Identifier
-
Mp00108:
Permutations
—cycle type⟶
Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00142: Dyck paths —promotion⟶ Dyck paths
St001232: Dyck paths ⟶ ℤ
Values
[1] => [1] => [1,0] => [1,0] => 0
[1,2] => [1,1] => [1,1,0,0] => [1,0,1,0] => 1
[2,1] => [2] => [1,0,1,0] => [1,1,0,0] => 0
[1,3,2] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 1
[2,1,3] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 1
[2,3,1] => [3] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 2
[3,1,2] => [3] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 2
[3,2,1] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 1
[2,1,4,3] => [2,2] => [1,1,1,0,0,0] => [1,0,1,1,0,0] => 2
[3,4,1,2] => [2,2] => [1,1,1,0,0,0] => [1,0,1,1,0,0] => 2
[4,3,2,1] => [2,2] => [1,1,1,0,0,0] => [1,0,1,1,0,0] => 2
[1,3,2,5,4] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0] => 3
[1,4,5,2,3] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0] => 3
[1,5,4,3,2] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0] => 3
[2,1,3,5,4] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0] => 3
[2,1,4,3,5] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0] => 3
[2,1,4,5,3] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0] => 2
[2,1,5,3,4] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0] => 2
[2,1,5,4,3] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0] => 3
[2,3,1,5,4] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0] => 2
[2,4,5,1,3] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0] => 2
[2,5,4,3,1] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0] => 2
[3,1,2,5,4] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0] => 2
[3,2,1,5,4] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0] => 3
[3,4,1,2,5] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0] => 3
[3,4,1,5,2] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0] => 2
[3,4,5,2,1] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0] => 2
[3,5,1,2,4] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0] => 2
[3,5,1,4,2] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0] => 3
[3,5,4,1,2] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0] => 2
[4,1,5,2,3] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0] => 2
[4,2,5,1,3] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0] => 3
[4,3,2,1,5] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0] => 3
[4,3,2,5,1] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0] => 2
[4,3,5,1,2] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0] => 2
[4,5,1,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0] => 2
[4,5,2,1,3] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0] => 2
[4,5,3,1,2] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0] => 3
[5,1,4,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0] => 2
[5,2,4,3,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0] => 3
[5,3,2,1,4] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0] => 2
[5,3,2,4,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0] => 3
[5,3,4,2,1] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0] => 2
[5,4,1,2,3] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0] => 2
[5,4,2,3,1] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0] => 2
[5,4,3,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0] => 3
[1,3,2,5,6,4] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[1,3,2,6,4,5] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[1,3,4,2,6,5] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[1,3,5,6,2,4] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[1,3,6,5,4,2] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[1,4,2,3,6,5] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[1,4,5,2,6,3] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[1,4,5,6,3,2] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[1,4,6,2,3,5] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[1,4,6,5,2,3] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[1,5,2,6,3,4] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[1,5,4,3,6,2] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[1,5,4,6,2,3] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[1,5,6,2,4,3] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[1,5,6,3,2,4] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[1,6,2,5,4,3] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[1,6,4,3,2,5] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[1,6,4,5,3,2] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[1,6,5,2,3,4] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[1,6,5,3,4,2] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[2,1,3,5,6,4] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[2,1,3,6,4,5] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[2,1,4,3,6,5] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0] => 3
[2,1,4,5,3,6] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[2,1,4,6,5,3] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[2,1,5,3,4,6] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[2,1,5,4,6,3] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[2,1,5,6,3,4] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0] => 3
[2,1,6,3,5,4] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[2,1,6,4,3,5] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[2,1,6,5,4,3] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0] => 3
[2,3,1,4,6,5] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[2,3,1,5,4,6] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[2,3,1,6,5,4] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[2,4,3,1,6,5] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[2,4,5,1,3,6] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[2,4,6,1,5,3] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[2,5,3,6,1,4] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[2,5,4,3,1,6] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[2,5,6,4,1,3] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[2,6,3,5,4,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[2,6,4,3,5,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[2,6,5,4,3,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[3,1,2,4,6,5] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[3,1,2,5,4,6] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[3,1,2,6,5,4] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[3,2,1,5,6,4] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[3,2,1,6,4,5] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[3,2,4,1,6,5] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[3,2,5,6,1,4] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[3,2,6,5,4,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[3,4,1,2,6,5] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0] => 3
[3,4,1,5,2,6] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[3,4,1,6,5,2] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[3,4,5,2,1,6] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
>>> Load all 1535 entries. <<<[3,4,6,2,5,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[3,5,1,2,4,6] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[3,5,1,4,6,2] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[3,5,1,6,2,4] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0] => 3
[3,5,4,1,2,6] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[3,5,6,4,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[3,6,1,2,5,4] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[3,6,1,4,2,5] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[3,6,1,5,4,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0] => 3
[3,6,4,1,5,2] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[3,6,5,4,1,2] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[4,1,3,2,6,5] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[4,1,5,2,3,6] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[4,1,6,2,5,3] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[4,2,1,3,6,5] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[4,2,5,1,6,3] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[4,2,5,6,3,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[4,2,6,1,3,5] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[4,2,6,5,1,3] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[4,3,2,1,6,5] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0] => 3
[4,3,2,5,1,6] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[4,3,2,6,5,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[4,3,5,1,2,6] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[4,3,6,1,5,2] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[4,5,1,3,2,6] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[4,5,2,1,3,6] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[4,5,3,1,6,2] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[4,5,3,6,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[4,5,6,1,2,3] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0] => 3
[4,6,1,3,5,2] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[4,6,2,1,5,3] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[4,6,3,1,2,5] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[4,6,3,5,1,2] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[4,6,5,1,3,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0] => 3
[5,1,3,6,2,4] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[5,1,4,3,2,6] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[5,1,6,4,2,3] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[5,2,1,6,3,4] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[5,2,4,3,6,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[5,2,4,6,1,3] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[5,2,6,1,4,3] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[5,2,6,3,1,4] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[5,3,2,1,4,6] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[5,3,2,4,6,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[5,3,2,6,1,4] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0] => 3
[5,3,4,2,1,6] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[5,3,6,4,1,2] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[5,4,1,2,3,6] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[5,4,2,3,1,6] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[5,4,3,2,6,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[5,4,3,6,1,2] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[5,4,6,2,1,3] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0] => 3
[5,6,1,4,3,2] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[5,6,2,4,1,3] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[5,6,3,1,4,2] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[5,6,3,2,1,4] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[5,6,4,3,1,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0] => 3
[6,1,3,5,4,2] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[6,1,4,3,5,2] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[6,1,5,4,3,2] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[6,2,1,5,4,3] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[6,2,4,3,1,5] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[6,2,4,5,3,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[6,2,5,1,3,4] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[6,2,5,3,4,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[6,3,2,1,5,4] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[6,3,2,4,1,5] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[6,3,2,5,4,1] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0] => 3
[6,3,4,2,5,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[6,3,5,4,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[6,4,1,2,5,3] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[6,4,2,3,5,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[6,4,3,2,1,5] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[6,4,3,5,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[6,4,5,2,3,1] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0] => 3
[6,5,1,4,2,3] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[6,5,2,4,3,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[6,5,3,1,2,4] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[6,5,3,2,4,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[6,5,4,3,2,1] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0] => 3
