Identifier
-
Mp00223:
Permutations
—runsort⟶
Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
St001934: Integer partitions ⟶ ℤ
Values
[1,2] => [1,2] => [1,0,1,0] => [1] => 1
[2,1] => [1,2] => [1,0,1,0] => [1] => 1
[1,2,3] => [1,2,3] => [1,0,1,0,1,0] => [2,1] => 1
[1,3,2] => [1,3,2] => [1,0,1,1,0,0] => [1,1] => 1
[2,1,3] => [1,3,2] => [1,0,1,1,0,0] => [1,1] => 1
[2,3,1] => [1,2,3] => [1,0,1,0,1,0] => [2,1] => 1
[3,1,2] => [1,2,3] => [1,0,1,0,1,0] => [2,1] => 1
[3,2,1] => [1,2,3] => [1,0,1,0,1,0] => [2,1] => 1
[1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [3,2,1] => 2
[1,2,4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0] => [2,2,1] => 1
[1,3,2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0] => [3,1,1] => 2
[1,3,4,2] => [1,3,4,2] => [1,0,1,1,0,1,0,0] => [2,1,1] => 1
[1,4,2,3] => [1,4,2,3] => [1,0,1,1,1,0,0,0] => [1,1,1] => 1
[1,4,3,2] => [1,4,2,3] => [1,0,1,1,1,0,0,0] => [1,1,1] => 1
[2,1,3,4] => [1,3,4,2] => [1,0,1,1,0,1,0,0] => [2,1,1] => 1
[2,1,4,3] => [1,4,2,3] => [1,0,1,1,1,0,0,0] => [1,1,1] => 1
[2,3,1,4] => [1,4,2,3] => [1,0,1,1,1,0,0,0] => [1,1,1] => 1
[2,3,4,1] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [3,2,1] => 2
[2,4,1,3] => [1,3,2,4] => [1,0,1,1,0,0,1,0] => [3,1,1] => 2
[2,4,3,1] => [1,2,4,3] => [1,0,1,0,1,1,0,0] => [2,2,1] => 1
[3,1,2,4] => [1,2,4,3] => [1,0,1,0,1,1,0,0] => [2,2,1] => 1
[3,1,4,2] => [1,4,2,3] => [1,0,1,1,1,0,0,0] => [1,1,1] => 1
[3,2,1,4] => [1,4,2,3] => [1,0,1,1,1,0,0,0] => [1,1,1] => 1
[3,2,4,1] => [1,2,4,3] => [1,0,1,0,1,1,0,0] => [2,2,1] => 1
[3,4,1,2] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [3,2,1] => 2
[3,4,2,1] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [3,2,1] => 2
[4,1,2,3] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [3,2,1] => 2
[4,1,3,2] => [1,3,2,4] => [1,0,1,1,0,0,1,0] => [3,1,1] => 2
[4,2,1,3] => [1,3,2,4] => [1,0,1,1,0,0,1,0] => [3,1,1] => 2
[4,2,3,1] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [3,2,1] => 2
[4,3,1,2] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [3,2,1] => 2
[4,3,2,1] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [3,2,1] => 2
[1,2,5,3,4] => [1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => 1
[1,2,5,4,3] => [1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => 1
[1,3,4,5,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => 2
[1,3,5,2,4] => [1,3,5,2,4] => [1,0,1,1,0,1,1,0,0,0] => [2,2,1,1] => 1
[1,3,5,4,2] => [1,3,5,2,4] => [1,0,1,1,0,1,1,0,0,0] => [2,2,1,1] => 1
[1,4,2,3,5] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => 5
[1,4,2,5,3] => [1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => 2
[1,4,3,2,5] => [1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => 2
[1,4,3,5,2] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => 5
[1,4,5,2,3] => [1,4,5,2,3] => [1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => 1
[1,4,5,3,2] => [1,4,5,2,3] => [1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => 1
[1,5,2,3,4] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 1
[1,5,2,4,3] => [1,5,2,4,3] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 1
[1,5,3,2,4] => [1,5,2,4,3] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 1
[1,5,3,4,2] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 1
[1,5,4,2,3] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 1
[1,5,4,3,2] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 1
[2,1,3,4,5] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => 2
[2,1,3,5,4] => [1,3,5,2,4] => [1,0,1,1,0,1,1,0,0,0] => [2,2,1,1] => 1
[2,1,4,3,5] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => 5
[2,1,4,5,3] => [1,4,5,2,3] => [1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => 1
[2,1,5,3,4] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 1
[2,1,5,4,3] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 1
[2,3,1,4,5] => [1,4,5,2,3] => [1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => 1
[2,3,1,5,4] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 1
[2,3,4,1,5] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 1
[2,3,5,1,4] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => 5
[2,4,1,3,5] => [1,3,5,2,4] => [1,0,1,1,0,1,1,0,0,0] => [2,2,1,1] => 1
[2,4,1,5,3] => [1,5,2,4,3] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 1
[2,4,3,1,5] => [1,5,2,4,3] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 1
[2,5,1,4,3] => [1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => 2
[2,5,3,1,4] => [1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => 2
[2,5,3,4,1] => [1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => 1
[2,5,4,3,1] => [1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => 1
[3,1,2,5,4] => [1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => 1
[3,1,4,2,5] => [1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => 2
[3,1,4,5,2] => [1,4,5,2,3] => [1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => 1
[3,1,5,2,4] => [1,5,2,4,3] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 1
[3,1,5,4,2] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 1
[3,2,1,4,5] => [1,4,5,2,3] => [1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => 1
[3,2,1,5,4] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 1
[3,2,4,1,5] => [1,5,2,4,3] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 1
[3,2,5,1,4] => [1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => 2
[3,2,5,4,1] => [1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => 1
[3,4,1,2,5] => [1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => 1
[3,4,1,5,2] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 1
[3,4,2,1,5] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 1
[3,4,2,5,1] => [1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => 1
[3,5,1,4,2] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => 5
[3,5,2,1,4] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => 5
[4,1,2,5,3] => [1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => 1
[4,1,3,5,2] => [1,3,5,2,4] => [1,0,1,1,0,1,1,0,0,0] => [2,2,1,1] => 1
[4,1,5,2,3] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 1
[4,1,5,3,2] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 1
[4,2,1,3,5] => [1,3,5,2,4] => [1,0,1,1,0,1,1,0,0,0] => [2,2,1,1] => 1
[4,2,1,5,3] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 1
[4,2,3,1,5] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 1
[4,2,5,3,1] => [1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => 1
[4,3,1,2,5] => [1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => 1
[4,3,1,5,2] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 1
[4,3,2,1,5] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 1
[4,3,2,5,1] => [1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => 1
[5,1,4,2,3] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => 5
[5,1,4,3,2] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => 5
[5,2,1,4,3] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => 5
[5,2,3,1,4] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => 5
[5,3,1,4,2] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => 5
[5,3,2,1,4] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => 5
[1,4,6,2,3,5] => [1,4,6,2,3,5] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 1
>>> Load all 1986 entries. <<<[1,4,6,2,5,3] => [1,4,6,2,5,3] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 1
[1,4,6,3,2,5] => [1,4,6,2,5,3] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 1
[1,4,6,3,5,2] => [1,4,6,2,3,5] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 1
[1,4,6,5,2,3] => [1,4,6,2,3,5] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 1
[1,4,6,5,3,2] => [1,4,6,2,3,5] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 1
[1,5,2,6,3,4] => [1,5,2,6,3,4] => [1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => 2
[1,5,2,6,4,3] => [1,5,2,6,3,4] => [1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => 2
[1,5,3,2,6,4] => [1,5,2,6,3,4] => [1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => 2
[1,5,3,4,2,6] => [1,5,2,6,3,4] => [1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => 2
[1,5,4,2,6,3] => [1,5,2,6,3,4] => [1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => 2
[1,5,4,3,2,6] => [1,5,2,6,3,4] => [1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => 2
[1,5,6,2,3,4] => [1,5,6,2,3,4] => [1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => 1
[1,5,6,2,4,3] => [1,5,6,2,4,3] => [1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => 1
[1,5,6,3,2,4] => [1,5,6,2,4,3] => [1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => 1
[1,5,6,3,4,2] => [1,5,6,2,3,4] => [1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => 1
[1,5,6,4,2,3] => [1,5,6,2,3,4] => [1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => 1
[1,5,6,4,3,2] => [1,5,6,2,3,4] => [1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => 1
[1,6,2,3,4,5] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[1,6,2,3,5,4] => [1,6,2,3,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[1,6,2,4,3,5] => [1,6,2,4,3,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[1,6,2,4,5,3] => [1,6,2,4,5,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[1,6,2,5,3,4] => [1,6,2,5,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[1,6,2,5,4,3] => [1,6,2,5,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[1,6,3,2,4,5] => [1,6,2,4,5,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[1,6,3,2,5,4] => [1,6,2,5,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[1,6,3,4,2,5] => [1,6,2,5,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[1,6,3,4,5,2] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[1,6,3,5,2,4] => [1,6,2,4,3,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[1,6,3,5,4,2] => [1,6,2,3,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[1,6,4,2,3,5] => [1,6,2,3,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[1,6,4,2,5,3] => [1,6,2,5,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[1,6,4,3,2,5] => [1,6,2,5,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[1,6,4,3,5,2] => [1,6,2,3,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[1,6,4,5,2,3] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[1,6,4,5,3,2] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[1,6,5,2,3,4] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[1,6,5,2,4,3] => [1,6,2,4,3,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[1,6,5,3,2,4] => [1,6,2,4,3,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[1,6,5,3,4,2] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[1,6,5,4,2,3] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[1,6,5,4,3,2] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[2,1,4,6,3,5] => [1,4,6,2,3,5] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 1
[2,1,4,6,5,3] => [1,4,6,2,3,5] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 1
[2,1,5,6,3,4] => [1,5,6,2,3,4] => [1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => 1
[2,1,5,6,4,3] => [1,5,6,2,3,4] => [1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => 1
[2,1,6,3,4,5] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[2,1,6,3,5,4] => [1,6,2,3,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[2,1,6,4,3,5] => [1,6,2,3,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[2,1,6,4,5,3] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[2,1,6,5,3,4] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[2,1,6,5,4,3] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[2,3,1,4,6,5] => [1,4,6,2,3,5] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 1
[2,3,1,5,6,4] => [1,5,6,2,3,4] => [1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => 1
[2,3,1,6,4,5] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[2,3,1,6,5,4] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[2,3,4,1,5,6] => [1,5,6,2,3,4] => [1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => 1
[2,3,4,1,6,5] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[2,3,4,5,1,6] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[2,3,5,1,4,6] => [1,4,6,2,3,5] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 1
[2,3,5,1,6,4] => [1,6,2,3,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[2,3,5,4,1,6] => [1,6,2,3,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[2,4,1,5,6,3] => [1,5,6,2,4,3] => [1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => 1
[2,4,1,6,3,5] => [1,6,2,4,3,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[2,4,1,6,5,3] => [1,6,2,4,3,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[2,4,3,1,5,6] => [1,5,6,2,4,3] => [1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => 1
[2,4,3,1,6,5] => [1,6,2,4,3,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[2,4,3,5,1,6] => [1,6,2,4,3,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[2,4,5,1,6,3] => [1,6,2,4,5,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[2,4,5,3,1,6] => [1,6,2,4,5,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[2,5,1,4,6,3] => [1,4,6,2,5,3] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 1
[2,5,1,6,3,4] => [1,6,2,5,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[2,5,1,6,4,3] => [1,6,2,5,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[2,5,3,1,4,6] => [1,4,6,2,5,3] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 1
[2,5,3,1,6,4] => [1,6,2,5,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[2,5,3,4,1,6] => [1,6,2,5,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[2,5,4,1,6,3] => [1,6,2,5,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[2,5,4,3,1,6] => [1,6,2,5,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[2,6,1,5,3,4] => [1,5,2,6,3,4] => [1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => 2
[2,6,1,5,4,3] => [1,5,2,6,3,4] => [1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => 2
[2,6,3,1,5,4] => [1,5,2,6,3,4] => [1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => 2
[2,6,3,4,1,5] => [1,5,2,6,3,4] => [1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => 2
[2,6,4,1,5,3] => [1,5,2,6,3,4] => [1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => 2
[2,6,4,3,1,5] => [1,5,2,6,3,4] => [1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => 2
[3,1,4,6,2,5] => [1,4,6,2,5,3] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 1
[3,1,4,6,5,2] => [1,4,6,2,3,5] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 1
[3,1,5,2,6,4] => [1,5,2,6,3,4] => [1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => 2
[3,1,5,4,2,6] => [1,5,2,6,3,4] => [1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => 2
[3,1,5,6,2,4] => [1,5,6,2,4,3] => [1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => 1
[3,1,5,6,4,2] => [1,5,6,2,3,4] => [1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => 1
[3,1,6,2,4,5] => [1,6,2,4,5,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[3,1,6,2,5,4] => [1,6,2,5,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[3,1,6,4,2,5] => [1,6,2,5,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[3,1,6,4,5,2] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[3,1,6,5,2,4] => [1,6,2,4,3,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[3,1,6,5,4,2] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[3,2,1,4,6,5] => [1,4,6,2,3,5] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 1
[3,2,1,5,6,4] => [1,5,6,2,3,4] => [1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => 1
[3,2,1,6,4,5] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[3,2,1,6,5,4] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[3,2,4,1,5,6] => [1,5,6,2,4,3] => [1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => 1
[3,2,4,1,6,5] => [1,6,2,4,3,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[3,2,4,5,1,6] => [1,6,2,4,5,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[3,2,5,1,4,6] => [1,4,6,2,5,3] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 1
[3,2,5,1,6,4] => [1,6,2,5,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[3,2,5,4,1,6] => [1,6,2,5,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[3,2,6,1,5,4] => [1,5,2,6,3,4] => [1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => 2
[3,2,6,4,1,5] => [1,5,2,6,3,4] => [1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => 2
[3,4,1,5,2,6] => [1,5,2,6,3,4] => [1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => 2
[3,4,1,5,6,2] => [1,5,6,2,3,4] => [1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => 1
[3,4,1,6,2,5] => [1,6,2,5,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[3,4,1,6,5,2] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[3,4,2,1,5,6] => [1,5,6,2,3,4] => [1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => 1
[3,4,2,1,6,5] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[3,4,2,5,1,6] => [1,6,2,5,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[3,4,2,6,1,5] => [1,5,2,6,3,4] => [1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => 2
[3,4,5,1,6,2] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[3,4,5,2,1,6] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[3,5,1,4,6,2] => [1,4,6,2,3,5] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 1
[3,5,1,6,2,4] => [1,6,2,4,3,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[3,5,1,6,4,2] => [1,6,2,3,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[3,5,2,1,4,6] => [1,4,6,2,3,5] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 1
[3,5,2,1,6,4] => [1,6,2,3,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[3,5,2,4,1,6] => [1,6,2,4,3,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[3,5,4,1,6,2] => [1,6,2,3,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[3,5,4,2,1,6] => [1,6,2,3,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[4,1,5,2,6,3] => [1,5,2,6,3,4] => [1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => 2
[4,1,5,3,2,6] => [1,5,2,6,3,4] => [1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => 2
[4,1,5,6,2,3] => [1,5,6,2,3,4] => [1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => 1
[4,1,5,6,3,2] => [1,5,6,2,3,4] => [1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => 1
[4,1,6,2,3,5] => [1,6,2,3,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[4,1,6,2,5,3] => [1,6,2,5,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[4,1,6,3,2,5] => [1,6,2,5,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[4,1,6,3,5,2] => [1,6,2,3,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[4,1,6,5,2,3] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[4,1,6,5,3,2] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[4,2,1,5,6,3] => [1,5,6,2,3,4] => [1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => 1
[4,2,1,6,3,5] => [1,6,2,3,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[4,2,1,6,5,3] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[4,2,3,1,5,6] => [1,5,6,2,3,4] => [1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => 1
