Identifier
-
Mp00129:
Dyck paths
—to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶
Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00030: Dyck paths —zeta map⟶ Dyck paths
St000386: Dyck paths ⟶ ℤ
Values
[1,0] => [1] => [1,0] => [1,0] => 0
[1,0,1,0] => [2,1] => [1,1,0,0] => [1,0,1,0] => 0
[1,1,0,0] => [1,2] => [1,0,1,0] => [1,1,0,0] => 0
[1,0,1,0,1,0] => [2,3,1] => [1,1,0,1,0,0] => [1,1,0,0,1,0] => 1
[1,0,1,1,0,0] => [2,1,3] => [1,1,0,0,1,0] => [1,1,0,1,0,0] => 0
[1,1,0,0,1,0] => [1,3,2] => [1,0,1,1,0,0] => [1,0,1,1,0,0] => 0
[1,1,0,1,0,0] => [3,1,2] => [1,1,1,0,0,0] => [1,0,1,0,1,0] => 0
[1,1,1,0,0,0] => [1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[1,0,1,0,1,0,1,0] => [2,3,4,1] => [1,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0] => 1
[1,0,1,0,1,1,0,0] => [2,3,1,4] => [1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 1
[1,0,1,1,0,0,1,0] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0] => 0
[1,0,1,1,0,1,0,0] => [2,4,1,3] => [1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,0,0,0] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0] => 0
[1,1,0,0,1,0,1,0] => [1,3,4,2] => [1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,0] => [1,3,2,4] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 0
[1,1,0,1,0,0,1,0] => [3,1,4,2] => [1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,0] => [3,4,1,2] => [1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,0] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0] => 0
[1,1,1,0,0,0,1,0] => [1,2,4,3] => [1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,1,0,0] => [1,4,2,3] => [1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0] => 0
[1,1,1,0,1,0,0,0] => [4,1,2,3] => [1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,0] => [2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,0] => [2,3,5,1,4] => [1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,0] => [2,3,1,4,5] => [1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0] => [2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,1,0,0] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0] => 0
[1,0,1,1,0,1,0,0,1,0] => [2,4,1,5,3] => [1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,0] => [2,4,5,1,3] => [1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,1,1,0,0,0] => [2,4,1,3,5] => [1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,0] => [2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 0
[1,0,1,1,1,0,0,1,0,0] => [2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0] => 0
[1,0,1,1,1,0,1,0,0,0] => [2,5,1,3,4] => [1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 0
[1,1,0,0,1,1,0,1,0,0] => [1,3,5,2,4] => [1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,0] => [1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,0] => [3,1,4,5,2] => [1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,0] => [3,1,4,2,5] => [1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,0] => [3,4,1,5,2] => [1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,0] => [3,4,5,1,2] => [1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,0,0,0] => [3,4,1,2,5] => [1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,0,1,0] => [3,1,2,5,4] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,1,1,0,0,1,0,0] => [3,1,5,2,4] => [1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,0] => [3,5,1,2,4] => [1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,0,0,0] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,0] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,0] => [1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,0] => [1,4,5,2,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,1,1,0,0,0] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,0] => [4,1,2,5,3] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,0] => [4,1,5,2,3] => [1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,0] => [4,5,1,2,3] => [1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,0] => [4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,0,0,0,0,1,0] => [1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,0,0] => [1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,0,1,0,0,0] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,0,1,0,0,0,0] => [5,1,2,3,4] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,1,6] => [1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,1,6,5] => [1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,6,1,5] => [1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,6] => [1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,1,5,6,4] => [1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,6] => [1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,5,1,6,4] => [1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,5,6,1,4] => [1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,0,1,1,0,1,1,0,0,0] => [2,3,5,1,4,6] => [1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,1,4,6,5] => [1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,6,4,5] => [1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,6,1,4,5] => [1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,5,6] => [1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,5,6,3] => [1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6] => [1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 0
[1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,6,3,5] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,5,6] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 0
[1,0,1,1,0,1,0,0,1,0,1,0] => [2,4,1,5,6,3] => [1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,0] => [2,4,1,5,3,6] => [1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [2,4,5,1,6,3] => [1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,5,6,1,3] => [1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,1,0,0,0] => [2,4,5,1,3,6] => [1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,0,0,1,0] => [2,4,1,3,6,5] => [1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => [2,4,1,6,3,5] => [1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,0] => [2,4,6,1,3,5] => [1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,4,1,3,5,6] => [1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,5,6,4] => [1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,5,4,6] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,3,6,4] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,6,3,4] => [1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,3,4,6] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,0,1,0] => [2,5,1,3,6,4] => [1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [2,5,1,6,3,4] => [1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,1,0,0,0] => [2,5,6,1,3,4] => [1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,5,1,3,4,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => 1
>>> Load all 1309 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,3,4,6,5] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,1,0,0] => [2,1,3,6,4,5] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,3,4,5] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,6,1,3,4,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,2] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,5,2,6] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,6,5] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,6,2,5] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,4,2,5,6] => [1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,6,4] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,6] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 0
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,5,2,6,4] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,5,6,2,4] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,5,2,4,6] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,4,6,5] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 0
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,4,5] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => 0
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,6,2,4,5] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,4,5,6] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,4,5,6,2] => [1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [3,1,4,5,2,6] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [3,1,4,6,2,5] => [1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,1,4,2,5,6] => [1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => [3,4,1,5,6,2] => [1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,0] => [3,4,1,5,2,6] => [1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,1,6,2] => [1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,1,2] => [1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,1,2,6] => [1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,0,0,1,0] => [3,4,1,2,6,5] => [1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => [3,4,1,6,2,5] => [1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 2
[1,1,0,1,0,1,1,0,1,0,0,0] => [3,4,6,1,2,5] => [1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,1,2,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,0] => [3,1,2,5,6,4] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 0
[1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,6,4] => [1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => [3,1,5,6,2,4] => [1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 2
[1,1,0,1,1,0,0,1,1,0,0,0] => [3,1,5,2,4,6] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,0] => [3,5,1,2,6,4] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 2
[1,1,0,1,1,0,1,0,0,1,0,0] => [3,5,1,6,2,4] => [1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,0] => [3,5,6,1,2,4] => [1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,5,1,2,4,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,4,6,5] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 0
[1,1,0,1,1,1,0,0,0,1,0,0] => [3,1,2,6,4,5] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,6,2,4,5] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,6,1,2,4,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,1,0,0,0,0,0] => [3,1,2,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,4,5,6,3] => [1,0,1,0,1,1,0,1,0,1,0,0] => [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] => [1,2,4,5,3,6] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,4,6,3,5] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,2,5,6,3] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,5,3,6] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,5,2,6,3] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,5,6,2,3] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,3,6] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,3,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 0
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,5] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,6,2,3,5] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,2,3,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,2,5,6,3] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,1,2,5,3,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,1,5,2,6,3] => [1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,1,5,6,2,3] => [1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,1,5,2,3,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,0] => [4,5,1,2,6,3] => [1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,1,0,0,1,0,0] => [4,5,1,6,2,3] => [1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 2