[1,3,2,5,4,7,6] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[1,3,2,6,7,4,5] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[1,3,2,7,6,5,4] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[1,4,5,2,3,7,6] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[1,4,6,2,7,3,5] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[1,4,7,2,6,5,3] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[1,5,4,3,2,7,6] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[1,5,6,7,2,3,4] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[1,5,7,6,2,4,3] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[1,6,4,3,7,2,5] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[1,6,5,7,3,2,4] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[1,6,7,5,4,2,3] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[1,7,4,3,6,5,2] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[1,7,5,6,3,4,2] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[1,7,6,5,4,3,2] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[2,1,3,5,4,7,6] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[2,1,3,6,7,4,5] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[2,1,3,7,6,5,4] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[2,1,4,3,5,7,6] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[2,1,4,3,6,5,7] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[2,1,4,3,6,7,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[2,1,4,3,7,5,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[2,1,4,3,7,6,5] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[2,1,4,5,3,7,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[2,1,4,6,7,3,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[2,1,4,7,6,5,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[2,1,5,3,4,7,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[2,1,5,4,3,7,6] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[2,1,5,6,3,4,7] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[2,1,5,6,3,7,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[2,1,5,6,7,4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[2,1,5,7,3,4,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[2,1,5,7,3,6,4] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[2,1,5,7,6,3,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[2,1,6,3,7,4,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[2,1,6,4,7,3,5] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[2,1,6,5,4,3,7] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[2,1,6,5,4,7,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[2,1,6,5,7,3,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[2,1,6,7,3,5,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[2,1,6,7,4,3,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[2,1,6,7,5,3,4] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[2,1,7,3,6,5,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[2,1,7,4,6,5,3] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[2,1,7,5,4,3,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[2,1,7,5,4,6,3] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[2,1,7,5,6,4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[2,1,7,6,3,4,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[2,1,7,6,4,5,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[2,1,7,6,5,4,3] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[2,3,1,5,4,7,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[2,3,1,6,7,4,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[2,3,1,7,6,5,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[2,4,5,1,3,7,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[2,4,6,1,7,3,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[2,4,7,1,6,5,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[2,5,4,3,1,7,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[2,5,6,7,1,3,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[2,5,7,6,1,4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[2,6,4,3,7,1,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[2,6,5,7,3,1,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[2,6,7,5,4,1,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[2,7,4,3,6,5,1] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[2,7,5,6,3,4,1] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[2,7,6,5,4,3,1] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[3,1,2,5,4,7,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[3,1,2,6,7,4,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[3,1,2,7,6,5,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[3,2,1,5,4,7,6] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[3,2,1,6,7,4,5] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[3,2,1,7,6,5,4] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[3,4,1,2,5,7,6] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[3,4,1,2,6,5,7] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[3,4,1,2,6,7,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[3,4,1,2,7,5,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[3,4,1,2,7,6,5] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[3,4,1,5,2,7,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[3,4,1,6,7,2,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[3,4,1,7,6,5,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[3,4,5,2,1,7,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[3,4,6,2,7,1,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[3,4,7,2,6,5,1] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[3,5,1,2,4,7,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[3,5,1,4,2,7,6] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[3,5,1,6,2,4,7] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[3,5,1,6,2,7,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[3,5,1,6,7,4,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[3,5,1,7,2,4,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[3,5,1,7,2,6,4] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[3,5,1,7,6,2,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[3,5,4,1,2,7,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[3,5,6,7,2,1,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[3,5,7,6,2,4,1] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[3,6,1,2,7,4,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[3,6,1,4,7,2,5] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[3,6,1,5,4,2,7] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[3,6,1,5,4,7,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[3,6,1,5,7,2,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[3,6,1,7,2,5,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[3,6,1,7,4,2,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[3,6,1,7,5,2,4] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[3,6,4,1,7,2,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[3,6,5,7,1,2,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[3,6,7,5,4,2,1] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[3,7,1,2,6,5,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[3,7,1,4,6,5,2] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[3,7,1,5,4,2,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[3,7,1,5,4,6,2] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[3,7,1,5,6,4,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[3,7,1,6,2,4,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[3,7,1,6,4,5,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[3,7,1,6,5,4,2] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[3,7,4,1,6,5,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[3,7,5,6,1,4,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[3,7,6,5,4,1,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[4,1,5,2,3,7,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[4,1,6,2,7,3,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[4,1,7,2,6,5,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[4,2,5,1,3,7,6] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[4,2,6,1,7,3,5] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[4,2,7,1,6,5,3] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[4,3,2,1,5,7,6] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[4,3,2,1,6,5,7] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[4,3,2,1,6,7,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[4,3,2,1,7,5,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[4,3,2,1,7,6,5] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[4,3,2,5,1,7,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[4,3,2,6,7,1,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[4,3,2,7,6,5,1] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[4,3,5,1,2,7,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[4,3,6,1,7,2,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[4,3,7,1,6,5,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[4,5,1,3,2,7,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[4,5,2,1,3,7,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[4,5,3,1,2,7,6] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[4,5,6,1,2,3,7] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[4,5,6,1,2,7,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[4,5,6,1,7,3,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[4,5,6,7,2,3,1] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[4,5,7,1,2,3,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[4,5,7,1,2,6,3] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[4,5,7,1,6,2,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[4,5,7,6,2,1,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[4,6,1,3,7,2,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[4,6,2,1,7,3,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[4,6,3,1,7,2,5] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[4,6,5,1,3,2,7] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[4,6,5,1,3,7,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[4,6,5,1,7,2,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[4,6,5,7,3,2,1] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[4,6,7,1,2,5,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[4,6,7,1,3,2,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[4,6,7,1,5,2,3] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[4,6,7,5,1,2,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[4,7,1,3,6,5,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[4,7,2,1,6,5,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[4,7,3,1,6,5,2] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[4,7,5,1,3,2,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[4,7,5,1,3,6,2] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[4,7,5,1,6,3,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[4,7,5,6,3,1,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[4,7,6,1,2,3,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[4,7,6,1,3,5,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[4,7,6,1,5,3,2] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[4,7,6,5,1,3,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[5,1,4,3,2,7,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[5,1,6,7,2,3,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[5,1,7,6,2,4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[5,2,4,3,1,7,6] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[5,2,6,7,1,3,4] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[5,2,7,6,1,4,3] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[5,3,2,1,4,7,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[5,3,2,4,1,7,6] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[5,3,2,6,1,4,7] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[5,3,2,6,1,7,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[5,3,2,6,7,4,1] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[5,3,2,7,1,4,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[5,3,2,7,1,6,4] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[5,3,2,7,6,1,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[5,3,4,2,1,7,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[5,3,6,7,1,2,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[5,3,7,6,1,4,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[5,4,1,2,3,7,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[5,4,2,3,1,7,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[5,4,3,2,1,7,6] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[5,4,6,2,1,3,7] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[5,4,6,2,1,7,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[5,4,6,2,7,3,1] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[5,4,6,7,1,3,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[5,4,7,2,1,3,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[5,4,7,2,1,6,3] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[5,4,7,2,6,1,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[5,4,7,6,1,2,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[5,6,1,7,3,2,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[5,6,2,7,1,3,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[5,6,3,7,1,2,4] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[5,6,4,3,1,2,7] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[5,6,4,3,1,7,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[5,6,4,3,7,2,1] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[5,6,4,7,1,2,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[5,6,7,1,4,2,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[5,6,7,2,1,4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[5,6,7,3,1,2,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[5,6,7,4,1,2,3] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[5,7,1,6,3,4,