3,5,6,1,4,7] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 5
[2,3,5,6,1,7,4] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 5
[2,3,5,6,4,1,7] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 5
[2,3,5,6,4,7,1] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 5
[2,3,5,6,7,1,4] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 5
[2,3,5,6,7,4,1] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 5
[2,3,5,7,1,4,6] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 7
[2,3,5,7,1,6,4] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 7
[2,3,5,7,4,1,6] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 7
[2,3,5,7,4,6,1] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 7
[2,3,5,7,6,1,4] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 7
[2,3,5,7,6,4,1] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 7
[2,3,6,1,4,5,7] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 6
[2,3,6,1,4,7,5] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 6
[2,3,6,1,5,4,7] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 6
[2,3,6,1,5,7,4] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 6
[2,3,6,1,7,4,5] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 6
[2,3,6,1,7,5,4] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 6
[2,3,6,4,1,5,7] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 6
[2,3,6,4,1,7,5] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 6
[2,3,6,4,5,1,7] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 6
[2,3,6,4,5,7,1] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 6
[2,3,6,4,7,1,5] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 6
[2,3,6,4,7,5,1] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 6
[2,3,6,5,1,4,7] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 6
[2,3,6,5,1,7,4] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 6
[2,3,6,5,4,1,7] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 6
[2,3,6,5,4,7,1] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 6
[2,3,6,5,7,1,4] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 6
[2,3,6,5,7,4,1] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 6
[2,3,6,7,1,4,5] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 6
[2,3,6,7,1,5,4] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 6
[2,3,6,7,4,1,5] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 6
[2,3,6,7,4,5,1] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 6
[2,3,6,7,5,1,4] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 6
[2,3,6,7,5,4,1] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 6
[2,3,7,1,4,5,6] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 7
[2,3,7,1,4,6,5] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 7
[2,3,7,1,5,4,6] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 7
[2,3,7,1,5,6,4] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 7
[2,3,7,1,6,4,5] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 7
[2,3,7,1,6,5,4] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 7
[2,3,7,4,1,5,6] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 7
[2,3,7,4,1,6,5] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 7
[2,3,7,4,5,1,6] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 7
[2,3,7,4,5,6,1] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 7
[2,3,7,4,6,1,5] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 7
[2,3,7,4,6,5,1] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 7
[2,3,7,5,1,4,6] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 7
[2,3,7,5,1,6,4] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 7
[2,3,7,5,4,1,6] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 7
[2,3,7,5,4,6,1] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 7
[2,3,7,5,6,1,4] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 7
[2,3,7,5,6,4,1] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 7
[2,3,7,6,1,4,5] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 7
[2,3,7,6,1,5,4] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 7
[2,3,7,6,4,1,5] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 7
[2,3,7,6,4,5,1] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 7
[2,3,7,6,5,1,4] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 7
[2,3,7,6,5,4,1] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 7
[2,4,1,3,5,6,7] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 5
[2,4,1,3,5,7,6] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 7
[2,4,1,3,6,5,7] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 7
[2,4,1,3,6,7,5] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 7
[2,4,1,3,7,5,6] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 8
[2,4,1,3,7,6,5] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 8
[2,4,1,5,3,6,7] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 5
[2,4,1,5,3,7,6] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 7
[2,4,1,5,6,3,7] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 5
[2,4,1,5,6,7,3] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 5
[2,4,1,5,7,3,6] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 7
[2,4,1,5,7,6,3] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 7
[2,4,1,6,3,5,7] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 7
[2,4,1,6,3,7,5] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 7
[2,4,1,6,5,3,7] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 7
[2,4,1,6,5,7,3] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 7
[2,4,1,6,7,3,5] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 7
[2,4,1,6,7,5,3] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 7
[2,4,1,7,3,5,6] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 8
[2,4,1,7,3,6,5] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 8
[2,4,1,7,5,3,6] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 8
[2,4,1,7,5,6,3] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 8
[2,4,1,7,6,3,5] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 8
[2,4,1,7,6,5,3] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 8
[2,4,3,1,5,6,7] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 5
[2,4,3,1,5,7,6] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 7
[2,4,3,1,6,5,7] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 7
[2,4,3,1,6,7,5] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 7
[2,4,3,1,7,5,6] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 8
[2,4,3,1,7,6,5] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 8
[2,4,3,5,1,6,7] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 5
[2,4,3,5,1,7,6] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 7
[2,4,3,5,6,1,7] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 5
[2,4,3,5,6,7,1] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 5
[2,4,3,5,7,1,6] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 7
[2,4,3,5,7,6,1] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 7
[2,4,3,6,1,5,7] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 7
[2,4,3,6,1,7,5] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 7
[2,4,3,6,5,1,7] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 7
[2,4,3,6,5,7,1] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 7
[2,4,3,6,7,1,5] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 7
[2,4,3,6,7,5,1] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 7
[2,4,3,7,1,5,6] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 8
[2,4,3,7,1,6,5] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 8
[2,4,3,7,5,1,6] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 8
[2,4,3,7,5,6,1] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 8
[2,4,3,7,6,1,5] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 8
[2,4,3,7,6,5,1] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 8
[2,4,5,1,3,6,7] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 5
[2,4,5,1,3,7,6] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 7
[2,4,5,1,6,3,7] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 5
[2,4,5,1,6,7,3] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 5
[2,4,5,1,7,3,6] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 7
[2,4,5,1,7,6,3] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 7
[2,4,5,3,1,6,7] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 5
[2,4,5,3,1,7,6] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 7
[2,4,5,3,6,1,7] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 5
[2,4,5,3,6,7,1] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 5
[2,4,5,3,7,1,6] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 7
[2,4,5,3,7,6,1] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 7
[2,4,5,6,1,3,7] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 5
[2,4,5,6,1,7,3] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 5
[2,4,5,6,3,1,7] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 5
[2,4,5,6,3,7,1] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 5
[2,4,5,6,7,1,3] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 5
[2,4,5,6,7,3,1] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 5
[2,4,5,7,1,3,6] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 7
[2,4,5,7,1,6,3] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 7
[2,4,5,7,3,1,6] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 7
[2,4,5,7,3,6,1] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 7
[2,4,5,7,6,1,3] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 7
[2,4,5,7,6,3,1] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 7
[2,4,6,1,3,5,7] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 7
[2,4,6,1,3,7,5] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 7
[2,4,6,1,5,3,7] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 7
[2,4,6,1,5,7,3] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 7
[2,4,6,1,7,3,5] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 7
[2,4,6,1,7,5,3] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 7
[2,4,6,3,1,5,7] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 7
[2,4,6,3,1,7,5] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 7
[2,4,6,3,5,1,7] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 7
[2,4,6,3,5,7,1] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 7
[2,4,6,3,7,1,5] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 7
[2,4,6,3,7,5,1] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 7
[2,4,6,5,1,3,7] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 7
[2,4,6,5,1,7,3] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 7
[2,4,6,5,3,1,7] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 7
[2,4,6,5,3,7,1] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 7
[2,4,6,5,7,1,3] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 7
[2,4,6,5,7,3,1] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 7
[2,4,6,7,1,3,5] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 7
[2,4,6,7,1,5,3] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 7
[2,4,6,7,3,1,5] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 7
[2,4,6,7,3,5,1] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 7
[2,4,6,7,5,1,3] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 7
[2,4,6,7,5,3,1] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 7
[2,4,7,1,3,5,6] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 8
[2,4,7,1,3,6,5] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 8
[2,4,7,1,5,3,6] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 8
[2,4,7,1,5,6,3] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 8
[2,4,7,1,6,3,5] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 8
[2,4,7,1,6,5,3] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 8
[2,4,7,3,1,5,6] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 8
[2,4,7,3,1,6,5] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 8
[2,4,7,3,5,1,6] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 8
[2,4,7,3,5,6,1] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 8
[2,4,7,3,6,1,5] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 8
[2,4,7,3,6,5,1] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 8
[2,4,7,5,1,3,6] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 8
[2,4,7,5,1,6,3] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 8
[2,4,7,5,3,1,6] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 8
[2,4,7,5,3,6,1] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 8
[2,4,7,5,6,1,3] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 8
[2,4,7,5,6,3,1] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 8
[2,4,7,6,1,3,5] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 8
[2,4,7,6,1,5,3] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 8
[2,4,7,6,3,1,5] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 8
[2,4,7,6,3,5,1] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 8
[2,4,7,6,5,1,3] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 8
[2,4,7,6,5,3,1] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 8
[2,5,1,3,4,6,7] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 6
[2,5,1,3,4,7,6] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 8
[2,5,1,3,6,4,7] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 6
[2,5,1,3,6,7,4] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 6
[2,5,1,3,7,4,6] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 8
[2,5,1,3,7,6,4] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 8
[2,5,1,4,3,6,7] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 6
[2,5,1,4,3,7,6] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 8
[2,5,1,4,6,3,7] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 6
[2,5,1,4,6,7,3] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 6
[2,5,1,4,7,3,6] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 8
[2,5,1,4,7,6,3] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 8
[2,5,1,6,3,4,7] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 6
[2,5,1,6,3,7,4] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 6
[2,5,1,6,4,3,7] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 6
[2,5,1,6,4,7,3] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 6
[2,5,1,6,7,3,4] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 6
[2,5,1,6,7,4,3] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 6
[2,5,1,7,3,4,6] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 8
[2,5,1,7,3,6,4] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 8
[2,5,1,7,4,3,6] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 8
[2,5,1,7,4,6,3] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 8
[2,5,1,7,6,3,4] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 8
[2,5,1,7,6,4,3] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 8
[2,5,3,1,4,6,7] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 6
[2,5,3,1,4,7,6] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 8
[2,5,3,1,6,4,7] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 6
[2,5,3,1,6,7,4] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 6
[2,5,3,1,7,4,6] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 8
[2,5,3,1,7,6,4] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 8
[2,5,3,4,1,6,7] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 6
[2,5,3,4,1,7,6] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 8
[2,5,3,4,6,1,7] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 6
[2,5,3,4,6,7,1] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 6
[2,5,3,4,7,1,6] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 8
[2,5,3,4,7,6,1] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 8
[2,5,3,6,1,4,7] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 6
[2,5,3,6,1,7,4] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 6
[2,5,3,6,4,1,7] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 6
[2,5,3,6,4,7,1] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 6
[2,5,3,6,7,1,4] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 6
[2,5,3,6,7,4,1] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 6
[2,5,3,7,1,4,6] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 8
[2,5,3,7,1,6,4] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 8
[2,5,3,7,4,1,6] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 8
[2,5,3,7,4,6,1] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 8
[2,5,3,7,6,1,4] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 8
[2,5,3,7,6,4,1] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 8
[2,5,4,1,3,6,7] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 6
[2,5,4,1,3,7,6] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 8
[2,5,4,1,6,3,7] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 6
[2,5,4,1,6,7,3] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 6
[2,5,4,1,7,3,6] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 8
[2,5,4,1,7,6,3] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 8
[2,5,4,3,1,6,7] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 6
[2,5,4,3,1,7,6] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 8
[2,5,4,3,6,1,7] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 6
[2,5,4,3,6,7,1] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 6
[2,5,4,3,7,1,6] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 8
[2,5,4,3,7,6,1] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 8
[2,5,4,6,1,3,7] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 6
[2,5,4,6,1,7,3] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 6
[2,5,4,6,3,1,7] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 6
[2,5,4,6,3,7,1] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 6
[2,5,4,6,7,1,3] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 6
[2,5,4,6,7,3,1] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 6
[2,5,4,7,1,3,6] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 8
[2,5,4,7,1,6,3] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 8
[2,5,4,7,3,1,6] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 8
[2,5,4,7,3,6,1] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 8
[2,5,4,7,6,1,3] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 8
[2,5,4,7,6,3,1] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 8
[2,5,6,1,3,4,7] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 6
[2,5,6,1,3,7,4] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 6
[2,5,6,1,4,3,7] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 6
[2,5,6,1,4,7,3] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 6
[2,5,6,1,7,3,4] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 6
[2,5,6,1,7,4,3] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 6
[2,5,6,3,1,4,7] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 6
[2,5,6,3,1,7,4] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 6
[2,5,6,3,4,1,7] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 6
[2,5,6,3,4,7,1] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 6
[2,5,6,3,7,1,4] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 6
[2,5,6,3,7,4,1] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 6
[2,5,6,4,1,3,7] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 6
[2,5,6,4,1,7,3] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 6
[2,5,6,4,3,1,7] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 6
[2,5,6,4,3,7,1] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 6
[2,5,6,4,7,1,3] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 6
[2,5,6,4,7,3,1] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 6
[2,5,6,7,1,3,4] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 6
[2,5,6,7,1,4,3] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 6
[2,5,6,7,3,1,4] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 6
[2,5,6,7,3,4,1] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 6
[2,5,6,7,4,1,3] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 6
[2,5,6,7,4,3,1] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 6
[2,5,7,1,3,4,6] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 8
[2,5,7,1,3,6,4] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 8
[2,5,7,1,4,3,6] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 8
[2,5,7,1,4,6,3] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 8
[2,5,7,1,6,3,4] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 8
[2,5,7,1,6,4,3] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 8
[2,5,7,3,1,4,6] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 8
[2,5,7,3,1,6,4] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 8
[2,5,7,3,4,1,6] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 8
[2,5,7,3,4,6,1] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 8
[2,5,7,3,6,1,4] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 8
[2,5,7,3,6,4,1] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 8
[2,5,7,4,1,3,6] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 8
[2,5,7,4,1,6,3] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 8
[2,5,7,4,3,1,6] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 8
[2,5,7,4,3,6,1] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 8
[2,5,7,4,6,1,3] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 8
[2,5,7,4,6,3,1] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 8
[2,5,7,6,1,3,4] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 8
[2,5,7,6,1,4,3] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 8
[2,5,7,6,3,1,4] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 8
[2,5,7,6,3,4,1] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 8
[2,5,7,6,4,1,3] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 8
[2,5,7,6,4,3,1] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 8
[2,6,1,3,4,5,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 7
[2,6,1,3,4,7,5] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 7
[2,6,1,3,5,4,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 7
[2,6,1,3,5,7,4] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 7
[2,6,1,3,7,4,5] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 7
[2,6,1,3,7,5,4] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 7
[2,6,1,4,3,5,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 7
[2,6,1,4,3,7,5] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 7
[2,6,1,4,5,3,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 7
[2,6,1,4,5,7,3] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 7
[2,6,1,4,7,3,5] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 7
[2,6,1,4,7,5,3] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 7
[2,6,1,5,3,4,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 7
[2,6,1,5,3,7,4] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 7
[2,6,1,5,4,3,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 7
[2,6,1,5,4,7,3] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 7
[2,6,1,5,7,3,4] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 7
[2,6,1,5,7,4,3] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 7
[2,6,1,7,3,4,5] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 7
[2,6,1,7,3,5,4] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 7
[2,6,1,7,4,3,5] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 7
[2,6,1,7,4,5,3] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 7
[2,6,1,7,5,3,4] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 7
[2,6,1,7,5,4,3] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 7
[2,6,3,1,4,5,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 7
[2,6,3,1,4,7,5] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 7
[2,6,3,1,5,4,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 7
[2,6,3,1,5,7,4] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 7
[2,6,3,1,7,4,5] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 7
[2,6,3,1,7,5,4] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 7
[2,6,3,4,1,5,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 7
[2,6,3,4,1,7,5] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 7
[2,6,3,4,5,1,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 7
[2,6,3,4,5,7,1] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 7
[2,6,3,4,7,1,5] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 7
[2,6,3,4,7,5,1] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 7
[2,6,3,5,1,4,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 7
[2,6,3,5,1,7,4] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 7
[2,6,3,5,4,1,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 7
[2,6,3,5,4,7,1] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 7
[2,6,3,5,7,1,4] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 7
[2,6,3,5,7,4,1] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 7
[2,6,3,7,1,4,5] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 7
[2,6,3,7,1,5,4] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 7
[2,6,3,7,4,1,5] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 7
[2,6,3,7,4,5,1] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 7
[2,6,3,7,5,1,4] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 7
[2,6,3,7,5,4,1] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 7
[2,6,4,1,3,5,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 7
[2,6,4,1,3,7,5] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 7
[2,6,4,1,5,3,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 7
[2,6,4,1,5,7,3] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 7
[2,6,4,1,7,3,5] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 7
[2,6,4,1,7,5,3] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 7
[2,6,4,3,1,5,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 7
[2,6,4,3,1,7,5] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 7
[2,6,4,3,5,1,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 7
[2,6,4,3,5,7,1] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 7
[2,6,4,3,7,1,5] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 7
[2,6,4,3,7,5,1] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 7
[2,6,4,5,1,3,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 7
[2,6,4,5,1,7,3] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 7
[2,6,4,5,3,1,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 7
[2,6,4,5,3,7,1] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 7
[2,6,4,5,7,1,3] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 7
[2,6,4,5,7,3,1] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 7
[2,6,4,7,1,3,5] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 7
[2,6,4,7,1,5,3] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 7
[2,6,4,7,3,1,5] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 7
[2,6,4,7,3,5,1] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 7
[2,6,4,7,5,1,3] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 7
[2,6,4,7,5,3,1] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 7
[2,6,5,1,3,4,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 7
[2,6,5,1,3,7,4] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 7
[2,6,5,1,4,3,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 7
[2,6,5,1,4,7,3] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 7
[2,6,5,1,7,3,4] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 7
[2,6,5,1,7,4,3] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 7
[2,6,5,3,1,4,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 7
[2,6,5,3,1,7,4] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 7
[2,6,5,3,4,1,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 7
[2,6,5,3,4,7,1] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 7
[2,6,5,3,7,1,4] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 7
[2,6,5,3,7,4,1] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 7
[2,6,5,4,1,3,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 7
[2,6,5,4,1,7,3] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 7
[2,6,5,4,3,1,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 7
[2,6,5,4,3,7,1] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 7
[2,6,5,4,7,1,3] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 7
[2,6,5,4,7,3,1] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 7
[2,6,5,7,1,3,4] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 7
[2,6,5,7,1,4,3] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 7
[2,6,5,7,3,1,4] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 7
[2,6,5,7,3,4,1] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 7
[2,6,5,7,4,1,3] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 7
[2,6,5,7,4,3,1] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 7
[2,6,7,1,3,4,5] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 7
[2,6,7,1,3,5,4] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 7
[2,6,7,1,4,3,5] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 7
[2,6,7,1,4,5,3] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 7
[2,6,7,1,5,3,4] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 7
[2,6,7,1,5,4,3] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 7
[2,6,7,3,1,4,5] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 7
[2,6,7,3,1,5,4] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 7
[2,6,7,3,4,1,5] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 7
[2,6,7,3,4,5,1] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 7
[2,6,7,3,5,1,4] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 7
[2,6,7,3,5,4,1] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 7
[2,6,7,4,1,3,5] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 7
[2,6,7,4,1,5,3] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 7
[2,6,7,4,3,1,5] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 7
[2,6,7,4,3,5,1] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 7
[2,6,7,4,5,1,3] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 7
[2,6,7,4,5,3,1] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 7
[2,6,7,5,1,3,4] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 7
[2,6,7,5,1,4,3] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 7
[2,6,7,5,3,1,4] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 7
[2,6,7,5,3,4,1] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 7
[2,6,7,5,4,1,3] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 7
[2,6,7,5,4,3,1] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 7
[2,7,1,3,4,5,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,1,3,4,6,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,1,3,5,4,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,1,3,5,6,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,1,3,6,4,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,1,3,6,5,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,1,4,3,5,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,1,4,3,6,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,1,4,5,3,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,1,4,5,6,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,1,4,6,3,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,1,4,6,5,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,1,5,3,4,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,1,5,3,6,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,1,5,4,3,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,1,5,4,6,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,1,5,6,3,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,1,5,6,4,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,1,6,3,4,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,1,6,3,5,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,1,6,4,3,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,1,6,4,5,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,1,6,5,3,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,1,6,5,4,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,3,1,4,5,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,3,1,4,6,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,3,1,5,4,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,3,1,5,6,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,3,1,6,4,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,3,1,6,5,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,3,4,1,5,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,3,4,1,6,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,3,4,5,1,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,3,4,5,6,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,3,4,6,1,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,3,4,6,5,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,3,5,1,4,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,3,5,1,6,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,3,5,4,1,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,3,5,4,6,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,3,5,6,1,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,3,5,6,4,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,3,6,1,4,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,3,6,1,5,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,3,6,4,1,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,3,6,4,5,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,3,6,5,1,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,3,6,5,4,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,4,1,3,5,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,4,1,3,6,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,4,1,5,3,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,4,1,5,6,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,4,1,6,3,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,4,1,6,5,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,4,3,1,5,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,4,3,1,6,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,4,3,5,1,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,4,3,5,6,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,4,3,6,1,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,4,3,6,5,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,4,5,1,3,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,4,5,1,6,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,4,5,3,1,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,4,5,3,6,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,4,5,6,1,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,4,5,6,3,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,4,6,1,3,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,4,6,1,5,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,4,6,3,1,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,4,6,3,5,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,4,6,5,1,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,4,6,5,3,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,5,1,3,4,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,5,1,3,6,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,5,1,4,3,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,5,1,4,6,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,5,1,6,3,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,5,1,6,4,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,5,3,1,4,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,5,3,1,6,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,5,3,4,1,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,5,3,4,6,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,5,3,6,1,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,5,3,6,4,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,5,4,1,3,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,5,4,1,6,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,5,4,3,1,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,5,4,3,6,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,5,4,6,1,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,5,4,6,3,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,5,6,1,3,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,5,6,1,4,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,5,6,3,1,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,5,6,3,4,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,5,6,4,1,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,5,6,4,3,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,6,1,3,4,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,6,1,3,5,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,6,1,4,3,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,6,1,4,5,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,6,1,5,3,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,6,1,5,4,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,6,3,1,4,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,6,3,1,5,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,6,3,4,1,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,6,3,4,5,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,6,3,5,1,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,6,3,5,4,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,6,4,1,3,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,6,4,1,5,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,6,4,3,1,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,6,4,3,5,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,6,4,5,1,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,6,4,5,3,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,6,5,1,3,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,6,5,1,4,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,6,5,3,1,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,6,5,3,4,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,6,5,4,1,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[2,7,6,5,4,3,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 8
