Identifier
-
Mp00023:
Dyck paths
—to non-crossing permutation⟶
Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00204: Permutations —LLPS⟶ Integer partitions
St000320: Integer partitions ⟶ ℤ (values match St000319The spin of an integer partition.)
Values
[1,0] => [1] => [1] => [1] => 0
[1,0,1,0] => [1,2] => [1,2] => [1,1] => 0
[1,1,0,0] => [2,1] => [2,1] => [2] => 1
[1,0,1,0,1,0] => [1,2,3] => [1,2,3] => [1,1,1] => 0
[1,0,1,1,0,0] => [1,3,2] => [1,3,2] => [2,1] => 1
[1,1,0,0,1,0] => [2,1,3] => [2,1,3] => [2,1] => 1
[1,1,0,1,0,0] => [2,3,1] => [3,1,2] => [2,1] => 1
[1,1,1,0,0,0] => [3,2,1] => [2,3,1] => [2,1] => 1
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [1,2,3,4] => [1,1,1,1] => 0
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [1,2,4,3] => [2,1,1] => 1
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [1,3,2,4] => [2,1,1] => 1
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [1,4,2,3] => [2,1,1] => 1
[1,0,1,1,1,0,0,0] => [1,4,3,2] => [1,3,4,2] => [2,1,1] => 1
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [2,1,3,4] => [2,1,1] => 1
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [2,1,4,3] => [2,2] => 1
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [3,1,2,4] => [2,1,1] => 1
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [4,1,2,3] => [2,1,1] => 1
[1,1,0,1,1,0,0,0] => [2,4,3,1] => [3,4,1,2] => [2,1,1] => 1
[1,1,1,0,0,0,1,0] => [3,2,1,4] => [2,3,1,4] => [2,1,1] => 1
[1,1,1,0,0,1,0,0] => [3,2,4,1] => [2,4,1,3] => [2,1,1] => 1
[1,1,1,0,1,0,0,0] => [4,2,3,1] => [2,3,4,1] => [2,1,1] => 1
[1,1,1,1,0,0,0,0] => [4,3,2,1] => [3,2,4,1] => [3,1] => 2
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [1,2,3,4,5] => [1,1,1,1,1] => 0
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [1,2,3,5,4] => [2,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [1,2,4,3,5] => [2,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [1,2,5,3,4] => [2,1,1,1] => 1
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [1,2,4,5,3] => [2,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [1,3,2,4,5] => [2,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [1,3,2,5,4] => [2,2,1] => 1
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [1,4,2,3,5] => [2,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [1,5,2,3,4] => [2,1,1,1] => 1
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [1,4,5,2,3] => [2,1,1,1] => 1
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [1,3,4,2,5] => [2,1,1,1] => 1
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [1,3,5,2,4] => [2,1,1,1] => 1
[1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => [1,3,4,5,2] => [2,1,1,1] => 1
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [1,4,3,5,2] => [3,1,1] => 2
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,1,1] => 1
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [2,1,3,5,4] => [2,2,1] => 1
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [2,1,4,3,5] => [2,2,1] => 1
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [2,1,5,3,4] => [2,2,1] => 1
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [2,1,4,5,3] => [2,2,1] => 1
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [3,1,2,4,5] => [2,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [3,1,2,5,4] => [2,2,1] => 1
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [4,1,2,3,5] => [2,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [5,1,2,3,4] => [2,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [4,5,1,2,3] => [2,1,1,1] => 1
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [3,4,1,2,5] => [2,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [3,5,1,2,4] => [2,1,1,1] => 1
[1,1,0,1,1,0,1,0,0,0] => [2,5,3,4,1] => [3,4,5,1,2] => [2,1,1,1] => 1
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [4,3,5,1,2] => [3,1,1] => 2
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [2,3,1,4,5] => [2,1,1,1] => 1
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [2,3,1,5,4] => [2,2,1] => 1
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [2,4,1,3,5] => [2,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [2,5,1,3,4] => [2,1,1,1] => 1
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [2,4,5,1,3] => [2,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => [2,3,4,1,5] => [2,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => [2,3,5,1,4] => [2,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => [2,3,4,5,1] => [2,1,1,1] => 1
[1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => [2,4,3,5,1] => [3,1,1] => 2
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [3,2,4,1,5] => [3,1,1] => 2
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [3,2,5,1,4] => [3,1,1] => 2
[1,1,1,1,0,0,1,0,0,0] => [5,3,2,4,1] => [3,2,4,5,1] => [3,1,1] => 2
[1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => [4,2,3,5,1] => [3,1,1] => 2
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [3,4,2,5,1] => [3,1,1] => 2
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => [2,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => [2,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [1,2,3,6,4,5] => [2,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [1,2,3,5,6,4] => [2,1,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => [2,1,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [2,2,1,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [1,2,5,3,4,6] => [2,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [1,2,6,3,4,5] => [2,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [1,2,5,6,3,4] => [2,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [1,2,4,5,3,6] => [2,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [1,2,4,6,3,5] => [2,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => [1,2,4,5,6,3] => [2,1,1,1,1] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [1,2,5,4,6,3] => [3,1,1,1] => 2
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => [2,1,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => [2,2,1,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => [2,2,1,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [1,3,2,6,4,5] => [2,2,1,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [1,3,2,5,6,4] => [2,2,1,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [1,4,2,3,5,6] => [2,1,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [1,4,2,3,6,5] => [2,2,1,1] => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [1,5,2,3,4,6] => [2,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [1,6,2,3,4,5] => [2,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [1,5,6,2,3,4] => [2,1,1,1,1] => 1
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [1,4,5,2,3,6] => [2,1,1,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [1,4,6,2,3,5] => [2,1,1,1,1] => 1
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,6,4,5,2] => [1,4,5,6,2,3] => [2,1,1,1,1] => 1
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [1,5,4,6,2,3] => [3,1,1,1] => 2
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [1,3,4,2,5,6] => [2,1,1,1,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [1,3,4,2,6,5] => [2,2,1,1] => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [1,3,5,2,4,6] => [2,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [1,3,6,2,4,5] => [2,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [1,3,5,6,2,4] => [2,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,5,3,4,2,6] => [1,3,4,5,2,6] => [2,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => [1,3,4,6,2,5] => [2,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,6,3,4,5,2] => [1,3,4,5,6,2] => [2,1,1,1,1] => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,6,3,5,4,2] => [1,3,5,4,6,2] => [3,1,1,1] => 2
>>> Load all 1866 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [1,4,3,5,2,6] => [3,1,1,1] => 2
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [1,4,3,6,2,5] => [3,1,1,1] => 2
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,6,4,3,5,2] => [1,4,3,5,6,2] => [3,1,1,1] => 2
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,6,4,5,3,2] => [1,5,3,4,6,2] => [3,1,1,1] => 2
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [1,4,5,3,6,2] => [3,1,1,1] => 2
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => [2,2,1,1] => 1
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => [2,2,1,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [2,1,3,6,4,5] => [2,2,1,1] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [2,1,3,5,6,4] => [2,2,1,1] => 1
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => [2,2,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [2,2,2] => 1
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [2,1,5,3,4,6] => [2,2,1,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [2,1,6,3,4,5] => [2,2,1,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [2,1,5,6,3,4] => [2,2,1,1] => 1
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [2,1,4,5,3,6] => [2,2,1,1] => 1
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [2,1,4,6,3,5] => [2,2,1,1] => 1
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,6,4,5,3] => [2,1,4,5,6,3] => [2,2,1,1] => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [2,1,5,4,6,3] => [3,2,1] => 2
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [3,1,2,4,5,6] => [2,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [3,1,2,4,6,5] => [2,2,1,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [3,1,2,5,4,6] => [2,2,1,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [3,1,2,6,4,5] => [2,2,1,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [3,1,2,5,6,4] => [2,2,1,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [4,1,2,3,5,6] => [2,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [4,1,2,3,6,5] => [2,2,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [5,1,2,3,4,6] => [2,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [6,1,2,3,4,5] => [2,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [5,6,1,2,3,4] => [2,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [4,5,1,2,3,6] => [2,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [4,6,1,2,3,5] => [2,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,6,4,5,1] => [4,5,6,1,2,3] => [2,1,1,1,1] => 1
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [5,4,6,1,2,3] => [3,1,1,1] => 2
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [3,4,1,2,5,6] => [2,1,1,1,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [3,4,1,2,6,5] => [2,2,1,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [3,5,1,2,4,6] => [2,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [3,6,1,2,4,5] => [2,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [3,5,6,1,2,4] => [2,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,5,3,4,1,6] => [3,4,5,1,2,6] => [2,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,5,3,4,6,1] => [3,4,6,1,2,5] => [2,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,6,3,4,5,1] => [3,4,5,6,1,2] => [2,1,1,1,1] => 1
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,6,3,5,4,1] => [3,5,4,6,1,2] => [3,1,1,1] => 2
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [4,3,5,1,2,6] => [3,1,1,1] => 2
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [4,3,6,1,2,5] => [3,1,1,1] => 2
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,6,4,3,5,1] => [4,3,5,6,1,2] => [3,1,1,1] => 2
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,6,4,5,3,1] => [5,3,4,6,1,2] => [3,1,1,1] => 2
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [4,5,3,6,1,2] => [3,1,1,1] => 2
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [2,3,1,4,5,6] => [2,1,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [2,3,1,4,6,5] => [2,2,1,1] => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [2,3,1,5,4,6] => [2,2,1,1] => 1
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [2,3,1,6,4,5] => [2,2,1,1] => 1
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [2,3,1,5,6,4] => [2,2,1,1] => 1
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [2,4,1,3,5,6] => [2,1,1,1,1] => 1
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [2,4,1,3,6,5] => [2,2,1,1] => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [2,5,1,3,4,6] => [2,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [2,6,1,3,4,5] => [2,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [2,5,6,1,3,4] => [2,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [2,4,5,1,3,6] => [2,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [2,4,6,1,3,5] => [2,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,6,4,5,1] => [2,4,5,6,1,3] => [2,1,1,1,1] => 1
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [2,5,4,6,1,3] => [3,1,1,1] => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,2,3,1,5,6] => [2,3,4,1,5,6] => [2,1,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,2,3,1,6,5] => [2,3,4,1,6,5] => [2,2,1,1] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,2,3,5,1,6] => [2,3,5,1,4,6] => [2,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => [2,3,6,1,4,5] => [2,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,2,3,6,5,1] => [2,3,5,6,1,4] => [2,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,3,4,1,6] => [2,3,4,5,1,6] => [2,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,2,3,4,6,1] => [2,3,4,6,1,5] => [2,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,0] => [6,2,3,4,5,1] => [2,3,4,5,6,1] => [2,1,1,1,1] => 1
[1,1,1,0,1,0,1,1,0,0,0,0] => [6,2,3,5,4,1] => [2,3,5,4,6,1] => [3,1,1,1] => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,2,4,3,1,6] => [2,4,3,5,1,6] => [3,1,1,1] => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,4,3,6,1] => [2,4,3,6,1,5] => [3,1,1,1] => 2
[1,1,1,0,1,1,0,0,1,0,0,0] => [6,2,4,3,5,1] => [2,4,3,5,6,1] => [3,1,1,1] => 2
[1,1,1,0,1,1,0,1,0,0,0,0] => [6,2,4,5,3,1] => [2,5,3,4,6,1] => [3,1,1,1] => 2
[1,1,1,0,1,1,1,0,0,0,0,0] => [6,2,5,4,3,1] => [2,4,5,3,6,1] => [3,1,1,1] => 2
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [3,2,4,1,5,6] => [3,1,1,1] => 2
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [3,2,4,1,6,5] => [3,2,1] => 2
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [3,2,5,1,4,6] => [3,1,1,1] => 2
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [3,2,6,1,4,5] => [3,1,1,1] => 2
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [3,2,5,6,1,4] => [3,1,1,1] => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,3,2,4,1,6] => [3,2,4,5,1,6] => [3,1,1,1] => 2
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [3,2,4,6,1,5] => [3,1,1,1] => 2
[1,1,1,1,0,0,1,0,1,0,0,0] => [6,3,2,4,5,1] => [3,2,4,5,6,1] => [3,1,1,1] => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => [6,3,2,5,4,1] => [3,2,5,4,6,1] => [3,2,1] => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,3,4,2,1,6] => [4,2,3,5,1,6] => [3,1,1,1] => 2
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,3,4,2,6,1] => [4,2,3,6,1,5] => [3,1,1,1] => 2
[1,1,1,1,0,1,0,0,1,0,0,0] => [6,3,4,2,5,1] => [4,2,3,5,6,1] => [3,1,1,1] => 2
[1,1,1,1,0,1,0,1,0,0,0,0] => [6,3,4,5,2,1] => [5,2,3,4,6,1] => [3,1,1,1] => 2
[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,5,4,2,1] => [4,5,2,3,6,1] => [3,1,1,1] => 2
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [3,4,2,5,1,6] => [3,1,1,1] => 2
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [3,4,2,6,1,5] => [3,1,1,1] => 2
[1,1,1,1,1,0,0,0,1,0,0,0] => [6,4,3,2,5,1] => [3,4,2,5,6,1] => [3,1,1,1] => 2
[1,1,1,1,1,0,0,1,0,0,0,0] => [6,4,3,5,2,1] => [3,5,2,4,6,1] => [3,1,1,1] => 2
[1,1,1,1,1,0,1,0,0,0,0,0] => [6,5,3,4,2,1] => [3,4,5,2,6,1] => [3,1,1,1] => 2
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [4,3,5,2,6,1] => [4,1,1] => 3
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [1,2,3,4,7,5,6] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => [1,2,3,4,6,7,5] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => [2,2,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [1,2,3,6,4,5,7] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [1,2,3,7,4,5,6] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => [1,2,3,6,7,4,5] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => [1,2,3,5,6,4,7] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => [1,2,3,5,7,4,6] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,7,5,6,4] => [1,2,3,5,6,7,4] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => [1,2,3,6,5,7,4] => [3,1,1,1,1] => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => [2,2,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [2,2,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [1,2,4,3,7,5,6] => [2,2,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => [1,2,4,3,6,7,5] => [2,2,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [1,2,5,3,4,6,7] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [1,2,5,3,4,7,6] => [2,2,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [1,2,6,3,4,5,7] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [1,2,7,3,4,5,6] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => [1,2,6,7,3,4,5] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => [1,2,5,6,3,4,7] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => [1,2,5,7,3,4,6] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,7,5,6,3] => [1,2,5,6,7,3,4] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => [1,2,6,5,7,3,4] => [3,1,1,1,1] => 2
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => [1,2,4,5,3,6,7] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => [1,2,4,5,3,7,6] => [2,2,1,1,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,4,6,3,7] => [1,2,4,6,3,5,7] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => [1,2,4,7,3,5,6] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => [1,2,4,6,7,3,5] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,6,4,5,3,7] => [1,2,4,5,6,3,7] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,6,4,5,7,3] => [1,2,4,5,7,3,6] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,7,4,5,6,3] => [1,2,4,5,6,7,3] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,7,4,6,5,3] => [1,2,4,6,5,7,3] => [3,1,1,1,1] => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => [1,2,5,4,6,3,7] => [3,1,1,1,1] => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => [1,2,5,4,7,3,6] => [3,1,1,1,1] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,7,5,4,6,3] => [1,2,5,4,6,7,3] => [3,1,1,1,1] => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,7,5,6,4,3] => [1,2,6,4,5,7,3] => [3,1,1,1,1] => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => [1,2,5,6,4,7,3] => [3,1,1,1,1] => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [1,3,2,4,5,7,6] => [2,2,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => [2,2,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [1,3,2,4,7,5,6] => [2,2,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => [1,3,2,4,6,7,5] => [2,2,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => [2,2,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => [1,3,2,5,4,7,6] => [2,2,2,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [1,3,2,6,4,5,7] => [2,2,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [1,3,2,7,4,5,6] => [2,2,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => [1,3,2,6,7,4,5] => [2,2,1,1,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => [1,3,2,5,6,4,7] => [2,2,1,1,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => [1,3,2,5,7,4,6] => [2,2,1,1,1] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,7,5,6,4] => [1,3,2,5,6,7,4] => [2,2,1,1,1] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => [1,3,2,6,5,7,4] => [3,2,1,1] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [1,4,2,3,5,6,7] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [1,4,2,3,5,7,6] => [2,2,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [1,4,2,3,6,5,7] => [2,2,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [1,4,2,3,7,5,6] => [2,2,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => [1,4,2,3,6,7,5] => [2,2,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [1,5,2,3,4,6,7] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [1,5,2,3,4,7,6] => [2,2,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [1,6,2,3,4,5,7] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [1,7,2,3,4,5,6] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => [1,6,7,2,3,4,5] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => [1,5,6,2,3,4,7] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => [1,5,7,2,3,4,6] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,7,5,6,2] => [1,5,6,7,2,3,4] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => [1,6,5,7,2,3,4] => [3,1,1,1,1] => 2
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => [1,4,5,2,3,6,7] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => [1,4,5,2,3,7,6] => [2,2,1,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => [1,4,6,2,3,5,7] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => [1,4,7,2,3,5,6] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => [1,4,6,7,2,3,5] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,6,4,5,2,7] => [1,4,5,6,2,3,7] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,6,4,5,7,2] => [1,4,5,7,2,3,6] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,7,4,5,6,2] => [1,4,5,6,7,2,3] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,7,4,6,5,2] => [1,4,6,5,7,2,3] => [3,1,1,1,1] => 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => [1,5,4,6,2,3,7] => [3,1,1,1,1] => 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => [1,5,4,7,2,3,6] => [3,1,1,1,1] => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,7,5,4,6,2] => [1,5,4,6,7,2,3] => [3,1,1,1,1] => 2
