Identifier
-
Mp00025:
Dyck paths
—to 132-avoiding permutation⟶
Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00028: Dyck paths —reverse⟶ Dyck paths
St001732: Dyck paths ⟶ ℤ
Values
[1,0] => [1] => [1,0] => [1,0] => 1
[1,0,1,0] => [2,1] => [1,1,0,0] => [1,1,0,0] => 1
[1,1,0,0] => [1,2] => [1,0,1,0] => [1,0,1,0] => 1
[1,0,1,0,1,0] => [3,2,1] => [1,1,1,0,0,0] => [1,1,1,0,0,0] => 1
[1,0,1,1,0,0] => [2,3,1] => [1,1,0,1,0,0] => [1,1,0,1,0,0] => 1
[1,1,0,0,1,0] => [3,1,2] => [1,1,1,0,0,0] => [1,1,1,0,0,0] => 1
[1,1,0,1,0,0] => [2,1,3] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 2
[1,1,1,0,0,0] => [1,2,3] => [1,0,1,0,1,0] => [1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0] => [4,3,2,1] => [1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,0] => [3,4,2,1] => [1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0] => 1
[1,0,1,1,0,0,1,0] => [4,2,3,1] => [1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,1,0,0] => [3,2,4,1] => [1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[1,0,1,1,1,0,0,0] => [2,3,4,1] => [1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,0,1,0] => [4,3,1,2] => [1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,0,0] => [3,4,1,2] => [1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0] => 1
[1,1,0,1,0,0,1,0] => [4,2,1,3] => [1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0] => 1
[1,1,0,1,0,1,0,0] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0] => 2
[1,1,0,1,1,0,0,0] => [2,3,1,4] => [1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0] => 2
[1,1,1,0,0,0,1,0] => [4,1,2,3] => [1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,0,0] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,0,0,0] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => [1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => [1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,0] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => [1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
[1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => [1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 2
[1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => [1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
[1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => [1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 2
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => [1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0] => 2
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => [1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => [1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,0,1,0,1,1,0,0,0] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0] => 2
[1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,0,0] => [4,2,3,1,5] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,0,1,1,0,1,0,0,0] => [3,2,4,1,5] => [1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 3
[1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 2
[1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => [1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,0] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,0,0,1,1,0,0,0] => [3,4,1,2,5] => [1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,0] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,0,1,0,1,0,0,0] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => [1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 2
[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0] => [5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,5,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,6,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [5,6,3,4,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,5,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,6,2,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,0,1,0,1,1,0,1,1,0,0,0] => [4,5,3,6,2,1] => [1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,4,5,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,4,6,2,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => [1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [5,6,4,2,3,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,5,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,6,2,3,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,0] => [5,6,3,2,4,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,0,1,1,0,1,0,1,1,0,0,0] => [4,5,3,2,6,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 2
[1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,4,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,4,2,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,5,2,6,1] => [1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,3,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => [5,6,2,3,4,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,3,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,3,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 2
>>> Load all 911 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,5,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,0] => [5,4,6,3,1,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,0,0] => [4,5,6,3,1,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,4,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,1,0,0] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,5,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,6,1,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => [4,5,3,6,1,2] => [1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,4,5,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,4,6,1,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,5,6,1,2] => [1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => [1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [5,6,4,2,1,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [6,4,5,2,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,6,2,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[1,1,0,1,0,0,1,1,1,0,0,0] => [4,5,6,2,1,3] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,0] => [5,6,3,2,1,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,0,1,0,1,0,1,1,0,0,0] => [4,5,3,2,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,4,2,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,4,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,5,2,1,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,2,1,6] => [1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,3,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,0] => [5,6,2,3,1,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,3,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,3,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,0,1,1,0,0,1,1,0,0,0] => [4,5,2,3,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,4,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,5,1,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,4,2,5,1,6] => [1,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => 3
[1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,3,4,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,3,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,3,5,1,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,5,1,6] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => 3
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 2
[1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,0] => [5,6,4,1,2,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,5,1,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,6,1,2,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,0] => [5,6,3,1,2,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,0,0,1,0,1,1,0,0,0] => [4,5,3,1,2,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,4,1,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,4,1,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,5,1,2,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => [1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [5,6,2,1,3,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,5,2,1,3,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,2,1,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,3,1,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,3,1,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,3,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,4,1,5,6] => [1,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => 3
[1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 2
[1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,2,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,2,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,2,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,2,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,2,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,3,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,3,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,2,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,2,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,2,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,2,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,2,1] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,2,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,2,1] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,2,1] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,2,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,2,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,2,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,2,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,2,1] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 2
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,2,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,2,1] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 3
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,2,1] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,2,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,2,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,2,1] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,2,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,2,1] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,2,1] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,2,1] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,2,1] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,2,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,3,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,3,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,3,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,3,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,3,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,3,1] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,3,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,3,1] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,3,1] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,4,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,4,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,4,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,5,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,7,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,7,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 3
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,7,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,5,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,7,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,7,1] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 3
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,7,1] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 3
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,7,1] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 3
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,7,1] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 3
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,7,1] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,4,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,4,1] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,4,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,5,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,7,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,7,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 3
