Identifier
-
Mp00031:
Dyck paths
—to 312-avoiding permutation⟶
Permutations
Mp00175: Permutations —inverse Foata bijection⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St000386: Dyck paths ⟶ ℤ
Values
[1,0] => [1] => [1] => [1,0] => 0
[1,0,1,0] => [1,2] => [1,2] => [1,0,1,0] => 0
[1,1,0,0] => [2,1] => [2,1] => [1,1,0,0] => 0
[1,0,1,0,1,0] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0] => 0
[1,0,1,1,0,0] => [1,3,2] => [3,1,2] => [1,1,1,0,0,0] => 0
[1,1,0,0,1,0] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0] => 1
[1,1,0,1,0,0] => [2,3,1] => [2,3,1] => [1,1,0,1,0,0] => 0
[1,1,1,0,0,0] => [3,2,1] => [3,2,1] => [1,1,1,0,0,0] => 0
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [4,1,2,3] => [1,1,1,1,0,0,0,0] => 0
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 1
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [3,4,1,2] => [1,1,1,0,1,0,0,0] => 0
[1,0,1,1,1,0,0,0] => [1,4,3,2] => [4,3,1,2] => [1,1,1,1,0,0,0,0] => 0
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [2,4,1,3] => [1,1,0,1,1,0,0,0] => 0
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [2,3,1,4] => [1,1,0,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [2,3,4,1] => [1,1,0,1,0,1,0,0] => 0
[1,1,0,1,1,0,0,0] => [2,4,3,1] => [4,2,3,1] => [1,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,0,1,0] => [3,2,1,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 1
[1,1,1,0,0,1,0,0] => [3,2,4,1] => [3,2,4,1] => [1,1,1,0,0,1,0,0] => 1
[1,1,1,0,1,0,0,0] => [3,4,2,1] => [3,4,2,1] => [1,1,1,0,1,0,0,0] => 0
[1,1,1,1,0,0,0,0] => [4,3,2,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [5,1,2,3,4] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [4,5,1,2,3] => [1,1,1,1,0,1,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [5,4,1,2,3] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [3,5,1,2,4] => [1,1,1,0,1,1,0,0,0,0] => 0
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [3,4,1,2,5] => [1,1,1,0,1,0,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [3,4,5,1,2] => [1,1,1,0,1,0,1,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [5,3,4,1,2] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [4,3,5,1,2] => [1,1,1,1,0,0,1,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,0] => [1,4,5,3,2] => [4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [2,5,1,3,4] => [1,1,0,1,1,1,0,0,0,0] => 0
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [2,4,1,3,5] => [1,1,0,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [2,4,5,1,3] => [1,1,0,1,1,0,1,0,0,0] => 0
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [5,2,4,1,3] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [2,3,1,4,5] => [1,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [2,3,5,1,4] => [1,1,0,1,0,1,1,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [4,2,3,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [4,2,3,5,1] => [1,1,1,1,0,0,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,0,0] => [2,4,5,3,1] => [4,5,2,3,1] => [1,1,1,1,0,1,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [5,4,2,3,1] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [3,2,5,1,4] => [1,1,1,0,0,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [3,2,4,1,5] => [1,1,1,0,0,1,0,0,1,0] => 2
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [3,2,4,5,1] => [1,1,1,0,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [3,5,2,4,1] => [1,1,1,0,1,1,0,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,0] => [3,4,2,1,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,0] => [3,4,2,5,1] => [3,4,2,5,1] => [1,1,1,0,1,0,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,0] => [3,4,5,2,1] => [3,4,5,2,1] => [1,1,1,0,1,0,1,0,0,0] => 0
[1,1,1,0,1,1,0,0,0,0] => [3,5,4,2,1] => [5,3,4,2,1] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [4,3,2,5,1] => [1,1,1,1,0,0,0,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,0] => [4,3,5,2,1] => [4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,0] => [4,5,3,2,1] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [6,1,2,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [5,1,2,3,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [5,6,1,2,3,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [6,5,1,2,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [4,1,2,3,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [4,6,1,2,3,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [4,5,1,2,3,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [4,5,6,1,2,3] => [1,1,1,1,0,1,0,1,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [6,4,5,1,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [5,4,1,2,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [5,4,6,1,2,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,4,3] => [5,6,4,1,2,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [6,5,4,1,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [3,1,2,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [3,6,1,2,4,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [3,5,1,2,4,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [3,5,6,1,2,4] => [1,1,1,0,1,1,0,1,0,0,0,0] => 0
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [6,3,5,1,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [3,4,1,2,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [3,4,6,1,2,5] => [1,1,1,0,1,0,1,1,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [3,4,5,1,2,6] => [1,1,1,0,1,0,1,0,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [3,4,5,6,1,2] => [1,1,1,0,1,0,1,0,1,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [6,3,4,5,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [5,3,4,1,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [5,3,4,6,1,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,4,2] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [6,5,3,4,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [4,3,1,2,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [4,3,6,1,2,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [4,3,5,1,2,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [4,3,5,6,1,2] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [4,6,3,5,1,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,3,2,6] => [4,5,3,1,2,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,3,6,2] => [4,5,3,6,1,2] => [1,1,1,1,0,1,0,0,1,0,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,3,2] => [4,5,6,3,1,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,5,3,2] => [6,4,5,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
>>> Load all 1331 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [5,4,3,1,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [5,4,3,6,1,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,4,6,3,2] => [5,4,6,3,1,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,4,3,2] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [2,6,1,3,4,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [2,5,1,3,4,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [2,5,6,1,3,4] => [1,1,0,1,1,1,0,1,0,0,0,0] => 0
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [6,2,5,1,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [2,4,1,3,5,6] => [1,1,0,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [2,4,6,1,3,5] => [1,1,0,1,1,0,1,1,0,0,0,0] => 0
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [2,4,5,1,3,6] => [1,1,0,1,1,0,1,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [2,4,5,6,1,3] => [1,1,0,1,1,0,1,0,1,0,0,0] => 0
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [6,2,4,5,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [5,2,4,1,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [5,2,4,6,1,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,4,3] => [5,6,2,4,1,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [6,5,2,4,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [2,3,1,4,5,6] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [2,3,6,1,4,5] => [1,1,0,1,0,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [2,3,5,1,4,6] => [1,1,0,1,0,1,1,0,0,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [2,3,5,6,1,4] => [1,1,0,1,0,1,1,0,1,0,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [6,2,3,5,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [2,3,4,1,5,6] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [2,3,4,6,1,5] => [1,1,0,1,0,1,0,1,1,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [2,3,4,5,1,6] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [6,2,3,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [5,2,3,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [5,2,3,4,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,4,1] => [5,6,2,3,4,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [6,5,2,3,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [4,2,3,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [4,2,3,6,1,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [4,2,3,5,1,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => 2
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [4,2,3,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [4,6,2,3,5,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,3,1,6] => [4,5,2,3,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,3,6,1] => [4,5,2,3,6,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,6,3,1] => [4,5,6,2,3,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,5,3,1] => [6,4,5,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [5,4,2,3,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [5,4,2,3,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,4,6,3,1] => [5,4,6,2,3,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,4,3,1] => [5,6,4,2,3,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [6,5,4,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [3,2,6,1,4,5] => [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] => [3,2,1,5,4,6] => [3,2,5,1,4,6] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [3,2,5,6,1,4] => [1,1,1,0,0,1,1,0,1,0,0,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [3,6,2,5,1,4] => [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] => [3,2,4,1,5,6] => [3,2,4,1,5,6] => [1,1,1,0,0,1,0,0,1,0,1,0] => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [3,2,4,6,1,5] => [1,1,1,0,0,1,0,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [3,2,4,5,1,6] => [1,1,1,0,0,1,0,1,0,0,1,0] => 2
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [3,2,4,5,6,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [3,6,2,4,5,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [3,5,2,4,1,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [3,5,2,4,6,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,6,4,1] => [3,5,6,2,4,1] => [1,1,1,0,1,1,0,1,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [6,3,5,2,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,2,1,5,6] => [3,4,2,1,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,2,1,6,5] => [3,4,2,6,1,5] => [1,1,1,0,1,0,0,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,2,5,1,6] => [3,4,2,5,1,6] => [1,1,1,0,1,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,2,5,6,1] => [3,4,2,5,6,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,2,6,5,1] => [3,4,6,2,5,1] => [1,1,1,0,1,0,1,1,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,2,1,6] => [3,4,5,2,1,6] => [1,1,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,2,6,1] => [3,4,5,2,6,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,2,1] => [3,4,5,6,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,5,2,1] => [6,3,4,5,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,4,2,1,6] => [5,3,4,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,4,2,6,1] => [5,3,4,2,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,4,6,2,1] => [5,3,4,6,2,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,4,2,1] => [5,6,3,4,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [4,3,2,6,1,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [4,3,2,5,1,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => 2
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [4,3,2,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [4,3,6,2,5,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,3,5,2,1,6] => [4,3,5,2,1,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => 2