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,7,5,6,4,2] => [1,6,4,5,7,2,3] => [3,1,1,1,1] => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => [1,5,6,4,7,2,3] => [3,1,1,1,1] => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => [1,3,4,2,5,6,7] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => [1,3,4,2,5,7,6] => [2,2,1,1,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => [1,3,4,2,6,5,7] => [2,2,1,1,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => [1,3,4,2,7,5,6] => [2,2,1,1,1] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => [1,3,4,2,6,7,5] => [2,2,1,1,1] => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => [1,3,5,2,4,6,7] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => [1,3,5,2,4,7,6] => [2,2,1,1,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => [1,3,6,2,4,5,7] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => [1,3,7,2,4,5,6] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => [1,3,6,7,2,4,5] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => [1,3,5,6,2,4,7] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => [1,3,5,7,2,4,6] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,7,5,6,2] => [1,3,5,6,7,2,4] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => [1,3,6,5,7,2,4] => [3,1,1,1,1] => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,5,3,4,2,6,7] => [1,3,4,5,2,6,7] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,5,3,4,2,7,6] => [1,3,4,5,2,7,6] => [2,2,1,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,5,3,4,6,2,7] => [1,3,4,6,2,5,7] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,5,3,4,6,7,2] => [1,3,4,7,2,5,6] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,5,3,4,7,6,2] => [1,3,4,6,7,2,5] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,6,3,4,5,2,7] => [1,3,4,5,6,2,7] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,6,3,4,5,7,2] => [1,3,4,5,7,2,6] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,7,3,4,5,6,2] => [1,3,4,5,6,7,2] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,7,3,4,6,5,2] => [1,3,4,6,5,7,2] => [3,1,1,1,1] => 2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,6,3,5,4,2,7] => [1,3,5,4,6,2,7] => [3,1,1,1,1] => 2
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,6,3,5,4,7,2] => [1,3,5,4,7,2,6] => [3,1,1,1,1] => 2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,7,3,5,4,6,2] => [1,3,5,4,6,7,2] => [3,1,1,1,1] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,7,3,5,6,4,2] => [1,3,6,4,5,7,2] => [3,1,1,1,1] => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,7,3,6,5,4,2] => [1,3,5,6,4,7,2] => [3,1,1,1,1] => 2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,4,3,2,6,7] => [1,4,3,5,2,6,7] => [3,1,1,1,1] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => [1,4,3,5,2,7,6] => [3,2,1,1] => 2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,4,3,6,2,7] => [1,4,3,6,2,5,7] => [3,1,1,1,1] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => [1,4,3,7,2,5,6] => [3,1,1,1,1] => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => [1,4,3,6,7,2,5] => [3,1,1,1,1] => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,6,4,3,5,2,7] => [1,4,3,5,6,2,7] => [3,1,1,1,1] => 2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,6,4,3,5,7,2] => [1,4,3,5,7,2,6] => [3,1,1,1,1] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,7,4,3,5,6,2] => [1,4,3,5,6,7,2] => [3,1,1,1,1] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,7,4,3,6,5,2] => [1,4,3,6,5,7,2] => [3,2,1,1] => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,6,4,5,3,2,7] => [1,5,3,4,6,2,7] => [3,1,1,1,1] => 2
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,6,4,5,3,7,2] => [1,5,3,4,7,2,6] => [3,1,1,1,1] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,7,4,5,3,6,2] => [1,5,3,4,6,7,2] => [3,1,1,1,1] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,7,4,5,6,3,2] => [1,6,3,4,5,7,2] => [3,1,1,1,1] => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,7,4,6,5,3,2] => [1,5,6,3,4,7,2] => [3,1,1,1,1] => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => [1,4,5,3,6,2,7] => [3,1,1,1,1] => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => [1,4,5,3,7,2,6] => [3,1,1,1,1] => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,7,5,4,3,6,2] => [1,4,5,3,6,7,2] => [3,1,1,1,1] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,7,5,4,6,3,2] => [1,4,6,3,5,7,2] => [3,1,1,1,1] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,7,6,4,5,3,2] => [1,4,5,6,3,7,2] => [3,1,1,1,1] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => [1,5,4,6,3,7,2] => [4,1,1,1] => 3
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [2,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => [2,1,3,4,5,7,6] => [2,2,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => [2,1,3,4,6,5,7] => [2,2,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => [2,1,3,4,7,5,6] => [2,2,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => [2,1,3,4,6,7,5] => [2,2,1,1,1] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => [2,1,3,5,4,6,7] => [2,2,1,1,1] => 1
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => [2,1,3,5,4,7,6] => [2,2,2,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => [2,1,3,6,4,5,7] => [2,2,1,1,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [2,1,3,7,4,5,6] => [2,2,1,1,1] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,6,4] => [2,1,3,6,7,4,5] => [2,2,1,1,1] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => [2,1,3,5,6,4,7] => [2,2,1,1,1] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,5,7,4] => [2,1,3,5,7,4,6] => [2,2,1,1,1] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,7,5,6,4] => [2,1,3,5,6,7,4] => [2,2,1,1,1] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => [2,1,3,6,5,7,4] => [3,2,1,1] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => [2,1,4,3,5,6,7] => [2,2,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => [2,1,4,3,5,7,6] => [2,2,2,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => [2,1,4,3,6,5,7] => [2,2,2,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => [2,1,4,3,7,5,6] => [2,2,2,1] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => [2,1,4,3,6,7,5] => [2,2,2,1] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [2,1,5,3,4,6,7] => [2,2,1,1,1] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [2,1,5,3,4,7,6] => [2,2,2,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [2,1,6,3,4,5,7] => [2,2,1,1,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [2,1,7,3,4,5,6] => [2,2,1,1,1] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => [2,1,6,7,3,4,5] => [2,2,1,1,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,5,3,7] => [2,1,5,6,3,4,7] => [2,2,1,1,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => [2,1,5,7,3,4,6] => [2,2,1,1,1] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,7,5,6,3] => [2,1,5,6,7,3,4] => [2,2,1,1,1] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => [2,1,6,5,7,3,4] => [3,2,1,1] => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,4,3,6,7] => [2,1,4,5,3,6,7] => [2,2,1,1,1] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,4,3,7,6] => [2,1,4,5,3,7,6] => [2,2,2,1] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,4,6,3,7] => [2,1,4,6,3,5,7] => [2,2,1,1,1] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,4,6,7,3] => [2,1,4,7,3,5,6] => [2,2,1,1,1] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,4,7,6,3] => [2,1,4,6,7,3,5] => [2,2,1,1,1] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,6,4,5,3,7] => [2,1,4,5,6,3,7] => [2,2,1,1,1] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,6,4,5,7,3] => [2,1,4,5,7,3,6] => [2,2,1,1,1] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,7,4,5,6,3] => [2,1,4,5,6,7,3] => [2,2,1,1,1] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,7,4,6,5,3] => [2,1,4,6,5,7,3] => [3,2,1,1] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,5,4,3,7] => [2,1,5,4,6,3,7] => [3,2,1,1] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,5,4,7,3] => [2,1,5,4,7,3,6] => [3,2,1,1] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,7,5,4,6,3] => [2,1,5,4,6,7,3] => [3,2,1,1] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,7,5,6,4,3] => [2,1,6,4,5,7,3] => [3,2,1,1] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => [2,1,5,6,4,7,3] => [3,2,1,1] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [3,1,2,4,5,6,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [3,1,2,4,5,7,6] => [2,2,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [3,1,2,4,6,5,7] => [2,2,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [3,1,2,4,7,5,6] => [2,2,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,6,5] => [3,1,2,4,6,7,5] => [2,2,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [3,1,2,5,4,6,7] => [2,2,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [3,1,2,5,4,7,6] => [2,2,2,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [3,1,2,6,4,5,7] => [2,2,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [3,1,2,7,4,5,6] => [2,2,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,6,4] => [3,1,2,6,7,4,5] => [2,2,1,1,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,5,4,7] => [3,1,2,5,6,4,7] => [2,2,1,1,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,5,7,4] => [3,1,2,5,7,4,6] => [2,2,1,1,1] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,7,5,6,4] => [3,1,2,5,6,7,4] => [2,2,1,1,1] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => [3,1,2,6,5,7,4] => [3,2,1,1] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [4,1,2,3,5,6,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [4,1,2,3,5,7,6] => [2,2,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [4,1,2,3,6,5,7] => [2,2,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [4,1,2,3,7,5,6] => [2,2,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => [4,1,2,3,6,7,5] => [2,2,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [5,1,2,3,4,6,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [5,1,2,3,4,7,6] => [2,2,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [6,1,2,3,4,5,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [7,1,2,3,4,5,6] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,6,1] => [6,7,1,2,3,4,5] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => [5,6,1,2,3,4,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,5,7,1] => [5,7,1,2,3,4,6] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,7,5,6,1] => [5,6,7,1,2,3,4] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,6,5,1] => [6,5,7,1,2,3,4] => [3,1,1,1,1] => 2
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => [4,5,1,2,3,6,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => [4,5,1,2,3,7,6] => [2,2,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,4,6,1,7] => [4,6,1,2,3,5,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,4,6,7,1] => [4,7,1,2,3,5,6] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,4,7,6,1] => [4,6,7,1,2,3,5] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,6,4,5,1,7] => [4,5,6,1,2,3,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,6,4,5,7,1] => [4,5,7,1,2,3,6] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,7,4,5,6,1] => [4,5,6,7,1,2,3] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,7,4,6,5,1] => [4,6,5,7,1,2,3] => [3,1,1,1,1] => 2
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => [5,4,6,1,2,3,7] => [3,1,1,1,1] => 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,5,4,7,1] => [5,4,7,1,2,3,6] => [3,1,1,1,1] => 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,7,5,4,6,1] => [5,4,6,7,1,2,3] => [3,1,1,1,1] => 2
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,7,5,6,4,1] => [6,4,5,7,1,2,3] => [3,1,1,1,1] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => [5,6,4,7,1,2,3] => [3,1,1,1,1] => 2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7] => [3,4,1,2,5,6,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,3,1,5,7,6] => [3,4,1,2,5,7,6] => [2,2,1,1,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,7] => [3,4,1,2,6,5,7] => [2,2,1,1,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3,1,6,7,5] => [3,4,1,2,7,5,6] => [2,2,1,1,1] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3,1,7,6,5] => [3,4,1,2,6,7,5] => [2,2,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,3,5,1,6,7] => [3,5,1,2,4,6,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,3,5,1,7,6] => [3,5,1,2,4,7,6] => [2,2,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,3,5,6,1,7] => [3,6,1,2,4,5,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,1] => [3,7,1,2,4,5,6] => [2,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,3,5,7,6,1] => [3,6,7,1,2,4,5] => [2,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,1,7] => [3,5,6,1,2,4,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,7,1] => [3,5,7,1,2,4,6] => [2,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,3,7,5,6,1] => [3,5,6,7,1,2,4] => [2,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => [3,6,5,7,1,2,4] => [3,1,1,1,1] => 2
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,5,3,4,1,6,7] => [3,4,5,1,2,6,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,5,3,4,1,7,6] => [3,4,5,1,2,7,6] => [2,2,1,1,1] => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,5,3,4,6,1,7] => [3,4,6,1,2,5,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,5,3,4,6,7,1] => [3,4,7,1,2,5,6] => [2,1,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,5,3,4,7,6,1] => [3,4,6,7,1,2,5] => [2,1,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,6,3,4,5,1,7] => [3,4,5,6,1,2,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,6,3,4,5,7,1] => [3,4,5,7,1,2,6] => [2,1,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,7,3,4,5,6,1] => [3,4,5,6,7,1,2] => [2,1,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,7,3,4,6,5,1] => [3,4,6,5,7,1,2] => [3,1,1,1,1] => 2
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,6,3,5,4,1,7] => [3,5,4,6,1,2,7] => [3,1,1,1,1] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,6,3,5,4,7,1] => [3,5,4,7,1,2,6] => [3,1,1,1,1] => 2
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,7,3,5,4,6,1] => [3,5,4,6,7,1,2] => [3,1,1,1,1] => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,7,3,5,6,4,1] => [3,6,4,5,7,1,2] => [3,1,1,1,1] => 2
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,7,3,6,5,4,1] => [3,5,6,4,7,1,2] => [3,1,1,1,1] => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => [4,3,5,1,2,6,7] => [3,1,1,1,1] => 2
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => [4,3,5,1,2,7,6] => [3,2,1,1] => 2
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,4,3,6,1,7] => [4,3,6,1,2,5,7] => [3,1,1,1,1] => 2
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,4,3,6,7,1] => [4,3,7,1,2,5,6] => [3,1,1,1,1] => 2
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,4,3,7,6,1] => [4,3,6,7,1,2,5] => [3,1,1,1,1] => 2
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,6,4,3,5,1,7] => [4,3,5,6,1,2,7] => [3,1,1,1,1] => 2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,6,4,3,5,7,1] => [4,3,5,7,1,2,6] => [3,1,1,1,1] => 2
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,7,4,3,5,6,1] => [4,3,5,6,7,1,2] => [3,1,1,1,1] => 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,7,4,3,6,5,1] => [4,3,6,5,7,1,2] => [3,2,1,1] => 2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,6,4,5,3,1,7] => [5,3,4,6,1,2,7] => [3,1,1,1,1] => 2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,6,4,5,3,7,1] => [5,3,4,7,1,2,6] => [3,1,1,1,1] => 2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,7,4,5,3,6,1] => [5,3,4,6,7,1,2] => [3,1,1,1,1] => 2
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,7,4,5,6,3,1] => [6,3,4,5,7,1,2] => [3,1,1,1,1] => 2
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,7,4,6,5,3,1] => [5,6,3,4,7,1,2] => [3,1,1,1,1] => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => [4,5,3,6,1,2,7] => [3,1,1,1,1] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => [4,5,3,7,1,2,6] => [3,1,1,1,1] => 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,7,5,4,3,6,1] => [4,5,3,6,7,1,2] => [3,1,1,1,1] => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,7,5,4,6,3,1] => [4,6,3,5,7,1,2] => [3,1,1,1,1] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,7,6,4,5,3,1] => [4,5,6,3,7,1,2] => [3,1,1,1,1] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => [5,4,6,3,7,1,2] => [4,1,1,1] => 3
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => [2,3,1,4,5,6,7] => [2,1,1,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,7,6] => [2,3,1,4,5,7,6] => [2,2,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,2,1,4,6,5,7] => [2,3,1,4,6,5,7] => [2,2,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,2,1,4,6,7,5] => [2,3,1,4,7,5,6] => [2,2,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => [2,3,1,4,6,7,5] => [2,2,1,1,1] => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,5,4,6,7] => [2,3,1,5,4,6,7] => [2,2,1,1,1] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => [2,3,1,5,4,7,6] => [2,2,2,1] => 1
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,5,6,4,7] => [2,3,1,6,4,5,7] => [2,2,1,1,1] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,5,6,7,4] => [2,3,1,7,4,5,6] => [2,2,1,1,1] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,1,5,7,6,4] => [2,3,1,6,7,4,5] => [2,2,1,1,1] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,2,1,6,5,4,7] => [2,3,1,5,6,4,7] => [2,2,1,1,1] => 1
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,2,1,6,5,7,4] => [2,3,1,5,7,4,6] => [2,2,1,1,1] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,2,1,7,5,6,4] => [2,3,1,5,6,7,4] => [2,2,1,1,1] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => [2,3,1,6,5,7,4] => [3,2,1,1] => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => [2,4,1,3,5,6,7] => [2,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => [2,4,1,3,5,7,6] => [2,2,1,1,1] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,7] => [2,4,1,3,6,5,7] => [2,2,1,1,1] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,2,4,1,6,7,5] => [2,4,1,3,7,5,6] => [2,2,1,1,1] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,4,1,7,6,5] => [2,4,1,3,6,7,5] => [2,2,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => [2,5,1,3,4,6,7] => [2,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => [2,5,1,3,4,7,6] => [2,2,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => [2,6,1,3,4,5,7] => [2,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => [2,7,1,3,4,5,6] => [2,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,7,6,1] => [2,6,7,1,3,4,5] => [2,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,4,6,5,1,7] => [2,5,6,1,3,4,7] => [2,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,2,4,6,5,7,1] => [2,5,7,1,3,4,6] => [2,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,7,5,6,1] => [2,5,6,7,1,3,4] => [2,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,2,4,7,6,5,1] => [2,6,5,7,1,3,4] => [3,1,1,1,1] => 2
