Identifier
-
Mp00060:
Permutations
—Robinson-Schensted tableau shape⟶
Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00222: Dyck paths —peaks-to-valleys⟶ Dyck paths
St001232: Dyck paths ⟶ ℤ
Values
[1] => [1] => [1,0] => [1,0] => 0
[1,2] => [2] => [1,0,1,0] => [1,1,0,0] => 0
[2,1] => [1,1] => [1,1,0,0] => [1,0,1,0] => 1
[1,2,3] => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 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] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 1
[3,1,2] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 1
[1,2,3,4] => [4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[1,2,4,3] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 1
[1,3,2,4] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 1
[1,3,4,2] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 1
[1,4,2,3] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 1
[2,1,3,4] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 1
[2,1,4,3] => [2,2] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 2
[2,3,1,4] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 1
[2,3,4,1] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 1
[2,4,1,3] => [2,2] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 2
[3,1,2,4] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 1
[3,1,4,2] => [2,2] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 2
[3,4,1,2] => [2,2] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 2
[4,1,2,3] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 1
[1,2,3,4,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,2,3,5,4] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,2,4,3,5] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,2,4,5,3] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,2,5,3,4] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,3,2,4,5] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,3,2,5,4] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 2
[1,3,4,2,5] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,3,4,5,2] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,3,5,2,4] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 2
[1,4,2,3,5] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,4,2,5,3] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 2
[1,4,5,2,3] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 2
[1,5,2,3,4] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[2,1,3,4,5] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[2,1,3,5,4] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 2
[2,1,4,3,5] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 2
[2,1,4,5,3] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 2
[2,1,5,3,4] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 2
[2,3,1,4,5] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[2,3,1,5,4] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 2
[2,3,4,1,5] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[2,3,4,5,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[2,3,5,1,4] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 2
[2,4,1,3,5] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 2
[2,4,1,5,3] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 2
[2,4,5,1,3] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 2
[2,5,1,3,4] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 2
[3,1,2,4,5] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[3,1,2,5,4] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 2
[3,1,4,2,5] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 2
[3,1,4,5,2] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 2
[3,1,5,2,4] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 2
[3,4,1,2,5] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 2
[3,4,1,5,2] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 2
[3,4,5,1,2] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 2
[3,5,1,2,4] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 2
[4,1,2,3,5] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[4,1,2,5,3] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 2
[4,1,5,2,3] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 2
[4,5,1,2,3] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 2
[5,1,2,3,4] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,2,3,4,5,6] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,2,3,4,6,5] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,2,3,5,4,6] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,2,3,5,6,4] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,2,3,6,4,5] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,2,4,3,5,6] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,2,4,3,6,5] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[1,2,4,5,3,6] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,2,4,5,6,3] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,2,4,6,3,5] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[1,2,5,3,4,6] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,2,5,3,6,4] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[1,2,5,6,3,4] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[1,2,6,3,4,5] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,3,2,4,5,6] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,3,2,4,6,5] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[1,3,2,5,4,6] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[1,3,2,5,6,4] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[1,3,2,6,4,5] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[1,3,4,2,5,6] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,3,4,2,6,5] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[1,3,4,5,2,6] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,3,4,5,6,2] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,3,4,6,2,5] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[1,3,5,2,4,6] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[1,3,5,2,6,4] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[1,3,5,6,2,4] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[1,3,6,2,4,5] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[1,4,2,3,5,6] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,4,2,3,6,5] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[1,4,2,5,3,6] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[1,4,2,5,6,3] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[1,4,2,6,3,5] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[1,4,5,2,3,6] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[1,4,5,2,6,3] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[1,4,5,6,2,3] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[1,4,6,2,3,5] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
>>> Load all 2909 entries. <<<[1,5,2,3,4,6] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,5,2,3,6,4] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[1,5,2,6,3,4] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[1,5,6,2,3,4] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[1,6,2,3,4,5] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[2,1,3,4,5,6] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[2,1,3,4,6,5] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[2,1,3,5,4,6] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[2,1,3,5,6,4] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[2,1,3,6,4,5] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[2,1,4,3,5,6] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[2,1,4,5,3,6] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[2,1,4,5,6,3] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[2,1,5,3,4,6] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[2,1,6,3,4,5] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[2,3,1,4,5,6] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[2,3,1,4,6,5] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[2,3,1,5,4,6] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[2,3,1,5,6,4] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[2,3,1,6,4,5] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[2,3,4,1,5,6] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[2,3,4,1,6,5] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[2,3,4,5,1,6] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[2,3,4,5,6,1] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[2,3,4,6,1,5] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[2,3,5,1,4,6] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[2,3,5,1,6,4] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[2,3,5,6,1,4] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[2,3,6,1,4,5] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[2,4,1,3,5,6] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[2,4,1,5,3,6] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[2,4,1,5,6,3] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[2,4,5,1,3,6] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[2,4,5,1,6,3] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[2,4,5,6,1,3] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[2,5,1,3,4,6] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[2,6,1,3,4,5] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[3,1,2,4,5,6] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[3,1,2,4,6,5] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[3,1,2,5,4,6] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[3,1,2,5,6,4] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[3,1,2,6,4,5] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[3,1,4,2,5,6] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[3,1,4,5,2,6] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[3,1,4,5,6,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[3,1,5,2,4,6] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[3,1,6,2,4,5] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[3,2,1,6,5,4] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0] => 3
[3,2,6,1,5,4] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0] => 3
[3,2,6,5,1,4] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0] => 3
[3,4,1,2,5,6] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[3,4,1,5,2,6] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[3,4,1,5,6,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[3,4,5,1,2,6] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[3,4,5,1,6,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[3,4,5,6,1,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[3,5,1,2,4,6] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[3,6,1,2,4,5] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[3,6,2,1,5,4] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0] => 3
[3,6,2,5,1,4] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0] => 3
[4,1,2,3,5,6] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[4,1,2,3,6,5] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[4,1,2,5,3,6] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[4,1,2,5,6,3] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[4,1,2,6,3,5] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[4,1,5,2,3,6] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[4,1,6,2,3,5] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[4,2,1,6,5,3] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0] => 3
[4,2,6,1,5,3] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0] => 3
[4,2,6,5,1,3] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0] => 3
[4,3,1,6,5,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0] => 3
[4,3,6,1,5,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0] => 3
[4,3,6,5,1,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0] => 3
[4,5,1,2,3,6] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[4,6,1,2,3,5] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[4,6,2,1,5,3] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0] => 3
[4,6,2,5,1,3] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0] => 3
[4,6,3,1,5,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0] => 3
[4,6,3,5,1,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0] => 3
[5,1,2,3,4,6] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[5,1,2,3,6,4] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[5,1,2,6,3,4] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[5,1,6,2,3,4] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[5,2,1,6,4,3] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0] => 3
[5,2,6,1,4,3] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0] => 3
[5,2,6,4,1,3] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0] => 3
[5,3,1,6,4,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0] => 3
[5,3,6,1,4,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0] => 3
[5,3,6,4,1,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0] => 3
[5,6,1,2,3,4] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[5,6,2,1,4,3] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0] => 3
[5,6,2,4,1,3] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0] => 3
[5,6,3,1,4,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0] => 3
[5,6,3,4,1,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0] => 3
[6,1,2,3,4,5] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,2,3,4,5,6,7] => [7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,2,3,4,5,7,6] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,2,3,4,6,5,7] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,2,3,4,6,7,5] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,2,3,4,7,5,6] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,2,3,5,4,6,7] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,2,3,5,4,7,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,2,3,5,6,4,7] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,2,3,5,6,7,4] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,2,3,5,7,4,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,2,3,6,4,5,7] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,2,3,6,4,7,5] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,2,3,6,7,4,5] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,2,3,7,4,5,6] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,2,4,3,5,6,7] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,2,4,3,5,7,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,2,4,3,6,5,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,2,4,3,6,7,5] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,2,4,3,7,5,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,2,4,5,3,6,7] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,2,4,5,3,7,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,2,4,5,6,3,7] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,2,4,5,6,7,3] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,2,4,5,7,3,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,2,4,6,3,5,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,2,4,6,3,7,5] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,2,4,6,7,3,5] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,2,4,7,3,5,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,2,5,3,4,6,7] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,2,5,3,4,7,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,2,5,3,6,4,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,2,5,3,6,7,4] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,2,5,3,7,4,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,2,5,6,3,4,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,2,5,6,3,7,4] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,2,5,6,7,3,4] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,2,5,7,3,4,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,2,6,3,4,5,7] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,2,6,3,4,7,5] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,2,6,3,7,4,5] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,2,6,7,3,4,5] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,2,7,3,4,5,6] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,3,2,4,5,6,7] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,3,2,4,5,7,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,3,2,4,6,5,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,3,2,4,6,7,5] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,3,2,4,7,5,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,3,2,5,4,6,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,3,2,5,6,4,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,3,2,5,6,7,4] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,3,2,6,4,5,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,3,2,7,4,5,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,3,4,2,5,6,7] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,3,4,2,5,7,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,3,4,2,6,5,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,3,4,2,6,7,5] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,3,4,2,7,5,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,3,4,5,2,6,7] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,3,4,5,2,7,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,3,4,5,6,2,7] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,3,4,5,6,7,2] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,3,4,5,7,2,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,3,4,6,2,5,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,3,4,6,2,7,5] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,3,4,6,7,2,5] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,3,4,7,2,5,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,3,5,2,4,6,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,3,5,2,6,4,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,3,5,2,6,7,4] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,3,5,6,2,4,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,3,5,6,2,7,4] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,3,5,6,7,2,4] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,3,6,2,4,5,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,3,7,2,4,5,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,4,2,3,5,6,7] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,4,2,3,5,7,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,4,2,3,6,5,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,4,2,3,6,7,5] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,4,2,3,7,5,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,4,2,5,3,6,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,4,2,5,6,3,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,4,2,5,6,7,3] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,4,2,6,3,5,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,4,2,7,3,5,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,4,3,2,7,6,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[1,4,3,7,2,6,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[1,4,3,7,6,2,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[1,4,5,2,3,6,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,4,5,2,6,3,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,4,5,2,6,7,3] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,4,5,6,2,3,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,4,5,6,2,7,3] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,4,5,6,7,2,3] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,4,6,2,3,5,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,4,7,2,3,5,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,4,7,3,2,6,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[1,4,7,3,6,2,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[1,5,2,3,4,6,7] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,5,2,3,4,7,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,5,2,3,6,4,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,5,2,3,6,7,4] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,5,2,3,7,4,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,5,2,6,3,4,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,5,2,7,3,4,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,5,3,2,7,6,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[1,5,3,7,2,6,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[1,5,3,7,6,2,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[1,5,4,2,7,6,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[1,5,4,7,2,6,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[1,5,4,7,6,2,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[1,5,6,2,3,4,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,5,7,2,3,4,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,5,7,3,2,6,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[1,5,7,3,6,2,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[1,5,7,4,2,6,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[1,5,7,4,6,2,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[1,6,2,3,4,5,7] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,6,2,3,4,7,5] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,6,2,3,7,4,5] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,6,2,7,3,4,5] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,6,3,2,7,5,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[1,6,3,7,2,5,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[1,6,3,7,5,2,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[1,6,4,2,7,5,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[1,6,4,7,2,5,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[1,6,4,7,5,2,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[1,6,7,2,3,4,5] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,6,7,3,2,5,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[1,6,7,3,5,2,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[1,6,7,4,2,5,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[1,6,7,4,5,2,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[1,7,2,3,4,5,6] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[2,1,3,4,5,6,7] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[2,1,3,4,5,7,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,1,3,4,6,5,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,1,3,4,6,7,5] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,1,3,4,7,5,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,1,3,5,4,6,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,1,3,5,6,4,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,1,3,5,6,7,4] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,1,3,6,4,5,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,1,3,7,4,5,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,1,4,3,5,6,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,1,4,5,3,6,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,1,4,5,6,3,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,1,4,5,6,7,3] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,1,5,3,4,6,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,1,6,3,4,5,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,1,7,3,4,5,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,3,1,4,5,6,7] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[2,3,1,4,5,7,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,3,1,4,6,5,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,3,1,4,6,7,5] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,3,1,4,7,5,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,3,1,5,4,6,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,3,1,5,6,4,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,3,1,5,6,7,4] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,3,1,6,4,5,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,3,1,7,4,5,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,3,4,1,5,6,7] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[2,3,4,1,5,7,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,3,4,1,6,5,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,3,4,1,6,7,5] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,3,4,1,7,5,