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,7,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,5,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,7,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,7,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,7,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,7,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,7,1] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 3
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,7,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,5,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,7,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,7,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,7,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,7,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,7,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,7,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,7,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,7,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,7,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,7,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,1,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,1,2] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,1,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 2
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,1,2] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,1,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,1,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,1,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,1,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,1,2] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,1,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,1,2] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,1,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,1,2] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 3
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,1,2] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,1,2] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,1,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,1,2] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,1,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,1,2] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,1,2] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,1,2] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,1,2] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,1,2] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,1,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,1,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 2
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,1,3] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,1,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,1,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,1,3] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 2
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,1,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,1,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,1,3] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,1,3] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,1,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,1,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,1,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,1,4] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 2
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,1,4] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,1,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,1,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,1,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,1,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,1,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,1,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 3
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,1,7] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,1,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,1,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,1,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,1,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,1,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,1,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 3
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,1,7] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 3
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,1,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,1,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 3
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,1,7] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 3
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,1,7] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,1,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,1,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,1,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,1,4] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 2
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,1,4] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,1,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,1,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,1,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,1,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,1,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,1,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 3
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,1,7] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,1,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,1,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,1,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,1,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,1,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,1,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 3
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,1,7] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 3
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,1,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,1,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 3
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,1,7] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 4
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,1,7] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 3
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,1,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,1,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,1,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,1,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,1,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,1,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 3
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,1,7] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 3
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,1,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,1,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 3
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,1,7] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 3
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,1,7] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 3
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,1,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,1,7] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 3
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,1,7] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 3
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,1,7] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 3
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,1,2,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,1,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,1,2,3] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,1,2,3] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,1,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,1,2,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,1,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,1,2,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,1,2,3] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,1,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,1,2,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,1,2,3] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,1,2,3] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,1,2,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,1,2,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,1,2,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,1,2,4] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,1,2,4] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,1,2,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,1,2,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,1,2,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,1,2,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,1,2,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,1,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,1,2,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 3
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,1,2,7] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,1,2,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,1,2,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,1,2,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,1,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,1,2,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,1,2,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,1,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,1,2,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 3
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,1,2,7] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 3
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,1,2,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,1,2,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,1,2,7] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 3
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,1,2,7] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,1,2,7] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,1,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,1,3,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,1,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,1,3,4] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,1,3,4] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,1,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,1,3,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,1,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,1,3,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,1,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,1,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,1,3,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 3
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,1,3,7] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,1,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,1,4,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,1,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,1,4,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,1,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,1,6,7] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,1,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,1,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,1,6,7] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,1,6,7] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,1,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,1,4,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,1,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,1,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,1,4,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,1,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,1,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,1,6,7] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,1,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,1,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,1,6,7] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,1,6,7] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,1,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,1,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,1,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,1,6,7] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,1,6,7] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [7,6,5,1,2,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [6,7,5,1,2,3,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [7,5,6,1,2,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [6,5,7,1,2,3,4] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [7,6,4,1,2,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [6,7,4,1,2,3,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [7,5,4,1,2,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,2,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,6,4,1,2,3,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [7,4,5,1,2,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,5,1,2,3,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,6,1,2,3,7] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 3