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,5,4,1,6,7] => [2,4,5,1,3,6,7] => [2,1,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => [2,4,5,1,3,7,6] => [2,2,1,1,1] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,5,4,6,1,7] => [2,4,6,1,3,5,7] => [2,1,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,5,4,6,7,1] => [2,4,7,1,3,5,6] => [2,1,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => [2,4,6,7,1,3,5] => [2,1,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,6,4,5,1,7] => [2,4,5,6,1,3,7] => [2,1,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,6,4,5,7,1] => [2,4,5,7,1,3,6] => [2,1,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,7,4,5,6,1] => [2,4,5,6,7,1,3] => [2,1,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,7,4,6,5,1] => [2,4,6,5,7,1,3] => [3,1,1,1,1] => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,2,6,5,4,1,7] => [2,5,4,6,1,3,7] => [3,1,1,1,1] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,2,6,5,4,7,1] => [2,5,4,7,1,3,6] => [3,1,1,1,1] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,2,7,5,4,6,1] => [2,5,4,6,7,1,3] => [3,1,1,1,1] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,7,5,6,4,1] => [2,6,4,5,7,1,3] => [3,1,1,1,1] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => [2,5,6,4,7,1,3] => [3,1,1,1,1] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7] => [2,3,4,1,5,6,7] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,2,3,1,5,7,6] => [2,3,4,1,5,7,6] => [2,2,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,2,3,1,6,5,7] => [2,3,4,1,6,5,7] => [2,2,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,2,3,1,6,7,5] => [2,3,4,1,7,5,6] => [2,2,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,2,3,1,7,6,5] => [2,3,4,1,6,7,5] => [2,2,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,2,3,5,1,6,7] => [2,3,5,1,4,6,7] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,2,3,5,1,7,6] => [2,3,5,1,4,7,6] => [2,2,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,2,3,5,6,1,7] => [2,3,6,1,4,5,7] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,1] => [2,3,7,1,4,5,6] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,2,3,5,7,6,1] => [2,3,6,7,1,4,5] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,2,3,6,5,1,7] => [2,3,5,6,1,4,7] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [4,2,3,6,5,7,1] => [2,3,5,7,1,4,6] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,2,3,7,5,6,1] => [2,3,5,6,7,1,4] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,2,3,7,6,5,1] => [2,3,6,5,7,1,4] => [3,1,1,1,1] => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [5,2,3,4,1,6,7] => [2,3,4,5,1,6,7] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,2,3,4,1,7,6] => [2,3,4,5,1,7,6] => [2,2,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [5,2,3,4,6,1,7] => [2,3,4,6,1,5,7] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,2,3,4,6,7,1] => [2,3,4,7,1,5,6] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,2,3,4,7,6,1] => [2,3,4,6,7,1,5] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,2,3,4,5,1,7] => [2,3,4,5,6,1,7] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,2,3,4,5,7,1] => [2,3,4,5,7,1,6] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7,2,3,4,5,6,1] => [2,3,4,5,6,7,1] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [7,2,3,4,6,5,1] => [2,3,4,6,5,7,1] => [3,1,1,1,1] => 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,3,5,4,1,7] => [2,3,5,4,6,1,7] => [3,1,1,1,1] => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,2,3,5,4,7,1] => [2,3,5,4,7,1,6] => [3,1,1,1,1] => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [7,2,3,5,4,6,1] => [2,3,5,4,6,7,1] => [3,1,1,1,1] => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [7,2,3,5,6,4,1] => [2,3,6,4,5,7,1] => [3,1,1,1,1] => 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [7,2,3,6,5,4,1] => [2,3,5,6,4,7,1] => [3,1,1,1,1] => 2
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,2,4,3,1,6,7] => [2,4,3,5,1,6,7] => [3,1,1,1,1] => 2
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,2,4,3,1,7,6] => [2,4,3,5,1,7,6] => [3,2,1,1] => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [5,2,4,3,6,1,7] => [2,4,3,6,1,5,7] => [3,1,1,1,1] => 2
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,2,4,3,6,7,1] => [2,4,3,7,1,5,6] => [3,1,1,1,1] => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,2,4,3,7,6,1] => [2,4,3,6,7,1,5] => [3,1,1,1,1] => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,2,4,3,5,1,7] => [2,4,3,5,6,1,7] => [3,1,1,1,1] => 2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,2,4,3,5,7,1] => [2,4,3,5,7,1,6] => [3,1,1,1,1] => 2
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7,2,4,3,5,6,1] => [2,4,3,5,6,7,1] => [3,1,1,1,1] => 2
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7,2,4,3,6,5,1] => [2,4,3,6,5,7,1] => [3,2,1,1] => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,4,5,3,1,7] => [2,5,3,4,6,1,7] => [3,1,1,1,1] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,2,4,5,3,7,1] => [2,5,3,4,7,1,6] => [3,1,1,1,1] => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7,2,4,5,3,6,1] => [2,5,3,4,6,7,1] => [3,1,1,1,1] => 2
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7,2,4,5,6,3,1] => [2,6,3,4,5,7,1] => [3,1,1,1,1] => 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7,2,4,6,5,3,1] => [2,5,6,3,4,7,1] => [3,1,1,1,1] => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,2,5,4,3,1,7] => [2,4,5,3,6,1,7] => [3,1,1,1,1] => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,5,4,3,7,1] => [2,4,5,3,7,1,6] => [3,1,1,1,1] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [7,2,5,4,3,6,1] => [2,4,5,3,6,7,1] => [3,1,1,1,1] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [7,2,5,4,6,3,1] => [2,4,6,3,5,7,1] => [3,1,1,1,1] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [7,2,6,4,5,3,1] => [2,4,5,6,3,7,1] => [3,1,1,1,1] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [7,2,6,5,4,3,1] => [2,5,4,6,3,7,1] => [4,1,1,1] => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => [3,2,4,1,5,6,7] => [3,1,1,1,1] => 2
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,3,2,1,5,7,6] => [3,2,4,1,5,7,6] => [3,2,1,1] => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,7] => [3,2,4,1,6,5,7] => [3,2,1,1] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3,2,1,6,7,5] => [3,2,4,1,7,5,6] => [3,2,1,1] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => [3,2,4,1,6,7,5] => [3,2,1,1] => 2
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,3,2,5,1,6,7] => [3,2,5,1,4,6,7] => [3,1,1,1,1] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => [3,2,5,1,4,7,6] => [3,2,1,1] => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => [3,2,6,1,4,5,7] => [3,1,1,1,1] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => [3,2,7,1,4,5,6] => [3,1,1,1,1] => 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,3,2,5,7,6,1] => [3,2,6,7,1,4,5] => [3,1,1,1,1] => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => [3,2,5,6,1,4,7] => [3,1,1,1,1] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,3,2,6,5,7,1] => [3,2,5,7,1,4,6] => [3,1,1,1,1] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,2,7,5,6,1] => [3,2,5,6,7,1,4] => [3,1,1,1,1] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,1] => [3,2,6,5,7,1,4] => [3,2,1,1] => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,3,2,4,1,6,7] => [3,2,4,5,1,6,7] => [3,1,1,1,1] => 2
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,3,2,4,1,7,6] => [3,2,4,5,1,7,6] => [3,2,1,1] => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [5,3,2,4,6,1,7] => [3,2,4,6,1,5,7] => [3,1,1,1,1] => 2
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,3,2,4,6,7,1] => [3,2,4,7,1,5,6] => [3,1,1,1,1] => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,3,2,4,7,6,1] => [3,2,4,6,7,1,5] => [3,1,1,1,1] => 2
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1,7] => [3,2,4,5,6,1,7] => [3,1,1,1,1] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,3,2,4,5,7,1] => [3,2,4,5,7,1,6] => [3,1,1,1,1] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [7,3,2,4,5,6,1] => [3,2,4,5,6,7,1] => [3,1,1,1,1] => 2
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [7,3,2,4,6,5,1] => [3,2,4,6,5,7,1] => [3,2,1,1] => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,3,2,5,4,1,7] => [3,2,5,4,6,1,7] => [3,2,1,1] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,2,5,4,7,1] => [3,2,5,4,7,1,6] => [3,2,1,1] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [7,3,2,5,4,6,1] => [3,2,5,4,6,7,1] => [3,2,1,1] => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [7,3,2,5,6,4,1] => [3,2,6,4,5,7,1] => [3,2,1,1] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [7,3,2,6,5,4,1] => [3,2,5,6,4,7,1] => [3,2,1,1] => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,3,4,2,1,6,7] => [4,2,3,5,1,6,7] => [3,1,1,1,1] => 2
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,3,4,2,1,7,6] => [4,2,3,5,1,7,6] => [3,2,1,1] => 2
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,3,4,2,6,1,7] => [4,2,3,6,1,5,7] => [3,1,1,1,1] => 2
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,3,4,2,6,7,1] => [4,2,3,7,1,5,6] => [3,1,1,1,1] => 2
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,3,4,2,7,6,1] => [4,2,3,6,7,1,5] => [3,1,1,1,1] => 2
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,4,2,5,1,7] => [4,2,3,5,6,1,7] => [3,1,1,1,1] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,3,4,2,5,7,1] => [4,2,3,5,7,1,6] => [3,1,1,1,1] => 2
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7,3,4,2,5,6,1] => [4,2,3,5,6,7,1] => [3,1,1,1,1] => 2
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7,3,4,2,6,5,1] => [4,2,3,6,5,7,1] => [3,2,1,1] => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,3,4,5,2,1,7] => [5,2,3,4,6,1,7] => [3,1,1,1,1] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [5,2,3,4,7,1,6] => [3,1,1,1,1] => 2
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7,3,4,5,2,6,1] => [5,2,3,4,6,7,1] => [3,1,1,1,1] => 2
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7,3,4,5,6,2,1] => [6,2,3,4,5,7,1] => [3,1,1,1,1] => 2
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7,3,4,6,5,2,1] => [5,6,2,3,4,7,1] => [3,1,1,1,1] => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,3,5,4,2,1,7] => [4,5,2,3,6,1,7] => [3,1,1,1,1] => 2
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,3,5,4,2,7,1] => [4,5,2,3,7,1,6] => [3,1,1,1,1] => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [7,3,5,4,2,6,1] => [4,5,2,3,6,7,1] => [3,1,1,1,1] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [7,3,5,4,6,2,1] => [4,6,2,3,5,7,1] => [3,1,1,1,1] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [7,3,6,4,5,2,1] => [4,5,6,2,3,7,1] => [3,1,1,1,1] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [7,3,6,5,4,2,1] => [5,4,6,2,3,7,1] => [4,1,1,1] => 3
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => [3,4,2,5,1,6,7] => [3,1,1,1,1] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => [3,4,2,5,1,7,6] => [3,2,1,1] => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => [3,4,2,6,1,5,7] => [3,1,1,1,1] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => [3,4,2,7,1,5,6] => [3,1,1,1,1] => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,4,3,2,7,6,1] => [3,4,2,6,7,1,5] => [3,1,1,1,1] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,4,3,2,5,1,7] => [3,4,2,5,6,1,7] => [3,1,1,1,1] => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [3,4,2,5,7,1,6] => [3,1,1,1,1] => 2
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [7,4,3,2,5,6,1] => [3,4,2,5,6,7,1] => [3,1,1,1,1] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [7,4,3,2,6,5,1] => [3,4,2,6,5,7,1] => [3,2,1,1] => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,4,3,5,2,1,7] => [3,5,2,4,6,1,7] => [3,1,1,1,1] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,4,3,5,2,7,1] => [3,5,2,4,7,1,6] => [3,1,1,1,1] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [7,4,3,5,2,6,1] => [3,5,2,4,6,7,1] => [3,1,1,1,1] => 2
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [7,4,3,5,6,2,1] => [3,6,2,4,5,7,1] => [3,1,1,1,1] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [7,4,3,6,5,2,1] => [3,5,6,2,4,7,1] => [3,1,1,1,1] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,5,3,4,2,1,7] => [3,4,5,2,6,1,7] => [3,1,1,1,1] => 2
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,5,3,4,2,7,1] => [3,4,5,2,7,1,6] => [3,1,1,1,1] => 2
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [7,5,3,4,2,6,1] => [3,4,5,2,6,7,1] => [3,1,1,1,1] => 2
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [7,5,3,4,6,2,1] => [3,4,6,2,5,7,1] => [3,1,1,1,1] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [7,6,3,4,5,2,1] => [3,4,5,6,2,7,1] => [3,1,1,1,1] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7,6,3,5,4,2,1] => [3,5,4,6,2,7,1] => [4,1,1,1] => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => [4,3,5,2,6,1,7] => [4,1,1,1] => 3
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,5,4,3,2,7,1] => [4,3,5,2,7,1,6] => [4,1,1,1] => 3
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [7,5,4,3,2,6,1] => [4,3,5,2,6,7,1] => [4,1,1,1] => 3
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [7,5,4,3,6,2,1] => [4,3,6,2,5,7,1] => [4,1,1,1] => 3
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [7,6,4,3,5,2,1] => [4,3,5,6,2,7,1] => [4,1,1,1] => 3
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7,6,4,5,3,2,1] => [5,3,4,6,2,7,1] => [4,1,1,1] => 3
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => [4,5,3,6,2,7,1] => [4,1,1,1] => 3
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => [1,2,3,4,5,7,6,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,7,8,6] => [1,2,3,4,5,8,6,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,7,6] => [1,2,3,4,5,7,8,6] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,6,5,7,8] => [1,2,3,4,6,5,7,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => [1,2,3,4,6,5,8,7] => [2,2,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,6,7,5,8] => [1,2,3,4,7,5,6,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,5] => [1,2,3,4,8,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,6,8,7,5] => [1,2,3,4,7,8,5,6] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,7,6,5,8] => [1,2,3,4,6,7,5,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,7,6,8,5] => [1,2,3,4,6,8,5,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,8,6,7,5] => [1,2,3,4,6,7,8,5] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,7,6,5] => [1,2,3,4,7,6,8,5] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,3,5,4,6,8,7] => [1,2,3,5,4,6,8,7] => [2,2,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => [1,2,3,5,4,7,6,8] => [2,2,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3,5,4,7,8,6] => [1,2,3,5,4,8,6,7] => [2,2,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,7,6] => [1,2,3,5,4,7,8,6] => [2,2,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,4,7,8] => [1,2,3,6,4,5,7,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,5,6,4,8,7] => [1,2,3,6,4,5,8,7] => [2,2,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,5,6,7,4,8] => [1,2,3,7,4,5,6,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => [1,2,3,8,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,8,7,4] => [1,2,3,7,8,4,5,6] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,3,5,7,6,4,8] => [1,2,3,6,7,4,5,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,3,5,7,6,8,4] => [1,2,3,6,8,4,5,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,5,8,6,7,4] => [1,2,3,6,7,8,4,5] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,5,8,7,6,4] => [1,2,3,7,6,8,4,5] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,6,5,4,7,8] => [1,2,3,5,6,4,7,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,5,4,8,7] => [1,2,3,5,6,4,8,7] => [2,2,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,3,6,5,7,4,8] => [1,2,3,5,7,4,6,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,6,5,7,8,4] => [1,2,3,5,8,4,6,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,6,5,8,7,4] => [1,2,3,5,7,8,4,6] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,3,7,5,6,4,8] => [1,2,3,5,6,7,4,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,7,5,6,8,4] => [1,2,3,5,6,8,4,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,8,5,6,7,4] => [1,2,3,5,6,7,8,4] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,8,5,7,6,4] => [1,2,3,5,7,6,8,4] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,7,6,5,4,8] => [1,2,3,6,5,7,4,8] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,3,7,6,5,8,4] => [1,2,3,6,5,8,4,7] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,8,6,5,7,4] => [1,2,3,6,5,7,8,4] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,8,6,7,5,4] => [1,2,3,7,5,6,8,4] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,7,6,5,4] => [1,2,3,6,7,5,8,4] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8] => [1,2,4,3,5,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,8,7] => [1,2,4,3,5,6,8,7] => [2,2,1,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5,7,6,8] => [1,2,4,3,5,7,6,8] => [2,2,1,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,4,3,5,7,8,6] => [1,2,4,3,5,8,6,7] => [2,2,1,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,4,3,5,8,7,6] => [1,2,4,3,5,7,8,6] => [2,2,1,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7,8] => [2,2,1,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => [1,2,4,3,6,5,8,7] => [2,2,2,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,4,3,6,7,5,8] => [1,2,4,3,7,5,6,8] => [2,2,1,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4,3,6,7,8,5] => [1,2,4,3,8,5,6,7] => [2,2,1,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,4,3,6,8,7,5] => [1,2,4,3,7,8,5,6] => [2,2,1,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,4,3,7,6,5,8] => [1,2,4,3,6,7,5,8] => [2,2,1,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,6,8,5] => [1,2,4,3,6,8,5,7] => [2,2,1,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,4,3,8,6,7,5] => [1,2,4,3,6,7,8,5] => [2,2,1,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,7,6,5] => [1,2,4,3,7,6,8,5] => [3,2,1,1,1] => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,2,4,5,3,6,7,8] => [1,2,5,3,4,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,2,4,5,3,6,8,7] => [1,2,5,3,4,6,8,7] => [2,2,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6,8] => [1,2,5,3,4,7,6,8] => [2,2,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,4,5,3,7,8,6] => [1,2,5,3,4,8,6,7] => [2,2,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,4,5,3,8,7,6] => [1,2,5,3,4,7,8,6] => [2,2,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,4,5,6,3,7,8] => [1,2,6,3,4,5,7,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,2,4,5,6,3,8,7] => [1,2,6,3,4,5,8,7] => [2,2,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,7,3,8] => [1,2,7,3,4,5,6,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,3] => [1,2,8,3,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,4,5,6,8,7,3] => [1,2,7,8,3,4,5,6] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,2,4,5,7,6,3,8] => [1,2,6,7,3,4,5,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,4,5,8,6,7,3] => [1,2,6,7,8,3,4,5] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,4,5,8,7,6,3] => [1,2,7,6,8,3,4,5] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,2,4,6,5,3,7,8] => [1,2,5,6,3,4,7,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,2,4,6,5,7,3,8] => [1,2,5,7,3,4,6,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,2,4,6,5,7,8,3] => [1,2,5,8,3,4,6,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,2,4,6,5,8,7,3] => [1,2,5,7,8,3,4,6] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,2,4,8,5,6,7,3] => [1,2,5,6,7,8,3,4] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,2,4,7,6,5,8,3] => [1,2,6,5,8,3,4,7] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,2,4,8,6,7,5,3] => [1,2,7,5,6,8,3,4] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4,8,7,6,5,3] => [1,2,6,7,5,8,3,4] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,2,5,4,3,7,6,8] => [1,2,4,5,3,7,6,8] => [2,2,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,5,4,3,7,8,6] => [1,2,4,5,3,8,6,7] => [2,2,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,4,3,8,7,6] => [1,2,4,5,3,7,8,6] => [2,2,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,2,5,4,6,3,7,8] => [1,2,4,6,3,5,7,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,2,5,4,6,3,8,7] => [1,2,4,6,3,5,8,7] => [2,2,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,2,5,4,6,7,3,8] => [1,2,4,7,3,5,6,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,3] => [1,2,4,8,3,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,2,5,4,6,8,7,3] => [1,2,4,7,8,3,5,6] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,2,5,4,7,6,3,8] => [1,2,4,6,7,3,5,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,2,5,4,7,6,8,3] => [1,2,4,6,8,3,5,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,2,5,4,8,6,7,3] => [1,2,4,6,7,8,3,5] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,2,6,4,5,3,7,8] => [1,2,4,5,6,3,7,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,2,6,4,5,7,8,3] => [1,2,4,5,8,3,6,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,2,6,4,5,8,7,3] => [1,2,4,5,7,8,3,6] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,2,7,4,5,6,3,8] => [1,2,4,5,6,7,3,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,2,7,4,5,6,8,3] => [1,2,4,5,6,8,3,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,8,4,5,6,7,3] => [1,2,4,5,6,7,8,3] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,2,7,4,6,5,8,3] => [1,2,4,6,5,8,3,7] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,2,8,4,6,7,5,3] => [1,2,4,7,5,6,8,3] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,6,5,4,7,8,3] => [1,2,5,4,8,3,6,7] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,6,5,4,8,7,3] => [1,2,5,4,7,8,3,6] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,2,7,5,4,6,3,8] => [1,2,5,4,6,7,3,8] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,8,5,4,6,7,3] => [1,2,5,4,6,7,8,3] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,8,5,4,7,6,3] => [1,2,5,4,7,6,8,3] => [3,2,1,1,1] => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,2,7,5,6,4,8,3] => [1,2,6,4,5,8,3,7] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,2,8,5,6,4,7,3] => [1,2,6,4,5,7,8,3] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,8,5,6,7,4,3] => [1,2,7,4,5,6,8,3] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,2,8,5,7,6,4,3] => [1,2,6,7,4,5,8,3] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,7,6,5,4,3,8] => [1,2,5,6,4,7,3,8] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,8,6,5,7,4,3] => [1,2,5,7,4,6,8,3] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,8,7,5,6,4,3] => [1,2,5,6,7,4,8,3] => [3,1,1,1,1,1] => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,8,7] => [1,3,2,4,5,6,8,7] => [2,2,1,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => [1,3,2,4,5,7,6,8] => [2,2,1,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,7,8,6] => [1,3,2,4,5,8,6,7] => [2,2,1,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,8,7,6] => [1,3,2,4,5,7,8,6] => [2,2,1,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,6,5,7,8] => [1,3,2,4,6,5,7,8] => [2,2,1,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,2,4,6,5,8,7] => [1,3,2,4,6,5,8,7] => [2,2,2,1,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,2,4,6,7,8,5] => [1,3,2,4,8,5,6,7] => [2,2,1,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,2,4,6,8,7,5] => [1,3,2,4,7,8,5,6] => [2,2,1,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,2,4,7,6,8,5] => [1,3,2,4,6,8,5,7] => [2,2,1,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,3,2,4,8,6,7,5] => [1,3,2,4,6,7,8,5] => [2,2,1,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,7,6,5] => [1,3,2,4,7,6,8,5] => [3,2,1,1,1] => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => [1,3,2,5,4,6,7,8] => [2,2,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => [1,3,2,5,4,7,6,8] => [2,2,2,1,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => [1,3,2,5,4,8,6,7] => [2,2,2,1,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,7,6] => [1,3,2,5,4,7,8,6] => [2,2,2,1,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,3,2,5,6,4,7,8] => [1,3,2,6,4,5,7,8] => [2,2,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,2,5,6,7,4,8] => [1,3,2,7,4,5,6,8] => [2,2,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,6,7,8,4] => [1,3,2,8,4,5,6,7] => [2,2,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,2,5,7,6,4,8] => [1,3,2,6,7,4,5,8] => [2,2,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,3,2,5,7,6,8,4] => [1,3,2,6,8,4,5,7] => [2,2,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,3,2,5,8,6,7,4] => [1,3,2,6,7,8,4,5] => [2,2,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,2,5,8,7,6,4] => [1,3,2,7,6,8,4,5] => [3,2,1,1,1] => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,6,5,4,7,8] => [1,3,2,5,6,4,7,8] => [2,2,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,6,5,4,8,7] => [1,3,2,5,6,4,8,7] => [2,2,2,1,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,5,7,4,8] => [1,3,2,5,7,4,6,8] => [2,2,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,5,7,8,4] => [1,3,2,5,8,4,6,7] => [2,2,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,5,8,7,4] => [1,3,2,5,7,8,4,6] => [2,2,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,3,2,7,5,6,4,8] => [1,3,2,5,6,7,4,8] => [2,2,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,3,2,8,5,6,7,4] => [1,3,2,5,6,7,8,4] => [2,2,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2,8,5,7,6,4] => [1,3,2,5,7,6,8,4] => [3,2,1,1,1] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,6,5,4,8] => [1,3,2,6,5,7,4,8] => [3,2,1,1,1] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,7,6,5,8,4] => [1,3,2,6,5,8,4,7] => [3,2,1,1,1] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,8,6,5,7,4] => [1,3,2,6,5,7,8,4] => [3,2,1,1,1] => 2