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,3,4,5,1,6,7] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[2,3,4,5,1,7,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,3,4,5,6,1,7] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[2,3,4,5,6,7,1] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[2,3,4,5,7,1,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,3,4,6,1,5,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,3,4,6,1,7,5] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,3,4,6,7,1,5] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,3,4,7,1,5,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,3,5,1,4,6,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,3,5,1,6,4,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,3,5,1,6,7,4] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,3,5,6,1,4,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,3,5,6,1,7,4] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,3,5,6,7,1,4] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,3,6,1,4,5,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,3,7,1,4,5,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,4,1,3,5,6,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,4,1,5,3,6,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,4,1,5,6,3,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,4,1,5,6,7,3] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,4,3,1,7,6,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[2,4,3,7,1,6,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[2,4,3,7,6,1,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[2,4,5,1,3,6,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,4,5,1,6,3,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,4,5,1,6,7,3] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,4,5,6,1,3,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,4,5,6,1,7,3] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,4,5,6,7,1,3] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,4,7,3,1,6,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[2,4,7,3,6,1,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[2,5,1,3,4,6,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,5,3,1,7,6,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[2,5,3,7,1,6,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[2,5,3,7,6,1,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[2,5,4,1,7,6,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[2,5,4,7,1,6,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[2,5,4,7,6,1,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[2,5,7,3,1,6,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[2,5,7,3,6,1,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[2,5,7,4,1,6,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[2,5,7,4,6,1,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[2,6,1,3,4,5,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[2,6,3,1,7,5,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[2,6,3,7,1,5,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[2,6,3,7,5,1,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[2,6,4,1,7,5,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[2,6,4,7,1,5,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[2,6,4,7,5,1,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[2,6,7,3,1,5,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[2,6,7,3,5,1,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[2,6,7,4,1,5,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[2,6,7,4,5,1,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[2,7,1,3,4,5,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[3,1,2,4,5,6,7] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[3,1,2,4,5,7,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[3,1,2,4,6,5,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[3,1,2,4,6,7,5] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[3,1,2,4,7,5,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[3,1,2,5,4,6,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[3,1,2,5,6,4,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[3,1,2,5,6,7,4] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[3,1,2,6,4,5,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[3,1,2,7,4,5,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[3,1,4,2,5,6,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[3,1,4,5,2,6,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[3,1,4,5,6,2,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[3,1,4,5,6,7,2] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[3,1,5,2,4,6,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[3,1,6,2,4,5,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[3,1,7,2,4,5,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[3,2,1,4,7,6,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,2,1,5,7,6,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,2,1,6,5,4,7] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,2,1,6,5,7,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,2,1,6,7,5,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,2,1,7,4,6,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,2,1,7,5,4,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,2,1,7,5,6,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,2,1,7,6,4,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,2,4,1,7,6,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,2,4,7,1,6,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,2,4,7,6,1,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,2,5,1,7,6,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,2,5,7,1,6,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,2,5,7,6,1,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,2,6,1,5,4,7] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,2,6,1,5,7,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,2,6,1,7,5,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,2,6,5,1,4,7] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,2,6,5,1,7,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,2,6,5,7,1,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,2,6,7,1,5,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,2,6,7,5,1,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,2,7,1,4,6,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,2,7,1,5,4,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,2,7,1,5,6,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,2,7,1,6,4,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,2,7,4,1,6,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,2,7,4,6,1,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,2,7,5,1,4,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,2,7,5,1,6,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,2,7,5,6,1,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,2,7,6,1,4,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,4,1,2,5,6,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[3,4,1,5,2,6,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[3,4,1,5,6,2,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[3,4,1,5,6,7,2] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[3,4,2,1,7,6,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,4,2,7,1,6,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,4,2,7,6,1,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,4,5,1,2,6,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[3,4,5,1,6,2,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[3,4,5,1,6,7,2] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[3,4,5,6,1,2,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[3,4,5,6,1,7,2] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[3,4,5,6,7,1,2] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[3,4,7,2,1,6,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,4,7,2,6,1,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,5,1,2,4,6,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[3,5,2,1,7,6,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,5,2,7,1,6,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,5,2,7,6,1,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,5,4,1,7,6,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,5,4,7,1,6,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,5,4,7,6,1,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,5,7,2,1,6,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,5,7,2,6,1,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,5,7,4,1,6,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,5,7,4,6,1,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,6,1,2,4,5,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[3,6,2,1,5,4,7] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,6,2,1,5,7,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,6,2,1,7,5,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,6,2,5,1,4,7] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,6,2,5,1,7,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,6,2,5,7,1,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,6,2,7,1,5,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,6,2,7,5,1,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,6,4,1,7,5,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,6,4,7,1,5,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,6,4,7,5,1,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,6,7,2,1,5,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,6,7,2,5,1,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,6,7,4,1,5,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,6,7,4,5,1,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,7,1,2,4,5,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[3,7,2,1,4,6,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,7,2,1,5,4,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,7,2,1,5,6,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,7,2,1,6,4,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,7,2,4,1,6,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,7,2,4,6,1,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,7,2,5,1,4,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,7,2,5,1,6,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,7,2,5,6,1,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[3,7,2,6,1,4,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,1,2,3,5,6,7] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[4,1,2,3,5,7,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[4,1,2,3,6,5,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[4,1,2,3,6,7,5] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[4,1,2,3,7,5,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[4,1,2,5,3,6,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[4,1,2,5,6,3,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[4,1,2,5,6,7,3] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[4,1,2,6,3,5,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[4,1,2,7,3,5,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[4,1,3,2,7,6,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,1,3,7,2,6,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,1,3,7,6,2,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,1,5,2,3,6,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[4,1,6,2,3,5,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[4,1,7,2,3,5,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[4,1,7,3,2,6,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,1,7,3,6,2,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,2,1,3,7,6,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,2,1,5,7,6,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,2,1,6,5,3,7] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,2,1,6,5,7,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,2,1,6,7,5,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,2,1,7,3,6,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,2,1,7,5,3,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,2,1,7,5,6,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,2,1,7,6,3,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,2,3,1,7,6,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,2,3,7,1,6,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,2,3,7,6,1,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,2,5,1,7,6,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,2,5,7,1,6,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,2,5,7,6,1,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,2,6,1,5,3,7] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,2,6,1,5,7,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,2,6,1,7,5,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,2,6,5,1,3,7] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,2,6,5,1,7,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,2,6,5,7,1,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,2,6,7,1,5,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,2,6,7,5,1,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,2,7,1,3,6,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,2,7,1,5,3,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,2,7,1,5,6,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,2,7,1,6,3,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,2,7,3,1,6,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,2,7,3,6,1,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,2,7,5,1,3,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,2,7,5,1,6,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,2,7,5,6,1,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,2,7,6,1,3,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,3,1,2,7,6,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,3,1,5,7,6,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,3,1,6,5,2,7] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,3,1,6,5,7,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,3,1,6,7,5,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,3,1,7,2,6,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,3,1,7,5,2,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,3,1,7,5,6,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,3,1,7,6,2,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,3,5,1,7,6,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,3,5,7,1,6,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,3,5,7,6,1,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,3,6,1,5,2,7] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,3,6,1,5,7,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,3,6,1,7,5,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,3,6,5,1,2,7] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,3,6,5,1,7,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,3,6,5,7,1,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,3,6,7,1,5,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,3,6,7,5,1,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,3,7,1,2,6,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,3,7,1,5,2,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,3,7,1,5,6,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,3,7,1,6,2,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,3,7,5,1,2,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,3,7,5,1,6,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,3,7,5,6,1,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,3,7,6,1,2,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,5,1,2,3,6,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[4,5,2,1,7,6,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,5,2,7,1,6,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,5,2,7,6,1,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,5,3,1,7,6,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,5,3,7,1,6,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,5,3,7,6,1,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,5,7,2,1,6,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,5,7,2,6,1,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,5,7,3,1,6,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,5,7,3,6,1,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,6,1,2,3,5,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[4,6,2,1,5,3,7] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,6,2,1,5,7,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,6,2,1,7,5,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,6,2,5,1,3,7] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,6,2,5,1,7,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,6,2,5,7,1,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,6,2,7,1,5,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,6,2,7,5,1,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,6,3,1,5,2,7] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,6,3,1,5,7,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,6,3,1,7,5,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,6,3,5,1,2,7] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,6,3,5,1,7,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,6,3,5,7,1,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,6,3,7,1,5,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,6,3,7,5,1,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,6,7,2,1,5,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,6,7,2,5,1,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,6,7,3,1,5,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,6,7,3,5,1,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,7,1,2,3,5,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[4,7,1,3,2,6,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,7,1,3,6,2,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,7,2,1,3,6,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,7,2,1,5,3,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,7,2,1,5,6,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,7,2,1,6,3,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,7,2,3,1,6,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,7,2,3,6,1,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,7,2,5,1,3,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,7,2,5,1,6,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,7,2,5,6,1,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,7,2,6,1,3,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,7,3,1,2,6,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,7,3,1,5,2,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,7,3,1,5,6,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,7,3,1,6,2,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,7,3,5,1,2,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,7,3,5,1,6,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,7,3,5,6,1,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[4,7,3,6,1,2,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,1,2,3,4,6,7] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[5,1,2,3,4,7,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[5,1,2,3,6,4,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[5,1,2,3,6,7,4] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[5,1,2,3,7,4,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[5,1,2,6,3,4,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[5,1,2,7,3,4,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[5,1,3,2,7,6,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,1,3,7,2,6,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,1,3,7,6,2,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,1,4,2,7,6,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,1,4,7,2,6,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,1,4,7,6,2,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,1,6,2,3,4,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[5,1,7,2,3,4,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[5,1,7,3,2,6,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,1,7,3,6,2,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,1,7,4,2,6,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,1,7,4,6,2,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,2,1,3,7,6,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,2,1,4,7,6,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,2,1,6,4,3,7] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,2,1,6,4,7,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,2,1,6,7,4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,2,1,7,3,6,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,2,1,7,4,3,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,2,1,7,4,6,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,2,1,7,6,3,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,2,3,1,7,6,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,2,3,7,1,6,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,2,3,7,6,1,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,2,4,1,7,6,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,2,4,7,1,6,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,2,4,7,6,1,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,2,6,1,4,3,7] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,2,6,1,4,7,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,2,6,1,7,4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,2,6,4,1,3,7] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,2,6,4,1,7,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,2,6,4,7,1,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,2,6,7,1,4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,2,6,7,4,1,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,2,7,1,3,6,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,2,7,1,4,3,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,2,7,1,4,6,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,2,7,1,6,3,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,2,7,3,1,6,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,2,7,3,6,1,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,2,7,4,1,3,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,2,7,4,1,6,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,2,7,4,6,1,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,2,7,6,1,3,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,3,1,2,7,6,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,3,1,4,7,6,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,3,1,6,4,2,7] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,3,1,6,4,7,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,3,1,6,7,4,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,3,1,7,2,6,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,3,1,7,4,2,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,3,1,7,4,6,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,3,1,7,6,2,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,3,4,1,7,6,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,3,4,7,1,6,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,3,4,7,6,1,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,3,6,1,4,2,7] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,3,6,1,4,7,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,3,6,1,7,4,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,3,6,4,1,2,7] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,3,6,4,1,7,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,3,6,4,7,1,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,3,6,7,1,4,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,3,6,7,4,1,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,3,7,1,2,6,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,3,7,1,4,2,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,3,7,1,4,6,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,3,7,1,6,2,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,3,7,4,1,2,