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [7,6,3,1,2,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [6,7,3,1,2,4,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1,2,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,2,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,6,3,1,2,4,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,2,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,2,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,2,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,5,3,1,2,6,7] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,4,1,2,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,4,1,2,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,4,1,2,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,5,1,2,6,7] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,4,5,1,2,6,7] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [7,6,2,1,3,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,7,2,1,3,4,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,3,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,3,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,6,2,1,3,4,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,3,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,3,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,3,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,2,1,3,6,7] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,4,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,4,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,4,2,1,5,6,7] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,3,1,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,3,1,4,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,3,1,4,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,3,1,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,4,1,5,6,7] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,2,3,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,2,3,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,2,3,4,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,6,1,2,3,4,7] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,2,3,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,2,3,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,2,3,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,5,1,2,3,6,7] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,2,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,2,4,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,2,4,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,2,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,4,1,2,5,6,7] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,3,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,3,4,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,3,4,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,3,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,4,5,6,7] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,5,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,2,3,4,6,7] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,2,3,5,6,7] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,2,4,5,6,7] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,2,1,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,1,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 3
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,2,1,8] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,2,1,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,2,1,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 3
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,3,2,1,8] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 3
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,2,1,8] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 3
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,2,1,8] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [6,7,5,3,4,2,1,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,2,1,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 3
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,2,1,8] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 2
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,5,2,1,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,2,1,8] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 3
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,2,1,8] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 3
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,6,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,2,1,8] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 4
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,2,1,8] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 3
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,2,1,8] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,3,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,2,3,1,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,2,3,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,2,3,1,8] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,3,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,1,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,3,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,2,3,1,8] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 3
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,2,3,1,8] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 3
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,2,3,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,2,3,1,8] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 3
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,3,1,8] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,4,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,2,4,1,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 3
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,2,4,1,8] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 2
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,5,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,5,1,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,6,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,7,1,8] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,2,7,1,8] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 3
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,2,6,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,2,7,1,8] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 4
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,2,5,1,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,2,6,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,2,7,1,8] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 3
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,6,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,7,1,8] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 4
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,2,7,1,8] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 4
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,2,7,1,8] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,2,7,1,8] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 4
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,2,7,1,8] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 4
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,7,1,8] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,3,4,1,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,4,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [6,5,7,2,3,4,1,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 3
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,4,1,8] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 2
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,5,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [6,7,4,2,3,5,1,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,3,6,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,3,7,1,8] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 4
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,5,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,5,1,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,6,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,4,7,1,8] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,7,1,8] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 3
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,5,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,5,1,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [7,4,2,3,5,6,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [6,4,2,3,5,7,1,8] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,6,7,1,8] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 3
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,6,7,1,8] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 3
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [6,3,2,4,5,7,1,8] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,7,1,8] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 3
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,7,1,8] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 3
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,6,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,5,7,1,8] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,7,1,8] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 3
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,7,1,8] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 3
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,1,8] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 3
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,1,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,1,2,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,1,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,1,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,1,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,1,2,8] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 3
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,1,2,8] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,1,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,1,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,1,2,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 3
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,1,2,8] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 3
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,7,1,2,8] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 3
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,5,1,2,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,1,2,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,1,2,8] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 3
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,1,2,8] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 3
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,1,2,8] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 3
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,1,2,8] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,1,2,8] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,1,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,2,1,3,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 3