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[5,7,2,6,1,4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[5,7,3,6,1,4,2] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[5,7,4,3,1,2,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[5,7,4,3,1,6,2] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[5,7,4,3,6,1,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[5,7,4,6,1,3,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[5,7,6,1,4,3,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[5,7,6,2,1,3,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[5,7,6,3,1,4,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[5,7,6,4,1,3,2] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[6,1,4,3,7,2,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[6,1,5,7,3,2,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[6,1,7,5,4,2,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[6,2,4,3,7,1,5] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[6,2,5,7,3,1,4] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[6,2,7,5,4,1,3] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[6,3,2,1,7,4,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[6,3,2,4,7,1,5] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[6,3,2,5,4,1,7] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[6,3,2,5,4,7,1] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[6,3,2,5,7,1,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[6,3,2,7,1,5,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[6,3,2,7,4,1,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[6,3,2,7,5,1,4] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[6,3,4,2,7,1,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[6,3,5,7,2,1,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[6,3,7,5,4,1,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[6,4,1,2,7,3,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[6,4,2,3,7,1,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[6,4,3,2,7,1,5] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[6,4,5,2,3,1,7] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[6,4,5,2,3,7,1] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[6,4,5,2,7,1,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[6,4,5,7,3,1,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[6,4,7,2,1,5,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[6,4,7,2,3,1,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[6,4,7,2,5,1,3] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[6,4,7,5,2,1,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[6,5,1,7,2,3,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[6,5,2,7,3,1,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[6,5,3,7,2,1,4] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[6,5,4,3,2,1,7] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[6,5,4,3,2,7,1] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[6,5,4,3,7,1,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[6,5,4,7,2,1,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[6,5,7,1,2,4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[6,5,7,2,4,1,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[6,5,7,3,2,1,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[6,5,7,4,2,1,3] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[6,7,1,5,4,3,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[6,7,2,5,4,1,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[6,7,3,5,4,1,2] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[6,7,4,3,1,5,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[6,7,4,3,2,1,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[6,7,4,3,5,1,2] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[6,7,4,5,3,1,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[6,7,5,1,3,4,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[6,7,5,2,3,1,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[6,7,5,3,4,1,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[6,7,5,4,3,1,2] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[7,1,4,3,6,5,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[7,1,5,6,3,4,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[7,1,6,5,4,3,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[7,2,4,3,6,5,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[7,2,5,6,3,4,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[7,2,6,5,4,3,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[7,3,2,1,6,5,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[7,3,2,4,6,5,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[7,3,2,5,4,1,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[7,3,2,5,4,6,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[7,3,2,5,6,4,1] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[7,3,2,6,1,4,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[7,3,2,6,4,5,1] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[7,3,2,6,5,4,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[7,3,4,2,6,5,1] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[7,3,5,6,2,4,1] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[7,3,6,5,4,2,1] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[7,4,1,2,6,5,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[7,4,2,3,6,5,1] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[7,4,3,2,6,5,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[7,4,5,2,3,1,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[7,4,5,2,3,6,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[7,4,5,2,6,3,1] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[7,4,5,6,3,2,1] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[7,4,6,2,1,3,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[7,4,6,2,3,5,1] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[7,4,6,2,5,3,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[7,4,6,5,2,3,1] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[7,5,1,6,2,4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[7,5,2,6,3,4,1] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[7,5,3,6,2,4,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[7,5,4,3,2,1,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[7,5,4,3,2,6,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[7,5,4,3,6,2,1] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[7,5,4,6,2,3,1] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[7,5,6,1,2,3,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[7,5,6,2,4,3,1] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[7,5,6,3,2,4,1] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[7,5,6,4,2,3,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[7,6,1,5,4,2,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[7,6,2,5,4,3,1] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[7,6,3,5,4,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[7,6,4,3,1,2,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[7,6,4,3,2,5,1] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[7,6,4,3,5,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[7,6,4,5,3,2,1] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[7,6,5,1,3,2,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[7,6,5,2,3,4,1] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[7,6,5,3,4,2,1] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[7,6,5,4,3,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 4
[8,7,5,4,6,3,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,5,6,4,7,3,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,7,6,4,3,5,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,7,4,5,3,6,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,6,5,4,3,7,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,6,4,3,5,7,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,7,5,4,3,8,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,6,5,4,7,2,3,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,6,7,4,3,2,5,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,7,5,4,3,2,6,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,7,4,3,5,2,6,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,6,4,5,3,2,7,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,6,5,3,4,2,7,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,5,4,3,6,2,7,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,6,4,3,2,5,7,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,6,5,4,3,2,8,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,6,4,3,5,2,8,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,5,6,4,2,3,8,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,5,4,3,2,6,8,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,4,5,2,3,6,8,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,5,6,4,8,3,1,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,8,4,5,3,6,1,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,6,5,4,3,8,1,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,7,8,4,3,1,2,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,8,5,4,3,2,1,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,7,5,4,3,1,2,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,6,5,4,3,2,1,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,5,6,4,2,3,1,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,5,4,3,2,6,1,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,4,5,2,3,6,1,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,6,4,5,3,2,1,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,6,5,3,4,2,1,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,5,4,3,6,2,1,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,6,4,3,7,2,1,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,5,4,6,2,3,1,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,5,6,7,2,3,1,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,6,5,2,3,4,1,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,6,4,3,2,5,1,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,5,4,3,2,7,1,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,5,4,3,7,1,2,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,6,4,7,1,2,3,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,7,5,2,3,1,4,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,6,7,3,1,2,4,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,7,4,3,2,1,5,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,6,4,3,1,2,5,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,5,4,3,2,1,6,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,7,6,4,8,3,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,7,8,6,5,4,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,8,7,6,5,4,3,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,2,8,7,6,5,4,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,3,2,8,7,6,5,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,4,3,2,8,7,6,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,5,4,3,2,8,7,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,5,7,6,8,4,3,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,4,7,8,6,5,3,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,3,8,7,6,5,4,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,5,4,3,8,7,6,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,7,6,5,4,3,8,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,5,7,8,6,4,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,6,7,5,8,4,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,4,8,7,6,5,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,5,4,8,7,6,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,7,6,5,4,8,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,2,1,6,7,8,5,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,2,1,7,6,5,8,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,3,1,8,7,6,5,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,3,2,5,8,7,6,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,3,2,7,6,5,8,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,3,6,7,8,5,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,3,2,1,7,6,8,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,4,3,1,8,7,6,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,2,4,1,8,7,6,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,3,4,2,8,7,6,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,4,3,6,8,7,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,4,3,7,6,8,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,3,1,4,8,7,6,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,4,3,2,1,7,8,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,4,5,2,1,8,7,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,5,4,3,1,8,7,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,3,2,5,1,8,7,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,5,4,3,2,7,8,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,4,5,3,8,7,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,3,2,5,4,7,8,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,3,5,4,7,8,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,3,2,1,5,7,8,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,4,3,5,7,8,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