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,3,7,4,1,6,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,3,7,4,6,1,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,3,7,6,1,2,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,4,1,2,7,6,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,4,1,7,2,6,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,4,1,7,6,2,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,4,7,1,2,6,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,4,7,1,6,2,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,4,7,6,1,2,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,6,1,2,3,4,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[5,6,2,1,4,3,7] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,6,2,1,4,7,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,6,2,1,7,4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,6,2,4,1,3,7] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,6,2,4,1,7,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,6,2,4,7,1,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,6,2,7,1,4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,6,2,7,4,1,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,6,3,1,4,2,7] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,6,3,1,4,7,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,6,3,1,7,4,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,6,3,4,1,2,7] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,6,3,4,1,7,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,6,3,4,7,1,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,6,3,7,1,4,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,6,3,7,4,1,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,6,7,2,1,4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,6,7,2,4,1,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,6,7,3,1,4,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,6,7,3,4,1,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,7,1,2,3,4,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[5,7,1,3,2,6,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,7,1,3,6,2,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,7,1,4,2,6,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,7,1,4,6,2,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,7,2,1,3,6,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,7,2,1,4,3,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,7,2,1,4,6,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,7,2,1,6,3,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,7,2,3,1,6,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,7,2,3,6,1,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,7,2,4,1,3,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,7,2,4,1,6,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,7,2,4,6,1,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,7,2,6,1,3,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,7,3,1,2,6,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,7,3,1,4,2,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,7,3,1,4,6,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,7,3,1,6,2,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,7,3,4,1,2,6] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,7,3,4,1,6,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,7,3,4,6,1,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,7,3,6,1,2,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,7,4,1,2,6,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,7,4,1,6,2,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[5,7,4,6,1,2,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,1,2,3,4,5,7] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[6,1,2,3,4,7,5] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[6,1,2,3,7,4,5] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[6,1,2,7,3,4,5] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[6,1,3,2,7,5,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,1,3,7,2,5,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,1,3,7,5,2,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,1,4,2,7,5,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,1,4,7,2,5,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,1,4,7,5,2,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,1,7,2,3,4,5] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[6,1,7,3,2,5,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,1,7,3,5,2,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,1,7,4,2,5,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,1,7,4,5,2,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,2,1,3,7,5,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,2,1,4,7,5,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,2,1,7,3,5,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,2,1,7,4,3,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,2,1,7,4,5,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,2,1,7,5,3,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,2,3,1,7,5,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,2,3,7,1,5,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,2,3,7,5,1,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,2,4,1,7,5,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,2,4,7,1,5,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,2,4,7,5,1,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,2,7,1,3,5,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,2,7,1,4,3,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,2,7,1,4,5,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,2,7,1,5,3,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,2,7,3,1,5,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,2,7,3,5,1,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,2,7,4,1,3,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,2,7,4,1,5,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,2,7,4,5,1,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,2,7,5,1,3,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,3,1,2,7,5,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,3,1,4,7,5,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,3,1,7,2,5,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,3,1,7,4,2,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,3,1,7,4,5,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,3,1,7,5,2,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,3,4,1,7,5,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,3,4,7,1,5,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,3,4,7,5,1,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,3,7,1,2,5,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,3,7,1,4,2,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,3,7,1,4,5,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,3,7,1,5,2,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,3,7,4,1,2,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,3,7,4,1,5,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,3,7,4,5,1,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,3,7,5,1,2,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,4,1,2,7,5,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,4,1,7,2,5,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,4,1,7,5,2,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,4,7,1,2,5,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,4,7,1,5,2,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,4,7,5,1,2,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,7,1,2,3,4,5] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[6,7,1,3,2,5,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,7,1,3,5,2,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,7,1,4,2,5,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,7,1,4,5,2,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,7,2,1,3,5,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,7,2,1,4,3,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,7,2,1,4,5,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,7,2,1,5,3,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,7,2,3,1,5,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,7,2,3,5,1,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,7,2,4,1,3,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,7,2,4,1,5,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,7,2,4,5,1,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,7,2,5,1,3,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,7,3,1,2,5,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,7,3,1,4,2,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,7,3,1,4,5,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,7,3,1,5,2,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,7,3,4,1,2,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,7,3,4,1,5,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,7,3,4,5,1,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,7,3,5,1,2,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,7,4,1,2,5,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,7,4,1,5,2,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[6,7,4,5,1,2,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[7,1,2,3,4,5,6] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[5,6,7,8,3,4,1,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,8,3,4,5,6,1,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,6,3,4,7,8,1,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,4,5,6,7,8,1,2] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[7,8,5,6,1,2,3,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,8,3,4,5,1,2,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,8,4,5,1,2,3,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,8,3,4,1,2,5,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,8,1,2,3,4,5,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[3,4,5,6,7,1,2,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[6,7,1,2,3,4,5,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[3,4,5,6,1,2,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[3,4,5,1,2,6,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[4,5,1,2,3,6,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[3,4,1,2,5,6,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,1,4,5,6,7,8,3] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[3,2,1,6,7,8,5,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,1,5,7,8,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,1,5,6,8,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,1,6,7,5,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,1,5,7,6,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,1,6,5,7,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,3,1,5,6,7,8,4] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,3,2,5,6,7,8,4] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,1,3,5,6,7,8,4] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[3,4,2,1,7,8,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,4,2,1,6,8,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,4,2,1,7,6,8,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,4,3,1,7,8,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,4,3,1,6,8,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,4,3,1,7,6,8,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,4,1,7,8,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,4,1,6,8,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,4,1,7,6,8,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,3,4,1,6,7,8,5] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,4,3,2,6,8,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,4,3,2,7,6,8,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,3,4,2,6,7,8,5] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,4,3,6,7,8,5] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[3,2,1,4,7,8,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,1,4,6,8,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,1,4,7,6,8,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,3,1,4,6,7,8,5] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,3,2,4,6,7,8,5] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,1,3,4,6,7,8,5] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[3,4,5,2,1,8,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,4,5,3,1,8,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,3,5,4,1,8,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,4,2,5,1,8,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,4,3,5,1,8,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,4,5,1,8,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,3,4,5,1,7,8,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,4,5,3,2,8,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,3,4,5,2,7,8,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,4,5,3,7,8,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,3,5,4,7,8,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,4,3,1,5,8,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,4,1,5,8,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,3,4,1,5,7,8,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,4,3,2,5,8,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,3,4,2,5,7,8,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,4,3,5,7,8,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[3,2,1,4,5,8,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,3,1,4,5,7,8,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,3,2,4,5,7,8,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,1,3,4,5,7,8,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,3,4,5,6,1,8,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,3,4,5,6,2,8,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,4,5,6,3,8,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,3,5,6,4,8,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,3,4,6,5,8,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,3,4,5,1,6,8,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,3,5,4,6,8,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,3,4,1,5,6,8,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,3,4,2,5,6,8,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,4,3,5,6,8,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,3,1,4,5,6,8,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,3,2,4,5,6,8,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,1,3,4,5,6,8,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,1,4,5,6,7,3,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[3,2,1,5,7,6,4,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,3,1,5,6,7,4,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,3,2,5,6,7,4,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[3,2,4,1,7,6,5,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,3,4,1,6,7,5,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,4,3,2,7,6,5,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,3,4,2,6,7,5,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,4,3,6,7,5,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[3,2,1,4,7,6,5,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,3,1,4,6,7,5,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,3,4,5,1,7,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,3,4,5,2,7,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,4,5,3,7,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,3,5,4,7,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,3,4,1,5,7,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,3,4,2,5,7,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,4,3,5,7,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,3,1,4,5,7,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,3,2,4,5,7,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,1,3,4,5,7,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,3,1,5,6,4,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,3,2,5,6,4,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,3,4,1,6,5,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,4,3,6,5,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,3,2,4,6,5,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,1,3,4,6,5,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,1,4,5,3,6,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,3,1,5,4,6,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,3,2,5,4,6,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,1,4,3,5,6,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,5,3,4,2,8,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,5,3,4,1,8,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,1,4,8,6,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,1,5,8,6,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,1,7,5,6,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,1,8,5,6,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,4,1,8,6,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,3,1,6,8,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,3,1,7,6,8,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,3,1,8,6,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,3,5,1,8,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,3,4,1,8,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,4,1,3,5,6,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,4,1,5,3,6,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,4,5,1,3,6,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,4,1,5,6,3,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,4,5,1,6,3,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,4,5,6,1,3,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,4,1,5,6,7,3,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,4,5,6,1,7,3,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,4,5,6,7,1,3,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,4,1,5,6,7,8,3] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,4,5,1,6,7,8,3] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,4,5,6,1,7,8,3] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,4,5,6,7,1,8,3] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,4,5,6,7,8,1,3] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,1,5,3,4,6,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,5,1,3,4,6,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,3,5,1,4,6,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,3,5,6,1,4,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,3,5,6,7,1,4,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,3,5,1,6,7,8,4] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,3,5,6,7,8,1,4] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,6,1,3,4,5,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,1,3,6,4,5,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,3,1,6,4,5,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,3,6,1,4,5,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,3,4,6,1,5,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,3,4,6,7,1,5,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,3,4,6,1,7,8,5] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,3,4,6,7,8,1,5] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,1,7,3,4,5,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,7,1,3,4,5,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,3,7,1,4,5,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,1,3,4,7,5,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,3,4,1,7,5,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,3,4,7,1,5,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,3,4,5,7,1,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,3,4,5,7,1,8,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,3,4,5,7,8,1,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,1,8,3,4,5,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,8,1,3,4,5,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,1,3,8,4,5,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,3,1,8,4,5,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,3,8,1,4,5,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,1,3,4,8,5,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,3,1,4,8,5,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,3,4,1,8,5,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,3,4,8,1,5,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,1,3,4,5,8,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,3,1,4,5,8,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,3,4,1,5,8,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,3,4,5,1,8,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,3,4,5,8,1,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[2,3,4,5,6,8,1,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[3,1,4,2,5,6,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[3,1,4,5,2,6,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[3,4,1,5,2,6,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[3,4,1,5,6,2,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[3,4,5,1,6,2,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[3,1,4,5,6,7,2,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[3,4,1,5,6,7,2,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[3,4,5,1,6,7,2,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[3,4,5,6,1,7,2,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[3,1,4,5,6,7,8,2] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[3,4,1,5,6,7,8,2] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[3,4,5,1,6,7,8,2] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[3,4,5,6,1,7,8,2] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[3,4,5,6,7,1,8,2] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[3,5,1,2,4,6,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,3,5,2,4,6,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,3,5,6,2,4,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[3,1,2,5,6,7,4,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,3,5,2,6,7,4,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,3,5,6,2,7,4,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,3,5,6,7,2,4,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[3,1,2,5,6,7,8,4] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,3,5,6,7,2,8,4] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,3,5,6,7,8,2,4] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[3,6,1,2,4,5,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,3,2,6,4,5,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,3,6,2,4,5,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,3,4,6,2,5,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,3,4,6,2,7,5,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,3,4,6,7,2,5,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[3,1,2,4,6,7,8,5] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,3,4,6,7,2,8,5] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[3,1,7,2,4,5,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[3,7,1,2,4,5,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[3,1,2,7,4,5,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,3,2,7,4,5,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,3,7,2,4,5,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[3,1,2,4,7,5,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,3,4,7,2,5,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[3,1,2,4,5,7,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[3,1,2,4,5,7,8,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,3,4,5,7,8,2,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[3,1,8,2,4,5,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[3,8,1,2,4,5,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[3,1,2,8,4,5,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,3,2,8,4,5,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,3,8,2,4,5,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[3,1,2,4,8,5,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