[4,2,3,1,6,5] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[4,2,3,5,1,6] => [1,6,2,3,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[4,2,5,1,6,3] => [1,6,2,5,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[4,2,5,3,1,6] => [1,6,2,5,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[4,2,6,1,5,3] => [1,5,2,6,3,4] => [1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => 2
[4,2,6,3,1,5] => [1,5,2,6,3,4] => [1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => 2
[4,3,1,5,2,6] => [1,5,2,6,3,4] => [1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => 2
[4,3,1,5,6,2] => [1,5,6,2,3,4] => [1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => 1
[4,3,1,6,2,5] => [1,6,2,5,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[4,3,1,6,5,2] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[4,3,2,1,5,6] => [1,5,6,2,3,4] => [1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => 1
[4,3,2,1,6,5] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[4,3,2,5,1,6] => [1,6,2,5,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[4,3,2,6,1,5] => [1,5,2,6,3,4] => [1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => 2
[4,3,5,1,6,2] => [1,6,2,3,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[4,3,5,2,1,6] => [1,6,2,3,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[4,5,1,6,2,3] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[4,5,1,6,3,2] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[4,5,2,1,6,3] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[4,5,2,3,1,6] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[4,5,3,1,6,2] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[4,5,3,2,1,6] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[5,1,4,6,2,3] => [1,4,6,2,3,5] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 1
[5,1,4,6,3,2] => [1,4,6,2,3,5] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 1
[5,1,6,2,3,4] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[5,1,6,2,4,3] => [1,6,2,4,3,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[5,1,6,3,2,4] => [1,6,2,4,3,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[5,1,6,3,4,2] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[5,1,6,4,2,3] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[5,1,6,4,3,2] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[5,2,1,4,6,3] => [1,4,6,2,3,5] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 1
[5,2,1,6,3,4] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[5,2,1,6,4,3] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[5,2,3,1,4,6] => [1,4,6,2,3,5] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 1
[5,2,3,1,6,4] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[5,2,3,4,1,6] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[5,2,4,1,6,3] => [1,6,2,4,3,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[5,2,4,3,1,6] => [1,6,2,4,3,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[5,3,1,4,6,2] => [1,4,6,2,3,5] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 1
[5,3,1,6,2,4] => [1,6,2,4,3,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[5,3,1,6,4,2] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[5,3,2,1,4,6] => [1,4,6,2,3,5] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 1
[5,3,2,1,6,4] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[5,3,2,4,1,6] => [1,6,2,4,3,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[5,3,4,1,6,2] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[5,3,4,2,1,6] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[5,4,1,6,2,3] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[5,4,1,6,3,2] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[5,4,2,1,6,3] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[5,4,2,3,1,6] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[5,4,3,1,6,2] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[5,4,3,2,1,6] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[1,6,7,2,3,4,5] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[1,6,7,2,3,5,4] => [1,6,7,2,3,5,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[1,6,7,2,4,3,5] => [1,6,7,2,4,3,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[1,6,7,2,4,5,3] => [1,6,7,2,4,5,3] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[1,6,7,2,5,3,4] => [1,6,7,2,5,3,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[1,6,7,2,5,4,3] => [1,6,7,2,5,3,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[1,6,7,3,2,4,5] => [1,6,7,2,4,5,3] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[1,6,7,3,2,5,4] => [1,6,7,2,5,3,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[1,6,7,3,4,2,5] => [1,6,7,2,5,3,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[1,6,7,3,4,5,2] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[1,6,7,3,5,2,4] => [1,6,7,2,4,3,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[1,6,7,3,5,4,2] => [1,6,7,2,3,5,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[1,6,7,4,2,3,5] => [1,6,7,2,3,5,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[1,6,7,4,2,5,3] => [1,6,7,2,5,3,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[1,6,7,4,3,2,5] => [1,6,7,2,5,3,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[1,6,7,4,3,5,2] => [1,6,7,2,3,5,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[1,6,7,4,5,2,3] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[1,6,7,4,5,3,2] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[1,6,7,5,2,3,4] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[1,6,7,5,2,4,3] => [1,6,7,2,4,3,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[1,6,7,5,3,2,4] => [1,6,7,2,4,3,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[1,6,7,5,3,4,2] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[1,6,7,5,4,2,3] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[1,6,7,5,4,3,2] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[1,7,2,3,4,5,6] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,2,3,4,6,5] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,2,3,5,4,6] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,2,3,5,6,4] => [1,7,2,3,5,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,2,3,6,4,5] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,2,3,6,5,4] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,2,4,3,5,6] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,2,4,3,6,5] => [1,7,2,4,3,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,2,4,5,3,6] => [1,7,2,4,5,3,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,2,4,5,6,3] => [1,7,2,4,5,6,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,2,4,6,3,5] => [1,7,2,4,6,3,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,2,4,6,5,3] => [1,7,2,4,6,3,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,2,5,3,4,6] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,2,5,3,6,4] => [1,7,2,5,3,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,2,5,4,3,6] => [1,7,2,5,3,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,2,5,4,6,3] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,2,5,6,3,4] => [1,7,2,5,6,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,2,5,6,4,3] => [1,7,2,5,6,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,2,6,3,4,5] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,2,6,3,5,4] => [1,7,2,6,3,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,2,6,4,3,5] => [1,7,2,6,3,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,2,6,4,5,3] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,2,6,5,3,4] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,2,6,5,4,3] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,3,2,4,5,6] => [1,7,2,4,5,6,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,3,2,4,6,5] => [1,7,2,4,6,3,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,3,2,5,4,6] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,3,2,5,6,4] => [1,7,2,5,6,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,3,2,6,4,5] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,3,2,6,5,4] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,3,4,2,5,6] => [1,7,2,5,6,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,3,4,2,6,5] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,3,4,5,2,6] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,3,4,5,6,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,3,4,6,2,5] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,3,4,6,5,2] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,3,5,2,4,6] => [1,7,2,4,6,3,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,3,5,2,6,4] => [1,7,2,6,3,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,3,5,4,2,6] => [1,7,2,6,3,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,3,5,4,6,2] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,3,5,6,2,4] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,3,5,6,4,2] => [1,7,2,3,5,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,3,6,2,4,5] => [1,7,2,4,5,3,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,3,6,2,5,4] => [1,7,2,5,3,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,3,6,4,2,5] => [1,7,2,5,3,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,3,6,4,5,2] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,3,6,5,2,4] => [1,7,2,4,3,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,3,6,5,4,2] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,4,2,3,5,6] => [1,7,2,3,5,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,4,2,3,6,5] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,4,2,5,3,6] => [1,7,2,5,3,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,4,2,5,6,3] => [1,7,2,5,6,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,4,2,6,3,5] => [1,7,2,6,3,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,4,2,6,5,3] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,4,3,2,5,6] => [1,7,2,5,6,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,4,3,2,6,5] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,4,3,5,2,6] => [1,7,2,6,3,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,4,3,5,6,2] => [1,7,2,3,5,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,4,3,6,2,5] => [1,7,2,5,3,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,4,3,6,5,2] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,4,5,2,3,6] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,4,5,2,6,3] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,4,5,3,2,6] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,4,5,3,6,2] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,4,5,6,2,3] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,4,5,6,3,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,4,6,2,3,5] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,4,6,2,5,3] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,4,6,3,2,5] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,4,6,3,5,2] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,4,6,5,2,3] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,4,6,5,3,2] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,5,2,3,4,6] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,5,2,3,6,4] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,5,2,4,3,6] => [1,7,2,4,3,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,5,2,4,6,3] => [1,7,2,4,6,3,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,5,2,6,3,4] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,5,2,6,4,3] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,5,3,2,4,6] => [1,7,2,4,6,3,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,5,3,2,6,4] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,5,3,4,2,6] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,5,3,4,6,2] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,5,3,6,2,4] => [1,7,2,4,3,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,5,3,6,4,2] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,5,4,2,3,6] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,5,4,2,6,3] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,5,4,3,2,6] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,5,4,3,6,2] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,5,4,6,2,3] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,5,4,6,3,2] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,5,6,2,3,4] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,5,6,2,4,3] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,5,6,3,2,4] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,5,6,3,4,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,5,6,4,2,3] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,5,6,4,3,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,6,2,3,4,5] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,6,2,3,5,4] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,6,2,4,3,5] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,6,2,4,5,3] => [1,7,2,4,5,3,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,6,2,5,3,4] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,6,2,5,4,3] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,6,3,2,4,5] => [1,7,2,4,5,3,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,6,3,2,5,4] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,6,3,4,2,5] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,6,3,4,5,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,6,3,5,2,4] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,6,3,5,4,2] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,6,4,2,3,5] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,6,4,2,5,3] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,6,4,3,2,5] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,6,4,3,5,2] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,6,4,5,2,3] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,6,4,5,3,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,6,5,2,3,4] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,6,5,2,4,3] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,6,5,3,2,4] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,6,5,3,4,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,6,5,4,2,3] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,7,6,5,4,3,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,1,6,7,3,4,5] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[2,1,6,7,3,5,4] => [1,6,7,2,3,5,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[2,1,6,7,4,3,5] => [1,6,7,2,3,5,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[2,1,6,7,4,5,3] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[2,1,6,7,5,3,4] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[2,1,6,7,5,4,3] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[2,1,7,3,4,5,6] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,1,7,3,4,6,5] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,1,7,3,5,4,6] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,1,7,3,5,6,4] => [1,7,2,3,5,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,1,7,3,6,4,5] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,1,7,3,6,5,4] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,1,7,4,3,5,6] => [1,7,2,3,5,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,1,7,4,3,6,5] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,1,7,4,5,3,6] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,1,7,4,5,6,3] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,1,7,4,6,3,5] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,1,7,4,6,5,3] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,1,7,5,3,4,6] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,1,7,5,3,6,4] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,1,7,5,4,3,6] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,1,7,5,4,6,3] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,1,7,5,6,3,4] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,1,7,5,6,4,3] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,1,7,6,3,4,5] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,1,7,6,3,5,4] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,1,7,6,4,3,5] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,1,7,6,4,5,3] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,1,7,6,5,3,4] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,1,7,6,5,4,3] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,3,1,6,7,4,5] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[2,3,1,6,7,5,4] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[2,3,1,7,4,5,6] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,3,1,7,4,6,5] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,3,1,7,5,4,6] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,3,1,7,5,6,4] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,3,1,7,6,4,5] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,3,1,7,6,5,4] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,3,4,1,6,7,5] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[2,3,4,1,7,5,6] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,3,4,1,7,6,5] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,3,4,5,1,6,7] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[2,3,4,5,1,7,6] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,3,4,5,6,1,7] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,3,4,6,1,7,5] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,3,4,6,5,1,7] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,3,5,1,6,7,4] => [1,6,7,2,3,5,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[2,3,5,1,7,4,6] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,3,5,1,7,6,4] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,3,5,4,1,6,7] => [1,6,7,2,3,5,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[2,3,5,4,1,7,6] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,3,5,4,6,1,7] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,3,5,6,1,7,4] => [1,7,2,3,5,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,3,5,6,4,1,7] => [1,7,2,3,5,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,3,6,1,7,4,5] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,3,6,1,7,5,4] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,3,6,4,1,7,5] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,3,6,4,5,1,7] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,3,6,5,1,7,4] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,3,6,5,4,1,7] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,4,1,6,7,3,5] => [1,6,7,2,4,3,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[2,4,1,6,7,5,3] => [1,6,7,2,4,3,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[2,4,1,7,3,5,6] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,4,1,7,3,6,5] => [1,7,2,4,3,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,4,1,7,5,3,6] => [1,7,2,4,3,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,4,1,7,5,6,3] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,4,1,7,6,3,5] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,4,1,7,6,5,3] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,4,3,1,6,7,5] => [1,6,7,2,4,3,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[2,4,3,1,7,5,6] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,4,3,1,7,6,5] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,4,3,5,1,6,7] => [1,6,7,2,4,3,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[2,4,3,5,1,7,6] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,4,3,5,6,1,7] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,4,3,6,1,7,5] => [1,7,2,4,3,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,4,3,6,5,1,7] => [1,7,2,4,3,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,4,5,1,6,7,3] => [1,6,7,2,4,5,3] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[2,4,5,1,7,3,6] => [1,7,2,4,5,3,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,4,5,1,7,6,3] => [1,7,2,4,5,3,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,4,5,3,1,6,7] => [1,6,7,2,4,5,3] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[2,4,5,3,1,7,6] => [1,7,2,4,5,3,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,4,5,3,6,1,7] => [1,7,2,4,5,3,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,4,5,6,1,7,3] => [1,7,2,4,5,6,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,4,5,6,3,1,7] => [1,7,2,4,5,6,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,4,6,1,7,3,5] => [1,7,2,4,6,3,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,4,6,1,7,5,3] => [1,7,2,4,6,3,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,4,6,3,1,7,5] => [1,7,2,4,6,3,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,4,6,3,5,1,7] => [1,7,2,4,6,3,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,4,6,5,1,7,3] => [1,7,2,4,6,3,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,4,6,5,3,1,7] => [1,7,2,4,6,3,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,5,1,6,7,3,4] => [1,6,7,2,5,3,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[2,5,1,6,7,4,3] => [1,6,7,2,5,3,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[2,5,1,7,3,4,6] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,5,1,7,3,6,4] => [1,7,2,5,3,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,5,1,7,4,3,6] => [1,7,2,5,3,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,5,1,7,4,6,3] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,5,1,7,6,3,4] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,5,1,7,6,4,3] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,5,3,1,6,7,4] => [1,6,7,2,5,3,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[2,5,3,1,7,4,6] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,5,3,1,7,6,4] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,5,3,4,1,6,7] => [1,6,7,2,5,3,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[2,5,3,4,1,7,6] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,5,3,4,6,1,7] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,5,3,6,1,7,4] => [1,7,2,5,3,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,5,3,6,4,1,7] => [1,7,2,5,3,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,5,4,1,6,7,3] => [1,6,7,2,5,3,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[2,5,4,1,7,3,6] => [1,7,2,5,3,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,5,4,1,7,6,3] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,5,4,3,1,6,7] => [1,6,7,2,5,3,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[2,5,4,3,1,7,6] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,5,4,3,6,1,7] => [1,7,2,5,3,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,5,4,6,1,7,3] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,5,4,6,3,1,7] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,5,6,1,7,3,4] => [1,7,2,5,6,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,5,6,1,7,4,3] => [1,7,2,5,6,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,5,6,3,1,7,4] => [1,7,2,5,6,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,5,6,3,4,1,7] => [1,7,2,5,6,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,5,6,4,1,7,3] => [1,7,2,5,6,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,5,6,4,3,1,7] => [1,7,2,5,6,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,6,1,7,3,4,5] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,6,1,7,3,5,4] => [1,7,2,6,3,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,6,1,7,4,3,5] => [1,7,2,6,3,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,6,1,7,4,5,3] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,6,1,7,5,3,4] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,6,1,7,5,4,3] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,6,3,1,7,4,5] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,6,3,1,7,5,4] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,6,3,4,1,7,5] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,6,3,4,5,1,7] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,6,3,5,1,7,4] => [1,7,2,6,3,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,6,3,5,4,1,7] => [1,7,2,6,3,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,6,4,1,7,3,5] => [1,7,2,6,3,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,6,4,1,7,5,3] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,6,4,3,1,7,5] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,6,4,3,5,1,7] => [1,7,2,6,3,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,6,4,5,1,7,3] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,6,4,5,3,1,7] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,6,5,1,7,3,4] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,6,5,1,7,4,3] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,6,5,3,1,7,4] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,6,5,3,4,1,7] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,6,5,4,1,7,3] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[2,6,5,4,3,1,7] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,1,6,7,2,4,5] => [1,6,7,2,4,5,3] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[3,1,6,7,2,5,4] => [1,6,7,2,5,3,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[3,1,6,7,4,2,5] => [1,6,7,2,5,3,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[3,1,6,7,4,5,2] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[3,1,6,7,5,2,4] => [1,6,7,2,4,3,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[3,1,6,7,5,4,2] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[3,1,7,2,4,5,6] => [1,7,2,4,5,6,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,1,7,2,4,6,5] => [1,7,2,4,6,3,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,1,7,2,5,4,6] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,1,7,2,5,6,4] => [1,7,2,5,6,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,1,7,2,6,4,5] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,1,7,2,6,5,4] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,1,7,4,2,5,6] => [1,7,2,5,6,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,1,7,4,2,6,5] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,1,7,4,5,2,6] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,1,7,4,5,6,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,1,7,4,6,2,5] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,1,7,4,6,5,2] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,1,7,5,2,4,6] => [1,7,2,4,6,3,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,1,7,5,2,6,4] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,1,7,5,4,2,6] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,1,7,5,4,6,2] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,1,7,5,6,2,4] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,1,7,5,6,4,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,1,7,6,2,4,5] => [1,7,2,4,5,3,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,1,7,6,2,5,4] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,1,7,6,4,2,5] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,1,7,6,4,5,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,1,7,6,5,2,4] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,1,7,6,5,4,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,2,1,6,7,4,5] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[3,2,1,6,7,5,4] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[3,2,1,7,4,5,6] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,2,1,7,4,6,5] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,2,1,7,5,4,6] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,2,1,7,5,6,4] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,2,1,7,6,4,5] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,2,1,7,6,5,4] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,2,4,1,6,7,5] => [1,6,7,2,4,3,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[3,2,4,1,7,5,6] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,2,4,1,7,6,5] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,2,4,5,1,6,7] => [1,6,7,2,4,5,3] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[3,2,4,5,1,7,6] => [1,7,2,4,5,3,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,2,4,5,6,1,7] => [1,7,2,4,5,6,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,2,4,6,1,7,5] => [1,7,2,4,6,3,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,2,4,6,5,1,7] => [1,7,2,4,6,3,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,2,5,1,6,7,4] => [1,6,7,2,5,3,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[3,2,5,1,7,4,6] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,2,5,1,7,6,4] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,2,5,4,1,6,7] => [1,6,7,2,5,3,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[3,2,5,4,1,7,6] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,2,5,4,6,1,7] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,2,5,6,1,7,4] => [1,7,2,5,6,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,2,5,6,4,1,7] => [1,7,2,5,6,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,2,6,1,7,4,5] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,2,6,1,7,5,4] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,2,6,4,1,7,5] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,2,6,4,5,1,7] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,2,6,5,1,7,4] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,2,6,5,4,1,7] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,4,1,6,7,2,5] => [1,6,7,2,5,3,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[3,4,1,6,7,5,2] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[3,4,1,7,2,5,6] => [1,7,2,5,6,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,4,1,7,2,6,5] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,4,1,7,5,2,6] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,4,1,7,5,6,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,4,1,7,6,2,5] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,4,1,7,6,5,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,4,2,1,6,7,5] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[3,4,2,1,7,5,6] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,4,2,1,7,6,5] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,4,2,5,1,6,7] => [1,6,7,2,5,3,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[3,4,2,5,1,7,6] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,4,2,5,6,1,7] => [1,7,2,5,6,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,4,2,6,1,7,5] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,4,2,6,5,1,7] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,4,5,1,6,7,2] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[3,4,5,1,7,2,6] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,4,5,1,7,6,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,4,5,2,1,6,7] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[3,4,5,2,1,7,6] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,4,5,2,6,1,7] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,4,5,6,1,7,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,4,5,6,2,1,7] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,4,6,1,7,2,5] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,4,6,1,7,5,2] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,4,6,2,1,7,5] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,4,6,2,5,1,7] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,4,6,5,1,7,2] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,4,6,5,2,1,7] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,5,1,6,7,2,4] => [1,6,7,2,4,3,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[3,5,1,6,7,4,2] => [1,6,7,2,3,5,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[3,5,1,7,2,4,6] => [1,7,2,4,6,3,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,5,1,7,2,6,4] => [1,7,2,6,3,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,5,1,7,4,2,6] => [1,7,2,6,3,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,5,1,7,4,6,2] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,5,1,7,6,2,4] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,5,1,7,6,4,2] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,5,2,1,6,7,4] => [1,6,7,2,3,5,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[3,5,2,1,7,4,6] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,5,2,1,7,6,4] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,5,2,4,1,6,7] => [1,6,7,2,4,3,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[3,5,2,4,1,7,6] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,5,2,4,6,1,7] => [1,7,2,4,6,3,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,5,2,6,1,7,4] => [1,7,2,6,3,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,5,2,6,4,1,7] => [1,7,2,6,3,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,5,4,1,6,7,2] => [1,6,7,2,3,5,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[3,5,4,1,7,2,6] => [1,7,2,6,3,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,5,4,1,7,6,2] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,5,4,2,1,6,7] => [1,6,7,2,3,5,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[3,5,4,2,1,7,6] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,5,4,2,6,1,7] => [1,7,2,6,3,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,5,4,6,1,7,2] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,5,4,6,2,1,7] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,5,6,1,7,2,4] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,5,6,1,7,4,2] => [1,7,2,3,5,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,5,6,2,1,7,4] => [1,7,2,3,5,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,5,6,2,4,1,7] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,5,6,4,1,7,2] => [1,7,2,3,5,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,5,6,4,2,1,7] => [1,7,2,3,5,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,6,1,7,2,4,5] => [1,7,2,4,5,3,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,6,1,7,2,5,4] => [1,7,2,5,3,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,6,1,7,4,2,5] => [1,7,2,5,3,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,6,1,7,4,5,2] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,6,1,7,5,2,4] => [1,7,2,4,3,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,6,1,7,5,4,2] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,6,2,1,7,4,5] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,6,2,1,7,5,4] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,6,2,4,1,7,5] => [1,7,2,4,3,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,6,2,4,5,1,7] => [1,7,2,4,5,3,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,6,2,5,1,7,4] => [1,7,2,5,3,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,6,2,5,4,1,7] => [1,7,2,5,3,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,6,4,1,7,2,5] => [1,7,2,5,3,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,6,4,1,7,5,2] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,6,4,2,1,7,5] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,6,4,2,5,1,7] => [1,7,2,5,3,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,6,4,5,1,7,2] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,6,4,5,2,1,7] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,6,5,1,7,2,4] => [1,7,2,4,3,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,6,5,1,7,4,2] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,6,5,2,1,7,4] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,6,5,2,4,1,7] => [1,7,2,4,3,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,6,5,4,1,7,2] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[3,6,5,4,2,1,7] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,1,6,7,2,3,5] => [1,6,7,2,3,5,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[4,1,6,7,2,5,3] => [1,6,7,2,5,3,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[4,1,6,7,3,2,5] => [1,6,7,2,5,3,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[4,1,6,7,3,5,2] => [1,6,7,2,3,5,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[4,1,6,7,5,2,3] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[4,1,6,7,5,3,2] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[4,1,7,2,3,5,6] => [1,7,2,3,5,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,1,7,2,3,6,5] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,1,7,2,5,3,6] => [1,7,2,5,3,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,1,7,2,5,6,3] => [1,7,2,5,6,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,1,7,2,6,3,5] => [1,7,2,6,3,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,1,7,2,6,5,3] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,1,7,3,2,5,6] => [1,7,2,5,6,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,1,7,3,2,6,5] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,1,7,3,5,2,6] => [1,7,2,6,3,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,1,7,3,5,6,2] => [1,7,2,3,5,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,1,7,3,6,2,5] => [1,7,2,5,3,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,1,7,3,6,5,2] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,1,7,5,2,3,6] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,1,7,5,2,6,3] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,1,7,5,3,2,6] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,1,7,5,3,6,2] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,1,7,5,6,2,3] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,1,7,5,6,3,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,1,7,6,2,3,5] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,1,7,6,2,5,3] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,1,7,6,3,2,5] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,1,7,6,3,5,2] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,1,7,6,5,2,3] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,1,7,6,5,3,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,2,1,6,7,3,5] => [1,6,7,2,3,5,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[4,2,1,6,7,5,3] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[4,2,1,7,3,5,6] => [1,7,2,3,5,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,2,1,7,3,6,5] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,2,1,7,5,3,6] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,2,1,7,5,6,3] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,2,1,7,6,3,5] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,2,1,7,6,5,3] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,2,3,1,6,7,5] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[4,2,3,1,7,5,6] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,2,3,1,7,6,5] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,2,3,5,1,6,7] => [1,6,7,2,3,5,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[4,2,3,5,1,7,6] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,2,3,5,6,1,7] => [1,7,2,3,5,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,2,3,6,1,7,5] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,2,3,6,5,1,7] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,2,5,1,6,7,3] => [1,6,7,2,5,3,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[4,2,5,1,7,3,6] => [1,7,2,5,3,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,2,5,1,7,6,3] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,2,5,3,1,6,7] => [1,6,7,2,5,3,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[4,2,5,3,1,7,6] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,2,5,3,6,1,7] => [1,7,2,5,3,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,2,5,6,1,7,3] => [1,7,2,5,6,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,2,5,6,3,1,7] => [1,7,2,5,6,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,2,6,1,7,3,5] => [1,7,2,6,3,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,2,6,1,7,5,3] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,2,6,3,1,7,5] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,2,6,3,5,1,7] => [1,7,2,6,3,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,2,6,5,1,7,3] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,2,6,5,3,1,7] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,3,1,6,7,2,5] => [1,6,7,2,5,3,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[4,3,1,6,7,5,2] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[4,3,1,7,2,5,6] => [1,7,2,5,6,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,3,1,7,2,6,5] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,3,1,7,5,2,6] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,3,1,7,5,6,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,3,1,7,6,2,5] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,3,1,7,6,5,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,3,2,1,6,7,5] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[4,3,2,1,7,5,6] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,3,2,1,7,6,5] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,3,2,5,1,6,7] => [1,6,7,2,5,3,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[4,3,2,5,1,7,6] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,3,2,5,6,1,7] => [1,7,2,5,6,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,3,2,6,1,7,5] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,3,2,6,5,1,7] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,3,5,1,6,7,2] => [1,6,7,2,3,5,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[4,3,5,1,7,2,6] => [1,7,2,6,3,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,3,5,1,7,6,2] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,3,5,2,1,6,7] => [1,6,7,2,3,5,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[4,3,5,2,1,7,6] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,3,5,2,6,1,7] => [1,7,2,6,3,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,3,5,6,1,7,2] => [1,7,2,3,5,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,3,5,6,2,1,7] => [1,7,2,3,5,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,3,6,1,7,2,5] => [1,7,2,5,3,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,3,6,1,7,5,2] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,3,6,2,1,7,5] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,3,6,2,5,1,7] => [1,7,2,5,3,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,3,6,5,1,7,2] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,3,6,5,2,1,7] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,5,1,6,7,2,3] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[4,5,1,6,7,3,2] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[4,5,1,7,2,3,6] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,5,1,7,2,6,3] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,5,1,7,3,2,6] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,5,1,7,3,6,2] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,5,1,7,6,2,3] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,5,1,7,6,3,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,5,2,1,6,7,3] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[4,5,2,1,7,3,6] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,5,2,1,7,6,3] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,5,2,3,1,6,7] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[4,5,2,3,1,7,6] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,5,2,3,6,1,7] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,5,2,6,1,7,3] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,5,2,6,3,1,7] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,5,3,1,6,7,2] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[4,5,3,1,7,2,6] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,5,3,1,7,6,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,5,3,2,1,6,7] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[4,5,3,2,1,7,6] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,5,3,2,6,1,7] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,5,3,6,1,7,2] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,5,3,6,2,1,7] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,5,6,1,7,2,3] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,5,6,1,7,3,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,5,6,2,1,7,3] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,5,6,2,3,1,7] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,5,6,3,1,7,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,5,6,3,2,1,7] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,6,1,7,2,3,5] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,6,1,7,2,5,3] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,6,1,7,3,2,5] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,6,1,7,3,5,2] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,6,1,7,5,2,3] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,6,1,7,5,3,2] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,6,2,1,7,3,5] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,6,2,1,7,5,3] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,6,2,3,1,7,5] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,6,2,3,5,1,7] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,6,2,5,1,7,3] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,6,2,5,3,1,7] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,6,3,1,7,2,5] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,6,3,1,7,5,2] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,6,3,2,1,7,5] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,6,3,2,5,1,7] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,6,3,5,1,7,2] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,6,3,5,2,1,7] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,6,5,1,7,2,3] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,6,5,1,7,3,2] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,6,5,2,1,7,3] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,6,5,2,3,1,7] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,6,5,3,1,7,2] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[4,6,5,3,2,1,7] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,1,6,7,2,3,4] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[5,1,6,7,2,4,3] => [1,6,7,2,4,3,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[5,1,6,7,3,2,4] => [1,6,7,2,4,3,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[5,1,6,7,3,4,2] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[5,1,6,7,4,2,3] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[5,1,6,7,4,3,2] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[5,1,7,2,3,4,6] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,1,7,2,3,6,4] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,1,7,2,4,3,6] => [1,7,2,4,3,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,1,7,2,4,6,3] => [1,7,2,4,6,3,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,1,7,2,6,3,4] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,1,7,2,6,4,3] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,1,7,3,2,4,6] => [1,7,2,4,6,3,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,1,7,3,2,6,4] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,1,7,3,4,2,6] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,1,7,3,4,6,2] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,1,7,3,6,2,4] => [1,7,2,4,3,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,1,7,3,6,4,2] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,1,7,4,2,3,6] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,1,7,4,2,6,3] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,1,7,4,3,2,6] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,1,7,4,3,6,2] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,1,7,4,6,2,3] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,1,7,4,6,3,2] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,1,7,6,2,3,4] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,1,7,6,2,4,3] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,1,7,6,3,2,4] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,1,7,6,3,4,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,1,7,6,4,2,3] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,1,7,6,4,3,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,2,1,6,7,3,4] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[5,2,1,6,7,4,3] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[5,2,1,7,3,4,6] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,2,1,7,3,6,4] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,2,1,7,4,3,6] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,2,1,7,4,6,3] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,2,1,7,6,3,4] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,2,1,7,6,4,3] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,2,3,1,6,7,4] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[5,2,3,1,7,4,6] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,2,3,1,7,6,4] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,2,3,4,1,6,7] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[5,2,3,4,1,7,6] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,2,3,4,6,1,7] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,2,3,6,1,7,4] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,2,3,6,4,1,7] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,2,4,1,6,7,3] => [1,6,7,2,4,3,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[5,2,4,1,7,3,6] => [1,7,2,4,3,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,2,4,1,7,6,3] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,2,4,3,1,6,7] => [1,6,7,2,4,3,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[5,2,4,3,1,7,6] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,2,4,3,6,1,7] => [1,7,2,4,3,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,2,4,6,1,7,3] => [1,7,2,4,6,3,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,2,4,6,3,1,7] => [1,7,2,4,6,3,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,2,6,1,7,3,4] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,2,6,1,7,4,3] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,2,6,3,1,7,4] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,2,6,3,4,1,7] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,2,6,4,1,7,3] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,2,6,4,3,1,7] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,3,1,6,7,2,4] => [1,6,7,2,4,3,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[5,3,1,6,7,4,2] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[5,3,1,7,2,4,6] => [1,7,2,4,6,3,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,3,1,7,2,6,4] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,3,1,7,4,2,6] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,3,1,7,4,6,2] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,3,1,7,6,2,4] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,3,1,7,6,4,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,3,2,1,6,7,4] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[5,3,2,1,7,4,6] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,3,2,1,7,6,4] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,3,2,4,1,6,7] => [1,6,7,2,4,3,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[5,3,2,4,1,7,6] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,3,2,4,6,1,7] => [1,7,2,4,6,3,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,3,2,6,1,7,4] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,3,2,6,4,1,7] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,3,4,1,6,7,2] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[5,3,4,1,7,2,6] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,3,4,1,7,6,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,3,4,2,1,6,7] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[5,3,4,2,1,7,6] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,3,4,2,6,1,7] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,3,4,6,1,7,2] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,3,4,6,2,1,7] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,3,6,1,7,2,4] => [1,7,2,4,3,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,3,6,1,7,4,2] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,3,6,2,1,7,4] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,3,6,2,4,1,7] => [1,7,2,4,3,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,3,6,4,1,7,2] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,3,6,4,2,1,7] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,4,1,6,7,2,3] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[5,4,1,6,7,3,2] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[5,4,1,7,2,3,6] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,4,1,7,2,6,3] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,4,1,7,3,2,6] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,4,1,7,3,6,2] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,4,1,7,6,2,3] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,4,1,7,6,3,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,4,2,1,6,7,3] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[5,4,2,1,7,3,6] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,4,2,1,7,6,3] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,4,2,3,1,6,7] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[5,4,2,3,1,7,6] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,4,2,3,6,1,7] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,4,2,6,1,7,3] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,4,2,6,3,1,7] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,4,3,1,6,7,2] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[5,4,3,1,7,2,6] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,4,3,1,7,6,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,4,3,2,1,6,7] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[5,4,3,2,1,7,6] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,4,3,2,6,1,7] => [1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,4,3,6,1,7,2] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,4,3,6,2,1,7] => [1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,4,6,1,7,2,3] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,4,6,1,7,3,2] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,4,6,2,1,7,3] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,4,6,2,3,1,7] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,4,6,3,1,7,2] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,4,6,3,2,1,7] => [1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,6,1,7,2,3,4] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,6,1,7,2,4,3] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,6,1,7,3,2,4] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,6,1,7,3,4,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,6,1,7,4,2,3] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,6,1,7,4,3,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,6,2,1,7,3,4] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,6,2,1,7,4,3] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,6,2,3,1,7,4] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,6,2,3,4,1,7] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,6,2,4,1,7,3] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,6,2,4,3,1,7] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,6,3,1,7,2,4] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,6,3,1,7,4,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,6,3,2,1,7,4] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,6,3,2,4,1,7] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,6,3,4,1,7,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,6,3,4,2,1,7] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,6,4,1,7,2,3] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,6,4,1,7,3,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,6,4,2,1,7,3] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,6,4,2,3,1,7] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,6,4,3,1,7,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[5,6,4,3,2,1,7] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,1,7,2,3,4,5] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,1,7,2,3,5,4] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,1,7,2,4,3,5] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,1,7,2,4,5,3] => [1,7,2,4,5,3,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,1,7,2,5,3,4] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,1,7,2,5,4,3] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,1,7,3,2,4,5] => [1,7,2,4,5,3,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,1,7,3,2,5,4] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,1,7,3,4,2,5] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,1,7,3,4,5,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,1,7,3,5,2,4] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,1,7,3,5,4,2] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,1,7,4,2,3,5] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,1,7,4,2,5,3] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,1,7,4,3,2,5] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,1,7,4,3,5,2] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,1,7,4,5,2,3] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,1,7,4,5,3,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,1,7,5,2,3,4] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,1,7,5,2,4,3] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,1,7,5,3,2,4] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,1,7,5,3,4,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,1,7,5,4,2,3] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,1,7,5,4,3,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,2,1,7,3,4,5] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