,5,6,4,2,1,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,5,3,6,2,1,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,6,5,4,3,1,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,3,2,6,5,1,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,4,3,2,6,1,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,3,6,5,4,2,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,4,6,5,3,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,5,4,6,3,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,3,1,6,5,4,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,3,2,5,6,4,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,3,5,6,4,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,4,3,1,6,5,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,2,4,1,6,5,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,3,4,2,6,5,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,3,1,4,6,5,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,4,5,2,1,6,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,5,4,3,1,6,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,4,5,3,6,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,6,5,7,3,2,1,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,7,6,5,4,3,1,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,5,6,7,4,3,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,4,3,6,7,5,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,4,5,2,1,7,6,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,5,4,3,1,7,6,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,3,1,5,4,7,6,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,3,2,8,6,7,5,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,3,8,5,4,7,6,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,7,4,3,6,5,8,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,6,4,5,3,2,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,8,4,7,6,5,3,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,8,6,5,4,7,3,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,8,7,5,6,4,3,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,3,8,6,7,5,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,4,8,5,7,6,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,4,8,6,5,7,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,7,4,6,5,8,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,8,4,6,7,5,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,8,5,6,4,7,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,8,5,7,6,4,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,8,6,5,7,4,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,6,3,5,4,1,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,8,3,5,4,7,6,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,8,3,7,6,5,4,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,6,4,3,5,1,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,8,4,3,5,7,6,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,8,4,3,6,5,7,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,8,4,3,7,6,5,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,8,5,4,3,7,6,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,8,7,4,6,5,3,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,8,7,5,4,6,3,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,2,1,8,6,7,5,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,2,8,5,4,7,6,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,2,4,3,6,1,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,2,4,3,6,5,8,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,2,4,3,6,7,5,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,2,4,5,3,7,6,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,2,4,7,6,5,3,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,2,6,5,4,7,3,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,2,7,5,6,4,3,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,3,2,8,5,7,6,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,3,2,4,6,1,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,3,2,5,4,7,1,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,3,2,5,7,6,4,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,3,2,6,5,7,4,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,3,4,2,1,6,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,3,4,2,1,8,7,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,3,4,2,5,1,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,3,5,4,2,1,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,3,7,4,6,5,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,3,6,5,4,2,1,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,3,6,5,4,2,7,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,3,7,6,5,4,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,4,3,2,6,5,8,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,4,3,2,6,7,5,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,4,3,5,2,1,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,6,3,5,4,2,8,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,7,3,5,6,4,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,5,4,3,7,6,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,7,4,6,5,3,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,4,5,1,3,7,6,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,4,3,5,8,6,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,5,6,3,7,4,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,5,7,3,4,6,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,5,3,4,6,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,6,3,7,4,5,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,3,6,7,4,8,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,3,6,4,5,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,3,7,4,8,5,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,3,1,4,7,8,5,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,4,1,2,6,7,5,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,4,1,2,7,5,6,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,4,1,5,2,7,6,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,4,1,2,5,7,8,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,4,1,2,5,8,6,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,5,1,6,2,7,4,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,5,1,7,2,4,6,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,5,1,2,4,7,6,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,1,2,5,4,7,6,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,3,2,5,7,8,4,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,3,5,7,2,8,4,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,3,2,5,4,8,6,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,5,1,2,4,6,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,1,2,5,4,6,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,3,5,6,2,4,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,3,2,6,7,4,8,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,3,6,7,8,2,4,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,3,2,6,8,4,5,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,1,2,4,6,5,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,3,2,7,4,8,5,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,1,2,4,7,8,5,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,3,4,2,7,8,5,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,5,6,1,2,7,3,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,1,5,2,3,7,6,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,4,5,2,3,7,8,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,4,5,2,7,8,3,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,4,5,2,3,8,6,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,4,5,2,6,3,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,1,6,2,7,3,5,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,4,6,2,7,3,8,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,4,6,2,8,3,5,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,4,6,2,3,5,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,4,2,3,6,5,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,4,7,2,3,8,5,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,4,2,3,7,8,5,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,5,6,7,2,3,8,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,5,6,8,2,3,4,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,5,2,6,3,4,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,5,2,7,3,8,4,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,6,2,7,8,3,4,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,3,6,7,1,2,4,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,2,6,8,1,3,4,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,2,6,7,1,3,4,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,8,3,7,1,2,4,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,3,2,7,1,4,6,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,3,2,6,1,4,5,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,6,3,7,1,2,4,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,7,3,6,8,1,2,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,7,3,5,8,1,2,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,4,3,7,8,1,2,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,4,7,2,6,1,3,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,4,8,2,5,1,3,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,5,3,8,2,7,1,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,5,4,8,2,6,1,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,6,3,8,2,5,1,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,4,7,2,5,1,8,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,3,2,1,8,6,5,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,3,2,8,1,6,4,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,3,2,7,1,6,8,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,3,2,1,5,8,6,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,1,8,4,7,2,5,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,5,2,8,3,7,6,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,2,1,8,3,7,6,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,6,8,4,7,1,5,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,5,3,8,1,7,6,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,2,1,3,8,7,6,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,4,2,3,8,7,6,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,1,3,2,8,7,6,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,1,3,8,2,7,6,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,3,5,8,2,7,6,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,1,2,4,8,7,6,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,2,5,8,1,7,6,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,1,3,2,6,5,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,6,3,5,4,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,1,6,2,5,3,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,2,6,1,4,3,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,4,3,8,5,7,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,6,3,8,4,7,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,1,6,2,8,3,7,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,2,8,3,7,1,5,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,7,4,8,3,6,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,5,8,2,4,6,1,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,6,7,8,5,2,1,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,3,7,8,1,6,2,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,7,2,8,5,1,3,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,5,3,6,2,4,1,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,4,5,8,3,6,1,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,2,6,7,8,3,1,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,4,1,2,3,8,7,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,2,5,1,6,3,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,6,4,7,3,8,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,2,6,1,7,3,8,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,2,6,8,7,3,5,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,5,3,1,2,4,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,6,3,5,1,2,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,5,3,7,2,1,4,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,6,3,2,1,4,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,4,3,6,1,2,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,8,7,5,3,4,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,6,8,5,7,3,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,6,3,8,1,7,2,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,7,8,5,4,3,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,7,3,8,1,4,2,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,5,3,8,2,4,1,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,5,3,6,2,8,1,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,7,3,6,1,8,2,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,7,6,5,8,3,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,5,3,7,2,8,4,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,6,3,7,1,8,4,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,2,5,8,3,7,6,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,8,6,7,2,3,4,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,2,1,8,7,4,5,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,5,2,7,3,1,4,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,5,2,8,3,1,7,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,8,3,5,4,2,1,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,8,1,6,5,4,3,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,7,5,8,3,6,1,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,1,7,2,6,5,3,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,8,5,6,1,4,7,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,8,7,6,5,4,1,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,7,8,6,5,4,1,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,4,8,5,2,6,1,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,6,1,8,5,2,3,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,7,2,8,1,6,3,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,3,7,8,5,1,2,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,6,3,1,4,2,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,7,8,5,3,6,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,7,3,8,1,2,6,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,3,1,6,7,8,9,4,5] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0] => 4