,3,2,4,8,5,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,3,4,2,8,5,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,3,4,8,2,5,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[3,1,2,4,5,8,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,3,2,4,5,8,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,3,4,2,5,8,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,3,4,5,2,8,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,3,4,5,8,2,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[3,1,2,4,5,6,8,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,3,4,5,6,8,2,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[4,1,5,2,3,6,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[4,1,2,5,3,6,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,4,2,5,3,6,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,4,5,2,3,6,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[4,1,2,5,6,3,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,4,5,2,6,3,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,4,5,6,2,3,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[4,1,2,5,6,7,3,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,4,2,5,6,7,3,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,4,5,2,6,7,3,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,4,5,6,2,7,3,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,4,5,6,7,2,3,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[4,1,2,5,6,7,8,3] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,4,2,5,6,7,8,3] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,4,5,2,6,7,8,3] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,4,5,6,2,7,8,3] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,4,5,6,7,2,8,3] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,4,5,6,7,8,2,3] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[4,1,6,2,3,5,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[4,6,1,2,3,5,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,4,2,6,3,5,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,4,6,2,3,5,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[4,1,2,3,6,5,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,4,2,3,6,5,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,4,6,3,5,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[4,1,2,3,6,7,5,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,4,2,3,6,7,5,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[4,1,2,3,6,7,8,5] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,4,2,3,6,7,8,5] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[4,1,7,2,3,5,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[4,7,1,2,3,5,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[4,1,2,7,3,5,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,4,2,7,3,5,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,4,7,2,3,5,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[4,1,2,3,7,5,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,4,2,3,7,5,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,4,3,7,5,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,4,7,3,5,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[4,1,2,3,5,7,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,4,2,3,5,7,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,4,5,7,3,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[4,1,2,3,5,7,8,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,4,2,3,5,7,8,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,4,5,7,8,3,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[4,1,8,2,3,5,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[4,8,1,2,3,5,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[4,1,2,8,3,5,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,4,2,8,3,5,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,4,8,2,3,5,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[4,1,2,3,8,5,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,4,2,3,8,5,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,4,3,8,5,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,4,8,3,5,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[4,1,2,3,5,8,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,4,2,3,5,8,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,4,3,5,8,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,4,5,3,8,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,4,5,8,3,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[4,1,2,3,5,6,8,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,4,2,3,5,6,8,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,4,5,6,8,3,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[5,1,6,2,3,4,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[5,1,2,6,3,4,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,5,2,6,3,4,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,5,6,2,3,4,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[5,1,2,3,6,4,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,5,2,3,6,4,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,5,3,6,4,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,5,6,3,4,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[5,1,2,3,6,7,4,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,5,2,3,6,7,4,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,5,6,3,7,4,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[5,1,2,3,6,7,8,4] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,5,2,3,6,7,8,4] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,5,3,6,7,8,4] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,5,6,3,7,8,4] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,5,6,7,3,8,4] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,5,6,7,8,3,4] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[5,1,7,2,3,4,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[5,7,1,2,3,4,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,5,2,7,3,4,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,5,2,3,7,4,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,5,3,7,4,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,5,7,3,4,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,5,2,3,4,7,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,5,3,4,7,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,3,5,7,4,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[5,1,2,3,4,7,8,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,5,2,3,4,7,8,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,5,3,4,7,8,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,3,5,7,4,8,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,3,5,7,8,4,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[5,8,1,2,3,4,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[5,1,2,8,3,4,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,5,2,8,3,4,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,5,8,2,3,4,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[5,1,2,3,8,4,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,5,2,3,8,4,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,5,3,8,4,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,5,8,3,4,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[5,1,2,3,4,8,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,5,2,3,4,8,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,5,3,4,8,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,3,5,4,8,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,3,5,8,4,6,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[5,1,2,3,4,6,8,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,5,2,3,4,6,8,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,5,3,4,6,8,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,3,5,6,8,4,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[6,1,7,2,3,4,5,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[6,1,2,7,3,4,5,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,6,2,7,3,4,5,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,6,7,2,3,4,5,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[6,1,2,3,7,4,5,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,6,2,3,7,4,5,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,6,3,7,4,5,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,6,7,3,4,5,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[6,1,2,3,4,7,5,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,6,2,3,4,7,5,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,6,3,4,7,5,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,3,6,4,7,5,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,3,6,7,4,5,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[6,1,2,3,4,7,8,5] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,6,2,3,4,7,8,5] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,6,3,4,7,8,5] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,3,6,4,7,8,5] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,3,6,7,4,8,5] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,3,6,7,8,4,5] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[6,1,8,2,3,4,5,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[6,8,1,2,3,4,5,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[6,1,2,8,3,4,5,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,6,2,8,3,4,5,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,6,8,2,3,4,5,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[6,1,2,3,8,4,5,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,6,2,3,8,4,5,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,6,3,8,4,5,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,6,8,3,4,5,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[6,1,2,3,4,8,5,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,6,2,3,4,8,5,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,6,3,4,8,5,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,3,6,4,8,5,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,3,6,8,4,5,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[6,1,2,3,4,5,8,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,6,2,3,4,5,8,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,6,3,4,5,8,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,3,6,4,5,8,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,3,4,6,8,5,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[7,1,8,2,3,4,5,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[7,1,2,8,3,4,5,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,7,2,8,3,4,5,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,7,8,2,3,4,5,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[7,1,2,3,8,4,5,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,7,2,3,8,4,5,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,7,3,8,4,5,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,7,8,3,4,5,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[7,1,2,3,4,8,5,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,7,2,3,4,8,5,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,7,3,4,8,5,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,3,7,4,8,5,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,3,7,8,4,5,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[7,1,2,3,4,5,8,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,7,2,3,4,5,8,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,7,3,4,5,8,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,3,7,4,5,8,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,3,4,7,5,8,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,2,3,4,7,8,5,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[4,6,2,5,1,3,7,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,6,3,5,1,2,7,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,7,2,5,1,4,6,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,7,3,5,1,2,6,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,7,2,6,1,4,5,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,7,3,6,1,2,5,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,7,2,6,1,3,4,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,7,2,5,1,3,4,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,8,2,5,1,3,6,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,8,2,4,1,3,6,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,8,3,4,1,2,6,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,8,3,6,1,2,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,8,4,6,1,2,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,3,5,1,2,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,8,2,7,1,4,5,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,8,2,7,1,3,5,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,8,3,7,1,2,5,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,8,2,7,1,3,4,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,8,3,7,1,2,4,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,2,7,1,3,4,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,5,7,1,2,3,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,8,2,4,1,3,5,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,8,2,5,1,3,4,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,8,3,5,1,2,4,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,8,4,6,1,2,3,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,4,2,8,7,3,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,1,2,8,7,4,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,4,1,2,8,7,3,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,1,8,2,7,5,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,1,5,2,7,3,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,1,8,6,2,5,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,1,8,7,2,5,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,8,1,5,6,2,3,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,3,8,1,2,7,4,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,4,1,2,7,3,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,5,1,2,7,3,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,3,8,1,6,2,4,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,8,4,1,6,2,3,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,8,5,1,6,2,3,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,3,8,5,1,2,4,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,3,8,6,1,2,4,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[8,1,4,9,7,2,3,5,6] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[8,1,9,5,6,2,3,4,7] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[4,5,7,3,1,8,6,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,6,7,3,8,1,5,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,6,7,3,8,5,1,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,6,7,8,3,1,4,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,5,2,7,1,8,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,6,2,7,8,1,5,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,6,2,7,8,5,1,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,6,7,2,8,5,1,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,6,7,2,8,1,5,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,5,7,2,1,8,6,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,6,7,8,2,1,4,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,6,7,8,2,4,1,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,6,7,4,5,8,1,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,7,4,5,2,3,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,4,7,6,2,3,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,5,4,7,6,8,1,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,5,3,7,8,6,1,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,3,8,4,5,7,1,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,5,6,1,8,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,8,4,5,1,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,8,1,4,5,2,3,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,1,3,2,8,6,5,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,8,3,1,5,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,3,8,1,6,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,5,2,7,8,1,6,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,5,3,7,1,6,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,3,7,2,6,4,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,7,3,2,5,4,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,6,7,3,1,5,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,6,7,2,1,8,5,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,5,8,7,1,2,3,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,4,8,1,7,2,3,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,8,3,1,2,6,4,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,1,8,2,7,4,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,1,2,8,7,5,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,1,3,8,5,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,8,4,1,2,7,3,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,4,1,7,2,3,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,3,1,8,7,2,4,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,3,1,8,6,2,4,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,4,8,1,6,2,3,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,4,8,1,2,7,3,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,5,8,6,1,2,3,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,1,3,2,8,5,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,3,2,8,4,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,3,2,8,4,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,4,2,8,3,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,4,2,8,3,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,5,2,8,3,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,6,7,3,1,8,4,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,4,7,8,2,6,1,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,6,7,2,8,5,1,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,6,2,1,7,8,4,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,6,2,7,1,8,4,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,6,7,2,1,8,4,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,6,7,8,1,5,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,4,1,7,8,5,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,8,1,3,4,2,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,6,2,7,1,8,5,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,6,4,7,8,1,5,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,6,2,7,8,1,5,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,6,7,8,4,1,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,4,7,8,5,2,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,5,1,2,3,8,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,4,1,2,3,8,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,4,1,2,3,8,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,4,1,2,8,3,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,5,1,2,8,3,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,5,1,7,6,8,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,6,1,7,5,8,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,6,5,7,1,8,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,6,4,7,1,8,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,6,1,7,4,8,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,5,1,7,6,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,6,1,7,5,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,6,5,7,1,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,6,5,7,1,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,6,1,7,5,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,5,1,7,6,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,6,1,7,4,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,6,4,7,1,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,7,8,4,5,1,2,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,8,2,1,5,6,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,4,3,1,8,5,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,1,3,2,6,8,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,1,8,5,6,7,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,6,3,7,1,8,4,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,8,7,1,4,5,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,8,2,1,7,3,5,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,8,1,7,4,5,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,1,8,7,4,5,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,4,6,8,2,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,1,5,7,6,8,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,6,7,4,1,8,5,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,6,3,7,4,8,1,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,8,1,3,5,2,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,8,2,1,4,6,5,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,5,6,2,1,8,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,1,8,3,6,2,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,8,1,7,2,5,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,8,3,4,5,1,6,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,6,7,3,8,4,1,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,3,4,5,8,7,1,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,4,2,7,6,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,7,2,4,1,6,3,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,8,2,1,5,6,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,6,4,7,8,1,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,5,1,2,8,6,3,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,8,7,1,2,5,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,8,7,1,2,4,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,2,1,7,3,4,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,8,3,7,1,5,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,6,4,5,8,7,1,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,1,8,7,2,4,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,8,3,7,2,4,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,3,8,1,7,2,4,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,2,8,6,1,3,4,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,7,8,3,6,2,4,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,2,8,4,5,6,1,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,3,7,5,2,4,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,3,8,5,1,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,7,1,5,6,8,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,1,3,8,4,6,2,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,7,3,5,8,6,1,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,4,7,8,6,1,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,4,7,2,8,6,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,2,1,8,7,6,5,12,11,10,9] => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 5