,2,1,7,3,5,4] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,2,1,7,4,3,5] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,2,1,7,4,5,3] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,2,1,7,5,3,4] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,2,1,7,5,4,3] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,2,3,1,7,4,5] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,2,3,1,7,5,4] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,2,3,4,1,7,5] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,2,3,4,5,1,7] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,2,3,5,1,7,4] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,2,3,5,4,1,7] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,2,4,1,7,3,5] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,2,4,1,7,5,3] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,2,4,3,1,7,5] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,2,4,3,5,1,7] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,2,4,5,1,7,3] => [1,7,2,4,5,3,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,2,4,5,3,1,7] => [1,7,2,4,5,3,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,2,5,1,7,3,4] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,2,5,1,7,4,3] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,2,5,3,1,7,4] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,2,5,3,4,1,7] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,2,5,4,1,7,3] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,2,5,4,3,1,7] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,3,1,7,2,4,5] => [1,7,2,4,5,3,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,3,1,7,2,5,4] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,3,1,7,4,2,5] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,3,1,7,4,5,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,3,1,7,5,2,4] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,3,1,7,5,4,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,3,2,1,7,4,5] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,3,2,1,7,5,4] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,3,2,4,1,7,5] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,3,2,4,5,1,7] => [1,7,2,4,5,3,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,3,2,5,1,7,4] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,3,2,5,4,1,7] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,3,4,1,7,2,5] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,3,4,1,7,5,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,3,4,2,1,7,5] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,3,4,2,5,1,7] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,3,4,5,1,7,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,3,4,5,2,1,7] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,3,5,1,7,2,4] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,3,5,1,7,4,2] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,3,5,2,1,7,4] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,3,5,2,4,1,7] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,3,5,4,1,7,2] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,3,5,4,2,1,7] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,4,1,7,2,3,5] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,4,1,7,2,5,3] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,4,1,7,3,2,5] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,4,1,7,3,5,2] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,4,1,7,5,2,3] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,4,1,7,5,3,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,4,2,1,7,3,5] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,4,2,1,7,5,3] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,4,2,3,1,7,5] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,4,2,3,5,1,7] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,4,2,5,1,7,3] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,4,2,5,3,1,7] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,4,3,1,7,2,5] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,4,3,1,7,5,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,4,3,2,1,7,5] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,4,3,2,5,1,7] => [1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,4,3,5,1,7,2] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,4,3,5,2,1,7] => [1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,4,5,1,7,2,3] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,4,5,1,7,3,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,4,5,2,1,7,3] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,4,5,2,3,1,7] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,4,5,3,1,7,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,4,5,3,2,1,7] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,5,1,7,2,3,4] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,5,1,7,2,4,3] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,5,1,7,3,2,4] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,5,1,7,3,4,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,5,1,7,4,2,3] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,5,1,7,4,3,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,5,2,1,7,3,4] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,5,2,1,7,4,3] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,5,2,3,1,7,4] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,5,2,3,4,1,7] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,5,2,4,1,7,3] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,5,2,4,3,1,7] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,5,3,1,7,2,4] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,5,3,1,7,4,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,5,3,2,1,7,4] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,5,3,2,4,1,7] => [1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,5,3,4,1,7,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,5,3,4,2,1,7] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,5,4,1,7,2,3] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,5,4,1,7,3,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,5,4,2,1,7,3] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,5,4,2,3,1,7] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,5,4,3,1,7,2] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[6,5,4,3,2,1,7] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[7,6,5,4,3,2,1,8] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,7,5,4,3,2,1,8] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,5,7,4,3,2,1,8] => [1,8,2,3,4,5,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,6,7,4,3,2,1,8] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,6,4,5,3,2,1,8] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,4,5,6,3,2,1,8] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,5,4,7,3,2,1,8] => [1,8,2,3,4,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,5,6,7,3,2,1,8] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,5,6,3,4,2,1,8] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,6,7,3,4,2,1,8] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,6,4,3,5,2,1,8] => [1,8,2,3,5,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,6,3,4,5,2,1,8] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,5,4,3,6,2,1,8] => [1,8,2,3,6,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,7,5,4,2,3,1,8] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,6,7,4,2,3,1,8] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,6,4,5,2,3,1,8] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,7,4,5,2,3,1,8] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,4,5,6,2,3,1,8] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,6,4,7,2,3,1,8] => [1,8,2,3,4,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,5,6,7,2,3,1,8] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,6,7,3,2,4,1,8] => [1,8,2,4,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,6,5,2,3,4,1,8] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,7,5,2,3,4,1,8] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,5,6,2,3,4,1,8] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,5,7,2,3,4,1,8] => [1,8,2,3,4,5,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,6,7,2,3,4,1,8] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,7,3,4,2,5,1,8] => [1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,4,5,2,3,6,1,8] => [1,8,2,3,6,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,6,3,4,2,7,1,8] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,5,3,6,2,7,1,8] => [1,8,2,7,3,6,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,4,3,2,6,7,1,8] => [1,8,2,6,7,3,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,2,4,5,6,7,1,8] => [1,8,2,4,5,6,7,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,3,4,5,6,7,1,8] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,7,6,5,4,3,2] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,1,8,7,6,5,4,3] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,2,1,8,7,6,5,4] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,3,1,8,7,6,5,4] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,3,2,1,8,7,6,5] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,4,2,1,8,7,6,5] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,4,3,1,8,7,6,5] => [1,8,2,4,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,2,4,1,8,7,6,5] => [1,8,2,4,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,3,4,1,8,7,6,5] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,4,3,2,1,8,7,6] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,5,3,2,1,8,7,6] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,5,4,2,1,8,7,6] => [1,8,2,3,5,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,3,5,2,1,8,7,6] => [1,8,2,3,5,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,4,5,2,1,8,7,6] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,5,4,3,1,8,7,6] => [1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,2,5,4,1,8,7,6] => [1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,3,5,4,1,8,7,6] => [1,8,2,3,5,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,3,2,5,1,8,7,6] => [1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,4,2,5,1,8,7,6] => [1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,4,3,5,1,8,7,6] => [1,8,2,4,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,3,4,5,1,8,7,6] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,5,4,3,2,1,8,7] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,6,4,3,2,1,8,7] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,5,6,3,2,1,8,7] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,6,5,4,2,1,8,7] => [1,8,2,3,6,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,3,6,5,2,1,8,7] => [1,8,2,3,6,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,4,3,6,2,1,8,7] => [1,8,2,3,6,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,5,3,6,2,1,8,7] => [1,8,2,3,6,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,3,5,6,2,1,8,7] => [1,8,2,3,5,6,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,3,6,5,4,1,8,7] => [1,8,2,3,6,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,4,3,6,5,1,8,7] => [1,8,2,4,3,6,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,4,3,2,6,1,8,7] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,5,3,2,6,1,8,7] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,3,5,2,6,1,8,7] => [1,8,2,6,3,5,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,2,5,4,6,1,8,7] => [1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,3,2,5,6,1,8,7] => [1,8,2,5,6,3,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,3,4,5,6,1,8,7] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,7,6,4,3,2,1,8] => [1,8,2,3,4,5,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,7,6,5,3,2,1,8] => [1,8,2,3,4,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,4,7,6,5,2,1,8] => [1,8,2,3,4,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,2,7,6,5,4,1,8] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,2,6,7,5,4,1,8] => [1,8,2,6,7,3,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,4,3,2,7,6,1,8] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,5,3,2,7,6,1,8] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,5,4,2,7,6,1,8] => [1,8,2,7,3,5,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,2,5,4,7,6,1,8] => [1,8,2,5,3,4,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,3,4,5,7,6,1,8] => [1,8,2,3,4,5,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,4,3,5,6,7,2] => [1,8,2,3,5,6,7,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,4,7,6,5,3,2] => [1,8,2,3,4,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,5,4,7,6,3,2] => [1,8,2,3,4,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,7,4,5,6,3,2] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,7,4,6,5,3,2] => [1,8,2,3,4,6,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,6,5,4,7,3,2] => [1,8,2,3,4,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,7,5,4,6,3,2] => [1,8,2,3,4,6,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,7,5,6,4,3,2] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,1,8,5,4,7,6,3] => [1,8,2,3,4,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,1,8,7,5,6,4,3] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,3,1,8,6,7,5,4] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,3,4,1,8,6,7,5] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,3,6,4,5,1,8,7] => [1,8,2,3,6,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,5,3,4,1,8,7,6] => [1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,2,1,8,5,6,7,4] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,2,1,8,5,7,6,4] => [1,8,2,3,4,5,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,2,1,8,6,5,7,4] => [1,8,2,3,4,5,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,2,1,8,6,7,5,4] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,2,4,1,8,6,7,5] => [1,8,2,4,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,2,7,5,4,6,1,8] => [1,8,2,7,3,4,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,2,3,1,8,6,7,5] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,2,3,1,8,7,6,5] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,2,3,5,1,8,7,6] => [1,8,2,3,5,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,2,3,4,1,8,7,6] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,2,3,4,6,5,1,8] => [1,8,2,3,4,6,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,2,3,6,5,4,1,8] => [1,8,2,3,6,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,2,4,3,1,8,7,6] => [1,8,2,4,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,2,4,3,6,1,8,7] => [1,8,2,4,3,6,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,3,2,1,8,6,7,5] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,3,2,4,1,8,7,6] => [1,8,2,4,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,3,2,5,4,1,8,7] => [1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,3,4,2,1,8,7,6] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,3,6,5,4,2,1,8] => [1,8,2,3,6,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,4,3,6,5,2,1,8] => [1,8,2,3,6,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,5,3,4,2,1,8,7] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,6,3,5,4,2,1,8] => [1,8,2,3,5,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,4,6,1,8,3,5,7] => [1,8,2,4,6,3,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,4,6,7,1,8,3,5] => [1,8,2,4,6,7,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,4,5,6,7,1,8,3] => [1,8,2,4,5,6,7,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,5,7,1,8,3,4,6] => [1,8,2,5,7,3,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,3,6,1,8,4,5,7] => [1,8,2,3,6,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,7,1,8,3,4,5,6] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,3,4,7,1,8,5,6] => [1,8,2,3,4,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,3,4,5,7,1,8,6] => [1,8,2,3,4,5,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,1,8,3,4,5,6,7] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,3,4,1,8,5,6,7] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,3,4,5,1,8,6,7] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,4,6,7,1,8,2,5] => [1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,4,7,1,8,2,5,6] => [1,8,2,5,6,3,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,4,5,6,7,1,8,2] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,1,8,2,4,5,6,7] => [1,8,2,4,5,6,7,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,5,6,7,1,8,2,3] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,6,7,1,8,2,3,5] => [1,8,2,3,5,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,6,1,8,2,3,5,7] => [1,8,2,3,5,7,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,7,1,8,2,3,5,6] => [1,8,2,3,5,6,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,7,1,8,2,3,4,5] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,1,8,2,3,4,5,7] => [1,8,2,3,4,5,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,1,8,2,3,4,5,6] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,2,3,4,5,6,7] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,4,5,2,3,1,8,7] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,7,4,3,1,8,2,6] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,1,8,6,7,4,5,3] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,7,6,1,8,3,2,5] => [1,8,2,5,3,4,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,4,7,2,1,8,3,6] => [1,8,2,3,6,4,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,3,2,7,1,8,4,6] => [1,8,2,7,3,4,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,5,1,8,2,7,6,4] => [1,8,2,7,3,5,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,6,1,8,7,2,5,4] => [1,8,2,5,3,6,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,7,1,8,6,5,2,4] => [1,8,2,4,3,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,1,8,2,6,7,4,5] => [1,8,2,6,7,3,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,1,8,6,2,7,4,5] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,1,8,5,2,3,4,6] => [1,8,2,3,4,6,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,1,8,6,2,3,4,5] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,1,8,5,6,7,2,4] => [1,8,2,4,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,4,1,8,2,3,5,6] => [1,8,2,3,5,6,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,3,1,8,7,2,5,6] => [1,8,2,5,6,3,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,3,1,8,6,7,2,5] => [1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,5,4,1,8,7,3,6] => [1,8,2,5,3,6,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,3,4,1,8,7,2,6] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,6,4,5,1,8,3,7] => [1,8,2,6,3,7,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,3,4,5,1,8,2,7] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,3,4,7,6,1,8,5] => [1,8,2,3,4,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,7,4,5,6,1,8,3] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,3,4,5,6,1,8,2] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,5,2,6,4,1,8,7] => [1,8,