[7,5,3,6,2,4,8,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,8,5,2,3,6,1,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,4,3,2,1,8,6,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,4,3,2,7,8,1,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,7,8,4,1,3,2,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,7,8,4,1,2,6,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,7,8,2,1,6,4,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,7,8,1,5,4,2,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,7,8,3,1,6,2,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,2,8,5,4,1,6,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,3,2,8,5,1,4,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,6,1,7,5,2,8,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,4,1,2,7,6,8,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,2,5,8,3,7,1,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,2,4,7,1,8,3,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,2,4,1,7,8,5,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,8,3,1,7,5,6,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,5,7,1,2,6,3,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,2,4,8,7,1,5,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,7,6,4,1,3,2,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,8,7,5,4,3,6,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,6,7,3,5,2,4,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,5,7,4,6,2,3,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,8,1,5,4,6,3,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,8,3,5,6,4,1,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,7,5,1,3,6,8,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,7,3,6,1,4,8,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,6,4,3,8,2,5,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,2,5,6,3,8,1,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,7,5,4,3,1,8,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,8,3,1,7,2,5,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,4,1,8,7,6,5,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,1,2,8,7,6,5,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,5,1,8,2,4,7,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,4,7,5,2,8,3,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,3,5,7,2,1,4,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,3,5,8,2,1,7,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,8,6,1,5,3,4,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,8,7,2,6,5,3,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,5,8,3,2,1,7,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,7,3,8,1,5,2,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,7,3,1,8,4,2,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,2,6,1,7,3,5,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,8,5,7,3,6,1,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,8,3,6,4,5,1,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,8,3,6,2,4,1,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,5,3,7,2,8,1,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,2,7,5,4,8,3,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,1,3,5,4,7,6,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,3,2,7,5,1,8,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,6,1,8,5,2,4,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,4,1,2,8,6,5,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,2,5,8,3,1,6,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,2,7,3,1,8,4,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,2,1,3,7,8,5,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,2,8,7,1,3,4,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,4,6,2,8,7,3,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,4,7,2,6,8,3,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,8,6,3,4,7,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,4,3,2,1,7,6,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,6,7,1,3,2,5,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,3,6,1,7,2,5,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,6,2,7,1,3,4,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,6,2,1,7,3,5,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,6,5,1,7,2,3,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,1,5,7,3,2,4,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,8,4,3,6,1,7,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,4,8,2,1,6,3,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,3,2,6,7,1,5,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,3,2,7,1,5,4,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,2,6,1,7,8,5,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,6,2,1,8,3,7,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,4,5,2,3,1,7,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,2,5,3,4,1,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,8,4,7,5,6,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,6,7,2,8,4,3,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,4,1,2,8,3,7,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,4,1,2,8,6,3,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,7,3,5,1,8,2,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,4,6,9,10,1,2,5,7,8] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[3,4,7,8,11,12,1,2,5,6,9,10] => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 5
[3,5,7,9,11,12,1,2,4,6,8,10] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 7
[8,3,2,1,7,6,5,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,8,3,7,6,5,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,8,1,2,7,6,5,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,4,2,3,1,8,7,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,4,6,8,3,7,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,2,1,8,7,5,6,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,4,6,2,7,8,5,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,3,8,5,4,6,1,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,8,7,5,4,6,1,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,8,3,5,4,7,1,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,3,6,1,8,2,7,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,8,9,1,2,3,4,5,6] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0] => 4
[10,8,9,1,2,3,4,5,6,7] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[3,4,6,2,7,1,5,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,8,1,7,2,6,4,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,8,5,4,3,1,2,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,2,1,3,6,5,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,1,8,6,5,4,2,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,5,3,6,2,7,4,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,7,6,5,4,8,2,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,7,1,4,8,3,2,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,6,4,3,5,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,2,6,1,8,3,5,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,4,3,8,6,5,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,3,6,1,5,2,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,5,8,2,4,1,7,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,6,8,1,5,2,4,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,4,8,2,6,1,7,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,6,5,8,3,7,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,5,7,4,8,1,3,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,7,4,3,8,5,2,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,7,3,5,8,4,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,5,1,4,6,2,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,8,1,2,5,7,6,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,5,7,3,6,8,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,5,6,7,8,3,4,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,2,8,3,6,5,1,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,6,3,8,7,1,5,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,4,8,2,3,7,6,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,4,1,2,7,3,5,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,8,3,5,4,1,6,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,8,2,5,4,6,1,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,2,7,1,8,3,6,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,2,5,1,3,7,6,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,4,8,2,7,3,5,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,5,8,4,1,7,6,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,3,8,4,1,7,6,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,8,3,7,6,1,4,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,8,3,7,4,1,5,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,6,8,3,7,2,5,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,1,7,6,5,4,3,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,6,5,1,3,2,7,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,5,3,1,2,8,4,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,6,8,7,4,2,5,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,8,6,5,4,3,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,3,8,6,5,4,1,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,1,4,3,2,8,7,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,6,2,8,7,3,5,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,6,2,4,7,3,5,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,1,5,4,3,8,2,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,4,7,2,5,8,1,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,5,7,2,4,8,3,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,7,6,2,8,3,4,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,5,7,6,2,4,8,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,7,3,1,2,8,5,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,7,8,1,2,6,5,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,8,4,3,7,2,5,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,2,5,6,8,4,1,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,3,2,7,6,8,4,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,4,8,6,5,2,1,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,7,5,4,3,8,1,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,8,4,3,7,6,1,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,7,4,3,1,6,2,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,1,2,7,8,6,4,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,5,8,1,2,3,7,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,8,3,6,7,4,1,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,3,1,6,8,4,7,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,6,3,5,8,2,1,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,1,6,4,7,3,5,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,1,5,4,3,7,6,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,6,5,4,1,2,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,1,6,7,5,3,4,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,5,8,7,6,3,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,7,6,4,1,8,2,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,6,8,4,1,7,2,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,7,4,8,1,6,2,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,4,8,7,1,6,2,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,7,5,2,3,8,4,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,4,8,1,5,7,6,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,8,5,7,1,6,4,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,2,8,5,1,7,6,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,6,1,4,7,8,5,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,8,1,6,5,4,2,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,7,3,6,4,5,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,8,6,5,4,3,2,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