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,3,2,8,6,7,5,4] => [1,3,2,7,5,6,8,4] => [3,2,1,1,1] => 2
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,7,6,5,4] => [1,3,2,6,7,5,8,4] => [3,2,1,1,1] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8] => [1,4,2,3,5,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,2,5,6,8,7] => [1,4,2,3,5,6,8,7] => [2,2,1,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,5,7,6,8] => [1,4,2,3,5,7,6,8] => [2,2,1,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,2,5,7,8,6] => [1,4,2,3,5,8,6,7] => [2,2,1,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,3,4,2,5,8,7,6] => [1,4,2,3,5,7,8,6] => [2,2,1,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7] => [1,4,2,3,6,5,8,7] => [2,2,2,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => [1,4,2,3,7,5,6,8] => [2,2,1,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4,2,6,7,8,5] => [1,4,2,3,8,5,6,7] => [2,2,1,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,3,4,2,6,8,7,5] => [1,4,2,3,7,8,5,6] => [2,2,1,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,3,4,2,7,6,5,8] => [1,4,2,3,6,7,5,8] => [2,2,1,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,3,4,2,8,6,7,5] => [1,4,2,3,6,7,8,5] => [2,2,1,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4,2,8,7,6,5] => [1,4,2,3,7,6,8,5] => [3,2,1,1,1] => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8] => [1,5,2,3,4,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,5,2,6,8,7] => [1,5,2,3,4,6,8,7] => [2,2,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6,8] => [1,5,2,3,4,7,6,8] => [2,2,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,5,2,7,8,6] => [1,5,2,3,4,8,6,7] => [2,2,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,5,2,8,7,6] => [1,5,2,3,4,7,8,6] => [2,2,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,2,7,8] => [1,6,2,3,4,5,7,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,2,8,7] => [1,6,2,3,4,5,8,7] => [2,2,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,2,8] => [1,7,2,3,4,5,6,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,2] => [1,8,2,3,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,8,7,2] => [1,7,8,2,3,4,5,6] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,5,7,6,2,8] => [1,6,7,2,3,4,5,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,5,7,6,8,2] => [1,6,8,2,3,4,5,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,5,8,6,7,2] => [1,6,7,8,2,3,4,5] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,5,8,7,6,2] => [1,7,6,8,2,3,4,5] => [3,1,1,1,1,1] => 2
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,3,4,6,5,2,7,8] => [1,5,6,2,3,4,7,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,3,4,6,5,2,8,7] => [1,5,6,2,3,4,8,7] => [2,2,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,3,4,6,5,7,2,8] => [1,5,7,2,3,4,6,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,4,6,5,7,8,2] => [1,5,8,2,3,4,6,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,3,4,6,5,8,7,2] => [1,5,7,8,2,3,4,6] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,3,4,7,5,6,8,2] => [1,5,6,8,2,3,4,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,8,5,6,7,2] => [1,5,6,7,8,2,3,4] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,4,7,6,5,8,2] => [1,6,5,8,2,3,4,7] => [3,1,1,1,1,1] => 2
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,3,4,8,6,5,7,2] => [1,6,5,7,8,2,3,4] => [3,1,1,1,1,1] => 2
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,8,7,6,5,2] => [1,6,7,5,8,2,3,4] => [3,1,1,1,1,1] => 2
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,3,5,4,2,6,7,8] => [1,4,5,2,3,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,3,5,4,2,7,6,8] => [1,4,5,2,3,7,6,8] => [2,2,1,1,1,1] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,3,5,4,2,7,8,6] => [1,4,5,2,3,8,6,7] => [2,2,1,1,1,1] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,3,5,4,2,8,7,6] => [1,4,5,2,3,7,8,6] => [2,2,1,1,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,3,5,4,6,2,7,8] => [1,4,6,2,3,5,7,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,3,5,4,6,7,2,8] => [1,4,7,2,3,5,6,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,3,5,4,6,7,8,2] => [1,4,8,2,3,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,3,5,4,6,8,7,2] => [1,4,7,8,2,3,5,6] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,3,5,4,7,6,2,8] => [1,4,6,7,2,3,5,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,5,4,7,6,8,2] => [1,4,6,8,2,3,5,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,5,4,8,7,6,2] => [1,4,7,6,8,2,3,5] => [3,1,1,1,1,1] => 2
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,3,6,4,5,2,8,7] => [1,4,5,6,2,3,8,7] => [2,2,1,1,1,1] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,3,6,4,5,7,2,8] => [1,4,5,7,2,3,6,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,3,6,4,5,8,7,2] => [1,4,5,7,8,2,3,6] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,3,7,4,5,6,2,8] => [1,4,5,6,7,2,3,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,7,4,5,6,8,2] => [1,4,5,6,8,2,3,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,8,4,5,6,7,2] => [1,4,5,6,7,8,2,3] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,3,7,4,6,5,2,8] => [1,4,6,5,7,2,3,8] => [3,1,1,1,1,1] => 2
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,8,4,6,7,5,2] => [1,4,7,5,6,8,2,3] => [3,1,1,1,1,1] => 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,3,6,5,4,2,7,8] => [1,5,4,6,2,3,7,8] => [3,1,1,1,1,1] => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,3,7,5,4,6,8,2] => [1,5,4,6,8,2,3,7] => [3,1,1,1,1,1] => 2
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,8,5,4,6,7,2] => [1,5,4,6,7,8,2,3] => [3,1,1,1,1,1] => 2
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,3,8,5,4,7,6,2] => [1,5,4,7,6,8,2,3] => [3,2,1,1,1] => 2
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,3,7,5,6,4,2,8] => [1,6,4,5,7,2,3,8] => [3,1,1,1,1,1] => 2
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,8,5,6,7,4,2] => [1,7,4,5,6,8,2,3] => [3,1,1,1,1,1] => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,3,7,6,5,4,2,8] => [1,5,6,4,7,2,3,8] => [3,1,1,1,1,1] => 2
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,8,7,5,6,4,2] => [1,5,6,7,4,8,2,3] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8] => [1,3,4,2,5,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,4,3,2,5,6,8,7] => [1,3,4,2,5,6,8,7] => [2,2,1,1,1,1] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,4,3,2,5,7,6,8] => [1,3,4,2,5,7,6,8] => [2,2,1,1,1,1] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,4,3,2,5,7,8,6] => [1,3,4,2,5,8,6,7] => [2,2,1,1,1,1] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,3,2,5,8,7,6] => [1,3,4,2,5,7,8,6] => [2,2,1,1,1,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,3,2,6,5,8,7] => [1,3,4,2,6,5,8,7] => [2,2,2,1,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,4,3,2,6,7,8,5] => [1,3,4,2,8,5,6,7] => [2,2,1,1,1,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,4,3,2,6,8,7,5] => [1,3,4,2,7,8,5,6] => [2,2,1,1,1,1] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => [1,3,4,2,6,7,5,8] => [2,2,1,1,1,1] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,4,3,2,8,6,7,5] => [1,3,4,2,6,7,8,5] => [2,2,1,1,1,1] => 1
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,3,2,8,7,6,5] => [1,3,4,2,7,6,8,5] => [3,2,1,1,1] => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,4,3,5,2,6,7,8] => [1,3,5,2,4,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,4,3,5,2,6,8,7] => [1,3,5,2,4,6,8,7] => [2,2,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,3,5,2,7,6,8] => [1,3,5,2,4,7,6,8] => [2,2,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,4,3,5,2,7,8,6] => [1,3,5,2,4,8,6,7] => [2,2,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,4,3,5,2,8,7,6] => [1,3,5,2,4,7,8,6] => [2,2,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,3,5,6,2,7,8] => [1,3,6,2,4,5,7,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,4,3,5,6,7,2,8] => [1,3,7,2,4,5,6,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,2] => [1,3,8,2,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,4,3,5,6,8,7,2] => [1,3,7,8,2,4,5,6] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,3,5,8,6,7,2] => [1,3,6,7,8,2,4,5] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,3,6,5,2,7,8] => [1,3,5,6,2,4,7,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,3,6,5,7,2,8] => [1,3,5,7,2,4,6,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,3,6,5,7,8,2] => [1,3,5,8,2,4,6,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,2] => [1,3,5,7,8,2,4,6] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,4,3,7,5,6,2,8] => [1,3,5,6,7,2,4,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,3,8,5,6,7,2] => [1,3,5,6,7,8,2,4] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,3,8,5,7,6,2] => [1,3,5,7,6,8,2,4] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,4,3,7,6,5,2,8] => [1,3,6,5,7,2,4,8] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,3,8,6,5,7,2] => [1,3,6,5,7,8,2,4] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,3,8,6,7,5,2] => [1,3,7,5,6,8,2,4] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,3,8,7,6,5,2] => [1,3,6,7,5,8,2,4] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,5,3,4,2,6,7,8] => [1,3,4,5,2,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,5,3,4,2,7,6,8] => [1,3,4,5,2,7,6,8] => [2,2,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,5,3,4,2,7,8,6] => [1,3,4,5,2,8,6,7] => [2,2,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,5,3,4,2,8,7,6] => [1,3,4,5,2,7,8,6] => [2,2,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,5,3,4,6,2,7,8] => [1,3,4,6,2,5,7,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,5,3,4,6,2,8,7] => [1,3,4,6,2,5,8,7] => [2,2,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,5,3,4,6,7,2,8] => [1,3,4,7,2,5,6,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,5,3,4,6,7,8,2] => [1,3,4,8,2,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,5,3,4,7,6,2,8] => [1,3,4,6,7,2,5,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,5,3,4,7,6,8,2] => [1,3,4,6,8,2,5,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,5,3,4,8,7,6,2] => [1,3,4,7,6,8,2,5] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,6,3,4,5,2,7,8] => [1,3,4,5,6,2,7,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,6,3,4,5,7,2,8] => [1,3,4,5,7,2,6,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,6,3,4,5,7,8,2] => [1,3,4,5,8,2,6,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,6,3,4,5,8,7,2] => [1,3,4,5,7,8,2,6] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,7,3,4,5,6,2,8] => [1,3,4,5,6,7,2,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,7,3,4,5,6,8,2] => [1,3,4,5,6,8,2,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,8,3,4,5,6,7,2] => [1,3,4,5,6,7,8,2] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,8,3,4,5,7,6,2] => [1,3,4,5,7,6,8,2] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,7,3,4,6,5,2,8] => [1,3,4,6,5,7,2,8] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,7,3,4,6,5,8,2] => [1,3,4,6,5,8,2,7] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,8,3,4,6,5,7,2] => [1,3,4,6,5,7,8,2] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,8,3,4,7,6,5,2] => [1,3,4,6,7,5,8,2] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,6,3,5,4,2,7,8] => [1,3,5,4,6,2,7,8] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,6,3,5,4,7,2,8] => [1,3,5,4,7,2,6,8] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,6,3,5,4,7,8,2] => [1,3,5,4,8,2,6,7] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,6,3,5,4,8,7,2] => [1,3,5,4,7,8,2,6] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,7,3,5,4,6,2,8] => [1,3,5,4,6,7,2,8] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,8,3,5,4,6,7,2] => [1,3,5,4,6,7,8,2] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,8,3,5,4,7,6,2] => [1,3,5,4,7,6,8,2] => [3,2,1,1,1] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,7,3,5,6,4,8,2] => [1,3,6,4,5,8,2,7] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,8,3,5,6,4,7,2] => [1,3,6,4,5,7,8,2] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,8,3,5,6,7,4,2] => [1,3,7,4,5,6,8,2] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,8,3,5,7,6,4,2] => [1,3,6,7,4,5,8,2] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,7,3,6,5,4,2,8] => [1,3,5,6,4,7,2,8] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,7,3,6,5,4,8,2] => [1,3,5,6,4,8,2,7] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,8,3,6,5,4,7,2] => [1,3,5,6,4,7,8,2] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,8,3,6,5,7,4,2] => [1,3,5,7,4,6,8,2] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,8,3,7,5,6,4,2] => [1,3,5,6,7,4,8,2] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,8,3,7,6,5,4,2] => [1,3,6,5,7,4,8,2] => [4,1,1,1,1] => 3
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,4,3,2,7,6,8] => [1,4,3,5,2,7,6,8] => [3,2,1,1,1] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,5,4,3,2,7,8,6] => [1,4,3,5,2,8,6,7] => [3,2,1,1,1] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,4,3,2,8,7,6] => [1,4,3,5,2,7,8,6] => [3,2,1,1,1] => 2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,5,4,3,6,2,7,8] => [1,4,3,6,2,5,7,8] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,4,3,6,7,8,2] => [1,4,3,8,2,5,6,7] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,4,3,6,8,7,2] => [1,4,3,7,8,2,5,6] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,5,4,3,7,6,8,2] => [1,4,3,6,8,2,5,7] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,5,4,3,8,7,6,2] => [1,4,3,7,6,8,2,5] => [3,2,1,1,1] => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,6,4,3,5,2,7,8] => [1,4,3,5,6,2,7,8] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,6,4,3,5,8,7,2] => [1,4,3,5,7,8,2,6] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,8,4,3,5,6,7,2] => [1,4,3,5,6,7,8,2] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,7,4,3,6,5,2,8] => [1,4,3,6,5,7,2,8] => [3,2,1,1,1] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,7,4,3,6,5,8,2] => [1,4,3,6,5,8,2,7] => [3,2,1,1,1] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,8,4,3,6,5,7,2] => [1,4,3,6,5,7,8,2] => [3,2,1,1,1] => 2
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,8,4,3,7,6,5,2] => [1,4,3,6,7,5,8,2] => [3,2,1,1,1] => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,6,4,5,3,2,7,8] => [1,5,3,4,6,2,7,8] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,6,4,5,3,2,8,7] => [1,5,3,4,6,2,8,7] => [3,2,1,1,1] => 2
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,6,4,5,3,8,7,2] => [1,5,3,4,7,8,2,6] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,7,4,5,3,6,8,2] => [1,5,3,4,6,8,2,7] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,8,4,5,3,6,7,2] => [1,5,3,4,6,7,8,2] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,7,4,5,6,3,8,2] => [1,6,3,4,5,8,2,7] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,8,4,5,6,7,3,2] => [1,7,3,4,5,6,8,2] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,8,4,5,7,6,3,2] => [1,6,7,3,4,5,8,2] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,7,4,6,5,3,2,8] => [1,5,6,3,4,7,2,8] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,8,4,6,5,3,7,2] => [1,5,6,3,4,7,8,2] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,8,4,6,5,7,3,2] => [1,5,7,3,4,6,8,2] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,8,4,7,5,6,3,2] => [1,5,6,7,3,4,8,2] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,8,4,7,6,5,3,2] => [1,6,5,7,3,4,8,2] => [4,1,1,1,1] => 3
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,6,5,4,3,2,7,8] => [1,4,5,3,6,2,7,8] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,6,5,4,3,7,2,8] => [1,4,5,3,7,2,6,8] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,6,5,4,3,7,8,2] => [1,4,5,3,8,2,6,7] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,5,4,3,8,7,2] => [1,4,5,3,7,8,2,6] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,7,5,4,3,6,2,8] => [1,4,5,3,6,7,2,8] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,8,5,4,3,6,7,2] => [1,4,5,3,6,7,8,2] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,8,5,4,6,3,7,2] => [1,4,6,3,5,7,8,2] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,8,5,4,6,7,3,2] => [1,4,7,3,5,6,8,2] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,8,5,4,7,6,3,2] => [1,4,6,7,3,5,8,2] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,7,6,4,5,3,2,8] => [1,4,5,6,3,7,2,8] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,8,6,4,5,7,3,2] => [1,4,5,7,3,6,8,2] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,8,7,4,5,6,3,2] => [1,4,5,6,7,3,8,2] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,8,7,4,6,5,3,2] => [1,4,6,5,7,3,8,2] => [4,1,1,1,1] => 3
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,6,5,4,3,2,8] => [1,5,4,6,3,7,2,8] => [4,1,1,1,1] => 3
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,6,5,4,3,8,2] => [1,5,4,6,3,8,2,7] => [4,1,1,1,1] => 3
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,8,6,5,4,3,7,2] => [1,5,4,6,3,7,8,2] => [4,1,1,1,1] => 3
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,8,6,5,4,7,3,2] => [1,5,4,7,3,6,8,2] => [4,1,1,1,1] => 3
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,8,7,5,4,6,3,2] => [1,5,4,6,7,3,8,2] => [4,1,1,1,1] => 3
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,8,7,5,6,4,3,2] => [1,6,4,5,7,3,8,2] => [4,1,1,1,1] => 3
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => [1,5,6,4,7,3,8,2] => [4,1,1,1,1] => 3
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,8,7] => [2,2,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,7,6,8] => [2,1,3,4,5,7,6,8] => [2,2,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,7,8,6] => [2,1,3,4,5,8,6,7] => [2,2,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,8,7,6] => [2,1,3,4,5,7,8,6] => [2,2,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,4,6,5,7,8] => [2,1,3,4,6,5,7,8] => [2,2,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,4,6,5,8,7] => [2,1,3,4,6,5,8,7] => [2,2,2,1,1] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,4,6,7,5,8] => [2,1,3,4,7,5,6,8] => [2,2,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,4,6,7,8,5] => [2,1,3,4,8,5,6,7] => [2,2,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,4,6,8,7,5] => [2,1,3,4,7,8,5,6] => [2,2,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,4,8,6,7,5] => [2,1,3,4,6,7,8,5] => [2,2,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,7,6,5] => [2,1,3,4,7,6,8,5] => [3,2,1,1,1] => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4,6,8,7] => [2,1,3,5,4,6,8,7] => [2,2,2,1,1] => 1