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,6,1] => [4,3,5,2,6,1] => [1,1,1,1,0,0,1,0,0,1,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,5,6,2,1] => [4,3,5,6,2,1] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,2,1] => [4,6,3,5,2,1] => [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] => [4,5,3,2,1,6] => [4,5,3,2,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,3,2,6,1] => [4,5,3,2,6,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,3,6,2,1] => [4,5,3,6,2,1] => [1,1,1,1,0,1,0,0,1,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,3,2,1] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => [6,4,5,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [5,4,3,2,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => [5,4,3,6,2,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => [5,4,6,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => [5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [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] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => [7,1,2,3,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [6,1,2,3,4,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [6,7,1,2,3,4,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => [7,6,1,2,3,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [5,7,1,2,3,4,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [5,6,1,2,3,4,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [5,6,7,1,2,3,4] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => [7,5,6,1,2,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => [6,5,1,2,3,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => [6,5,7,1,2,3,4] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,6,7,5,4] => [6,7,5,1,2,3,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => [7,6,5,1,2,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [4,1,2,3,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [4,7,1,2,3,5,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [4,6,1,2,3,5,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [4,6,7,1,2,3,5] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => [7,4,6,1,2,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [4,5,1,2,3,6,7] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [4,5,7,1,2,3,6] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [4,5,6,1,2,3,7] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [4,5,6,7,1,2,3] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => [7,4,5,6,1,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => [6,4,5,1,2,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => [6,4,5,7,1,2,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,7,5,3] => [6,7,4,5,1,2,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => [7,6,4,5,1,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => [5,4,1,2,3,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => [5,4,7,1,2,3,6] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,4,6,3,7] => [5,4,6,1,2,3,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => [5,4,6,7,1,2,3] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => [5,7,4,6,1,2,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,5,6,4,3,7] => [5,6,4,1,2,3,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,5,6,4,7,3] => [5,6,4,7,1,2,3] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,5,6,7,4,3] => [5,6,7,4,1,2,3] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5,7,6,4,3] => [7,5,6,4,1,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => [6,5,4,1,2,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => [6,5,4,7,1,2,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,6,5,7,4,3] => [6,5,7,4,1,2,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,6,7,5,4,3] => [6,7,5,4,1,2,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => [7,6,5,4,1,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [3,1,2,4,5,6,7] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [3,7,1,2,4,5,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [3,6,1,2,4,5,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [3,6,7,1,2,4,5] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 0
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => [7,3,6,1,2,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [3,5,1,2,4,6,7] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => [3,5,7,1,2,4,6] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 0
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [3,5,6,1,2,4,7] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [3,5,6,7,1,2,4] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 0
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => [7,3,5,6,1,2,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => [6,3,5,1,2,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => [6,3,5,7,1,2,4] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,6,7,5,4] => [6,7,3,5,1,2,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => [7,6,3,5,1,2,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [3,4,1,2,5,6,7] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [3,4,7,1,2,5,6] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [3,4,6,1,2,5,7] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [3,4,6,7,1,2,5] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 0
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => [7,3,4,6,1,2,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [3,4,5,1,2,6,7] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [3,4,5,7,1,2,6] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [3,4,5,6,1,2,7] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [3,4,5,6,7,1,2] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => [7,3,4,5,6,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => [6,3,4,5,1,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => [6,3,4,5,7,1,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,6,7,5,2] => [6,7,3,4,5,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => [7,6,3,4,5,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => [5,3,4,1,2,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => [5,3,4,7,1,2,6] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => [5,3,4,6,1,2,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => [5,3,4,6,7,1,2] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => [5,7,3,4,6,1,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,5,6,4,2,7] => [5,6,3,4,1,2,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,5,6,4,7,2] => [5,6,3,4,7,1,2] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,6,7,4,2] => [5,6,7,3,4,1,2] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,6,4,2] => [7,5,6,3,4,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => [6,5,3,4,1,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => [6,5,3,4,7,1,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,6,5,7,4,2] => [6,5,7,3,4,1,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,6,7,5,4,2] => [6,7,5,3,4,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => [7,6,5,3,4,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => [4,3,1,2,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => [4,3,7,1,2,5,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => [4,3,6,1,2,5,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => [4,3,6,7,1,2,5] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => [4,7,3,6,1,2,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => [4,3,5,1,2,6,7] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => [4,3,5,7,1,2,6] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => [4,3,5,6,1,2,7] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => [4,3,5,6,7,1,2] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => [4,7,3,5,6,1,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => [4,6,3,5,1,2,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => [4,6,3,5,7,1,2] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,6,7,5,2] => [4,6,7,3,5,1,2] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => [7,4,6,3,5,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,5,3,2,6,7] => [4,5,3,1,2,6,7] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,5,3,2,7,6] => [4,5,3,7,1,2,6] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,4,5,3,6,2,7] => [4,5,3,6,1,2,7] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,5,3,6,7,2] => [4,5,3,6,7,1,2] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,5,3,7,6,2] => [4,5,7,3,6,1,2] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,3,2,7] => [4,5,6,3,1,2,7] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,3,7,2] => [4,5,6,3,7,1,2] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,3,2] => [4,5,6,7,3,1,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,4,5,7,6,3,2] => [7,4,5,6,3,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,4,6,5,3,2,7] => [6,4,5,3,1,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,5,3,7,2] => [6,4,5,3,7,1,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,4,6,5,7,3,2] => [6,4,5,7,3,1,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,4,6,7,5,3,2] => [6,7,4,5,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,4,7,6,5,3,2] => [7,6,4,5,3,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,4,3,2,6,7] => [5,4,3,1,2,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => [5,4,3,7,1,2,6] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,4,3,6,2,7] => [5,4,3,6,1,2,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => [5,4,3,6,7,1,2] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => [5,4,7,3,6,1,2] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,4,6,3,2,7] => [5,4,6,3,1,2,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,4,6,3,7,2] => [5,4,6,3,7,1,2] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,4,6,7,3,2] => [5,4,6,7,3,1,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,4,7,6,3,2] => [5,7,4,6,3,1,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,5,6,4,3,2,7] => [5,6,4,3,1,2,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,6,4,3,7,2] => [5,6,4,3,7,1,2] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,5,6,4,7,3,2] => [5,6,4,7,3,1,2] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,5,6,7,4,3,2] => [5,6,7,4,3,1,2] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,5,7,6,4,3,2] => [7,5,6,4,3,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => [6,5,4,3,1,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => [6,5,4,3,7,1,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,6,5,4,7,3,2] => [6,5,4,7,3,1,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,5,7,4,3,2] => [6,5,7,4,3,1,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,6,7,5,4,3,2] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => [7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => [2,7,1,3,4,5,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => [2,6,1,3,4,5,7] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => [2,6,7,1,3,4,5] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => [7,2,6,1,3,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => [2,5,1,3,4,6,7] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => [2,5,7,1,3,4,6] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => [2,5,6,1,3,4,7] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [2,5,6,7,1,3,4] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 0
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,6,4] => [7,2,5,6,1,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => [6,2,5,1,3,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,5,7,4] => [6,2,5,7,1,3,4] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,6,7,5,4] => [6,7,2,5,1,3,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => [7,6,2,5,1,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => [2,4,1,3,5,6,7] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => [2,4,7,1,3,5,6] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => [2,4,6,1,3,5,7] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => [2,4,6,7,1,3,5] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 0
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => [7,2,4,6,1,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [2,4,5,1,3,6,7] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [2,4,5,7,1,3,6] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 0
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [2,4,5,6,1,3,7] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [2,4,5,6,7,1,3] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 0
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => [7,2,4,5,6,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,5,3,7] => [6,2,4,5,1,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => [6,2,4,5,7,1,3] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,6,7,5,3] => [6,7,2,4,5,1,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => [7,6,2,4,5,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,4,3,6,7] => [5,2,4,1,3,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,4,3,7,6] => [5,2,4,7,1,3,6] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,4,6,3,7] => [5,2,4,6,1,3,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,4,6,7,3] => [5,2,4,6,7,1,3] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,4,7,6,3] => [5,7,2,4,6,1,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,5,6,4,3,7] => [5,6,2,4,1,3,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,5,6,4,7,3] => [5,6,2,4,7,1,3] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,5,6,7,4,3] => [5,6,7,2,4,1,3] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,5,7,6,4,3] => [7,5,6,2,4,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,5,4,3,7] => [6,5,2,4,1,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,5,4,7,3] => [6,5,2,4,7,1,3] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,5,7,4,3] => [6,5,7,2,4,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,6,7,5,4,3] => [6,7,5,2,4,1,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => [7,6,5,2,4,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [2,3,1,4,5,6,7] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [2,3,7,1,4,5,6] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [2,3,6,1,4,5,7] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [2,3,6,7,1,4,5] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,6,5] => [7,2,3,6,1,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [2,3,5,1,4,6,7] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [2,3,5,7,1,4,6] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [2,3,5,6,1,4,7] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [2,3,5,6,7,1,4] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 0
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,6,4] => [7,2,3,5,6,1,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,5,4,7] => [6,2,3,5,1,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,5,7,4] => [6,2,3,5,7,1,4] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,6,7,5,4] => [6,7,2,3,5,1,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => [7,6,2,3,5,1,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [2,3,4,1,5,6,7] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [2,3,4,7,1,5,6] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [2,3,4,6,1,5,7] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [2,3,4,6,7,1,5] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => [7,2,3,4,6,1,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [2,3,4,5,1,6,7] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [2,3,4,5,7,1,6] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [2,3,4,5,6,1,7] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [2,3,4,5,6,7,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,6,1] => [7,2,3,4,5,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => [6,2,3,4,5,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,5,7,1] => [6,2,3,4,5,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,6,7,5,1] => [6,7,2,3,4,5,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,6,5,1] => [7,6,2,3,4,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => [5,2,3,4,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => [5,2,3,4,7,1,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,4,6,1,7] => [5,2,3,4,6,1,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 2