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,5,6,1,2,3] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,1,2,3,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,2,6,3,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,1,6,2,3,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,0] => [4,6,1,2,3,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,0] => [4,1,2,3,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,3,5,6,4] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,3,5,4,6] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,2,5,3,6,4] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,5,6,3,4] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,5,3,4,6] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,2,3,6,4] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,2,6,3,4] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,6,2,3,4] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1,2,3,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,1,2,6,3,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,0] => [5,1,6,2,3,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,0,0,0] => [5,6,1,2,3,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,0] => [5,1,2,3,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,3,4,6,5] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,3,6,4,5] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,0] => [6,1,2,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [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] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,1,7] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,7,1,6] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,5,1,6,7] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,7,5] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,7] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,4,6,1,7,5] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,4,6,7,1,5] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,3,4,6,1,5,7] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,4,1,5,7,6] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,5,6] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,4,7,1,5,6] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,4,1,5,6,7] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,6,7,4] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,3,1,5,6,4,7] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,3,1,5,7,4,6] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,3,1,5,4,6,7] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,3,5,1,6,7,4] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,3,5,1,6,4,7] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,3,5,6,1,7,4] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,5,6,7,1,4] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,3,5,6,1,4,7] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [2,3,5,1,4,7,6] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,3,5,1,7,4,6] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,3,5,7,1,4,6] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,3,5,1,4,6,7] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,4,6,7,5] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,3,1,4,6,5,7] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,4,7,5] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,6,7,4,5] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,4,5,7] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,3,6,1,4,7,5] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,3,6,1,7,4,5] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,3,6,7,1,4,5] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,3,6,1,4,5,7] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,3,1,4,5,7,6] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,4,7,5,6] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,3,1,7,4,5,6] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,7,1,4,5,6] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,5,6,7,3] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,5,6,3,7] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,4,5,3,7,6] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,5,7,3,6] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,5,3,6,7] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,7] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 0
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,6,3,7,5] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,6,7,3,5] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,3,5,7] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,4,3,5,7,6] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 0
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,5,6] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 0
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,7,3,5,6] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,5,6,7] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,4,1,5,6,7,3] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,4,1,5,6,3,7] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,4,1,5,3,7,6] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,4,1,5,7,3,6] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,4,1,5,3,6,7] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,4,5,1,6,7,3] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,4,5,1,6,3,7] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,4,5,6,1,7,3] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,4,5,6,7,1,3] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,4,5,6,1,3,7] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,4,5,1,3,7,6] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,4,5,1,7,3,6] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,4,5,7,1,3,6] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,4,5,1,3,6,7] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,1,3,6,7,5] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,1,3,6,5,7] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,1,6,3,7,5] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,1,6,7,3,5] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,5,7] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,6,1,3,7,5] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,6,1,7,3,5] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,6,7,1,3,5] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,1,3,5,7] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,4,1,3,5,7,6] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,4,1,3,7,5,6] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,4,1,7,3,5,6] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,4,7,1,3,5,6] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,4,1,3,5,6,7] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,3,5,6,7,4] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,3,5,6,4,7] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,3,5,4,7,6] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 0
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,1,3,5,7,4,6] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,3,5,4,6,7] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,1,5,3,6,7,4] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,3,6,4,7] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,5,6,3,7,4] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,6,7,3,4] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,5,6,3,4,7] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,1,5,3,4,7,6] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,3,7,4,6] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,7,3,4,6] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,3,4,6,7] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,5,1,3,6,7,4] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,5,1,3,6,4,7] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,5,1,6,3,7,4] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,5,1,6,7,3,4] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,5,1,6,3,4,7] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,5,6,1,3,7,4] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,5,6,1,7,3,4] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,5,6,7,1,3,4] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,5,6,1,3,4,7] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,5,1,3,4,7,6] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,5,1,3,7,4,6] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,5,1,7,3,4,6] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,5,7,1,3,4,6] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,5,1,3,4,6,7] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,1,3,4,6,7,5] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,3,4,6,5,7] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,1,3,6,4,7,5] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,1,3,6,7,4,5] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,1,3,6,4,5,7] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,1,6,3,4,7,5] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,6,3,7,4,5] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,6,7,3,4,5] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,6,3,4,5,7] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,6,1,3,4,7,5] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,6,1,3,7,4,5] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,6,1,7,3,4,5] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,6,7,1,3,4,5] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,6,1,3,4,5,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,3,4,5,7,6] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,3,4,7,5,6] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,3,7,4,5,6] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,7,3,4,5,6] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,7,1,3,4,5,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,2] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,4,5,6,2,7] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,4,5,7,2,6] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,4,5,2,6,7] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,4,2,6,7,5] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,7] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,3,4,6,2,7,5] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,4,6,7,2,5] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,4,6,2,5,7] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,4,2,5,7,6] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,5,6] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,3,4,7,2,5,6] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,4,2,5,6,7] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,6,7,4] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,5,6,4,7] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,7,4,6] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,6,7] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 0
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,3,5,2,6,7,4] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,5,2,6,4,7] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,5,6,2,7,4] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,5,6,7,2,4] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,3,5,6,2,4,7] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,2,4,7,6] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,2,7,4,6] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,7,2,4,6] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,5,2,4,6,7] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,4,6,7,5] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,4,6,5,7] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,4,7,5] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,7,4,5] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,4,5,7] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 0
