Identifier
-
Mp00031:
Dyck paths
—to 312-avoiding permutation⟶
Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
St001137: Dyck paths ⟶ ℤ
Values
[1,0] => [1] => [1] => [1,0] => 0
[1,0,1,0] => [1,2] => [2] => [1,1,0,0] => 0
[1,1,0,0] => [2,1] => [1,1] => [1,0,1,0] => 0
[1,0,1,0,1,0] => [1,2,3] => [3] => [1,1,1,0,0,0] => 0
[1,0,1,1,0,0] => [1,3,2] => [2,1] => [1,1,0,0,1,0] => 0
[1,1,0,0,1,0] => [2,1,3] => [1,2] => [1,0,1,1,0,0] => 0
[1,1,0,1,0,0] => [2,3,1] => [2,1] => [1,1,0,0,1,0] => 0
[1,1,1,0,0,0] => [3,2,1] => [1,1,1] => [1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [4] => [1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [3,1] => [1,1,1,0,0,0,1,0] => 0
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [2,2] => [1,1,0,0,1,1,0,0] => 0
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [3,1] => [1,1,1,0,0,0,1,0] => 0
[1,0,1,1,1,0,0,0] => [1,4,3,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [1,3] => [1,0,1,1,1,0,0,0] => 0
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => 0
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [2,2] => [1,1,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [3,1] => [1,1,1,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,0] => [2,4,3,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,0] => [3,2,1,4] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,0] => [3,2,4,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => 0
[1,1,1,0,1,0,0,0] => [3,4,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,0] => [4,3,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [5] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 0
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 0
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 0
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 0
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,1,0,1,0,0,0] => [1,4,5,3,2] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,0] => [2,4,5,3,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,0] => [3,4,2,1,5] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,0] => [3,4,2,5,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,0] => [3,4,5,2,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,0] => [3,5,4,2,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,0,0] => [4,3,5,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,0] => [4,5,3,2,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,4,3] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,4,2] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,3,2,6] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,3,6,2] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,3,2] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,5,3,2] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 0
>>> Load all 1946 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,4,6,3,2] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,4,3,2] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,4,3] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,4,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,3,1,6] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,3,6,1] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,6,3,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,5,3,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,4,6,3,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,4,3,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,6,4,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,2,1,5,6] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,2,1,6,5] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,2,5,1,6] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,2,5,6,1] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,2,6,5,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,2,1,6] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,2,6,1] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,2,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,5,2,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,4,2,1,6] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,4,2,6,1] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,4,6,2,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,4,2,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,3,5,2,1,6] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,6,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,5,6,2,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,2,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,3,2,1,6] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,3,2,6,1] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,3,6,2,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,3,2,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,6,7,5,4] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,7,5,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,4,6,3,7] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,5,6,4,3,7] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,5,6,4,7,3] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,5,6,7,4,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5,7,6,4,3] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,6,5,7,4,3] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,6,7,5,4,3] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,6,7,5,4] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,6,7,5,2] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,5,6,4,2,7] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,5,6,4,7,2] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,6,7,4,2] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,6,4,2] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,6,5,7,4,2] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,6,7,5,4,2] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,6,7,5,2] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,5,3,2,6,7] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,5,3,2,7,6] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,4,5,3,6,2,7] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,5,3,6,7,2] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,5,3,7,6,2] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,3,2,7] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,3,7,2] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,3,2] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,4,5,7,6,3,2] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,4,6,5,3,2,7] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,5,3,7,2] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,4,6,5,7,3,2] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,4,6,7,5,3,2] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,4,7,6,5,3,2] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,4,3,2,6,7] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,4,3,6,2,7] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,4,6,3,2,7] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,4,6,3,7,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,4,6,7,3,2] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,4,7,6,3,2] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,5,6,4,3,2,7] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,6,4,3,7,2] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,5,6,4,7,3,2] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,5,6,7,4,3,2] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,5,7,6,4,3,2] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,6,5,4,7,3,2] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,5,7,4,3,2] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,6,7,5,4,3,2] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,6,4] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,5,7,4] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,6,7,5,4] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,5,3,7] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,6,7,5,3] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,4,3,6,7] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,4,3,7,6] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,4,6,3,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,4,6,7,3] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,4,7,6,3] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,5,6,4,3,7] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,5,6,4,7,3] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,5,6,7,4,3] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,5,7,6,4,3] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,5,4,3,7] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,5,4,7,3] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,5,7,4,3] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,6,7,5,4,3] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,6,5] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,6,4] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,5,4,7] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,5,7,4] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,6,7,5,4] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,6,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,5,7,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,6,7,5,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,6,5,1] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,4,6,1,7] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,4,6,7,1] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,4,7,6,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,5,6,4,1,7] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,5,6,4,7,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,6,7,4,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,7,6,4,1] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,5,4,7,1] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,6,5,7,4,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,6,7,5,4,1] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,3,1,5,7,6] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,7] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3,1,6,7,5] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3,1,7,6,5] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,3,5,1,6,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,3,5,1,7,6] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,3,5,6,1,7] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,1] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,3,5,7,6,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,1,7] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,7,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,3,6,7,5,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,4,5,3,1,6,7] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,4,5,3,1,7,6] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,4,5,3,6,1,7] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,4,5,3,6,7,1] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,4,5,3,7,6,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,3,1,7] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,3,7,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,3,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,4,5,7,6,3,1] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,4,6,5,3,1,7] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,4,6,5,3,7,1] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,4,6,5,7,3,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,4,6,7,5,3,1] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,4,7,6,5,3,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,4,3,6,1,7] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,4,3,6,7,1] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,4,3,7,6,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,5,4,6,3,1,7] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,5,4,6,3,7,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,5,4,6,7,3,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,5,4,7,6,3,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,5,6,4,3,1,7] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,5,6,4,3,7,1] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,5,6,4,7,3,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,5,6,7,4,3,1] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,5,7,6,4,3,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,6,5,4,7,3,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,6,5,7,4,3,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,6,7,5,4,3,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,7,6] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,2,1,4,6,5,7] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,2,1,4,6,7,5] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,5,4,6,7] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,5,6,4,7] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,5,6,7,4] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,1,5,7,6,4] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,2,1,6,5,4,7] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,2,1,6,5,7,4] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,2,1,6,7,5,4] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,2,4,1,6,7,5] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,4,1,7,6,5] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,7,6,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,4,6,5,1,7] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,2,4,6,5,7,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,6,7,5,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,2,4,7,6,5,1] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,5,4,1,6,7] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,5,4,6,