,7,6,8,2,3,5,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,3,2,5,8,6,1,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,2,5,8,6,3,1,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,6,4,8,1,2,7,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,1,3,6,7,4,5,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,4,2,3,1,6,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,8,2,4,1,7,6,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,5,7,4,1,8,3,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,3,2,8,1,6,5,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,8,2,4,7,1,5,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,7,1,8,2,6,5,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,2,1,7,6,5,4,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,4,7,2,1,5,3,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,3,2,1,5,4,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,5,8,1,2,6,3,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,7,8,3,6,5,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,6,1,4,3,2,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,7,1,8,3,6,2,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,6,8,1,4,2,7,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,2,7,5,4,1,8,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,6,7,5,4,2,8,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,5,2,1,3,8,7,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,8,3,1,2,7,6,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,3,2,4,6,5,1,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,8,6,2,1,3,7,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,6,7,8,2,5,3,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,5,7,8,2,3,6,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,5,7,8,6,2,3,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,3,6,8,7,4,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,1,7,4,6,5,3,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,2,7,3,6,5,4,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,4,7,6,5,2,3,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,7,4,3,5,1,8,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,7,3,5,4,8,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,4,6,2,5,7,3,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,3,6,4,7,2,5,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,8,1,4,7,2,5,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,7,1,6,5,4,8,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,4,7,2,8,5,3,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,2,4,3,7,5,6,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,6,1,4,7,2,8,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,8,5,7,3,2,4,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,6,8,4,7,2,5,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,8,2,7,6,5,4,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,6,2,5,4,3,1,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,2,8,1,6,5,4,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,8,7,5,1,6,3,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,8,6,7,5,3,1,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,5,4,8,2,1,7,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,3,2,8,5,7,1,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,2,5,7,1,8,4,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,5,4,3,2,1,7,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,3,2,5,4,1,6,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,2,1,5,7,8,4,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,2,1,6,8,4,5,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,3,2,8,7,4,5,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,8,4,3,6,5,2,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,6,1,4,2,5,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,5,8,3,6,4,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,8,1,3,5,7,6,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,3,2,6,1,4,7,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,7,4,8,5,1,2,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,8,1,5,6,4,7,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,6,3,1,7,8,5,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,5,6,7,8,9,1,2,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0] => 4
[4,5,6,7,8,9,10,2,3,1] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[4,8,3,7,6,5,1,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,2,8,7,6,1,4,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,2,8,7,1,5,4,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,8,3,1,6,5,4,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,2,4,3,8,1,5,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,8,2,5,4,7,6,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,1,4,3,6,5,7,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,6,8,3,5,7,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,8,3,6,5,7,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,7,1,5,4,6,8,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,8,1,5,4,6,2,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,4,1,2,6,8,7,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,6,1,5,4,8,7,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,6,1,5,4,7,2,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,7,1,5,4,2,6,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,8,1,5,4,2,7,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,4,1,2,8,5,7,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,6,3,1,8,2,4,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,3,6,4,8,2,1,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,1,6,4,2,3,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,3,2,4,7,1,5,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,7,5,8,1,6,2,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,6,7,1,4,2,3,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,5,3,1,7,8,2,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,1,3,5,4,8,2,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,2,1,7,3,8,4,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,5,7,8,1,6,3,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,4,5,2,3,8,7,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[10,6,9,3,5,8,1,2,4,7] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 5
[1,8,4,6,7,3,5,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,7,8,5,4,6,1,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,7,4,3,8,6,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,3,2,1,4,8,7,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,5,7,4,2,8,3,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,2,7,1,8,5,3,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,4,3,7,1,8,2,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,8,3,6,7,1,5,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,4,1,2,5,8,3,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,6,1,3,7,2,5,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,4,2,3,6,5,7,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,8,3,2,7,1,5,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,4,3,5,2,8,1,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,5,7,1,2,6,8,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,2,7,5,4,1,3,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,7,6,1,5,3,8,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,7,6,4,1,3,8,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,8,7,2,5,1,3,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,8,7,2,1,6,3,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,6,7,1,5,2,3,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,1,7,8,5,2,3,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,6,8,3,1,2,7,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,6,8,3,5,2,1,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,7,8,3,5,1,2,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,4,3,2,8,5,1,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,7,4,3,1,2,6,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,1,4,3,8,2,7,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,8,3,6,1,7,4,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,5,8,1,2,6,4,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,10,11,6,7,8,9,4,5,12,1,2] => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 5
[3,10,11,8,9,4,5,6,7,12,1,2] => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 5
[5,6,7,8,9,10,11,12,1,2,3,4] => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 5
[11,12,1,6,7,8,9,4,5,2,3,10] => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 5
[11,12,1,8,9,4,5,6,7,2,3,10] => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 5
[9,10,11,12,1,2,3,4,5,6,7,8] => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 5
[1,7,5,3,4,8,2,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,8,7,4,1,2,3,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,8,3,7,2,1,4,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,7,6,1,2,3,5,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,5,8,7,2,3,4,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,8,7,6,4,5,3,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,8,7,3,6,5,4,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,4,1,7,8,6,2,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,2,5,8,3,1,4,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,2,1,8,4,7,6,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,6,3,7,8,2,4,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,5,3,7,6,2,4,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,8,5,2,3,1,7,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,6,2,1,5,3,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,5,1,6,2,8,7,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,6,5,8,3,1,7,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,4,3,8,7,1,5,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,8,7,6,2,4,3,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,8,4,3,7,6,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,7,3,2,8,1,4,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,4,1,2,6,5,3,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,8,5,6,3,1,7,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,6,1,4,8,2,3,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,2,7,8,3,1,5,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,6,7,4,8,1,3,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,5,3,2,4,8,1,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,6,7,4,1,2,8,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,5,1,7,8,6,4,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,1,4,3,5,2,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,4,8,2,5,7,6,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,2,4,8,6,5,1,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,1,3,8,7,2,5,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,5,8,3,2,7,6,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,5,3,8,2,1,4,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,5,8,7,2,6,4,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,8,2,7,1,6,4,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,5,7,8,2,6,1,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,8,1,7,3,6,4,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,1,8,4,6,5,2,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,7,1,5,4,6,2,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,2,8,6,7,1,5,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,7,8,1,3,6,2,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,4,6,2,1,3,7,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,5,1,3,2,7,6,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,5,6,8,4,7,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,7,4,1,8,6,2,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,3,2,6,7,4,1,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,7,1,6,3,4,2,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,8,5,6,3,4,2,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,7,1,4,2,8,5,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,5,1,4,2,8,6,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,8,3,5,7,1,4,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,2,4,3,6,5,1,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,2,7,1,8,4,3,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,5,4,3,8,1,7,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,4,1,5,2,8,7,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,5,1,6,7,4,2,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,5,6,1,7,3,2,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,7,2,5,4,8,3,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,2,1,5,4,8,3,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,2,7,5,4,8,1,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,3,7,5,4,8,2,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,1,3,2,7,8,5,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,4,3,1,7,8,5,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,7,3,5,4,8,1,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