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,3,6,2,4,7,5] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,6,2,7,4,5] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,3,6,7,2,4,5] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,6,2,4,5,7] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,4,5,7,6] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,4,7,5,6] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,7,4,5,6] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 0
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,3,7,2,4,5,6] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,4,5,6,7] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,2] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,1,4,5,6,2,7] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,4,5,2,7,6] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [3,1,4,5,7,2,6] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,1,4,5,2,6,7] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,4,2,6,7,5] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,4,2,6,5,7] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [3,1,4,6,2,7,5] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,1,4,6,7,2,5] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [3,1,4,6,2,5,7] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,1,4,2,5,7,6] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,1,4,2,7,5,6] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [3,1,4,7,2,5,6] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,1,4,2,5,6,7] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,4,1,5,6,7,2] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [3,4,1,5,6,2,7] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,4,1,5,2,7,6] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [3,4,1,5,7,2,6] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [3,4,1,5,2,6,7] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,4,5,1,6,7,2] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,4,5,1,6,2,7] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,6,1,7,2] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,1,2] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,6,1,2,7] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [3,4,5,1,2,7,6] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [3,4,5,1,7,2,6] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [3,4,5,7,1,2,6] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6,7] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [3,4,1,2,6,7,5] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [3,4,1,2,6,5,7] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [3,4,1,6,2,7,5] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 2
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [3,4,1,6,7,2,5] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 3
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [3,4,1,6,2,5,7] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 2
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [3,4,6,1,2,7,5] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 2
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [3,4,6,1,7,2,5] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [3,4,6,7,1,2,5] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,4,6,1,2,5,7] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [3,4,1,2,5,7,6] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [3,4,1,2,7,5,6] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [3,4,1,7,2,5,6] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 2
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,4,7,1,2,5,6] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,1,2,5,6,7] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [3,1,2,5,6,7,4] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2,5,6,4,7] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,2,5,4,7,6] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 0
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [3,1,2,5,7,4,6] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [3,1,2,5,4,6,7] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [3,1,5,2,6,7,4] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [3,1,5,2,6,4,7] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [3,1,5,6,2,7,4] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [3,1,5,6,7,2,4] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 2
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [3,1,5,6,2,4,7] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [3,1,5,2,4,7,6] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,7,4,6] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [3,1,5,7,2,4,6] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 2
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,1,5,2,4,6,7] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [3,5,1,2,6,7,4] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [3,5,1,2,6,4,7] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [3,5,1,6,2,7,4] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 2
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [3,5,1,6,7,2,4] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [3,5,1,6,2,4,7] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [3,5,6,1,2,7,4] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [3,5,6,1,7,2,4] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [3,5,6,7,1,2,4] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,5,6,1,2,4,7] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [3,5,1,2,4,7,6] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [3,5,1,2,7,4,6] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 2
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [3,5,1,7,2,4,6] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,5,7,1,2,4,6] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,5,1,2,4,6,7] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [3,1,2,4,6,7,5] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [3,1,2,4,6,5,7] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [3,1,2,6,4,7,5] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [3,1,2,6,7,4,5] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [3,1,2,6,4,5,7] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 0
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [3,1,6,2,4,7,5] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [3,1,6,2,7,4,5] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 2
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [3,1,6,7,2,4,5] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,1,6,2,4,5,7] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [3,6,1,2,4,7,5] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [3,6,1,2,7,4,5] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [3,6,1,7,2,4,5] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,6,7,1,2,4,5] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,6,1,2,4,5,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,2,4,5,7,6] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [3,1,2,4,7,5,6] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [3,1,2,7,4,5,6] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,7,2,4,5,6] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,7,1,2,4,5,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,4,5,6,7] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,7,3] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,2,4,5,6,3,7] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,2,4,5,7,3,6] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,2,4,5,3,6,7] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,7,5] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,7] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,2,4,6,3,7,5] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,2,4,6,7,3,5] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,2,4,6,3,5,7] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,2,4,3,5,7,6] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,5,6] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,2,4,7,3,5,6] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,5,6,7] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,4,2,5,6,7,3] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,4,2,5,6,3,7] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,2,5,3,7,6] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,4,2,5,7,3,6] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,4,2,5,3,6,7] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,5,2,6,7,3] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,4,5,2,6,3,7] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,4,5,6,2,7,3] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,5,6,7,2,3] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,4,5,6,2,3,7] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,5,2,3,7,6] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,5,2,7,3,6] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,5,7,2,3,6] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,5,2,3,6,7] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,2,3,6,7,5] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5,7] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,2,6,3,7,5] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,2,6,7,3,5] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,2,6,3,5,7] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,4,6,2,3,7,5] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,4,6,2,7,3,5] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,6,7,2,3,5] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,6,2,3,5,7] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,4,2,3,5,7,6] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,4,2,3,7,5,6] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,2,7,3,5,6] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,7,2,3,5,6] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,2,3,5,6,7] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,1,2,5,6,7,3] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,1,2,5,6,3,7] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,1,2,5,3,7,6] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,1,2,5,7,3,6] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,1,2,5,3,6,7] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,1,5,2,6,7,3] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,1,5,2,6,3,7] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,1,5,6,2,7,3] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [4,1,5,6,7,2,3] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,1,5,6,2,3,7] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,1,5,2,3,7,6] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [4,1,5,2,7,3,6] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,1,5,7,2,3,6] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,1,5,2,3,6,7] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [4,5,1,2,6,7,3] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 2
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [4,5,1,2,6,3,7] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [4,5,1,6,2,7,3] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [4,5,1,6,7,2,3] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 2