1,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,5,4,6,7,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,5,6,4,1,7] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,5,6,4,7,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,5,6,7,4,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,5,7,6,4,1] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,2,6,5,4,1,7] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,2,6,5,4,7,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,2,6,5,7,4,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,6,7,5,4,1] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,4,2,1,5,7,6] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,4,2,1,6,5,7] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,2,1,6,7,5] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,2,1,7,6,5] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,2,5,1,6,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,2,5,1,7,6] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,2,5,6,1,7] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,1] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [3,4,2,5,7,6,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,4,2,6,5,1,7] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [3,4,2,6,5,7,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,2,6,7,5,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,4,2,7,6,5,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,2,1,6,7] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,2,1,7,6] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,2,6,1,7] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,2,6,7,1] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,2,7,6,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,2,1,7] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,2,7,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,2,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,7,6,2,1] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,4,6,5,2,1,7] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [3,4,6,5,2,7,1] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,6,5,7,2,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,6,7,5,2,1] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,7,6,5,2,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,5,4,2,1,6,7] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,5,4,2,1,7,6] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,5,4,2,6,1,7] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,5,4,2,6,7,1] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,5,4,2,7,6,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,5,4,6,2,1,7] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,5,4,6,2,7,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,5,4,6,7,2,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,5,4,7,6,2,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,5,6,4,2,1,7] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,5,6,4,2,7,1] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [3,5,6,4,7,2,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,5,6,7,4,2,1] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,5,7,6,4,2,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,6,5,4,2,1,7] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [3,6,5,4,2,7,1] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,6,5,4,7,2,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,6,5,7,4,2,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,6,7,5,4,2,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,7,6,5,4,2,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,3,2,1,5,7,6] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,7] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3,2,1,6,7,5] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,3,2,5,1,6,7] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,3,2,5,7,6,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,3,2,6,5,7,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,2,6,7,5,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [4,3,5,2,1,6,7] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [4,3,5,2,1,7,6] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [4,3,5,2,6,1,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [4,3,5,2,6,7,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,3,5,2,7,6,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [4,3,5,6,2,1,7] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [4,3,5,6,2,7,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,5,6,7,2,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,3,5,7,6,2,1] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [4,3,6,5,2,1,7] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [4,3,6,5,2,7,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,3,6,5,7,2,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,6,7,5,2,1] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,3,7,6,5,2,1] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [4,5,3,2,1,6,7] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [4,5,3,2,1,7,6] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [4,5,3,2,6,1,7] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [4,5,3,2,6,7,1] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,5,3,2,7,6,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [4,5,3,6,2,1,7] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [4,5,3,6,2,7,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,5,3,6,7,2,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,3,7,6,2,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,3,2,1,7] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,3,2,7,1] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,3,7,2,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,3,2,1] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,7,6,3,2,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [4,6,5,3,2,1,7] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [4,6,5,3,2,7,1] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,6,5,3,7,2,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,6,5,7,3,2,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,6,7,5,3,2,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [4,7,6,5,3,2,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,4,3,2,7,6,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [5,4,3,6,2,1,7] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,4,3,6,2,7,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,4,3,7,6,2,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,4,6,3,2,1,7] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,4,6,3,2,7,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,4,6,3,7,2,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,6,7,3,2,1] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [5,4,7,6,3,2,1] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [5,6,4,3,2,1,7] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,6,4,3,2,7,1] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,6,4,3,7,2,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,6,4,7,3,2,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [5,6,7,4,3,2,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [5,7,6,4,3,2,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,5,4,3,2,7,1] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,5,4,3,7,2,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [6,5,4,7,3,2,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [6,5,7,4,3,2,1] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [6,7,5,4,3,2,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,7,8,6] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,7,6] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,6,5,7,8] => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => [5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,6,7,5,8] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,5] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,6,8,7,5] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,7,6,5,8] => [5,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,7,6,8,5] => [5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,7,8,6,5] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,7,6,5] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,3,5,4,6,8,7] => [4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3,5,4,7,8,6] => [4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,7,6] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,4,7,8] => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,5,6,4,8,7] => [5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,5,6,7,4,8] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,8,7,4] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,3,5,7,6,4,8] => [5,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,3,5,7,6,8,4] => [5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,5,7,8,6,4] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,5,8,7,6,4] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,6,5,4,7,8] => [4,1,3] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,5,4,8,7] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,3,6,5,7,4,8] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,6,5,7,8,4] => [4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,6,5,8,7,4] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,3,6,7,5,4,8] => [5,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,6,7,5,8,4] => [5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => 0
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,6,7,8,5,4] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,6,8,7,5,4] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,7,6,5,4,8] => [4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,3,7,6,5,8,4] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,7,6,8,5,4] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,7,8,6,5,4] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,7,6,5,4] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8] => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,8,7] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5,7,6,8] => [3,3,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,4,3,5,7,8,6] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,4,3,5,8,7,6] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => [3,2,3] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,4,3,6,7,5,8] => [3,3,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4,3,6,7,8,5] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,4,3,6,8,7,5] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,4,3,7,6,5,8] => [3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,6,8,5] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,4,3,7,8,6,5] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,7,6,5] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,2,4,5,3,6,7,8] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,2,4,5,3,6,8,7] => [4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6,8] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,4,5,3,7,8,6] => [4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,4,5,3,8,7,6] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,4,5,6,3,7,8] => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,2,4,5,6,3,8,7] => [5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,7,3,8] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,3] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,4,5,6,8,7,3] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,2,4,5,7,6,3,8] => [5,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,4,5,7,8,6,3] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,4,5,8,7,6,3] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,2,4,6,5,3,7,8] => [4,1,3] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,2,4,6,5,3,8,7] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,2,4,6,5,7,3,8] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,2,4,6,5,7,8,3] => [4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,2,4,6,5,8,7,3] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,2,4,6,7,5,3,8] => [5,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,2,4,6,7,5,8,3] => [5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,2,4,6,7,8,5,3] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,2,4,6,8,7,5,3] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,2,4,7,6,5,3,8] => [4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,2,4,7,6,5,8,3] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,2,4,7,6,8,5,3] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,2,4,7,8,6,5,3] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4,8,7,6,5,3] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,5,4,3,6,7,8] => [3,1,4] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,5,4,3,6,8,7] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,2,5,4,3,7,6,8] => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,5,4,3,7,8,6] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,4,3,8,7,6] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,2,5,4,6,3,7,8] => [3,2,3] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,2,5,4,6,3,8,7] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,2,5,4,6,7,3,8] => [3,3,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,3] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,2,5,4,6,8,7,3] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,2,5,4,7,6,3,8] => [3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,2,5,4,7,6,8,3] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,2,5,4,8,7,6,3] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,2,5,6,4,3,7,8] => [4,1,3] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,2,5,6,4,3,8,7] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,2,5,6,4,7,3,8] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,2,5,6,4,7,8,3] => [4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,2,5,6,4,8,7,3] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,2,5,6,7,4,3,8] => [5,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,2,5,6,7,4,8,3] => [5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => 0