[3,1,2,4,5,6,7] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 4
[3,1,2,4,5,7,6] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 6
[3,1,2,4,6,5,7] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 6
[3,1,2,4,6,7,5] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 6
[3,1,2,4,7,5,6] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 7
[3,1,2,4,7,6,5] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 7
[3,1,2,5,4,6,7] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 6
[3,1,2,5,4,7,6] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 8
[3,1,2,5,6,4,7] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 6
[3,1,2,5,6,7,4] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 6
[3,1,2,5,7,4,6] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 8
[3,1,2,5,7,6,4] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 8
[3,1,2,6,4,5,7] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 7
[3,1,2,6,4,7,5] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 7
[3,1,2,6,5,4,7] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 7
[3,1,2,6,5,7,4] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 7
[3,1,2,6,7,4,5] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 7
[3,1,2,6,7,5,4] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 7
[3,1,2,7,4,5,6] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 8
[3,1,2,7,4,6,5] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 8
[3,1,2,7,5,4,6] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 8
[3,1,2,7,5,6,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 8
[3,1,2,7,6,4,5] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 8
[3,1,2,7,6,5,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 8
[3,1,4,2,5,6,7] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 4
[3,1,4,2,5,7,6] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 6
[3,1,4,2,6,5,7] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 6
[3,1,4,2,6,7,5] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 6
[3,1,4,2,7,5,6] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 7
[3,1,4,2,7,6,5] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 7
[3,1,4,5,2,6,7] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 4
[3,1,4,5,2,7,6] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 6
[3,1,4,5,6,2,7] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 4
[3,1,4,5,6,7,2] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 4
[3,1,4,5,7,2,6] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 6
[3,1,4,5,7,6,2] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 6
[3,1,4,6,2,5,7] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 6
[3,1,4,6,2,7,5] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 6
[3,1,4,6,5,2,7] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 6
[3,1,4,6,5,7,2] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 6
[3,1,4,6,7,2,5] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 6
[3,1,4,6,7,5,2] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 6
[3,1,4,7,2,5,6] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 7
[3,1,4,7,2,6,5] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 7
[3,1,4,7,5,2,6] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 7
[3,1,4,7,5,6,2] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 7
[3,1,4,7,6,2,5] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 7
[3,1,4,7,6,5,2] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 7
[3,1,5,2,4,6,7] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 6
[3,1,5,2,4,7,6] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 8
[3,1,5,2,6,4,7] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 6
[3,1,5,2,6,7,4] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 6
[3,1,5,2,7,4,6] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 8
[3,1,5,2,7,6,4] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 8
[3,1,5,4,2,6,7] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 6
[3,1,5,4,2,7,6] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 8
[3,1,5,4,6,2,7] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 6
[3,1,5,4,6,7,2] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 6
[3,1,5,4,7,2,6] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 8
[3,1,5,4,7,6,2] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 8
[3,1,5,6,2,4,7] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 6
[3,1,5,6,2,7,4] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 6
[3,1,5,6,4,2,7] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 6
[3,1,5,6,4,7,2] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 6
[3,1,5,6,7,2,4] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 6
[3,1,5,6,7,4,2] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 6
[3,1,5,7,2,4,6] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 8
[3,1,5,7,2,6,4] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 8
[3,1,5,7,4,2,6] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 8
[3,1,5,7,4,6,2] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 8
[3,1,5,7,6,2,4] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 8
[3,1,5,7,6,4,2] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 8
[3,1,6,2,4,5,7] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 7
[3,1,6,2,4,7,5] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 7
[3,1,6,2,5,4,7] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 7
[3,1,6,2,5,7,4] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 7
[3,1,6,2,7,4,5] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 7
[3,1,6,2,7,5,4] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 7
[3,1,6,4,2,5,7] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 7
[3,1,6,4,2,7,5] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 7
[3,1,6,4,5,2,7] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 7
[3,1,6,4,5,7,2] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 7
[3,1,6,4,7,2,5] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 7
[3,1,6,4,7,5,2] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 7
[3,1,6,5,2,4,7] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 7
[3,1,6,5,2,7,4] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 7
[3,1,6,5,4,2,7] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 7
[3,1,6,5,4,7,2] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 7
[3,1,6,5,7,2,4] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 7
[3,1,6,5,7,4,2] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 7
[3,1,6,7,2,4,5] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 7
[3,1,6,7,2,5,4] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 7
[3,1,6,7,4,2,5] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 7
[3,1,6,7,4,5,2] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 7
[3,1,6,7,5,2,4] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 7
[3,1,6,7,5,4,2] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 7
[3,1,7,2,4,5,6] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[3,1,7,2,4,6,5] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[3,1,7,2,5,4,6] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[3,1,7,2,5,6,4] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[3,1,7,2,6,4,5] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[3,1,7,2,6,5,4] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[3,1,7,4,2,5,6] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[3,1,7,4,2,6,5] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[3,1,7,4,5,2,6] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[3,1,7,4,5,6,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[3,1,7,4,6,2,5] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[3,1,7,4,6,5,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[3,1,7,5,2,4,6] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[3,1,7,5,2,6,4] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[3,1,7,5,4,2,6] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[3,1,7,5,4,6,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[3,1,7,5,6,2,4] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[3,1,7,5,6,4,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[3,1,7,6,2,4,5] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[3,1,7,6,2,5,4] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[3,1,7,6,4,2,5] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[3,1,7,6,4,5,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[3,1,7,6,5,2,4] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[3,1,7,6,5,4,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[3,2,1,4,5,6,7] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 4
[3,2,1,4,5,7,6] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 6
[3,2,1,4,6,5,7] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 6
[3,2,1,4,6,7,5] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 6
[3,2,1,4,7,5,6] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 7
[3,2,1,4,7,6,5] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 7
[3,2,1,5,4,6,7] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 6
[3,2,1,5,4,7,6] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 8
[3,2,1,5,6,4,7] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 6
[3,2,1,5,6,7,4] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 6
[3,2,1,5,7,4,6] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 8
[3,2,1,5,7,6,4] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 8
[3,2,1,6,4,5,7] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 7
[3,2,1,6,4,7,5] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 7
[3,2,1,6,5,4,7] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 7
[3,2,1,6,5,7,4] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 7
[3,2,1,6,7,4,5] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 7
[3,2,1,6,7,5,4] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 7
[3,2,1,7,4,5,6] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 8
[3,2,1,7,4,6,5] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 8
[3,2,1,7,5,4,6] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 8
[3,2,1,7,5,6,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 8
[3,2,1,7,6,4,5] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 8
[3,2,1,7,6,5,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 8
[3,2,4,1,5,6,7] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 4
[3,2,4,1,5,7,6] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 6
[3,2,4,1,6,5,7] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 6
[3,2,4,1,6,7,5] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 6
[3,2,4,1,7,5,6] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 7
[3,2,4,1,7,6,5] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 7
[3,2,4,5,1,6,7] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 4
[3,2,4,5,1,7,6] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 6
[3,2,4,5,6,1,7] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 4
[3,2,4,5,6,7,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 4
[3,2,4,5,7,1,6] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 6
[3,2,4,5,7,6,1] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 6
[3,2,4,6,1,5,7] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 6
[3,2,4,6,1,7,5] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 6
[3,2,4,6,5,1,7] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 6
[3,2,4,6,5,7,1] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 6
[3,2,4,6,7,1,5] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 6
[3,2,4,6,7,5,1] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 6
[3,2,4,7,1,5,6] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 7
[3,2,4,7,1,6,5] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 7
[3,2,4,7,5,1,6] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 7
[3,2,4,7,5,6,1] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 7
[3,2,4,7,6,1,5] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 7
[3,2,4,7,6,5,1] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 7
[3,2,5,1,4,6,7] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 6
[3,2,5,1,4,7,6] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 8
[3,2,5,1,6,4,7] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 6
[3,2,5,1,6,7,4] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 6
[3,2,5,1,7,4,6] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 8
[3,2,5,1,7,6,4] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 8
[3,2,5,4,1,6,7] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 6
[3,2,5,4,1,7,6] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 8
[3,2,5,4,6,1,7] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 6
[3,2,5,4,6,7,1] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 6
[3,2,5,4,7,1,6] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 8
[3,2,5,4,7,6,1] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 8
[3,2,5,6,1,4,7] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 6
[3,2,5,6,1,7,4] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 6
[3,2,5,6,4,1,7] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 6
[3,2,5,6,4,7,1] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 6
[3,2,5,6,7,1,4] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 6
[3,2,5,6,7,4,1] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 6
[3,2,5,7,1,4,6] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 8
[3,2,5,7,1,6,4] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 8
[3,2,5,7,4,1,6] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 8
[3,2,5,7,4,6,1] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 8
[3,2,5,7,6,1,4] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 8
[3,2,5,7,6,4,1] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 8
[3,2,6,1,4,5,7] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 7
[3,2,6,1,4,7,5] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 7
[3,2,6,1,5,4,7] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 7
[3,2,6,1,5,7,4] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 7
[3,2,6,1,7,4,5] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 7
[3,2,6,1,7,5,4] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 7
[3,2,6,4,1,5,7] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 7
[3,2,6,4,1,7,5] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 7
[3,2,6,4,5,1,7] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 7
[3,2,6,4,5,7,1] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 7
[3,2,6,4,7,1,5] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 7
[3,2,6,4,7,5,1] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 7
[3,2,6,5,1,4,7] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 7
[3,2,6,5,1,7,4] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 7
[3,2,6,5,4,1,7] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 7
[3,2,6,5,4,7,1] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 7
[3,2,6,5,7,1,4] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 7
[3,2,6,5,7,4,1] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 7
[3,2,6,7,1,4,5] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 7
[3,2,6,7,1,5,4] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 7
[3,2,6,7,4,1,5] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 7
[3,2,6,7,4,5,1] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 7
[3,2,6,7,5,1,4] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 7
[3,2,6,7,5,4,1] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 7
[3,2,7,1,4,5,6] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[3,2,7,1,4,6,5] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[3,2,7,1,5,4,6] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[3,2,7,1,5,6,4] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[3,2,7,1,6,4,5] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[3,2,7,1,6,5,4] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[3,2,7,4,1,5,6] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[3,2,7,4,1,6,5] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[3,2,7,4,5,1,6] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[3,2,7,4,5,6,1] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[3,2,7,4,6,1,5] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[3,2,7,4,6,5,1] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[3,2,7,5,1,4,6] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[3,2,7,5,1,6,4] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[3,2,7,5,4,1,6] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[3,2,7,5,4,6,1] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[3,2,7,5,6,1,4] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[3,2,7,5,6,4,1] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[3,2,7,6,1,4,5] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[3,2,7,6,1,5,4] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[3,2,7,6,4,1,5] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[3,2,7,6,4,5,1] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[3,2,7,6,5,1,4] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[3,2,7,6,5,4,1] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 8
[3,4,1,2,5,6,7] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 4
[3,4,1,2,5,7,6] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 6
[3,4,1,2,6,5,7] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 6
[3,4,1,2,6,7,5] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 6
[3,4,1,2,7,5,6] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 7
[3,4,1,2,7,6,5] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 7
[3,4,1,5,2,6,7] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 4
[3,4,1,5,2,7,6] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 6
[3,4,1,5,6,2,7] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 4
[3,4,1,5,6,7,2] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 4
[3,4,1,5,7,2,6] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 6
[3,4,1,5,7,6,2] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 6
[3,4,1,6,2,5,7] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 6
[3,4,1,6,2,7,5] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 6
[3,4,1,6,5,2,7] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 6
[3,4,1,6,5,7,2] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 6
[3,4,1,6,7,2,5] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 6
[3,4,1,6,7,5,2] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 6
[3,4,1,7,2,5,6] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 7
[3,4,1,7,2,6,5] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 7
[3,4,1,7,5,2,6] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 7
[3,4,1,7,5,6,2] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 7
[3,4,1,7,6,2,5] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 7
[3,4,1,7,6,5,2] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 7
[3,4,2,1,5,6,7] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 4
[3,4,2,1,5,7,6] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 6
[3,4,2,1,6,5,7] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 6
[3,4,2,1,6,7,5] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 6
[3,4,2,1,7,5,6] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 7
[3,4,2,1,7,6,5] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 7
[3,4,2,5,1,6,7] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 4
[3,4,2,5,1,7,6] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 6
[3,4,2,5,6,1,7] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 4
[3,4,2,5,6,7,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 4
[3,4,2,5,7,1,6] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 6
[3,4,2,5,7,6,1] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 6
[3,4,2,6,1,5,7] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 6
[3,4,2,6,1,7,5] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 6
[3,4,2,6,5,1,7] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 6
[3,4,2,6,5,7,1] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 6
[3,4,2,6,7,1,5] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 6
[3,4,2,6,7,5,1] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 6
[3,4,2,7,1,5,6] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 7
[3,4,2,7,1,6,5] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 7
[3,4,2,7,5,1,6] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 7
[3,4,2,7,5,6,1] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 7
[3,4,2,7,6,1,5] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 7
[3,4,2,7,6,5,1] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 7
[3,4,5,1,2,6,7] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 4
[3,4,5,1,2,7,6] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 6
[3,4,5,1,6,2,7] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 4
[3,4,5,1,6,7,2] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 4
[3,4,5,1,7,2,6] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 6
[3,4,5,1,7,6,2] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 6
[3,4,5,2,1,6,7] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 4
[3,4,5,2,1,7,6] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 6
[3,4,5,2,6,1,7] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 4
[3,4,5,2,6,7,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 4
[3,4,5,2,7,1,6] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 6
[3,4,5,2,7,6,1] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 6
[3,4,5,6,1,2,7] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 4
[3,4,5,6,1,7,2] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 4
[3,4,5,6,2,1,7] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 4
[3,4,5,6,2,7,1] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 4
[3,4,5,6,7,1,2] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 4
[3,4,5,6,7,2,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 4
[3,4,5,7,1,2,6] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 6
[3,4,5,7,1,6,2] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 6
[3,4,5,7,2,1,6] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 6
[3,4,5,7,2,6,1] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 6
[3,4,5,7,6,1,2] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 6
[3,4,5,7,6,2,1] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 6
[3,4,6,1,2,5,7] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 6
[3,4,6,1,2,7,5] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 6
[3,4,6,1,5,2,7] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 6
[3,4,6,1,5,7,2] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 6
[3,4,6,1,7,2,5] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 6
[3,4,6,1,7,5,2] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 6
[3,4,6,2,1,5,7] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 6
[3,4,6,2,1,7,5] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 6
[3,4,6,2,5,1,7] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 6
[3,4,6,2,5,7,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 6
[3,4,6,2,7,1,5] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 6
[3,4,6,2,7,5,1] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 6
[3,4,6,5,1,2,7] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 6
[3,4,6,5,1,7,2] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 6
[3,4,6,5,2,1,7] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 6
[3,4,6,5,2,7,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 6
[3,4,6,5,7,1,2] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 6
[3,4,6,5,7,2,1] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 6
[3,4,6,7,1,2,5] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 6
[3,4,6,7,1,5,2] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 6
[3,4,6,7,2,1,5] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 6
[3,4,6,7,2,5,1] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 6
[3,4,6,7,5,1,2] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 6
[3,4,6,7,5,2,1] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 6
[3,4,7,1,2,5,6] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 7
[3,4,7,1,2,6,5] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 7
[3,4,7,1,5,2,6] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 7
[3,4,7,1,5,6,2] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 7
[3,4,7,1,6,2,5] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 7
[3,4,7,1,6,5,2] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 7
[3,4,7,2,1,5,6] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 7
[3,4,7,2,1,6,5] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 7
[3,4,7,2,5,1,6] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 7
[3,4,7,2,5,6,1] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 7
[3,4,7,2,6,1,5] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 7
[3,4,7,2,6,5,1] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 7
[3,4,7,5,1,2,6] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 7
[3,4,7,5,1,6,2] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 7
[3,4,7,5,2,1,6] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 7
[3,4,7,5,2,6,1] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 7
[3,4,7,5,6,1,2] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 7
[3,4,7,5,6,2,1] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 7
[3,4,7,6,1,2,5] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 7
[3,4,7,6,1,5,2] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 7
[3,4,7,6,2,1,5] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 7
[3,4,7,6,2,5,1] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 7
[3,4,7,6,5,1,2] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 7
[3,4,7,6,5,2,1] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 7
[3,5,1,2,4,6,7] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 6
[3,5,1,2,4,7,6] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 8
[3,5,1,2,6,4,7] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 6
[3,5,1,2,6,7,4] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 6
[3,5,1,2,7,4,6] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 8
[3,5,1,2,7,6,4] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 8
[3,5,1,4,2,6,7] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 6
[3,5,1,4,2,7,6] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 8
[3,5,1,4,6,2,7] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 6
[3,5,1,4,6,7,2] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 6
[3,5,1,4,7,2,6] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 8
[3,5,1,4,7,6,2] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 8
[3,5,1,6,2,4,7] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 6
[3,5,1,6,2,7,4] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 6
[3,5,1,6,4,2,7] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 6
[3,5,1,6,4,7,2] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 6
[3,5,1,6,7,2,4] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 6
[3,5,1,6,7,4,2] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 6
[3,5,1,7,2,4,6] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 8
[3,5,1,7,2,6,4] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 8
[3,5,1,7,4,2,6] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 8
[3,5,1,7,4,6,2] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 8
[3,5,1,7,6,2,4] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 8
[3,5,1,7,6,4,2] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 8
[3,5,2,1,4,6,7] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 6
[3,5,2,1,4,7,6] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 8
[3,5,2,1,6,4,7] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 6
[3,5,2,1,6,7,4] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 6
[3,5,2,1,7,4,6] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 8
[3,5,2,1,7,6,4] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 8
[3,5,2,4,1,6,7] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 6
[3,5,2,4,1,7,6] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 8
[3,5,2,4,6,1,7] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 6
[3,5,2,4,6,7,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 6
[3,5,2,4,7,1,6] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 8
[3,5,2,4,7,6,1] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 8
[3,5,2,6,1,4,7] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 6
[3,5,2,6,1,7,4] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 6
[3,5,2,6,4,1,7] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 6
[3,5,2,6,4,7,1] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 6
[3,5,2,6,7,1,4] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 6
[3,5,2,6,7,4,1] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 6
[3,5,2,7,1,4,6] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 8
[3,5,2,7,1,6,4] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 8
[3,5,2,7,4,1,6] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 8
[3,5,2,7,4,6,1] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 8
[3,5,2,7,6,1,4] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 8
[3,5,2,7,6,4,1] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 8
[3,5,4,1,2,6,7] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 6
[3,5,4,1,2,7,6] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 8
[3,5,4,1,6,2,7] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 6
[3,5,4,1,6,7,2] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 6
[3,5,4,1,7,2,6] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 8
[3,5,4,1,7,6,2] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 8
[3,5,4,2,1,6,7] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 6
[3,5,4,2,1,7,6] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 8
[3,5,4,2,6,1,7] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 6
[3,5,4,2,6,7,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 6
[3,5,4,2,7,1,6] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 8
[3,5,4,2,7,6,1] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 8
[3,5,4,6,1,2,7] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 6
[3,5,4,6,1,7,2] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 6
[3,5,4,6,2,1,7] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 6
[3,5,4,6,2,7,1] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 6
[3,5,4,6,7,1,2] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 6
[3,5,4,6,7,2,1] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 6
[3,5,4,7,1,2,6] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 8
[3,5,4,7,1,6,2] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 8
[3,5,4,7,2,1,6] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 8
[3,5,4,7,2,6,1] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 8
[3,5,4,7,6,1,2] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 8
[3,5,4,7,6,2,1] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 8
[3,5,6,1,2,4,7] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 6
[3,5,6,1,2,7,4] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 6
[3,5,6,1,4,2,7] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 6
[3,5,6,1,4,7,2] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 6
[3,5,6,1,7,2,4] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 6
[3,5,6,1,7,4,2] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 6
[3,5,6,2,1,4,7] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 6
[3,5,6,2,1,7,4] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 6
[3,5,6,2,4,1,7] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 6
[3,5,6,2,4,7,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 6
[3,5,6,2,7,1,4] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 6
[3,5,6,2,7,4,1] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 6
[3,5,6,4,1,2,7] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 6
[3,5,6,4,1,7,2] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 6
[3,5,6,4,2,1,7] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 6
[3,5,6,4,2,7,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 6