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [4,5,1,6,2,3,7] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [4,5,6,1,2,7,3] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [4,5,6,1,7,2,3] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,5,6,7,1,2,3] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [4,5,1,2,3,7,6] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [4,5,1,2,7,3,6] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,5,1,7,2,3,6] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,5,7,1,2,3,6] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,1,2,3,6,7] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [4,1,2,3,6,7,5] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,6,5,7] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [4,1,2,6,3,7,5] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [4,1,2,6,7,3,5] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,1,2,6,3,5,7] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [4,1,6,2,3,7,5] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [4,1,6,2,7,3,5] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,1,6,7,2,3,5] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,1,6,2,3,5,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [4,6,1,2,3,7,5] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [4,6,1,2,7,3,5] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,6,1,7,2,3,5] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,6,7,1,2,3,5] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [4,6,1,2,3,5,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [4,1,2,3,5,7,6] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [4,1,2,3,7,5,6] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,2,7,3,5,6] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,1,7,2,3,5,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,7,1,2,3,5,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [4,1,2,3,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,2,3,5,6,7,4] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,2,3,5,6,4,7] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,2,3,5,7,4,6] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,2,3,5,4,6,7] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,2,5,3,6,7,4] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,2,5,3,6,4,7] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,2,5,6,3,7,4] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,2,5,6,7,3,4] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,2,5,6,3,4,7] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,2,5,3,4,7,6] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,2,5,3,7,4,6] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,2,5,7,3,4,6] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,2,5,3,4,6,7] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,5,2,3,6,7,4] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,5,2,3,6,4,7] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,5,2,6,3,7,4] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,5,2,6,7,3,4] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,5,2,6,3,4,7] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,5,6,2,3,7,4] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,5,6,2,7,3,4] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,5,6,7,2,3,4] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,5,6,2,3,4,7] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,2,3,4,7,6] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,5,2,3,7,4,6] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,5,2,7,3,4,6] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,5,7,2,3,4,6] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,5,2,3,4,6,7] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,1,2,3,6,7,4] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,1,2,3,6,4,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,1,2,6,3,7,4] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 2
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,1,2,6,7,3,4] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,1,2,6,3,4,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [5,1,6,2,3,7,4] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,1,6,2,7,3,4] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 2
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,1,6,7,2,3,4] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [5,1,6,2,3,4,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [5,6,1,2,3,7,4] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,6,1,2,7,3,4] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,6,1,7,2,3,4] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,6,7,1,2,3,4] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [5,6,1,2,3,4,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,2,3,7,4,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,1,2,7,3,4,6] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [5,1,7,2,3,4,6] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [5,7,1,2,3,4,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [5,1,2,3,4,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,2,3,4,6,7,5] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,2,3,4,6,5,7] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,2,3,6,7,4,5] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,2,3,6,4,5,7] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,2,6,3,4,7,5] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,2,6,3,7,4,5] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,2,6,7,3,4,5] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,2,6,3,4,5,7] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,2,3,4,7,5] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,2,3,7,4,5] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,6,2,7,3,4,5] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,6,7,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,6,2,3,4,5,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,1,2,3,7,4,5] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [6,1,2,7,3,4,5] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [6,1,7,2,3,4,5] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [6,7,1,2,3,4,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [6,1,2,3,4,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,2,3,4,5,7,6] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,2,3,4,7,5,6] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,2,3,7,4,5,6] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,2,7,3,4,5,6] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7,1,2,3,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,7,1,8] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,5,6,1,8,7] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,6,8,1,7] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,5,6,1,7,8] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,4,5,1,7,8,6] => [1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,4,5,7,8,1,6] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,3,4,5,7,1,6,8] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,4,5,1,6,8,7] => [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,4,5,1,8,6,7] => [1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,4,5,8,1,6,7] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1,6,7,8] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,3,4,1,6,7,8,5] => [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,8,5,7] => [1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,3,4,1,6,5,7,8] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,3,4,6,1,7,8,5] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,4,6,7,8,1,5] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,3,4,6,7,1,5,8] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,3,4,6,8,1,5,7] => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,3,4,6,1,5,7,8] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,3,4,1,5,7,8,6] => [1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,3,4,1,5,7,6,8] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,4,1,7,8,5,6] => [1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,3,4,1,7,5,6,8] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,3,4,7,1,5,8,6] => [1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,3,4,7,8,1,5,6] => [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,3,4,7,1,5,6,8] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,3,4,1,5,6,8,7] => [1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,3,4,1,5,8,6,7] => [1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,3,4,1,8,5,6,7] => [1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 1
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,4,8,1,5,6,7] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6,7,8] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,5,6,8,4,7] => [1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,5,6,4,7,8] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,7,8,4,6] => [1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,5,4,6,7,8] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,5,1,6,7,8,4] => [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,8,1,4,7] => [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,5,6,1,4,7,8] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,3,5,7,1,4,8,6] => [1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,7,1,4,6,8] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,3,5,1,8,4,6,7] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,3,5,8,1,4,6,7] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,5,1,4,6,7,8] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,1,4,6,7,8,5] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,3,1,6,8,4,5,7] => [1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,3,1,6,4,5,7,8] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,3,6,1,4,7,8,5] => [1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,3,6,1,4,7,5,8] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,3,6,7,1,4,8,5] => [1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,3,6,7,1,4,5,8] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,3,6,1,4,5,8,7] => [1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,3,6,8,1,4,5,7] => [1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,6,1,4,5,7,8] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,3,1,4,7,8,5,6] => [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,3,1,4,7,5,6,8] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,3,1,7,4,5,8,6] => [1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,3,1,7,4,8,5,6] => [1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,3,1,7,8,4,5,6] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,3,7,1,4,5,8,6] => [1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,3,7,1,4,8,5,6] => [1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,3,7,8,1,4,5,6] => [1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,7,1,4,5,6,8] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,3,1,4,5,6,8,7] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,3,1,4,5,8,6,7] => [1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,3,1,4,8,5,6,7] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,3,1,8,4,5,6,7] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,3,8,1,4,5,6,7] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,4,5,6,8,3,7] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,4,5,7,8,3,6] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,4,5,8,3,6,7] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,4,5,3,6,7,8] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,8,5,7] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,6,5,7,8] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => 0