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,5,6,7,8,4,3] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,2,5,6,8,7,4,3] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,2,5,7,6,4,3,8] => [4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,2,5,7,6,4,8,3] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,2,5,7,6,8,4,3] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,2,5,7,8,6,4,3] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,5,8,7,6,4,3] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,6,5,4,3,7,8] => [3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,6,5,4,3,8,7] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,6,5,4,7,8,3] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,6,5,4,8,7,3] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,2,6,5,7,4,8,3] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,6,5,7,8,4,3] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,6,5,8,7,4,3] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,2,6,7,5,4,3,8] => [4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,2,6,7,5,4,8,3] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,2,6,7,5,8,4,3] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,6,7,8,5,4,3] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,2,6,8,7,5,4,3] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,7,6,5,4,3,8] => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,7,6,5,4,8,3] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,7,6,5,8,4,3] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,7,6,8,5,4,3] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,7,8,6,5,4,3] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,7,6,5,4,3] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,8,7] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,7,8,6] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,8,7,6] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,6,5,7,8] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,2,4,6,5,8,7] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,2,4,6,7,8,5] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,2,4,6,8,7,5] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,2,4,7,6,5,8] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,2,4,7,6,8,5] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,3,2,4,7,8,6,5] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,7,6,5] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,5,4,6,8,7] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,7,6] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,3,2,5,6,4,7,8] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,2,5,6,4,8,7] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,2,5,6,7,4,8] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,6,7,8,4] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,3,2,5,6,8,7,4] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,2,5,7,6,4,8] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,3,2,5,7,6,8,4] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,3,2,5,7,8,6,4] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,2,5,8,7,6,4] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,6,5,4,7,8] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,6,5,4,8,7] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,5,7,4,8] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,5,7,8,4] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,5,8,7,4] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,3,2,6,7,5,4,8] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,2,6,7,5,8,4] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,3,2,6,7,8,5,4] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2,6,8,7,5,4] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,6,5,4,8] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,7,6,5,8,4] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,7,6,8,5,4] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,3,2,7,8,6,5,4] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,7,6,5,4] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8] => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,2,5,6,8,7] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,5,7,6,8] => [3,3,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,2,5,7,8,6] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,3,4,2,5,8,7,6] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => [3,3,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4,2,6,7,8,5] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,3,4,2,6,8,7,5] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,3,4,2,7,6,5,8] => [3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,6,8,5] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,3,4,2,7,8,6,5] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4,2,8,7,6,5] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,5,2,6,8,7] => [4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6,8] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,5,2,7,8,6] => [4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,5,2,8,7,6] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,2,7,8] => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,2,8,7] => [5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,2,8] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,2] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,8,7,2] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,5,7,6,2,8] => [5,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,5,7,6,8,2] => [5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,5,7,8,6,2] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,5,8,7,6,2] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,3,4,6,5,2,7,8] => [4,1,3] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,3,4,6,5,2,8,7] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,3,4,6,5,7,2,8] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,4,6,5,7,8,2] => [4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,3,4,6,5,8,7,2] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,3,4,6,7,5,2,8] => [5,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,3,4,6,7,5,8,2] => [5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,6,7,8,5,2] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,3,4,6,8,7,5,2] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,4,7,6,5,8,2] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,3,4,7,6,8,5,2] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,3,4,7,8,6,5,2] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,8,7,6,5,2] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,3,5,4,2,6,7,8] => [3,1,4] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,3,5,4,2,6,8,7] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,3,5,4,2,7,6,8] => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,3,5,4,2,7,8,6] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,3,5,4,2,8,7,6] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,3,5,4,6,2,7,8] => [3,2,3] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,3,5,4,6,7,2,8] => [3,3,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,3,5,4,6,7,8,2] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,3,5,4,6,8,7,2] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,3,5,4,7,6,2,8] => [3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,5,4,7,6,8,2] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,3,5,4,7,8,6,2] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,5,4,8,7,6,2] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,3,5,6,4,2,7,8] => [4,1,3] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,3,5,6,4,2,8,7] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,3,5,6,4,7,2,8] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,3,5,6,4,7,8,2] => [4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,3,5,6,4,8,7,2] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,3,5,6,7,4,2,8] => [5,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,5,6,7,4,8,2] => [5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,5,6,7,8,4,2] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,3,5,6,8,7,4,2] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,3,5,7,6,4,2,8] => [4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,3,5,7,6,4,8,2] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,3,5,7,6,8,4,2] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,5,7,8,6,4,2] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,3,5,8,7,6,4,2] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,3,6,5,4,2,7,8] => [3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,3,6,5,4,2,8,7] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,3,6,5,4,7,2,8] => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,6,5,4,8,7,2] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,3,6,5,7,4,2,8] => [3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,3,6,5,7,4,8,2] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,6,5,7,8,4,2] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,3,6,5,8,7,4,2] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,3,6,7,5,4,2,8] => [4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,3,6,7,5,8,4,2] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,6,7,8,5,4,2] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,3,6,8,7,5,4,2] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,3,7,6,5,4,2,8] => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,3,7,6,5,8,4,2] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,7,6,8,5,4,2] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,7,8,6,5,4,2] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,8,7,6,5,4,2] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,4,3,2,5,6,8,7] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,4,3,2,5,7,6,8] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,4,3,2,5,7,8,6] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,3,2,5,8,7,6] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,4,3,2,6,5,7,8] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,3,2,6,5,8,7] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,4,3,2,6,7,5,8] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,4,3,2,6,7,8,5] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,4,3,2,6,8,7,5] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,4,3,2,7,6,8,5] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,4,3,2,7,8,6,5] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,3,2,8,7,6,5] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,4,3,5,2,6,8,7] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,3,5,2,7,6,8] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,4,3,5,2,7,8,6] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,4,3,5,2,8,7,6] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,3,5,6,2,7,8] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,2] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,4,3,5,6,8,7,2] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,3,5,7,6,2,8] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,3,5,7,6,8,2] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,3,5,7,8,6,2] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,3,5,8,7,6,2] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,3,6,5,2,7,8] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,3,6,5,7,2,8] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,3,6,5,7,8,2] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,2] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,4,3,6,7,5,8,2] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,3,6,7,8,5,2] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,3,6,8,7,5,2] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,4,3,7,6,5,2,8] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,3,7,6,8,5,2] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,3,7,8,6,5,2] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,3,8,7,6,5,2] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,4,5,3,2,6,7,8] => [3,1,4] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,4,5,3,2,6,8,7] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,4,5,3,2,7,6,8] => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,4,5,3,2,7,8,6] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,4,5,3,2,8,7,6] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,4,5,3,6,2,7,8] => [3,2,3] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,4,5,3,6,7,2,8] => [3,3,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,4,5,3,6,7,8,2] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,4,5,3,6,8,7,2] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,4,5,3,7,6,2,8] => [3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,4,5,3,7,8,6,2] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,4,5,3,8,7,6,2] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,4,5,6,3,2,7,8] => [4,1,3] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,4,5,6,3,2,8,7] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,4,5,6,3,7,2,8] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,4,5,6,3,7,8,2] => [4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,4,5,6,3,8,7,2] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,7,3,2,8] => [5,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,7,3,8,2] => [5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