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,1,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,1,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,2,1,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,2,1,3,8] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 3
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,1,3,8] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,1,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,1,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,1,5,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,1,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,1,7,8] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,2,1,7,8] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,2,1,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,2,1,7,8] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 3
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,2,1,7,8] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,2,1,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,2,1,5,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,2,1,7,8] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,2,1,7,8] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,1,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,1,7,8] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 3
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,2,1,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,2,1,7,8] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,1,7,8] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,1,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,3,1,4,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,1,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [6,5,7,2,3,1,4,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 3
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,1,4,8] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 2
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,1,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [6,7,4,2,3,1,5,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [7,5,4,2,3,1,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,3,1,7,8] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 3
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,1,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,1,5,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,1,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [5,6,3,2,4,1,7,8] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,5,1,7,8] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,1,7,8] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,6,1,7,8] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 3
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,6,1,7,8] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 4
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,1,7,8] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 3
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,1,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,1,5,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,4,1,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [6,5,2,3,4,1,7,8] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [5,6,2,3,4,1,7,8] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [7,4,2,3,5,1,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,6,1,7,8] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,1,7,8] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,1,7,8] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 3
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,1,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,5,1,7,8] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,1,7,8] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,1,7,8] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,1,7,8] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 3
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,1,2,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,1,2,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,1,2,3,8] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,1,2,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,1,2,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,1,2,3,8] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 3
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,1,2,3,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,1,2,3,8] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 3
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,1,2,3,8] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,1,2,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,1,2,4,8] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,1,2,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,1,2,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,1,2,7,8] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,1,2,7,8] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,1,2,7,8] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,1,2,7,8] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 3
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,1,2,5,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,1,2,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,1,2,7,8] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,1,2,7,8] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,1,2,7,8] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,1,2,7,8] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 3
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,1,2,7,8] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,1,3,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,1,3,4,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,1,3,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,1,3,4,8] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,1,3,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,1,3,7,8] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [5,6,4,2,1,3,7,8] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,1,3,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [6,4,5,2,1,3,7,8] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,1,3,7,8] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 3
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,5,6,2,1,3,7,8] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,1,4,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,1,4,5,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,1,4,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,1,4,7,8] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [5,6,3,2,1,4,7,8] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,1,5,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,1,5,7,8] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1,6,7,8] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,1,6,7,8] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [6,3,4,2,1,5,7,8] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [5,3,4,2,1,6,7,8] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,1,6,7,8] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,1,6,7,8] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,1,4,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,1,4,5,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,1,4,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,1,6,7,8] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,1,6,7,8] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,1,6,7,8] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,1,6,7,8] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,1,6,7,8] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,1,5,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,1,6,7,8] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,1,6,7,8] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,1,6,7,8] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [7,6,5,1,2,3,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [6,7,5,1,2,3,4,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [7,5,6,1,2,3,4,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [6,5,7,1,2,3,4,8] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,6,7,1,2,3,4,8] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3,7,8] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [7,4,5,1,2,3,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [4,5,6,1,2,3,7,8] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [6,7,3,1,2,4,5,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [7,5,3,1,2,4,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [7,4,3,1,2,5,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [6,4,3,1,2,5,7,8] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3,1,2,6,7,8] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [7,3,4,1,2,5,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [5,3,4,1,2,6,7,8] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [4,3,5,1,2,6,7,8] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [3,4,5,1,2,6,7,8] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [5,6,2,1,3,4,7,8] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [6,4,2,1,3,5,7,8] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1,3,6,7,8] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [4,5,2,1,3,6,7,8] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [7,3,2,1,4,5,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [6,3,2,1,4,5,7,8] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1,4,6,7,8] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,5,6,7,8] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [3,4,2,1,5,6,7,8] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [7,2,3,1,4,5,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [6,2,3,1,4,5,7,8] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,2,3,1,4,6,7,8] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [4,2,3,1,5,6,7,8] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,4,1,5,6,7,8] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [7,6,1,2,3,4,5,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,7,1,2,3,4,5,8] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [7,5,1,2,3,4,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1,2,3,4,7,8] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [7,4,1,2,3,5,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,4,1,2,3,5,7,8] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,2,3,6,7,8] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,5,1,2,3,6,7,8] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [7,3,1,2,4,5,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1,2,4,5,7,8] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1,2,4,6,7,8] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,2,5,6,7,8] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1,3,4,5,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1,3,4,5,7,8] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,3,4,6,7,8] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,3,5,6,7,8] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,2,3,4,5,6,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,2,3,4,5,7,8] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,2,3,4,6,7,8] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,2,3,5,6,7,8] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
4,1 9,5 23,18,1 65,59,8 197,190,41,1
F1=q
F2=2 q
F3=4 q+q2
F4=9 q+5 q2
F5=23 q+18 q2+q3
F6=65 q+59 q2+8 q3
F7=197 q+190 q2+41 q3+q4
Description
The number of peaks visible from the left.
This is, the number of left-to-right maxima of the heights of the peaks of a Dyck path.
This is, the number of left-to-right maxima of the heights of the peaks of a Dyck path.
Map
left-to-right-maxima to Dyck path
Description
The left-to-right maxima of a permutation as a Dyck path.
Let (c1,…,ck) be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are c1,c1+c2,…,c1+⋯+ck.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
Let (c1,…,ck) be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are c1,c1+c2,…,c1+⋯+ck.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
Map
reverse
Description
The reversal of a Dyck path.
This is the Dyck path obtained by reading the path backwards.
This is the Dyck path obtained by reading the path backwards.
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
This bijection is defined in [1, Section 2].
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