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,3,5,4,8,7,6] => [2,1,3,5,4,7,8,6] => [2,2,2,1,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,3,5,6,4,7,8] => [2,1,3,6,4,5,7,8] => [2,2,1,1,1,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,5,6,4,8,7] => [2,1,3,6,4,5,8,7] => [2,2,2,1,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,4] => [2,1,3,8,4,5,6,7] => [2,2,1,1,1,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,1,3,5,6,8,7,4] => [2,1,3,7,8,4,5,6] => [2,2,1,1,1,1] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,1,3,5,8,6,7,4] => [2,1,3,6,7,8,4,5] => [2,2,1,1,1,1] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,6,5,4,8,7] => [2,1,3,5,6,4,8,7] => [2,2,2,1,1] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,3,6,5,7,8,4] => [2,1,3,5,8,4,6,7] => [2,2,1,1,1,1] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,8,5,6,7,4] => [2,1,3,5,6,7,8,4] => [2,2,1,1,1,1] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,1,3,7,6,5,8,4] => [2,1,3,6,5,8,4,7] => [3,2,1,1,1] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => [2,1,4,3,5,6,7,8] => [2,2,1,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,3,5,6,8,7] => [2,1,4,3,5,6,8,7] => [2,2,2,1,1] => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,3,5,7,8,6] => [2,1,4,3,5,8,6,7] => [2,2,2,1,1] => 1
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,3,5,8,7,6] => [2,1,4,3,5,7,8,6] => [2,2,2,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => [2,1,4,3,6,5,7,8] => [2,2,2,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => [2,2,2,2] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,5] => [2,1,4,3,8,5,6,7] => [2,2,2,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,7,5] => [2,1,4,3,7,8,5,6] => [2,2,2,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,6,8,5] => [2,1,4,3,6,8,5,7] => [2,2,2,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,8,6,7,5] => [2,1,4,3,6,7,8,5] => [2,2,2,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => [2,1,4,3,7,6,8,5] => [3,2,2,1] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8] => [2,1,5,3,4,6,7,8] => [2,2,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6,8,7] => [2,1,5,3,4,6,8,7] => [2,2,2,1,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,4,5,6,3,8,7] => [2,1,6,3,4,5,8,7] => [2,2,2,1,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,3,8] => [2,1,7,3,4,5,6,8] => [2,2,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,3] => [2,1,8,3,4,5,6,7] => [2,2,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,1,4,5,6,8,7,3] => [2,1,7,8,3,4,5,6] => [2,2,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,1,4,5,7,6,8,3] => [2,1,6,8,3,4,5,7] => [2,2,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,4,5,8,6,7,3] => [2,1,6,7,8,3,4,5] => [2,2,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,4,5,8,7,6,3] => [2,1,7,6,8,3,4,5] => [3,2,1,1,1] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,4,6,5,3,7,8] => [2,1,5,6,3,4,7,8] => [2,2,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7] => [2,1,5,6,3,4,8,7] => [2,2,2,1,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,1,4,6,5,7,3,8] => [2,1,5,7,3,4,6,8] => [2,2,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,1,4,6,5,7,8,3] => [2,1,5,8,3,4,6,7] => [2,2,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,1,4,6,5,8,7,3] => [2,1,5,7,8,3,4,6] => [2,2,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,1,4,7,5,6,8,3] => [2,1,5,6,8,3,4,7] => [2,2,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,1,4,8,5,6,7,3] => [2,1,5,6,7,8,3,4] => [2,2,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,1,4,8,6,5,7,3] => [2,1,6,5,7,8,3,4] => [3,2,1,1,1] => 2
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,4,8,6,7,5,3] => [2,1,7,5,6,8,3,4] => [3,2,1,1,1] => 2
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4,8,7,6,5,3] => [2,1,6,7,5,8,3,4] => [3,2,1,1,1] => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,4,3,6,7,8] => [2,1,4,5,3,6,7,8] => [2,2,1,1,1,1] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,5,4,3,6,8,7] => [2,1,4,5,3,6,8,7] => [2,2,2,1,1] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,1,5,4,6,3,7,8] => [2,1,4,6,3,5,7,8] => [2,2,1,1,1,1] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7] => [2,1,4,6,3,5,8,7] => [2,2,2,1,1] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,4,6,7,8,3] => [2,1,4,8,3,5,6,7] => [2,2,1,1,1,1] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,5,4,6,8,7,3] => [2,1,4,7,8,3,5,6] => [2,2,1,1,1,1] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,1,5,4,7,6,3,8] => [2,1,4,6,7,3,5,8] => [2,2,1,1,1,1] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,8,3] => [2,1,4,6,8,3,5,7] => [2,2,1,1,1,1] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,4,8,6,7,3] => [2,1,4,6,7,8,3,5] => [2,2,1,1,1,1] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,6,4,5,3,8,7] => [2,1,4,5,6,3,8,7] => [2,2,2,1,1] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,1,6,4,5,7,8,3] => [2,1,4,5,8,3,6,7] => [2,2,1,1,1,1] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,1,6,4,5,8,7,3] => [2,1,4,5,7,8,3,6] => [2,2,1,1,1,1] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,1,7,4,5,6,3,8] => [2,1,4,5,6,7,3,8] => [2,2,1,1,1,1] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,1,7,4,5,6,8,3] => [2,1,4,5,6,8,3,7] => [2,2,1,1,1,1] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,1,8,4,5,6,7,3] => [2,1,4,5,6,7,8,3] => [2,2,1,1,1,1] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,1,7,4,6,5,8,3] => [2,1,4,6,5,8,3,7] => [3,2,1,1,1] => 2
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,1,8,4,7,6,5,3] => [2,1,4,6,7,5,8,3] => [3,2,1,1,1] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => [2,1,5,4,6,3,8,7] => [3,2,2,1] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,1,6,5,4,7,8,3] => [2,1,5,4,8,3,6,7] => [3,2,1,1,1] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,8,5,4,6,7,3] => [2,1,5,4,6,7,8,3] => [3,2,1,1,1] => 2
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,8,5,4,7,6,3] => [2,1,5,4,7,6,8,3] => [3,2,2,1] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,1,7,5,6,4,8,3] => [2,1,6,4,5,8,3,7] => [3,2,1,1,1] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,1,8,5,6,4,7,3] => [2,1,6,4,5,7,8,3] => [3,2,1,1,1] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,7,6,5,4,8,3] => [2,1,5,6,4,8,3,7] => [3,2,1,1,1] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,8,6,5,4,7,3] => [2,1,5,6,4,7,8,3] => [3,2,1,1,1] => 2
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,8,6,5,7,4,3] => [2,1,5,7,4,6,8,3] => [3,2,1,1,1] => 2
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,8,7,5,6,4,3] => [2,1,5,6,7,4,8,3] => [3,2,1,1,1] => 2
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => [2,1,6,5,7,4,8,3] => [4,2,1,1] => 3
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8] => [3,1,2,4,5,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,8,7] => [3,1,2,4,5,6,8,7] => [2,2,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,3,1,4,5,7,6,8] => [3,1,2,4,5,7,6,8] => [2,2,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => [3,1,2,4,5,8,6,7] => [2,2,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,3,1,4,5,8,7,6] => [3,1,2,4,5,7,8,6] => [2,2,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,4,6,5,8,7] => [3,1,2,4,6,5,8,7] => [2,2,2,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,3,1,4,6,7,5,8] => [3,1,2,4,7,5,6,8] => [2,2,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,1,4,6,7,8,5] => [3,1,2,4,8,5,6,7] => [2,2,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,3,1,4,6,8,7,5] => [3,1,2,4,7,8,5,6] => [2,2,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,7,6,8,5] => [3,1,2,4,6,8,5,7] => [2,2,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,3,1,4,8,6,7,5] => [3,1,2,4,6,7,8,5] => [2,2,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,8,7,6,5] => [3,1,2,4,7,6,8,5] => [3,2,1,1,1] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,8] => [3,1,2,5,4,7,6,8] => [2,2,2,1,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,6,4,8,7] => [3,1,2,6,4,5,8,7] => [2,2,2,1,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,3,1,5,6,7,4,8] => [3,1,2,7,4,5,6,8] => [2,2,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,4] => [3,1,2,8,4,5,6,7] => [2,2,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,3,1,5,6,8,7,4] => [3,1,2,7,8,4,5,6] => [2,2,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,7,6,8,4] => [3,1,2,6,8,4,5,7] => [2,2,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,3,1,5,8,6,7,4] => [3,1,2,6,7,8,4,5] => [2,2,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,6,5,4,7,8] => [3,1,2,5,6,4,7,8] => [2,2,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,5,7,4,8] => [3,1,2,5,7,4,6,8] => [2,2,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,6,5,7,8,4] => [3,1,2,5,8,4,6,7] => [2,2,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,5,8,7,4] => [3,1,2,5,7,8,4,6] => [2,2,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,3,1,7,5,6,4,8] => [3,1,2,5,6,7,4,8] => [2,2,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,3,1,7,5,6,8,4] => [3,1,2,5,6,8,4,7] => [2,2,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,8,5,6,7,4] => [3,1,2,5,6,7,8,4] => [2,2,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,3,1,8,5,7,6,4] => [3,1,2,5,7,6,8,4] => [3,2,1,1,1] => 2
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,3,1,8,6,5,7,4] => [3,1,2,6,5,7,8,4] => [3,2,1,1,1] => 2
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,1,8,6,7,5,4] => [3,1,2,7,5,6,8,4] => [3,2,1,1,1] => 2
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,8,7,6,5,4] => [3,1,2,6,7,5,8,4] => [3,2,1,1,1] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8] => [4,1,2,3,5,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5,6,8,7] => [4,1,2,3,5,6,8,7] => [2,2,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,4,1,5,7,6,8] => [4,1,2,3,5,7,6,8] => [2,2,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,4,1,5,7,8,6] => [4,1,2,3,5,8,6,7] => [2,2,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,8,7,6] => [4,1,2,3,5,7,8,6] => [2,2,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,5,7,8] => [4,1,2,3,6,5,7,8] => [2,2,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7] => [4,1,2,3,6,5,8,7] => [2,2,2,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,4,1,6,7,5,8] => [4,1,2,3,7,5,6,8] => [2,2,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => [4,1,2,3,8,5,6,7] => [2,2,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,4,1,6,8,7,5] => [4,1,2,3,7,8,5,6] => [2,2,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,4,1,7,6,5,8] => [4,1,2,3,6,7,5,8] => [2,2,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,6,8,5] => [4,1,2,3,6,8,5,7] => [2,2,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,4,1,8,6,7,5] => [4,1,2,3,6,7,8,5] => [2,2,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,8,7,6,5] => [4,1,2,3,7,6,8,5] => [3,2,1,1,1] => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => [5,1,2,3,4,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,5,1,6,8,7] => [5,1,2,3,4,6,8,7] => [2,2,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,1,7,8,6] => [5,1,2,3,4,8,6,7] => [2,2,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,8,7,6] => [5,1,2,3,4,7,8,6] => [2,2,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => [6,1,2,3,4,5,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => [6,1,2,3,4,5,8,7] => [2,2,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => [7,1,2,3,4,5,6,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => [8,1,2,3,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,8,7,1] => [7,8,1,2,3,4,5,6] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,7,6,1,8] => [6,7,1,2,3,4,5,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,7,6,8,1] => [6,8,1,2,3,4,5,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,8,6,7,1] => [6,7,8,1,2,3,4,5] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,8,7,6,1] => [7,6,8,1,2,3,4,5] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,4,6,5,1,8,7] => [5,6,1,2,3,4,8,7] => [2,2,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,4,6,5,7,1,8] => [5,7,1,2,3,4,6,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,4,6,5,7,8,1] => [5,8,1,2,3,4,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,4,6,5,8,7,1] => [5,7,8,1,2,3,4,6] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,4,7,5,6,1,8] => [5,6,7,1,2,3,4,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,4,7,5,6,8,1] => [5,6,8,1,2,3,4,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,8,5,6,7,1] => [5,6,7,8,1,2,3,4] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,4,8,5,7,6,1] => [5,7,6,8,1,2,3,4] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,4,7,6,5,1,8] => [6,5,7,1,2,3,4,8] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,4,7,6,5,8,1] => [6,5,8,1,2,3,4,7] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,8,6,5,7,1] => [6,5,7,8,1,2,3,4] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,8,6,7,5,1] => [7,5,6,8,1,2,3,4] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,8,7,6,5,1] => [6,7,5,8,1,2,3,4] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,5,4,1,6,7,8] => [4,5,1,2,3,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,4,1,7,6,8] => [4,5,1,2,3,7,6,8] => [2,2,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,3,5,4,1,7,8,6] => [4,5,1,2,3,8,6,7] => [2,2,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,3,5,4,6,1,7,8] => [4,6,1,2,3,5,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,3,5,4,6,7,1,8] => [4,7,1,2,3,5,6,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,5,4,6,7,8,1] => [4,8,1,2,3,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,3,5,4,7,6,1,8] => [4,6,7,1,2,3,5,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,3,5,4,7,6,8,1] => [4,6,8,1,2,3,5,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,3,6,4,5,1,7,8] => [4,5,6,1,2,3,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,3,6,4,5,1,8,7] => [4,5,6,1,2,3,8,7] => [2,2,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,3,6,4,5,7,8,1] => [4,5,8,1,2,3,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,3,6,4,5,8,7,1] => [4,5,7,8,1,2,3,6] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,3,7,4,5,6,1,8] => [4,5,6,7,1,2,3,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,3,7,4,5,6,8,1] => [4,5,6,8,1,2,3,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,8,4,5,6,7,1] => [4,5,6,7,8,1,2,3] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,3,8,4,5,7,6,1] => [4,5,7,6,8,1,2,3] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,3,7,4,6,5,1,8] => [4,6,5,7,1,2,3,8] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,3,8,4,6,5,7,1] => [4,6,5,7,8,1,2,3] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,3,8,4,6,7,5,1] => [4,7,5,6,8,1,2,3] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,3,8,4,7,6,5,1] => [4,6,7,5,8,1,2,3] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,6,5,4,1,8,7] => [5,4,6,1,2,3,8,7] => [3,2,1,1,1] => 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,3,6,5,4,7,8,1] => [5,4,8,1,2,3,6,7] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,3,7,5,4,6,1,8] => [5,4,6,7,1,2,3,8] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,3,8,5,4,6,7,1] => [5,4,6,7,8,1,2,3] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,3,8,5,4,7,6,1] => [5,4,7,6,8,1,2,3] => [3,2,1,1,1] => 2
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,3,7,5,6,4,8,1] => [6,4,5,8,1,2,3,7] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,3,8,5,7,6,4,1] => [6,7,4,5,8,1,2,3] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,3,8,6,5,4,7,1] => [5,6,4,7,8,1,2,3] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,3,8,6,5,7,4,1] => [5,7,4,6,8,1,2,3] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,3,8,7,5,6,4,1] => [5,6,7,4,8,1,2,3] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,8,7,6,5,4,1] => [6,5,7,4,8,1,2,3] => [4,1,1,1,1] => 3
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8] => [3,4,1,2,5,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [2,4,3,1,5,6,8,7] => [3,4,1,2,5,6,8,7] => [2,2,1,1,1,1] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [2,4,3,1,5,7,6,8] => [3,4,1,2,5,7,6,8] => [2,2,1,1,1,1] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [2,4,3,1,5,7,8,6] => [3,4,1,2,5,8,6,7] => [2,2,1,1,1,1] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,4,3,1,5,8,7,6] => [3,4,1,2,5,7,8,6] => [2,2,1,1,1,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,4,3,1,6,5,7,8] => [3,4,1,2,6,5,7,8] => [2,2,1,1,1,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7] => [3,4,1,2,6,5,8,7] => [2,2,2,1,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,4,3,1,6,7,8,5] => [3,4,1,2,8,5,6,7] => [2,2,1,1,1,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,8,7,5] => [3,4,1,2,7,8,5,6] => [2,2,1,1,1,1] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,3,1,7,6,8,5] => [3,4,1,2,6,8,5,7] => [2,2,1,1,1,1] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,4,3,1,8,6,7,5] => [3,4,1,2,6,7,8,5] => [2,2,1,1,1,1] => 1
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,4,3,1,8,7,6,5] => [3,4,1,2,7,6,8,5] => [3,2,1,1,1] => 2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,4,3,5,1,6,7,8] => [3,5,1,2,4,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,4,3,5,1,6,8,7] => [3,5,1,2,4,6,8,7] => [2,2,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,4,3,5,1,7,6,8] => [3,5,1,2,4,7,6,8] => [2,2,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,4,3,5,1,7,8,6] => [3,5,1,2,4,8,6,7] => [2,2,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,4,3,5,1,8,7,6] => [3,5,1,2,4,7,8,6] => [2,2,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [2,4,3,5,6,1,7,8] => [3,6,1,2,4,5,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,4,3,5,6,1,8,7] => [3,6,1,2,4,5,8,7] => [2,2,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,4,3,5,6,7,1,8] => [3,7,1,2,4,5,6,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,8,1] => [3,8,1,2,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,4,3,5,6,8,7,1] => [3,7,8,1,2,4,5,6] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [2,4,3,5,7,6,1,8] => [3,6,7,1,2,4,5,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,4,3,5,7,6,8,1] => [3,6,8,1,2,4,5,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,4,3,5,8,6,7,1] => [3,6,7,8,1,2,4,5] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,4,3,6,5,1,7,8] => [3,5,6,1,2,4,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,3,6,5,1,8,7] => [3,5,6,1,2,4,8,7] => [2,2,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,4,3,6,5,7,1,8] => [3,5,7,1,2,4,6,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,1] => [3,5,7,8,1,2,4,6] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [2,4,3,7,5,6,1,8] => [3,5,6,7,1,2,4,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,4,3,7,5,6,8,1] => [3,5,6,8,1,2,4,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,4,3,8,5,6,7,1] => [3,5,6,7,8,1,2,4] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,4,3,7,6,5,8,1] => [3,6,5,8,1,2,4,7] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [2,4,3,8,6,7,5,1] => [3,7,5,6,8,1,2,4] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,4,3,8,7,6,5,1] => [3,6,7,5,8,1,2,4] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,5,3,4,1,6,7,8] => [3,4,5,1,2,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,5,3,4,1,8,7,6] => [3,4,5,1,2,7,8,6] => [2,2,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [2,5,3,4,6,1,8,7] => [3,4,6,1,2,5,8,7] => [2,2,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,5,3,4,6,7,8,1] => [3,4,8,1,2,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,5,3,4,6,8,7,1] => [3,4,7,8,1,2,5,6] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,5,3,4,8,6,7,1] => [3,4,6,7,8,1,2,5] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [2,5,3,4,8,7,6,1] => [3,4,7,6,8,1,2,5] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,6,3,4,5,1,7,8] => [3,4,5,6,1,2,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [2,6,3,4,5,1,8,7] => [3,4,5,6,1,2,8,7] => [2,2,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,6,3,4,5,7,8,1] => [3,4,5,8,1,2,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,6,3,4,5,8,7,1] => [3,4,5,7,8,1,2,6] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,7,3,4,5,6,1,8] => [3,4,5,6,7,1,2,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [2,7,3,4,5,6,8,1] => [3,4,5,6,8,1,2,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,8,3,4,5,6,7,1] => [3,4,5,6,7,8,1,2] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [2,8,3,4,5,7,6,1] => [3,4,5,7,6,8,1,2] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,6,3,5,4,1,8,7] => [3,5,4,6,1,2,8,7] => [3,2,1,1,1] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,6,3,5,4,8,7,1] => [3,5,4,7,8,1,2,6] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,7,3,5,4,6,8,1] => [3,5,4,6,8,1,2,7] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [2,8,3,5,4,6,7,1] => [3,5,4,6,7,8,1,2] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,8,3,5,4,7,6,1] => [3,5,4,7,6,8,1,2] => [3,2,1,1,1] => 2