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,4,6,7,1] => [5,2,3,4,6,7,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,4,7,6,1] => [5,7,2,3,4,6,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,5,6,4,1,7] => [5,6,2,3,4,1,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,5,6,4,7,1] => [5,6,2,3,4,7,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,6,7,4,1] => [5,6,7,2,3,4,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,7,6,4,1] => [7,5,6,2,3,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => [6,5,2,3,4,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,5,4,7,1] => [6,5,2,3,4,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,6,5,7,4,1] => [6,5,7,2,3,4,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,6,7,5,4,1] => [6,7,5,2,3,4,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => [7,6,5,2,3,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7] => [4,2,3,1,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,3,1,5,7,6] => [4,2,3,7,1,5,6] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,7] => [4,2,3,6,1,5,7] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3,1,6,7,5] => [4,2,3,6,7,1,5] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3,1,7,6,5] => [4,7,2,3,6,1,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,3,5,1,6,7] => [4,2,3,5,1,6,7] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 2
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,3,5,1,7,6] => [4,2,3,5,7,1,6] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,3,5,6,1,7] => [4,2,3,5,6,1,7] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,1] => [4,2,3,5,6,7,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,3,5,7,6,1] => [4,7,2,3,5,6,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,1,7] => [4,6,2,3,5,1,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,7,1] => [4,6,2,3,5,7,1] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,3,6,7,5,1] => [4,6,7,2,3,5,1] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => [7,4,6,2,3,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,4,5,3,1,6,7] => [4,5,2,3,1,6,7] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,4,5,3,1,7,6] => [4,5,2,3,7,1,6] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,4,5,3,6,1,7] => [4,5,2,3,6,1,7] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 2
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,4,5,3,6,7,1] => [4,5,2,3,6,7,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,4,5,3,7,6,1] => [4,5,7,2,3,6,1] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,3,1,7] => [4,5,6,2,3,1,7] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,3,7,1] => [4,5,6,2,3,7,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,3,1] => [4,5,6,7,2,3,1] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,4,5,7,6,3,1] => [7,4,5,6,2,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,4,6,5,3,1,7] => [6,4,5,2,3,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,4,6,5,3,7,1] => [6,4,5,2,3,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,4,6,5,7,3,1] => [6,4,5,7,2,3,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,4,6,7,5,3,1] => [6,7,4,5,2,3,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,4,7,6,5,3,1] => [7,6,4,5,2,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => [5,4,2,3,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => [5,4,2,3,7,1,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,4,3,6,1,7] => [5,4,2,3,6,1,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 2
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,4,3,6,7,1] => [5,4,2,3,6,7,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,4,3,7,6,1] => [5,4,7,2,3,6,1] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,5,4,6,3,1,7] => [5,4,6,2,3,1,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,5,4,6,3,7,1] => [5,4,6,2,3,7,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 2
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,5,4,6,7,3,1] => [5,4,6,7,2,3,1] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,5,4,7,6,3,1] => [5,7,4,6,2,3,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,5,6,4,3,1,7] => [5,6,4,2,3,1,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,5,6,4,3,7,1] => [5,6,4,2,3,7,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,5,6,4,7,3,1] => [5,6,4,7,2,3,1] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,5,6,7,4,3,1] => [5,6,7,4,2,3,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,5,7,6,4,3,1] => [7,5,6,4,2,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => [6,5,4,2,3,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => [6,5,4,2,3,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,6,5,4,7,3,1] => [6,5,4,7,2,3,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,6,5,7,4,3,1] => [6,5,7,4,2,3,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,6,7,5,4,3,1] => [6,7,5,4,2,3,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => [7,6,5,4,2,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => [3,2,1,4,5,6,7] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,7,6] => [3,2,7,1,4,5,6] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,2,1,4,6,5,7] => [3,2,6,1,4,5,7] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,2,1,4,6,7,5] => [3,2,6,7,1,4,5] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => [3,7,2,6,1,4,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,5,4,6,7] => [3,2,5,1,4,6,7] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => [3,2,5,7,1,4,6] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,5,6,4,7] => [3,2,5,6,1,4,7] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,5,6,7,4] => [3,2,5,6,7,1,4] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,1,5,7,6,4] => [3,7,2,5,6,1,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,2,1,6,5,4,7] => [3,6,2,5,1,4,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,2,1,6,5,7,4] => [3,6,2,5,7,1,4] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,2,1,6,7,5,4] => [3,6,7,2,5,1,4] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => [7,3,6,2,5,1,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => [3,2,4,1,5,6,7] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => [3,2,4,7,1,5,6] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,7] => [3,2,4,6,1,5,7] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,2,4,1,6,7,5] => [3,2,4,6,7,1,5] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,4,1,7,6,5] => [3,7,2,4,6,1,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => [3,2,4,5,1,6,7] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => [3,2,4,5,7,1,6] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => [3,2,4,5,6,1,7] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => [3,2,4,5,6,7,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,7,6,1] => [3,7,2,4,5,6,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,4,6,5,1,7] => [3,6,2,4,5,1,7] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,2,4,6,5,7,1] => [3,6,2,4,5,7,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,6,7,5,1] => [3,6,7,2,4,5,1] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,2,4,7,6,5,1] => [7,3,6,2,4,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,5,4,1,6,7] => [3,5,2,4,1,6,7] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => [3,5,2,4,7,1,6] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,5,4,6,1,7] => [3,5,2,4,6,1,7] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,5,4,6,7,1] => [3,5,2,4,6,7,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => [3,5,7,2,4,6,1] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,5,6,4,1,7] => [3,5,6,2,4,1,7] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,5,6,4,7,1] => [3,5,6,2,4,7,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,5,6,7,4,1] => [3,5,6,7,2,4,1] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,5,7,6,4,1] => [7,3,5,6,2,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,2,6,5,4,1,7] => [6,3,5,2,4,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,2,6,5,4,7,1] => [6,3,5,2,4,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,2,6,5,7,4,1] => [6,3,5,7,2,4,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,6,7,5,4,1] => [6,7,3,5,2,4,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => [7,6,3,5,2,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7] => [3,4,2,1,5,6,7] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,4,2,1,5,7,6] => [3,4,2,7,1,5,6] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,4,2,1,6,5,7] => [3,4,2,6,1,5,7] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,2,1,6,7,5] => [3,4,2,6,7,1,5] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,2,1,7,6,5] => [3,4,7,2,6,1,5] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,2,5,1,6,7] => [3,4,2,5,1,6,7] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,2,5,1,7,6] => [3,4,2,5,7,1,6] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,2,5,6,1,7] => [3,4,2,5,6,1,7] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,1] => [3,4,2,5,6,7,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [3,4,2,5,7,6,1] => [3,4,7,2,5,6,1] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,4,2,6,5,1,7] => [3,4,6,2,5,1,7] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [3,4,2,6,5,7,1] => [3,4,6,2,5,7,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,2,6,7,5,1] => [3,4,6,7,2,5,1] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,4,2,7,6,5,1] => [7,3,4,6,2,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,2,1,6,7] => [3,4,5,2,1,6,7] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,2,1,7,6] => [3,4,5,2,7,1,6] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,2,6,1,7] => [3,4,5,2,6,1,7] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,2,6,7,1] => [3,4,5,2,6,7,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,2,7,6,1] => [3,4,5,7,2,6,1] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,2,1,7] => [3,4,5,6,2,1,7] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,2,7,1] => [3,4,5,6,2,7,1] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,2,1] => [3,4,5,6,7,2,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,7,6,2,1] => [7,3,4,5,6,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,4,6,5,2,1,7] => [6,3,4,5,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [3,4,6,5,2,7,1] => [6,3,4,5,2,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,6,5,7,2,1] => [6,3,4,5,7,2,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,6,7,5,2,1] => [6,7,3,4,5,2,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,7,6,5,2,1] => [7,6,3,4,5,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,5,4,2,1,6,7] => [5,3,4,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,5,4,2,1,7,6] => [5,3,4,2,7,1,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,5,4,2,6,1,7] => [5,3,4,2,6,1,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,5,4,2,6,7,1] => [5,3,4,2,6,7,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,5,4,2,7,6,1] => [5,3,4,7,2,6,1] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,5,4,6,2,1,7] => [5,3,4,6,2,1,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,5,4,6,2,7,1] => [5,3,4,6,2,7,1] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 2
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,5,4,6,7,2,1] => [5,3,4,6,7,2,1] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,5,4,7,6,2,1] => [5,7,3,4,6,2,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,5,6,4,2,1,7] => [5,6,3,4,2,1,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,5,6,4,2,7,1] => [5,6,3,4,2,7,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [3,5,6,4,7,2,1] => [5,6,3,4,7,2,1] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,5,6,7,4,2,1] => [5,6,7,3,4,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,5,7,6,4,2,1] => [7,5,6,3,4,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,6,5,4,2,1,7] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [3,6,5,4,2,7,1] => [6,5,3,4,2,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,6,5,4,7,2,1] => [6,5,3,4,7,2,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,6,5,7,4,2,1] => [6,5,7,3,4,2,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,6,7,5,4,2,1] => [6,7,5,3,4,2,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,7,6,5,4,2,1] => [7,6,5,3,4,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,3,2,1,5,7,6] => [4,3,2,7,1,5,6] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,7] => [4,3,2,6,1,5,7] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3,2,1,6,7,5] => [4,3,2,6,7,1,5] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => [4,3,7,2,6,1,5] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,3,2,5,1,6,7] => [4,3,2,5,1,6,7] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => [4,3,2,5,7,1,6] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => [4,3,2,5,6,1,7] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => [4,3,2,5,6,7,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,3,2,5,7,6,1] => [4,3,7,2,5,6,1] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => [4,3,6,2,5,1,7] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,3,2,6,5,7,1] => [4,3,6,2,5,7,1] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,2,6,7,5,1] => [4,3,6,7,2,5,1] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,1] => [4,7,3,6,2,5,1] => [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] => [4,3,5,2,1,6,7] => [4,3,5,2,1,6,7] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 2
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [4,3,5,2,1,7,6] => [4,3,5,2,7,1,6] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [4,3,5,2,6,1,7] => [4,3,5,2,6,1,7] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 3