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,6,7,3,5,8] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,6,8,3,5,7] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,6,3,5,7,8] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,4,3,7,8,5,6] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,4,7,3,5,8,6] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,4,7,8,3,5,6] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,4,3,5,8,6,7] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 0
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,4,3,8,5,6,7] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 0
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,4,8,3,5,6,7] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,4,3,5,6,7,8] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,4,1,5,6,7,8,3] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,4,1,5,6,7,3,8] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,4,1,5,6,3,7,8] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,4,1,5,8,3,6,7] => [1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,4,5,6,1,7,8,3] => [1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,4,5,6,8,1,3,7] => [1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,7,1,3,8,6] => [1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,7,8,1,3,6] => [1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,4,5,1,8,3,6,7] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,4,5,1,3,6,7,8] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,1,6,3,7,8,5] => [1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,1,6,8,3,5,7] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,4,6,1,3,7,8,5] => [1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,4,6,1,3,7,5,8] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,4,6,7,1,3,8,5] => [1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 3
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,4,6,7,1,3,5,8] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,4,6,1,3,5,8,7] => [1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,4,6,8,1,3,5,7] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,4,6,1,3,5,7,8] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,4,1,3,5,7,8,6] => [1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,4,1,7,3,5,8,6] => [1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,4,1,7,8,3,5,6] => [1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,4,7,1,3,5,8,6] => [1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,4,7,1,3,8,5,6] => [1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,4,7,8,1,3,5,6] => [1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,4,1,3,8,5,6,7] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 1
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,4,1,8,3,5,6,7] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 1
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,4,8,1,3,5,6,7] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,4,1,3,5,6,7,8] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,8,4,7] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,1,3,5,8,4,6,7] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,1,3,5,4,6,7,8] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,1,5,6,8,3,4,7] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [2,1,5,6,3,4,7,8] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [2,1,5,7,3,4,8,6] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,1,5,7,8,3,4,6] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,1,5,7,3,4,6,8] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,1,5,3,8,4,6,7] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [2,1,5,8,3,4,6,7] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,1,5,3,4,6,7,8] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,5,1,3,6,7,8,4] => [1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [2,5,1,3,6,4,8,7] => [1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,5,1,3,6,4,7,8] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,5,6,1,3,7,8,4] => [1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [2,5,6,1,3,7,4,8] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [2,5,6,1,3,4,8,7] => [1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [2,5,6,8,1,3,4,7] => [1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [2,5,7,1,3,4,8,6] => [1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,5,7,1,3,8,4,6] => [1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,5,7,8,1,3,4,6] => [1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [2,5,1,8,3,4,6,7] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,5,8,1,3,4,6,7] => [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,5,1,3,4,6,7,8] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,1,3,4,6,5,7,8] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,1,3,6,4,5,7,8] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,1,6,3,4,7,8,5] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,1,6,7,3,4,8,5] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,1,6,3,4,5,8,7] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,1,6,3,4,8,5,7] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,1,6,8,3,4,5,7] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [2,6,1,3,4,7,8,5] => [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [2,6,1,3,4,7,5,8] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [2,6,1,3,7,4,8,5] => [1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [2,6,1,3,7,8,4,5] => [1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [2,6,1,7,3,4,5,8] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,6,7,1,3,4,8,5] => [1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,6,7,1,3,8,4,5] => [1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,6,7,1,3,4,5,8] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [2,6,1,3,4,5,8,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [2,6,1,3,4,8,5,7] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,6,8,1,3,4,5,7] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,6,1,3,4,5,7,8] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,1,3,4,5,7,6,8] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,1,3,4,7,8,5,6] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,1,3,4,7,5,6,8] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,1,3,7,4,8,5,6] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,1,3,7,8,4,5,6] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [2,1,7,3,4,5,8,6] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,1,7,3,4,8,5,6] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [2,1,7,3,8,4,5,6] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,1,7,8,3,4,5,6] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,1,7,3,4,5,6,8] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,7,1,3,4,5,8,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [2,7,1,3,8,4,5,6] => [1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,7,1,8,3,4,5,6] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,7,8,1,3,4,5,6] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,7,1,3,4,5,6,8] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,8,7] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,1,3,4,5,8,6,7] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,1,3,4,8,5,6,7] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,1,3,8,4,5,6,7] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 0
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,1,8,3,4,5,6,7] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,8,1,3,4,5,6,7] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,8,2] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,3,4,5,6,8,2,7] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,3,4,5,7,2,8,6] => [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,7,8,2,6] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,3,4,5,7,2,6,8] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,3,4,5,2,8,6,7] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,3,4,5,8,2,6,7] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,3,4,5,2,6,7,8] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,7,2,5,8] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,4,6,8,2,5,7] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,4,6,2,5,7,8] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,3,4,2,7,8,5,6] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,3,4,7,2,5,8,6] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,3,4,7,8,2,5,6] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,3,4,7,2,5,6,8] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,3,4,2,5,6,8,7] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,3,4,2,5,8,6,7] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,3,4,2,8,5,6,7] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,3,4,8,2,5,6,7] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,3,4,2,5,6,7,8] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,7,8,4,6] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,4,6,8] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,5,4,8,6,7] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 0
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,5,8,4,6,7] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,5,4,6,7,8] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,5,2,6,7,8,4] => [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,5,6,7,8,2,4] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,5,6,8,2,4,7] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,6,2,4,7,8] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,5,7,2,4,8,6] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,7,8,2,4,6] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,2,4,6,8] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,5,2,8,4,6,7] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,5,8,2,4,6,7] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,5,2,4,6,7,8] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,3,2,4,6,8,5,7] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,3,2,4,6,5,7,8] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,3,2,6,7,4,5,8] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,3,2,6,8,4,5,7] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,3,2,6,4,5,7,8] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,3,6,2,4,7,8,5] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,3,6,2,4,7,5,8] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,3,6,2,7,8,4,5] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,3,6,7,2,4,8,5] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,3,6,2,4,5,8,7] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,3,6,2,4,5,7,8] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,3,2,4,7,8,5,6] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,3,2,7,4,5,6,8] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,3,7,2,4,5,8,6] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,3,7,2,4,8,5,6] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,3,7,2,8,4,5,6] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,3,7,8,2,4,5,6] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,3,7,2,4,5,6,8] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,3,2,4,5,8,6,7] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,3,2,4,8,5,6,7] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,3,2,8,4,5,6,7] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 0