[4,6,2,1,7,5,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,3,2,7,6,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,5,3,1,7,6,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,1,2,7,6,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,1,2,7,6,8,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,3,1,7,6,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,5,2,1,7,6,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,4,1,7,5,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,1,3,7,6,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,4,2,7,5,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,3,2,7,6,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,1,3,2,7,6,8,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,1,3,7,6,8,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,2,3,5,7,1,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,7,1,3,5,8,2,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,3,4,1,8,5,6,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,5,6,2,1,8,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,4,2,7,5,3,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,3,2,7,6,4,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,5,3,1,7,8,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,6,4,1,7,8,5,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,4,1,2,8,5,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,1,2,8,6,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,1,2,8,6,5,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,3,1,8,6,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,5,2,1,6,8,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,4,1,8,5,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,1,3,8,7,4,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,1,3,8,7,5,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,1,7,3,6,2,8,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,7,3,6,2,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,7,3,5,1,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,3,1,8,5,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,4,1,8,6,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,8,4,6,2,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,3,8,4,5,1,6,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,8,2,4,5,6,1,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,8,2,1,6,3,4,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,5,7,4,1,6,2,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,8,4,6,1,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,5,3,1,7,6,2,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,5,2,7,8,1,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,5,6,1,8,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,5,3,1,6,8,7,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,2,7,5,3,8,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,4,1,7,5,2,3,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,3,7,5,2,4,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,4,7,5,1,8,6,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,7,4,1,5,8,6,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,8,1,3,7,4,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,6,8,3,1,5,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,6,4,8,5,1,7,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,3,7,4,5,1,8,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,6,3,7,5,8,1,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,7,2,3,6,8,1,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,7,3,6,8,1,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,7,3,4,6,1,8,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,8,4,6,1,7,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,8,3,6,7,1,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,8,3,1,7,2,5,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,3,1,8,2,4,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,8,1,2,6,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,7,4,1,6,2,3,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,8,4,2,7,3,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,2,8,5,3,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,5,7,8,3,1,6,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,8,2,4,6,7,1,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,5,6,8,2,7,1,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,8,3,5,6,1,7,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,4,2,8,3,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,4,2,8,7,3,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,1,8,7,3,4,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,2,6,5,3,8,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,1,8,3,2,4,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,7,4,2,8,3,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,7,2,8,5,3,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,7,4,2,8,6,3,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,1,8,3,2,6,4,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,2,1,8,6,3,4,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,4,1,8,2,3,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,6,4,1,8,5,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,1,7,6,4,5,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,1,3,7,6,2,5,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,7,3,6,2,4,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,8,2,4,7,3,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,8,3,2,7,4,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,1,3,8,2,7,5,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,1,8,4,7,5,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,7,8,2,5,6,3,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,8,4,2,7,3,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,4,8,2,7,3,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,6,2,1,5,3,7,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,6,1,5,4,7,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,7,1,4,6,5,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,7,2,1,3,6,5,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,7,1,3,2,6,4,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,1,2,4,3,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,8,1,3,2,4,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,8,2,1,3,5,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,8,1,4,5,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,8,1,4,6,7,2,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,7,3,8,5,6,1,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,7,4,8,5,6,1,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,7,4,8,5,6,2,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,7,3,8,5,6,2,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,7,3,8,4,6,2,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,7,3,8,4,6,1,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,2,8,5,7,3,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,2,8,4,7,3,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,8,1,5,2,6,3,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,2,1,3,8,6,4,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,5,8,3,1,7,4,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,7,3,8,5,2,4,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,7,3,2,8,6,4,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,5,7,8,6,1,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,2,3,1,8,5,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,1,8,3,4,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,8,3,5,1,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,4,8,5,7,1,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,4,7,5,8,1,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,8,2,1,4,3,5,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,7,2,3,1,6,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,3,8,2,4,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,8,1,2,7,4,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,8,3,2,6,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,7,3,1,2,6,4,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,8,4,2,7,3,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,5,2,6,8,1,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,4,8,2,7,3,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,8,7,1,3,4,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,8,1,3,4,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,6,1,5,2,7,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,6,3,1,5,2,7,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,6,4,1,2,7,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,6,1,5,7,4,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,6,1,5,3,7,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,1,7,5,3,6,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,6,4,1,3,7,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,4,5,8,2,1,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,4,5,2,8,1,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,8,2,4,7,1,5,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,4,1,8,7,5,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,5,1,6,8,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,4,1,8,5,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,5,1,7,6,4,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,5,1,8,6,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,5,1,8,6,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,4,1,8,6,5,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,5,1,7,8,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,6,3,7,1,8,5,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,6,3,7,5,1,8,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,6,1,7,5,3,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,5,7,4,1,6,3,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,5,7,4,1,6,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,5,8,1,6,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,5,4,6,8,1,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,8,4,1,6,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,6,4,1,8,5,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,5,8,4,1,6,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,5,2,8,1,6,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,8,2,5,1,6,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,5,7,4,8,1,6,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,5,7,8,1,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,5,7,1,6,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,5,7,1,6,4,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,6,1,7,8,5,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,3,1,8,5,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,1,3,2,8,6,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,4,8,3,6,1,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,3,1,8,4,5,7,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,4,1,2,8,7,3,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,2,8,4,3,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,4,1,2,8,3,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,8,1,3,7,2,4,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,1,2,8,4,3,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,4,1,2,8,6,3,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,7,3,4,1,5,2,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,7,3,4,1,6,2,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,8,3,5,1,6,2,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,6,2,4,1,7,3,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,6,2,7,4,8,1,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,8,1,5,6,7,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,6,8,4,5,7,1,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,8,4,5,7,2,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,8,2,1,5,6,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,5,3,8,6,1,7,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,6,3,1,4,8,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,4,1,2,3,8,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,3,1,2,4,8,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,2,1,3,4,8,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,3,1,4,8,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,4,3,6,1,8,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,4,3,6,8,1,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,4,6,3,8,1,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,4,6,8,3,1,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,1,3,7,2,4,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,8,2,1,7,3,4,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,4,8,7,2,3,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,7,8,3,6,1,4,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,8,3,7,1,4,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,4,8,7,2,3,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,8,2,1,4,5,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,7,1,4,6,8,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,8,1,4,6,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,8,2,1,4,7,5,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,8,2,1,7,4,5,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,8,2,1,4,5,6,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,6,1,5,7,2,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,3,6,8,5,7,2,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,8,2,3,4,1,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,6,7,2,5,8,1,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,5,1,8,6,2,3,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,7,4,2,8,5,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,7,3,8,5,2,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,1,8,3,5,6,2,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,3,1,8,4,2,5,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,5,3,7,8,1,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,4,8,6,1,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,8,1,3,6,7,2,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,8,1,3,6,2,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,7,4,2,6,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,5,1,2,8,7,3,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,1,6,4,2,7,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,4,5,8,2,7,1,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,5,2,6,8,1,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,4,7,2,8,1,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,3,8,4,5,6,1,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,5,6,4,8,7,1,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,3,2,7,5,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,3,8,5,7,2,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,4,2,8,5,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,8,2,5,6,1,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,3,7,8,6,2,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,4,7,8,5,6,1,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,6,7,5,8,1,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,8,1,2,5,6,3,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,7,4,1,6,2,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,8,2,1,4,5,3,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,4,7,5,8,2,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,7,4,1,8,5,2,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,8,2,1,3,6,5,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,2,1,4,3,5,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,1,3,8,6,5,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,1,8,3,6,5,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,1,8,6,3,5,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,8,1,3,6,5,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,8,6,1,3,5,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,8,3,4,2,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,8,4,6,1,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,2,4,1,8,5,6,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,1,3,2,8,5,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,1,8,5,3,6,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,3,4,7,5,8,1,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,7,4,5,8,2,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,1,6,7,8,4,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,6,1,7,8,4,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,6,1,7,8,5,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,4,3,7,6,8,2,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,4,3,7,2,6,5,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,4,8,2,6,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,2,4,5,7,1,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,4,1,8,2,6,3,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,1,8,4,2,6,3,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,3,8,5,2,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,3,8,5,2,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,8,1,3,5,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,3,8,1,5,2,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,8,1,2,4,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,8,4,7,2,3,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,1,4,7,2,3,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,1,7,3,2,6,5,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,1,5,8,2,6,3,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,1,4,5,2,8,6,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,4,3,8,2,6,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,3,4,2,8,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,7,2,4,3,8,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,2,7,4,8,6,3,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,8,1,2,7,5,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,3,8,4,1,5,2,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,8,3,6,1,5,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,4,7,2,5,3,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,4,8,2,5,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,8,2,4,3,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,8,2,4,7,3,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,7,3,4,2,8,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,2,4,3,8,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,5,2,3,8,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,8,3,2,4,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,8,4,2,3,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,8,5,2,3,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,7,4,2,8,5,3,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,4,2,3,8,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,4,3,7,8,6,1,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,4,8,3,6,2,5,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,7,2,8,5,6,3,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,8,1,4,2,6,3,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,8,1,4,2,5,3,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,3,2,4,8,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,6,4,7,5,1,8,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,6,3,5,8,7,1,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,5,2,7,6,1,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,2,8,1,3,6,4,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,5,1,7,2,3,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,5,2,8,6,1,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,4,8,2,6,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,8,2,5,1,6,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,1,8,5,6,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,4,8,2,6,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,3,4,8,5,1,7,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,4,8,1,6,7,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,5,2,8,1,6,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,7,2,3,6,1,8,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,1,3,7,6,2,8,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,6,7,3,5,1,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,7,8,2,5,3,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,7,8,2,4,3,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,5,3,1,8,6,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,8,3,1,6,5,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,6,3,1,8,5,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,1,8,3,5,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,1,8,3,7,5,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,8,5,1,6,7,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,4,8,6,1,5,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,5,7,6,1,4,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,8,3,6,7,2,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,1,3,5,7,2,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,4,1,2,7,5,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,7,3,5,8,6,2,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,4,6,5,8,1,7,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,1,5,7,2,3,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,1,2,5,8,6,3,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,7,2,5,8,6,3,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,1,4,2,8,5,6,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,6,7,1,4,2,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,6,7,1,4,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,4,1,5,8,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,3,7,8,5,1,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,6,2,4,1,7,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,4,2,7,8,5,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,7,4,1,6,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,8,1,6,2,5,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,4,3,8,2,6,5,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,1,3,8,2,6,5,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,4,2,1,8,6,5,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,1,8,2,6,5,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,4,8,1,6,5,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,4,8,3,6,1,5,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,7,4,8,5,1,2,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,5,8,2,6,1,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,7,3,2,6,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,7,3,2,5,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,7,4,1,6,8,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,7,6,1,4,5,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,8,3,1,5,6,7,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,8,2,1,5,4,6,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,7,1,5,4,6,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,1,6,7,4,8,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,1,6,5,7,8,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,5,8,2,6,7,1,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,7,8,3,5,6,1,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,4,1,8,5,2,3,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,1,4,2,8,3,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,1,8,2,5,3,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,7,4,6,8,1,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,7,8,4,6,2,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,5,7,8,6,1,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,7,4,5,2,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,3,7,5,8,2,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,5,3,7,8,6,1,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,7,4,5,1,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,3,7,5,8,1,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,8,1,5,6,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,5,7,4,1,8,6,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,6,2,1,7,8,5,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,3,2,8,7,4,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,5,6,8,7,1,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,3,7,1,8,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,8,2,3,6,7,1,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,5,2,7,6,1,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,3,2,5,8,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,5,6,8,7,1,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,8,5,6,7,1,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,4,7,1,8,6,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,4,7,1,8,6,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,1,5,8,6,7,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,4,7,8,2,1,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,3,2,8,6,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,1,2,8,6,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,3,1,6,8,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,1,3,6,8,