,4,8,1,6,5,7,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,8,4,3,1,5,7,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,3,2,1,7,4,5,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,3,2,7,6,1,4,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,2,8,1,7,3,5,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,6,3,8,4,2,1,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,1,5,4,3,2,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,8,6,2,5,3,1,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,3,1,7,8,6,4,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,5,6,1,2,8,7,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,1,2,6,8,4,7,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,7,3,8,4,1,2,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,5,1,4,2,3,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,8,6,7,5,3,4,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,8,7,3,6,4,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,8,6,1,5,3,2,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,8,6,4,1,3,2,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,4,8,7,5,1,2,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,7,6,8,5,1,2,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,6,7,8,5,1,3,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,6,4,8,5,2,1,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,3,2,6,8,1,7,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,4,6,2,3,5,1,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,2,4,3,7,8,1,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,2,1,7,6,8,4,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,6,3,7,4,2,5,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,4,5,1,3,8,7,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,7,5,8,6,3,2,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,5,1,6,8,4,7,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,6,2,8,1,3,7,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,5,1,7,2,6,8,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,6,7,1,5,8,3,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,4,3,2,8,1,6,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,3,2,1,8,4,7,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,8,4,3,7,5,6,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,2,8,6,7,4,5,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,2,7,1,3,8,5,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,3,7,6,1,4,2,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,7,5,4,1,8,2,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,8,4,1,7,6,5,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,2,6,8,7,1,5,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,3,2,1,4,7,6,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,6,4,3,8,1,7,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,5,6,8,2,1,7,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,2,5,6,3,1,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,6,7,5,8,2,3,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,5,3,7,1,8,4,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,2,6,7,8,1,4,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,5,4,3,7,8,2,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,4,7,5,2,6,3,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,4,7,5,2,1,3,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,1,4,3,5,7,6,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,1,8,4,2,7,6,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,7,8,5,4,3,2,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,7,2,4,6,5,3,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,6,4,3,7,8,5,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,3,2,6,5,4,1,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,8,1,5,7,6,4,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,4,8,2,7,6,5,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,8,2,1,7,6,5,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,1,8,7,2,6,4,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,1,4,3,7,6,5,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,8,1,3,7,6,5,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,3,8,1,7,6,5,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,7,5,8,6,3,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,3,8,4,6,5,1,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,3,6,4,1,2,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,2,5,1,7,8,3,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,4,8,2,6,5,7,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,8,5,6,3,4,7,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,1,5,8,3,2,7,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,8,2,6,1,4,7,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,7,4,6,8,3,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,8,3,5,7,6,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,8,12,5,7,11,10,9,2,4,1,3] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 7
[3,5,8,2,4,7,6,10,12,1,9,11] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 7
[5,8,4,7,6,12,3,11,10,9,2,1] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 7
[6,5,3,2,4,1,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,8,7,5,4,6,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,6,5,8,7,2,3,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,4,6,2,8,3,7,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,3,5,1,2,7,6,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,8,7,6,5,1,3,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,2,8,6,4,5,1,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,5,8,6,3,7,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,8,4,6,1,3,7,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,4,8,1,7,6,5,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,3,8,1,5,7,6,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,6,8,5,4,2,7,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,6,4,1,8,2,7,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,6,4,1,5,2,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,8,6,5,1,3,7,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,3,2,7,4,6,5,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,8,1,9,2,3,4,5,7] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0] => 4
[1,8,4,3,2,7,6,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,4,2,3,5,1,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,8,6,4,5,7,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,8,9,10,1,3,4,5,6,7] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[5,3,2,6,8,4,7,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,2,7,6,1,4,3,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,6,1,7,5,2,4,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,8,1,7,5,2,4,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,1,3,7,6,5,4,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,2,8,1,7,5,6,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,2,6,5,4,3,1,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,2,7,6,4,5,3,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,7,3,5,4,2,6,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,5,8,6,2,1,7,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,6,5,2,3,4,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,8,1,4,6,5,3,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,3,2,4,7,1,8,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,5,8,6,2,4,3,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,6,4,7,8,2,3,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,2,4,6,1,3,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,4,8,6,1,2,7,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,3,8,4,7,1,5,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,4,8,2,3,1,7,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,4,7,2,3,1,5,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,8,3,2,1,7,6,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,4,3,8,1,7,6,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,8,2,6,5,4,1,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,5,7,3,2,8,4,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,6,5,7,3,8,4,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,6,7,5,4,1,3,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,7,4,3,1,5,2,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,2,8,1,3,7,6,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,2,7,8,4,1,3,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,2,5,1,3,7,8,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,8,7,1,5,2,3,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,7,5,1,3,6,2,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,4,3,2,7,5,6,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,8,2,4,6,5,1,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,7,3,1,6,5,2,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,6,8,7,5,1,4,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,6,3,2,8,4,1,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,3,8,6,5,4,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,3,2,8,6,5,4,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,3,8,7,1,6,4,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,8,7,3,1,6,4,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,8,4,7,1,6,3,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,5,7,8,2,4,3,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,5,6,8,7,3,2,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,5,8,6,2,7,4,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,4,6,7,8,3,2,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,2,7,5,1,8,3,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,7,3,6,8,4,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,7,6,1,5,3,2,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,1,2,7,5,8,4,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,6,7,8,4,2,3,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,2,4,5,3,8,1,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,5,8,2,4,7,6,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,8,1,4,7,3,5,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,6,8,2,7,4,5,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,2,4,6,8,3,1,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,2,4,7,8,1,3,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,2,6,3,8,4,1,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,2,4,3,8,5,1,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,4,3,2,8,7,1,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,2,6,8,1,3,5,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,3,6,8,7,2,5,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,8,7,1,5,4,3,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,7,8,5,6,4,2,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,5,7,4,2,1,3,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,6,8,4,1,2,3,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,3,2,7,8,5,4,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,7,4,3,8,5,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,2,7,6,4,5,1,10,8,9] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 5
[5,4,2,3,7,6,1,10,8,9] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 5
[5,4,2,3,9,8,6,7,1,10] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 5
[5,4,2,3,9,8,6,7,1,12,10,11] => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 5
[5,4,2,3,1,12,11,10,6,7,8,9] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 7
[9,8,7,6,2,3,4,5,1,12,10,11] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 7
[4,3,2,7,5,8,1,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,1,5,2,3,8,7,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,5,8,7,6,2,4,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,8,6,4,7,3,5,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,7,3,1,8,5,2,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,3,2,5,7,1,4,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,2,5,6,7,4,3,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,2,5,3,4,7,6,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,6,1,4,7,2,5,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,7,1,4,6,5,2,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,3,8,7,4,5,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,4,5,2,8,1,7,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,5,3,1,8,7,6,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,7,8,4,1,5,2,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,3,2,6,8,7,4,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,4,5,6,1,2,9,7,8] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0] => 4