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,3,8,2,4,5,6,7] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,3,2,4,5,6,7,8] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,8,2] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,4,5,6,7,2,8] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,4,5,6,2,8,7] => [1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [3,1,4,5,8,2,6,7] => [1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,2,6,7,8] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [3,1,4,6,8,2,5,7] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [3,1,4,7,2,5,8,6] => [1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [3,1,4,2,8,5,6,7] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,1,4,8,2,5,6,7] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,2,5,6,7,8] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,4,1,5,6,7,8,2] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [3,4,1,5,8,2,6,7] => [1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,4,5,1,6,7,8,2] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [3,4,5,6,8,1,2,7] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,6,1,2,7,8] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [3,4,5,7,1,2,8,6] => [1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [3,4,5,7,8,1,2,6] => [1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,4,5,7,1,2,6,8] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,4,5,8,1,2,6,7] => [1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,4,1,2,6,5,8,7] => [1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [3,4,1,6,8,2,5,7] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 3
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [3,4,6,1,2,7,8,5] => [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 2
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [3,4,6,1,2,7,5,8] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [3,4,6,7,1,2,8,5] => [1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,7,1,2,5,8] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [3,4,6,1,2,5,8,7] => [1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,4,6,8,1,2,5,7] => [1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [3,4,1,7,2,5,8,6] => [1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 2
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [3,4,7,1,2,5,8,6] => [1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 2
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,4,7,8,1,2,5,6] => [1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [3,4,1,2,8,5,6,7] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,4,1,8,2,5,6,7] => [1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 2
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,4,8,1,2,5,6,7] => [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,2,5,6,4,7,8] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,1,2,5,8,4,6,7] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,1,5,2,6,7,8,4] => [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,1,5,6,8,2,4,7] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 2
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,1,5,7,2,4,8,6] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 2
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,1,5,7,8,2,4,6] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 3
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,1,5,7,2,4,6,8] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,1,5,2,4,8,6,7] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,1,5,2,8,4,6,7] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,1,5,8,2,4,6,7] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 2
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,5,1,2,6,7,8,4] => [1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 2
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,5,1,2,6,7,4,8] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,5,1,2,6,4,8,7] => [1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,5,6,1,2,7,8,4] => [1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,5,6,1,2,7,4,8] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,5,6,1,2,4,8,7] => [1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,5,6,8,1,2,4,7] => [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,5,6,1,2,4,7,8] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,5,1,2,4,7,8,6] => [1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 2
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,5,1,2,4,7,6,8] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,5,1,2,7,4,8,6] => [1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,5,7,1,2,4,8,6] => [1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,5,7,1,2,8,4,6] => [1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 2
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,5,7,8,1,2,4,6] => [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,5,7,1,2,4,6,8] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,5,1,2,4,6,8,7] => [1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 1
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,5,1,8,2,4,6,7] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,5,1,2,4,6,7,8] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [3,1,2,6,4,5,8,7] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 0
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [3,1,6,2,4,7,8,5] => [1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [3,1,6,2,4,7,5,8] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,1,6,7,2,4,5,8] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [3,1,6,2,4,5,8,7] => [1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,1,6,8,2,4,5,7] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 2
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,1,6,2,4,5,7,8] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [3,6,1,2,4,7,8,5] => [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 2
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [3,6,1,2,4,7,5,8] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [3,6,1,2,7,4,8,5] => [1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 2
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [3,6,1,2,7,8,4,5] => [1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [3,6,7,1,2,4,8,5] => [1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [3,6,7,1,2,8,4,5] => [1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 2
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,6,7,1,2,4,5,8] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [3,6,1,2,4,5,8,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [3,6,1,2,4,8,5,7] => [1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 2
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,6,1,2,4,5,7,8] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [3,1,2,7,4,8,5,6] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [3,1,2,7,8,4,5,6] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,1,2,7,4,5,6,8] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [3,1,7,2,4,5,8,6] => [1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,1,7,8,2,4,5,6] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 2
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,1,7,2,4,5,6,8] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [3,7,1,2,4,5,8,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [3,7,1,2,4,8,5,6] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [3,7,1,2,8,4,5,6] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,7,8,1,2,4,5,6] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,7,1,2,4,5,6,8] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [3,1,2,4,8,5,6,7] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 0
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3,1,2,8,4,5,6,7] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,8,2,4,5,6,7] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,8,1,2,4,5,6,7] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,6,8,3,7] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,2,4,5,6,3,7,8] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,7,8,3,6] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,5,7,3,6,8] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [1,2,4,5,3,8,6,7] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [1,2,4,5,8,3,6,7] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,2,4,5,3,6,7,8] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,8,5,7] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,6,5,7,8] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,6,7,3,5,8] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,8,3,5,7] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,6,3,5,7,8] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [1,2,4,3,7,8,5,6] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,2,4,3,7,5,6,8] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [1,2,4,7,3,5,8,6] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [1,2,4,7,8,3,5,6] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,2,4,7,3,5,6,8] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,2,4,3,5,8,6,7] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,2,4,3,8,5,6,7] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,2,4,8,3,5,6,7] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,4,3,5,6,7,8] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,4,2,5,6,7,8,3] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [1,4,2,5,8,3,6,7] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [1,4,5,2,6,7,8,3] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [1,4,5,2,6,8,3,7] => [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [1,4,5,6,2,7,8,3] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [1,4,5,6,8,2,3,7] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [1,4,5,7,2,3,8,6] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [1,4,5,7,8,2,3,6] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,4,5,7,2,3,6,8] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [1,4,5,2,8,3,6,7] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 2
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,4,5,2,3,6,7,8] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [1,4,2,3,6,5,8,7] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,8,5,7] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,4,2,6,8,3,5,7] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 2
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [1,4,6,2,3,7,8,5] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,4,6,7,2,3,5,8] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,4,6,2,3,5,8,7] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,4,6,8,2,3,5,7] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,4,6,2,3,5,7,8] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [1,4,2,7,3,5,8,6] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [1,4,2,7,8,3,5,6] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,4,2,7,3,5,6,8] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [1,4,7,2,3,5,8,6] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [1,4,7,2,3,8,5,6] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [1,4,7,8,2,3,5,6] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,4,7,2,3,5,6,8] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [1,4,2,3,8,5,6,7] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 0