[3,5,6,4,7,1,2] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 6
[3,5,6,4,7,2,1] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 6
[3,5,6,7,1,2,4] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 6
[3,5,6,7,1,4,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 6
[3,5,6,7,2,1,4] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 6
[3,5,6,7,2,4,1] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 6
[3,5,6,7,4,1,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 6
[3,5,6,7,4,2,1] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 6
[3,5,7,1,2,4,6] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 8
[3,5,7,1,2,6,4] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 8
[3,5,7,1,4,2,6] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 8
[3,5,7,1,4,6,2] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 8
[3,5,7,1,6,2,4] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 8
[3,5,7,1,6,4,2] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 8
[3,5,7,2,1,4,6] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 8
[3,5,7,2,1,6,4] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 8
[3,5,7,2,4,1,6] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 8
[3,5,7,2,4,6,1] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 8
[3,5,7,2,6,1,4] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 8
[3,5,7,2,6,4,1] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 8
[3,5,7,4,1,2,6] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 8
[3,5,7,4,1,6,2] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 8
[3,5,7,4,2,1,6] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 8
[3,5,7,4,2,6,1] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 8
[3,5,7,4,6,1,2] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 8
[3,5,7,4,6,2,1] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 8
[3,5,7,6,1,2,4] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 8
[3,5,7,6,1,4,2] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 8
[3,5,7,6,2,1,4] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 8
[3,5,7,6,2,4,1] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 8
[3,5,7,6,4,1,2] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 8
[3,5,7,6,4,2,1] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 8
[3,6,1,2,4,5,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 7
[3,6,1,2,4,7,5] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 7
[3,6,1,2,5,4,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 7
[3,6,1,2,5,7,4] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 7
[3,6,1,2,7,4,5] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 7
[3,6,1,2,7,5,4] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 7
[3,6,1,4,2,5,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 7
[3,6,1,4,2,7,5] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 7
[3,6,1,4,5,2,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 7
[3,6,1,4,5,7,2] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 7
[3,6,1,4,7,2,5] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 7
[3,6,1,4,7,5,2] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 7
[3,6,1,5,2,4,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 7
[3,6,1,5,2,7,4] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 7
[3,6,1,5,4,2,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 7
[3,6,1,5,4,7,2] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 7
[3,6,1,5,7,2,4] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 7
[3,6,1,5,7,4,2] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 7
[3,6,1,7,2,4,5] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 7
[3,6,1,7,2,5,4] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 7
[3,6,1,7,4,2,5] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 7
[3,6,1,7,4,5,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 7
[3,6,1,7,5,2,4] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 7
[3,6,1,7,5,4,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 7
[3,6,2,1,4,5,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 7
[3,6,2,1,4,7,5] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 7
[3,6,2,1,5,4,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 7
[3,6,2,1,5,7,4] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 7
[3,6,2,1,7,4,5] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 7
[3,6,2,1,7,5,4] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 7
[3,6,2,4,1,5,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 7
[3,6,2,4,1,7,5] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 7
[3,6,2,4,5,1,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 7
[3,6,2,4,5,7,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 7
[3,6,2,4,7,1,5] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 7
[3,6,2,4,7,5,1] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 7
[3,6,2,5,1,4,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 7
[3,6,2,5,1,7,4] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 7
[3,6,2,5,4,1,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 7
[3,6,2,5,4,7,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 7
[3,6,2,5,7,1,4] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 7
[3,6,2,5,7,4,1] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 7
[3,6,2,7,1,4,5] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 7
[3,6,2,7,1,5,4] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 7
[3,6,2,7,4,1,5] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 7
[3,6,2,7,4,5,1] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 7
[3,6,2,7,5,1,4] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 7
[3,6,2,7,5,4,1] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 7
[3,6,4,1,2,5,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 7
[3,6,4,1,2,7,5] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 7
[3,6,4,1,5,2,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 7
[3,6,4,1,5,7,2] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 7
[3,6,4,1,7,2,5] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 7
[3,6,4,1,7,5,2] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 7
[3,6,4,2,1,5,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 7
[3,6,4,2,1,7,5] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 7
[3,6,4,2,5,1,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 7
[3,6,4,2,5,7,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 7
[3,6,4,2,7,1,5] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 7
[3,6,4,2,7,5,1] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 7
[3,6,4,5,1,2,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 7
[3,6,4,5,1,7,2] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 7
[3,6,4,5,2,1,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 7
[3,6,4,5,2,7,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 7
[3,6,4,5,7,1,2] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 7
[3,6,4,5,7,2,1] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 7
[3,6,4,7,1,2,5] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 7
[3,6,4,7,1,5,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 7
[3,6,4,7,2,1,5] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 7
[3,6,4,7,2,5,1] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 7
[3,6,4,7,5,1,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 7
[3,6,4,7,5,2,1] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 7
[3,6,5,1,2,4,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 7
[3,6,5,1,2,7,4] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 7
[3,6,5,1,4,2,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 7
[3,6,5,1,4,7,2] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 7
[3,6,5,1,7,2,4] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 7
[3,6,5,1,7,4,2] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 7
[3,6,5,2,1,4,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 7
[3,6,5,2,1,7,4] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 7
[3,6,5,2,4,1,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 7
[3,6,5,2,4,7,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 7
[3,6,5,2,7,1,4] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 7
[3,6,5,2,7,4,1] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 7
[3,6,5,4,1,2,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 7
[3,6,5,4,1,7,2] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 7
[3,6,5,4,2,1,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 7
[3,6,5,4,2,7,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 7
[3,6,5,4,7,1,2] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 7
[3,6,5,4,7,2,1] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 7
[3,6,5,7,1,2,4] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 7
[3,6,5,7,1,4,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 7
[3,6,5,7,2,1,4] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 7
[3,6,5,7,2,4,1] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 7
[3,6,5,7,4,1,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 7
[3,6,5,7,4,2,1] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 7
[3,6,7,1,2,4,5] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 7
[3,6,7,1,2,5,4] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 7
[3,6,7,1,4,2,5] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 7
[3,6,7,1,4,5,2] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 7
[3,6,7,1,5,2,4] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 7
[3,6,7,1,5,4,2] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 7
[3,6,7,2,1,4,5] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 7
[3,6,7,2,1,5,4] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 7
[3,6,7,2,4,1,5] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 7
[3,6,7,2,4,5,1] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 7
[3,6,7,2,5,1,4] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 7
[3,6,7,2,5,4,1] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 7
[3,6,7,4,1,2,5] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 7
[3,6,7,4,1,5,2] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 7
[3,6,7,4,2,1,5] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 7
[3,6,7,4,2,5,1] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 7
[3,6,7,4,5,1,2] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 7
[3,6,7,4,5,2,1] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 7
[3,6,7,5,1,2,4] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 7
[3,6,7,5,1,4,2] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 7
[3,6,7,5,2,1,4] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 7
[3,6,7,5,2,4,1] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 7
[3,6,7,5,4,1,2] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 7
[3,6,7,5,4,2,1] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 7
[3,7,1,2,4,5,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,1,2,4,6,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,1,2,5,4,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,1,2,5,6,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,1,2,6,4,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,1,2,6,5,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,1,4,2,5,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,1,4,2,6,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,1,4,5,2,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,1,4,5,6,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,1,4,6,2,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,1,4,6,5,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,1,5,2,4,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,1,5,2,6,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,1,5,4,2,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,1,5,4,6,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,1,5,6,2,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,1,5,6,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,1,6,2,4,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,1,6,2,5,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,1,6,4,2,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,1,6,4,5,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,1,6,5,2,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,2,1,4,5,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,2,1,4,6,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,2,1,5,4,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,2,1,5,6,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,2,1,6,4,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,2,1,6,5,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,2,4,1,5,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,2,4,1,6,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,2,4,5,1,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,2,4,5,6,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,2,4,6,1,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,2,4,6,5,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,2,5,1,4,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,2,5,1,6,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,2,5,4,1,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,2,5,4,6,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,2,5,6,1,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,2,5,6,4,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,2,6,1,4,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,2,6,1,5,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,2,6,4,1,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,2,6,4,5,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,2,6,5,1,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,2,6,5,4,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,4,1,2,5,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,4,1,2,6,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,4,1,5,2,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,4,1,5,6,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,4,1,6,2,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,4,1,6,5,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,4,2,1,5,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,4,2,1,6,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,4,2,5,1,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,4,2,5,6,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,4,2,6,1,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,4,2,6,5,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,4,5,1,2,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,4,5,1,6,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,4,5,2,1,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,4,5,2,6,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,4,5,6,1,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,4,5,6,2,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,4,6,1,2,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,4,6,1,5,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,4,6,2,1,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,4,6,2,5,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,4,6,5,1,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,4,6,5,2,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,5,1,2,4,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,5,1,2,6,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,5,1,4,2,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,5,1,4,6,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,5,1,6,2,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,5,1,6,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,5,2,1,4,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,5,2,1,6,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,5,2,4,1,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,5,2,4,6,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,5,2,6,1,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,5,2,6,4,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,5,4,1,2,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,5,4,1,6,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,5,4,2,1,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,5,4,2,6,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,5,4,6,1,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,5,4,6,2,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,5,6,1,2,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,5,6,1,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,5,6,2,1,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,5,6,2,4,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,5,6,4,1,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,5,6,4,2,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,6,1,2,4,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,6,1,2,5,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,6,1,4,2,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,6,1,4,5,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,6,1,5,2,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,6,1,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,6,2,1,4,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,6,2,1,5,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,6,2,4,1,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,6,2,4,5,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,6,2,5,1,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,6,2,5,4,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,6,4,1,2,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,6,4,1,5,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,6,4,2,1,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,6,4,2,5,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,6,4,5,1,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,6,4,5,2,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,6,5,1,2,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,6,5,1,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,6,5,2,1,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,6,5,2,4,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,6,5,4,1,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[3,7,6,5,4,2,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[4,1,2,3,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 5
[4,1,2,3,5,7,6] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 7
[4,1,2,3,6,5,7] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 7
[4,1,2,3,6,7,5] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 7
[4,1,2,3,7,5,6] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 8
[4,1,2,3,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 8
[4,1,2,5,3,6,7] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 5
[4,1,2,5,3,7,6] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 7
[4,1,2,5,6,3,7] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 5
[4,1,2,5,6,7,3] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 5
[4,1,2,5,7,3,6] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 7
[4,1,2,5,7,6,3] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 7
[4,1,2,6,3,5,7] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 7
[4,1,2,6,3,7,5] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 7
[4,1,2,6,5,3,7] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 7
[4,1,2,6,5,7,3] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 7
[4,1,2,6,7,3,5] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 7
[4,1,2,6,7,5,3] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 7
[4,1,2,7,3,5,6] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 8
[4,1,2,7,3,6,5] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 8
[4,1,2,7,5,3,6] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 8
[4,1,2,7,5,6,3] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 8
[4,1,2,7,6,3,5] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 8
[4,1,2,7,6,5,3] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 8
[4,1,3,2,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 5
[4,1,3,2,5,7,6] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 7
[4,1,3,2,6,5,7] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 7
[4,1,3,2,6,7,5] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 7
[4,1,3,2,7,5,6] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 8
[4,1,3,2,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 8
[4,1,3,5,2,6,7] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 5
[4,1,3,5,2,7,6] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 7
[4,1,3,5,6,2,7] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 5
[4,1,3,5,6,7,2] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 5
[4,1,3,5,7,2,6] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 7
[4,1,3,5,7,6,2] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 7
[4,1,3,6,2,5,7] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 7
[4,1,3,6,2,7,5] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 7
[4,1,3,6,5,2,7] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 7
[4,1,3,6,5,7,2] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 7
[4,1,3,6,7,2,5] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 7
[4,1,3,6,7,5,2] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 7
[4,1,3,7,2,5,6] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 8
[4,1,3,7,2,6,5] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 8
[4,1,3,7,5,2,6] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 8
[4,1,3,7,5,6,2] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 8
[4,1,3,7,6,2,5] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 8
[4,1,3,7,6,5,2] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 8
[4,1,5,2,3,6,7] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 5
[4,1,5,2,3,7,6] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 7
[4,1,5,2,6,3,7] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 5
[4,1,5,2,6,7,3] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 5
[4,1,5,2,7,3,6] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 7
[4,1,5,2,7,6,3] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 7
[4,1,5,3,2,6,7] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 5
[4,1,5,3,2,7,6] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 7
[4,1,5,3,6,2,7] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 5
[4,1,5,3,6,7,2] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 5
[4,1,5,3,7,2,6] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 7
[4,1,5,3,7,6,2] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 7
[4,1,5,6,2,3,7] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 5
[4,1,5,6,2,7,3] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 5
[4,1,5,6,3,2,7] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 5
[4,1,5,6,3,7,2] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 5
[4,1,5,6,7,2,3] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 5
[4,1,5,6,7,3,2] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 5
[4,1,5,7,2,3,6] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 7
[4,1,5,7,2,6,3] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 7
[4,1,5,7,3,2,6] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 7
[4,1,5,7,3,6,2] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 7
[4,1,5,7,6,2,3] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 7
[4,1,5,7,6,3,2] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 7
[4,1,6,2,3,5,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 7
[4,1,6,2,3,7,5] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 7
[4,1,6,2,5,3,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 7
[4,1,6,2,5,7,3] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 7
[4,1,6,2,7,3,5] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 7
[4,1,6,2,7,5,3] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 7
[4,1,6,3,2,5,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 7
[4,1,6,3,2,7,5] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 7
[4,1,6,3,5,2,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 7
[4,1,6,3,5,7,2] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 7
[4,1,6,3,7,2,5] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 7
[4,1,6,3,7,5,2] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 7
[4,1,6,5,2,3,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 7
[4,1,6,5,2,7,3] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 7
[4,1,6,5,3,2,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 7
[4,1,6,5,3,7,2] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 7
[4,1,6,5,7,2,3] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 7
[4,1,6,5,7,3,2] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 7
[4,1,6,7,2,3,5] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 7
[4,1,6,7,2,5,3] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 7
[4,1,6,7,3,2,5] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 7
[4,1,6,7,3,5,2] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 7
[4,1,6,7,5,2,3] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 7
[4,1,6,7,5,3,2] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 7
[4,1,7,2,3,5,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,1,7,2,3,6,5] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,1,7,2,5,3,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,1,7,2,5,6,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,1,7,2,6,3,5] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,1,7,2,6,5,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,1,7,3,2,5,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,1,7,3,2,6,5] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,1,7,3,5,2,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,1,7,3,5,6,2] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,1,7,3,6,2,5] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,1,7,3,6,5,2] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,1,7,5,2,3,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,1,7,5,2,6,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,1,7,5,3,2,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,1,7,5,3,6,2] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,1,7,5,6,2,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,1,7,5,6,3,2] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,1,7,6,2,3,5] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,1,7,6,2,5,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,1,7,6,3,2,5] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,1,7,6,3,5,2] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,1,7,6,5,2,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,1,7,6,5,3,2] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,2,1,3,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 5
[4,2,1,3,5,7,6] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 7
[4,2,1,3,6,5,7] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 7
[4,2,1,3,6,7,5] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 7
[4,2,1,3,7,5,6] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 8
[4,2,1,3,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 8
[4,2,1,5,3,6,7] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 5
[4,2,1,5,3,7,6] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 7
[4,2,1,5,6,3,7] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 5
[4,2,1,5,6,7,3] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 5
[4,2,1,5,7,3,6] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 7
[4,2,1,5,7,6,3] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 7
[4,2,1,6,3,5,7] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 7
[4,2,1,6,3,7,5] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 7
[4,2,1,6,5,3,7] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 7
[4,2,1,6,5,7,3] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 7
[4,2,1,6,7,3,5] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 7
[4,2,1,6,7,5,3] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 7
[4,2,1,7,3,5,6] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 8
[4,2,1,7,3,6,5] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 8
[4,2,1,7,5,3,6] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 8
[4,2,1,7,5,6,3] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 8
[4,2,1,7,6,3,5] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 8
[4,2,1,7,6,5,3] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 8
[4,2,3,1,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 5
[4,2,3,1,5,7,6] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 7
[4,2,3,1,6,5,7] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 7
[4,2,3,1,6,7,5] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 7
[4,2,3,1,7,5,6] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 8
[4,2,3,1,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 8
[4,2,3,5,1,6,7] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 5
[4,2,3,5,1,7,6] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 7
[4,2,3,5,6,1,7] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 5
[4,2,3,5,6,7,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 5
[4,2,3,5,7,1,6] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 7
[4,2,3,5,7,6,1] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 7
[4,2,3,6,1,5,7] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 7
[4,2,3,6,1,7,5] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 7
[4,2,3,6,5,1,7] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 7
[4,2,3,6,5,7,1] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 7
[4,2,3,6,7,1,5] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 7
[4,2,3,6,7,5,1] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 7
[4,2,3,7,1,5,6] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 8
[4,2,3,7,1,6,5] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 8
[4,2,3,7,5,1,6] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 8
[4,2,3,7,5,6,1] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 8
[4,2,3,7,6,1,5] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 8
[4,2,3,7,6,5,1] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 8
[4,2,5,1,3,6,7] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 5
[4,2,5,1,3,7,6] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 7
[4,2,5,1,6,3,7] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 5
[4,2,5,1,6,7,3] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 5
[4,2,5,1,7,3,6] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 7
[4,2,5,1,7,6,3] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 7
[4,2,5,3,1,6,7] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 5
[4,2,5,3,1,7,6] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 7
[4,2,5,3,6,1,7] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 5
[4,2,5,3,6,7,1] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 5
[4,2,5,3,7,1,6] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 7
[4,2,5,3,7,6,1] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 7
[4,2,5,6,1,3,7] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 5
[4,2,5,6,1,7,3] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 5
[4,2,5,6,3,1,7] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 5
[4,2,5,6,3,7,1] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 5
[4,2,5,6,7,1,3] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 5
[4,2,5,6,7,3,1] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 5
[4,2,5,7,1,3,6] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 7
[4,2,5,7,1,6,3] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 7
[4,2,5,7,3,1,6] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 7
[4,2,5,7,3,6,1] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 7
[4,2,5,7,6,1,3] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 7
[4,2,5,7,6,3,1] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 7
[4,2,6,1,3,5,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 7
[4,2,6,1,3,7,5] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 7
[4,2,6,1,5,3,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 7
[4,2,6,1,5,7,3] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 7
[4,2,6,1,7,3,5] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 7
[4,2,6,1,7,5,3] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 7
[4,2,6,3,1,5,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 7
[4,2,6,3,1,7,5] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 7
[4,2,6,3,5,1,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 7
[4,2,6,3,5,7,1] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 7
[4,2,6,3,7,1,5] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 7
[4,2,6,3,7,5,1] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 7
[4,2,6,5,1,3,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 7
[4,2,6,5,1,7,3] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 7
[4,2,6,5,3,1,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 7
[4,2,6,5,3,7,1] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 7
[4,2,6,5,7,1,3] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 7
[4,2,6,5,7,3,1] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 7
[4,2,6,7,1,3,5] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 7
[4,2,6,7,1,5,3] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 7
[4,2,6,7,3,1,5] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 7
[4,2,6,7,3,5,1] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 7
[4,2,6,7,5,1,3] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 7
[4,2,6,7,5,3,1] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 7
[4,2,7,1,3,5,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,2,7,1,3,6,5] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,2,7,1,5,3,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,2,7,1,5,6,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,2,7,1,6,3,5] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,2,7,1,6,5,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,2,7,3,1,5,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,2,7,3,1,6,5] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,2,7,3,5,1,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,2,7,3,5,6,1] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,2,7,3,6,1,5] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,2,7,3,6,5,1] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,2,7,5,1,3,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,2,7,5,1,6,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,2,7,5,3,1,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,2,7,5,3,6,1] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,2,7,5,6,1,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,2,7,5,6,3,1] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,2,7,6,1,3,5] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,2,7,6,1,5,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,2,7,6,3,1,5] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,2,7,6,3,5,1] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,2,7,6,5,1,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,2,7,6,5,3,1] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,3,1,2,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 5