2,6,3,5,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,5,6,2,3,1,8,7] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,5,7,3,1,8,2,6] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,5,7,3,1,8,6,2] => [1,8,2,3,4,5,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,6,7,1,8,3,5,2] => [1,8,2,3,5,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,6,7,1,8,3,2,5] => [1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,5,7,2,1,8,3,6] => [1,8,2,3,6,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,5,2,7,1,8,4,6] => [1,8,2,7,3,5,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,5,2,7,1,8,6,4] => [1,8,2,7,3,5,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,5,7,2,1,8,6,3] => [1,8,2,3,4,5,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,6,7,1,8,2,5,3] => [1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,6,7,1,8,5,2,3] => [1,8,2,3,4,6,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,6,7,1,8,5,3,2] => [1,8,2,3,4,6,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,6,7,4,5,1,8,3] => [1,8,2,6,7,3,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,5,4,7,6,1,8,3] => [1,8,2,5,3,4,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,2,5,6,1,8,7,4] => [1,8,2,5,6,3,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,1,8,3,2,5,4,7] => [1,8,2,5,3,4,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,4,1,8,7,2,3,6] => [1,8,2,3,6,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,3,1,8,2,7,4,6] => [1,8,2,7,3,4,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,2,1,8,3,4,7,6] => [1,8,2,3,4,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,6,4,1,8,2,3,5] => [1,8,2,3,5,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,7,4,1,8,2,3,5] => [1,8,2,3,5,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,1,8,6,7,3,4,5] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,4,6,1,8,2,3,5] => [1,8,2,3,5,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,5,1,8,2,7,4,6] => [1,8,2,7,3,5,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,1,8,7,6,3,4,5] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,4,7,2,5,1,8,3] => [1,8,2,5,3,4,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,4,2,7,6,1,8,3] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,4,2,6,7,1,8,3] => [1,8,2,6,7,3,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,3,2,6,1,8,7,4] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,3,2,6,1,8,4,7] => [1,8,2,6,3,4,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,3,2,1,8,6,5,7] => [1,8,2,3,4,5,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,3,2,7,1,8,6,4] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,3,2,1,8,7,5,6] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,3,2,1,8,5,7,6] => [1,8,2,3,4,5,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,3,2,1,8,5,6,7] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,1,8,4,7,2,5,3] => [1,8,2,5,3,4,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,1,8,3,2,7,5,4] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,5,1,8,3,7,6,4] => [1,8,2,5,3,7,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,3,1,8,2,7,6,4] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,4,1,8,7,2,6,3] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,5,1,8,7,2,6,3] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,1,8,2,5,4,7,6] => [1,8,2,5,3,4,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,1,8,2,5,3,7,6] => [1,8,2,5,3,7,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,1,8,2,6,3,7,4] => [1,8,2,6,3,7,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,1,8,2,6,3,7,5] => [1,8,2,6,3,7,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,1,8,2,6,4,7,5] => [1,8,2,6,3,4,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,1,8,3,6,4,7,5] => [1,8,2,3,6,4,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,1,8,3,7,2,6,4] => [1,8,2,6,3,7,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,1,8,3,7,2,6,5] => [1,8,2,6,3,7,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,1,8,4,7,2,6,5] => [1,8,2,6,3,4,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,1,8,4,7,3,6,5] => [1,8,2,3,6,4,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,7,4,1,8,3,2,5] => [1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,4,5,3,1,8,2,6] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,6,7,3,1,8,4,2] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,6,7,3,2,1,8,4] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,6,2,7,3,1,8,4] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,7,2,1,8,3,4,5] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,7,3,1,8,2,4,6] => [1,8,2,4,6,3,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,4,2,5,1,8,3,6] => [1,8,2,5,3,6,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,7,4,2,1,8,3,5] => [1,8,2,3,5,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,6,2,7,1,8,4,3] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,6,7,2,1,8,4,3] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,4,7,1,8,2,5,3] => [1,8,2,5,3,4,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,6,7,1,8,4,3,2] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,3,2,7,4,1,8,6] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,5,3,7,1,8,2,6] => [1,8,2,6,3,7,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,3,2,7,1,8,5,4] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,6,2,7,1,8,5,4] => [1,8,2,7,3,6,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,4,3,7,2,5,1,8] => [1,8,2,5,3,7,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,6,2,7,3,5,1,8] => [1,8,2,7,3,5,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,2,6,7,4,5,1,8] => [1,8,2,6,7,3,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,7,2,6,5,3,1,8] => [1,8,2,6,3,4,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,6,7,4,5,3,2] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,5,2,3,1,8,7,6] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,4,3,1,8,2,6,5] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,2,7,1,8,4,6,5] => [1,8,2,7,3,4,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,7,2,1,8,3,6,5] => [1,8,2,3,6,4,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,7,1,8,2,3,5,4] => [1,8,2,3,5,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,6,1,8,3,2,5,4] => [1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,1,8,2,7,6,4,3] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,1,8,7,2,5,4,3] => [1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,1,8,6,5,2,4,3] => [1,8,2,4,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,4,1,8,2,3,5,7] => [1,8,2,3,5,7,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,6,7,3,4,5,2] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,6,1,8,2,3,5,4] => [1,8,2,3,5,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,1,8,2,7,4,6,5] => [1,8,2,7,3,4,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,1,8,2,7,4,6,3] => [1,8,2,7,3,4,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,7,6,3,4,5,2] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,2,5,4,7,1,8,6] => [1,8,2,5,3,4,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,2,5,3,7,1,8,6] => [1,8,2,5,3,7,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,2,5,3,6,1,8,7] => [1,8,2,5,3,6,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,3,5,2,7,1,8,6] => [1,8,2,7,3,5,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,3,6,2,7,1,8,5] => [1,8,2,7,3,6,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,3,6,5,7,1,8,2] => [1,8,2,3,6,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,3,6,4,7,1,8,2] => [1,8,2,3,6,4,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,3,6,2,7,1,8,4] => [1,8,2,7,3,6,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,2,6,3,7,1,8,4] => [1,8,2,6,3,7,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,2,6,3,7,1,8,5] => [1,8,2,6,3,7,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,2,6,4,7,1,8,5] => [1,8,2,6,3,4,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,2,6,5,7,1,8,4] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,2,6,5,7,1,8,3] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,2,6,4,7,1,8,3] => [1,8,2,6,3,4,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,4,6,2,7,1,8,3] => [1,8,2,7,3,4,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,7,5,2,4,1,8,6] => [1,8,2,4,3,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,7,4,3,2,1,8,6] => [1,8,2,3,4,5,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,4,7,3,1,8,2,6] => [1,8,2,6,3,4,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,6,4,1,8,7,5,2] => [1,8,2,3,6,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,6,1,8,7,2,5,3] => [1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,1,8,7,5,3,4,6] => [1,8,2,3,4,6,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,1,8,4,7,6,2,3] => [1,8,2,3,4,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,1,8,3,5,6,7,2] => [1,8,2,3,5,6,7,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,1,8,2,5,6,7,4] => [1,8,2,5,6,7,3,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,1,8,3,4,6,7,5] => [1,8,2,3,4,6,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,1,8,4,5,3,2,6] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,7,3,6,1,8,2,4] => [1,8,2,4,3,6,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,4,1,8,5,6,7,3] => [1,8,2,4,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,3,1,8,5,6,7,2] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,6,3,1,8,2,7,4] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,4,3,2,7,1,8,6] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,5,4,3,1,8,2,6] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,5,3,1,8,6,4,2] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,6,1,8,7,3,5,2] => [1,8,2,3,5,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,6,5,3,2,1,8,4] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,2,7,6,3,1,8,4] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,2,7,4,1,8,3,6] => [1,8,2,7,3,6,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,7,2,6,3,1,8,5] => [1,8,2,6,3,4,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,3,6,2,4,1,8,5] => [1,8,2,4,3,6,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,2,7,1,8,6,4,3] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,6,2,1,8,5,4,3] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,5,1,8,2,6,4,3] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,7,1,8,6,2,5,3] => [1,8,2,5,3,4,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,1,8,6,5,4,3,2] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,4,2,7,3,5,1,8] => [1,8,2,7,3,5,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,4,2,6,3,5,1,8] => [1,8,2,6,3,5,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,2,7,6,4,5,1,8] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,7,2,6,3,5,1,8] => [1,8,2,6,3,5,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,7,6,2,3,4,1,8] => [1,8,2,3,4,5,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,5,2,7,3,4,6] => [1,8,2,7,3,4,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,6,7,2,3,4,5] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,2,5,4,1,8,6,7] => [1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,5,2,3,1,8,6,7] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,4,2,3,1,8,6,7] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,4,2,1,8,3,5,6] => [1,8,2,3,5,6,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,2,7,1,8,4,5,6] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,7,2,1,8,3,5,6] => [1,8,2,3,5,6,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,6,1,8,2,3,4,5] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,2,1,8,7,4,5,6] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,1,8,2,7,3,4,6] => [1,8,2,7,3,4,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,1,8,7,2,3,4,5] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,7,6,2,3,4,5] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,5,2,7,1,8,3,4] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,1,8,5,7,3,4,6] => [1,8,2,3,4,6,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,5,4,6,7,1,8,3] => [1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,3,7,4,1,8,2,5] => [1,8,2,5,3,7,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,1,8,2,7,6,5,4] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,3,4,1,8,5,7,6] => [1,8,2,3,4,5,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,3,6,1,8,7,2,4] => [1,8,2,4,3,6,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,1,8,6,5,7,3,4] => [1,8,2,3,4,5,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,7,3,5,2,1,8,4] => [1,8,2,3,5,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,3,5,4,6,1,8,2] => [1,8,2,3,5,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,5,2,6,3,1,8,7] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,6,3,2,4,1,8,7] => [1,8,2,4,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,1,8,7,4,3,6,5] => [1,8,2,3,6,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,4,1,8,7,6,5,3] => [1,8,2,4,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,3,1,8,6,7,5,2] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,6,2,1,8,7,3,4] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,4,3,1,8,5,6,7] => [1,8,2,4,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,1,8,5,4,3,6,2] => [1,8,2,3,6,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,1,8,3,6,5,2,7] => [1,8,2,7,3,6,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,5,7,2,4,6,1,8] => [1,8,2,4,6,3,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,5,6,2,1,8,7,4] => [1,8,2,3,5,6,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,5,2,7,3,1,8,4] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,5,2,7,3,4,1,8] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,1,8,3,6,5,7,2] => [1,8,2,3,6,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,1,8,3,6,2,7,5] => [1,8,2,7,3,6,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,5,2,6,3,7,1,8] => [1,8,2,6,3,7,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,1,8,7,5,4,3,6] => [1,8,2,3,6,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,3,6,2,7,4,1,8] => [1,8,2,7,3,6,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,3,1,8,4,2,7,5] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,5,7,3,6,4,2] => [1,8,2,3,6,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,5,7,6,1,8,3,2] => [1,8,2,3,4,5,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,7,5,6,3,1,8,2] => [1,8,2,3,4,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,2,4,1,8,3,7,5] => [1,8,2,4,3,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,1,8,7,6,5,3,4] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,1,8,6,2,3,5,7] => [1,8,2,3,5,7,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,5,3,6,1,8,2,4] => [1,8,2,4,3,6,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,7,2,6,1,8,3,4] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,6,3,7,1,8,2,5] => [1,8,2,5,3,7,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,5,3,7,1,8,2,4] => [1,8,2,4,3,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,4,1,8,6,2,3,5] => [1,8,2,3,5,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,6,1,8,5,2,3,4] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,1,8,4,2,6,5,3] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,5,3,1,8,4,7,2] => [1,8,2,3,4,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,3,2,5,1,8,4,7] => [1,8,2,5,3,4,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,5,2,1,8,3,4,6] => [1,8,2,3,4,6,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,6,2,3,1,8,4,7] => [1,8,2,3,4,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,2,6,5,1,8,3,7] => [1,8,2,6,3,7,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,2,7,3,4,5,6] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,2,5,7,1,8,3,6] => [1,8,2,5,7,3,6,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,6,2,7,1,8,4,5] => [1,8,2,7,3,6,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,2,6,1,8,3,4,5] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,3,1,8,7,2,4,6] => [1,8,2,4,6,3,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,1,8,7,3,4,5,6] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,4,3,2,1,8,6,7] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,5,3,1,8,2,7,4] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,5,4,1,8,7,2,3] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,6,1,8,4,5,2,3] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,5,4,7,1,8,2,3] => [1,8,2,3,4,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,5,2,1,8,7,4,3] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,4,7,1,8,2,6,5] => [1,8,2,6,3,4,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,2,4,3,5,6,7] => [1,8,2,4,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,2,5,3,4,6,7] => [1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,2,6,3,4,5,7] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,2,7,3,5,4,6] => [1,8,2,7,3,5,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,2,6,3,5,4,7] => [1,8,2,6,3,5,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,2,5,3,6,4,7] => [1,8,2,5,3,6,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,2,4,3,6,5,7] => [1,8,2,4,3,6,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,2,3,4,6,5,7] => [1,8,2,3,4,6,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,2,3,4,7,5,6] => [1,8,2,3,4,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,2,4,3,7,5,6] => [1,8,2,4,3,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,2,5,3,7,4,6] => [1,8,2,5,3,7,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,2,6,3,7,4,5] => [1,8,2,6,3,7,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,2,7,3,6,4,5] => [1,8,2,7,3,6,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,6,3,7,2,5,1,8] => [1,8,2,5,3,7,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,6,2,7,5,3,1,8] => [1,8,2,7,3,4,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,6,7,2,4,3,1,8] => [1,8,2,4,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,5,2,7,4,1,8,3] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,3,1,8,6,4,7,2] => [1,8,2,3,4,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,6,1,8,7,2,4,3] => [1,8,2,4,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,2,1,8,7,6,3,4] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,2,4,7,1,8,3,6] => [1,8,2,4,7,3,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,3,6,4,1,8,7,2] => [1,8,2,3,6,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,3,5,1,8,2,7,4] => [1,8,2,7,3,5,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,3,4,5,7,1,8,2] => [1,8,2,3,4,5,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,6,3,2,5,4,1,8] => [1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,3,2,5,4,7,6] => [1,8,2,5,3,4,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,5,4,3,2,7,6] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,6,4,3,7,2,5] => [1,8,2,5,3,7,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,5,7,4,3,1,8,2] => [1,8,2,3,4,5,