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,8,3,5,6,7,4,1] => [3,7,4,5,6,8,1,2] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,8,3,5,7,6,4,1] => [3,6,7,4,5,8,1,2] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [2,8,3,6,5,4,7,1] => [3,5,6,4,7,8,1,2] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [2,8,3,6,5,7,4,1] => [3,5,7,4,6,8,1,2] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,8,3,7,6,5,4,1] => [3,6,5,7,4,8,1,2] => [4,1,1,1,1] => 3
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,5,4,3,1,6,7,8] => [4,3,5,1,2,6,7,8] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,5,4,3,1,7,6,8] => [4,3,5,1,2,7,6,8] => [3,2,1,1,1] => 2
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,5,4,3,6,8,7,1] => [4,3,7,8,1,2,5,6] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,5,4,3,7,6,8,1] => [4,3,6,8,1,2,5,7] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,5,4,3,8,6,7,1] => [4,3,6,7,8,1,2,5] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,5,4,3,8,7,6,1] => [4,3,7,6,8,1,2,5] => [3,2,1,1,1] => 2
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,6,4,3,5,1,7,8] => [4,3,5,6,1,2,7,8] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,6,4,3,5,1,8,7] => [4,3,5,6,1,2,8,7] => [3,2,1,1,1] => 2
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,8,4,3,5,6,7,1] => [4,3,5,6,7,8,1,2] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,8,4,3,5,7,6,1] => [4,3,5,7,6,8,1,2] => [3,2,1,1,1] => 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,7,4,3,6,5,1,8] => [4,3,6,5,7,1,2,8] => [3,2,1,1,1] => 2
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,8,4,3,6,5,7,1] => [4,3,6,5,7,8,1,2] => [3,2,1,1,1] => 2
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,8,4,3,6,7,5,1] => [4,3,7,5,6,8,1,2] => [3,2,1,1,1] => 2
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,8,4,3,7,6,5,1] => [4,3,6,7,5,8,1,2] => [3,2,1,1,1] => 2
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [2,6,4,5,3,8,7,1] => [5,3,4,7,8,1,2,6] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,8,4,5,3,6,7,1] => [5,3,4,6,7,8,1,2] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,7,4,5,6,3,1,8] => [6,3,4,5,7,1,2,8] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,7,4,5,6,3,8,1] => [6,3,4,5,8,1,2,7] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,8,4,5,6,3,7,1] => [6,3,4,5,7,8,1,2] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,8,4,5,6,7,3,1] => [7,3,4,5,6,8,1,2] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [2,8,4,6,5,3,7,1] => [5,6,3,4,7,8,1,2] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [2,8,4,6,5,7,3,1] => [5,7,3,4,6,8,1,2] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,6,5,4,3,1,8,7] => [4,5,3,6,1,2,8,7] => [3,2,1,1,1] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,6,5,4,3,7,1,8] => [4,5,3,7,1,2,6,8] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,6,5,4,3,8,7,1] => [4,5,3,7,8,1,2,6] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,7,5,4,3,6,8,1] => [4,5,3,6,8,1,2,7] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,8,5,4,3,6,7,1] => [4,5,3,6,7,8,1,2] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,8,5,4,3,7,6,1] => [4,5,3,7,6,8,1,2] => [3,2,1,1,1] => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,7,5,4,6,3,8,1] => [4,6,3,5,8,1,2,7] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,8,5,4,7,6,3,1] => [4,6,7,3,5,8,1,2] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [2,8,6,4,5,3,7,1] => [4,5,6,3,7,8,1,2] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,8,6,4,5,7,3,1] => [4,5,7,3,6,8,1,2] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,8,7,4,5,6,3,1] => [4,5,6,7,3,8,1,2] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,8,7,4,6,5,3,1] => [4,6,5,7,3,8,1,2] => [4,1,1,1,1] => 3
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,8,6,5,4,3,7,1] => [5,4,6,3,7,8,1,2] => [4,1,1,1,1] => 3
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,8,6,5,4,7,3,1] => [5,4,7,3,6,8,1,2] => [4,1,1,1,1] => 3
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,8,7,5,4,6,3,1] => [5,4,6,7,3,8,1,2] => [4,1,1,1,1] => 3
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,8,7,6,5,4,3,1] => [5,6,4,7,3,8,1,2] => [4,1,1,1,1] => 3
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8] => [2,3,1,4,5,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,6,8,7] => [2,3,1,4,5,6,8,7] => [2,2,1,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [3,2,1,4,5,7,6,8] => [2,3,1,4,5,7,6,8] => [2,2,1,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,2,1,4,5,7,8,6] => [2,3,1,4,5,8,6,7] => [2,2,1,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,2,1,4,5,8,7,6] => [2,3,1,4,5,7,8,6] => [2,2,1,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [3,2,1,4,6,5,8,7] => [2,3,1,4,6,5,8,7] => [2,2,2,1,1] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [3,2,1,4,6,7,5,8] => [2,3,1,4,7,5,6,8] => [2,2,1,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,2,1,4,6,7,8,5] => [2,3,1,4,8,5,6,7] => [2,2,1,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,2,1,4,6,8,7,5] => [2,3,1,4,7,8,5,6] => [2,2,1,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,2,1,4,7,6,5,8] => [2,3,1,4,6,7,5,8] => [2,2,1,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,2,1,4,8,6,7,5] => [2,3,1,4,6,7,8,5] => [2,2,1,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,2,1,4,8,7,6,5] => [2,3,1,4,7,6,8,5] => [3,2,1,1,1] => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,5,4,6,7,8] => [2,3,1,5,4,6,7,8] => [2,2,1,1,1,1] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,1,5,4,7,6,8] => [2,3,1,5,4,7,6,8] => [2,2,2,1,1] => 1
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,2,1,5,6,4,7,8] => [2,3,1,6,4,5,7,8] => [2,2,1,1,1,1] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,2,1,5,6,7,8,4] => [2,3,1,8,4,5,6,7] => [2,2,1,1,1,1] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,2,1,5,6,8,7,4] => [2,3,1,7,8,4,5,6] => [2,2,1,1,1,1] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [3,2,1,5,7,6,8,4] => [2,3,1,6,8,4,5,7] => [2,2,1,1,1,1] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,2,1,5,8,6,7,4] => [2,3,1,6,7,8,4,5] => [2,2,1,1,1,1] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [3,2,1,6,5,4,7,8] => [2,3,1,5,6,4,7,8] => [2,2,1,1,1,1] => 1
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,2,1,6,5,8,7,4] => [2,3,1,5,7,8,4,6] => [2,2,1,1,1,1] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [3,2,1,7,5,6,4,8] => [2,3,1,5,6,7,4,8] => [2,2,1,1,1,1] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,2,1,7,5,6,8,4] => [2,3,1,5,6,8,4,7] => [2,2,1,1,1,1] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,8,5,6,7,4] => [2,3,1,5,6,7,8,4] => [2,2,1,1,1,1] => 1
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,2,1,8,5,7,6,4] => [2,3,1,5,7,6,8,4] => [3,2,1,1,1] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,2,1,7,6,5,4,8] => [2,3,1,6,5,7,4,8] => [3,2,1,1,1] => 2
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => [2,3,1,6,7,5,8,4] => [3,2,1,1,1] => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8] => [2,4,1,3,5,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [3,2,4,1,6,5,7,8] => [2,4,1,3,6,5,7,8] => [2,2,1,1,1,1] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7] => [2,4,1,3,6,5,8,7] => [2,2,2,1,1] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [3,2,4,1,6,7,8,5] => [2,4,1,3,8,5,6,7] => [2,2,1,1,1,1] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,2,4,1,6,8,7,5] => [2,4,1,3,7,8,5,6] => [2,2,1,1,1,1] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,7,6,8,5] => [2,4,1,3,6,8,5,7] => [2,2,1,1,1,1] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,2,4,1,8,6,7,5] => [2,4,1,3,6,7,8,5] => [2,2,1,1,1,1] => 1
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,2,4,1,8,7,6,5] => [2,4,1,3,7,6,8,5] => [3,2,1,1,1] => 2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,2,4,5,1,6,7,8] => [2,5,1,3,4,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,6,1,7,8] => [2,6,1,3,4,5,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,1,8] => [2,7,1,3,4,5,6,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,1] => [2,8,1,3,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,6,8,7,1] => [2,7,8,1,3,4,5,6] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [3,2,4,5,7,6,1,8] => [2,6,7,1,3,4,5,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [3,2,4,5,7,6,8,1] => [2,6,8,1,3,4,5,7] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,2,4,5,8,6,7,1] => [2,6,7,8,1,3,4,5] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [3,2,4,6,5,1,8,7] => [2,5,6,1,3,4,8,7] => [2,2,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [3,2,4,8,5,6,7,1] => [2,5,6,7,8,1,3,4] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [3,2,4,7,6,5,1,8] => [2,6,5,7,1,3,4,8] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [3,2,4,7,6,5,8,1] => [2,6,5,8,1,3,4,7] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,8,6,7,5,1] => [2,7,5,6,8,1,3,4] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,2,4,8,7,6,5,1] => [2,6,7,5,8,1,3,4] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [3,2,5,4,1,6,7,8] => [2,4,5,1,3,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,2,5,4,1,7,6,8] => [2,4,5,1,3,7,6,8] => [2,2,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,2,5,4,1,8,7,6] => [2,4,5,1,3,7,8,6] => [2,2,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [3,2,5,4,6,1,7,8] => [2,4,6,1,3,5,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,6,1,8,7] => [2,4,6,1,3,5,8,7] => [2,2,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [3,2,5,4,6,7,8,1] => [2,4,8,1,3,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [3,2,5,4,6,8,7,1] => [2,4,7,8,1,3,5,6] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,7,6,1,8] => [2,4,6,7,1,3,5,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,8,1] => [2,4,6,8,1,3,5,7] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,4,8,6,7,1] => [2,4,6,7,8,1,3,5] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [3,2,6,4,5,1,7,8] => [2,4,5,6,1,3,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [3,2,6,4,5,1,8,7] => [2,4,5,6,1,3,8,7] => [2,2,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [3,2,7,4,5,6,1,8] => [2,4,5,6,7,1,3,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [3,2,8,4,5,6,7,1] => [2,4,5,6,7,8,1,3] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,2,7,4,6,5,8,1] => [2,4,6,5,8,1,3,7] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [3,2,8,4,6,5,7,1] => [2,4,6,5,7,8,1,3] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,2,6,5,4,8,7,1] => [2,5,4,7,8,1,3,6] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [3,2,7,5,4,6,1,8] => [2,5,4,6,7,1,3,8] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [3,2,8,5,4,7,6,1] => [2,5,4,7,6,8,1,3] => [3,2,1,1,1] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,2,7,5,6,4,1,8] => [2,6,4,5,7,1,3,8] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [3,2,7,5,6,4,8,1] => [2,6,4,5,8,1,3,7] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [3,2,8,5,6,4,7,1] => [2,6,4,5,7,8,1,3] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [3,2,8,5,6,7,4,1] => [2,7,4,5,6,8,1,3] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,2,8,5,7,6,4,1] => [2,6,7,4,5,8,1,3] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,2,7,6,5,4,1,8] => [2,5,6,4,7,1,3,8] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [3,2,7,6,5,4,8,1] => [2,5,6,4,8,1,3,7] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [3,2,8,6,5,7,4,1] => [2,5,7,4,6,8,1,3] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7,8] => [2,3,4,1,5,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [4,2,3,1,5,6,8,7] => [2,3,4,1,5,6,8,7] => [2,2,1,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [4,2,3,1,5,7,6,8] => [2,3,4,1,5,7,6,8] => [2,2,1,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [4,2,3,1,5,7,8,6] => [2,3,4,1,5,8,6,7] => [2,2,1,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [4,2,3,1,5,8,7,6] => [2,3,4,1,5,7,8,6] => [2,2,1,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [4,2,3,1,6,5,7,8] => [2,3,4,1,6,5,7,8] => [2,2,1,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [4,2,3,1,6,5,8,7] => [2,3,4,1,6,5,8,7] => [2,2,2,1,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [4,2,3,1,6,7,5,8] => [2,3,4,1,7,5,6,8] => [2,2,1,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [4,2,3,1,6,7,8,5] => [2,3,4,1,8,5,6,7] => [2,2,1,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [4,2,3,1,6,8,7,5] => [2,3,4,1,7,8,5,6] => [2,2,1,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [4,2,3,1,7,6,5,8] => [2,3,4,1,6,7,5,8] => [2,2,1,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [4,2,3,1,7,6,8,5] => [2,3,4,1,6,8,5,7] => [2,2,1,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [4,2,3,1,8,6,7,5] => [2,3,4,1,6,7,8,5] => [2,2,1,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,2,3,1,8,7,6,5] => [2,3,4,1,7,6,8,5] => [3,2,1,1,1] => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [4,2,3,5,1,6,7,8] => [2,3,5,1,4,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [4,2,3,5,1,7,6,8] => [2,3,5,1,4,7,6,8] => [2,2,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [4,2,3,5,1,7,8,6] => [2,3,5,1,4,8,6,7] => [2,2,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [4,2,3,5,6,1,7,8] => [2,3,6,1,4,5,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [4,2,3,5,6,1,8,7] => [2,3,6,1,4,5,8,7] => [2,2,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [4,2,3,5,6,7,1,8] => [2,3,7,1,4,5,6,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,8,1] => [2,3,8,1,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [4,2,3,5,6,8,7,1] => [2,3,7,8,1,4,5,6] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [4,2,3,5,7,6,1,8] => [2,3,6,7,1,4,5,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [4,2,3,5,7,6,8,1] => [2,3,6,8,1,4,5,7] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [4,2,3,6,5,1,7,8] => [2,3,5,6,1,4,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [4,2,3,6,5,1,8,7] => [2,3,5,6,1,4,8,7] => [2,2,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [4,2,3,6,5,8,7,1] => [2,3,5,7,8,1,4,6] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [4,2,3,7,5,6,1,8] => [2,3,5,6,7,1,4,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [4,2,3,7,5,6,8,1] => [2,3,5,6,8,1,4,7] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [4,2,3,8,5,6,7,1] => [2,3,5,6,7,8,1,4] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,2,3,8,5,7,6,1] => [2,3,5,7,6,8,1,4] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [4,2,3,7,6,5,8,1] => [2,3,6,5,8,1,4,7] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [4,2,3,8,6,5,7,1] => [2,3,6,5,7,8,1,4] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,2,3,8,7,6,5,1] => [2,3,6,7,5,8,1,4] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [5,2,3,4,1,6,7,8] => [2,3,4,5,1,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [5,2,3,4,1,6,8,7] => [2,3,4,5,1,6,8,7] => [2,2,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [5,2,3,4,1,7,6,8] => [2,3,4,5,1,7,6,8] => [2,2,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [5,2,3,4,1,7,8,6] => [2,3,4,5,1,8,6,7] => [2,2,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [5,2,3,4,1,8,7,6] => [2,3,4,5,1,7,8,6] => [2,2,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [5,2,3,4,6,1,7,8] => [2,3,4,6,1,5,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [5,2,3,4,6,7,1,8] => [2,3,4,7,1,5,6,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [5,2,3,4,6,7,8,1] => [2,3,4,8,1,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [5,2,3,4,6,8,7,1] => [2,3,4,7,8,1,5,6] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [5,2,3,4,7,6,1,8] => [2,3,4,6,7,1,5,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [5,2,3,4,7,6,8,1] => [2,3,4,6,8,1,5,7] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [5,2,3,4,8,6,7,1] => [2,3,4,6,7,8,1,5] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [5,2,3,4,8,7,6,1] => [2,3,4,7,6,8,1,5] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [6,2,3,4,5,1,7,8] => [2,3,4,5,6,1,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [6,2,3,4,5,1,8,7] => [2,3,4,5,6,1,8,7] => [2,2,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [6,2,3,4,5,7,1,8] => [2,3,4,5,7,1,6,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [6,2,3,4,5,7,8,1] => [2,3,4,5,8,1,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [6,2,3,4,5,8,7,1] => [2,3,4,5,7,8,1,6] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [7,2,3,4,5,6,1,8] => [2,3,4,5,6,7,1,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,2,3,4,5,6,8,1] => [2,3,4,5,6,8,1,7] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,2,3,4,5,6,7,1] => [2,3,4,5,6,7,8,1] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [8,2,3,4,5,7,6,1] => [2,3,4,5,7,6,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [7,2,3,4,6,5,1,8] => [2,3,4,6,5,7,1,8] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [7,2,3,4,6,5,8,1] => [2,3,4,6,5,8,1,7] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [8,2,3,4,6,5,7,1] => [2,3,4,6,5,7,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [8,2,3,4,6,7,5,1] => [2,3,4,7,5,6,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [8,2,3,4,7,6,5,1] => [2,3,4,6,7,5,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [6,2,3,5,4,1,7,8] => [2,3,5,4,6,1,7,8] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [7,2,3,5,4,6,1,8] => [2,3,5,4,6,7,1,8] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [8,2,3,5,4,6,7,1] => [2,3,5,4,6,7,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [8,2,3,5,4,7,6,1] => [2,3,5,4,7,6,8,1] => [3,2,1,1,1] => 2
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [8,2,3,5,6,4,7,1] => [2,3,6,4,5,7,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [8,2,3,5,6,7,4,1] => [2,3,7,4,5,6,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [8,2,3,5,7,6,4,1] => [2,3,6,7,4,5,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,6,5,4,1,8] => [2,3,5,6,4,7,1,8] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [8,2,3,6,5,4,7,1] => [2,3,5,6,4,7,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [8,2,3,6,5,7,4,1] => [2,3,5,7,4,6,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [8,2,3,7,5,6,4,1] => [2,3,5,6,7,4,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [5,2,4,3,1,6,7,8] => [2,4,3,5,1,6,7,8] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [5,2,4,3,1,6,8,7] => [2,4,3,5,1,6,8,7] => [3,2,1,1,1] => 2
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [5,2,4,3,1,7,6,8] => [2,4,3,5,1,7,6,8] => [3,2,1,1,1] => 2
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [5,2,4,3,1,7,8,6] => [2,4,3,5,1,8,6,7] => [3,2,1,1,1] => 2
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,2,4,3,1,8,7,6] => [2,4,3,5,1,7,8,6] => [3,2,1,1,1] => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [5,2,4,3,6,1,8,7] => [2,4,3,6,1,5,8,7] => [3,2,1,1,1] => 2
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [5,2,4,3,6,7,8,1] => [2,4,3,8,1,5,6,7] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [5,2,4,3,7,6,1,8] => [2,4,3,6,7,1,5,8] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [5,2,4,3,7,6,8,1] => [2,4,3,6,8,1,5,7] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [6,2,4,3,5,1,8,7] => [2,4,3,5,6,1,8,7] => [3,2,1,1,1] => 2
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [7,2,4,3,5,6,8,1] => [2,4,3,5,6,8,1,7] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [8,2,4,3,5,6,7,1] => [2,4,3,5,6,7,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [8,2,4,3,5,7,6,1] => [2,4,3,5,7,6,8,1] => [3,2,1,1,1] => 2
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [7,2,4,3,6,5,1,8] => [2,4,3,6,5,7,1,8] => [3,2,1,1,1] => 2
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [7,2,4,3,6,5,8,1] => [2,4,3,6,5,8,1,7] => [3,2,1,1,1] => 2
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [8,2,4,3,6,5,7,1] => [2,4,3,6,5,7,8,1] => [3,2,1,1,1] => 2
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [8,2,4,3,6,7,5,1] => [2,4,3,7,5,6,8,1] => [3,2,1,1,1] => 2
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [8,2,4,3,7,6,5,1] => [2,4,3,6,7,5,8,1] => [3,2,1,1,1] => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [7,2,4,5,3,6,1,8] => [2,5,3,4,6,7,1,8] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [7,2,4,5,3,6,8,1] => [2,5,3,4,6,8,1,7] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [8,2,4,5,3,6,7,1] => [2,5,3,4,6,7,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [8,2,4,5,3,7,6,1] => [2,5,3,4,7,6,8,1] => [3,2,1,1,1] => 2
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [7,2,4,5,6,3,8,1] => [2,6,3,4,5,8,1,7] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [8,2,4,5,6,3,7,1] => [2,6,3,4,5,7,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,4,6,5,3,1,8] => [2,5,6,3,4,7,1,8] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [7,2,4,6,5,3,8,1] => [2,5,6,3,4,8,1,7] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [8,2,4,6,5,3,7,1] => [2,5,6,3,4,7,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [8,2,4,7,6,5,3,1] => [2,6,5,7,3,4,8,1] => [4,1,1,1,1] => 3