[4,3,1,2,5,7,6] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 7
[4,3,1,2,6,5,7] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 7
[4,3,1,2,6,7,5] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 7
[4,3,1,2,7,5,6] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 8
[4,3,1,2,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 8
[4,3,1,5,2,6,7] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 5
[4,3,1,5,2,7,6] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 7
[4,3,1,5,6,2,7] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 5
[4,3,1,5,6,7,2] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 5
[4,3,1,5,7,2,6] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 7
[4,3,1,5,7,6,2] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 7
[4,3,1,6,2,5,7] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 7
[4,3,1,6,2,7,5] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 7
[4,3,1,6,5,2,7] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 7
[4,3,1,6,5,7,2] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 7
[4,3,1,6,7,2,5] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 7
[4,3,1,6,7,5,2] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 7
[4,3,1,7,2,5,6] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 8
[4,3,1,7,2,6,5] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 8
[4,3,1,7,5,2,6] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 8
[4,3,1,7,5,6,2] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 8
[4,3,1,7,6,2,5] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 8
[4,3,1,7,6,5,2] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 8
[4,3,2,1,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 5
[4,3,2,1,5,7,6] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 7
[4,3,2,1,6,5,7] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 7
[4,3,2,1,6,7,5] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 7
[4,3,2,1,7,5,6] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 8
[4,3,2,1,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 8
[4,3,2,5,1,6,7] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 5
[4,3,2,5,1,7,6] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 7
[4,3,2,5,6,1,7] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 5
[4,3,2,5,6,7,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 5
[4,3,2,5,7,1,6] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 7
[4,3,2,5,7,6,1] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 7
[4,3,2,6,1,5,7] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 7
[4,3,2,6,1,7,5] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 7
[4,3,2,6,5,1,7] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 7
[4,3,2,6,5,7,1] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 7
[4,3,2,6,7,1,5] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 7
[4,3,2,6,7,5,1] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 7
[4,3,2,7,1,5,6] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 8
[4,3,2,7,1,6,5] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 8
[4,3,2,7,5,1,6] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 8
[4,3,2,7,5,6,1] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 8
[4,3,2,7,6,1,5] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 8
[4,3,2,7,6,5,1] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 8
[4,3,5,1,2,6,7] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 5
[4,3,5,1,2,7,6] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 7
[4,3,5,1,6,2,7] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 5
[4,3,5,1,6,7,2] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 5
[4,3,5,1,7,2,6] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 7
[4,3,5,1,7,6,2] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 7
[4,3,5,2,1,6,7] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 5
[4,3,5,2,1,7,6] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 7
[4,3,5,2,6,1,7] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 5
[4,3,5,2,6,7,1] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 5
[4,3,5,2,7,1,6] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 7
[4,3,5,2,7,6,1] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 7
[4,3,5,6,1,2,7] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 5
[4,3,5,6,1,7,2] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 5
[4,3,5,6,2,1,7] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 5
[4,3,5,6,2,7,1] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 5
[4,3,5,6,7,1,2] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 5
[4,3,5,6,7,2,1] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 5
[4,3,5,7,1,2,6] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 7
[4,3,5,7,1,6,2] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 7
[4,3,5,7,2,1,6] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 7
[4,3,5,7,2,6,1] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 7
[4,3,5,7,6,1,2] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 7
[4,3,5,7,6,2,1] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 7
[4,3,6,1,2,5,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 7
[4,3,6,1,2,7,5] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 7
[4,3,6,1,5,2,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 7
[4,3,6,1,5,7,2] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 7
[4,3,6,1,7,2,5] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 7
[4,3,6,1,7,5,2] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 7
[4,3,6,2,1,5,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 7
[4,3,6,2,1,7,5] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 7
[4,3,6,2,5,1,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 7
[4,3,6,2,5,7,1] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 7
[4,3,6,2,7,1,5] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 7
[4,3,6,2,7,5,1] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 7
[4,3,6,5,1,2,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 7
[4,3,6,5,1,7,2] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 7
[4,3,6,5,2,1,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 7
[4,3,6,5,2,7,1] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 7
[4,3,6,5,7,1,2] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 7
[4,3,6,5,7,2,1] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 7
[4,3,6,7,1,2,5] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 7
[4,3,6,7,1,5,2] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 7
[4,3,6,7,2,1,5] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 7
[4,3,6,7,2,5,1] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 7
[4,3,6,7,5,1,2] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 7
[4,3,6,7,5,2,1] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 7
[4,3,7,1,2,5,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,3,7,1,2,6,5] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,3,7,1,5,2,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,3,7,1,5,6,2] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,3,7,1,6,2,5] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,3,7,1,6,5,2] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,3,7,2,1,5,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,3,7,2,1,6,5] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,3,7,2,5,1,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,3,7,2,5,6,1] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,3,7,2,6,1,5] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,3,7,2,6,5,1] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,3,7,5,1,2,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,3,7,5,1,6,2] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,3,7,5,2,1,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,3,7,5,2,6,1] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,3,7,5,6,1,2] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,3,7,5,6,2,1] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,3,7,6,1,2,5] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,3,7,6,1,5,2] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,3,7,6,2,1,5] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,3,7,6,2,5,1] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,3,7,6,5,1,2] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,3,7,6,5,2,1] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[4,5,1,2,3,6,7] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 5
[4,5,1,2,3,7,6] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 7
[4,5,1,2,6,3,7] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 5
[4,5,1,2,6,7,3] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 5
[4,5,1,2,7,3,6] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 7
[4,5,1,2,7,6,3] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 7
[4,5,1,3,2,6,7] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 5
[4,5,1,3,2,7,6] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 7
[4,5,1,3,6,2,7] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 5
[4,5,1,3,6,7,2] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 5
[4,5,1,3,7,2,6] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 7
[4,5,1,3,7,6,2] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 7
[4,5,1,6,2,3,7] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 5
[4,5,1,6,2,7,3] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 5
[4,5,1,6,3,2,7] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 5
[4,5,1,6,3,7,2] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 5
[4,5,1,6,7,2,3] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 5
[4,5,1,6,7,3,2] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 5
[4,5,1,7,2,3,6] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 7
[4,5,1,7,2,6,3] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 7
[4,5,1,7,3,2,6] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 7
[4,5,1,7,3,6,2] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 7
[4,5,1,7,6,2,3] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 7
[4,5,1,7,6,3,2] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 7
[4,5,2,1,3,6,7] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 5
[4,5,2,1,3,7,6] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 7
[4,5,2,1,6,3,7] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 5
[4,5,2,1,6,7,3] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 5
[4,5,2,1,7,3,6] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 7
[4,5,2,1,7,6,3] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 7
[4,5,2,3,1,6,7] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 5
[4,5,2,3,1,7,6] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 7
[4,5,2,3,6,1,7] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 5
[4,5,2,3,6,7,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 5
[4,5,2,3,7,1,6] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 7
[4,5,2,3,7,6,1] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 7
[4,5,2,6,1,3,7] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 5
[4,5,2,6,1,7,3] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 5
[4,5,2,6,3,1,7] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 5
[4,5,2,6,3,7,1] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 5
[4,5,2,6,7,1,3] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 5
[4,5,2,6,7,3,1] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 5
[4,5,2,7,1,3,6] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 7
[4,5,2,7,1,6,3] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 7
[4,5,2,7,3,1,6] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 7
[4,5,2,7,3,6,1] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 7
[4,5,2,7,6,1,3] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 7
[4,5,2,7,6,3,1] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 7
[4,5,3,1,2,6,7] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 5
[4,5,3,1,2,7,6] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 7
[4,5,3,1,6,2,7] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 5
[4,5,3,1,6,7,2] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 5
[4,5,3,1,7,2,6] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 7
[4,5,3,1,7,6,2] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 7
[4,5,3,2,1,6,7] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 5
[4,5,3,2,1,7,6] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 7
[4,5,3,2,6,1,7] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 5
[4,5,3,2,6,7,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 5
[4,5,3,2,7,1,6] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 7
[4,5,3,2,7,6,1] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 7
[4,5,3,6,1,2,7] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 5
[4,5,3,6,1,7,2] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 5
[4,5,3,6,2,1,7] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 5
[4,5,3,6,2,7,1] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 5
[4,5,3,6,7,1,2] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 5
[4,5,3,6,7,2,1] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 5
[4,5,3,7,1,2,6] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 7
[4,5,3,7,1,6,2] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 7
[4,5,3,7,2,1,6] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 7
[4,5,3,7,2,6,1] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 7
[4,5,3,7,6,1,2] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 7
[4,5,3,7,6,2,1] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 7
[4,5,6,1,2,3,7] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 5
[4,5,6,1,2,7,3] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 5
[4,5,6,1,3,2,7] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 5
[4,5,6,1,3,7,2] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 5
[4,5,6,1,7,2,3] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 5
[4,5,6,1,7,3,2] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 5
[4,5,6,2,1,3,7] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 5
[4,5,6,2,1,7,3] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 5
[4,5,6,2,3,1,7] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 5
[4,5,6,2,3,7,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 5
[4,5,6,2,7,1,3] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 5
[4,5,6,2,7,3,1] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 5
[4,5,6,3,1,2,7] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 5
[4,5,6,3,1,7,2] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 5
[4,5,6,3,2,1,7] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 5
[4,5,6,3,2,7,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 5
[4,5,6,3,7,1,2] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 5
[4,5,6,3,7,2,1] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 5
[4,5,6,7,1,2,3] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 5
[4,5,6,7,1,3,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 5
[4,5,6,7,2,1,3] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 5
[4,5,6,7,2,3,1] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 5
[4,5,6,7,3,1,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 5
[4,5,6,7,3,2,1] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 5
[4,5,7,1,2,3,6] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 7
[4,5,7,1,2,6,3] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 7
[4,5,7,1,3,2,6] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 7
[4,5,7,1,3,6,2] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 7
[4,5,7,1,6,2,3] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 7
[4,5,7,1,6,3,2] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 7
[4,5,7,2,1,3,6] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 7
[4,5,7,2,1,6,3] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 7
[4,5,7,2,3,1,6] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 7
[4,5,7,2,3,6,1] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 7
[4,5,7,2,6,1,3] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 7
[4,5,7,2,6,3,1] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 7
[4,5,7,3,1,2,6] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 7
[4,5,7,3,1,6,2] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 7
[4,5,7,3,2,1,6] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 7
[4,5,7,3,2,6,1] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 7
[4,5,7,3,6,1,2] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 7
[4,5,7,3,6,2,1] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 7
[4,5,7,6,1,2,3] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 7
[4,5,7,6,1,3,2] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 7
[4,5,7,6,2,1,3] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 7
[4,5,7,6,2,3,1] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 7
[4,5,7,6,3,1,2] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 7
[4,5,7,6,3,2,1] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 7
[4,6,1,2,3,5,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 7
[4,6,1,2,3,7,5] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 7
[4,6,1,2,5,3,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 7
[4,6,1,2,5,7,3] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 7
[4,6,1,2,7,3,5] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 7
[4,6,1,2,7,5,3] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 7
[4,6,1,3,2,5,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 7
[4,6,1,3,2,7,5] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 7
[4,6,1,3,5,2,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 7
[4,6,1,3,5,7,2] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 7
[4,6,1,3,7,2,5] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 7
[4,6,1,3,7,5,2] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 7
[4,6,1,5,2,3,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 7
[4,6,1,5,2,7,3] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 7
[4,6,1,5,3,2,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 7
[4,6,1,5,3,7,2] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 7
[4,6,1,5,7,2,3] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 7
[4,6,1,5,7,3,2] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 7
[4,6,1,7,2,3,5] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 7
[4,6,1,7,2,5,3] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 7
[4,6,1,7,3,2,5] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 7
[4,6,1,7,3,5,2] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 7
[4,6,1,7,5,2,3] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 7
[4,6,1,7,5,3,2] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 7
[4,6,2,1,3,5,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 7
[4,6,2,1,3,7,5] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 7
[4,6,2,1,5,3,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 7
[4,6,2,1,5,7,3] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 7
[4,6,2,1,7,3,5] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 7
[4,6,2,1,7,5,3] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 7
[4,6,2,3,1,5,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 7
[4,6,2,3,1,7,5] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 7
[4,6,2,3,5,1,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 7
[4,6,2,3,5,7,1] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 7
[4,6,2,3,7,1,5] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 7
[4,6,2,3,7,5,1] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 7
[4,6,2,5,1,3,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 7
[4,6,2,5,1,7,3] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 7
[4,6,2,5,3,1,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 7
[4,6,2,5,3,7,1] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 7
[4,6,2,5,7,1,3] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 7
[4,6,2,5,7,3,1] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 7
[4,6,2,7,1,3,5] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 7
[4,6,2,7,1,5,3] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 7
[4,6,2,7,3,1,5] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 7
[4,6,2,7,3,5,1] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 7
[4,6,2,7,5,1,3] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 7
[4,6,2,7,5,3,1] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 7
[4,6,3,1,2,5,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 7
[4,6,3,1,2,7,5] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 7
[4,6,3,1,5,2,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 7
[4,6,3,1,5,7,2] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 7
[4,6,3,1,7,2,5] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 7
[4,6,3,1,7,5,2] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 7
[4,6,3,2,1,5,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 7
[4,6,3,2,1,7,5] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 7
[4,6,3,2,5,1,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 7
[4,6,3,2,5,7,1] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 7
[4,6,3,2,7,1,5] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 7
[4,6,3,2,7,5,1] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 7
[4,6,3,5,1,2,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 7
[4,6,3,5,1,7,2] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 7
[4,6,3,5,2,1,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 7
[4,6,3,5,2,7,1] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 7
[4,6,3,5,7,1,2] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 7
[4,6,3,5,7,2,1] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 7
[4,6,3,7,1,2,5] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 7
[4,6,3,7,1,5,2] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 7
[4,6,3,7,2,1,5] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 7
[4,6,3,7,2,5,1] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 7
[4,6,3,7,5,1,2] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 7
[4,6,3,7,5,2,1] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 7
[4,6,5,1,2,3,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 7
[4,6,5,1,2,7,3] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 7
[4,6,5,1,3,2,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 7
[4,6,5,1,3,7,2] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 7
[4,6,5,1,7,2,3] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 7
[4,6,5,1,7,3,2] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 7
[4,6,5,2,1,3,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 7
[4,6,5,2,1,7,3] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 7
[4,6,5,2,3,1,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 7
[4,6,5,2,3,7,1] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 7
[4,6,5,2,7,1,3] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 7
[4,6,5,2,7,3,1] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 7
[4,6,5,3,1,2,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 7
[4,6,5,3,1,7,2] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 7
[4,6,5,3,2,1,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 7
[4,6,5,3,2,7,1] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 7
[4,6,5,3,7,1,2] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 7
[4,6,5,3,7,2,1] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 7
[4,6,5,7,1,2,3] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 7
[4,6,5,7,1,3,2] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 7
[4,6,5,7,2,1,3] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 7
[4,6,5,7,2,3,1] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 7
[4,6,5,7,3,1,2] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 7
[4,6,5,7,3,2,1] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 7
[4,6,7,1,2,3,5] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 7
[4,6,7,1,2,5,3] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 7
[4,6,7,1,3,2,5] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 7
[4,6,7,1,3,5,2] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 7
[4,6,7,1,5,2,3] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 7
[4,6,7,1,5,3,2] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 7
[4,6,7,2,1,3,5] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 7
[4,6,7,2,1,5,3] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 7
[4,6,7,2,3,1,5] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 7
[4,6,7,2,3,5,1] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 7
[4,6,7,2,5,1,3] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 7
[4,6,7,2,5,3,1] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 7
[4,6,7,3,1,2,5] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 7
[4,6,7,3,1,5,2] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 7
[4,6,7,3,2,1,5] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 7
[4,6,7,3,2,5,1] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 7
[4,6,7,3,5,1,2] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 7
[4,6,7,3,5,2,1] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 7
[4,6,7,5,1,2,3] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 7
[4,6,7,5,1,3,2] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 7
[4,6,7,5,2,1,3] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 7
[4,6,7,5,2,3,1] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 7
[4,6,7,5,3,1,2] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 7
[4,6,7,5,3,2,1] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 7
[4,7,1,2,3,5,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,1,2,3,6,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,1,2,5,3,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,1,2,5,6,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,1,2,6,3,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,1,2,6,5,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,1,3,2,5,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,1,3,2,6,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,1,3,5,2,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,1,3,5,6,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,1,3,6,2,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,1,3,6,5,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,1,5,2,3,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,1,5,2,6,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,1,5,3,2,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,1,5,3,6,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,1,5,6,2,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,1,5,6,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,1,6,2,3,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,1,6,2,5,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,1,6,3,2,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,1,6,3,5,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,1,6,5,2,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,1,6,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,2,1,3,5,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,2,1,3,6,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,2,1,5,3,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,2,1,5,6,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,2,1,6,3,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,2,1,6,5,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,2,3,1,5,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,2,3,1,6,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,2,3,5,1,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,2,3,5,6,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,2,3,6,1,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,2,3,6,5,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,2,5,1,3,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,2,5,1,6,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,2,5,3,1,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,2,5,3,6,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,2,5,6,1,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,2,5,6,3,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,2,6,1,3,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,2,6,1,5,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,2,6,3,1,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,2,6,3,5,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,2,6,5,1,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,2,6,5,3,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,3,1,2,5,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,3,1,2,6,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,3,1,5,2,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,3,1,5,6,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,3,1,6,2,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,3,1,6,5,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,3,2,1,5,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,3,2,1,6,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,3,2,5,1,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,3,2,5,6,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,3,2,6,1,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,3,2,6,5,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,3,5,1,2,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,3,5,1,6,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,3,5,2,1,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,3,5,2,6,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,3,5,6,1,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,3,5,6,2,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,3,6,1,2,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,3,6,1,5,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,3,6,2,1,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,3,6,2,5,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,3,6,5,1,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,3,6,5,2,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,5,1,2,3,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,5,1,2,6,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,5,1,3,2,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,5,1,3,6,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,5,1,6,2,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,5,1,6,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,5,2,1,3,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,5,2,1,6,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,5,2,3,1,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,5,2,3,6,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,5,2,6,1,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,5,2,6,3,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,5,3,1,2,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,5,3,1,6,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,5,3,2,1,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,5,3,2,6,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,5,3,6,1,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,5,3,6,2,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,5,6,1,2,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,5,6,1,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,5,6,2,1,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,5,6,2,3,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,5,6,3,1,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,5,6,3,2,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,6,1,2,3,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,6,1,2,5,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,6,1,3,2,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,6,1,3,5,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,6,1,5,2,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,6,2,1,3,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,6,2,1,5,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,6,2,3,1,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,6,2,3,5,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,6,2,5,1,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,6,2,5,3,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,6,3,1,2,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,6,3,1,5,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,6,3,2,1,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,6,3,2,5,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,6,3,5,1,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,6,3,5,2,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,6,5,1,2,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,6,5,1,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,6,5,2,1,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,6,5,2,3,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,6,5,3,1,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[4,7,6,5,3,2,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[5,1,2,3,4,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[5,1,2,3,4,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 8
[5,1,2,3,6,4,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 6
[5,1,2,3,6,7,4] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 6
[5,1,2,3,7,4,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8
[5,1,2,3,7,6,4] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8
[5,1,2,4,3,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[5,1,2,4,3,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 8
[5,1,2,4,6,3,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 6
[5,1,2,4,6,7,3] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 6
[5,1,2,4,7,3,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8
[5,1,2,4,7,6,3] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8
[5,1,2,6,3,4,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 6
[5,1,2,6,3,7,4] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 6
[5,1,2,6,4,3,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 6
[5,1,2,6,4,7,3] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 6
[5,1,2,6,7,3,4] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 6
[5,1,2,6,7,4,3] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 6