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,2,1,8,5,4,7,6] => [1,8,2,3,4,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,7,4,3,6,5,2] => [1,8,2,3,6,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,7,5,6,3,4,2] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,2,1,8,6,7,4,5] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,4,7,6,1,8,3,2] => [1,8,2,3,4,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,5,6,7,2,3,4] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,4,6,7,1,8,2,3] => [1,8,2,3,4,6,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,5,4,7,2,1,8,3] => [1,8,2,3,4,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,4,6,2,7,3,5] => [1,8,2,7,3,5,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,3,2,6,7,4,5] => [1,8,2,6,7,3,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,5,3,2,7,1,8,4] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,3,2,7,6,5,4] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,4,7,2,6,5,3] => [1,8,2,6,3,4,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,3,5,1,8,2,7,6] => [1,8,2,7,3,5,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,3,6,1,8,7,2,5] => [1,8,2,5,3,6,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,6,7,5,4,2,3] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,4,6,1,8,3,5,2] => [1,8,2,3,5,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,5,6,1,8,3,4,2] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,4,6,5,7,1,8,2] => [1,8,2,3,4,6,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,7,5,6,1,8,3,2] => [1,8,2,3,4,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,7,5,1,8,4,3,2] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,7,5,3,1,8,4,2] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,4,2,6,7,5,3] => [1,8,2,6,7,3,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,5,2,1,8,3,4,7] => [1,8,2,3,4,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,7,1,8,6,5,2,3] => [1,8,2,3,4,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,2,7,1,8,6,5,3] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,7,5,3,4,6,2] => [1,8,2,3,4,6,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,7,3,5,4,6,2] => [1,8,2,3,5,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,7,5,4,3,6,2] => [1,8,2,3,6,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,7,4,5,3,6,2] => [1,8,2,3,6,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,7,4,3,5,6,2] => [1,8,2,3,5,6,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,7,3,4,5,6,2] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,5,4,2,3,1,8,7] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,1,8,7,6,4,3,5] => [1,8,2,3,5,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,1,8,7,6,4,5,3] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,1,8,5,4,7,3,6] => [1,8,2,3,6,4,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,1,8,7,6,3,5,4] => [1,8,2,3,5,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,3,5,1,8,4,6,2] => [1,8,2,3,5,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,3,4,1,8,5,6,2] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,5,6,2,1,8,7,3] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,4,3,1,8,6,5,2] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,6,5,1,8,4,3,2] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,6,4,1,8,5,3,2] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,4,2,1,8,7,5,3] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,3,2,1,8,7,6,4] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,2,3,1,8,6,7,4] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,2,5,1,8,4,7,3] => [1,8,2,5,3,4,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,4,5,2,3,1,8,6] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,3,5,2,4,1,8,6] => [1,8,2,4,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,3,5,2,4,1,8,7] => [1,8,2,4,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,2,6,3,4,1,8,7] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,2,7,3,4,1,8,6] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,2,7,3,4,1,8,5] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,1,8,6,7,4,5,2] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,1,8,6,7,3,5,2] => [1,8,2,3,5,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,1,8,4,7,3,6,2] => [1,8,2,3,6,4,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,1,8,5,7,3,6,2] => [1,8,2,3,6,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,1,8,5,7,4,6,2] => [1,8,2,3,4,6,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,1,8,5,7,4,6,3] => [1,8,2,3,4,6,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,2,7,3,5,1,8,4] => [1,8,2,7,3,5,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,3,6,2,5,1,8,4] => [1,8,2,5,3,6,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,4,6,2,3,1,8,5] => [1,8,2,3,4,6,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,2,3,1,8,5,7,4] => [1,8,2,3,4,5,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,2,4,1,8,6,7,3] => [1,8,2,4,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,1,8,4,6,2,7,3] => [1,8,2,7,3,4,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,1,8,5,6,2,7,3] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,1,8,5,6,2,7,4] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,6,2,5,3,1,8,7] => [1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,5,3,6,2,4,1,8] => [1,8,2,4,3,6,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,6,1,8,4,2,5,7] => [1,8,2,5,7,3,6,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,7,1,8,5,3,4,6] => [1,8,2,7,3,4,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,1,8,5,4,6,7,2] => [1,8,2,3,4,6,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,1,8,3,6,2,5,7] => [1,8,2,5,7,3,6,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,6,4,1,8,3,7,5] => [1,8,2,6,3,7,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,5,2,7,1,8,4,3] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,7,6,4,1,8,3,2] => [1,8,2,3,4,5,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,7,5,4,3,1,8,2] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,5,3,7,6,1,8,4] => [1,8,2,5,3,7,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,3,4,1,8,6,7,2] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,1,8,6,7,5,3,2] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,5,6,1,8,4,7,2] => [1,8,2,3,5,6,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,2,5,6,1,8,7,3] => [1,8,2,5,6,3,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,4,7,5,1,8,6,2] => [1,8,2,3,4,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,7,3,4,6,1,8,2] => [1,8,2,3,4,6,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,1,8,4,2,7,3,6] => [1,8,2,7,3,6,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,4,7,2,5,3,6] => [1,8,2,5,3,6,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,3,2,7,5,4,6] => [1,8,2,7,3,4,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,4,1,8,7,6,5,2] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,3,1,8,7,6,5,2] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,2,1,8,7,6,5,3] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,1,8,7,2,6,3,4] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,1,8,7,2,6,3,5] => [1,8,2,6,3,5,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,1,8,2,7,6,4,5] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,2,5,1,8,3,4,6] => [1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,2,1,8,7,3,4,5] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,6,2,1,8,3,4,5] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,3,7,1,8,2,5,6] => [1,8,2,5,6,3,7,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,1,8,3,2,4,6,5] => [1,8,2,4,6,3,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,7,3,2,4,6,5] => [1,8,2,4,6,3,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,6,4,2,7,3,5] => [1,8,2,7,3,5,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,5,2,6,3,7,4] => [1,8,2,6,3,7,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,1,8,3,2,6,4,5] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,2,1,8,6,3,4,5] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,7,3,2,6,4,5] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,1,8,7,6,2,4,3] => [1,8,2,4,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,1,8,6,3,4,5,2] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,3,5,7,2,1,8,4] => [1,8,2,3,5,7,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,3,4,1,8,6,5,7] => [1,8,2,3,4,5,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,4,5,6,3,1,8,2] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,6,4,1,8,5,7,3] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,7,6,1,8,3,4,5] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,4,1,8,3,2,7,5] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,3,4,1,8,7,5,6] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,6,5,2,7,3,4] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,1,8,2,6,4,3,5] => [1,8,2,6,3,5,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,1,8,3,2,7,4,6] => [1,8,2,7,3,4,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,2,1,8,4,7,5,6] => [1,8,2,3,4,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,7,2,6,5,3,4] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,7,4,5,1,8,3,2] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,5,6,7,1,8,3,2] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,5,6,1,8,7,4,3] => [1,8,2,5,6,3,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,7,2,1,8,5,4,3] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,1,8,7,2,3,6,5] => [1,8,2,3,6,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,1,8,3,4,7,6,5] => [1,8,2,3,4,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,2,3,4,5,7,6] => [1,8,2,3,4,5,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,2,6,4,1,8,7,3] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,6,2,3,1,8,7,4] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,6,3,2,1,8,7,4] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,7,3,1,8,2,6,4] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,7,1,8,3,5,2,4] => [1,8,2,4,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,7,1,8,3,2,5,4] => [1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,7,2,1,8,3,6,4] => [1,8,2,3,6,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,2,7,1,8,4,6,3] => [1,8,2,7,3,4,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,7,2,1,8,6,3,4] => [1,8,2,3,4,5,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,7,1,8,2,5,3,4] => [1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,7,1,8,5,2,3,4] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,7,1,8,5,3,2,4] => [1,8,2,4,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,4,7,1,8,6,5,2] => [1,8,2,3,4,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,6,1,8,7,3,2,4] => [1,8,2,4,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,5,4,3,1,8,2,7] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,5,4,1,8,3,2,6] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,7,4,2,1,8,3,6] => [1,8,2,3,6,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,4,6,3,1,8,2,7] => [1,8,2,7,3,4,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,6,3,7,5,2,4] => [1,8,2,4,3,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,7,3,1,8,4,2,5] => [1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,6,1,8,4,3,2,5] => [1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,2,6,1,8,4,3,5] => [1,8,2,6,3,5,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,4,2,7,1,8,3,6] => [1,8,2,7,3,6,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,5,1,8,7,4,2,3] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,1,8,3,7,6,2,4] => [1,8,2,4,3,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,1,8,7,5,6,3,4] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,1,8,6,5,3,2,4] => [1,8,2,4,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,7,6,5,4,2,3] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,6,7,4,5,2,3] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,5,7,4,6,2,3] => [1,8,2,3,4,6,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,7,1,8,5,6,2,3] => [1,8,2,3,4,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,7,1,8,5,6,2,4] => [1,8,2,4,3,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,5,6,2,7,3,4] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,7,1,8,4,6,2,5] => [1,8,2,5,3,7,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,4,7,3,6,2,5] => [1,8,2,5,3,6,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,5,7,3,6,2,4] => [1,8,2,4,3,6,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,6,7,3,5,2,4] => [1,8,2,4,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,5,1,8,6,7,3,4] => [1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,6,1,8,5,7,3,4] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,6,1,8,4,7,3,5] => [1,8,2,6,3,5,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,7,2,6,1,8,4,5] => [1,8,2,6,3,7,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,7,3,6,1,8,4,5] => [1,8,2,7,3,6,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,7,4,6,2,3,1,8] => [1,8,2,3,4,6,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,6,3,7,2,4,1,8] => [1,8,2,4,3,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,6,3,5,2,7,1,8] => [1,8,2,7,3,5,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,7,3,6,2,5,1,8] => [1,8,2,5,3,6,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,7,3,6,2,4,1,8] => [1,8,2,4,3,6,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,7,3,5,2,4,1,8] => [1,8,2,4,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,7,3,4,2,6,1,8] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,7,3,5,2,6,1,8] => [1,8,2,6,3,5,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,5,3,7,2,6,1,8] => [1,8,2,6,3,7,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,7,5,2,1,8,3,6] => [1,8,2,3,6,4,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,6,4,2,3,1,8,7] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,6,1,8,7,4,2,5] => [1,8,2,5,3,6,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,1,8,6,7,5,3,4] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,1,8,3,4,5,7,2] => [1,8,2,3,4,5,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,3,2,7,5,1,8,4] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,6,1,8,5,2,4,7] => [1,8,2,4,7,3,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,2,7,3,1,8,4,6] => [1,8,2,7,3,4,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,1,8,6,4,2,7,5] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,1,8,3,2,4,6,7] => [1,8,2,4,6,7,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,2,3,1,8,5,6,4] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,2,1,8,3,4,7,5] => [1,8,2,3,4,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,6,4,2,3,1,8,5] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,2,6,3,1,8,7,4] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,7,4,3,2,5,6] => [1,8,2,5,6,3,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,1,8,3,2,6,4,7] => [1,8,2,6,3,4,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,3,2,4,5,6,7] => [1,8,2,4,5,6,7,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,7,5,1,8,2,4,6] => [1,8,2,4,6,3,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,3,7,1,8,2,4,6] => [1,8,2,4,6,3,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,7,3,4,2,5,6] => [1,8,2,5,6,3,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,1,8,6,3,4,7,5] => [1,8,2,3,4,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,6,4,7,2,5,1,8] => [1,8,2,5,3,6,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,4,3,2,1,8,5,7] => [1,8,2,3,4,5,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,4,3,2,1,8,5,6] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,4,3,2,1,8,6,5] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,4,3,2,1,8,7,5] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,5,3,2,6,1,8,4] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,5,3,2,7,1,8,6] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,5,2,7,4,6,1,8] => [1,8,2,7,3,5,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,3,1,8,5,4,7,6] => [1,8,2,3,4,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,4,5,1,8,2,7,6] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,4,5,3,2,7,6] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,4,6,3,7,2,5] => [1,8,2,5,3,7,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,5,6,7,3,4,2] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,5,6,7,3,2,4] => [1,8,2,4,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,5,6,7,2,1,8,3] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,4,6,1,8,7,2,5] => [1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,3,1,8,6,7,4,5] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,3,2,6,7,5,4] => [1,8,2,6,7,3,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,4,6,1,8,7,5,2] => [1,8,2,3,4,6,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,4,6,2,7,5,3] => [1,8,2,7,3,4,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,5,6,7,2,4,3] => [1,8,2,4,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,5,6,7,3,1,8,2] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,5,6,7,4,2,3] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,5,6,7,4,3,2] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,2,5,6,1,8,3,7] => [1,8,2,5,6,3,7,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,3,5,6,7,1,8,2] => [1,8,2,3,5,6,7,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,2,5,1,8,4,6,7] => [1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,7,6,1,8,3,4,2] => [1,8,2,3,4,5,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,2,5,1,8,7,4,6] => [1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,2,4,1,8,7,5,6] => [1,8,2,4,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,2,4,1,8,5,6,7] => [1,8,2,4,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,2,5,1,8,4,7,6] => [1,8,2,5,3,4,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,2,6,1,8,3,7,5] => [1,8,2,6,3,7,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,2,6,1,8,3,7,4] => [1,8,2,6,3,7,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,2,6,1,8,4,7,3] => [1,8,2,6,3,4,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,2,5,1,8,6,4,7] => [1,8,2,5,3,4,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,2,6,1,8,5,7,3] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,2,5,1,8,6,7,4] => [1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,2,5,1,8,7,6,4] => [1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,5,7,3,1,8,4,2] => [1,8,2,3,4,5,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,4,7,3,6,1,8,2] => [1,8,2,3,6,4,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,6,2,1,8,5,7,3] => [1,8,2,3,4,6,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,6,4,1,8,5,3,7] => [1,8,2,6,3,7,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,2,5,6,1,8,4,7] => [1,8,2,5,6,3,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,3,2,1,8,4,6,7] => [1,8,2,3,4,6,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