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [4,3,5,2,6,7,1] => [4,3,5,2,6,7,1] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,3,5,2,7,6,1] => [4,3,5,7,2,6,1] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [4,3,5,6,2,1,7] => [4,3,5,6,2,1,7] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [4,3,5,6,2,7,1] => [4,3,5,6,2,7,1] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,5,6,7,2,1] => [4,3,5,6,7,2,1] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,3,5,7,6,2,1] => [4,7,3,5,6,2,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [4,3,6,5,2,1,7] => [4,6,3,5,2,1,7] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [4,3,6,5,2,7,1] => [4,6,3,5,2,7,1] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,3,6,5,7,2,1] => [4,6,3,5,7,2,1] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,6,7,5,2,1] => [4,6,7,3,5,2,1] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,3,7,6,5,2,1] => [7,4,6,3,5,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [4,5,3,2,1,6,7] => [4,5,3,2,1,6,7] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [4,5,3,2,1,7,6] => [4,5,3,2,7,1,6] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [4,5,3,2,6,1,7] => [4,5,3,2,6,1,7] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 2
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [4,5,3,2,6,7,1] => [4,5,3,2,6,7,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,5,3,2,7,6,1] => [4,5,3,7,2,6,1] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [4,5,3,6,2,1,7] => [4,5,3,6,2,1,7] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [4,5,3,6,2,7,1] => [4,5,3,6,2,7,1] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,5,3,6,7,2,1] => [4,5,3,6,7,2,1] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,3,7,6,2,1] => [4,5,7,3,6,2,1] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,3,2,1,7] => [4,5,6,3,2,1,7] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,3,2,7,1] => [4,5,6,3,2,7,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,3,7,2,1] => [4,5,6,3,7,2,1] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,3,2,1] => [4,5,6,7,3,2,1] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,7,6,3,2,1] => [7,4,5,6,3,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [4,6,5,3,2,1,7] => [6,4,5,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [4,6,5,3,2,7,1] => [6,4,5,3,2,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,6,5,3,7,2,1] => [6,4,5,3,7,2,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,6,5,7,3,2,1] => [6,4,5,7,3,2,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,6,7,5,3,2,1] => [6,7,4,5,3,2,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [4,7,6,5,3,2,1] => [7,6,4,5,3,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => [5,4,3,2,7,1,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => [5,4,3,2,6,1,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => [5,4,3,2,6,7,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,4,3,2,7,6,1] => [5,4,3,7,2,6,1] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [5,4,3,6,2,1,7] => [5,4,3,6,2,1,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,4,3,6,2,7,1] => [5,4,3,6,2,7,1] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 2
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => [5,4,3,6,7,2,1] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,4,3,7,6,2,1] => [5,4,7,3,6,2,1] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,4,6,3,2,1,7] => [5,4,6,3,2,1,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,4,6,3,2,7,1] => [5,4,6,3,2,7,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,4,6,3,7,2,1] => [5,4,6,3,7,2,1] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 2
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,6,7,3,2,1] => [5,4,6,7,3,2,1] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [5,4,7,6,3,2,1] => [5,7,4,6,3,2,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [5,6,4,3,2,1,7] => [5,6,4,3,2,1,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,6,4,3,2,7,1] => [5,6,4,3,2,7,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,6,4,3,7,2,1] => [5,6,4,3,7,2,1] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,6,4,7,3,2,1] => [5,6,4,7,3,2,1] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [5,6,7,4,3,2,1] => [5,6,7,4,3,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [5,7,6,4,3,2,1] => [7,5,6,4,3,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,5,4,3,2,7,1] => [6,5,4,3,2,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,5,4,3,7,2,1] => [6,5,4,3,7,2,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [6,5,4,7,3,2,1] => [6,5,4,7,3,2,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [6,5,7,4,3,2,1] => [6,5,7,4,3,2,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [6,7,5,4,3,2,1] => [6,7,5,4,3,2,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => [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] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => [8,1,2,3,4,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => [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
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,7,8,6] => [7,8,1,2,3,4,5,6] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,7,6] => [8,7,1,2,3,4,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => [6,8,1,2,3,4,5,7] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,6,7,5,8] => [6,7,1,2,3,4,5,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,5] => [6,7,8,1,2,3,4,5] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,6,8,7,5] => [8,6,7,1,2,3,4,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,7,6,5,8] => [7,6,1,2,3,4,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,7,6,8,5] => [7,6,8,1,2,3,4,5] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,7,8,6,5] => [7,8,6,1,2,3,4,5] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,7,6,5] => [8,7,6,1,2,3,4,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,3,5,4,6,8,7] => [5,8,1,2,3,4,6,7] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => [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
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3,5,4,7,8,6] => [5,7,8,1,2,3,4,6] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,7,6] => [8,5,7,1,2,3,4,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,5,6,4,8,7] => [5,6,8,1,2,3,4,7] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,5,6,7,4,8] => [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
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => [5,6,7,8,1,2,3,4] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,8,7,4] => [8,5,6,7,1,2,3,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,3,5,7,6,4,8] => [7,5,6,1,2,3,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,3,5,7,6,8,4] => [7,5,6,8,1,2,3,4] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,5,7,8,6,4] => [7,8,5,6,1,2,3,4] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,5,8,7,6,4] => [8,7,5,6,1,2,3,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,5,4,8,7] => [6,5,8,1,2,3,4,7] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,3,6,5,7,4,8] => [6,5,7,1,2,3,4,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,6,5,7,8,4] => [6,5,7,8,1,2,3,4] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,6,5,8,7,4] => [6,8,5,7,1,2,3,4] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,3,6,7,5,4,8] => [6,7,5,1,2,3,4,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,6,7,5,8,4] => [6,7,5,8,1,2,3,4] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,6,7,8,5,4] => [6,7,8,5,1,2,3,4] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,6,8,7,5,4] => [8,6,7,5,1,2,3,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,7,6,5,4,8] => [7,6,5,1,2,3,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,3,7,6,5,8,4] => [7,6,5,8,1,2,3,4] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,7,6,8,5,4] => [7,6,8,5,1,2,3,4] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,7,8,6,5,4] => [7,8,6,5,1,2,3,4] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,7,6,5,4] => [8,7,6,5,1,2,3,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,8,7] => [4,8,1,2,3,5,6,7] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,4,3,5,7,8,6] => [4,7,8,1,2,3,5,6] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,4,3,5,8,7,6] => [8,4,7,1,2,3,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => [4,6,8,1,2,3,5,7] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,4,3,6,8,7,5] => [8,4,6,7,1,2,3,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,4,3,7,6,5,8] => [7,4,6,1,2,3,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,6,8,5] => [7,4,6,8,1,2,3,5] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,4,3,7,8,6,5] => [7,8,4,6,1,2,3,5] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,7,6,5] => [8,7,4,6,1,2,3,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,2,4,5,3,6,8,7] => [4,5,8,1,2,3,6,7] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,4,5,3,7,8,6] => [4,5,7,8,1,2,3,6] => [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,4,5,6,8,7,3] => [8,4,5,6,7,1,2,3] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,2,4,5,7,6,3,8] => [7,4,5,6,1,2,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,4,5,7,8,6,3] => [7,8,4,5,6,1,2,3] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,4,5,8,7,6,3] => [8,7,4,5,6,1,2,3] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,2,4,6,5,3,8,7] => [6,4,5,8,1,2,3,7] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,2,4,6,5,7,8,3] => [6,4,5,7,8,1,2,3] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,2,4,6,5,8,7,3] => [6,8,4,5,7,1,2,3] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,2,4,6,7,5,8,3] => [6,7,4,5,8,1,2,3] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,2,4,6,7,8,5,3] => [6,7,8,4,5,1,2,3] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,2,4,6,8,7,5,3] => [8,6,7,4,5,1,2,3] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,2,4,7,6,5,3,8] => [7,6,4,5,1,2,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,2,4,7,6,5,8,3] => [7,6,4,5,8,1,2,3] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4,8,7,6,5,3] => [8,7,6,4,5,1,2,3] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,5,4,3,6,8,7] => [5,4,8,1,2,3,6,7] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,2,5,4,3,7,6,8] => [5,4,7,1,2,3,6,8] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,4,3,8,7,6] => [5,8,4,7,1,2,3,6] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,2,5,4,6,8,7,3] => [5,8,4,6,7,1,2,3] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,2,5,4,7,6,8,3] => [5,7,4,6,8,1,2,3] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,2,5,6,7,4,3,8] => [5,6,7,4,1,2,3,8] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,5,6,7,8,4,3] => [5,6,7,8,4,1,2,3] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,2,5,6,8,7,4,3] => [8,5,6,7,4,1,2,3] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,2,5,7,6,4,3,8] => [7,5,6,4,1,2,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,2,5,7,6,4,8,3] => [7,5,6,4,8,1,2,3] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,2,5,7,6,8,4,3] => [7,5,6,8,4,1,2,3] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,2,5,7,8,6,4,3] => [7,8,5,6,4,1,2,3] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,6,5,4,3,8,7] => [6,5,4,8,1,2,3,7] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,6,5,4,7,8,3] => [6,5,4,7,8,1,2,3] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,2,6,5,7,4,8,3] => [6,5,7,4,8,1,2,3] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,6,5,7,8,4,3] => [6,5,7,8,4,1,2,3] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,6,5,8,7,4,3] => [6,8,5,7,4,1,2,3] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,2,6,7,5,4,8,3] => [6,7,5,4,8,1,2,3] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,2,6,7,5,8,4,3] => [6,7,5,8,4,1,2,3] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,6,7,8,5,4,3] => [6,7,8,5,4,1,2,3] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,7,6,5,4,3,8] => [7,6,5,4,1,2,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,7,6,5,4,8,3] => [7,6,5,4,8,1,2,3] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,7,6,5,8,4,3] => [7,6,5,8,4,1,2,3] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,7,6,8,5,4,3] => [7,6,8,5,4,1,2,3] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,7,8,6,5,4,3] => [7,8,6,5,4,1,2,3] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,7,6,5,4,3] => [8,7,6,5,4,1,2,3] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => [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
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,8,7] => [3,8,1,2,4,5,6,7] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => [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
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,7,8,6] => [3,7,8,1,2,4,5,6] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,8,7,6] => [8,3,7,1,2,4,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,2,4,7,6,5,8] => [7,3,6,1,2,4,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,7,6,5] => [8,7,3,6,1,2,4,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,7,6] => [8,3,5,7,1,2,4,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,3,2,5,6,8,7,4] => [8,3,5,6,7,1,2,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,2,5,7,6,4,8] => [7,3,5,6,1,2,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,3,2,5,7,6,8,4] => [7,3,5,6,8,1,2,4] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,3,2,5,7,8,6,4] => [7,8,3,5,6,1,2,4] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,2,5,8,7,6,4] => [8,7,3,5,6,1,2,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,6,5,4,8,7] => [6,3,5,8,1,2,4,7] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,5,7,4,8] => [6,3,5,7,1,2,4,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,5,8,7,4] => [6,8,3,5,7,1,2,4] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,2,6,7,5,8,4] => [6,7,3,5,8,1,2,4] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,3,2,6,7,8,5,4] => [6,7,8,3,5,1,2,4] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2,6,8,7,5,4] => [8,6,7,3,5,1,2,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,6,5,4,8] => [7,6,3,5,1,2,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,7,6,5,8,4] => [7,6,3,5,8,1,2,4] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,7,6,8,5,4] => [7,6,8,3,5,1,2,4] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,3,2,7,8,6,5,4] => [7,8,6,3,5,1,2,4] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,7,6,5,4] => [8,7,6,3,5,1,2,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,3,4,2,7,6,5,8] => [7,3,4,6,1,2,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,6,8,5] => [7,3,4,6,8,1,2,5] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,3,4,2,7,8,6,5] => [7,8,3,4,6,1,2,5] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4,2,8,7,6,5] => [8,7,3,4,6,1,2,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8] => [3,4,5,1,2,6,7,8] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,5,2,8,7,6] => [8,3,4,5,7,1,2,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,2,7,8] => [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