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,4,2,8,3,5,6,7] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,4,8,2,3,5,6,7] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,4,2,3,5,6,7,8] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,2,5,6,7,8,3] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [4,1,2,5,6,7,3,8] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,5,6,3,8,7] => [1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3,7,8] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [4,1,2,5,3,7,8,6] => [1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [4,1,2,5,3,7,6,8] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [4,1,2,5,7,3,8,6] => [1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [4,1,2,5,7,8,3,6] => [1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => 2
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,5,3,6,7,8] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [4,1,5,6,2,3,7,8] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [4,1,5,2,7,8,3,6] => [1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => 3
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,1,5,7,2,3,6,8] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [4,1,5,2,3,8,6,7] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [4,5,1,2,6,7,8,3] => [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [4,5,1,2,6,7,3,8] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [4,5,1,2,6,3,8,7] => [1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [4,5,1,6,2,3,8,7] => [1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [4,5,6,8,1,2,3,7] => [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [4,5,1,2,3,7,6,8] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [4,5,1,7,2,3,6,8] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [4,5,7,1,2,3,8,6] => [1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [4,5,7,1,2,8,3,6] => [1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 2
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [4,5,7,8,1,2,3,6] => [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [4,5,1,2,3,8,6,7] => [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [4,5,1,8,2,3,6,7] => [1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 2
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [4,5,8,1,2,3,6,7] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [4,5,1,2,3,6,7,8] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,2,3,6,7,8,5] => [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [4,1,2,3,6,7,5,8] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [4,1,2,3,6,5,8,7] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 0
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [4,1,2,3,6,5,7,8] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [4,1,2,6,3,8,5,7] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [4,1,6,2,3,5,8,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [4,1,6,2,8,3,5,7] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,1,6,8,2,3,5,7] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [4,6,1,2,3,7,5,8] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [4,6,1,2,7,8,3,5] => [1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [4,6,1,2,7,3,5,8] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [4,6,7,1,2,3,8,5] => [1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [4,6,7,1,2,8,3,5] => [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 3
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [4,6,7,1,2,3,5,8] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [4,6,1,2,3,5,8,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [4,6,1,2,3,8,5,7] => [1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,6,1,8,2,3,5,7] => [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [4,6,8,1,2,3,5,7] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [4,6,1,2,3,5,7,8] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [4,1,2,3,5,7,8,6] => [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [4,1,2,3,5,7,6,8] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [4,1,2,3,7,8,5,6] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [4,1,2,3,7,5,6,8] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [4,1,2,7,8,3,5,6] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [4,1,2,7,3,5,6,8] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [4,1,7,2,3,5,8,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [4,1,7,2,3,8,5,6] => [1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [4,1,7,8,2,3,5,6] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [4,1,7,2,3,5,6,8] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [4,7,1,2,3,8,5,6] => [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [4,7,1,2,8,3,5,6] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,7,1,8,2,3,5,6] => [1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,7,8,1,2,3,5,6] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [4,1,2,3,5,6,8,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [4,1,2,3,5,8,6,7] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [4,1,2,3,8,5,6,7] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,2,8,3,5,6,7] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,1,8,2,3,5,6,7] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [4,8,1,2,3,5,6,7] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,2,3,5,6,7,8,4] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,8,4,7] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,2,3,5,7,8,4,6] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,4,6,8] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,2,3,5,4,8,6,7] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,2,3,5,8,4,6,7] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,2,3,5,4,6,7,8] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [1,2,5,6,8,3,4,7] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [1,2,5,6,3,4,7,8] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [1,2,5,7,3,4,8,6] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [1,2,5,7,8,3,4,6] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,2,5,7,3,4,6,8] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [1,2,5,3,4,8,6,7] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [1,2,5,3,8,4,6,7] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,2,5,8,3,4,6,7] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,2,5,3,4,6,7,8] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [1,5,2,3,6,7,8,4] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [1,5,2,3,6,7,4,8] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [1,5,2,3,6,4,8,7] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [1,5,2,3,6,4,7,8] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [1,5,6,2,3,7,8,4] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [1,5,6,2,3,4,8,7] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [1,5,6,8,2,3,4,7] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [1,5,6,2,3,4,7,8] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [1,5,2,3,4,7,8,6] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6,8] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [1,5,7,2,3,4,8,6] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [1,5,7,2,3,8,4,6] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [1,5,7,8,2,3,4,6] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [1,5,7,2,3,4,6,8] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [1,5,2,3,4,6,8,7] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [1,5,2,3,4,8,6,7] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 0
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [1,5,2,3,8,4,6,7] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [1,5,2,8,3,4,6,7] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,5,2,3,4,6,7,8] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,1,2,3,6,7,8,4] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [5,1,2,3,6,7,4,8] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [5,1,2,3,6,8,4,7] => [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,1,2,3,6,4,7,8] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [5,1,2,6,3,7,8,4] => [1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 2
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [5,1,2,6,3,7,4,8] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [5,1,2,6,7,3,8,4] => [1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 2
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [5,1,2,6,7,8,3,4] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [5,1,2,6,7,3,4,8] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [5,1,2,6,3,8,4,7] => [1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 2
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [5,1,2,6,3,4,7,8] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [5,1,6,2,3,4,7,8] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [5,6,1,2,3,7,8,4] => [1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [5,6,1,2,7,3,8,4] => [1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [5,6,1,2,7,8,3,4] => [1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [5,6,1,2,7,3,4,8] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,6,7,1,2,3,4,8] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [5,6,1,2,3,4,8,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [5,6,1,2,3,8,4,7] => [1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [5,6,1,2,8,3,4,7] => [1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [5,6,8,1,2,3,4,7] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [5,1,2,3,4,7,8,6] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [5,1,2,3,7,4,8,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [5,1,2,3,7,8,4,6] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,1,7,2,8,3,4,6] => [1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [5,7,1,2,3,4,8,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,7,1,2,8,3,4,6] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [5,7,8,1,2,3,4,6] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [5,7,1,2,3,4,6,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,8,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [5,1,2,3,4,8,6,7] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,2,3,8,4,6,7] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [5,1,2,8,3,4,6,7] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [5,1,8,2,3,4,6,7] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [5,8,1,2,3,4,6,7] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [5,1,2,3,4,6,7,8] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [1,2,3,4,6,8,5,7] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,2,3,4,6,5,7,8] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [1,2,3,6,4,7,8,5] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [1,2,3,6,7,4,5,8] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [1,2,3,6,8,4,5,7] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,2,3,6,4,5,7,8] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [1,2,6,3,4,7,8,5] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [1,2,6,3,4,7,5,8] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [1,2,6,7,3,4,8,5] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [1,2,6,7,3,4,5,8] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [1,2,6,3,4,5,8,7] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [1,2,6,8,3,4,5,7] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,2,6,3,4,5,7,8] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [1,6,2,3,4,7,8,5] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [1,6,2,3,4,7,5,8] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [1,6,2,3,7,4,8,5] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [1,6,2,3,7,8,4,5] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [1,6,2,3,7,4,5,8] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [1,6,2,7,3,4,5,8] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [1,6,7,2,3,4,8,5] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [1,6,7,2,3,8,4,5] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,6,7,8,2,3,4,5] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [1,6,7,2,3,4,5,8] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [1,6,2,3,4,5,8,7] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,8,5,7] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [1,6,2,3,8,4,5,7] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,6,8,2,3,4,5,7] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [1,6,2,3,4,5,7,8] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [6,1,2,3,4,7,8,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,1,2,3,4,7,5,8] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [6,1,2,3,7,4,8,5] => [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 2