,2,5,3,4,1,8,7] => [1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,1,8,4,7,5,6,3] => [1,8,2,3,4,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,2,3,1,8,5,7,6] => [1,8,2,3,4,5,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,1,8,6,7,3,5,4] => [1,8,2,3,5,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,1,8,5,7,3,6,4] => [1,8,2,3,6,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,6,1,8,4,5,7,3] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,3,1,8,4,5,7,2] => [1,8,2,3,4,5,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,6,1,8,4,2,5,3] => [1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,2,1,8,4,6,5,3] => [1,8,2,3,4,6,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,4,2,1,8,5,6,7] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,7,1,8,3,4,6,2] => [1,8,2,3,4,6,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,2,3,1,8,5,6,7] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,4,2,5,3,6,7] => [1,8,2,5,3,6,7,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,7,3,4,1,8,2,5] => [1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,7,3,4,1,8,2,6] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,6,2,7,3,4,1,8] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,7,3,5,1,8,2,6] => [1,8,2,6,3,5,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,6,2,4,1,8,3,7] => [1,8,2,4,3,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,6,2,5,1,8,3,7] => [1,8,2,5,3,7,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,5,1,8,3,7,2,6] => [1,8,2,6,3,7,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,5,1,8,3,6,2,7] => [1,8,2,7,3,6,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,6,3,5,2,1,8,7] => [1,8,2,3,5,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,1,8,4,7,6,3,2] => [1,8,2,3,4,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,1,8,4,5,7,2,3] => [1,8,2,3,4,5,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,1,8,2,5,6,7,3] => [1,8,2,5,6,7,3,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,4,1,8,5,6,7,2] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,5,7,1,8,6,4,3] => [1,8,2,5,7,3,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,1,8,7,2,6,5,3] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,7,1,8,2,5,4,3] => [1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,7,1,8,4,5,2,3] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,6,5,1,8,3,7,4] => [1,8,2,6,3,7,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,6,5,1,8,2,7,4] => [1,8,2,7,3,6,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,6,5,1,8,7,2,3] => [1,8,2,3,4,6,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,6,4,1,8,7,2,3] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,4,5,1,8,7,2,3] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,4,6,1,8,7,2,3] => [1,8,2,3,4,6,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,5,6,1,8,7,2,3] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,5,6,1,8,3,7,4] => [1,8,2,5,6,3,7,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,3,6,1,8,2,7,4] => [1,8,2,7,3,6,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,2,5,1,8,3,7,4] => [1,8,2,5,3,7,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,2,5,3,1,8,7,6] => [1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,4,2,3,1,8,7,6] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,5,2,4,1,8,7,6] => [1,8,2,4,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,4,6,3,5,1,8,7] => [1,8,2,4,6,3,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,2,6,5,3,1,8,7] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,2,6,5,1,8,7,3] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,4,6,1,8,5,7,3] => [1,8,2,4,6,3,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,4,6,1,8,5,3,7] => [1,8,2,4,6,3,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,4,6,3,1,8,5,7] => [1,8,2,4,6,3,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,4,3,6,1,8,5,7] => [1,8,2,4,3,6,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,4,3,6,1,8,7,5] => [1,8,2,4,3,6,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,4,6,3,1,8,7,5] => [1,8,2,4,6,3,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,4,6,1,8,3,7,5] => [1,8,2,4,6,3,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,6,4,1,8,7,5,3] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,6,4,1,8,7,3,5] => [1,8,2,6,3,5,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,7,2,1,8,3,4,6] => [1,8,2,3,4,6,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,5,3,4,1,8,6,7] => [1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,3,5,2,1,8,6,7] => [1,8,2,3,5,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,7,2,5,1,8,3,6] => [1,8,2,5,3,6,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,2,7,6,1,8,3,5] => [1,8,2,7,3,5,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,2,1,8,7,5,6,4] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,2,6,1,8,4,7,5] => [1,8,2,6,3,4,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,2,7,1,8,6,4,5] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,2,6,1,8,7,4,5] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,1,8,5,4,2,6,7] => [1,8,2,6,7,3,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,2,5,7,3,6,4] => [1,8,2,5,7,3,6,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,3,6,1,8,2,7,5] => [1,8,2,7,3,6,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,1,8,6,4,3,2,5] => [1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,7,6,4,3,2,5] => [1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,4,6,3,7,1,8,5] => [1,8,2,4,6,3,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,2,3,5,4,1,8,6] => [1,8,2,3,5,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,5,7,4,3,2,6] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,1,8,7,4,3,2,6] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,5,1,8,4,3,2,7] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,6,3,2,7,1,8,4] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,6,3,2,1,8,4,7] => [1,8,2,3,4,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,6,4,3,2,1,8,5] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,4,7,2,1,8,6,3] => [1,8,2,3,4,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,3,7,2,5,1,8,4] => [1,8,2,5,3,7,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,3,5,2,1,8,4,6] => [1,8,2,3,5,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,7,6,5,1,8,3,4] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,7,6,5,1,8,4,3] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,3,5,1,8,4,2,6] => [1,8,2,6,3,5,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,3,5,1,8,6,4,2] => [1,8,2,3,5,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,7,6,4,1,8,5,3] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,7,6,4,1,8,3,5] => [1,8,2,7,3,5,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,3,5,1,8,6,2,4] => [1,8,2,4,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,7,3,6,1,8,4,2] => [1,8,2,3,6,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,6,7,2,5,3,4] => [1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,5,7,2,6,3,4] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,2,7,5,6,3,4] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,2,7,4,6,3,5] => [1,8,2,7,3,5,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,4,7,2,6,3,5] => [1,8,2,6,3,5,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,4,7,5,6,2,3] => [1,8,2,3,4,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,3,7,5,6,2,4] => [1,8,2,4,3,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,3,7,4,6,2,5] => [1,8,2,5,3,7,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,3,7,2,6,4,5] => [1,8,2,6,3,7,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,5,1,8,6,2,3,4] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,1,8,4,5,2,6,3] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,1,8,3,5,6,2,4] => [1,8,2,4,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,3,1,8,4,2,5,6] => [1,8,2,5,6,3,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,6,2,7,5,1,8,4] => [1,8,2,7,3,6,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,2,5,7,1,8,6,3] => [1,8,2,5,7,3,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,7,1,8,4,3,2,6] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,7,6,5,1,8,2,4] => [1,8,2,4,3,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,5,2,7,3,6,4] => [1,8,2,7,3,6,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,2,7,5,1,8,6,3] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,1,8,6,3,4,2,5] => [1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,3,5,4,2,7,6] => [1,8,2,7,3,5,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,4,6,7,3,1,8,5] => [1,8,2,4,6,7,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,2,5,7,6,3,4] => [1,8,2,5,7,3,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,1,8,6,2,7,3,4] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,2,6,5,4,1,8,3] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,5,6,2,4,1,8,3] => [1,8,2,4,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,5,6,3,7,2,4] => [1,8,2,4,3,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,3,6,5,7,2,4] => [1,8,2,4,3,6,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,5,6,4,2,1,8,3] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,4,6,2,5,1,8,3] => [1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,2,6,4,5,1,8,3] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,3,6,2,5,1,8,7] => [1,8,2,5,3,6,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,1,8,7,2,3,6,4] => [1,8,2,3,6,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,4,7,5,1,8,3,6] => [1,8,2,4,7,3,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,4,7,3,6,1,8,5] => [1,8,2,4,7,3,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,2,6,1,8,5,3,7] => [1,8,2,6,3,7,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,5,1,8,2,7,4,3] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,6,1,8,5,3,2,4] => [1,8,2,4,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,1,8,6,5,4,2,3] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,4,7,1,8,3,2,6] => [1,8,2,6,3,4,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,7,4,1,8,5,2,6] => [1,8,2,6,3,7,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,7,1,8,4,5,3,6] => [1,8,2,7,3,6,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,4,2,1,8,5,3,6] => [1,8,2,3,6,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,1,8,7,4,6,3,5] => [1,8,2,3,5,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,4,1,8,7,6,2,3] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,4,2,1,8,3,5,7] => [1,8,2,3,5,7,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,6,2,1,8,3,5,7] => [1,8,2,3,5,7,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,1,8,4,3,6,5,7] => [1,8,2,3,6,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,1,8,4,6,3,5,7] => [1,8,2,3,5,7,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,2,1,8,3,6,5,7] => [1,8,2,3,6,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,2,1,8,6,3,5,7] => [1,8,2,3,5,7,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,2,1,8,4,3,5,7] => [1,8,2,3,5,7,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,4,1,8,3,6,5,7] => [1,8,2,4,3,6,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,1,8,6,4,3,5,7] => [1,8,2,3,5,7,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,1,8,3,4,2,7,6] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,2,7,1,8,5,6,4] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,2,4,1,8,5,6,3] => [1,8,2,4,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,1,8,5,6,2,4,3] => [1,8,2,4,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,1,8,2,6,4,5,3] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,5,7,1,8,3,4,2] => [1,8,2,3,4,5,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,4,7,1,8,3,6,2] => [1,8,2,3,6,4,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,5,3,4,7,1,8,6] => [1,8,2,5,3,4,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,2,5,3,1,8,6,7] => [1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,5,4,3,2,6,7] => [1,8,2,6,7,3,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,7,4,6,3,1,8,5] => [1,8,2,7,3,4,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,2,6,3,4,1,8,5] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,7,1,8,3,5,4,6] => [1,8,2,7,3,5,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,5,2,6,7,4,3] => [1,8,2,6,7,3,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,2,1,8,6,7,4,3] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,6,7,5,4,3,2] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,1,8,5,7,4,3,6] => [1,8,2,3,6,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,7,3,5,1,8,2,4] => [1,8,2,4,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,6,2,1,8,7,5,3] => [1,8,2,3,4,6,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,6,3,1,8,7,2,4] => [1,8,2,4,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,5,6,4,7,1,8,2] => [1,8,2,3,5,6,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,3,5,2,6,4,1,8] => [1,8,2,6,3,5,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,4,5,7,3,1,8,2] => [1,8,2,3,4,5,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,4,6,7,1,8,3,2] => [1,8,2,3,4,6,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,4,5,7,2,1,8,3] => [1,8,2,3,4,5,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,3,5,2,7,1,8,4] => [1,8,2,7,3,5,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,4,5,7,2,1,8,6] => [1,8,2,3,4,5,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,4,6,7,1,8,5,2] => [1,8,2,3,4,6,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,4,6,7,1,8,5,3] => [1,8,2,4,6,7,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,5,1,8,6,2,4,3] => [1,8,2,4,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,4,1,8,2,6,3,5] => [1,8,2,6,3,5,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,1,8,4,2,6,3,5] => [1,8,2,6,3,5,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,1,8,3,6,2,5,4] => [1,8,2,5,3,6,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,3,1,8,4,2,6,5] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,1,8,2,3,6,5,4] => [1,8,2,3,6,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,2,4,1,8,7,3,5] => [1,8,2,4,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,5,1,8,3,4,7,6] => [1,8,2,5,3,4,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,2,6,1,8,7,3,5] => [1,8,2,6,3,5,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,3,5,1,8,7,6,4] => [1,8,2,3,5,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,3,6,2,4,7,1,8] => [1,8,2,4,7,3,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,2,7,1,8,3,6,5] => [1,8,2,7,3,6,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,7,6,5,1,8,3,2] => [1,8,2,3,4,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,7,6,5,3,1,8,2] => [1,8,2,3,4,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,7,6,5,2,4,1,8] => [1,8,2,4,3,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,7,2,5,3,1,8,6] => [1,8,2,5,3,4,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,5,4,3,2,1,8,6] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,1,8,5,3,6,4,2] => [1,8,2,3,6,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,6,3,2,7,5,4] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,5,7,4,3,6,2] => [1,8,2,3,6,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,5,7,2,4,6,3] => [1,8,2,4,6,3,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,3,5,1,8,4,2,7] => [1,8,2,7,3,5,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,3,1,8,4,7,5,2] => [1,8,2,3,4,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,7,1,8,3,6,2,5] => [1,8,2,5,3,6,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,1,8,4,7,2,3,6] => [1,8,2,3,6,4,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,1,8,7,5,2,3,6] => [1,8,2,3,6,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,1,8,5,4,3,2,6] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,7,3,2,4,1,8,5] => [1,8,2,4,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[7,6,2,4,3,1,8,5] => [1,8,2,4,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,1,8,2,7,6,3,4] => [1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[2,5,1,8,7,6,3,4] => [1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[4,1,8,7,6,5,3,2] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[6,3,1,8,7,2,5,4] => [1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,1,8,4,7,2,6,3] => [1,8,2,6,3,4,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[5,6,2,4,3,1,8,7] => [1,8,2,4,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,5,1,8,7,4,6,2] => [1,8,2,3,5,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[3,5,1,8,7,2,6,4] => [1,8,2,6,3,5,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,8,4,5,7,2,6,3] => [1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
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Generating function
$F_{2} = 2\ q$
$F_{3} = 6\ q$
$F_{4} = 12\ q + 12\ q^{2}$
Description
The number of monotone factorisations of genus zero of a permutation of given cycle type.
A monotone factorisation of genus zero of a permutation $\pi\in\mathfrak S_n$ with $\ell$ cycles, including fixed points, is a tuple of $r = n - \ell$ transpositions
$$ (a_1, b_1),\dots,(a_r, b_r) $$
with $b_1 \leq \dots \leq b_r$ and $a_i < b_i$ for all $i$, whose product, in this order, is $\pi$.
For example, the cycle $(2,3,1)$ has the two factorizations $(2,3)(1,3)$ and $(1,2)(2,3)$.
A monotone factorisation of genus zero of a permutation $\pi\in\mathfrak S_n$ with $\ell$ cycles, including fixed points, is a tuple of $r = n - \ell$ transpositions
$$ (a_1, b_1),\dots,(a_r, b_r) $$
with $b_1 \leq \dots \leq b_r$ and $a_i < b_i$ for all $i$, whose product, in this order, is $\pi$.
For example, the cycle $(2,3,1)$ has the two factorizations $(2,3)(1,3)$ and $(1,2)(2,3)$.
Map
left-to-right-maxima to Dyck path
Description
The left-to-right maxima of a permutation as a Dyck path.
Let $(c_1, \dots, c_k)$ be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are $c_1, c_1+c_2, \dots, c_1+\dots+c_k$.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
Let $(c_1, \dots, c_k)$ be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are $c_1, c_1+c_2, \dots, c_1+\dots+c_k$.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
Map
to partition
Description
The cut-out partition of a Dyck path.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ is the number of down-steps before the $(n+1-i)$-th up-step of $D$.
This map is a bijection between Dyck paths of size $n$ and partitions inside the staircase partition $(n-1,\ldots,2,1)$.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ is the number of down-steps before the $(n+1-i)$-th up-step of $D$.
This map is a bijection between Dyck paths of size $n$ and partitions inside the staircase partition $(n-1,\ldots,2,1)$.
Map
runsort
Description
The permutation obtained by sorting the increasing runs lexicographically.
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