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,4,7,3,8,1,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,5,7,2,6,1,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,3,8,5,7,2,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,5,7,8,4,1,6,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,8,1,5,6,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,8,5,1,6,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,4,7,2,1,8,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,5,7,8,4,1,6,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,5,7,3,8,1,6,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,6,2,7,8,5,1,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,6,2,7,8,4,1,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,4,1,8,2,3,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,8,1,2,4,3,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,7,4,2,6,3,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,3,4,5,1,7,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,6,2,1,7,5,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,1,4,2,7,3,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,4,1,6,8,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,5,7,6,1,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,5,6,1,8,7,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,4,1,7,6,8,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,2,4,8,7,3,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,2,6,4,8,7,3,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,2,7,8,5,6,3,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,2,7,4,8,3,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,2,6,4,8,3,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,2,4,8,3,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,2,6,8,5,3,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,6,4,1,5,8,7,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,2,4,8,7,3,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,1,2,8,5,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,2,4,8,3,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,6,4,5,1,8,7,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,6,1,7,8,4,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,4,1,7,8,6,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,1,2,8,6,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,4,2,8,6,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,1,4,2,5,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,5,3,7,6,8,1,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,7,1,3,2,6,5,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,6,3,7,1,5,4,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,7,4,1,5,3,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,8,2,5,3,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,1,4,8,5,2,3,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,8,3,1,2,4,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,3,8,1,2,4,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,1,8,4,5,2,3,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,1,4,2,3,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,3,1,2,7,4,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,4,2,7,8,1,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,8,6,1,2,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,1,3,5,8,2,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,3,1,4,7,5,8,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,1,3,8,2,6,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,8,4,7,2,3,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,7,4,5,8,1,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,1,3,2,8,5,4,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,8,3,2,7,4,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,6,4,8,2,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,2,5,8,4,7,3,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,3,6,5,8,7,1,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,7,4,6,8,1,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,5,7,3,6,8,1,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,1,2,8,4,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,3,1,2,8,4,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,3,1,8,4,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,7,5,8,2,3,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,1,3,6,8,2,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,7,6,1,2,4,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,2,3,5,1,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,8,1,2,6,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,7,4,1,3,6,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,4,6,5,2,8,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,6,3,7,5,8,1,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,2,3,8,5,6,1,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,7,3,6,8,1,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,4,1,7,2,6,3,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,7,4,2,5,3,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,5,4,7,1,8,6,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,1,6,5,3,7,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,1,5,7,6,3,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,5,4,7,1,6,2,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,5,1,6,8,7,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,1,3,2,8,4,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,1,8,2,4,3,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,1,5,2,8,3,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,8,2,4,3,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,8,2,4,3,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,8,2,5,3,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,4,8,1,5,2,3,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,7,4,2,6,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,8,3,1,2,5,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,8,2,1,3,5,4,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,3,7,1,8,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,5,3,6,1,8,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,8,3,1,7,4,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,1,2,7,8,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,4,7,8,6,1,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,3,7,2,6,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,4,7,8,1,6,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,5,7,6,8,1,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,4,2,1,8,7,5,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,8,4,1,5,2,3,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,6,7,4,5,1,3,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,1,7,2,6,8,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,3,4,5,8,1,7,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,1,7,5,6,8,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,3,4,5,8,6,1,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,3,4,5,8,1,6,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,1,7,3,5,4,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,1,8,3,6,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,1,7,3,5,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,7,5,6,1,8,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,8,5,6,1,7,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,8,3,7,2,4,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,2,6,8,4,7,3,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,5,7,4,8,6,1,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,6,7,4,1,5,8,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,4,8,6,1,2,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,5,7,8,3,1,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,5,7,8,2,1,6,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,5,7,8,2,1,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,6,7,5,1,4,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,2,1,3,5,8,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,7,3,5,6,1,8,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,4,6,8,5,1,7,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,2,1,3,5,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,7,8,4,1,5,6,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,2,3,4,8,1,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,2,3,8,5,1,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,8,2,3,6,1,4,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,5,8,4,1,6,7,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,3,4,2,8,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,1,3,4,8,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,3,1,7,8,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,4,2,1,8,6,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,8,1,5,3,6,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,4,1,2,3,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,4,1,2,5,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,6,1,5,7,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,8,4,2,5,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,8,4,1,5,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,8,1,5,4,6,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,3,2,8,6,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,8,3,1,2,4,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,4,1,2,5,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,1,4,7,6,3,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,1,3,5,8,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,6,7,3,1,5,2,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,1,3,5,2,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,3,1,4,5,7,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,5,1,8,2,3,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,3,1,4,8,5,6,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,2,4,8,1,5,3,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,6,3,1,7,8,5,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,1,6,7,8,4,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,8,2,3,6,1,5,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,6,4,7,8,5,1,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,3,7,8,5,2,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,4,1,8,2,5,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,1,3,5,8,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,1,8,3,5,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,1,3,8,5,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,8,1,3,5,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,8,1,3,5,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,3,1,4,2,5,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,3,8,1,4,2,5,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,7,3,1,4,2,5,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,7,3,1,4,5,2,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,7,3,1,4,5,8,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,3,8,1,4,5,2,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,3,8,1,4,5,6,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,3,1,4,5,2,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,5,8,3,1,4,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,5,2,8,6,1,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,5,4,1,8,6,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,6,3,8,1,4,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,3,1,7,2,4,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,7,2,5,6,1,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,5,3,7,1,6,4,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,8,1,4,5,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,1,2,4,8,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,4,5,1,8,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,4,5,2,8,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,8,3,5,6,7,1,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,8,2,5,6,7,1,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,3,1,8,2,7,4,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,1,4,8,6,2,3,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,5,4,8,6,1,2,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,1,3,7,8,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,1,7,3,6,5,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,2,8,4,3,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,7,4,1,2,5,3,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,1,8,2,5,6,3,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,5,8,2,7,3,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,5,2,8,1,6,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,8,1,2,5,3,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,3,8,2,6,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,4,8,3,2,5,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,8,2,5,6,1,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,5,7,2,1,8,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,4,7,1,8,5,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,6,2,7,1,8,5,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,7,4,8,5,2,6,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,3,7,8,5,2,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,4,7,8,2,5,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,3,8,6,7,1,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,4,8,1,6,2,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,5,3,7,1,6,2,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,7,4,2,8,6,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,4,3,7,8,6,2,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,3,6,8,2,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,6,5,7,8,1,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,5,6,8,1,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,6,7,4,1,8,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,3,1,2,5,8,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,3,7,6,1,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,8,1,4,6,5,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,4,2,3,8,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,4,5,2,8,7,1,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,1,3,4,8,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,4,2,8,5,1,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,3,4,1,5,7,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,8,2,1,6,4,5,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,7,2,4,6,1,8,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,7,2,4,6,8,1,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,4,8,6,7,1,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,7,3,6,1,8,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,8,2,4,1,6,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,7,5,6,1,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,1,4,5,8,6,2,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,1,3,7,8,6,2,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,6,4,8,5,1,2,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,1,8,3,4,2,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,6,2,1,5,4,7,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,7,1,4,2,6,3,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,6,2,4,7,8,1,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,1,2,8,5,6,3,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,1,3,5,8,6,2,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,8,3,5,2,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,8,2,3,1,6,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,2,3,5,1,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,8,2,3,5,6,1,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,6,3,5,1,8,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,3,8,1,4,2,5,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,3,2,8,4,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,3,2,8,7,4,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,3,1,2,8,4,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,2,8,4,7,3,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,4,8,6,1,2,3,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,1,5,8,6,2,3,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,8,3,1,2,6,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,5,8,6,1,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,1,5,8,6,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,1,8,5,4,6,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,1,6,7,8,5,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,1,8,6,4,5,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,1,8,4,6,5,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,1,8,4,6,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,1,8,4,5,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,5,4,1,7,8,6,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,1,5,7,8,6,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,1,8,5,6,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,8,3,2,6,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,8,3,2,5,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,3,8,2,6,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,7,2,1,3,6,8,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,7,1,3,2,6,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,8,1,3,2,6,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,8,2,1,3,6,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,4,8,1,2,3,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,8,3,1,4,2,5,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,6,7,8,1,5,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,4,7,3,8,6,2,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,3,7,8,4,1,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,7,3,2,8,5,4,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,5,2,1,8,6,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,2,3,4,1,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,8,2,1,5,6,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,8,2,3,4,6,1,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,1,3,4,7,2,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,2,8,5,7,3,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,3,8,5,2,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,6,7,5,8,1,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,6,7,2,1,4,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,2,3,4,8,6,1,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,1,5,2,3,8,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,4,2,7,5,3,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,8,3,1,5,2,4,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,5,8,1,2,7,3,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,6,7,1,5,8,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,6,3,5,1,7,8,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,6,7,4,5,8,1,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,7,2,4,6,8,1,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,5,7,2,6,8,1,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,6,3,7,4,1,8,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,6,7,3,1,4,8,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,7,3,4,1,5,8,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,6,7,2,4,1,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,7,3,1,4,6,2,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,7,4,1,2,6,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,7,1,4,2,6,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,5,3,4,8,1,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,4,5,8,1,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,3,1,8,7,5,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,5,7,8,3,6,1,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,4,8,1,2,5,6,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,6,1,5,7,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,5,7,4,8,6,1,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,6,2,7,5,1,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,3,6,2,8,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,5,2,8,3,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,5,1,2,8,3,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,5,7,8,2,6,1,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,3,4,8,7,1,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,2,3,4,1,8,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,4,8,5,2,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,7,4,8,6,2,3,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,6,2,5,7,8,1,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,7,4,6,8,1,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,6,7,1,8,4,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,7,5,2,8,6,3,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,8,4,2,6,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,5,7,4,1,6,8,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,5,1,2,3,8,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,7,1,3,2,5,4,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,8,2,4,1,5,3,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,7,8,4,2,6,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,5,7,6,1,8,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,1,6,4,3,7,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,6,2,7,1,5,3,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,4,3,8,1,7,5,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,6,7,4,8,5,1,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,2,1,8,4,5,3,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,8,1,3,6,2,4,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,2,1,8,4,5,6,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,7,8,4,2,5,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,7,4,5,1,8,6,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,8,2,4,6,7,1,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,1,3,4,2,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,7,3,1,4,2,6,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,2,8,4,5,1,3,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,2,8,4,1,5,6,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,5,8,1,2,6,3,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,2,4,8,7,3,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,7,4,1,6,3,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,7,3,1,5,6,2,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,8,3,4,1,6,7,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,7,8,4,5,6,2,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,8,4,2,6,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,3,8,5,2,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,7,3,4,8,6,2,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,4,6,8,2,1,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,4,6,2,1,8,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,5,1,8,2,7,3,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,5,1,8,7,2,3,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,3,8,1,5,2,4,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,6,2,1,5,7,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,6,2,7,1,4,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,3,8,1,7,4,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,6,8,3,4,7,1,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,6,2,7,5,1,3,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,6,3,1,8,7,4,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,3,8,4,1,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,3,7,8,1,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,8,3,1,7,2,4,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,7,4,2,6,3,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,1,8,3,6,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,8,1,7,3,5,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,4,1,2,8,6,