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [6,2,5,4,3,1,8,7] => [2,4,5,3,6,1,8,7] => [3,2,1,1,1] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [7,2,5,4,3,6,8,1] => [2,4,5,3,6,8,1,7] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [8,2,5,4,3,6,7,1] => [2,4,5,3,6,7,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [7,2,5,4,6,3,1,8] => [2,4,6,3,5,7,1,8] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [7,2,5,4,6,3,8,1] => [2,4,6,3,5,8,1,7] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [8,2,5,4,6,3,7,1] => [2,4,6,3,5,7,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [8,2,5,4,6,7,3,1] => [2,4,7,3,5,6,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [8,2,5,4,7,6,3,1] => [2,4,6,7,3,5,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [7,2,6,4,5,3,8,1] => [2,4,5,6,3,8,1,7] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [8,2,6,4,5,3,7,1] => [2,4,5,6,3,7,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [8,2,6,4,5,7,3,1] => [2,4,5,7,3,6,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [8,2,7,4,5,6,3,1] => [2,4,5,6,7,3,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [8,2,7,4,6,5,3,1] => [2,4,6,5,7,3,8,1] => [4,1,1,1,1] => 3
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [7,2,6,5,4,3,1,8] => [2,5,4,6,3,7,1,8] => [4,1,1,1,1] => 3
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [8,2,6,5,4,3,7,1] => [2,5,4,6,3,7,8,1] => [4,1,1,1,1] => 3
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [8,2,7,5,4,6,3,1] => [2,5,4,6,7,3,8,1] => [4,1,1,1,1] => 3
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [8,2,7,5,6,4,3,1] => [2,6,4,5,7,3,8,1] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8] => [3,2,4,1,5,6,7,8] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,3,2,1,5,6,8,7] => [3,2,4,1,5,6,8,7] => [3,2,1,1,1] => 2
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,3,2,1,5,7,6,8] => [3,2,4,1,5,7,6,8] => [3,2,1,1,1] => 2
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,3,2,1,5,7,8,6] => [3,2,4,1,5,8,6,7] => [3,2,1,1,1] => 2
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,3,2,1,5,8,7,6] => [3,2,4,1,5,7,8,6] => [3,2,1,1,1] => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,3,2,1,6,5,7,8] => [3,2,4,1,6,5,7,8] => [3,2,1,1,1] => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => [3,2,4,1,6,5,8,7] => [3,2,2,1] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,3,2,1,6,7,5,8] => [3,2,4,1,7,5,6,8] => [3,2,1,1,1] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,3,2,1,6,7,8,5] => [3,2,4,1,8,5,6,7] => [3,2,1,1,1] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,3,2,1,6,8,7,5] => [3,2,4,1,7,8,5,6] => [3,2,1,1,1] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,3,2,1,7,6,5,8] => [3,2,4,1,6,7,5,8] => [3,2,1,1,1] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,3,2,1,7,6,8,5] => [3,2,4,1,6,8,5,7] => [3,2,1,1,1] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,2,1,8,6,7,5] => [3,2,4,1,6,7,8,5] => [3,2,1,1,1] => 2
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => [3,2,4,1,7,6,8,5] => [3,3,1,1] => 3
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,3,2,5,1,6,7,8] => [3,2,5,1,4,6,7,8] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [4,3,2,5,1,6,8,7] => [3,2,5,1,4,6,8,7] => [3,2,1,1,1] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [4,3,2,5,1,7,6,8] => [3,2,5,1,4,7,6,8] => [3,2,1,1,1] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,3,2,5,1,8,7,6] => [3,2,5,1,4,7,8,6] => [3,2,1,1,1] => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [4,3,2,5,6,1,7,8] => [3,2,6,1,4,5,7,8] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [4,3,2,5,6,1,8,7] => [3,2,6,1,4,5,8,7] => [3,2,1,1,1] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,1] => [3,2,8,1,4,5,6,7] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [4,3,2,5,6,8,7,1] => [3,2,7,8,1,4,5,6] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,3,2,5,8,7,6,1] => [3,2,7,6,8,1,4,5] => [3,2,1,1,1] => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [4,3,2,6,5,1,7,8] => [3,2,5,6,1,4,7,8] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [4,3,2,6,5,7,1,8] => [3,2,5,7,1,4,6,8] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [4,3,2,7,5,6,8,1] => [3,2,5,6,8,1,4,7] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,8,5,6,7,1] => [3,2,5,6,7,8,1,4] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,3,2,8,5,7,6,1] => [3,2,5,7,6,8,1,4] => [3,2,1,1,1] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [4,3,2,7,6,5,1,8] => [3,2,6,5,7,1,4,8] => [3,2,1,1,1] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [4,3,2,8,6,5,7,1] => [3,2,6,5,7,8,1,4] => [3,2,1,1,1] => 2
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,2,8,6,7,5,1] => [3,2,7,5,6,8,1,4] => [3,2,1,1,1] => 2
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,3,2,8,7,6,5,1] => [3,2,6,7,5,8,1,4] => [3,2,1,1,1] => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [5,3,2,4,1,6,7,8] => [3,2,4,5,1,6,7,8] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [5,3,2,4,6,1,7,8] => [3,2,4,6,1,5,7,8] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,3,2,4,6,1,8,7] => [3,2,4,6,1,5,8,7] => [3,2,1,1,1] => 2
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [5,3,2,4,6,7,8,1] => [3,2,4,8,1,5,6,7] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [5,3,2,4,6,8,7,1] => [3,2,4,7,8,1,5,6] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [5,3,2,4,7,6,8,1] => [3,2,4,6,8,1,5,7] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [5,3,2,4,8,6,7,1] => [3,2,4,6,7,8,1,5] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [6,3,2,4,5,1,7,8] => [3,2,4,5,6,1,7,8] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [6,3,2,4,5,7,8,1] => [3,2,4,5,8,1,6,7] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [7,3,2,4,5,6,1,8] => [3,2,4,5,6,7,1,8] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [7,3,2,4,5,6,8,1] => [3,2,4,5,6,8,1,7] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [8,3,2,4,5,6,7,1] => [3,2,4,5,6,7,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [8,3,2,4,5,7,6,1] => [3,2,4,5,7,6,8,1] => [3,2,1,1,1] => 2
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [8,3,2,4,6,7,5,1] => [3,2,4,7,5,6,8,1] => [3,2,1,1,1] => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,3,2,5,4,1,8,7] => [3,2,5,4,6,1,8,7] => [3,2,2,1] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [6,3,2,5,4,7,1,8] => [3,2,5,4,7,1,6,8] => [3,2,1,1,1] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [6,3,2,5,4,7,8,1] => [3,2,5,4,8,1,6,7] => [3,2,1,1,1] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [6,3,2,5,4,8,7,1] => [3,2,5,4,7,8,1,6] => [3,2,1,1,1] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [8,3,2,5,4,6,7,1] => [3,2,5,4,6,7,8,1] => [3,2,1,1,1] => 2
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [8,3,2,5,4,7,6,1] => [3,2,5,4,7,6,8,1] => [3,2,2,1] => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [7,3,2,5,6,4,8,1] => [3,2,6,4,5,8,1,7] => [3,2,1,1,1] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [8,3,2,6,5,4,7,1] => [3,2,5,6,4,7,8,1] => [3,2,1,1,1] => 2
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [8,3,2,6,5,7,4,1] => [3,2,5,7,4,6,8,1] => [3,2,1,1,1] => 2
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [8,3,2,7,5,6,4,1] => [3,2,5,6,7,4,8,1] => [3,2,1,1,1] => 2
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [8,3,2,7,6,5,4,1] => [3,2,6,5,7,4,8,1] => [4,2,1,1] => 3
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,3,4,2,1,6,7,8] => [4,2,3,5,1,6,7,8] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [5,3,4,2,1,6,8,7] => [4,2,3,5,1,6,8,7] => [3,2,1,1,1] => 2
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [5,3,4,2,1,7,8,6] => [4,2,3,5,1,8,6,7] => [3,2,1,1,1] => 2
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,3,4,2,1,8,7,6] => [4,2,3,5,1,7,8,6] => [3,2,1,1,1] => 2
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [5,3,4,2,6,1,8,7] => [4,2,3,6,1,5,8,7] => [3,2,1,1,1] => 2
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [5,3,4,2,6,7,8,1] => [4,2,3,8,1,5,6,7] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [5,3,4,2,7,6,8,1] => [4,2,3,6,8,1,5,7] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [5,3,4,2,8,6,7,1] => [4,2,3,6,7,8,1,5] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [6,3,4,2,5,1,7,8] => [4,2,3,5,6,1,7,8] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [6,3,4,2,5,1,8,7] => [4,2,3,5,6,1,8,7] => [3,2,1,1,1] => 2
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [7,3,4,2,5,6,8,1] => [4,2,3,5,6,8,1,7] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [8,3,4,2,5,6,7,1] => [4,2,3,5,6,7,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [8,3,4,2,6,7,5,1] => [4,2,3,7,5,6,8,1] => [3,2,1,1,1] => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [6,3,4,5,2,1,7,8] => [5,2,3,4,6,1,7,8] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [6,3,4,5,2,1,8,7] => [5,2,3,4,6,1,8,7] => [3,2,1,1,1] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [6,3,4,5,2,7,1,8] => [5,2,3,4,7,1,6,8] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [6,3,4,5,2,7,8,1] => [5,2,3,4,8,1,6,7] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [7,3,4,5,2,6,1,8] => [5,2,3,4,6,7,1,8] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [7,3,4,5,2,6,8,1] => [5,2,3,4,6,8,1,7] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [8,3,4,5,2,6,7,1] => [5,2,3,4,6,7,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1,8] => [6,2,3,4,5,7,1,8] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,3,4,5,6,2,8,1] => [6,2,3,4,5,8,1,7] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [8,3,4,5,6,2,7,1] => [6,2,3,4,5,7,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [8,3,4,5,6,7,2,1] => [7,2,3,4,5,6,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [8,3,4,5,7,6,2,1] => [6,7,2,3,4,5,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [8,3,4,6,5,7,2,1] => [5,7,2,3,4,6,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [8,3,4,7,5,6,2,1] => [5,6,7,2,3,4,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,3,5,4,2,1,8,7] => [4,5,2,3,6,1,8,7] => [3,2,1,1,1] => 2
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [6,3,5,4,2,7,8,1] => [4,5,2,3,8,1,6,7] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [7,3,5,4,2,6,1,8] => [4,5,2,3,6,7,1,8] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [8,3,5,4,2,6,7,1] => [4,5,2,3,6,7,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [7,3,5,4,6,2,1,8] => [4,6,2,3,5,7,1,8] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [7,3,5,4,6,2,8,1] => [4,6,2,3,5,8,1,7] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [8,3,5,4,7,6,2,1] => [4,6,7,2,3,5,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [7,3,6,4,5,2,8,1] => [4,5,6,2,3,8,1,7] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [8,3,6,4,5,2,7,1] => [4,5,6,2,3,7,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [8,3,6,4,5,7,2,1] => [4,5,7,2,3,6,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [8,3,7,4,5,6,2,1] => [4,5,6,7,2,3,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [8,3,7,4,6,5,2,1] => [4,6,5,7,2,3,8,1] => [4,1,1,1,1] => 3
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,3,6,5,4,2,1,8] => [5,4,6,2,3,7,1,8] => [4,1,1,1,1] => 3
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [8,3,6,5,4,7,2,1] => [5,4,7,2,3,6,8,1] => [4,1,1,1,1] => 3
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [8,3,7,5,4,6,2,1] => [5,4,6,7,2,3,8,1] => [4,1,1,1,1] => 3
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [8,3,7,5,6,4,2,1] => [6,4,5,7,2,3,8,1] => [4,1,1,1,1] => 3
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [8,3,7,6,5,4,2,1] => [5,6,4,7,2,3,8,1] => [4,1,1,1,1] => 3
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8] => [3,4,2,5,1,6,7,8] => [3,1,1,1,1,1] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,4,3,2,1,7,6,8] => [3,4,2,5,1,7,6,8] => [3,2,1,1,1] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,4,3,2,1,7,8,6] => [3,4,2,5,1,8,6,7] => [3,2,1,1,1] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => [3,4,2,5,1,7,8,6] => [3,2,1,1,1] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [5,4,3,2,6,7,1,8] => [3,4,2,7,1,5,6,8] => [3,1,1,1,1,1] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,1] => [3,4,2,8,1,5,6,7] => [3,1,1,1,1,1] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,4,3,2,6,8,7,1] => [3,4,2,7,8,1,5,6] => [3,1,1,1,1,1] => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [5,4,3,2,7,6,1,8] => [3,4,2,6,7,1,5,8] => [3,1,1,1,1,1] => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [5,4,3,2,7,6,8,1] => [3,4,2,6,8,1,5,7] => [3,1,1,1,1,1] => 2
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,3,2,8,6,7,1] => [3,4,2,6,7,8,1,5] => [3,1,1,1,1,1] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [6,4,3,2,5,1,7,8] => [3,4,2,5,6,1,7,8] => [3,1,1,1,1,1] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,4,3,2,5,1,8,7] => [3,4,2,5,6,1,8,7] => [3,2,1,1,1] => 2
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,6,1,8] => [3,4,2,5,6,7,1,8] => [3,1,1,1,1,1] => 2
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [7,4,3,2,5,6,8,1] => [3,4,2,5,6,8,1,7] => [3,1,1,1,1,1] => 2
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [8,4,3,2,5,6,7,1] => [3,4,2,5,6,7,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [8,4,3,2,5,7,6,1] => [3,4,2,5,7,6,8,1] => [3,2,1,1,1] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [7,4,3,2,6,5,1,8] => [3,4,2,6,5,7,1,8] => [3,2,1,1,1] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [7,4,3,2,6,5,8,1] => [3,4,2,6,5,8,1,7] => [3,2,1,1,1] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [8,4,3,2,6,5,7,1] => [3,4,2,6,5,7,8,1] => [3,2,1,1,1] => 2
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [8,4,3,2,7,6,5,1] => [3,4,2,6,7,5,8,1] => [3,2,1,1,1] => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,4,3,5,2,1,8,7] => [3,5,2,4,6,1,8,7] => [3,2,1,1,1] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [6,4,3,5,2,7,1,8] => [3,5,2,4,7,1,6,8] => [3,1,1,1,1,1] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [6,4,3,5,2,7,8,1] => [3,5,2,4,8,1,6,7] => [3,1,1,1,1,1] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [7,4,3,5,2,6,8,1] => [3,5,2,4,6,8,1,7] => [3,1,1,1,1,1] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [8,4,3,5,2,6,7,1] => [3,5,2,4,6,7,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [8,4,3,5,2,7,6,1] => [3,5,2,4,7,6,8,1] => [3,2,1,1,1] => 2
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [7,4,3,5,6,2,1,8] => [3,6,2,4,5,7,1,8] => [3,1,1,1,1,1] => 2
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [8,4,3,5,7,6,2,1] => [3,6,7,2,4,5,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [7,4,3,6,5,2,1,8] => [3,5,6,2,4,7,1,8] => [3,1,1,1,1,1] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [7,4,3,6,5,2,8,1] => [3,5,6,2,4,8,1,7] => [3,1,1,1,1,1] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [8,4,3,6,5,2,7,1] => [3,5,6,2,4,7,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [8,4,3,6,5,7,2,1] => [3,5,7,2,4,6,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [8,4,3,7,5,6,2,1] => [3,5,6,7,2,4,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [6,5,3,4,2,1,7,8] => [3,4,5,2,6,1,7,8] => [3,1,1,1,1,1] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,5,3,4,2,1,8,7] => [3,4,5,2,6,1,8,7] => [3,2,1,1,1] => 2
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [8,5,3,4,2,6,7,1] => [3,4,5,2,6,7,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [8,5,3,4,2,7,6,1] => [3,4,5,2,7,6,8,1] => [3,2,1,1,1] => 2
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [8,5,3,4,6,7,2,1] => [3,4,7,2,5,6,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [8,5,3,4,7,6,2,1] => [3,4,6,7,2,5,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,6,3,4,5,2,1,8] => [3,4,5,6,2,7,1,8] => [3,1,1,1,1,1] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [8,6,3,4,5,2,7,1] => [3,4,5,6,2,7,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [8,6,3,4,5,7,2,1] => [3,4,5,7,2,6,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [8,7,3,4,5,6,2,1] => [3,4,5,6,7,2,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [8,7,3,4,6,5,2,1] => [3,4,6,5,7,2,8,1] => [4,1,1,1,1] => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,6,3,5,4,2,1,8] => [3,5,4,6,2,7,1,8] => [4,1,1,1,1] => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [7,6,3,5,4,2,8,1] => [3,5,4,6,2,8,1,7] => [4,1,1,1,1] => 3
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [8,6,3,5,4,2,7,1] => [3,5,4,6,2,7,8,1] => [4,1,1,1,1] => 3
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [8,6,3,5,4,7,2,1] => [3,5,4,7,2,6,8,1] => [4,1,1,1,1] => 3
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [8,7,3,5,4,6,2,1] => [3,5,4,6,7,2,8,1] => [4,1,1,1,1] => 3
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [8,7,3,5,6,4,2,1] => [3,6,4,5,7,2,8,1] => [4,1,1,1,1] => 3
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [8,7,3,6,5,4,2,1] => [3,5,6,4,7,2,8,1] => [4,1,1,1,1] => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,5,4,3,2,1,7,8] => [4,3,5,2,6,1,7,8] => [4,1,1,1,1] => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => [4,3,5,2,6,1,8,7] => [4,2,1,1] => 3
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,5,4,3,2,7,1,8] => [4,3,5,2,7,1,6,8] => [4,1,1,1,1] => 3
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5,4,3,2,7,8,1] => [4,3,5,2,8,1,6,7] => [4,1,1,1,1] => 3
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [7,5,4,3,2,6,8,1] => [4,3,5,2,6,8,1,7] => [4,1,1,1,1] => 3
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [8,5,4,3,2,6,7,1] => [4,3,5,2,6,7,8,1] => [4,1,1,1,1] => 3
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [8,5,4,3,2,7,6,1] => [4,3,5,2,7,6,8,1] => [4,2,1,1] => 3
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,5,4,3,6,2,1,8] => [4,3,6,2,5,7,1,8] => [4,1,1,1,1] => 3
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [8,5,4,3,6,2,7,1] => [4,3,6,2,5,7,8,1] => [4,1,1,1,1] => 3
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [8,5,4,3,6,7,2,1] => [4,3,7,2,5,6,8,1] => [4,1,1,1,1] => 3
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,6,4,3,5,2,1,8] => [4,3,5,6,2,7,1,8] => [4,1,1,1,1] => 3
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [7,6,4,3,5,2,8,1] => [4,3,5,6,2,8,1,7] => [4,1,1,1,1] => 3
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [8,6,4,3,5,2,7,1] => [4,3,5,6,2,7,8,1] => [4,1,1,1,1] => 3
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [8,6,4,3,5,7,2,1] => [4,3,5,7,2,6,8,1] => [4,1,1,1,1] => 3
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [8,7,4,3,6,5,2,1] => [4,3,6,5,7,2,8,1] => [4,2,1,1] => 3
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,6,4,5,3,2,1,8] => [5,3,4,6,2,7,1,8] => [4,1,1,1,1] => 3
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,6,4,5,3,2,8,1] => [5,3,4,6,2,8,1,7] => [4,1,1,1,1] => 3
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [8,7,4,5,6,3,2,1] => [6,3,4,5,7,2,8,1] => [4,1,1,1,1] => 3
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [8,7,4,6,5,3,2,1] => [5,6,3,4,7,2,8,1] => [4,1,1,1,1] => 3
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => [4,5,3,6,2,7,1,8] => [4,1,1,1,1] => 3
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,6,5,4,3,2,8,1] => [4,5,3,6,2,8,1,7] => [4,1,1,1,1] => 3
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [8,7,5,4,3,6,2,1] => [4,5,3,6,7,2,8,1] => [4,1,1,1,1] => 3
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [8,7,5,4,6,3,2,1] => [4,6,3,5,7,2,8,1] => [4,1,1,1,1] => 3
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [8,7,6,4,5,3,2,1] => [4,5,6,3,7,2,8,1] => [4,1,1,1,1] => 3
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,7,6,5,4,3,2,1] => [5,4,6,3,7,2,8,1] => [5,1,1,1] => 4
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,7,6,5,4,3,2,1,9] => [5,4,6,3,7,2,8,1,9] => [5,1,1,1,1] => 4
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,8,7,6,5,4,3,2] => [1,6,5,7,4,8,3,9,2] => [5,1,1,1,1] => 4
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,8,7,6,5,4,3,2,1,10] => [5,6,4,7,3,8,2,9,1,10] => [5,1,1,1,1,1] => 4
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,7,6,4,5,3,2,1,9] => [4,5,6,3,7,2,8,1,9] => [4,1,1,1,1,1] => 3
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,9,8,7,5,6,4,3,2] => [1,5,6,7,4,8,3,9,2] => [4,1,1,1,1,1] => 3
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,9,8,7,6,5,4,3,2] => [1,6,7,5,8,4,9,3,10,2] => [5,1,1,1,1,1] => 4
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,8,7,5,6,4,3,2,1,10] => [6,4,5,7,3,8,2,9,1,10] => [5,1,1,1,1,1] => 4
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [8,7,5,4,6,3,2,1,9] => [4,6,3,5,7,2,8,1,9] => [4,1,1,1,1,1] => 3
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [8,7,4,6,5,3,2,1,9] => [5,6,3,4,7,2,8,1,9] => [4,1,1,1,1,1] => 3
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,9,8,6,5,7,4,3,2] => [1,5,7,4,6,8,3,9,2] => [4,1,1,1,1,1] => 3
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,9,8,5,7,6,4,3,2] => [1,6,7,4,5,8,3,9,2] => [4,1,1,1,1,1] => 3
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,10,9,8,6,7,5,4,3,2] => [1,7,5,6,8,4,9,3,10,2] => [5,1,1,1,1,1] => 4
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9] => [4,5,3,6,2,7,1,8,9] => [4,1,1,1,1,1] => 3
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,7,6,5,4,3,2,1,10,9] => [5,4,6,3,7,2,8,1,10,9] => [5,2,1,1,1] => 4
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,9,8,7,6,5,4,3] => [2,1,7,6,8,5,9,4,10,3] => [5,2,1,1,1] => 4
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [8,7,6,5,4,3,2,1,9,10] => [5,4,6,3,7,2,8,1,9,10] => [5,1,1,1,1,1] => 4