[5,1,2,7,3,4,6] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,1,2,7,3,6,4] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,1,2,7,4,3,6] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,1,2,7,4,6,3] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,1,2,7,6,3,4] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,1,2,7,6,4,3] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,1,3,2,4,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[5,1,3,2,4,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 8
[5,1,3,2,6,4,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 6
[5,1,3,2,6,7,4] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 6
[5,1,3,2,7,4,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8
[5,1,3,2,7,6,4] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8
[5,1,3,4,2,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[5,1,3,4,2,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 8
[5,1,3,4,6,2,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 6
[5,1,3,4,6,7,2] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 6
[5,1,3,4,7,2,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8
[5,1,3,4,7,6,2] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8
[5,1,3,6,2,4,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 6
[5,1,3,6,2,7,4] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 6
[5,1,3,6,4,2,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 6
[5,1,3,6,4,7,2] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 6
[5,1,3,6,7,2,4] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 6
[5,1,3,6,7,4,2] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 6
[5,1,3,7,2,4,6] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,1,3,7,2,6,4] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,1,3,7,4,2,6] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,1,3,7,4,6,2] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,1,3,7,6,2,4] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,1,3,7,6,4,2] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,1,4,2,3,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[5,1,4,2,3,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 8
[5,1,4,2,6,3,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 6
[5,1,4,2,6,7,3] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 6
[5,1,4,2,7,3,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8
[5,1,4,2,7,6,3] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8
[5,1,4,3,2,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[5,1,4,3,2,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 8
[5,1,4,3,6,2,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 6
[5,1,4,3,6,7,2] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 6
[5,1,4,3,7,2,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8
[5,1,4,3,7,6,2] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8
[5,1,4,6,2,3,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 6
[5,1,4,6,2,7,3] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 6
[5,1,4,6,3,2,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 6
[5,1,4,6,3,7,2] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 6
[5,1,4,6,7,2,3] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 6
[5,1,4,6,7,3,2] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 6
[5,1,4,7,2,3,6] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,1,4,7,2,6,3] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,1,4,7,3,2,6] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,1,4,7,3,6,2] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,1,4,7,6,2,3] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,1,4,7,6,3,2] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,1,6,2,3,4,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 6
[5,1,6,2,3,7,4] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 6
[5,1,6,2,4,3,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 6
[5,1,6,2,4,7,3] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 6
[5,1,6,2,7,3,4] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 6
[5,1,6,2,7,4,3] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 6
[5,1,6,3,2,4,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 6
[5,1,6,3,2,7,4] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 6
[5,1,6,3,4,2,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 6
[5,1,6,3,4,7,2] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 6
[5,1,6,3,7,2,4] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 6
[5,1,6,3,7,4,2] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 6
[5,1,6,4,2,3,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 6
[5,1,6,4,2,7,3] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 6
[5,1,6,4,3,2,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 6
[5,1,6,4,3,7,2] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 6
[5,1,6,4,7,2,3] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 6
[5,1,6,4,7,3,2] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 6
[5,1,6,7,2,3,4] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 6
[5,1,6,7,2,4,3] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 6
[5,1,6,7,3,2,4] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 6
[5,1,6,7,3,4,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 6
[5,1,6,7,4,2,3] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 6
[5,1,6,7,4,3,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 6
[5,1,7,2,3,4,6] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,1,7,2,3,6,4] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,1,7,2,4,3,6] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,1,7,2,4,6,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,1,7,2,6,3,4] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,1,7,2,6,4,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,1,7,3,2,4,6] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,1,7,3,2,6,4] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,1,7,3,4,2,6] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,1,7,3,4,6,2] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,1,7,3,6,2,4] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,1,7,3,6,4,2] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,1,7,4,2,3,6] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,1,7,4,2,6,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,1,7,4,3,2,6] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,1,7,4,3,6,2] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,1,7,4,6,2,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,1,7,4,6,3,2] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,1,7,6,2,3,4] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,1,7,6,2,4,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,1,7,6,3,2,4] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,1,7,6,3,4,2] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,1,7,6,4,2,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,1,7,6,4,3,2] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,2,1,3,4,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[5,2,1,3,4,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 8
[5,2,1,3,6,4,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 6
[5,2,1,3,6,7,4] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 6
[5,2,1,3,7,4,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8
[5,2,1,3,7,6,4] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8
[5,2,1,4,3,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[5,2,1,4,3,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 8
[5,2,1,4,6,3,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 6
[5,2,1,4,6,7,3] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 6
[5,2,1,4,7,3,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8
[5,2,1,4,7,6,3] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8
[5,2,1,6,3,4,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 6
[5,2,1,6,3,7,4] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 6
[5,2,1,6,4,3,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 6
[5,2,1,6,4,7,3] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 6
[5,2,1,6,7,3,4] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 6
[5,2,1,6,7,4,3] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 6
[5,2,1,7,3,4,6] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,2,1,7,3,6,4] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,2,1,7,4,3,6] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,2,1,7,4,6,3] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,2,1,7,6,3,4] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,2,1,7,6,4,3] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,2,3,1,4,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[5,2,3,1,4,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 8
[5,2,3,1,6,4,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 6
[5,2,3,1,6,7,4] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 6
[5,2,3,1,7,4,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8
[5,2,3,1,7,6,4] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8
[5,2,3,4,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[5,2,3,4,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 8
[5,2,3,4,6,1,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 6
[5,2,3,4,6,7,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 6
[5,2,3,4,7,1,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8
[5,2,3,4,7,6,1] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8
[5,2,3,6,1,4,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 6
[5,2,3,6,1,7,4] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 6
[5,2,3,6,4,1,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 6
[5,2,3,6,4,7,1] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 6
[5,2,3,6,7,1,4] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 6
[5,2,3,6,7,4,1] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 6
[5,2,3,7,1,4,6] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,2,3,7,1,6,4] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,2,3,7,4,1,6] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,2,3,7,4,6,1] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,2,3,7,6,1,4] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,2,3,7,6,4,1] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,2,4,1,3,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[5,2,4,1,3,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 8
[5,2,4,1,6,3,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 6
[5,2,4,1,6,7,3] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 6
[5,2,4,1,7,3,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8
[5,2,4,1,7,6,3] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8
[5,2,4,3,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[5,2,4,3,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 8
[5,2,4,3,6,1,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 6
[5,2,4,3,6,7,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 6
[5,2,4,3,7,1,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8
[5,2,4,3,7,6,1] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8
[5,2,4,6,1,3,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 6
[5,2,4,6,1,7,3] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 6
[5,2,4,6,3,1,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 6
[5,2,4,6,3,7,1] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 6
[5,2,4,6,7,1,3] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 6
[5,2,4,6,7,3,1] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 6
[5,2,4,7,1,3,6] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,2,4,7,1,6,3] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,2,4,7,3,1,6] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,2,4,7,3,6,1] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,2,4,7,6,1,3] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,2,4,7,6,3,1] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,2,6,1,3,4,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 6
[5,2,6,1,3,7,4] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 6
[5,2,6,1,4,3,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 6
[5,2,6,1,4,7,3] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 6
[5,2,6,1,7,3,4] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 6
[5,2,6,1,7,4,3] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 6
[5,2,6,3,1,4,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 6
[5,2,6,3,1,7,4] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 6
[5,2,6,3,4,1,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 6
[5,2,6,3,4,7,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 6
[5,2,6,3,7,1,4] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 6
[5,2,6,3,7,4,1] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 6
[5,2,6,4,1,3,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 6
[5,2,6,4,1,7,3] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 6
[5,2,6,4,3,1,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 6
[5,2,6,4,3,7,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 6
[5,2,6,4,7,1,3] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 6
[5,2,6,4,7,3,1] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 6
[5,2,6,7,1,3,4] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 6
[5,2,6,7,1,4,3] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 6
[5,2,6,7,3,1,4] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 6
[5,2,6,7,3,4,1] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 6
[5,2,6,7,4,1,3] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 6
[5,2,6,7,4,3,1] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 6
[5,2,7,1,3,4,6] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,2,7,1,3,6,4] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,2,7,1,4,3,6] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,2,7,1,4,6,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,2,7,1,6,3,4] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,2,7,1,6,4,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,2,7,3,1,4,6] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,2,7,3,1,6,4] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,2,7,3,4,1,6] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,2,7,3,4,6,1] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,2,7,3,6,1,4] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,2,7,3,6,4,1] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,2,7,4,1,3,6] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,2,7,4,1,6,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,2,7,4,3,1,6] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,2,7,4,3,6,1] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,2,7,4,6,1,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,2,7,4,6,3,1] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,2,7,6,1,3,4] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,2,7,6,1,4,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,2,7,6,3,1,4] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,2,7,6,3,4,1] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,2,7,6,4,1,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,2,7,6,4,3,1] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,3,1,2,4,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[5,3,1,2,4,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 8
[5,3,1,2,6,4,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 6
[5,3,1,2,6,7,4] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 6
[5,3,1,2,7,4,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8
[5,3,1,2,7,6,4] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8
[5,3,1,4,2,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[5,3,1,4,2,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 8
[5,3,1,4,6,2,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 6
[5,3,1,4,6,7,2] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 6
[5,3,1,4,7,2,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8
[5,3,1,4,7,6,2] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8
[5,3,1,6,2,4,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 6
[5,3,1,6,2,7,4] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 6
[5,3,1,6,4,2,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 6
[5,3,1,6,4,7,2] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 6
[5,3,1,6,7,2,4] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 6
[5,3,1,6,7,4,2] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 6
[5,3,1,7,2,4,6] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,3,1,7,2,6,4] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,3,1,7,4,2,6] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,3,1,7,4,6,2] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,3,1,7,6,2,4] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,3,1,7,6,4,2] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,3,2,1,4,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[5,3,2,1,4,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 8
[5,3,2,1,6,4,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 6
[5,3,2,1,6,7,4] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 6
[5,3,2,1,7,4,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8
[5,3,2,1,7,6,4] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8
[5,3,2,4,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[5,3,2,4,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 8
[5,3,2,4,6,1,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 6
[5,3,2,4,6,7,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 6
[5,3,2,4,7,1,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8
[5,3,2,4,7,6,1] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8
[5,3,2,6,1,4,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 6
[5,3,2,6,1,7,4] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 6
[5,3,2,6,4,1,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 6
[5,3,2,6,4,7,1] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 6
[5,3,2,6,7,1,4] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 6
[5,3,2,6,7,4,1] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 6
[5,3,2,7,1,4,6] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,3,2,7,1,6,4] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,3,2,7,4,1,6] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,3,2,7,4,6,1] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,3,2,7,6,1,4] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,3,2,7,6,4,1] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,3,4,1,2,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[5,3,4,1,2,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 8
[5,3,4,1,6,2,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 6
[5,3,4,1,6,7,2] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 6
[5,3,4,1,7,2,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8
[5,3,4,1,7,6,2] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8
[5,3,4,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[5,3,4,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 8
[5,3,4,2,6,1,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 6
[5,3,4,2,6,7,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 6
[5,3,4,2,7,1,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8
[5,3,4,2,7,6,1] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8
[5,3,4,6,1,2,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 6
[5,3,4,6,1,7,2] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 6
[5,3,4,6,2,1,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 6
[5,3,4,6,2,7,1] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 6
[5,3,4,6,7,1,2] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 6
[5,3,4,6,7,2,1] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 6
[5,3,4,7,1,2,6] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,3,4,7,1,6,2] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,3,4,7,2,1,6] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,3,4,7,2,6,1] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,3,4,7,6,1,2] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,3,4,7,6,2,1] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,3,6,1,2,4,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 6
[5,3,6,1,2,7,4] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 6
[5,3,6,1,4,2,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 6
[5,3,6,1,4,7,2] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 6
[5,3,6,1,7,2,4] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 6
[5,3,6,1,7,4,2] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 6
[5,3,6,2,1,4,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 6
[5,3,6,2,1,7,4] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 6
[5,3,6,2,4,1,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 6
[5,3,6,2,4,7,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 6
[5,3,6,2,7,1,4] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 6
[5,3,6,2,7,4,1] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 6
[5,3,6,4,1,2,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 6
[5,3,6,4,1,7,2] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 6
[5,3,6,4,2,1,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 6
[5,3,6,4,2,7,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 6
[5,3,6,4,7,1,2] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 6
[5,3,6,4,7,2,1] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 6
[5,3,6,7,1,2,4] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 6
[5,3,6,7,1,4,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 6
[5,3,6,7,2,1,4] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 6
[5,3,6,7,2,4,1] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 6
[5,3,6,7,4,1,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 6
[5,3,6,7,4,2,1] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 6
[5,3,7,1,2,4,6] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,3,7,1,2,6,4] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,3,7,1,4,2,6] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,3,7,1,4,6,2] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,3,7,1,6,2,4] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,3,7,1,6,4,2] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,3,7,2,1,4,6] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,3,7,2,1,6,4] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,3,7,2,4,1,6] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,3,7,2,4,6,1] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,3,7,2,6,1,4] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,3,7,2,6,4,1] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,3,7,4,1,2,6] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,3,7,4,1,6,2] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,3,7,4,2,1,6] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,3,7,4,2,6,1] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,3,7,4,6,1,2] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,3,7,4,6,2,1] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,3,7,6,1,2,4] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,3,7,6,1,4,2] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,3,7,6,2,1,4] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,3,7,6,2,4,1] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,3,7,6,4,1,2] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,3,7,6,4,2,1] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,4,1,2,3,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[5,4,1,2,3,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 8
[5,4,1,2,6,3,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 6
[5,4,1,2,6,7,3] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 6
[5,4,1,2,7,3,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8
[5,4,1,2,7,6,3] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8
[5,4,1,3,2,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[5,4,1,3,2,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 8
[5,4,1,3,6,2,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 6
[5,4,1,3,6,7,2] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 6
[5,4,1,3,7,2,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8
[5,4,1,3,7,6,2] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8
[5,4,1,6,2,3,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 6
[5,4,1,6,2,7,3] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 6
[5,4,1,6,3,2,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 6
[5,4,1,6,3,7,2] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 6
[5,4,1,6,7,2,3] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 6
[5,4,1,6,7,3,2] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 6
[5,4,1,7,2,3,6] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,4,1,7,2,6,3] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,4,1,7,3,2,6] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,4,1,7,3,6,2] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,4,1,7,6,2,3] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,4,1,7,6,3,2] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,4,2,1,3,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[5,4,2,1,3,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 8
[5,4,2,1,6,3,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 6
[5,4,2,1,6,7,3] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 6
[5,4,2,1,7,3,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8
[5,4,2,1,7,6,3] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8
[5,4,2,3,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[5,4,2,3,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 8
[5,4,2,3,6,1,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 6
[5,4,2,3,6,7,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 6
[5,4,2,3,7,1,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8
[5,4,2,3,7,6,1] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8
[5,4,2,6,1,3,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 6
[5,4,2,6,1,7,3] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 6
[5,4,2,6,3,1,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 6
[5,4,2,6,3,7,1] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 6
[5,4,2,6,7,1,3] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 6
[5,4,2,6,7,3,1] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 6
[5,4,2,7,1,3,6] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,4,2,7,1,6,3] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,4,2,7,3,1,6] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,4,2,7,3,6,1] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,4,2,7,6,1,3] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,4,2,7,6,3,1] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,4,3,1,2,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[5,4,3,1,2,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 8
[5,4,3,1,6,2,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 6
[5,4,3,1,6,7,2] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 6
[5,4,3,1,7,2,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8
[5,4,3,1,7,6,2] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8
[5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[5,4,3,2,1,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 8
[5,4,3,2,6,1,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 6
[5,4,3,2,6,7,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 6
[5,4,3,2,7,1,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8
[5,4,3,2,7,6,1] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 8
[5,4,3,6,1,2,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 6
[5,4,3,6,1,7,2] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 6
[5,4,3,6,2,1,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 6
[5,4,3,6,2,7,1] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 6
[5,4,3,6,7,1,2] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 6
[5,4,3,6,7,2,1] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 6
[5,4,3,7,1,2,6] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,4,3,7,1,6,2] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,4,3,7,2,1,6] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,4,3,7,2,6,1] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,4,3,7,6,1,2] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,4,3,7,6,2,1] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 8
[5,4,6,1,2,3,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 6
[5,4,6,1,2,7,3] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 6
[5,4,6,1,3,2,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 6
[5,4,6,1,3,7,2] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 6
[5,4,6,1,7,2,3] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 6
[5,4,6,1,7,3,2] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 6
[5,4,6,2,1,3,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 6
[5,4,6,2,1,7,3] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 6
[5,4,6,2,3,1,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 6
[5,4,6,2,3,7,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 6
[5,4,6,2,7,1,3] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 6
[5,4,6,2,7,3,1] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 6
[5,4,6,3,1,2,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 6
[5,4,6,3,1,7,2] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 6
[5,4,6,3,2,1,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 6
[5,4,6,3,2,7,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 6
[5,4,6,3,7,1,2] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 6
[5,4,6,3,7,2,1] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 6
[5,4,6,7,1,2,3] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 6
[5,4,6,7,1,3,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 6
[5,4,6,7,2,1,3] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 6
[5,4,6,7,2,3,1] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 6
[5,4,6,7,3,1,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 6
[5,4,6,7,3,2,1] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 6
[5,4,7,1,2,3,6] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,4,7,1,2,6,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,4,7,1,3,2,6] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,4,7,1,3,6,2] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,4,7,1,6,2,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,4,7,1,6,3,2] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,4,7,2,1,3,6] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,4,7,2,1,6,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,4,7,2,3,1,6] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,4,7,2,3,6,1] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,4,7,2,6,1,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,4,7,2,6,3,1] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,4,7,3,1,2,6] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,4,7,3,1,6,2] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,4,7,3,2,1,6] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,4,7,3,2,6,1] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,4,7,3,6,1,2] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,4,7,3,6,2,1] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,4,7,6,1,2,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,4,7,6,1,3,2] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,4,7,6,2,1,3] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,4,7,6,2,3,1] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,4,7,6,3,1,2] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,4,7,6,3,2,1] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[5,6,1,2,3,4,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 6
[5,6,1,2,3,7,4] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 6
[5,6,1,2,4,3,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 6
[5,6,1,2,4,7,3] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 6
[5,6,1,2,7,3,4] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 6
[5,6,1,2,7,4,3] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 6
[5,6,1,3,2,4,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 6
[5,6,1,3,2,7,4] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 6
[5,6,1,3,4,2,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 6
[5,6,1,3,4,7,2] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 6
[5,6,1,3,7,2,4] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 6
[5,6,1,3,7,4,2] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 6
[5,6,1,4,2,3,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 6
[5,6,1,4,2,7,3] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 6
[5,6,1,4,3,2,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 6
[5,6,1,4,3,7,2] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 6
[5,6,1,4,7,2,3] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 6
[5,6,1,4,7,3,2] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 6
[5,6,1,7,2,3,4] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 6
[5,6,1,7,2,4,3] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 6
[5,6,1,7,3,2,4] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 6
[5,6,1,7,3,4,2] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 6
[5,6,1,7,4,2,3] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 6
[5,6,1,7,4,3,2] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 6
[5,6,2,1,3,4,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 6
[5,6,2,1,3,7,4] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 6
[5,6,2,1,4,3,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 6
[5,6,2,1,4,7,3] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 6
[5,6,2,1,7,3,4] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 6
[5,6,2,1,7,4,3] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 6
[5,6,2,3,1,4,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 6
[5,6,2,3,1,7,4] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 6
[5,6,2,3,4,1,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 6
[5,6,2,3,4,7,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 6
[5,6,2,3,7,1,4] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 6
[5,6,2,3,7,4,1] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 6
[5,6,2,4,1,3,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 6
[5,6,2,4,1,7,3] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 6
[5,6,2,4,3,1,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 6
[5,6,2,4,3,7,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 6
[5,6,2,4,7,1,3] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 6
[5,6,2,4,7,3,1] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 6
[5,6,2,7,1,3,4] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 6
[5,6,2,7,1,4,3] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 6
[5,6,2,7,3,1,4] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 6
[5,6,2,7,3,4,1] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 6