,8,3,2] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,4,5,7,6,3,2,8] => [4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,4,5,7,6,3,8,2] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,4,5,7,6,8,3,2] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,4,5,7,8,6,3,2] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,4,5,8,7,6,3,2] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,4,6,5,3,2,7,8] => [3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,4,6,5,3,7,2,8] => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,4,6,5,3,7,8,2] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,4,6,5,3,8,7,2] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,4,6,5,7,3,2,8] => [3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,4,6,5,7,3,8,2] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,4,6,5,8,7,3,2] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,4,6,7,5,3,2,8] => [4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,4,6,7,5,3,8,2] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,4,6,7,5,8,3,2] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,4,6,7,8,5,3,2] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,4,6,8,7,5,3,2] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,4,7,6,5,3,2,8] => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,4,7,6,5,3,8,2] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,4,7,6,5,8,3,2] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,4,7,6,8,5,3,2] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,4,7,8,6,5,3,2] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,4,8,7,6,5,3,2] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,5,4,3,2,6,7,8] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,5,4,3,2,6,8,7] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,4,3,2,7,6,8] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,5,4,3,2,7,8,6] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,4,3,2,8,7,6] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,5,4,3,6,2,7,8] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,5,4,3,6,7,2,8] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,4,3,6,7,8,2] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,4,3,6,8,7,2] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,5,4,3,7,6,8,2] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,5,4,3,7,8,6,2] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,5,4,3,8,7,6,2] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,5,4,6,3,2,7,8] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,5,4,6,3,2,8,7] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,5,4,6,3,7,2,8] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,5,4,6,3,7,8,2] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,5,4,6,3,8,7,2] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,5,4,6,7,3,2,8] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,5,4,6,7,3,8,2] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,5,4,6,7,8,3,2] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,4,7,6,3,2,8] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,5,4,7,6,3,8,2] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,5,4,7,6,8,3,2] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,5,4,7,8,6,3,2] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,5,4,8,7,6,3,2] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,5,6,4,3,2,7,8] => [3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,5,6,4,3,2,8,7] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,5,6,4,3,7,2,8] => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,5,6,4,3,8,7,2] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,5,6,4,7,3,2,8] => [3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,5,6,4,7,3,8,2] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,5,6,4,7,8,3,2] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,5,6,7,4,3,2,8] => [4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,5,6,7,4,3,8,2] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,5,6,7,4,8,3,2] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,5,6,7,8,4,3,2] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,5,6,8,7,4,3,2] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,5,7,6,4,3,2,8] => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,5,7,6,4,3,8,2] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,5,7,6,8,4,3,2] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,5,7,8,6,4,3,2] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,5,8,7,6,4,3,2] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,6,5,4,3,2,7,8] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,5,4,3,2,8,7] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,6,5,4,3,7,2,8] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,6,5,4,3,7,8,2] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,5,4,3,8,7,2] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,6,5,4,7,3,8,2] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,6,5,4,7,8,3,2] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,6,5,4,8,7,3,2] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,5,7,4,3,2,8] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,5,7,4,3,8,2] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,6,5,7,4,8,3,2] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,6,5,7,8,4,3,2] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,6,5,8,7,4,3,2] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,6,7,5,4,3,2,8] => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,6,7,5,4,3,8,2] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,6,7,5,8,4,3,2] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,6,7,8,5,4,3,2] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,6,8,7,5,4,3,2] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,6,5,4,3,2,8] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,6,5,4,3,8,2] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,7,6,5,4,8,3,2] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,7,6,5,8,4,3,2] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7,6,8,5,4,3,2] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,7,8,6,5,4,3,2] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,7,6,8] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,7,8,6] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,8,7,6] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,4,6,5,7,8] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,4,6,5,8,7] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,4,6,7,5,8] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,4,6,7,8,5] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,4,6,8,7,5] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,4,7,6,8,5] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,4,7,8,6,5] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,7,6,5] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,3,5,4,6,7,8] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4,6,8,7] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,3,5,4,7,6,8] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,3,5,4,7,8,6] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,3,5,4,8,7,6] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,3,5,6,4,7,8] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,5,6,4,8,7] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,4] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,1,3,5,6,8,7,4] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,1,3,5,7,6,8,4] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,1,3,5,7,8,6,4] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,1,3,5,8,7,6,4] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,6,5,4,7,8] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,3,6,5,7,4,8] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,3,6,5,7,8,4] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,3,6,5,8,7,4] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,3,6,7,5,4,8] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,1,3,6,7,5,8,4] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,6,7,8,5,4] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,1,3,6,8,7,5,4] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,3,7,6,5,4,8] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,1,3,7,6,5,8,4] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,3,7,6,8,5,4] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,3,7,8,6,5,4] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,7,6,5,4] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,3,5,6,8,7] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,3,5,7,8,6] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,3,5,8,7,6] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,5] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,7,5] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,6,8,5] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,7,8,6,5] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6,8,7] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3,7,8,6] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,1,4,5,3,8,7,6] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,1,4,5,6,3,7,8] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,4,5,6,3,8,7] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,3,8] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,3] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,1,4,5,6,8,7,3] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,1,4,5,7,6,3,8] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,1,4,5,7,6,8,3] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,4,5,7,8,6,3] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,4,5,8,7,6,3] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,4,6,5,3,7,8] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,1,4,6,5,7,8,3] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,1,4,6,5,8,7,3] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,1,4,6,7,5,3,8] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,1,4,6,7,5,8,3] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,1,4,6,7,8,5,3] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,1,4,6,8,7,5,3] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,1,4,7,6,5,3,8] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,1,4,7,6,5,8,3] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,1,4,7,6,8,5,3] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,4,7,8,6,5,3] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4,8,7,6,5,3] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,4,3,6,7,8] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,5,4,3,6,8,7] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,5,4,3,7,6,8] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,1,5,4,3,7,8,6] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,5,4,3,8,7,6] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,1,5,4,6,3,7,8] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,5,4,6,7,3,8] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,4,6,7,8,3] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,5,4,6,8,7,3] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,1,5,4,7,6,3,8] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,8,3] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,4,7,8,6,3] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,4,8,7,6,3] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,1,5,6,4,3,7,8] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,5,6,4,3,8,7] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,1,5,6,4,7,8,3] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,1,5,6,4,8,7,3] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,1,5,6,7,4,3,8] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,1,5,6,7,4,8,3] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,1,5,6,7,8,4,3] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,1,5,6,8,7,4,3] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,1,5,7,6,4,8,3] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,1,5,7,6,8,4,3] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,5,7,8,6,4,3] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,1,5,8,7,6,4,3] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,1,6,5,4,7,8,3] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,1,6,5,4,8,7,3] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,6,5,7,4,8,3] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,6,5,7,8,4,3] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,6,5,8,7,4,3] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,1,6,7,5,4,3,8] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,1,6,7,5,4,8,3] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,1,6,7,5,8,4,3] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,6,7,8,5,4,3] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,1,6,8,7,5,4,3] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,6,5,4,3,8] => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,7,6,5,4,8,3] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,7,6,5,8,4,3] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,7,6,8,5,4,3] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,7,8,6,5,4,3] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,8,7] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,3,1,4,5,7,6,8] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,3,1,4,5,8,7,6] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,3,1,4,6,5,7,8] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,4,6,5,8,7] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,3,1,4,6,7,5,8] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,1,4,6,7,8,5] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,3,1,4,6,8,7,5] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,7,6,8,5] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,3,1,4,7,8,6,5] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,8,7,6,5] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,8] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,3,1,5,4,7,8,6] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,5,6,4,7,8] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,3,1,5,6,7,4,8] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,4] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,3,1,5,6,8,7,4] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,7,6,8,4] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,3,1,5,7,8,6,4] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,3,1,5,8,7,6,4] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,6,5,4,7,8] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,1,6,5,4,8,7] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,5,7,4,8] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,6,5,7,8,4] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,5,8,7,4] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,3,1,6,7,5,4,8] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,3,1,6,7,5,8,4] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,6,7,8,5,4] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,3,1,6,8,7,5,4] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,3,1,7,6,5,4,8] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,7,6,5,8,4] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,3,1,7,6,8,5,4] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,1,7,8,6,5,4] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,8,7,6,5,4] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8] => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5,6,8,7] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,4,1,5,7,6,8] => [3,3,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,4,1,5,7,8,6] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,8,7,6] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,5,7,8] => [3,2,3] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,4,1,6,7,5,8] => [3,3,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,4,1,6,8,7,5] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,4,1,7,6,5,8] => [3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,6,8,5] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,4,1,7,8,6,5] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,8,7,6,5] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,5,1,6,8,7] => [4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,8] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,1,7,8,6] => [4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,8,7,6] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => [5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,8,7,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,7,6,1,8] => [5,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,7,6,8,1] => [5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,7,8,6,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,8,7,6,1] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,6,5,1,7,8] => [4,1,3] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,4,6,5,1,8,7] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,4,6,5,7,1,8] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,4,6,5,7,8,1] => [4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,4,6,5,8,7,1] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,4,6,7,5,1,8] => [5,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,4,6,7,5,8,1] => [5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,6,7,8,5,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,4,6,8,7,5,1] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,4,7,6,5,1,8] => [4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,4,7,6,5,8,1] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,7,6,8,5,1] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,7,8,6,5,1] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,8,7,6,5,1] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,5,4,1,6,7,8] => [3,1,4] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,3,5,4,1,6,8,7] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,4,1,7,6,8] => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,3,5,4,1,7,8,6] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,4,1,8,7,6] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,3,5,4,6,1,7,8] => [3,2,3] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,3,5,4,6,7,1,8] => [3,3,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,5,4,6,7,8,1] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,3,5,4,7,6,1,8] => [3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,3,5,4,7,6,8,1] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,3,5,4,7,8,6,1] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,3,5,4,8,7,6,1] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,3,5,6,4,1,7,8] => [4,1,3] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,3,5,6,4,1,8,7] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,3,5,6,4,7,1,8] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,3,5,6,4,7,8,1] => [4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,3,5,6,4,8,7,1] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,3,5,6,7,4,1,8] => [5,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,3,5,6,7,4,8,1] => [5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,5,6,7,8,4,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,3,5,6,8,7,4,1] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,3,5,7,6,4,1,8] => [4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,3,5,7,6,4,8,1] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,3,5,7,6,8,4,1] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,3,5,7,8,6,4,1] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,3,6,5,4,1,7,8] => [3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,6,5,4,1,8,7] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,3,6,5,4,7,8,1] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,3,6,5,7,4,1,8] => [3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,3,6,5,7,8,4,1] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,3,6,5,8,7,4,1] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,3,6,7,5,4,1,8] => [4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,3,6,7,5,4,8,1] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,3,6,7,5,8,4,1] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,6,7,8,5,4,1] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,3,6,8,7,5,4,1] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,3,7,6,5,4,1,8] => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,3,7,6,5,4,8,1] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,3,7,6,5,8,4,1] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,3,7,6,8,5,4,1] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,3,7,8,6,5,4,1] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,8,7,6,5,4,1] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [2,4,3,1,5,6,8,7] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [2,4,3,1,5,7,6,8] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [2,4,3,1,5,7,8,6] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,4,3,1,5,8,7,6] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,4,3,1,6,5,7,8] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,4,3,1,6,7,8,5] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,8,7,5] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,3,1,7,6,8,5] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,4,3,1,7,8,6,5] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,4,3,1,8,7,6,5] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,4,3,5,1,6,7,8] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,4,3,5,1,6,8,7] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,4,3,5,1,7,6,8] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,4,3,5,1,7,8,6] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,4,3,5,1,8,7,6] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [2,4,3,5,6,1,7,8] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,4,3,5,6,1,8,7] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,4,3,5,6,7,1,8] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,8,1] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,4,3,5,6,8,7,1] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [2,4,3,5,7,6,1,8] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,4,3,5,7,6,8,1] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,4,3,5,7,8,6,1] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [2,4,3,5,8,7,6,1] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,4,3,6,5,1,7,8] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,3,6,5,1,8,7] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,4,3,6,5,7,1,8] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,4,3,6,5,7,8,1] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,1] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,4,3,6,7,5,8,1] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,4,3,6,7,8,5,1] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,4,3,6,8,7,5,1] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [2,4,3,7,6,5,1,8] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,4,3,7,6,5,8,1] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,4,3,7,6,8,5,1] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [2,4,3,7,8,6,5,1] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,4,3,8,7,6,5,1] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,4,5,3,1,6,7,8] => [3,1,4] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [2,4,5,3,1,6,8,7] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [2,4,5,3,1,7,6,8] => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,4,5,3,1,7,8,6] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,4,5,3,1,8,7,6] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [2,4,5,3,6,1,8,7] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,4,5,3,6,7,1,8] => [3,3,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,4,5,3,6,7,8,1] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,4,5,3,6,8,7,1] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [2,4,5,3,7,6,8,1] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,4,5,3,7,8,6,1] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [2,4,5,3,8,7,6,1] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,4,5,6,3,1,7,8] => [4,1,3] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [2,4,5,6,3,1,8,7] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [2,4,5,6,3,7,1,8] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,4,5,6,3,7,8,1] => [4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,4,5,6,3,8,7,1] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,7,3,1,8] => [5,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,7,3,8,1] => [5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,8,3,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [2,4,5,6,8,7,3,1] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [2,4,5,7,6,3,1,8] => [4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [2,4,5,7,6,3,8,1] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [2,4,5,7,8,6,3,1] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [2,4,6,5,3,1,7,8] => [3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,4,6,5,3,1,8,7] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [2,4,6,5,3,7,1,8] => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,4,6,5,3,7,8,1] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,4,6,5,3,8,7,1] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,4,6,5,7,3,8,1] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [2,4,6,5,7,8,3,1] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,4,6,5,8,7,3,1] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [2,4,6,7,5,3,1,8] => [4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,4,6,7,5,3,8,1] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [2,4,6,7,5,8,3,1] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,4,6,7,8,5,3,1] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,4,6,8,7,5,3,1] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [2,4,7,6,5,3,1,8] => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [2,4,7,6,5,3,8,1] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [2,4,7,6,5,8,3,1] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,4,7,8,6,5,3,1] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,4,8,7,6,5,3,1] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,5,4,3,1,6,7,8] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,5,4,3,1,6,8,7] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,5,4,3,1,7,6,8] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,5,4,3,1,7,8,6] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,5,4,3,1,8,7,6] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [2,5,4,3,6,1,7,8] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,5,4,3,6,1,8,7] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,5,4,3,6,7,1,8] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,5,4,3,6,7,8,1] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,5,4,3,6,8,7,1] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [2,5,4,3,7,6,1,8] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,5,4,3,7,6,8,1] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,5,4,3,7,8,6,1] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,5,4,3,8,7,6,1] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,5,4,6,3,1,7,8] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,5,4,6,3,1,8,7] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,5,4,6,3,7,1,8] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,5,4,6,3,7,8,1] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,5,4,6,7,3,1,8] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,5,4,6,7,3,8,1] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,5,4,6,7,8,3,1] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,5,4,7,6,3,1,8] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,5,4,7,6,3,8,1] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,5,4,7,6,8,3,1] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,5,4,7,8,6,3,1] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,5,4,8,7,6,3,1] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [2,5,6,4,3,1,8,7] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [2,5,6,4,3,7,8,1] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [2,5,6,4,7,3,1,8] => [3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [2,5,6,4,7,3,8,1] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,5,6,4,7,8,3,1] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [2,5,6,4,8,7,3,1] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,5,6,7,4,3,1,8] => [4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,5,6,7,4,3,8,1] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,5,6,7,4,8,3,1] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,5,6,7,8,4,3,1] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,5,6,8,7,4,3,1] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [2,5,7,6,4,3,1,8] => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [2,5,7,6,4,3,8,1] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [2,5,7,6,4,8,3,1] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [2,5,7,6,8,4,3,1] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,5,7,8,6,4,3,1] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,5,8,7,6,4,3,1] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,6,5,4,3,1,8,7] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,6,5,4,3,7,1,8] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,6,5,4,3,7,8,1] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,6,5,4,3,8,7,1] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,6,5,4,7,8,3,1] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,6,5,4,8,7,3,1] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [2,6,5,7,4,3,1,8] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,6,5,7,4,3,8,1] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [2,6,5,7,4,8,3,1] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,6,5,7,8,4,3,1] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,6,5,8,7,4,3,1] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,6,7,5,4,3,1,8] => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [2,6,7,5,4,8,3,1] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,6,7,5,8,4,3,1] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,6,7,8,5,4,3,1] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,6,8,7,5,4,3,1] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,7,6,5,4,3,1,8] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,7,6,5,4,3,8,1] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,7,6,5,4,8,3,1] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,7,6,5,8,4,3,1] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,7,6,8,5,4,3,1] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,7,8,6,5,4,3,1] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,8,7,6,5,4,3,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,6,8,7] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [3,2,1,4,5,7,6,8] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,2,1,4,5,7,8,6] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,2,1,4,5,8,7,6] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [3,2,1,4,6,5,7,8] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [3,2,1,4,6,5,8,7] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [3,2,1,4,6,7,5,8] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,2,1,4,6,7,8,5] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,2,1,4,6,8,7,5] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,2,1,4,7,6,5,8] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [3,2,1,4,7,6,8,5] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,2,1,4,7,8,6,5] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,2,1,4,8,7,6,5] => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,5,4,6,7,8] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [3,2,1,5,4,6,8,7] => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,1,5,4,7,6,8] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [3,2,1,5,4,7,8,6] => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [3,2,1,5,4,8,7,6] => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,2,1,5,6,4,7,8] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [3,2,1,5,6,4,8,7] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [3,2,1,5,6,7,4,8] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,2,1,5,6,7,8,4] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,2,1,5,6,8,7,4] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,2,1,5,7,6,4,8] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [3,2,1,5,7,6,8,4] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,2,1,5,7,8,6,4] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,2,1,5,8,7,6,4] => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [3,2,1,6,5,4,7,8] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,2,1,6,5,4,8,7] => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [3,2,1,6,5,7,4,8] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,2,1,6,5,7,8,4] => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,2,1,6,5,8,7,4] => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [3,2,1,6,7,5,4,8] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,2,1,6,7,5,8,4] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,6,7,8,5,4] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,2,1,6,8,7,5,4] => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,2,1,7,6,5,4,8] => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [3,2,1,7,6,5,8,4] => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,2,1,7,6,8,5,4] => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,1,7,8,6,5,4] => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [3,2,4,1,5,6,8,7] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [3,2,4,1,5,7,6,8] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [3,2,4,1,5,7,8,6] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [3,2,4,1,5,8,7,6] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [3,2,4,1,6,5,7,8] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [3,2,4,1,6,7,5,8] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [3,2,4,1,6,7,8,5] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,2,4,1,6,8,7,5] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [3,2,4,1,7,6,5,8] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,7,6,8,5] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,2,4,1,7,8,6,5] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,2,4,1,8,7,6,5] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,2,4,5,1,6,7,8] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [3,2,4,5,1,6,8,7] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [3,2,4,5,1,7,6,8] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [3,2,4,5,1,7,8,6] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [3,2,4,5,1,8,7,6] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,6,1,7,8] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,1,8] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,6,8,7,1] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [3,2,4,5,7,6,1,8] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [3,2,4,5,7,6,8,1] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,2,4,5,7,8,6,1] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [3,2,4,6,5,1,8,7] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [3,2,4,6,5,7,1,8] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [3,2,4,6,5,8,7,1] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [3,2,4,6,7,5,1,8] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [3,2,4,6,7,5,8,1] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [3,2,4,6,7,8,5,1] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [3,2,4,7,6,5,1,8] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [3,2,4,7,6,5,8,1] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [3,2,4,7,6,8,5,1] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,7,8,6,5,1] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,2,4,8,7,6,5,1] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [3,2,5,4,1,6,7,8] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [3,2,5,4,1,6,8,7] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,2,5,4,1,7,6,8] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [3,2,5,4,1,7,8,6] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,2,5,4,1,8,7,6] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [3,2,5,4,6,1,7,8] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,6,1,8,7] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [3,2,5,4,6,7,1,8] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [3,2,5,4,6,7,8,1] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [3,2,5,4,6,8,7,1] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,7,6,1,8] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,8,1] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,4,7,8,6,1] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [3,2,5,6,4,1,8,7] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [3,2,5,6,4,7,8,1] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [3,2,5,6,7,4,1,8] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [3,2,5,6,7,4,8,1] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [3,2,5,6,7,8,4,1] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [3,2,5,6,8,7,4,1] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [3,2,5,7,6,4,1,8] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,2,5,7,6,4,8,1] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [3,2,5,7,6,8,4,1] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,5,7,8,6,4,1] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,2,5,8,7,6,4,1] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [3,2,6,5,4,1,8,7] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [3,2,6,5,4,7,1,8] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,2,6,5,4,8,7,1] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [3,2,6,5,7,4,1,8] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,2,6,5,7,4,8,1] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [3,2,6,5,7,8,4,1] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [3,2,6,5,8,7,4,1] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,2,6,7,5,4,1,8] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [3,2,6,7,5,4,8,1] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [3,2,6,7,5,8,4,1] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,2,6,8,7,5,4,1] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,2,7,6,5,4,1,8] => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [3,2,7,6,5,4,8,1] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [3,2,7,6,5,8,4,1] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [3,2,7,6,8,5,4,1] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,7,8,6,5,4,1] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,2,8,7,6,5,4,1] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7,8] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [3,4,2,1,5,6,8,7] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [3,4,2,1,5,7,6,8] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [3,4,2,1,5,8,7,6] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [3,4,2,1,6,5,7,8] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [3,4,2,1,6,5,8,7] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [3,4,2,1,6,7,8,5] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [3,4,2,1,6,8,7,5] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [3,4,2,1,7,6,8,5] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [3,4,2,1,7,8,6,5] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [3,4,2,1,8,7,6,5] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [3,4,2,5,1,6,7,8] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [3,4,2,5,1,6,8,7] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [3,4,2,5,1,7,6,8] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [3,4,2,5,1,7,8,6] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [3,4,2,5,1,8,7,6] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [3,4,2,5,6,1,7,8] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [3,4,2,5,6,1,8,7] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [3,4,2,5,6,7,1,8] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,8,1] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [3,4,2,5,6,8,7,1] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [3,4,2,5,7,6,1,8] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [3,4,2,5,7,6,8,1] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [3,4,2,5,7,8,6,1] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [3,4,2,5,8,7,6,1] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [3,4,2,6,5,1,7,8] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [3,4,2,6,5,1,8,7] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [3,4,2,6,5,7,1,8] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [3,4,2,6,5,7,8,1] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [3,4,2,6,5,8,7,1] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [3,4,2,6,7,5,1,8] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [3,4,2,6,7,5,8,1] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [3,4,2,6,7,8,5,1] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [3,4,2,6,8,7,5,1] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [3,4,2,7,6,5,1,8] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [3,4,2,7,6,5,8,1] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [3,4,2