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [6,1,2,3,7,8,4,5] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [6,1,2,7,3,4,8,5] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [6,1,2,7,3,8,4,5] => [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 2
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [6,1,2,7,8,3,4,5] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [6,1,2,7,3,4,5,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [6,1,7,2,3,4,8,5] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [6,1,7,2,3,4,5,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [6,7,1,2,3,4,8,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [6,7,1,2,3,8,4,5] => [1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [6,7,1,2,8,3,4,5] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [6,7,8,1,2,3,4,5] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [6,7,1,2,3,4,5,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,8,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,8,5,7] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [6,1,2,3,8,4,5,7] => [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [6,1,2,8,3,4,5,7] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [6,8,1,2,3,4,5,7] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [6,1,2,3,4,5,7,8] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,2,3,4,5,7,8,6] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,2,3,4,5,7,6,8] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,2,3,4,7,8,5,6] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,2,3,4,7,5,6,8] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [1,2,3,7,4,5,8,6] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [1,2,3,7,4,8,5,6] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,2,3,7,8,4,5,6] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,2,3,7,4,5,6,8] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [1,2,7,3,4,8,5,6] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [1,2,7,3,8,4,5,6] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,2,7,8,3,4,5,6] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,2,7,3,4,5,6,8] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,2,3,4,5,8,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [1,7,2,3,4,8,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,7,2,3,8,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,7,2,8,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,7,8,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,7,2,3,4,5,6,8] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,1,2,3,4,8,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [7,1,2,3,8,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [7,1,2,8,3,4,5,6] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [7,1,8,2,3,4,5,6] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [7,8,1,2,3,4,5,6] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,8,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,2,3,4,5,8,6,7] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,2,3,4,8,5,6,7] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,2,3,8,4,5,6,7] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,2,8,3,4,5,6,7] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [8,1,2,3,4,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,9,8] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,8,1,3,4,5,6,7,9] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10,11] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,8,9,1,3,4,5,6,7] => [1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [1,2,3,4,5,6,8,7,9] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,2,4,5,6,7,8,9] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,4,1,3,5,6,7,8,9] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [1,2,3,4,5,6,8,9,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,9,8] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,3,9,2,4,5,6,7,8] => [1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8,10] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,4,1,3,5,6,7,8,9,10] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [1,2,3,4,5,6,7,9,10,8] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9,10] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => 1
[] => [] => [] => [] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [3,4,5,6,7,9,1,2,8] => [1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8,9] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,4,2,3,5,6,7,8,9] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [4,1,2,3,5,9,6,7,8] => [1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 0
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,2,3,9,4,6,7,8] => [1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [6,7,9,1,2,3,4,5,8] => [1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [7,8,9,1,2,3,4,5,6] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [1,8,9,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [8,9,1,2,3,4,5,6,7] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [8,1,2,3,4,5,6,7,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,2,3,4,5,6,9,7,8] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,9,2,3,4,5,6,7,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,9,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,7,8,1,9] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,6,7,9,1,8] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,4,5,6,8,9,1,7] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,9,10,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,7,8,9,1,10] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,5,6,7,1,8,9] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,6,7,8,10,1,9] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,9,10,11,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,7,8,9,10,1,11] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,4,5,6,9,1,7,8] => [1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,4,5,6,7,10,1,8,9] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,5,6,7,1,9,8] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,4,5,6,1,8,9,7] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,8,9,2] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [1,2,3,4,5,7,6,8,9] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,5,6,7,8,1,10,9] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,8,9,10,2] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,8,9,2] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,4,1,5,6,7,8,9,2] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,8,9,10,2] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,8,9,10,11,2] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,3,4,5,6,7,9,2,8] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [9,1,2,3,4,5,6,7,8,10] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [1,10,2,3,4,5,6,7,8,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [10,1,2,3,4,5,6,7,8,9,11] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [1,11,2,3,4,5,6,7,8,9,10] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,1,4,5,6,7,8,2,9] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => 1
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [1,2,3,4,5,6,7,10,8,9] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,4,2,5,6,7,8,9,3] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,2,5,6,7,8,9] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,4,5,1,6,7,8,9,3] => [1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,5,1,6,7,8,9,4] => [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,5,2,6,7,8,9,4] => [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [1,2,3,4,5,7,9,6,8] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8,9,10] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10,11] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0] => [5,1,2,3,6,7,8,9,4] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,4,1,5,6,7,8,9,3] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [9,10,1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [8,9,10,1,2,3,4,5,6,7] => [1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0] => [1,2,3,4,5,6,7,8,10,11,9] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,4,1,5,6,7,8,9,10,3] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9,10,11] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => 1
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
4,1 8,6 16,24,2 32,80,20 64,240,120,5
F1=1
F2=2
F3=4+q
F4=8+6 q
F5=16+24 q+2 q2
F6=32+80 q+20 q2
F7=64+240 q+120 q2+5 q3
Description
The number of factors DDU in a Dyck path.
Map
to 321-avoiding permutation (Billey-Jockusch-Stanley)
Description
The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.
Map
left-to-right-maxima to Dyck path
Description
The left-to-right maxima of a permutation as a Dyck path.
Let (c1,…,ck) be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are c1,c1+c2,…,c1+⋯+ck.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
Let (c1,…,ck) be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are c1,c1+c2,…,c1+⋯+ck.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
Map
zeta map
Description
The zeta map on Dyck paths.
The zeta map ζ is a bijection on Dyck paths of semilength n.
It was defined in [1, Theorem 1], see also [2, Theorem 3.15] and sends the bistatistic (area, dinv) to the bistatistic (bounce, area). It is defined by sending a Dyck path D with corresponding area sequence a=(a1,…,an) to a Dyck path as follows:
The zeta map ζ is a bijection on Dyck paths of semilength n.
It was defined in [1, Theorem 1], see also [2, Theorem 3.15] and sends the bistatistic (area, dinv) to the bistatistic (bounce, area). It is defined by sending a Dyck path D with corresponding area sequence a=(a1,…,an) to a Dyck path as follows:
- First, build an intermediate Dyck path consisting of d1 north steps, followed by d1 east steps, followed by d2 north steps and d2 east steps, and so on, where di is the number of i−1's within the sequence a.
For example, given a=(0,1,2,2,2,3,1,2), we build the path
NE NNEE NNNNEEEE NE. - Next, the rectangles between two consecutive peaks are filled. Observe that such the rectangle between the kth and the (k+1)st peak must be filled by dk east steps and dk+1 north steps. In the above example, the rectangle between the second and the third peak must be filled by 2 east and 4 north steps, the 2 being the number of 1's in a, and 4 being the number of 2's. To fill such a rectangle, scan through the sequence a from left to right, and add east or north steps whenever you see a k−1 or k, respectively. So to fill the 2×4 rectangle, we look for 1's and 2's in the sequence and see 122212, so this rectangle gets filled with ENNNEN.
The complete path we obtain in thus
NENNENNNENEEENEE.
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