[5,6,2,7,4,1,3] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 6
[5,6,2,7,4,3,1] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 6
[5,6,3,1,2,4,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 6
[5,6,3,1,2,7,4] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 6
[5,6,3,1,4,2,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 6
[5,6,3,1,4,7,2] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 6
[5,6,3,1,7,2,4] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 6
[5,6,3,1,7,4,2] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 6
[5,6,3,2,1,4,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 6
[5,6,3,2,1,7,4] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 6
[5,6,3,2,4,1,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 6
[5,6,3,2,4,7,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 6
[5,6,3,2,7,1,4] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 6
[5,6,3,2,7,4,1] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 6
[5,6,3,4,1,2,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 6
[5,6,3,4,1,7,2] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 6
[5,6,3,4,2,1,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 6
[5,6,3,4,2,7,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 6
[5,6,3,4,7,1,2] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 6
[5,6,3,4,7,2,1] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 6
[5,6,3,7,1,2,4] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 6
[5,6,3,7,1,4,2] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 6
[5,6,3,7,2,1,4] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 6
[5,6,3,7,2,4,1] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 6
[5,6,3,7,4,1,2] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 6
[5,6,3,7,4,2,1] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 6
[5,6,4,1,2,3,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 6
[5,6,4,1,2,7,3] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 6
[5,6,4,1,3,2,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 6
[5,6,4,1,3,7,2] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 6
[5,6,4,1,7,2,3] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 6
[5,6,4,1,7,3,2] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 6
[5,6,4,2,1,3,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 6
[5,6,4,2,1,7,3] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 6
[5,6,4,2,3,1,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 6
[5,6,4,2,3,7,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 6
[5,6,4,2,7,1,3] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 6
[5,6,4,2,7,3,1] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 6
[5,6,4,3,1,2,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 6
[5,6,4,3,1,7,2] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 6
[5,6,4,3,2,1,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 6
[5,6,4,3,2,7,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 6
[5,6,4,3,7,1,2] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 6
[5,6,4,3,7,2,1] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 6
[5,6,4,7,1,2,3] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 6
[5,6,4,7,1,3,2] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 6
[5,6,4,7,2,1,3] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 6
[5,6,4,7,2,3,1] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 6
[5,6,4,7,3,1,2] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 6
[5,6,4,7,3,2,1] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 6
[5,6,7,1,2,3,4] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 6
[5,6,7,1,2,4,3] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 6
[5,6,7,1,3,2,4] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 6
[5,6,7,1,3,4,2] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 6
[5,6,7,1,4,2,3] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 6
[5,6,7,1,4,3,2] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 6
[5,6,7,2,1,3,4] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 6
[5,6,7,2,1,4,3] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 6
[5,6,7,2,3,1,4] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 6
[5,6,7,2,3,4,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 6
[5,6,7,2,4,1,3] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 6
[5,6,7,2,4,3,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 6
[5,6,7,3,1,2,4] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 6
[5,6,7,3,1,4,2] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 6
[5,6,7,3,2,1,4] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 6
[5,6,7,3,2,4,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 6
[5,6,7,3,4,1,2] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 6
[5,6,7,3,4,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 6
[5,6,7,4,1,2,3] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 6
[5,6,7,4,1,3,2] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 6
[5,6,7,4,2,1,3] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 6
[5,6,7,4,2,3,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 6
[5,6,7,4,3,1,2] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 6
[5,6,7,4,3,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 6
[5,7,1,2,3,4,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,1,2,3,6,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,1,2,4,3,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,1,2,4,6,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,1,2,6,3,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,1,2,6,4,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,1,3,2,4,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,1,3,2,6,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,1,3,4,2,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,1,3,4,6,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,1,3,6,2,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,1,3,6,4,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,1,4,2,3,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,1,4,2,6,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,1,4,3,2,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,1,4,3,6,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,1,4,6,2,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,1,4,6,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,1,6,2,3,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,1,6,2,4,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,1,6,3,2,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,1,6,3,4,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,1,6,4,2,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,1,6,4,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,2,1,3,4,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,2,1,3,6,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,2,1,4,3,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,2,1,4,6,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,2,1,6,3,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,2,1,6,4,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,2,3,1,4,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,2,3,1,6,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,2,3,4,1,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,2,3,4,6,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,2,3,6,1,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,2,3,6,4,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,2,4,1,3,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,2,4,1,6,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,2,4,3,1,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,2,4,3,6,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,2,4,6,1,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,2,4,6,3,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,2,6,1,3,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,2,6,1,4,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,2,6,3,1,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,2,6,3,4,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,2,6,4,1,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,2,6,4,3,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,3,1,2,4,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,3,1,2,6,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,3,1,4,2,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,3,1,4,6,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,3,1,6,2,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,3,1,6,4,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,3,2,1,4,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,3,2,1,6,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,3,2,4,1,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,3,2,4,6,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,3,2,6,1,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,3,2,6,4,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,3,4,1,2,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,3,4,1,6,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,3,4,2,1,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,3,4,2,6,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,3,4,6,1,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,3,4,6,2,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,3,6,1,2,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,3,6,1,4,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,3,6,2,1,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,3,6,2,4,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,3,6,4,1,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,3,6,4,2,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,4,1,2,3,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,4,1,2,6,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,4,1,3,2,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,4,1,3,6,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,4,1,6,2,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,4,1,6,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,4,2,1,3,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,4,2,1,6,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,4,2,3,1,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,4,2,3,6,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,4,2,6,1,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,4,2,6,3,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,4,3,1,2,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,4,3,1,6,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,4,3,2,1,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,4,3,2,6,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,4,3,6,1,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,4,3,6,2,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,4,6,1,2,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,4,6,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,4,6,2,1,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,4,6,2,3,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,4,6,3,1,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,4,6,3,2,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,6,1,2,3,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,6,1,2,4,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,6,1,3,2,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,6,1,3,4,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,6,1,4,2,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,6,1,4,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,6,2,1,3,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,6,2,1,4,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,6,2,3,1,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,6,2,3,4,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,6,2,4,1,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,6,2,4,3,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,6,3,1,2,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,6,3,1,4,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,6,3,2,1,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,6,3,2,4,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,6,3,4,1,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,6,3,4,2,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,6,4,1,2,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,6,4,2,1,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,6,4,2,3,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,6,4,3,1,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[5,7,6,4,3,2,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[6,1,2,3,4,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,1,2,3,4,7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,1,2,3,5,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,1,2,3,5,7,4] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,1,2,3,7,4,5] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,1,2,3,7,5,4] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,1,2,4,3,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,1,2,4,3,7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,1,2,4,5,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,1,2,4,5,7,3] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,1,2,4,7,3,5] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,1,2,4,7,5,3] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,1,2,5,3,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,1,2,5,3,7,4] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,1,2,5,4,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,1,2,5,4,7,3] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,1,2,5,7,3,4] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,1,2,5,7,4,3] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,1,2,7,3,4,5] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,1,2,7,3,5,4] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,1,2,7,4,3,5] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,1,2,7,4,5,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,1,2,7,5,3,4] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,1,2,7,5,4,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,1,3,2,4,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,1,3,2,4,7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,1,3,2,5,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,1,3,2,5,7,4] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,1,3,2,7,4,5] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,1,3,2,7,5,4] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,1,3,4,2,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,1,3,4,2,7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,1,3,4,5,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,1,3,4,5,7,2] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,1,3,4,7,2,5] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,1,3,4,7,5,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,1,3,5,2,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,1,3,5,2,7,4] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,1,3,5,4,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,1,3,5,4,7,2] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,1,3,5,7,2,4] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,1,3,5,7,4,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,1,3,7,2,4,5] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,1,3,7,2,5,4] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,1,3,7,4,2,5] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,1,3,7,4,5,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,1,3,7,5,2,4] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,1,3,7,5,4,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,1,4,2,3,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,1,4,2,3,7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,1,4,2,5,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,1,4,2,5,7,3] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,1,4,2,7,3,5] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,1,4,2,7,5,3] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,1,4,3,2,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,1,4,3,2,7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,1,4,3,5,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,1,4,3,5,7,2] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,1,4,3,7,2,5] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,1,4,3,7,5,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,1,4,5,2,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,1,4,5,2,7,3] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,1,4,5,3,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,1,4,5,3,7,2] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,1,4,5,7,2,3] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,1,4,5,7,3,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,1,4,7,2,3,5] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,1,4,7,2,5,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,1,4,7,3,2,5] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,1,4,7,3,5,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,1,4,7,5,2,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,1,4,7,5,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,1,5,2,3,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,1,5,2,3,7,4] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,1,5,2,4,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,1,5,2,4,7,3] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,1,5,2,7,3,4] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,1,5,2,7,4,3] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,1,5,3,2,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,1,5,3,2,7,4] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,1,5,3,4,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,1,5,3,4,7,2] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,1,5,3,7,2,4] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,1,5,3,7,4,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,1,5,4,2,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,1,5,4,2,7,3] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,1,5,4,3,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,1,5,4,3,7,2] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,1,5,4,7,2,3] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,1,5,4,7,3,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,1,5,7,2,3,4] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,1,5,7,2,4,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,1,5,7,3,2,4] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,1,5,7,3,4,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,1,5,7,4,2,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,1,5,7,4,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,1,7,2,3,4,5] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,1,7,2,3,5,4] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,1,7,2,4,3,5] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,1,7,2,4,5,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,1,7,2,5,3,4] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,1,7,2,5,4,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,1,7,3,2,4,5] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,1,7,3,2,5,4] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,1,7,3,4,2,5] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,1,7,3,4,5,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,1,7,3,5,2,4] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,1,7,3,5,4,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,1,7,4,2,3,5] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,1,7,4,2,5,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,1,7,4,3,2,5] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,1,7,4,3,5,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,1,7,4,5,2,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,1,7,4,5,3,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,1,7,5,2,3,4] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,1,7,5,2,4,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,1,7,5,3,2,4] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,1,7,5,3,4,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,1,7,5,4,2,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,1,7,5,4,3,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,2,1,3,4,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,2,1,3,4,7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,2,1,3,5,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,2,1,3,5,7,4] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,2,1,3,7,4,5] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,2,1,3,7,5,4] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,2,1,4,3,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,2,1,4,3,7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,2,1,4,5,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,2,1,4,5,7,3] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,2,1,4,7,3,5] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,2,1,4,7,5,3] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,2,1,5,3,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,2,1,5,3,7,4] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,2,1,5,4,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,2,1,5,4,7,3] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,2,1,5,7,3,4] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,2,1,5,7,4,3] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,2,1,7,3,4,5] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,2,1,7,3,5,4] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,2,1,7,4,3,5] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,2,1,7,4,5,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,2,1,7,5,3,4] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,2,1,7,5,4,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,2,3,1,4,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,2,3,1,4,7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,2,3,1,5,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,2,3,1,5,7,4] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,2,3,1,7,4,5] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,2,3,1,7,5,4] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,2,3,4,1,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,2,3,4,1,7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,2,3,4,5,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,2,3,4,5,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,2,3,4,7,1,5] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,2,3,4,7,5,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,2,3,5,1,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,2,3,5,1,7,4] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,2,3,5,4,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,2,3,5,4,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,2,3,5,7,1,4] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,2,3,5,7,4,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,2,3,7,1,4,5] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,2,3,7,1,5,4] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,2,3,7,4,1,5] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,2,3,7,4,5,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,2,3,7,5,1,4] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,2,3,7,5,4,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,2,4,1,3,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,2,4,1,3,7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,2,4,1,5,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,2,4,1,5,7,3] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,2,4,1,7,3,5] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,2,4,1,7,5,3] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,2,4,3,1,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,2,4,3,1,7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,2,4,3,5,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,2,4,3,5,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,2,4,3,7,1,5] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,2,4,3,7,5,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,2,4,5,1,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,2,4,5,1,7,3] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,2,4,5,3,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,2,4,5,3,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,2,4,5,7,1,3] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,2,4,5,7,3,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,2,4,7,1,3,5] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,2,4,7,1,5,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,2,4,7,3,1,5] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,2,4,7,3,5,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,2,4,7,5,1,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,2,4,7,5,3,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,2,5,1,3,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,2,5,1,3,7,4] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,2,5,1,4,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,2,5,1,4,7,3] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,2,5,1,7,3,4] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,2,5,1,7,4,3] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,2,5,3,1,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,2,5,3,1,7,4] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,2,5,3,4,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,2,5,3,4,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,2,5,3,7,1,4] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,2,5,3,7,4,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,2,5,4,1,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,2,5,4,1,7,3] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,2,5,4,3,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,2,5,4,3,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,2,5,4,7,1,3] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,2,5,4,7,3,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,2,5,7,1,3,4] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,2,5,7,1,4,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,2,5,7,3,1,4] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,2,5,7,3,4,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,2,5,7,4,1,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,2,5,7,4,3,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,2,7,1,3,4,5] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,2,7,1,3,5,4] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,2,7,1,4,3,5] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,2,7,1,4,5,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,2,7,1,5,3,4] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,2,7,1,5,4,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,2,7,3,1,4,5] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,2,7,3,1,5,4] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,2,7,3,4,1,5] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,2,7,3,4,5,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,2,7,3,5,1,4] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,2,7,3,5,4,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,2,7,4,1,3,5] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,2,7,4,1,5,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,2,7,4,3,1,5] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,2,7,4,3,5,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,2,7,4,5,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,2,7,4,5,3,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,2,7,5,1,3,4] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,2,7,5,1,4,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,2,7,5,3,1,4] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,2,7,5,3,4,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,2,7,5,4,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,2,7,5,4,3,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,3,1,2,4,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,3,1,2,4,7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,3,1,2,5,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,3,1,2,5,7,4] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,3,1,2,7,4,5] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,3,1,2,7,5,4] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,3,1,4,2,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,3,1,4,2,7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,3,1,4,5,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,3,1,4,5,7,2] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,3,1,4,7,2,5] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,3,1,4,7,5,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,3,1,5,2,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,3,1,5,2,7,4] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,3,1,5,4,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,3,1,5,4,7,2] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,3,1,5,7,2,4] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,3,1,5,7,4,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,3,1,7,2,4,5] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,3,1,7,2,5,4] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,3,1,7,4,2,5] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,3,1,7,4,5,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,3,1,7,5,2,4] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,3,1,7,5,4,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,3,2,1,4,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,3,2,1,4,7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,3,2,1,5,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,3,2,1,5,7,4] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,3,2,1,7,4,5] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,3,2,1,7,5,4] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,3,2,4,1,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,3,2,4,1,7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,3,2,4,5,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,3,2,4,5,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,3,2,4,7,1,5] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,3,2,4,7,5,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,3,2,5,1,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,3,2,5,1,7,4] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,3,2,5,4,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,3,2,5,4,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,3,2,5,7,1,4] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,3,2,5,7,4,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,3,2,7,1,4,5] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,3,2,7,1,5,4] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,3,2,7,4,1,5] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,3,2,7,4,5,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,3,2,7,5,1,4] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,3,2,7,5,4,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,3,4,1,2,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,3,4,1,2,7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,3,4,1,5,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,3,4,1,5,7,2] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,3,4,1,7,2,5] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,3,4,1,7,5,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,3,4,2,1,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,3,4,2,1,7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,3,4,2,5,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,3,4,2,5,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,3,4,2,7,1,5] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,3,4,2,7,5,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,3,4,5,1,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,3,4,5,1,7,2] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,3,4,5,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,3,4,5,2,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,3,4,5,7,1,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,3,4,5,7,2,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,3,4,7,1,2,5] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,3,4,7,1,5,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,3,4,7,2,1,5] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,3,4,7,2,5,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,3,4,7,5,1,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,3,4,7,5,2,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,3,5,1,2,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,3,5,1,2,7,4] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,3,5,1,4,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,3,5,1,4,7,2] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,3,5,1,7,2,4] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,3,5,1,7,4,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,3,5,2,1,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,3,5,2,1,7,4] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,3,5,2,4,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,3,5,2,4,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,3,5,2,7,1,4] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,3,5,2,7,4,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,3,5,4,1,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,3,5,4,1,7,2] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,3,5,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,3,5,4,2,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,3,5,4,7,1,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,3,5,4,7,2,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,3,5,7,1,2,4] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,3,5,7,1,4,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,3,5,7,2,1,4] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,3,5,7,2,4,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,3,5,7,4,1,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,3,5,7,4,2,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,3,7,1,2,4,5] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,3,7,1,2,5,4] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,3,7,1,4,2,5] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,3,7,1,4,5,