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,2,8,7] => [3,4,5,6,8,1,2,7] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,2,8] => [3,4,5,6,7,1,2,8] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,2] => [3,4,5,6,7,8,1,2] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,8,7,2] => [8,3,4,5,6,7,1,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,5,7,6,8,2] => [7,3,4,5,6,8,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,5,7,8,6,2] => [7,8,3,4,5,6,1,2] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,5,8,7,6,2] => [8,7,3,4,5,6,1,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,3,4,6,5,8,7,2] => [6,8,3,4,5,7,1,2] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,3,4,6,7,5,2,8] => [6,7,3,4,5,1,2,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,6,7,8,5,2] => [6,7,8,3,4,5,1,2] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,3,4,6,8,7,5,2] => [8,6,7,3,4,5,1,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,4,7,6,5,8,2] => [7,6,3,4,5,8,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 1
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,3,4,7,8,6,5,2] => [7,8,6,3,4,5,1,2] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,8,7,6,5,2] => [8,7,6,3,4,5,1,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,3,5,4,2,7,6,8] => [5,3,4,7,1,2,6,8] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,3,5,4,7,6,2,8] => [5,7,3,4,6,1,2,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,5,4,7,6,8,2] => [5,7,3,4,6,8,1,2] => [1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,3,5,4,7,8,6,2] => [5,7,8,3,4,6,1,2] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,5,6,7,8,4,2] => [5,6,7,8,3,4,1,2] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,3,5,6,8,7,4,2] => [8,5,6,7,3,4,1,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,3,5,7,6,4,2,8] => [7,5,6,3,4,1,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,3,5,7,6,4,8,2] => [7,5,6,3,4,8,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,3,5,7,6,8,4,2] => [7,5,6,8,3,4,1,2] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,5,7,8,6,4,2] => [7,8,5,6,3,4,1,2] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,3,5,8,7,6,4,2] => [8,7,5,6,3,4,1,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,3,6,5,7,4,2,8] => [6,5,7,3,4,1,2,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 2
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,6,5,7,8,4,2] => [6,5,7,8,3,4,1,2] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,3,6,5,8,7,4,2] => [6,8,5,7,3,4,1,2] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,3,6,7,5,8,4,2] => [6,7,5,8,3,4,1,2] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,6,7,8,5,4,2] => [6,7,8,5,3,4,1,2] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,3,7,6,5,4,2,8] => [7,6,5,3,4,1,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,3,7,6,5,8,4,2] => [7,6,5,8,3,4,1,2] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,7,6,8,5,4,2] => [7,6,8,5,3,4,1,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,7,8,6,5,4,2] => [7,8,6,5,3,4,1,2] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,8,7,6,5,4,2] => [8,7,6,5,3,4,1,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,3,2,5,8,7,6] => [4,8,3,7,1,2,5,6] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,4,3,2,6,8,7,5] => [4,8,3,6,7,1,2,5] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => [4,7,3,6,1,2,5,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,4,3,2,7,6,8,5] => [4,7,3,6,8,1,2,5] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,3,2,8,7,6,5] => [8,4,7,3,6,1,2,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,4,3,5,2,8,7,6] => [4,8,3,5,7,1,2,6] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,2] => [4,3,5,6,7,8,1,2] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,4,3,5,6,8,7,2] => [4,8,3,5,6,7,1,2] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,3,5,7,6,2,8] => [4,7,3,5,6,1,2,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,3,5,7,8,6,2] => [4,7,8,3,5,6,1,2] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,2] => [4,6,8,3,5,7,1,2] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,3,7,6,8,5,2] => [7,4,6,8,3,5,1,2] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,3,7,8,6,5,2] => [7,8,4,6,3,5,1,2] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,3,8,7,6,5,2] => [8,7,4,6,3,5,1,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,4,5,3,2,8,7,6] => [4,5,8,3,7,1,2,6] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,4,5,3,6,8,7,2] => [4,5,8,3,6,7,1,2] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,4,5,3,7,6,2,8] => [4,5,7,3,6,1,2,8] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,4,5,3,8,7,6,2] => [8,4,5,7,3,6,1,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,4,5,7,6,3,2,8] => [7,4,5,6,3,1,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,4,5,7,8,6,3,2] => [7,8,4,5,6,3,1,2] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,4,6,5,3,8,7,2] => [6,4,5,8,3,7,1,2] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,4,6,7,5,8,3,2] => [6,7,4,5,8,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => 1
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,4,6,7,8,5,3,2] => [6,7,8,4,5,3,1,2] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,4,6,8,7,5,3,2] => [8,6,7,4,5,3,1,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,4,7,6,5,3,2,8] => [7,6,4,5,3,1,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,4,7,6,5,8,3,2] => [7,6,4,5,8,3,1,2] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 1
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,4,7,8,6,5,3,2] => [7,8,6,4,5,3,1,2] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,4,8,7,6,5,3,2] => [8,7,6,4,5,3,1,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,5,4,3,2,6,8,7] => [5,4,3,8,1,2,6,7] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,4,3,2,7,6,8] => [5,4,3,7,1,2,6,8] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,4,3,2,8,7,6] => [5,4,8,3,7,1,2,6] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,4,3,6,8,7,2] => [5,4,8,3,6,7,1,2] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,5,4,3,7,6,8,2] => [5,4,7,3,6,8,1,2] => [1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,5,4,3,8,7,6,2] => [5,8,4,7,3,6,1,2] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,5,4,7,6,3,8,2] => [5,7,4,6,3,8,1,2] => [1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => 1
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,5,6,7,8,4,3,2] => [5,6,7,8,4,3,1,2] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,5,7,6,4,3,2,8] => [7,5,6,4,3,1,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,5,7,6,4,3,8,2] => [7,5,6,4,3,8,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 1
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,5,7,6,8,4,3,2] => [7,5,6,8,4,3,1,2] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,5,7,8,6,4,3,2] => [7,8,5,6,4,3,1,2] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,5,8,7,6,4,3,2] => [8,7,5,6,4,3,1,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,5,4,3,8,7,2] => [6,5,4,8,3,7,1,2] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,6,5,4,7,8,3,2] => [6,5,4,7,8,3,1,2] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,6,5,7,4,8,3,2] => [6,5,7,4,8,3,1,2] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => 2
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,6,5,7,8,4,3,2] => [6,5,7,8,4,3,1,2] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,6,7,5,4,3,2,8] => [6,7,5,4,3,1,2,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,6,7,5,8,4,3,2] => [6,7,5,8,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,6,7,8,5,4,3,2] => [6,7,8,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,6,8,7,5,4,3,2] => [8,6,7,5,4,3,1,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,6,5,4,3,2,8] => [7,6,5,4,3,1,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,6,5,4,3,8,2] => [7,6,5,4,3,8,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,7,6,5,4,8,3,2] => [7,6,5,4,8,3,1,2] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,7,6,5,8,4,3,2] => [7,6,5,8,4,3,1,2] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7,6,8,5,4,3,2] => [7,6,8,5,4,3,1,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,7,8,6,5,4,3,2] => [7,8,6,5,4,3,1,2] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => [8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => [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
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => [2,8,1,3,4,5,6,7] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,7,8,6] => [2,7,8,1,3,4,5,6] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,4,6,8,7,5] => [8,2,6,7,1,3,4,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,7,6,5] => [8,7,2,6,1,3,4,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,1,3,5,6,8,7,4] => [8,2,5,6,7,1,3,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,1,3,5,7,6,8,4] => [7,2,5,6,8,1,3,4] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,1,3,5,7,8,6,4] => [7,8,2,5,6,1,3,4] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,1,3,5,8,7,6,4] => [8,7,2,5,6,1,3,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,6,5,4,8,7] => [6,2,5,8,1,3,4,7] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,3,6,5,7,8,4] => [6,2,5,7,8,1,3,4] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,3,6,5,8,7,4] => [6,8,2,5,7,1,3,4] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,3,6,7,5,4,8] => [6,7,2,5,1,3,4,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,1,3,6,8,7,5,4] => [8,6,7,2,5,1,3,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,3,7,6,8,5,4] => [7,6,8,2,5,1,3,4] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,3,7,8,6,5,4] => [7,8,6,2,5,1,3,4] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,7,6,5,4] => [8,7,6,2,5,1,3,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => [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
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,3,6,7,5,8] => [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
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,7,5] => [8,2,4,6,7,1,3,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,4,3,7,6,5,8] => [7,2,4,6,1,3,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,6,8,5] => [7,2,4,6,8,1,3,5] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,7,8,6,5] => [7,8,2,4,6,1,3,5] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => [8,7,2,4,6,1,3,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,1,4,5,7,6,8,3] => [7,2,4,5,6,8,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,4,5,7,8,6,3] => [7,8,2,4,5,6,1,3] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,1,4,6,5,8,7,3] => [6,8,2,4,5,7,1,3] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,1,4,6,8,7,5,3] => [8,6,7,2,4,5,1,3] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,1,4,7,6,5,8,3] => [7,6,2,4,5,8,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,1,4,7,6,8,5,3] => [7,6,8,2,4,5,1,3] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,5,4,3,6,8,7] => [5,2,4,8,1,3,6,7] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,5,4,3,7,6,8] => [5,2,4,7,1,3,6,8] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => 2
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,5,4,3,8,7,6] => [5,8,2,4,7,1,3,6] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,5,4,6,8,7,3] => [5,8,2,4,6,7,1,3] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,8,3] => [5,7,2,4,6,8,1,3] => [1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,4,7,8,6,3] => [5,7,8,2,4,6,1,3] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,1,5,6,4,8,7,3] => [5,6,8,2,4,7,1,3] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,1,5,6,7,8,4,3] => [5,6,7,8,2,4,1,3] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,1,5,7,6,8,4,3] => [7,5,6,8,2,4,1,3] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,5,7,8,6,4,3] => [7,8,5,6,2,4,1,3] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,1,5,8,7,6,4,3] => [8,7,5,6,2,4,1,3] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,6,5,7,8,4,3] => [6,5,7,8,2,4,1,3] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,6,5,8,7,4,3] => [6,8,5,7,2,4,1,3] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,1,6,7,5,8,4,3] => [6,7,5,8,2,4,1,3] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,6,7,8,5,4,3] => [6,7,8,5,2,4,1,3] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,7,6,5,4,8,3] => [7,6,5,2,4,8,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,7,6,5,8,4,3] => [7,6,5,8,2,4,1,3] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,7,6,8,5,4,3] => [7,6,8,5,2,4,1,3] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => [8,7,6,5,2,4,1,3] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8] => [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
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,3,1,4,5,8,7,6] => [8,2,3,7,1,4,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,3,1,4,6,8,7,5] => [8,2,3,6,7,1,4,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,7,6,8,5] => [7,2,3,6,8,1,4,5] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,3,1,4,7,8,6,5] => [7,8,2,3,6,1,4,5] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,8,7,6,5] => [8,7,2,3,6,1,4,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8] => [2,3,5,1,4,6,7,8] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,3,1,5,6,8,7,4] => [8,2,3,5,6,7,1,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,3,1,5,7,8,6,4] => [7,8,2,3,5,6,1,4] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,5,8,7,4] => [6,8,2,3,5,7,1,4] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,3,1,7,6,5,4,8] => [7,6,2,3,5,1,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,7,6,5,8,4] => [7,6,2,3,5,8,1,4] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,3,1,7,6,8,5,4] => [7,6,8,2,3,5,1,4] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,1,7,8,6,5,4] => [7,8,6,2,3,5,1,4] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,8,7,6] => [8,2,3,4,7,1,5,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => [2,3,4,6,7,8,1,5] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,4,1,6,8,7,5] => [8,2,3,4,6,7,1,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,6,8,5] => [7,2,3,4,6,8,1,5] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,4,1,7,8,6,5] => [7,8,2,3,4,6,1,5] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,8,7,6,5] => [8,7,2,3,4,6,1,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => [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