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,6,7,8,3,1,5,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,8,1,7,2,4,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,5,8,3,1,6,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,8,1,5,6,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,8,3,2,6,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,7,8,3,4,6,1,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,7,3,1,8,6,4,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,7,1,3,5,2,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,7,2,3,6,8,1,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,7,8,4,1,5,6,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,7,3,5,8,2,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,3,7,4,8,2,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,5,8,2,3,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,6,7,3,8,1,5,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,3,4,1,8,5,2,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,1,8,7,3,4,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,8,1,3,2,7,5,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,4,8,5,2,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,6,4,7,8,1,5,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,7,3,8,2,5,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,4,7,8,5,2,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,3,8,4,1,2,5,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,3,7,8,5,6,1,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,5,3,1,8,6,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,6,4,8,5,1,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,3,4,8,5,6,1,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,7,2,4,8,6,3,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,3,8,4,2,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,8,6,1,3,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,8,1,3,5,7,2,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,6,2,7,8,1,4,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,6,2,7,4,1,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,5,3,6,8,1,7,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,5,2,6,1,8,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,8,1,3,5,6,2,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,7,8,3,5,6,2,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,3,7,5,8,2,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,2,3,7,1,4,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,8,1,7,3,4,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,8,3,7,1,4,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,8,4,6,1,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,5,8,2,6,1,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,6,8,3,7,1,4,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,8,3,7,2,4,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,8,4,6,2,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,8,4,1,6,2,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,4,8,1,6,2,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,4,8,1,5,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,8,1,4,6,7,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,1,8,4,5,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,2,1,8,5,3,4,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,7,4,2,5,8,6,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,1,8,7,3,5,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,4,2,8,6,1,5,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,1,8,4,6,2,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,3,2,4,8,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,1,3,8,4,2,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,8,4,5,2,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,5,2,7,1,6,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,5,7,3,1,6,8,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,5,7,2,8,6,1,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,6,7,2,1,5,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,4,7,5,8,6,1,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,6,1,4,2,7,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,3,7,4,8,6,2,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,3,8,6,1,5,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,8,1,6,2,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,2,8,1,6,3,4,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,8,4,1,2,5,3,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,7,4,1,2,6,3,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,8,2,3,1,5,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,7,8,4,2,3,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,8,3,4,2,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,3,8,1,2,6,4,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,4,8,1,5,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,4,8,3,1,7,5,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,1,3,7,2,6,8,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,4,8,2,1,6,5,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,4,3,8,7,1,5,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,5,4,7,6,1,2,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,5,4,7,6,1,8,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,5,7,4,6,1,8,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,5,7,4,6,1,2,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,5,7,2,6,1,4,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,5,2,7,6,1,4,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,5,7,2,1,6,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,5,2,7,1,6,4,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,5,7,2,1,6,4,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,7,1,6,2,4,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,5,4,7,1,6,8,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,5,6,8,1,7,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,5,8,1,6,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,8,2,4,1,6,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,6,7,1,5,4,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,4,8,6,7,1,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,7,5,1,4,6,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,7,2,1,5,4,6,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,1,7,5,4,6,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,6,4,8,7,2,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,4,2,8,5,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,2,3,1,5,8,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,5,6,8,2,1,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,8,3,5,7,1,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,3,1,7,5,2,4,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,3,1,4,7,5,2,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,3,7,4,1,5,2,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,7,3,8,1,5,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,5,7,2,8,1,6,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,8,1,2,4,3,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,7,1,3,6,8,2,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,6,4,1,7,8,5,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,2,3,1,8,6,4,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,5,4,7,8,1,6,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,8,3,1,4,2,6,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,8,1,3,2,7,4,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,4,8,2,3,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,5,8,2,6,1,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,7,3,1,2,6,8,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,7,2,3,1,6,8,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,7,2,3,1,5,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,6,7,2,5,8,1,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,6,8,3,7,2,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,8,3,2,5,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,4,7,6,2,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,7,2,5,3,8,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,8,4,1,2,6,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,4,8,3,7,1,5,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,8,4,1,6,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,8,12,3,7,11,2,6,10,1,5,9] => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 5
[6,8,1,4,5,2,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,8,4,6,2,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,5,8,7,2,3,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,8,5,7,2,3,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,7,4,8,2,5,3,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,1,8,2,4,6,3,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,3,7,5,8,2,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,5,7,4,6,1,3,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,6,7,8,1,4,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,7,2,4,1,6,5,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,3,8,4,5,1,2,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,3,7,4,1,2,5,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,2,7,8,4,3,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,2,5,3,8,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,8,1,3,2,6,5,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,6,3,8,1,5,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,5,2,1,8,6,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,5,8,3,1,6,7,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,5,8,4,6,1,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,5,3,8,6,1,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,6,3,5,8,1,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,6,2,4,7,1,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,8,3,6,1,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,6,3,7,1,4,8,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,2,8,1,5,3,4,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,8,2,3,4,7,1,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,1,8,3,2,6,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,4,5,2,8,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,6,1,4,7,2,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,8,4,1,6,2,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,8,2,1,6,3,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,7,8,4,1,5,2,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,4,3,6,8,7,2,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,5,7,6,8,1,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,3,7,1,6,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,2,4,3,8,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,3,7,8,1,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,4,1,8,5,2,9,6,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 4
[5,3,1,6,4,2,7,8,9] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[7,4,1,8,5,2,9,6,3,10] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 4
[6,2,3,1,8,7,4,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,7,4,1,5,8,6,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,2,1,4,5,8,6,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,6,7,2,1,8,5,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,7,8,4,5,1,6,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,3,1,7,2,5,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,4,2,6,8,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,8,1,3,6,7,2,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,3,7,8,5,6,2,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,4,8,2,6,7,1,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[8,2,3,9,5,6,7,1,4] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[8,2,9,4,5,6,7,1,3] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[8,9,3,4,5,6,7,1,2] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[7,1,8,3,5,2,4,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,2,4,8,1,5,6,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,1,8,4,2,5,6,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,7,4,8,1,5,6,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,8,3,4,1,5,6,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,3,1,8,2,5,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,2,3,8,1,5,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,2,1,8,3,5,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,8,4,7,2,3,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,6,4,1,7,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,4,3,6,8,7,1,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,4,6,3,8,7,1,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,4,6,5,8,7,1,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,4,6,8,5,7,1,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,4,6,8,3,7,1,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,4,6,5,8,1,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,4,6,8,5,1,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,4,7,5,8,2,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,3,2,7,8,5,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,6,3,1,7,4,8,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,3,8,2,7,4,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,3,4,1,7,9,8,6] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[6,2,3,5,8,1,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,3,1,6,9,7,8,5] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[5,2,4,8,1,6,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,1,5,9,6,7,8,4] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[6,3,1,2,4,8,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,5,7,8,4,6,1,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,1,7,4,5,3,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,6,8,4,2,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,4,2,7,8,6,1,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,5,7,3,8,6,1,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,3,8,4,1,5,6,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,3,1,2,8,5,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,8,2,1,4,6,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,6,7,2,8,1,5,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,5,7,1,8,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,2,8,4,5,1,6,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,5,8,6,7,1,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,4,8,3,5,7,1,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,1,7,4,6,5,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,6,5,1,7,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,7,3,2,6,4,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,3,7,2,6,4,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,4,8,2,7,3,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,4,7,2,6,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,2,8,4,3,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,7,3,5,2,8,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,8,3,2,7,4,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,4,3,8,7,2,5,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,8,3,1,2,6,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,4,3,1,8,7,5,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,1,2,6,8,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,7,3,6,8,2,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,7,3,6,8,2,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,5,2,1,6,8,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,4,1,5,2,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,8,1,6,4,5,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,1,3,7,6,4,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,4,1,2,8,3,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,8,4,1,2,3,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,1,5,8,2,3,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,4,1,8,2,5,6,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,3,4,7,1,8,5,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,5,1,6,8,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,7,8,5,2,6,3,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,7,3,8,6,2,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,7,4,1,2,5,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,7,4,2,5,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,1,8,3,2,5,4,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,7,8,3,6,2,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,3,8,4,2,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,4,7,8,6,1,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,4,8,2,5,1,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,8,3,5,2,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,4,7,8,5,6,1,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,6,3,8,5,1,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,6,7,1,8,5,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,1,8,3,5,2,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,8,5,1,3,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,4,7,2,5,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,7,8,4,6,2,3,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,1,8,4,6,2,3,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,8,3,4,7,2,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,1,8,4,2,5,3,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,2,5,4,8,7,3,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,2,6,8,4,3,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,7,3,8,2,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,3,7,5,8,6,2,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,1,7,4,6,8,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,8,2,4,6,1,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,4,8,5,2,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,4,8,1,2,6,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,3,8,1,7,4,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,3,2,8,6,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,7,8,4,5,2,3,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,8,4,1,3,6,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,8,5,1,6,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,5,7,3,1,6,2,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,4,3,7,1,8,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,8,3,4,6,1,7,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,7,4,2,5,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,1,4,8,5,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,1,4,8,6,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,1,5,8,6,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,3,1,4,8,5,2,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,7,4,1,6,5,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,7,3,1,6,5,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,7,3,1,6,4,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,7,3,1,5,4,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,8,5,1,6,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,8,4,1,5,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,1,4,7,5,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,3,6,8,4,1,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[8,2,3,4,5,1,9,7,6] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[7,9,3,4,5,6,1,8,2] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[8,2,3,4,1,6,9,7,5] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[6,9,3,4,5,1,7,8,2] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[5,1,4,6,2,8,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,7,2,1,3,6,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,4,7,8,6,2,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,2,4,8,5,1,6,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,6,7,3,1,8,5,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,4,2,5,8,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,3,6,8,7,2,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,6,2,7,5,8,1,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,8,1,5,2,6,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,8,3,4,6,1,2,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,4,8,5,1,2,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,8,1,2,5,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,6,3,1,5,8,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,3,5,8,4,7,2,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,5,6,8,3,1,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,4,7,5,2,3,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,6,7,8,1,5,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,3,7,8,1,5,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,6,3,7,8,1,5,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,2,8,5,3,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,3,1,7,8,5,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,1,3,8,4,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,2,8,4,3,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,2,1,8,4,3,5,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,1,3,7,5,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,4,7,2,8,5,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,1,8,5,2,6,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,5,4,8,6,1,7,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,7,3,8,2,4,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,3,8,4,2,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,3,8,1,2,5,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,7,4,8,5,2,3,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,4,7,5,2,8,6,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,3,2,6,8,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,3,2,8,5,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,8,5,2,7,3,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,8,5,6,7,1,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,4,7,2,1,6,5,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,4,7,2,1,6,8,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,6,3,7,1,5,2,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,7,1,5,2,6,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,6,5,7,1,4,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,6,2,1,4,3,7,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,8,3,6,2,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,7,4,5,8,1,6,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,5,1,8,6,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,5,3,7,1,6,8,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,4,7,2,6,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,7,4,5,2,8,6,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,6,2,1,7,5,4,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,6,7,3,1,5,4,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,1,3,8,6,2,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,3,6,5,1,8,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,3,7,5,1,8,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,3,1,2,8,7,4,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,6,8,4,5,1,7,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,3,1,2,8,6,4,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,8,3,1,4,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,8,3,2,4,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,3,7,2,5,4,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,3,2,4,8,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,3,2,7,5,4,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,4,6,3,2,8,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,3,2,8,4,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,3,5,2,8,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,4,1,8,2,6,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,1,8,2,6,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,4,3,7,2,8,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,2,8,1,4,5,6,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,4,3,1,8,10,7,9,5,6] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 4