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,3,7,1,5,2,4] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,3,7,1,5,4,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,3,7,2,1,4,5] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,3,7,2,1,5,4] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,3,7,2,4,1,5] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,3,7,2,4,5,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,3,7,2,5,1,4] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,3,7,2,5,4,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,3,7,4,1,2,5] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,3,7,4,1,5,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,3,7,4,2,1,5] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,3,7,4,2,5,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,3,7,4,5,1,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,3,7,4,5,2,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,3,7,5,1,2,4] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,3,7,5,1,4,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,3,7,5,2,1,4] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,3,7,5,2,4,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,3,7,5,4,1,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,3,7,5,4,2,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,4,1,2,3,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,4,1,2,3,7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,4,1,2,5,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,4,1,2,5,7,3] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,4,1,2,7,3,5] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,4,1,2,7,5,3] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,4,1,3,2,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,4,1,3,2,7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,4,1,3,5,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,4,1,3,5,7,2] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,4,1,3,7,2,5] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,4,1,3,7,5,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,4,1,5,2,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,4,1,5,2,7,3] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,4,1,5,3,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,4,1,5,3,7,2] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,4,1,5,7,2,3] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,4,1,5,7,3,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,4,1,7,2,3,5] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,4,1,7,2,5,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,4,1,7,3,2,5] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,4,1,7,3,5,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,4,1,7,5,2,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,4,1,7,5,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,4,2,1,3,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,4,2,1,3,7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,4,2,1,5,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,4,2,1,5,7,3] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,4,2,1,7,3,5] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,4,2,1,7,5,3] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,4,2,3,1,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,4,2,3,1,7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,4,2,3,5,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,4,2,3,5,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,4,2,3,7,1,5] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,4,2,3,7,5,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,4,2,5,1,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,4,2,5,1,7,3] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,4,2,5,3,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,4,2,5,3,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,4,2,5,7,1,3] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,4,2,5,7,3,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,4,2,7,1,3,5] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,4,2,7,1,5,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,4,2,7,3,1,5] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,4,2,7,3,5,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,4,2,7,5,1,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,4,2,7,5,3,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,4,3,1,2,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,4,3,1,2,7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,4,3,1,5,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,4,3,1,5,7,2] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,4,3,1,7,2,5] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,4,3,1,7,5,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,4,3,2,1,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,4,3,2,1,7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,4,3,2,5,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,4,3,2,5,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,4,3,2,7,1,5] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,4,3,2,7,5,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,4,3,5,1,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,4,3,5,1,7,2] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,4,3,5,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,4,3,5,2,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,4,3,5,7,1,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,4,3,5,7,2,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,4,3,7,1,2,5] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,4,3,7,1,5,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,4,3,7,2,1,5] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,4,3,7,2,5,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,4,3,7,5,1,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,4,3,7,5,2,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,4,5,1,2,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,4,5,1,2,7,3] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,4,5,1,3,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,4,5,1,3,7,2] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,4,5,1,7,2,3] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,4,5,1,7,3,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,4,5,2,1,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,4,5,2,1,7,3] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,4,5,2,3,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,4,5,2,3,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,4,5,2,7,1,3] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,4,5,2,7,3,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,4,5,3,1,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,4,5,3,1,7,2] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,4,5,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,4,5,3,2,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,4,5,3,7,1,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,4,5,3,7,2,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,4,5,7,1,2,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,4,5,7,1,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,4,5,7,2,1,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,4,5,7,2,3,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,4,5,7,3,1,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,4,5,7,3,2,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,4,7,1,2,3,5] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,4,7,1,2,5,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,4,7,1,3,2,5] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,4,7,1,3,5,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,4,7,1,5,2,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,4,7,1,5,3,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,4,7,2,1,3,5] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,4,7,2,1,5,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,4,7,2,3,1,5] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,4,7,2,3,5,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,4,7,2,5,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,4,7,2,5,3,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,4,7,3,1,2,5] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,4,7,3,1,5,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,4,7,3,2,1,5] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,4,7,3,2,5,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,4,7,3,5,1,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,4,7,3,5,2,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,4,7,5,1,2,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,4,7,5,1,3,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,4,7,5,2,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,4,7,5,2,3,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,4,7,5,3,1,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,4,7,5,3,2,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,5,1,2,3,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,5,1,2,3,7,4] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,5,1,2,4,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,5,1,2,4,7,3] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,5,1,2,7,3,4] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,5,1,2,7,4,3] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,5,1,3,2,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,5,1,3,2,7,4] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,5,1,3,4,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,5,1,3,4,7,2] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,5,1,3,7,2,4] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,5,1,3,7,4,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,5,1,4,2,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,5,1,4,2,7,3] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,5,1,4,3,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,5,1,4,3,7,2] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,5,1,4,7,2,3] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,5,1,4,7,3,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,5,1,7,2,3,4] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,5,1,7,2,4,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,5,1,7,3,2,4] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,5,1,7,3,4,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,5,1,7,4,2,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,5,1,7,4,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,5,2,1,3,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,5,2,1,3,7,4] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,5,2,1,4,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,5,2,1,4,7,3] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,5,2,1,7,3,4] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,5,2,1,7,4,3] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,5,2,3,1,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,5,2,3,1,7,4] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,5,2,3,4,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,5,2,3,4,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,5,2,3,7,1,4] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,5,2,3,7,4,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,5,2,4,1,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,5,2,4,1,7,3] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,5,2,4,3,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,5,2,4,3,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,5,2,4,7,1,3] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,5,2,4,7,3,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,5,2,7,1,3,4] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,5,2,7,1,4,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,5,2,7,3,1,4] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,5,2,7,3,4,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,5,2,7,4,1,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,5,2,7,4,3,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,5,3,1,2,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,5,3,1,2,7,4] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,5,3,1,4,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,5,3,1,4,7,2] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,5,3,1,7,2,4] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,5,3,1,7,4,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,5,3,2,1,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,5,3,2,1,7,4] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,5,3,2,4,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,5,3,2,4,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,5,3,2,7,1,4] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,5,3,2,7,4,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,5,3,4,1,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,5,3,4,1,7,2] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,5,3,4,2,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,5,3,4,7,1,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,5,3,4,7,2,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,5,3,7,1,2,4] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,5,3,7,1,4,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,5,3,7,2,1,4] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,5,3,7,2,4,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,5,3,7,4,1,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,5,3,7,4,2,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,5,4,1,2,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,5,4,1,2,7,3] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,5,4,1,3,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,5,4,1,3,7,2] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,5,4,1,7,2,3] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,5,4,1,7,3,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,5,4,2,1,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,5,4,2,1,7,3] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,5,4,2,3,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,5,4,2,3,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,5,4,2,7,1,3] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,5,4,2,7,3,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,5,4,3,1,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,5,4,3,1,7,2] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,5,4,3,2,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[6,5,4,3,7,1,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,5,4,3,7,2,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[6,5,4,7,1,2,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,5,4,7,1,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,5,4,7,2,1,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,5,4,7,2,3,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,5,4,7,3,1,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,5,4,7,3,2,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 7
[6,5,7,1,2,3,4] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,5,7,1,2,4,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,5,7,1,3,2,4] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,5,7,1,3,4,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,5,7,1,4,2,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,5,7,1,4,3,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,5,7,2,1,3,4] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,5,7,2,1,4,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,5,7,2,3,1,4] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,5,7,2,3,4,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,5,7,2,4,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,5,7,2,4,3,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,5,7,3,1,2,4] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,5,7,3,1,4,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,5,7,3,2,1,4] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,5,7,3,2,4,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,5,7,3,4,1,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,5,7,3,4,2,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,5,7,4,1,2,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,5,7,4,1,3,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,5,7,4,2,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,5,7,4,2,3,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,5,7,4,3,1,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,5,7,4,3,2,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[6,7,1,2,3,4,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,1,2,3,5,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,1,2,4,3,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,1,2,4,5,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,1,2,5,3,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,1,2,5,4,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,1,3,2,4,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,1,3,2,5,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,1,3,4,2,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,1,3,4,5,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,1,3,5,2,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,1,3,5,4,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,1,4,2,3,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,1,4,2,5,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,1,4,3,2,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,1,4,3,5,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,1,4,5,2,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,1,4,5,3,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,1,5,2,3,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,1,5,2,4,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,1,5,3,2,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,1,5,3,4,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,1,5,4,2,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,1,5,4,3,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,2,1,3,4,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,2,1,3,5,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,2,1,4,3,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,2,1,4,5,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,2,1,5,3,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,2,1,5,4,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,2,3,1,4,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,2,3,1,5,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,2,3,4,1,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,2,3,4,5,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,2,3,5,1,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,2,3,5,4,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,2,4,1,3,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,2,4,1,5,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,2,4,3,1,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,2,4,3,5,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,2,4,5,1,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,2,4,5,3,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,2,5,1,3,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,2,5,1,4,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,2,5,3,1,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,2,5,3,4,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,2,5,4,1,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,2,5,4,3,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,3,1,2,4,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,3,1,2,5,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,3,1,4,2,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,3,1,4,5,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,3,1,5,2,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,3,1,5,4,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,3,2,1,4,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,3,2,1,5,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,3,2,4,1,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,3,2,4,5,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,3,2,5,1,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,3,2,5,4,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,3,4,1,2,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,3,4,1,5,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,3,4,2,1,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,3,4,2,5,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,3,4,5,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,3,4,5,2,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,3,5,1,2,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,3,5,1,4,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,3,5,2,1,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,3,5,2,4,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,3,5,4,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,3,5,4,2,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,4,1,2,3,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,4,1,2,5,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,4,1,3,2,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,4,1,3,5,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,4,1,5,2,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,4,1,5,3,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,4,2,1,3,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,4,2,1,5,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,4,2,3,1,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,4,2,3,5,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,4,2,5,1,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,4,2,5,3,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,4,3,1,2,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,4,3,1,5,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,4,3,2,1,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,4,3,2,5,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,4,3,5,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,4,3,5,2,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,4,5,1,2,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,4,5,1,3,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,4,5,2,1,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,4,5,2,3,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,4,5,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,4,5,3,2,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,5,1,2,3,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,5,1,2,4,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,5,1,3,2,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,5,1,3,4,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,5,1,4,2,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,5,1,4,3,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,5,2,1,3,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,5,2,1,4,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,5,2,3,1,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,5,2,3,4,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,5,2,4,1,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,5,2,4,3,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,5,3,1,2,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,5,3,1,4,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,5,3,2,1,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,5,3,2,4,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,5,3,4,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,5,3,4,2,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,5,4,1,2,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,5,4,1,3,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,5,4,2,1,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,5,4,2,3,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[6,7,5,4,3,2,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[7,1,2,3,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,2,3,4,6,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,2,3,5,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,2,3,5,6,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,2,3,6,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,2,3,6,5,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,2,4,3,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,2,4,3,6,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,2,4,5,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,2,4,5,6,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,2,4,6,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,2,4,6,5,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,2,5,3,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,2,5,3,6,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,2,5,4,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,2,5,4,6,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,2,5,6,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,2,5,6,4,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,2,6,3,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,2,6,3,5,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,2,6,4,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,2,6,4,5,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,2,6,5,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,2,6,5,4,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,3,2,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,3,2,4,6,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,3,2,5,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,3,2,5,6,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,3,2,6,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,3,2,6,5,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,3,4,2,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,3,4,2,6,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,3,4,5,2,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,3,4,5,6,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,3,4,6,2,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,3,4,6,5,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,3,5,2,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,3,5,2,6,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,3,5,4,2,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,3,5,4,6,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,3,5,6,2,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,3,5,6,4,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,3,6,2,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,3,6,2,5,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,3,6,4,2,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,3,6,4,5,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,3,6,5,2,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,3,6,5,4,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,4,2,3,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,4,2,3,6,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,4,2,5,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,4,2,5,6,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,4,2,6,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,4,2,6,5,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,4,3,2,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,4,3,2,6,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,4,3,5,2,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,4,3,5,6,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,4,3,6,2,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,4,3,6,5,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,4,5,2,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,4,5,2,6,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,4,5,3,2,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,4,5,3,6,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,4,5,6,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,4,5,6,3,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,4,6,2,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,4,6,2,5,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,4,6,3,2,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,4,6,3,5,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,4,6,5,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,4,6,5,3,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,5,2,3,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,5,2,3,6,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,5,2,4,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,5,2,4,6,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,5,2,6,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,5,2,6,4,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,5,3,2,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,5,3,2,6,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,5,3,4,2,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,5,3,4,6,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,5,3,6,2,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,5,3,6,4,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,5,4,2,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,5,4,2,6,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,5,4,3,2,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,5,4,3,6,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,5,4,6,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,5,4,6,3,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,5,6,2,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,5,6,2,4,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,5,6,3,2,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,5,6,3,4,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,5,6,4,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,5,6,4,3,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,6,2,3,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,6,2,3,5,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,6,2,4,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,6,2,4,5,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,6,2,5,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,6,2,5,4,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,6,3,2,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,6,3,2,5,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,6,3,4,2,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,6,3,4,5,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,6,3,5,2,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,6,3,5,4,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,6,4,2,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,6,4,2,5,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,6,4,3,2,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,6,4,3,5,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,6,4,5,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,6,4,5,3,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,6,5,2,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,6,5,2,4,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,6,5,3,2,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,6,5,3,4,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,6,5,4,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1,6,5,4,3,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,1,3,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,1,3,4,6,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,1,3,5,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,1,3,5,6,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,1,3,6,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,1,3,6,5,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,1,4,3,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,1,4,3,6,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,1,4,5,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,1,4,5,6,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,1,4,6,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,1,4,6,5,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,1,5,3,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,1,5,3,6,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,1,5,4,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,1,5,4,6,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,1,5,6,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,1,5,6,4,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,1,6,3,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,1,6,3,5,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,1,6,4,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,1,6,4,5,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,1,6,5,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,1,6,5,4,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,3,1,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,3,1,4,6,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,3,1,5,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,3,1,5,6,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,3,1,6,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,3,1,6,5,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,3,4,1,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,3,4,1,6,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,3,4,5,1,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,3,4,5,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,3,4,6,1,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,3,4,6,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,3,5,1,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,3,5,1,6,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,3,5,4,1,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,3,5,4,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,3,5,6,1,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,3,5,6,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,3,6,1,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,3,6,1,5,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,3,6,4,1,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,3,6,4,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,3,6,5,1,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,3,6,5,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,4,1,3,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,4,1,3,6,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,4,1,5,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,4,1,5,6,