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,5,1,6,8,7] => [2,3,4,5,8,1,6,7] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,1,7,8,6] => [2,3,4,5,7,8,1,6] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,8,7,6] => [8,2,3,4,5,7,1,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => [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
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => [2,3,4,5,6,8,1,7] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => [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
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => [2,3,4,5,6,7,8,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,8,7,1] => [8,2,3,4,5,6,7,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,7,6,1,8] => [7,2,3,4,5,6,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,7,6,8,1] => [7,2,3,4,5,6,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,7,8,6,1] => [7,8,2,3,4,5,6,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,8,7,6,1] => [8,7,2,3,4,5,6,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,4,6,7,5,1,8] => [6,7,2,3,4,5,1,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,4,6,7,5,8,1] => [6,7,2,3,4,5,8,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,6,7,8,5,1] => [6,7,8,2,3,4,5,1] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,4,6,8,7,5,1] => [8,6,7,2,3,4,5,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,4,7,6,5,1,8] => [7,6,2,3,4,5,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,4,7,6,5,8,1] => [7,6,2,3,4,5,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,7,6,8,5,1] => [7,6,8,2,3,4,5,1] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,7,8,6,5,1] => [7,8,6,2,3,4,5,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,8,7,6,5,1] => [8,7,6,2,3,4,5,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,4,1,8,7,6] => [5,8,2,3,4,7,1,6] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,3,5,4,7,6,8,1] => [5,7,2,3,4,6,8,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,3,5,6,4,8,7,1] => [5,6,8,2,3,4,7,1] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,3,5,6,7,4,1,8] => [5,6,7,2,3,4,1,8] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,3,5,6,7,4,8,1] => [5,6,7,2,3,4,8,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,5,6,7,8,4,1] => [5,6,7,8,2,3,4,1] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,3,5,6,8,7,4,1] => [8,5,6,7,2,3,4,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,3,5,7,6,4,8,1] => [7,5,6,2,3,4,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,3,5,7,8,6,4,1] => [7,8,5,6,2,3,4,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,3,5,8,7,6,4,1] => [8,7,5,6,2,3,4,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,3,6,5,7,8,4,1] => [6,5,7,8,2,3,4,1] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,3,6,7,5,8,4,1] => [6,7,5,8,2,3,4,1] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => 1
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,6,7,8,5,4,1] => [6,7,8,5,2,3,4,1] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,3,6,8,7,5,4,1] => [8,6,7,5,2,3,4,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,3,7,6,5,4,1,8] => [7,6,5,2,3,4,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,3,7,6,5,4,8,1] => [7,6,5,2,3,4,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,3,7,6,5,8,4,1] => [7,6,5,8,2,3,4,1] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 1
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,3,7,6,8,5,4,1] => [7,6,8,5,2,3,4,1] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,8,7,6,5,4,1] => [8,7,6,5,2,3,4,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,8,7,5] => [4,8,2,3,6,7,1,5] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,3,1,7,6,8,5] => [4,7,2,3,6,8,1,5] => [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,4,3,1,8,7,6,5] => [8,4,7,2,3,6,1,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,4,3,5,1,8,7,6] => [4,8,2,3,5,7,1,6] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,4,3,5,6,8,7,1] => [4,8,2,3,5,6,7,1] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [2,4,3,5,7,6,1,8] => [4,7,2,3,5,6,1,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [2,4,3,5,8,7,6,1] => [8,4,7,2,3,5,6,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,1] => [4,6,8,2,3,5,7,1] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,4,3,6,8,7,5,1] => [8,4,6,7,2,3,5,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [2,4,3,7,6,5,1,8] => [7,4,6,2,3,5,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,4,3,7,6,5,8,1] => [7,4,6,2,3,5,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,4,5,3,1,8,7,6] => [4,5,8,2,3,7,1,6] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,4,5,3,6,8,7,1] => [4,5,8,2,3,6,7,1] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [2,4,5,6,8,7,3,1] => [8,4,5,6,7,2,3,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [2,4,5,7,6,3,1,8] => [7,4,5,6,2,3,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [2,4,5,7,6,3,8,1] => [7,4,5,6,2,3,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [2,4,5,7,8,6,3,1] => [7,8,4,5,6,2,3,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,4,6,5,3,8,7,1] => [6,4,5,8,2,3,7,1] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,4,6,5,7,3,8,1] => [6,4,5,7,2,3,8,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => 2
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,4,6,5,8,7,3,1] => [6,8,4,5,7,2,3,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [2,4,6,7,5,3,1,8] => [6,7,4,5,2,3,1,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,4,6,7,5,3,8,1] => [6,7,4,5,2,3,8,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [2,4,6,7,5,8,3,1] => [6,7,4,5,8,2,3,1] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => 1
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,4,6,7,8,5,3,1] => [6,7,8,4,5,2,3,1] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,4,6,8,7,5,3,1] => [8,6,7,4,5,2,3,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [2,4,7,6,5,3,1,8] => [7,6,4,5,2,3,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [2,4,7,6,5,3,8,1] => [7,6,4,5,2,3,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => 1
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [2,4,7,6,5,8,3,1] => [7,6,4,5,8,2,3,1] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 1
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,4,8,7,6,5,3,1] => [8,7,6,4,5,2,3,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,5,4,3,6,8,7,1] => [5,4,8,2,3,6,7,1] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,5,4,3,8,7,6,1] => [5,8,4,7,2,3,6,1] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,5,4,7,6,3,1,8] => [5,7,4,6,2,3,1,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,5,4,8,7,6,3,1] => [8,5,7,4,6,2,3,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [2,5,6,4,8,7,3,1] => [5,6,8,4,7,2,3,1] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,5,6,7,4,3,8,1] => [5,6,7,4,2,3,8,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,5,6,7,8,4,3,1] => [5,6,7,8,4,2,3,1] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,5,6,8,7,4,3,1] => [8,5,6,7,4,2,3,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [2,5,7,6,4,3,1,8] => [7,5,6,4,2,3,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [2,5,7,6,4,3,8,1] => [7,5,6,4,2,3,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [2,5,7,6,4,8,3,1] => [7,5,6,4,8,2,3,1] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 1
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [2,5,7,6,8,4,3,1] => [7,5,6,8,4,2,3,1] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 1
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,5,8,7,6,4,3,1] => [8,7,5,6,4,2,3,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,6,5,4,8,7,3,1] => [6,5,8,4,7,2,3,1] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,6,5,7,4,3,8,1] => [6,5,7,4,2,3,8,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => 2
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [2,6,5,7,4,8,3,1] => [6,5,7,4,8,2,3,1] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => 2
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,6,5,8,7,4,3,1] => [6,8,5,7,4,2,3,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,6,7,5,4,3,1,8] => [6,7,5,4,2,3,1,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,6,7,5,8,4,3,1] => [6,7,5,8,4,2,3,1] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => 1
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,6,8,7,5,4,3,1] => [8,6,7,5,4,2,3,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,7,6,5,4,3,1,8] => [7,6,5,4,2,3,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,7,6,5,4,3,8,1] => [7,6,5,4,2,3,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,7,6,5,4,8,3,1] => [7,6,5,4,8,2,3,1] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 1
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,7,6,5,8,4,3,1] => [7,6,5,8,4,2,3,1] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 1
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,7,6,8,5,4,3,1] => [7,6,8,5,4,2,3,1] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,7,8,6,5,4,3,1] => [7,8,6,5,4,2,3,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,8,7,6,5,4,3,1] => [8,7,6,5,4,2,3,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8] => [3,2,1,4,5,6,7,8] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,2,1,4,5,8,7,6] => [3,8,2,7,1,4,5,6] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,2,1,4,6,8,7,5] => [3,8,2,6,7,1,4,5] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,2,1,4,7,6,5,8] => [3,7,2,6,1,4,5,8] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [3,2,1,4,7,6,8,5] => [3,7,2,6,8,1,4,5] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,2,1,4,7,8,6,5] => [3,7,8,2,6,1,4,5] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,2,1,4,8,7,6,5] => [8,3,7,2,6,1,4,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [3,2,1,5,4,8,7,6] => [3,8,2,5,7,1,4,6] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,2,1,5,6,8,7,4] => [3,8,2,5,6,7,1,4] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,2,1,5,7,8,6,4] => [3,7,8,2,5,6,1,4] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,2,1,5,8,7,6,4] => [8,3,7,2,5,6,1,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,2,1,7,6,5,4,8] => [7,3,6,2,5,1,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,1,7,8,6,5,4] => [7,8,3,6,2,5,1,4] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => [8,7,3,6,2,5,1,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [3,2,4,1,5,8,7,6] => [3,8,2,4,7,1,5,6] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,2,4,1,6,8,7,5] => [3,8,2,4,6,7,1,5] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,7,6,8,5] => [3,7,2,4,6,8,1,5] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,2,4,1,7,8,6,5] => [3,7,8,2,4,6,1,5] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,2,4,1,8,7,6,5] => [8,3,7,2,4,6,1,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,6,1,7,8] => [3,2,4,5,6,1,7,8] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,1,8] => [3,2,4,5,6,7,1,8] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,1] => [3,2,4,5,6,7,8,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,6,8,7,1] => [3,8,2,4,5,6,7,1] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [3,2,4,5,7,6,1,8] => [3,7,2,4,5,6,1,8] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,2,4,5,7,8,6,1] => [3,7,8,2,4,5,6,1] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [3,2,4,7,6,5,8,1] => [7,3,6,2,4,5,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [3,2,4,7,6,8,5,1] => [7,3,6,8,2,4,5,1] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,7,8,6,5,1] => [7,8,3,6,2,4,5,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,2,6,5,4,8,7,1] => [6,3,5,8,2,4,7,1] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,2,6,5,7,4,8,1] => [6,3,5,7,2,4,8,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [3,2,6,5,7,8,4,1] => [6,3,5,7,8,2,4,1] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => 1
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [3,2,6,5,8,7,4,1] => [6,8,3,5,7,2,4,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,2,6,7,5,4,1,8] => [6,7,3,5,2,4,1,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [3,2,6,7,5,4,8,1] => [6,7,3,5,2,4,8,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => 1
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,2,6,8,7,5,4,1] => [8,6,7,3,5,2,4,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,2,7,6,5,4,1,8] => [7,6,3,5,2,4,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [3,2,7,6,5,4,8,1] => [7,6,3,5,2,4,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [3,2,7,6,5,8,4,1] => [7,6,3,5,8,2,4,1] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 1
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [3,2,7,6,8,5,4,1] => [7,6,8,3,5,2,4,1] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,2,8,7,6,5,4,1] => [8,7,6,3,5,2,4,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [3,4,2,1,8,7,6,5] => [8,3,4,7,2,6,1,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,8,1] => [3,4,2,5,6,7,8,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [3,4,2,5,8,7,6,1] => [8,3,4,7,2,5,6,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,5,2,1,6,7,8] => [3,4,5,2,1,6,7,8] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,5,2,6,7,8,1] => [3,4,5,2,6,7,8,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,6,2,1,7,8] => [3,4,5,6,2,1,7,8] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,6,2,8,7,1] => [3,4,5,6,8,2,7,1] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,7,2,1,8] => [3,4,5,6,7,2,1,8] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,7,2,8,1] => [3,4,5,6,7,2,8,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,2,1] => [3,4,5,6,7,8,2,1] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,6,8,7,2,1] => [8,3,4,5,6,7,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [3,4,5,7,6,2,8,1] => [7,3,4,5,6,2,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,5,7,6,8,2,1] => [7,3,4,5,6,8,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,5,7,8,6,2,1] => [7,8,3,4,5,6,2,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,8,7,6,2,1] => [8,7,3,4,5,6,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [3,4,6,5,8,7,2,1] => [6,8,3,4,5,7,2,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [3,4,6,7,8,5,2,1] => [6,7,8,3,4,5,2,1] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,4,6,8,7,5,2,1] => [8,6,7,3,4,5,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [3,4,7,6,5,2,1,8] => [7,6,3,4,5,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [3,4,7,6,5,2,8,1] => [7,6,3,4,5,2,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [3,4,7,6,5,8,2,1] => [7,6,3,4,5,8,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 1