[5,6,3,8,7,2,1,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,8,5,3,4,7,6,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,2,8,7,6,5,1,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,2,1,6,7,4,5,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,2,8,1,6,7,5,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,6,1,3,5,2,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,4,8,2,6,5,3,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,6,5,7,8,2,4,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,5,6,7,2,8,4,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,5,7,6,2,8,3,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,6,5,8,1,2,7,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,4,7,8,1,6,3,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,6,5,8,3,2,7,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,7,5,8,3,6,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,3,6,8,5,2,1,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,8,4,7,5,1,3,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,8,3,7,1,4,6,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,2,7,8,1,5,3,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,2,1,6,3,4,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,8,3,1,4,7,6,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,4,8,2,1,3,7,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,3,2,4,8,5,1,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,4,5,2,6,3,7,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,7,3,1,6,8,2,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,7,4,6,8,3,2,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,6,1,3,8,2,7,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,5,4,7,2,8,3,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,2,8,7,1,4,6,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,8,2,7,5,1,4,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,4,6,2,7,3,1,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,2,7,6,8,4,1,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,2,5,3,4,8,1,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,2,5,6,3,7,4,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,7,8,1,4,6,2,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,2,1,5,4,3,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,1,3,6,2,4,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,7,4,1,5,8,2,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,7,8,6,3,4,2,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,3,2,1,8,6,4,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,3,2,1,6,5,7,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,8,9,10,2,3,4,5,6,7] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 5
[1,5,6,7,8,9,10,2,3,4] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 5
[4,5,3,1,2,8,6,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,8,2,6,7,4,5,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,1,7,4,8,2,3,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,1,2,8,6,5,7,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,5,6,2,4,3,7,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,3,7,6,8,4,2,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,5,7,6,2,4,1,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,4,3,6,7,2,5,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,2,1,6,7,4,8,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,3,2,7,8,6,4,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,3,2,1,4,6,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,7,8,5,1,6,2,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,6,7,8,3,2,5,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,3,2,7,8,4,6,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,7,2,5,1,8,3,9,6] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0] => 4
[4,7,2,5,1,8,3,9,6,10] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 5
[5,3,8,6,4,1,9,2,10,7] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[4,3,8,1,6,5,7,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,8,7,1,4,6,3,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,6,3,7,8,2,1,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,8,4,5,3,1,7,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,8,5,4,7,1,3,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,7,8,5,4,2,6,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,4,8,2,5,7,1,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,6,1,2,3,4,9,7,8] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0] => 4
[6,3,2,7,5,8,4,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,7,6,8,4,3,2,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,8,7,4,6,1,3,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,8,10,1,2,3,4,5,6,9] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[4,5,6,7,8,10,1,2,3,9] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[2,1,3,8,7,5,6,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,8,1,4,6,5,2,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,5,2,6,3,4,7,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,4,1,2,7,6,5,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,1,5,7,3,6,4,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,1,4,2,8,5,9,6,10,7] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[4,1,5,2,6,3,9,7,10,8] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[4,1,5,2,8,3,9,6,10,7] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[2,1,5,3,6,4,10,7,11,8,12,9] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 7
[2,1,6,3,7,4,8,5,11,9,12,10] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 7
[2,1,6,3,7,4,10,5,11,8,12,9] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 7
[3,1,4,2,6,5,10,7,11,8,12,9] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 7
[3,1,4,2,8,5,9,6,10,7,12,11] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 7
[3,1,4,2,8,5,10,6,11,7,12,9] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 7
[4,1,5,2,6,3,8,7,11,9,12,10] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 7
[4,1,5,2,6,3,9,7,10,8,12,11] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 7
[4,1,5,2,6,3,10,7,11,8,12,9] => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 5
[4,1,5,2,8,3,9,6,10,7,12,11] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 7
[4,1,5,2,8,3,10,6,11,7,12,9] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 7
[4,1,6,2,7,3,8,5,11,9,12,10] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 7
[4,1,6,2,7,3,10,5,11,8,12,9] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 7
[4,1,7,2,8,3,10,5,11,6,12,9] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 7
[7,6,2,4,8,3,1,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,7,3,8,6,4,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,8,9,10,2,1,6,5,4,3] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[8,9,10,3,4,2,1,7,6,5] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[9,10,4,5,6,3,2,1,8,7] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[10,5,6,7,8,4,3,2,1,9] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[8,9,10,11,12,2,1,7,6,5,4,3] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 7
[12,6,7,8,9,10,5,4,3,2,1,11] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 7
[8,2,7,6,3,4,5,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,7,6,3,4,5,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,3,7,8,4,6,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,3,8,4,7,6,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,8,7,4,6,5,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,6,3,7,8,1,4,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,2,5,6,3,4,8,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[12,10,7,9,6,3,5,2,4,8,1,11] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 7
[12,10,5,9,7,4,3,2,6,8,1,11] => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 5
[12,10,4,9,6,8,3,5,7,2,1,11] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 7
[12,10,6,9,8,5,4,3,7,2,1,11] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 7
[1,4,8,6,7,2,5,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,5,3,8,6,2,1,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,7,4,8,5,3,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,5,6,7,8,9,10,1,3,4] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[8,6,1,5,4,2,7,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,1,4,3,2,6,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,4,7,2,3,6,5,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,6,8,1,2,5,7,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,8,5,4,3,7,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[9,6,10,1,3,7,8,2,4,5] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[2,5,6,4,1,3,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,5,8,6,2,4,7,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,4,2,3,5,7,6,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,2,7,3,8,1,4,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,7,8,3,6,5,2,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,4,7,8,6,3,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,4,5,2,7,6,3,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,4,7,2,1,6,3,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[3,10,11,12,4,7,9,2,6,8,1,5] => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 5
[4,5,2,1,3,7,6,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,1,9,10,2,3,4,5,6,7] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[1,6,8,7,3,2,4,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,5,1,7,2,3,4,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,7,6,4,8,3,1,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,4,7,2,6,5,8,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,7,3,6,1,4,2,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,1,5,6,3,8,7,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,5,8,1,6,2,7,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,6,3,1,7,2,8,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,3,7,1,5,8,2,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,8,7,3,5,1,4,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,5,8,6,7,4,2,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,1,7,2,5,8,3,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,5,4,1,6,2,9,3,10,7] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[8,2,5,1,6,3,9,4,10,7] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 5
[3,5,7,4,2,8,1,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[9,1,10,7,4,2,5,3,6,8] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[9,1,10,6,2,7,4,3,5,8] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[4,6,8,1,5,7,2,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[4,5,1,3,2,6,8,7] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,7,2,5,4,1,3,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,3,2,4,8,7,1,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,3,2,6,5,8,1,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,4,5,2,6,3,1,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[7,5,8,4,2,1,6,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,4,5,2,7,1,3,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,6,8,5,4,7,2,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,4,3,2,7,8,5,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[6,8,5,4,3,7,1,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[8,9,10,11,2,3,12,4,5,6,1,7] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 7
[1,5,2,9,3,10,4,6,7,8] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 5
[4,6,8,7,3,9,10,5,2,1] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[1,7,2,8,6,5,3,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,6,8,7,2,5,4,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[5,1,6,7,8,9,10,2,3,4] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[8,9,10,1,6,7,5,4,3,2] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[10,1,8,9,6,7,5,4,3,2] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[5,2,6,7,8,9,10,1,3,4] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 5
[10,8,5,1,9,6,2,7,3,4] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 5
[5,6,7,8,10,9,4,3,2,1] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[6,5,7,8,9,10,4,3,2,1] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
[1,3,8,6,7,4,5,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
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Generating function
$F_{1} = 1$
$F_{2} = 1 + q$
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Map
cycle type
Description
The cycle type of a permutation as a partition.
Map
parallelogram polyomino
Description
Return the Dyck path corresponding to the partition interpreted as a parallogram polyomino.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
Map
promotion
Description
The promotion of the two-row standard Young tableau of a Dyck path.
Dyck paths of semilength $n$ are in bijection with standard Young tableaux of shape $(n^2)$, see Mp00033to two-row standard tableau.
This map is the bijection on such standard Young tableaux given by Schützenberger's promotion. For definitions and details, see [1] and the references therein.
Dyck paths of semilength $n$ are in bijection with standard Young tableaux of shape $(n^2)$, see Mp00033to two-row standard tableau.
This map is the bijection on such standard Young tableaux given by Schützenberger's promotion. For definitions and details, see [1] and the references therein.
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