,7,6,8,5,1] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [3,4,2,7,8,6,5,1] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,2,8,7,6,5,1] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,5,2,1,6,7,8] => [3,1,4] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [3,4,5,2,1,6,8,7] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [3,4,5,2,1,7,6,8] => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,5,2,1,7,8,6] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,5,2,1,8,7,6] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,5,2,6,1,7,8] => [3,2,3] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,5,2,6,1,8,7] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,5,2,6,7,1,8] => [3,3,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,5,2,6,7,8,1] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [3,4,5,2,6,8,7,1] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [3,4,5,2,7,6,1,8] => [3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [3,4,5,2,7,6,8,1] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,5,2,7,8,6,1] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [3,4,5,2,8,7,6,1] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,6,2,1,7,8] => [4,1,3] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,6,2,1,8,7] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,6,2,7,1,8] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,6,2,7,8,1] => [4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,6,2,8,7,1] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,7,2,1,8] => [5,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,7,2,8,1] => [5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,2,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,6,8,7,2,1] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [3,4,5,7,6,2,8,1] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,5,7,6,8,2,1] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,5,7,8,6,2,1] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,8,7,6,2,1] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [3,4,6,5,2,1,8,7] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [3,4,6,5,2,7,1,8] => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [3,4,6,5,2,7,8,1] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [3,4,6,5,7,2,8,1] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [3,4,6,5,7,8,2,1] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [3,4,6,5,8,7,2,1] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [3,4,6,7,5,2,8,1] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [3,4,6,7,5,8,2,1] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [3,4,6,7,8,5,2,1] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,4,6,8,7,5,2,1] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [3,4,7,6,5,2,1,8] => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [3,4,7,6,5,2,8,1] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [3,4,7,6,5,8,2,1] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [3,4,7,6,8,5,2,1] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,4,7,8,6,5,2,1] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,8,7,6,5,2,1] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [3,5,4,2,1,6,7,8] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [3,5,4,2,1,6,8,7] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [3,5,4,2,1,7,6,8] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [3,5,4,2,1,7,8,6] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [3,5,4,2,1,8,7,6] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [3,5,4,2,6,1,7,8] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [3,5,4,2,6,1,8,7] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [3,5,4,2,6,7,1,8] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [3,5,4,2,6,7,8,1] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [3,5,4,2,6,8,7,1] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [3,5,4,2,7,6,1,8] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [3,5,4,2,7,6,8,1] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [3,5,4,2,7,8,6,1] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [3,5,4,6,2,1,7,8] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [3,5,4,6,2,1,8,7] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [3,5,4,6,2,7,1,8] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [3,5,4,6,2,7,8,1] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [3,5,4,6,2,8,7,1] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [3,5,4,6,7,2,8,1] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [3,5,4,6,7,8,2,1] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [3,5,4,6,8,7,2,1] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [3,5,4,7,6,2,1,8] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [3,5,4,7,6,2,8,1] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [3,5,4,7,6,8,2,1] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [3,5,4,7,8,6,2,1] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,5,4,8,7,6,2,1] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [3,5,6,4,2,1,7,8] => [3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [3,5,6,4,2,1,8,7] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [3,5,6,4,2,7,1,8] => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [3,5,6,4,2,7,8,1] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [3,5,6,4,2,8,7,1] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [3,5,6,4,7,2,1,8] => [3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [3,5,6,4,7,2,8,1] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [3,5,6,4,7,8,2,1] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [3,5,6,4,8,7,2,1] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [3,5,6,7,4,2,1,8] => [4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [3,5,6,7,4,2,8,1] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [3,5,6,7,4,8,2,1] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [3,5,6,7,8,4,2,1] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,5,6,8,7,4,2,1] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [3,5,7,6,4,2,1,8] => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [3,5,7,6,4,2,8,1] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [3,5,7,6,4,8,2,1] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [3,5,7,6,8,4,2,1] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,5,7,8,6,4,2,1] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [3,5,8,7,6,4,2,1] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [3,6,5,4,2,1,7,8] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [3,6,5,4,2,1,8,7] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [3,6,5,4,2,7,1,8] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [3,6,5,4,2,7,8,1] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [3,6,5,4,2,8,7,1] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [3,6,5,4,7,2,1,8] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [3,6,5,4,7,2,8,1] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [3,6,5,4,7,8,2,1] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [3,6,5,4,8,7,2,1] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [3,6,5,7,4,2,8,1] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [3,6,5,7,4,8,2,1] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [3,6,5,7,8,4,2,1] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,6,5,8,7,4,2,1] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [3,6,7,5,4,2,8,1] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [3,6,7,5,4,8,2,1] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [3,6,7,5,8,4,2,1] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,6,7,8,5,4,2,1] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [3,6,8,7,5,4,2,1] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [3,7,6,5,4,2,1,8] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [3,7,6,5,4,2,8,1] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [3,7,6,5,4,8,2,1] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [3,7,6,5,8,4,2,1] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,7,6,8,5,4,2,1] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,7,8,6,5,4,2,1] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,8,7,6,5,4,2,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,3,2,1,5,6,8,7] => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,3,2,1,5,7,6,8] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,3,2,1,5,7,8,6] => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,3,2,1,5,8,7,6] => [1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,3,2,1,6,5,7,8] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,3,2,1,6,7,5,8] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,3,2,1,6,7,8,5] => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,3,2,1,6,8,7,5] => [1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,3,2,1,7,6,5,8] => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,3,2,1,7,6,8,5] => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,2,1,7,8,6,5] => [1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,3,2,5,1,6,7,8] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [4,3,2,5,1,6,8,7] => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [4,3,2,5,1,7,6,8] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,3,2,5,1,7,8,6] => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,3,2,5,1,8,7,6] => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [4,3,2,5,6,1,7,8] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [4,3,2,5,6,1,8,7] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,3,2,5,6,7,1,8] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,1] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [4,3,2,5,6,8,7,1] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [4,3,2,5,7,6,1,8] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [4,3,2,5,7,6,8,1] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [4,3,2,5,7,8,6,1] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,3,2,5,8,7,6,1] => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [4,3,2,6,5,1,7,8] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [4,3,2,6,5,1,8,7] => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [4,3,2,6,5,7,1,8] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [4,3,2,6,5,7,8,1] => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [4,3,2,6,5,8,7,1] => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [4,3,2,6,7,5,1,8] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [4,3,2,6,7,5,8,1] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,6,7,8,5,1] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,3,2,6,8,7,5,1] => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [4,3,2,7,6,5,1,8] => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [4,3,2,7,6,5,8,1] => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,2,7,8,6,5,1] => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,3,2,8,7,6,5,1] => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [4,3,5,2,1,6,7,8] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [4,3,5,2,1,6,8,7] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [4,3,5,2,1,7,6,8] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [4,3,5,2,1,7,8,6] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [4,3,5,2,1,8,7,6] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [4,3,5,2,6,1,7,8] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,3,5,2,6,1,8,7] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [4,3,5,2,6,7,8,1] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [4,3,5,2,6,8,7,1] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [4,3,5,2,7,6,1,8] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,3,5,2,7,6,8,1] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [4,3,5,6,2,1,7,8] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [4,3,5,6,2,1,8,7] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [4,3,5,6,2,7,1,8] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [4,3,5,6,2,7,8,1] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [4,3,5,6,7,2,8,1] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [4,3,5,6,7,8,2,1] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,3,5,6,8,7,2,1] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [4,3,5,7,6,2,1,8] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [4,3,5,7,6,2,8,1] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [4,3,5,7,6,8,2,1] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,5,7,8,6,2,1] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [4,3,5,8,7,6,2,1] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [4,3,6,5,2,1,7,8] => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [4,3,6,5,2,1,8,7] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [4,3,6,5,2,7,1,8] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [4,3,6,5,2,7,8,1] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [4,3,6,5,2,8,7,1] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [4,3,6,5,7,2,1,8] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,3,6,5,7,2,8,1] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [4,3,6,5,7,8,2,1] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,8,7,2,1] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [4,3,6,7,5,2,8,1] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [4,3,6,7,5,8,2,1] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,6,7,8,5,2,1] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [4,3,6,8,7,5,2,1] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [4,3,7,6,5,2,1,8] => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [4,3,7,6,5,2,8,1] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [4,3,7,6,5,8,2,1] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,3,7,6,8,5,2,1] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,7,8,6,5,2,1] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [4,3,8,7,6,5,2,1] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [4,5,3,2,1,6,7,8] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [4,5,3,2,1,6,8,7] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [4,5,3,2,1,7,6,8] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [4,5,3,2,1,7,8,6] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [4,5,3,2,1,8,7,6] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [4,5,3,2,6,1,7,8] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [4,5,3,2,6,1,8,7] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [4,5,3,2,6,7,1,8] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [4,5,3,2,6,7,8,1] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [4,5,3,2,6,8,7,1] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [4,5,3,2,7,6,1,8] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [4,5,3,2,7,6,8,1] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [4,5,3,2,7,8,6,1] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,5,3,2,8,7,6,1] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [4,5,3,6,2,1,7,8] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [4,5,3,6,2,1,8,7] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [4,5,3,6,2,7,1,8] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [4,5,3,6,2,7,8,1] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [4,5,3,6,2,8,7,1] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [4,5,3,6,7,2,1,8] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [4,5,3,6,7,2,8,1] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [4,5,3,6,7,8,2,1] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,5,3,6,8,7,2,1] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [4,5,3,7,6,2,1,8] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [4,5,3,7,6,2,8,1] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [4,5,3,7,6,8,2,1] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,5,3,7,8,6,2,1] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,5,3,8,7,6,2,1] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [4,5,6,3,2,1,7,8] => [3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [4,5,6,3,2,1,8,7] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [4,5,6,3,2,7,8,1] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [4,5,6,3,2,8,7,1] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [4,5,6,3,7,2,1,8] => [3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [4,5,6,3,7,2,8,1] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [4,5,6,3,7,8,2,1] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,5,6,3,8,7,2,1] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,7,3,2,1,8] => [4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,7,3,2,8,1] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,7,3,8,2,1] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,3,2,1] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,6,8,7,3,2,1] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [4,5,7,6,3,2,1,8] => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [4,5,7,6,3,2,8,1] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [4,5,7,6,3,8,2,1] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,5,7,6,8,3,2,1] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,5,7,8,6,3,2,1] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [4,5,8,7,6,3,2,1] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [4,6,5,3,2,1,8,7] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [4,6,5,3,2,7,8,1] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [4,6,5,3,2,8,7,1] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [4,6,5,3,7,2,1,8] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [4,6,5,3,7,2,8,1] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [4,6,5,3,7,8,2,1] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,6,5,3,8,7,2,1] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [4,6,5,7,3,2,1,8] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [4,6,5,7,3,2,8,1] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [4,6,5,7,3,8,2,1] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,6,5,7,8,3,2,1] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,6,5,8,7,3,2,1] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [4,6,7,5,3,2,1,8] => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [4,6,7,5,3,2,8,1] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [4,6,7,5,3,8,2,1] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,6,7,5,8,3,2,1] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,6,7,8,5,3,2,1] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [4,6,8,7,5,3,2,1] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [4,7,6,5,3,2,1,8] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [4,7,6,5,3,2,8,1] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [4,7,6,5,3,8,2,1] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,7,6,5,8,3,2,1] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [4,7,6,8,5,3,2,1] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [4,7,8,6,5,3,2,1] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [4,8,7,6,5,3,2,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,4,3,2,1,6,8,7] => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,4,3,2,1,7,6,8] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,4,3,2,1,7,8,6] => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [5,4,3,2,6,1,7,8] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,4,3,2,6,1,8,7] => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [5,4,3,2,6,7,1,8] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,1] => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,4,3,2,6,8,7,1] => [1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [5,4,3,2,7,6,1,8] => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [5,4,3,2,7,6,8,1] => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,3,2,7,8,6,1] => [1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,4,3,2,8,7,6,1] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [5,4,3,6,2,1,7,8] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [5,4,3,6,2,1,8,7] => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [5,4,3,6,2,7,1,8] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [5,4,3,6,2,7,8,1] => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,4,3,6,2,8,7,1] => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [5,4,3,6,7,2,1,8] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [5,4,3,6,7,2,8,1] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3,6,7,8,2,1] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [5,4,3,6,8,7,2,1] => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [5,4,3,7,6,2,1,8] => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [5,4,3,7,6,2,8,1] => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,4,3,7,6,8,2,1] => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [5,4,3,7,8,6,2,1] => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [5,4,3,8,7,6,2,1] => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [5,4,6,3,2,1,7,8] => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [5,4,6,3,2,1,8,7] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [5,4,6,3,2,7,1,8] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [5,4,6,3,2,7,8,1] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,4,6,3,2,8,7,1] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [5,4,6,3,7,2,1,8] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,4,6,3,7,2,8,1] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [5,4,6,3,7,8,2,1] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [5,4,6,3,8,7,2,1] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [5,4,6,7,3,2,1,8] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [5,4,6,7,3,2,8,1] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,4,6,7,3,8,2,1] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,6,7,8,3,2,1] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [5,4,6,8,7,3,2,1] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [5,4,7,6,3,2,1,8] => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [5,4,7,6,3,2,8,1] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,4,7,6,3,8,2,1] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [5,4,7,6,8,3,2,1] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [5,4,7,8,6,3,2,1] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [5,4,8,7,6,3,2,1] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [5,6,4,3,2,1,7,8] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [5,6,4,3,2,1,8,7] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [5,6,4,3,2,8,7,1] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [5,6,4,3,7,2,1,8] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [5,6,4,3,7,2,8,1] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,6,4,3,7,8,2,1] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [5,6,4,3,8,7,2,1] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [5,6,4,7,3,2,1,8] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [5,6,4,7,3,2,8,1] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,6,4,7,3,8,2,1] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,6,4,7,8,3,2,1] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [5,6,4,8,7,3,2,1] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [5,6,7,4,3,2,1,8] => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [5,6,7,4,3,2,8,1] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,6,7,4,3,8,2,1] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,6,7,4,8,3,2,1] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,4,3,2,1] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [5,6,8,7,4,3,2,1] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [5,7,6,4,3,2,1,8] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [5,7,6,4,3,2,8,1] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,7,6,4,3,8,2,1] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,7,6,4,8,3,2,1] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [5,7,6,8,4,3,2,1] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [5,7,8,6,4,3,2,1] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [5,8,7,6,4,3,2,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,5,4,3,2,1,7,8] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,5,4,3,2,7,1,8] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5,4,3,2,7,8,1] => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,5,4,3,2,8,7,1] => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [6,5,4,3,7,2,1,8] => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,5,4,3,7,2,8,1] => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,4,3,7,8,2,1] => [1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [6,5,4,3,8,7,2,1] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [6,5,4,7,3,2,1,8] => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,5,4,7,3,2,8,1] => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,5,4,7,3,8,2,1] => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [6,5,4,7,8,3,2,1] => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [6,5,4,8,7,3,2,1] => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [6,5,7,4,3,2,1,8] => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,5,7,4,3,2,8,1] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,5,7,4,3,8,2,1] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [6,5,7,4,8,3,2,1] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [6,5,7,8,4,3,2,1] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [6,5,8,7,4,3,2,1] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [6,7,5,4,3,2,1,8] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,7,5,4,3,2,8,1] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [6,7,5,4,3,8,2,1] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [6,7,5,4,8,3,2,1] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [6,7,5,8,4,3,2,1] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,5,4,3,2,1] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [6,8,7,5,4,3,2,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,6,5,4,3,2,8,1] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [7,6,5,4,3,8,2,1] => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [7,6,5,4,8,3,2,1] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [7,6,5,8,4,3,2,1] => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [7,6,8,5,4,3,2,1] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [7,8,6,5,4,3,2,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
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Generating function
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Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
4,1 10,4 27,15 79,50,3 240,168,21
$F_{1} = 1$
$F_{2} = 2$
$F_{3} = 4 + q$
$F_{4} = 10 + 4\ q$
$F_{5} = 27 + 15\ q$
$F_{6} = 79 + 50\ q + 3\ q^{2}$
$F_{7} = 240 + 168\ q + 21\ q^{2}$
Description
Number of simple modules that are 3-regular in the corresponding Nakayama algebra.
Map
descent composition
Description
The descent composition of a permutation.
The descent composition of a permutation $\pi$ of length $n$ is the integer composition of $n$ whose descent set equals the descent set of $\pi$. The descent set of a permutation $\pi$ is $\{i \mid 1 \leq i < n, \pi(i) > \pi(i+1)\}$. The descent set of a composition $c = (i_1, i_2, \ldots, i_k)$ is the set $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.
The descent composition of a permutation $\pi$ of length $n$ is the integer composition of $n$ whose descent set equals the descent set of $\pi$. The descent set of a permutation $\pi$ is $\{i \mid 1 \leq i < n, \pi(i) > \pi(i+1)\}$. The descent set of a composition $c = (i_1, i_2, \ldots, i_k)$ is the set $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.
Map
bounce path
Description
The bounce path determined by an integer composition.
Map
to 312-avoiding permutation
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