[4,6,3,5,1,2,8,10,9,7] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 4
[6,2,8,3,5,1,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,2,5,8,7,3,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,4,8,3,2,7,5,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,2,3,4,7,1,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,3,2,6,8,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,3,8,7,2,4,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,6,5,1,2,7,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,6,4,8,1,5,2,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,6,8,4,1,5,2,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,1,4,8,2,3,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,6,3,8,2,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,4,5,3,8,2,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,8,2,1,4,6,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,5,8,3,6,1,2,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,4,1,8,2,5,3,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,5,6,8,4,7,1,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,3,7,1,2,5,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,4,7,8,2,6,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,6,4,1,5,8,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,5,2,8,7,3,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,6,1,7,8,5,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,1,6,4,7,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,6,8,3,1,7,4,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,6,3,1,4,2,7,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,4,7,8,5,1,6,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,4,8,6,2,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,3,7,2,8,5,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,4,3,7,6,1,8,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,1,8,6,2,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,4,2,8,6,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,4,8,6,2,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,2,1,9,4,5,6,3,8] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[6,2,3,1,8,5,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,2,3,1,9,5,6,4,8] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[4,5,2,8,6,1,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,6,7,2,8,4,1,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,4,2,8,7,3,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,7,3,1,8,5,4,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,5,7,8,2,6,1,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,7,1,3,2,5,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,3,7,8,4,2,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,7,3,1,4,8,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,5,4,7,1,8,6,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,2,7,4,3,8,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,4,2,3,8,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,7,5,6,1,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,1,4,2,3,8,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,4,2,8,6,7,1,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,6,7,2,5,1,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,6,2,5,1,7,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,1,4,2,5,8,6,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,3,7,6,2,4,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,3,8,4,2,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,2,8,1,4,5,3,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,8,5,2,7,3,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,5,1,7,8,6,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,6,5,1,7,8,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,6,8,4,7,2,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,1,4,5,7,2,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,5,1,8,6,7,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,6,4,2,8,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,5,6,3,8,1,7,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,1,7,6,2,5,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,3,2,7,5,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,4,2,8,7,3,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,8,3,5,2,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,4,7,3,2,8,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,7,3,2,8,4,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,4,8,7,2,3,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,8,5,7,2,3,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,2,1,3,5,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,8,2,5,6,1,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,8,1,3,4,2,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,6,3,2,8,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,7,3,2,8,5,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,8,2,1,4,3,6,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,8,2,4,1,6,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,8,1,4,6,2,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,8,4,6,7,2,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,8,4,6,7,2,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,5,4,1,8,6,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,6,7,2,5,1,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,3,2,8,5,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,7,1,4,6,8,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,5,6,4,8,1,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,7,2,4,5,1,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,2,8,4,1,3,5,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,7,8,3,2,5,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,7,1,4,6,2,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,5,1,7,6,8,3,9] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[4,1,3,8,5,2,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,3,1,2,7,8,5,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,5,4,6,8,7,9,1,3] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[5,1,4,7,6,8,2,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,8,3,1,4,6,7,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,5,3,8,1,6,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,6,3,4,1,7,8,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,2,3,1,5,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,6,1,7,5,3,8,9] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[3,5,2,7,1,8,6,4,9] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[5,8,9,2,1,6,3,10,7,4] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 4
[1,5,4,7,2,6,3,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,4,5,8,3,1,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,2,3,1,8,4,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,3,4,5,1,8,6,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,5,2,1,7,6,3,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,5,2,8,7,3,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,5,8,1,6,2,3,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,8,4,2,5,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,2,4,8,3,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,4,2,8,6,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,5,7,1,6,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,5,4,7,6,1,3,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,3,7,6,1,4,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,3,7,6,1,5,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,7,3,5,1,4,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,2,3,1,5,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,8,2,3,1,6,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,7,2,1,4,6,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,7,1,5,6,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,3,8,1,7,5,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,5,3,7,8,1,6,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,4,2,8,1,6,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,7,5,1,6,2,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,6,1,4,3,7,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,7,2,5,1,6,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,6,3,8,7,2,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,8,4,5,7,1,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,6,4,7,8,5,1,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,8,5,6,1,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,4,8,2,6,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,8,3,1,6,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,3,1,8,4,5,6,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,3,1,2,4,8,7,5,9] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[5,3,1,2,4,9,7,6,8] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[1,4,3,8,5,7,2,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,8,1,3,6,2,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,3,8,1,5,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,4,2,8,3,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,7,3,5,8,2,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,6,3,7,8,1,5,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,3,1,8,4,5,2,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,3,1,2,5,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,4,7,3,6,8,2,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,4,7,3,6,8,1,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,8,1,4,2,7,3,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,4,6,1,8,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,7,5,2,3,8,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,1,8,2,4,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,8,3,2,4,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,2,1,3,8,5,4,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,2,7,8,4,6,3,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,7,4,6,1,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[10,11,12,5,6,2,1,4,3,9,8,7] => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 5
[3,4,8,2,7,1,5,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,8,1,2,4,6,3,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,3,6,8,5,1,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,4,8,6,1,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,6,5,7,8,1,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,4,6,8,5,7,2,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,2,1,5,3,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,2,8,3,6,1,4,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,7,1,2,6,8,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,7,3,2,4,8,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,1,8,2,6,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,8,1,3,2,5,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,5,3,8,1,4,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,4,3,8,1,5,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,7,3,8,5,1,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,6,2,5,1,7,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,5,2,1,7,8,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,4,8,1,2,3,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,7,1,4,6,3,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,4,3,8,5,7,1,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,8,5,1,4,6,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,8,1,4,2,6,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,4,7,5,8,6,2,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,5,8,1,2,3,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,6,7,3,1,5,8,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,3,8,4,7,2,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,4,1,2,7,6,3,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,2,4,3,8,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,2,4,5,1,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,8,4,2,3,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,5,7,2,1,6,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,7,3,2,8,5,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,5,2,7,8,6,1,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,6,7,2,1,5,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,6,4,7,1,8,5,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,4,3,7,6,2,8,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,4,3,8,2,5,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,4,1,7,8,6,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,3,7,5,8,6,1,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,3,6,4,8,2,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,6,7,4,8,5,1,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,5,7,4,6,8,1,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,8,2,4,3,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,1,3,2,5,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,6,7,4,8,1,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,6,7,8,1,4,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,6,7,8,2,1,5,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,4,5,3,8,7,1,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,5,8,4,6,1,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,4,7,2,5,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,4,3,8,5,1,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,1,3,8,2,6,4,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,5,8,2,1,6,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,4,8,3,2,6,5,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,6,9,10,2,4,8,1,3,7] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 4
[3,4,9,10,2,6,8,1,5,7] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 4
[10,11,12,5,6,9,2,4,8,1,3,7] => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 5
[5,2,1,4,8,6,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,8,4,1,6,5,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,1,8,4,2,3,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,5,6,8,2,1,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,8,1,4,6,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,6,3,7,8,1,4,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,3,7,1,5,4,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,9,10,2,6,7,1,3,4,8] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 4
[4,2,3,7,6,1,8,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,4,1,7,6,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,1,4,8,6,2,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,8,5,2,9,6,3,10,7,4] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 4
[7,2,4,1,8,5,3,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,4,7,8,3,1,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,7,4,5,8,1,6,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,4,6,5,8,2,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,3,8,7,1,4,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,2,1,4,5,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,3,4,8,2,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,7,2,4,6,1,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,4,5,3,8,1,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,2,8,3,5,6,1,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,2,3,8,4,6,1,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,6,7,4,1,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,7,3,8,4,1,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,8,3,4,7,2,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,8,1,4,6,2,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,1,3,7,2,8,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,3,2,8,7,4,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,3,7,8,4,6,2,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,9,2,1,5,6,7,8,4] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[3,8,2,4,5,1,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,9,2,4,1,6,7,8,5] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[3,7,2,1,5,6,4,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,5,4,1,7,8,6,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,7,3,1,6,8,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,3,8,2,7,4,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,1,3,2,9,6,10,5,8,7] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 4
[5,2,6,1,4,3,10,7,9,8] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 4
[5,3,7,4,6,1,8,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,5,8,6,1,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,8,1,5,6,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,4,7,5,8,2,6,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,7,2,1,3,6,4,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,4,7,8,6,2,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,7,5,2,8,6,3,10,9,4] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 4
[1,7,5,2,9,6,3,10,8,4] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 4
[6,1,9,4,2,7,3,10,8,5] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 4
[5,8,2,1,3,6,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,8,1,3,7,5,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,6,7,5,1,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,4,8,1,5,2,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,4,7,6,1,8,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,3,8,6,1,2,5,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,8,1,3,4,7,2,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,4,7,8,1,6,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,4,8,2,3,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,5,7,2,1,8,6,4,9] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[1,4,8,3,6,2,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,6,8,3,4,2,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,1,4,2,8,5,3,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,7,4,1,2,6,8,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,7,4,2,8,5,6,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,1,7,4,6,8,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,1,3,8,6,2,4,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,1,4,7,6,2,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,8,1,4,6,2,7,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,2,7,5,6,8,1,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,5,9,3,10,7,1,8,2,6] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 4
[4,9,3,10,5,7,1,8,2,6] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 4
[4,9,3,10,7,1,8,2,5,6] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 4
[1,7,8,4,2,6,3,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,3,9,6,1,2,4,10,8,5] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 4
[6,1,3,9,7,2,4,10,8,5] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 4
[7,2,8,3,10,6,1,4,9,5] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 4
[9,4,11,8,2,5,12,10,7,1,3,6] => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 5
[2,4,7,5,1,8,6,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,4,7,6,8,1,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,2,6,5,8,3,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,7,3,8,2,5,4,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,2,7,1,4,3,5,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,2,4,8,3,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,2,3,8,6,4,9,7,5] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[5,3,1,8,4,2,6,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,4,3,8,6,1,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,3,2,5,8,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,5,8,3,6,1,7,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,7,1,3,6,2,4,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,5,3,8,4,7,2,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,6,7,8,3,1,5,2,9] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[2,7,3,1,8,5,6,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,1,7,3,2,6,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,8,1,2,4,7,3,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,3,6,4,7,1,8,2,9] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[4,6,2,7,5,8,1,9,3] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[7,1,4,2,8,6,3,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[2,3,7,4,8,1,6,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,1,4,8,2,3,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,8,1,4,5,6,2,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[8,9,10,1,5,6,7,2,3,4] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 4
[3,2,7,5,1,6,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,7,3,1,6,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,4,3,8,6,2,5,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[4,1,3,8,6,2,5,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,4,1,2,8,5,6,3] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,4,1,8,5,2,3,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[6,3,4,8,5,1,2,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,4,5,6,9,2,1,8,7] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[3,4,5,8,2,9,1,7,6] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[3,6,2,7,8,9,1,5,4] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[5,2,6,7,8,9,1,4,3] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[3,4,5,8,9,6,1,7,2] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[3,4,5,9,2,6,1,8,7] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[3,6,7,4,8,9,1,5,2] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[5,6,3,7,8,9,1,4,2] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[6,2,3,7,8,9,1,5,4] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[2,6,3,1,7,8,5,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[3,2,8,5,6,7,1,9,4] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[4,2,3,8,6,7,1,9,5] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[8,9,10,4,5,6,1,2,3,7] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 4
[8,1,9,3,2,4,6,5,7] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[3,4,5,8,9,6,7,1,2] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[3,4,7,8,5,9,6,1,2] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[5,6,3,7,8,9,4,1,2] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
[3,7,8,4,5,6,1,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[5,2,3,8,6,1,4,7] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[7,8,5,1,2,6,3,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,4,3,7,6,2,5,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
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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
peaks-to-valleys
Description
Return the path that has a valley wherever the original path has a peak of height at least one.
More precisely, the height of a valley in the image is the height of the corresponding peak minus $2$.
This is also (the inverse of) rowmotion on Dyck paths regarded as order ideals in the triangular poset.
More precisely, the height of a valley in the image is the height of the corresponding peak minus $2$.
This is also (the inverse of) rowmotion on Dyck paths regarded as order ideals in the triangular poset.
Map
Robinson-Schensted tableau shape
Description
Sends a permutation to its Robinson-Schensted tableau shape.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to the shape of its corresponding insertion and recording tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to the shape of its corresponding insertion and recording tableau.
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.
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