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,4,1,6,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,4,1,6,5,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,4,3,1,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,4,3,1,6,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,4,3,5,1,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,4,3,5,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,4,3,6,1,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,4,3,6,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,4,5,1,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,4,5,1,6,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,4,5,3,1,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,4,5,3,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,4,5,6,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,4,5,6,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,4,6,1,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,4,6,1,5,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,4,6,3,1,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,4,6,3,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,4,6,5,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,4,6,5,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,5,1,3,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,5,1,3,6,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,5,1,4,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,5,1,4,6,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,5,1,6,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,5,1,6,4,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,5,3,1,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,5,3,1,6,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,5,3,4,1,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,5,3,4,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,5,3,6,1,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,5,3,6,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,5,4,1,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,5,4,1,6,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,5,4,3,1,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,5,4,3,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,5,4,6,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,5,4,6,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,5,6,1,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,5,6,1,4,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,5,6,3,1,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,5,6,3,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,5,6,4,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,5,6,4,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,6,1,3,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,6,1,3,5,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,6,1,4,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,6,1,4,5,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,6,1,5,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,6,1,5,4,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,6,3,1,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,6,3,1,5,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,6,3,4,1,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,6,3,4,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,6,3,5,1,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,6,3,5,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,6,4,1,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,6,4,1,5,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,6,4,3,1,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,6,4,3,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,6,4,5,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,6,4,5,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,6,5,1,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,6,5,1,4,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,6,5,3,1,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,6,5,3,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,6,5,4,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2,6,5,4,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,1,2,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,1,2,4,6,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,1,2,5,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,1,2,5,6,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,1,2,6,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,1,2,6,5,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,1,4,2,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,1,4,2,6,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,1,4,5,2,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,1,4,5,6,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,1,4,6,2,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,1,4,6,5,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,1,5,2,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,1,5,2,6,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,1,5,4,2,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,1,5,4,6,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,1,5,6,2,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,1,5,6,4,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,1,6,2,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,1,6,2,5,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,1,6,4,2,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,1,6,4,5,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,1,6,5,2,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,1,6,5,4,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,2,1,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,2,1,4,6,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,2,1,5,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,2,1,5,6,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,2,1,6,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,2,1,6,5,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,2,4,1,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,2,4,1,6,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,2,4,5,1,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,2,4,5,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,2,4,6,1,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,2,4,6,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,2,5,1,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,2,5,1,6,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,2,5,4,1,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,2,5,4,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,2,5,6,1,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,2,5,6,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,2,6,1,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,2,6,1,5,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,2,6,4,1,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,2,6,4,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,2,6,5,1,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,2,6,5,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,4,1,2,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,4,1,2,6,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,4,1,5,2,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,4,1,5,6,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,4,1,6,2,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,4,1,6,5,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,4,2,1,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,4,2,1,6,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,4,2,5,1,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,4,2,5,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,4,2,6,1,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,4,2,6,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,4,5,1,2,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,4,5,1,6,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,4,5,2,1,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,4,5,2,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,4,5,6,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,4,5,6,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,4,6,1,2,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,4,6,1,5,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,4,6,2,1,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,4,6,2,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,4,6,5,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,4,6,5,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,5,1,2,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,5,1,2,6,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,5,1,4,2,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,5,1,4,6,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,5,1,6,2,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,5,1,6,4,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,5,2,1,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,5,2,1,6,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,5,2,4,1,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,5,2,4,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,5,2,6,1,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,5,2,6,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,5,4,1,2,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,5,4,1,6,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,5,4,2,1,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,5,4,2,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,5,4,6,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,5,4,6,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,5,6,1,2,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,5,6,1,4,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,5,6,2,1,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,5,6,2,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,5,6,4,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,5,6,4,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,6,1,2,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,6,1,2,5,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,6,1,4,2,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,6,1,4,5,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,6,1,5,2,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,6,1,5,4,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,6,2,1,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,6,2,1,5,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,6,2,4,1,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,6,2,4,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,6,2,5,1,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,6,2,5,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,6,4,1,2,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,6,4,1,5,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,6,4,2,1,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,6,4,2,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,6,4,5,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,6,4,5,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,6,5,1,2,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,6,5,1,4,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,6,5,2,1,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,6,5,2,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,6,5,4,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3,6,5,4,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,1,2,3,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,1,2,3,6,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,1,2,5,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,1,2,5,6,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,1,2,6,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,1,2,6,5,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,1,3,2,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,1,3,2,6,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,1,3,5,2,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,1,3,5,6,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,1,3,6,2,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,1,3,6,5,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,1,5,2,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,1,5,2,6,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,1,5,3,2,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,1,5,3,6,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,1,5,6,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,1,5,6,3,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,1,6,2,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,1,6,2,5,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,1,6,3,2,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,1,6,3,5,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,1,6,5,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,1,6,5,3,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,2,1,3,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,2,1,3,6,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,2,1,5,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,2,1,5,6,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,2,1,6,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,2,1,6,5,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,2,3,1,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,2,3,1,6,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,2,3,5,1,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,2,3,5,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,2,3,6,1,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,2,3,6,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,2,5,1,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,2,5,1,6,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,2,5,3,1,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,2,5,3,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,2,5,6,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,2,5,6,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,2,6,1,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,2,6,1,5,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,2,6,3,1,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,2,6,3,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,2,6,5,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,2,6,5,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,3,1,2,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,3,1,2,6,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,3,1,5,2,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,3,1,5,6,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,3,1,6,2,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,3,1,6,5,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,3,2,1,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,3,2,1,6,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,3,2,5,1,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,3,2,5,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,3,2,6,1,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,3,2,6,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,3,5,1,2,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,3,5,1,6,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,3,5,2,1,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,3,5,2,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,3,5,6,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,3,5,6,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,3,6,1,2,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,3,6,1,5,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,3,6,2,1,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,3,6,2,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,3,6,5,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,3,6,5,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,5,1,2,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,5,1,2,6,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,5,1,3,2,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,5,1,3,6,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,5,1,6,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,5,1,6,3,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,5,2,1,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,5,2,1,6,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,5,2,3,1,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,5,2,3,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,5,2,6,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,5,2,6,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,5,3,1,2,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,5,3,1,6,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,5,3,2,1,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,5,3,2,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,5,3,6,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,5,3,6,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,5,6,1,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,5,6,1,3,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,5,6,2,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,5,6,2,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,5,6,3,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,5,6,3,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,6,1,2,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,6,1,2,5,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,6,1,3,2,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,6,1,3,5,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,6,1,5,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,6,1,5,3,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,6,2,1,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,6,2,1,5,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,6,2,3,1,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,6,2,3,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,6,2,5,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,6,2,5,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,6,3,1,2,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,6,3,1,5,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,6,3,2,1,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,6,3,2,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,6,3,5,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,6,3,5,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,6,5,1,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,6,5,1,3,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,6,5,2,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,6,5,2,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,6,5,3,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4,6,5,3,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,1,2,3,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,1,2,3,6,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,1,2,4,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,1,2,4,6,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,1,2,6,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,1,2,6,4,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,1,3,2,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,1,3,2,6,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,1,3,4,2,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,1,3,4,6,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,1,3,6,2,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,1,3,6,4,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,1,4,2,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,1,4,2,6,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,1,4,3,2,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,1,4,3,6,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,1,4,6,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,1,4,6,3,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,1,6,2,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,1,6,2,4,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,1,6,3,2,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,1,6,3,4,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,1,6,4,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,1,6,4,3,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,2,1,3,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,2,1,3,6,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,2,1,4,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,2,1,4,6,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,2,1,6,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,2,1,6,4,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,2,3,1,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,2,3,1,6,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,2,3,4,1,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,2,3,4,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,2,3,6,1,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,2,3,6,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,2,4,1,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,2,4,1,6,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,2,4,3,1,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,2,4,3,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,2,4,6,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,2,4,6,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,2,6,1,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,2,6,1,4,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,2,6,3,1,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,2,6,3,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,2,6,4,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,2,6,4,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,3,1,2,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,3,1,2,6,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,3,1,4,2,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,3,1,4,6,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,3,1,6,2,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,3,1,6,4,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,3,2,1,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,3,2,1,6,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,3,2,4,1,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,3,2,4,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,3,2,6,1,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,3,2,6,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,3,4,1,2,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,3,4,1,6,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,3,4,2,1,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,3,4,2,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,3,4,6,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,3,4,6,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,3,6,1,2,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,3,6,1,4,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,3,6,2,1,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,3,6,2,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,3,6,4,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,3,6,4,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,4,1,2,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,4,1,2,6,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,4,1,3,2,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,4,1,3,6,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,4,1,6,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,4,1,6,3,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,4,2,1,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,4,2,1,6,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,4,2,3,1,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,4,2,3,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,4,2,6,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,4,2,6,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,4,3,1,2,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,4,3,1,6,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,4,3,2,1,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,4,3,2,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,4,3,6,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,4,3,6,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,4,6,1,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,4,6,1,3,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,4,6,2,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,4,6,2,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,4,6,3,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,4,6,3,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,6,1,2,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,6,1,2,4,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,6,1,3,2,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,6,1,3,4,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,6,1,4,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,6,1,4,3,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,6,2,1,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,6,2,1,4,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,6,2,3,1,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,6,2,3,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,6,2,4,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,6,2,4,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,6,3,1,2,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,6,3,1,4,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,6,3,2,1,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,6,3,2,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,6,3,4,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,6,3,4,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,6,4,1,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,6,4,1,3,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,6,4,2,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,6,4,2,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,6,4,3,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5,6,4,3,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,1,2,3,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,1,2,3,5,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,1,2,4,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,1,2,4,5,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,1,2,5,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,1,2,5,4,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,1,3,2,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,1,3,2,5,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,1,3,4,2,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,1,3,4,5,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,1,3,5,2,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,1,3,5,4,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,1,4,2,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,1,4,2,5,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,1,4,3,2,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,1,4,3,5,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,1,4,5,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,1,4,5,3,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,1,5,2,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,1,5,2,4,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,1,5,3,2,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,1,5,3,4,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,1,5,4,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,1,5,4,3,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,2,1,3,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,2,1,3,5,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,2,1,4,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,2,1,4,5,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,2,1,5,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,2,1,5,4,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,2,3,1,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,2,3,1,5,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,2,3,4,1,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,2,3,4,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,2,3,5,1,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,2,3,5,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,2,4,1,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,2,4,1,5,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,2,4,3,1,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,2,4,3,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,2,4,5,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,2,4,5,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,2,5,1,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,2,5,1,4,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,2,5,3,1,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,2,5,3,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,2,5,4,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,2,5,4,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,3,1,2,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,3,1,2,5,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,3,1,4,2,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,3,1,4,5,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,3,1,5,2,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,3,1,5,4,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,3,2,1,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,3,2,1,5,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,3,2,4,1,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,3,2,4,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,3,2,5,1,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,3,2,5,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,3,4,1,2,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,3,4,1,5,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,3,4,2,1,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,3,4,2,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,3,4,5,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,3,4,5,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,3,5,1,2,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,3,5,1,4,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,3,5,2,1,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,3,5,2,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,3,5,4,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,3,5,4,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,4,1,2,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,4,1,2,5,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,4,1,3,2,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,4,1,3,5,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,4,1,5,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,4,1,5,3,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,4,2,1,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,4,2,1,5,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,4,2,3,1,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,4,2,3,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,4,2,5,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,4,2,5,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,4,3,1,2,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,4,3,1,5,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,4,3,2,1,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,4,3,2,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,4,3,5,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,4,3,5,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,4,5,1,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,4,5,1,3,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,4,5,2,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,4,5,2,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,4,5,3,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,4,5,3,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,5,1,2,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,5,1,2,4,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,5,1,3,2,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,5,1,3,4,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,5,1,4,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,5,1,4,3,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,5,2,1,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,5,2,1,4,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,5,2,3,1,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,5,2,3,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,5,2,4,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,5,2,4,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,5,3,1,2,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,5,3,1,4,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,5,3,2,1,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,5,3,2,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,5,3,4,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,5,3,4,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,5,4,1,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,5,4,1,3,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,5,4,2,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,5,4,2,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
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
Generating function
click to show known generating functions
Search the OEIS for these generating functions
Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,2,3 1,3,9,11 1,4,18,44,53 1,5,30,110,265,309 1,6,45,220,795,1854,2119
F1=q2
F2=q2+q3
F3=q2+2 q3+3 q4
F4=q2+3 q3+9 q4+11 q5
F5=q2+4 q3+18 q4+44 q5+53 q6
F6=q2+5 q3+30 q4+110 q5+265 q6+309 q7
F7=q2+6 q3+45 q4+220 q5+795 q6+1854 q7+2119 q8
Description
The sum of all indegrees of vertices with indegree at least two in the resolution quiver of a Nakayama algebra corresponding to the Dyck path.
Map
left-to-right-maxima to Dyck path
Description
The left-to-right maxima of a permutation as a Dyck path.
Let (c1,…,ck) be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are c1,c1+c2,…,c1+⋯+ck.
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.
Let (c1,…,ck) be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are c1,c1+c2,…,c1+⋯+ck.
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.
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!