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [3,4,7,6,8,5,2,1] => [7,6,8,3,4,5,2,1] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,4,7,8,6,5,2,1] => [7,8,6,3,4,5,2,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,8,7,6,5,2,1] => [8,7,6,3,4,5,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [3,5,4,2,6,8,7,1] => [5,3,4,8,2,6,7,1] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [3,5,4,2,7,6,1,8] => [5,3,4,7,2,6,1,8] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => 2
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [3,5,4,6,8,7,2,1] => [5,8,3,4,6,7,2,1] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [3,5,4,7,6,2,8,1] => [5,7,3,4,6,2,8,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [3,5,4,7,6,8,2,1] => [5,7,3,4,6,8,2,1] => [1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [3,5,4,7,8,6,2,1] => [5,7,8,3,4,6,2,1] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,5,4,8,7,6,2,1] => [8,5,7,3,4,6,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [3,5,6,7,8,4,2,1] => [5,6,7,8,3,4,2,1] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,5,6,8,7,4,2,1] => [8,5,6,7,3,4,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [3,5,7,6,4,2,1,8] => [7,5,6,3,4,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [3,5,7,6,4,2,8,1] => [7,5,6,3,4,2,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => 1
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,5,7,8,6,4,2,1] => [7,8,5,6,3,4,2,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [3,5,8,7,6,4,2,1] => [8,7,5,6,3,4,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [3,6,5,7,4,2,8,1] => [6,5,7,3,4,2,8,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => 2
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [3,6,5,7,8,4,2,1] => [6,5,7,8,3,4,2,1] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => 1
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,6,5,8,7,4,2,1] => [6,8,5,7,3,4,2,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [3,6,7,5,8,4,2,1] => [6,7,5,8,3,4,2,1] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => 1
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [3,6,8,7,5,4,2,1] => [8,6,7,5,3,4,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [3,7,6,5,4,2,1,8] => [7,6,5,3,4,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [3,7,6,5,4,2,8,1] => [7,6,5,3,4,2,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [3,7,6,5,4,8,2,1] => [7,6,5,3,4,8,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 1
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [3,7,6,5,8,4,2,1] => [7,6,5,8,3,4,2,1] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 1
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,7,6,8,5,4,2,1] => [7,6,8,5,3,4,2,1] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 1
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,7,8,6,5,4,2,1] => [7,8,6,5,3,4,2,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,8,7,6,5,4,2,1] => [8,7,6,5,3,4,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => [4,8,3,7,2,6,1,5] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,3,2,5,8,7,6,1] => [4,8,3,7,2,5,6,1] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,3,2,6,8,7,5,1] => [4,8,3,6,7,2,5,1] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [4,3,2,7,6,5,1,8] => [4,7,3,6,2,5,1,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [4,3,2,7,6,5,8,1] => [4,7,3,6,2,5,8,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => 1
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,2,7,8,6,5,1] => [4,7,8,3,6,2,5,1] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,3,2,8,7,6,5,1] => [8,4,7,3,6,2,5,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,3,5,2,8,7,6,1] => [4,8,3,5,7,2,6,1] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [4,3,5,6,7,8,2,1] => [4,3,5,6,7,8,2,1] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,3,5,6,8,7,2,1] => [4,8,3,5,6,7,2,1] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [4,3,5,7,6,2,1,8] => [4,7,3,5,6,2,1,8] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [4,3,5,7,6,2,8,1] => [4,7,3,5,6,2,8,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [4,3,5,7,6,8,2,1] => [4,7,3,5,6,8,2,1] => [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,5,7,8,6,2,1] => [4,7,8,3,5,6,2,1] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [4,3,5,8,7,6,2,1] => [8,4,7,3,5,6,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,8,7,2,1] => [4,6,8,3,5,7,2,1] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [4,3,7,6,5,2,1,8] => [7,4,6,3,5,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [4,3,7,6,5,2,8,1] => [7,4,6,3,5,2,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => 1
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [4,3,8,7,6,5,2,1] => [8,7,4,6,3,5,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,5,3,2,8,7,6,1] => [4,5,8,3,7,2,6,1] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [4,5,3,6,2,7,1,8] => [4,5,3,6,2,7,1,8] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => 3
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,5,3,6,8,7,2,1] => [4,5,8,3,6,7,2,1] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [4,5,3,7,6,8,2,1] => [4,5,7,3,6,8,2,1] => [1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => 1
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,5,3,7,8,6,2,1] => [4,5,7,8,3,6,2,1] => [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,5,3,8,7,6,2,1] => [8,4,5,7,3,6,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,6,8,7,3,2,1] => [8,4,5,6,7,3,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [4,5,7,6,3,2,1,8] => [7,4,5,6,3,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [4,5,7,6,3,2,8,1] => [7,4,5,6,3,2,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [4,5,7,6,3,8,2,1] => [7,4,5,6,3,8,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 1
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,5,7,6,8,3,2,1] => [7,4,5,6,8,3,2,1] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 1
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [4,5,8,7,6,3,2,1] => [8,7,4,5,6,3,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,6,5,3,8,7,2,1] => [6,4,5,8,3,7,2,1] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [4,6,5,7,3,2,8,1] => [6,4,5,7,3,2,8,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => 2
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,6,5,7,8,3,2,1] => [6,4,5,7,8,3,2,1] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [4,6,7,5,3,2,1,8] => [6,7,4,5,3,2,1,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [4,6,7,5,3,2,8,1] => [6,7,4,5,3,2,8,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,6,7,5,8,3,2,1] => [6,7,4,5,8,3,2,1] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => 1
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,6,7,8,5,3,2,1] => [6,7,8,4,5,3,2,1] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [4,6,8,7,5,3,2,1] => [8,6,7,4,5,3,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [4,7,6,5,3,2,1,8] => [7,6,4,5,3,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [4,7,6,5,3,2,8,1] => [7,6,4,5,3,2,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [4,7,6,5,3,8,2,1] => [7,6,4,5,3,8,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 1
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,7,6,5,8,3,2,1] => [7,6,4,5,8,3,2,1] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 1
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [4,7,6,8,5,3,2,1] => [7,6,8,4,5,3,2,1] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [4,7,8,6,5,3,2,1] => [7,8,6,4,5,3,2,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [4,8,7,6,5,3,2,1] => [8,7,6,4,5,3,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => [5,4,3,8,2,7,1,6] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,4,3,2,6,8,7,1] => [5,4,3,8,2,6,7,1] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [5,4,3,2,7,6,1,8] => [5,4,3,7,2,6,1,8] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => 2
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,4,3,2,8,7,6,1] => [5,4,8,3,7,2,6,1] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [5,4,3,7,6,2,1,8] => [5,4,7,3,6,2,1,8] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,4,3,7,6,8,2,1] => [5,4,7,3,6,8,2,1] => [1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => 2
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [5,4,3,8,7,6,2,1] => [5,8,4,7,3,6,2,1] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [5,4,7,6,3,2,1,8] => [5,7,4,6,3,2,1,8] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,4,7,6,3,8,2,1] => [5,7,4,6,3,8,2,1] => [1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => 1
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [5,4,7,6,8,3,2,1] => [5,7,4,6,8,3,2,1] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => 1
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [5,4,7,8,6,3,2,1] => [5,7,8,4,6,3,2,1] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [5,4,8,7,6,3,2,1] => [8,5,7,4,6,3,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [5,6,4,8,7,3,2,1] => [5,6,8,4,7,3,2,1] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [5,6,7,4,3,2,1,8] => [5,6,7,4,3,2,1,8] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,4,3,2,1] => [5,6,7,8,4,3,2,1] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [5,6,8,7,4,3,2,1] => [8,5,6,7,4,3,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [5,7,6,4,3,2,1,8] => [7,5,6,4,3,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [5,7,6,4,3,2,8,1] => [7,5,6,4,3,2,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,7,6,4,3,8,2,1] => [7,5,6,4,3,8,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 1
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,7,6,4,8,3,2,1] => [7,5,6,4,8,3,2,1] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 1
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [5,7,6,8,4,3,2,1] => [7,5,6,8,4,3,2,1] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 1
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [5,7,8,6,4,3,2,1] => [7,8,5,6,4,3,2,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [5,8,7,6,4,3,2,1] => [8,7,5,6,4,3,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [6,5,4,3,8,7,2,1] => [6,5,4,8,3,7,2,1] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [6,5,4,7,3,2,1,8] => [6,5,4,7,3,2,1,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 2
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [6,5,4,7,8,3,2,1] => [6,5,4,7,8,3,2,1] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [6,5,4,8,7,3,2,1] => [6,5,8,4,7,3,2,1] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [6,5,7,4,3,2,1,8] => [6,5,7,4,3,2,1,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,5,7,4,3,2,8,1] => [6,5,7,4,3,2,8,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => 2
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [6,5,7,4,8,3,2,1] => [6,5,7,4,8,3,2,1] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [6,5,7,8,4,3,2,1] => [6,5,7,8,4,3,2,1] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [6,5,8,7,4,3,2,1] => [6,8,5,7,4,3,2,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [6,7,5,4,3,2,1,8] => [6,7,5,4,3,2,1,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,7,5,4,3,2,8,1] => [6,7,5,4,3,2,8,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [6,7,5,4,8,3,2,1] => [6,7,5,4,8,3,2,1] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [6,7,5,8,4,3,2,1] => [6,7,5,8,4,3,2,1] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,5,4,3,2,1] => [6,7,8,5,4,3,2,1] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [6,8,7,5,4,3,2,1] => [8,6,7,5,4,3,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,6,5,4,3,2,8,1] => [7,6,5,4,3,2,8,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [7,6,5,4,3,8,2,1] => [7,6,5,4,3,8,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [7,6,5,4,8,3,2,1] => [7,6,5,4,8,3,2,1] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [7,6,5,8,4,3,2,1] => [7,6,5,8,4,3,2,1] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [7,6,8,5,4,3,2,1] => [7,6,8,5,4,3,2,1] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [7,8,6,5,4,3,2,1] => [7,8,6,5,4,3,2,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => [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] => [8,7,6,5,4,3,2,1,9] => [8,7,6,5,4,3,2,1,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,8,7,6,5,4,3,2] => [9,8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,8,7,6,5,4,3,2,1,10] => [9,8,7,6,5,4,3,2,1,10] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [7,8,6,5,4,3,2,1,9] => [7,8,6,5,4,3,2,1,9] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,8,9,7,6,5,4,3,2] => [8,9,7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,9,8,7,6,5,4,3,2] => [10,9,8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10,9,8,7,6,5,4,3,2,1,11] => [10,9,8,7,6,5,4,3,2,1,11] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [8,9,7,6,5,4,3,2,1,10] => [8,9,7,6,5,4,3,2,1,10] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [7,6,8,5,4,3,2,1,9] => [7,6,8,5,4,3,2,1,9] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => 2
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [6,8,7,5,4,3,2,1,9] => [8,6,7,5,4,3,2,1,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,8,7,9,6,5,4,3,2] => [8,7,9,6,5,4,3,1,2] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,7,9,8,6,5,4,3,2] => [9,7,8,6,5,4,3,1,2] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,9,10,8,7,6,5,4,3,2] => [9,10,8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,10,9,8,7,6,5,4,3,2] => [11,10,9,8,7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => [5,8,7,6,4,3,2,1,9] => [8,7,5,6,4,3,2,1,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,9,8,10,7,6,5,4,3,2] => [9,8,10,7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [4,8,7,6,5,3,2,1,9] => [8,7,6,4,5,3,2,1,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [5,9,8,7,6,4,3,2,1,10] => [9,8,7,5,6,4,3,2,1,10] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [4,9,8,7,6,5,3,2,1,10] => [9,8,7,6,4,5,3,2,1,10] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,8,7,6,5,4,3,1,9] => [8,7,6,5,4,2,3,1,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,8,7,6,5,4,3] => [9,8,7,6,5,2,4,1,3] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,9,8,7,6,5,4,2] => [9,8,7,6,5,3,4,1,2] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,8,7,6,5,4,3,2,9] => [8,7,6,5,4,3,1,2,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,9,8,7,6,5,4,3] => [9,8,7,6,5,4,1,2,3] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,9,8,7,6,5,4,3] => [10,9,8,7,6,5,2,4,1,3] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,9,8,7,6,5,4,3,2,10] => [9,8,7,6,5,4,3,1,2,10] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,10,9,8,7,6,5,4,3] => [10,9,8,7,6,5,4,1,2,3] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[] => [] => [] => [] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,1] => [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] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,9,8,1] => [9,2,3,4,5,6,7,8,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,6,8,7,9,1] => [8,2,3,4,5,6,7,9,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,6,8,9,7,1] => [8,9,2,3,4,5,6,7,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,6,9,8,7,1] => [9,8,2,3,4,5,6,7,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,9,8,7,6,5,4,1] => [9,8,7,6,5,2,3,4,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [2,8,7,6,5,4,3,9,1] => [8,7,6,5,4,2,3,9,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => 1
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2,8,7,9,6,5,4,3,1] => [8,7,9,6,5,4,2,3,1] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,8,9,7,6,5,4,3,1] => [8,9,7,6,5,4,2,3,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,9,8,7,6,5,4,3,1] => [9,8,7,6,5,4,2,3,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,1] => [3,2,4,5,6,7,8,9,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,8,9,1] => [3,4,2,5,6,7,8,9,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,7,8,2,9,1] => [3,4,5,6,7,8,2,9,1] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,9,2,1] => [3,4,5,6,7,8,9,2,1] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 0
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [3,8,7,6,5,4,9,2,1] => [8,7,6,5,3,4,9,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => 1
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,9,8,7,6,5,4,2,1] => [9,8,7,6,5,3,4,2,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [4,9,8,7,6,5,3,2,1] => [9,8,7,6,4,5,3,2,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [5,9,8,7,6,4,3,2,1] => [9,8,7,5,6,4,3,2,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [6,7,9,8,5,4,3,2,1] => [9,6,7,8,5,4,3,2,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [6,8,9,7,5,4,3,2,1] => [8,9,6,7,5,4,3,2,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [7,6,9,8,5,4,3,2,1] => [7,9,6,8,5,4,3,2,1] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [7,8,6,5,4,3,2,9,1] => [7,8,6,5,4,3,2,9,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [7,9,8,6,5,4,3,2,1] => [9,7,8,6,5,4,3,2,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,7,6,5,4,3,2,9,1] => [8,7,6,5,4,3,2,9,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [8,7,6,5,4,3,9,2,1] => [8,7,6,5,4,3,9,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [8,7,9,6,5,4,3,2,1] => [8,7,9,6,5,4,3,2,1] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [8,9,7,6,5,4,3,2,1] => [8,9,7,6,5,4,3,2,1] => [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] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8] => [9,1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,8,9,7] => [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] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,2] => [3,4,5,6,7,8,9,1,2] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9] => [10,1,2,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,9,8,7] => [9,8,1,2,3,4,5,6,7] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,7,9,10,8] => [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] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,5,8,7,9,6] => [8,7,9,1,2,3,4,5,6] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,2] => [3,4,5,6,7,8,9,10,1,2] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,1] => [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] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,9,11,10] => [11,1,2,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,10,9,8] => [10,9,1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,9,8,7,6] => [9,8,7,1,2,3,4,5,6] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,10,1] => [3,2,4,5,6,7,8,9,10,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,11,2] => [3,4,5,6,7,8,9,10,11,1,2] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => [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] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,8,11,10,9] => [11,10,1,2,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,6,10,9,8,7] => [10,9,8,1,2,3,4,5,6,7] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,9,8,7,6,5] => [9,8,7,6,1,2,3,4,5] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5,10,9,8,7,6] => [10,9,8,7,1,2,3,4,5,6] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,9,8,7,6,5,4] => [9,8,7,6,5,1,2,3,4] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,10,9,8,7,6,5] => [10,9,8,7,6,1,2,3,4,5] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,8,7,9] => [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
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,7,6,9,8] => [7,9,1,2,3,4,5,6,8] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,4,6,5,9,8,7] => [9,6,8,1,2,3,4,5,7] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,3,5,4,9,8,7,6] => [9,8,5,7,1,2,3,4,6] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,4,3,9,8,7,6,5] => [9,8,7,4,6,1,2,3,5] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,2,8,7,6,5,4,3,9] => [8,7,6,5,4,1,2,3,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9] => [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
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,7,9,8] => [3,9,1,2,4,5,6,7,8] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,3,2,9,8,7,6,5,4] => [9,8,7,6,3,5,1,2,4] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9] => [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
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,9,8] => [2,9,1,3,4,5,6,7,8] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8,9] => [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
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,6,5,9,8,7] => [9,2,4,6,8,1,3,5,7] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,4,3,9,8,7,6,5] => [9,8,7,2,4,6,1,3,5] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9] => [3,2,1,4,5,6,7,8,9] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,2,1,9,8,7,6,5,4] => [9,8,7,3,6,2,5,1,4] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,3,2,1,9,8,7,6,5] => [9,4,8,3,7,2,6,1,5] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,9,8,10] => [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
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,10,9,8,7,6,5,4] => [10,9,8,7,6,5,1,2,3,4] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9,10] => [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
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,7,6,10,9,8] => [10,3,5,7,9,1,2,4,6,8] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,2,10,9,8,7,6,5,4] => [10,9,8,7,6,3,5,1,2,4] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10] => [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
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,8,10,9] => [2,10,1,3,4,5,6,7,8,9] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9,10] => [3,2,1,4,5,6,7,8,9,10] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,6,5,4,10,9,8,7] => [10,3,6,9,2,5,8,1,4,7] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,2,1,10,9,8,7,6,5,4] => [10,9,8,7,3,6,2,5,1,4] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,3,2,1,10,9,8,7,6,5] => [10,9,4,8,3,7,2,6,1,5] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [10,9,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9] => [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
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,1,9] => [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
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,6,8,7,1,9] => [8,2,3,4,5,6,7,1,9] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,9,1,10] => [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
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10,11] => [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
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,6,8,9,7] => [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] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,8,10,9,1] => [10,2,3,4,5,6,7,8,9,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [8,10,9,7,6,5,4,3,2,1] => [10,8,9,7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [9,8,10,7,6,5,4,3,2,1] => [9,8,10,7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [9,11,10,8,7,6,5,4,3,2,1] => [11,9,10,8,7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [10,9,11,8,7,6,5,4,3,2,1] => [10,9,11,8,7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,7,8,2,1,9] => [3,4,5,6,7,8,2,1,9] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,10,9,8,7,6,5,4,3,1] => [10,9,8,7,6,5,4,2,3,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,8,7,6,5,4,3,2,10,1] => [9,8,7,6,5,4,3,2,10,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [10,9,8,7,6,5,4,3,2,11,1] => [10,9,8,7,6,5,4,3,2,11,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [9,10,8,7,6,5,4,3,2,1] => [9,10,8,7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [6,10,9,8,7,5,4,3,2,1] => [10,9,8,6,7,5,4,3,2,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [5,10,9,8,7,6,4,3,2,1] => [10,9,8,7,5,6,4,3,2,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [10,11,9,8,7,6,5,4,3,2,1] => [10,11,9,8,7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,8,1,9] => [3,2,4,5,6,7,8,1,9] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,7,9,8,2] => [9,3,4,5,6,7,8,1,2] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,1,9,8] => [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] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,6,7,10,9,8,1] => [10,9,2,3,4,5,6,7,8,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,9,10,2,1] => [3,4,5,6,7,8,9,10,2,1] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,8,9,11,10,1] => [11,2,3,4,5,6,7,8,9,10,1] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,9,10,11,2,1] => [3,4,5,6,7,8,9,10,11,2,1] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,3,5,7,9,10,8,6,4,2] => [9,10,7,8,5,6,3,4,1,2] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [5,6,4,7,3,8,2,9,1,10] => [5,6,4,7,3,8,2,9,1,10] => [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => 4
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [11,10,9,8,7,6,5,4,3,2,1] => [11,10,9,8,7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [7,9,10,8,6,5,4,3,2,1] => [9,10,7,8,6,5,4,3,2,1] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,2,4,9,8,7,6,5,3] => [9,8,7,6,4,5,1,2,3] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,3,5,9,8,7,6,4] => [9,8,7,5,6,1,2,3,4] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,4,6,9,8,7,5] => [9,8,6,7,1,2,3,4,5] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,5,7,9,8,6] => [9,7,8,1,2,3,4,5,6] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9,11] => [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
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,8,2,9] => [3,4,5,6,7,8,1,2,9] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,2,10,9,8,7,6,5,4,1] => [10,9,8,7,6,3,5,2,4,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,8,1,10,9] => [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] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,8,9,2,10] => [3,4,5,6,7,8,9,1,2,10] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,7,8,10,9,2] => [10,3,4,5,6,7,8,9,1,2] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,7,2,8,9] => [3,4,5,6,7,1,2,8,9] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,6,7,9,8,1,10] => [9,2,3,4,5,6,7,8,1,10] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,5,6,9,8,7,2] => [9,8,3,4,5,6,7,1,2] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
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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 9,5 22,19,1 57,66,9 154,222,52,1
$F_{1} = 1$
$F_{2} = 2$
$F_{3} = 4 + q$
$F_{4} = 9 + 5\ q$
$F_{5} = 22 + 19\ q + q^{2}$
$F_{6} = 57 + 66\ q + 9\ q^{2}$
$F_{7} = 154 + 222\ q + 52\ q^{2} + q^{3}$
Description
The number of factors DDU in a Dyck path.
Map
to 312-avoiding permutation
Description
Map
left-to-right-maxima to Dyck path
Description
The left-to-right maxima of a permutation as a Dyck path.
Let $(c_1, \dots, c_k)$ be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are $c_1, c_1+c_2, \dots, c_1+\dots+c_k$.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
Let $(c_1, \dots, c_k)$ be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are $c_1, c_1+c_2, \dots, c_1+\dots+c_k$.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
Map
inverse Foata bijection
Description
The inverse of Foata's bijection.
See Mp00067Foata bijection.
See Mp00067Foata bijection.
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