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,1] => [9,1,2,3,4,5,6,7,8] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,9,8,1] => [8,9,1,2,3,4,5,6,7] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,6,8,7,9,1] => [7,9,1,2,3,4,5,6,8] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,6,9,7,8,1] => [7,8,9,1,2,3,4,5,6] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,6,9,8,7,1] => [8,7,9,1,2,3,4,5,6] => [3,1,1,1,1,1,1] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,4,5,8,6,7,9,1] => [6,7,9,1,2,3,4,5,8] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,5,9,6,7,8,1] => [6,7,8,9,1,2,3,4,5] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,5,9,7,6,8,1] => [7,6,8,9,1,2,3,4,5] => [3,1,1,1,1,1,1] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,4,6,5,7,8,9,1] => [5,9,1,2,3,4,6,7,8] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,4,9,5,6,7,8,1] => [5,6,7,8,9,1,2,3,4] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,3,4,9,6,5,7,8,1] => [6,5,7,8,9,1,2,3,4] => [3,1,1,1,1,1,1] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,9,4,5,6,7,8,1] => [4,5,6,7,8,9,1,2,3] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,3,9,5,4,6,7,8,1] => [5,4,6,7,8,9,1,2,3] => [3,1,1,1,1,1,1] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,8,9,1] => [3,9,1,2,4,5,6,7,8] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,8,7,9,1] => [3,5,7,9,1,2,4,6,8] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,9,3,4,5,6,7,8,1] => [3,4,5,6,7,8,9,1,2] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [2,9,4,3,5,6,7,8,1] => [4,3,5,6,7,8,9,1,2] => [3,1,1,1,1,1,1] => 2
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [2,9,4,5,3,6,7,8,1] => [5,3,4,6,7,8,9,1,2] => [3,1,1,1,1,1,1] => 2
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [2,9,5,4,3,6,7,8,1] => [4,5,3,6,7,8,9,1,2] => [3,1,1,1,1,1,1] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,1] => [2,9,1,3,4,5,6,7,8] => [2,1,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,8,9,1] => [2,3,9,1,4,5,6,7,8] => [2,1,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [8,2,3,4,5,6,7,9,1] => [2,3,4,5,6,7,9,1,8] => [2,1,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,2,3,4,5,6,7,8,1] => [2,3,4,5,6,7,8,9,1] => [2,1,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [9,2,3,4,5,6,8,7,1] => [2,3,4,5,6,8,7,9,1] => [3,1,1,1,1,1,1] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,9,1] => [3,2,9,1,4,5,6,7,8] => [3,1,1,1,1,1,1] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,3,2,4,5,6,7,8,1] => [3,2,4,5,6,7,8,9,1] => [3,1,1,1,1,1,1] => 2
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0] => [9,3,4,2,5,6,7,8,1] => [4,2,3,5,6,7,8,9,1] => [3,1,1,1,1,1,1] => 2
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [9,3,4,5,6,7,8,2,1] => [8,2,3,4,5,6,7,9,1] => [3,1,1,1,1,1,1] => 2
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0] => [9,4,3,2,5,6,7,8,1] => [3,4,2,5,6,7,8,9,1] => [3,1,1,1,1,1,1] => 2
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [9,8,3,4,5,6,7,2,1] => [3,4,5,6,7,8,2,9,1] => [3,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,7,6,5,4,3,2,9,1] => [5,4,6,3,7,2,9,1,8] => [5,1,1,1,1] => 4
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [9,8,7,6,5,4,3,2,1] => [5,6,4,7,3,8,2,9,1] => [5,1,1,1,1] => 4
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,9,8] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,8,9,7] => [1,2,3,4,5,6,9,7,8] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,6] => [1,2,3,4,5,9,6,7,8] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,5] => [1,2,3,4,9,5,6,7,8] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,4] => [1,2,3,9,4,5,6,7,8] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,3] => [1,2,9,3,4,5,6,7,8] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,2] => [1,9,2,3,4,5,6,7,8] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,10,9] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,9,8,7] => [1,2,3,4,5,6,8,9,7] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,7,9,10,8] => [1,2,3,4,5,6,7,10,8,9] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,5,8,7,9,6] => [1,2,3,4,5,7,9,6,8] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,6,8,9,10,7] => [1,2,3,4,5,6,10,7,8,9] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,4,7,6,8,9,5] => [1,2,3,4,6,9,5,7,8] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,10,6] => [1,2,3,4,5,10,6,7,8,9] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,3,6,5,7,8,9,4] => [1,2,3,5,9,4,6,7,8] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,10,5] => [1,2,3,4,10,5,6,7,8,9] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,9,3] => [1,2,4,9,3,5,6,7,8] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,10,4] => [1,2,3,10,4,5,6,7,8,9] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,9,2] => [1,3,9,2,4,5,6,7,8] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,10,3] => [1,2,10,3,4,5,6,7,8,9] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,2] => [1,10,2,3,4,5,6,7,8,9] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,1] => [10,1,2,3,4,5,6,7,8,9] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,10,9,8] => [1,2,3,4,5,6,7,9,10,8] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,5,9,7,8,6] => [1,2,3,4,5,7,8,9,6] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,9,8,7,6] => [1,2,3,4,5,8,7,9,6] => [3,1,1,1,1,1,1] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,10,1] => [2,10,1,3,4,5,6,7,8,9] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,5,6,10,8,9,7] => [1,2,3,4,5,6,8,9,10,7] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,4,9,6,7,8,5] => [1,2,3,4,6,7,8,9,5] => [2,1,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,8,9,10,1] => [2,3,10,1,4,5,6,7,8,9] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,4,5,10,7,8,9,6] => [1,2,3,4,5,7,8,9,10,6] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,3,9,5,6,7,8,4] => [1,2,3,5,6,7,8,9,4] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,3,4,10,6,7,8,9,5] => [1,2,3,4,6,7,8,9,10,5] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,9,4,5,6,7,8,3] => [1,2,4,5,6,7,8,9,3] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,8,3,4,5,6,7,9,2] => [1,3,4,5,6,7,9,2,8] => [2,1,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [6,2,3,4,5,7,8,9,10,1] => [2,3,4,5,10,1,6,7,8,9] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,3,10,5,6,7,8,9,4] => [1,2,3,5,6,7,8,9,10,4] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,9,3,4,5,6,7,8,2] => [1,3,4,5,6,7,8,9,2] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,9,4,5,6,7,8,3,2] => [1,8,3,4,5,6,7,9,2] => [3,1,1,1,1,1,1] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,10,4,5,6,7,8,9,3] => [1,2,4,5,6,7,8,9,10,3] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,10,3,4,5,6,7,8,9,2] => [1,3,4,5,6,7,8,9,10,2] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [9,2,3,4,5,6,7,8,10,1] => [2,3,4,5,6,7,8,10,1,9] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,8,7,9] => [1,2,3,4,5,6,8,7,9] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9] => [1,2,3,4,5,7,6,8,9] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,7,6,9,8] => [1,2,3,4,5,7,6,9,8] => [2,2,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9] => [1,2,3,4,6,5,7,8,9] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,4,6,5,8,7,9] => [1,2,3,4,6,5,8,7,9] => [2,2,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9] => [1,2,3,5,4,6,7,8,9] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6,9,8] => [1,2,3,5,4,7,6,9,8] => [2,2,2,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9] => [1,2,4,3,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,8,7,9] => [1,2,4,3,6,5,8,7,9] => [2,2,2,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9] => [1,3,2,4,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,7,9,8] => [1,3,2,4,5,6,7,9,8] => [2,2,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,6,9,8,7] => [1,3,2,4,5,6,8,9,7] => [2,2,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8,9] => [1,3,2,5,4,6,7,8,9] => [2,2,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => [1,3,2,5,4,7,6,9,8] => [2,2,2,2,1] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8,9] => [1,3,4,2,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,9,8] => [2,1,3,4,5,6,7,9,8] => [2,2,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,6,8,7,9] => [2,1,3,4,5,6,8,7,9] => [2,2,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,6,9,8,7] => [2,1,3,4,5,6,8,9,7] => [2,2,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8,9] => [2,1,4,3,5,6,7,8,9] => [2,2,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,9] => [2,1,4,3,6,5,8,7,9] => [2,2,2,2,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9] => [2,3,1,4,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,6,7,9,8] => [2,3,1,4,5,6,7,9,8] => [2,2,1,1,1,1,1] => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,2,1,5,4,6,7,8,9] => [2,3,1,5,4,6,7,8,9] => [2,2,1,1,1,1,1] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6,9,8] => [2,3,1,5,4,7,6,9,8] => [2,2,2,2,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9] => [3,2,4,1,5,6,7,8,9] => [3,1,1,1,1,1,1] => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,8,7,9] => [3,2,4,1,6,5,8,7,9] => [3,2,2,1,1] => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9] => [3,4,2,5,1,6,7,8,9] => [3,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9] => [4,3,5,2,6,1,7,8,9] => [4,1,1,1,1,1] => 3
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,9,8,10] => [1,2,3,4,5,6,7,9,8,10] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,6,8,7,9,10] => [1,2,3,4,5,6,8,7,9,10] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9,10] => [1,2,3,4,5,7,6,8,9,10] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9,10] => [1,2,3,4,6,5,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9,10] => [1,2,3,5,4,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,9,8,10] => [1,2,3,5,4,7,6,9,8,10] => [2,2,2,1,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9,10] => [1,2,4,3,5,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9,10] => [1,3,2,4,5,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8,10] => [1,3,2,5,4,7,6,9,8,10] => [2,2,2,2,1,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,7,6,10,9,8] => [1,3,2,5,4,7,6,9,10,8] => [2,2,2,2,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,8,10,9] => [2,1,3,4,5,6,7,8,10,9] => [2,2,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => [2,1,4,3,6,5,8,7,10,9] => [2,2,2,2,2] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,6,5,10,9,8,7] => [2,1,4,3,6,5,9,8,10,7] => [3,2,2,2,1] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3,10,9,8,7] => [2,1,5,4,6,3,9,8,10,7] => [3,3,2,1,1] => 3
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,1,8,7,6,5,4,3,10,9] => [2,1,6,5,7,4,8,3,10,9] => [4,2,2,1,1] => 3
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9,10] => [2,3,1,4,5,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,1,5,4,7,6,9,8,10] => [2,3,1,5,4,7,6,9,8,10] => [2,2,2,2,1,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9,10] => [3,2,4,1,5,6,7,8,9,10] => [3,1,1,1,1,1,1,1] => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7,10,9] => [3,2,4,1,6,5,8,7,10,9] => [3,2,2,2,1] => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,6,5,10,9,8,7] => [3,2,4,1,6,5,9,8,10,7] => [3,3,2,1,1] => 3
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,8,7,6,5,10,9] => [3,2,4,1,7,6,8,5,10,9] => [3,3,2,1,1] => 3
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,3,2,1,10,9,8,7,6,5] => [3,2,4,1,8,7,9,6,10,5] => [4,3,1,1,1] => 4
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9,10] => [3,4,2,5,1,6,7,8,9,10] => [3,1,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9,10] => [4,3,5,2,6,1,7,8,9,10] => [4,1,1,1,1,1,1] => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,5,4,3,2,1,10,9,8,7] => [4,3,5,2,6,1,9,8,10,7] => [4,3,1,1,1] => 4
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9,10] => [4,5,3,6,2,7,1,8,9,10] => [4,1,1,1,1,1,1] => 3
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [10,9,8,7,6,5,4,3,2,1] => [6,5,7,4,8,3,9,2,10,1] => [6,1,1,1,1] => 5
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9] => [3,1,2,4,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8,9] => [4,1,2,3,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9] => [5,1,2,3,4,6,7,8,9] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,1,7,8,9] => [6,1,2,3,4,5,7,8,9] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9] => [7,1,2,3,4,5,6,8,9] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,1,9] => [8,1,2,3,4,5,6,7,9] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9,10] => [3,1,2,4,5,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8,9] => [3,4,1,2,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8,9,10] => [4,1,2,3,5,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9,10] => [5,1,2,3,4,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1,7,8,9,10] => [6,1,2,3,4,5,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9,10] => [7,1,2,3,4,5,6,8,9,10] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,6,8,7,1,9] => [7,8,1,2,3,4,5,6,9] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,8,1,9,10] => [8,1,2,3,4,5,6,7,9,10] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,9,1,10] => [9,1,2,3,4,5,6,7,8,10] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,6,8,9,7] => [2,1,3,4,5,6,9,7,8] => [2,2,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,8,10,9,1] => [9,10,1,2,3,4,5,6,7,8] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,6,7,9,10,8] => [2,1,3,4,5,6,7,10,8,9] => [2,2,1,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,6,8,9,7] => [1,3,2,4,5,6,9,7,8] => [2,2,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,7,9,8] => [3,1,2,4,5,6,7,9,8] => [2,2,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,2,3,4,5,6,7,1,9] => [2,3,4,5,6,7,8,1,9] => [2,1,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [7,2,3,4,5,6,1,8,9] => [2,3,4,5,6,7,1,8,9] => [2,1,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [6,2,3,4,5,1,7,8,9] => [2,3,4,5,6,1,7,8,9] => [2,1,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [5,2,3,4,1,6,7,8,9] => [2,3,4,5,1,6,7,8,9] => [2,1,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7,8,9] => [2,3,4,1,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,8,7,6,5,4,3,2,10,1] => [5,6,4,7,3,8,2,10,1,9] => [5,1,1,1,1,1] => 4
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [4,3,2,5,1,6,7,8,9] => [3,2,5,1,4,6,7,8,9] => [3,1,1,1,1,1,1] => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8,9] => [2,4,1,3,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [7,2,3,4,5,6,1,9,8] => [2,3,4,5,6,7,1,9,8] => [2,2,1,1,1,1,1] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,1,9,4,5,6,7,8,3] => [2,1,4,5,6,7,8,9,3] => [2,2,1,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [2,8,3,4,5,6,7,1,9] => [3,4,5,6,7,8,1,2,9] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,10,3,4,5,6,7,8,9,1] => [3,4,5,6,7,8,9,10,1,2] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,3,4,6,5,7,8,9,10,1] => [5,10,1,2,3,4,6,7,8,9] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,9,4,3,5,6,7,8,2] => [1,4,3,5,6,7,8,9,2] => [3,1,1,1,1,1,1] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,8,1,9] => [2,8,1,3,4,5,6,7,9] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,7,9,8,2] => [1,8,9,2,3,4,5,6,7] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,1,9,8] => [7,1,2,3,4,5,6,9,8] => [2,2,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,9,3] => [2,1,9,3,4,5,6,7,8] => [2,2,1,1,1,1,1] => 1
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,10,4,5,6,7,8,9,3,1] => [9,3,4,5,6,7,8,10,1,2] => [3,1,1,1,1,1,1,1] => 2
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [10,3,4,5,6,7,8,9,2,1] => [9,2,3,4,5,6,7,8,10,1] => [3,1,1,1,1,1,1,1] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,4,5,10,6,7,8,9,1] => [6,7,8,9,10,1,2,3,4,5] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,5,1,7,6,8,9] => [5,1,2,3,4,7,6,8,9] => [2,2,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,8,7,9] => [3,4,1,2,6,5,8,7,9] => [2,2,2,1,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,3,6,5,7,1,9,8] => [3,5,7,1,2,4,6,9,8] => [2,2,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [2,4,3,5,1,7,6,9,8] => [3,5,1,2,4,7,6,9,8] => [2,2,2,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6,9,8] => [3,1,2,5,4,7,6,9,8] => [2,2,2,2,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7,10,9] => [3,4,1,2,6,5,8,7,10,9] => [2,2,2,2,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,10,9,1] => [3,5,7,9,10,1,2,4,6,8] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,4,3,6,5,8,7,9,1,10] => [3,5,7,9,1,2,4,6,8,10] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,3,1,6,5,7,4,9,8] => [3,1,2,5,7,4,6,9,8] => [2,2,2,1,1,1] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6,9,8] => [1,3,5,2,4,7,6,9,8] => [2,2,2,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,9,8,10] => [3,1,2,5,4,7,6,9,8,10] => [2,2,2,2,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,6,7,10,8,9,1] => [8,9,10,1,2,3,4,5,6,7] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,5,6,10,7,8,9,1] => [7,8,9,10,1,2,3,4,5,6] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,4,10,5,6,7,8,9,1] => [5,6,7,8,9,10,1,2,3,4] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,10,4,5,6,7,8,9,1] => [4,5,6,7,8,9,10,1,2,3] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10,2,3,4,5,6,7,8,9,1] => [2,3,4,5,6,7,8,9,10,1] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,10,4,3,5,6,7,8,9,1] => [4,3,5,6,7,8,9,10,1,2] => [3,1,1,1,1,1,1,1] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10,3,2,4,5,6,7,8,9,1] => [3,2,4,5,6,7,8,9,10,1] => [3,1,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [10,9,8,5,4,7,6,3,2,1] => [5,4,7,6,8,3,9,2,10,1] => [5,2,1,1,1] => 4
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [10,5,4,3,2,9,8,7,6,1] => [4,3,5,2,8,7,9,6,10,1] => [4,3,1,1,1] => 4
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [9,2,3,4,5,6,7,8,1,10] => [2,3,4,5,6,7,8,9,1,10] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,5,7,9,8,6] => [1,2,3,4,5,8,9,6,7] => [2,1,1,1,1,1,1,1] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [3,2,1,5,6,7,8,9,4] => [2,3,1,9,4,5,6,7,8] => [2,2,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0] => [10,7,6,5,4,3,2,9,8,1] => [5,4,6,3,7,2,9,8,10,1] => [5,2,1,1,1] => 4
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8,9] => [1,4,2,3,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,9,10,3] => [2,1,10,3,4,5,6,7,8,9] => [2,2,1,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,9,4] => [3,1,2,9,4,5,6,7,8] => [2,2,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,5,6,1,8,9,10,7] => [6,1,2,3,4,5,10,7,8,9] => [2,2,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,7,2,9,8] => [1,7,2,3,4,5,6,9,8] => [2,2,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,8,2,9] => [1,8,2,3,4,5,6,7,9] => [2,1,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [6,2,3,4,5,1,9,8,7] => [2,3,4,5,6,1,8,9,7] => [2,2,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,4,5,7,6,8,1,9] => [6,8,1,2,3,4,5,7,9] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,3,9,4,5,6,7,8,2] => [1,4,5,6,7,8,9,2,3] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,8,1,10,9] => [8,1,2,3,4,5,6,7,10,9] => [2,2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,6,1,8,9,7] => [6,1,2,3,4,5,9,7,8] => [2,2,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,2,3,1,6,5,8,7,10,9] => [2,3,4,1,6,5,8,7,10,9] => [2,2,2,2,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,8,9,2,10] => [1,9,2,3,4,5,6,7,8,10] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,9,5] => [4,1,2,3,9,5,6,7,8] => [2,2,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,5,6,8,10,9,7] => [1,2,3,4,5,6,9,10,7,8] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7,10,9] => [2,4,1,3,6,5,8,7,10,9] => [2,2,2,2,1,1] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,9,8,10,1] => [2,4,6,8,10,1,3,5,7,9] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,2,9,5,4,6,7,8,3] => [1,2,5,4,6,7,8,9,3] => [3,1,1,1,1,1,1] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,5,6,8,7,9,2] => [1,7,9,2,3,4,5,6,8] => [2,1,1,1,1,1,1,1] => 1
[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [10,3,2,9,8,7,6,5,4,1] => [3,2,7,6,8,5,9,4,10,1] => [5,2,1,1,1] => 4
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,2,1,10,7,6,9,8,5] => [3,2,4,1,7,6,9,8,10,5] => [3,3,2,1,1] => 3
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,7,8,10,9,2] => [1,9,10,2,3,4,5,6,7,8] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,8,3,9] => [2,1,8,3,4,5,6,7,9] => [2,2,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,4,9,7,6,8,5] => [1,2,3,4,7,6,8,9,5] => [3,1,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,3,9,6,5,7,8,4] => [1,2,3,6,5,7,8,9,4] => [3,1,1,1,1,1,1] => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8,9,10] => [2,4,1,3,5,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,7,2,8,9] => [1,7,2,3,4,5,6,8,9] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,6,7,9,8,1,10] => [8,9,1,2,3,4,5,6,7,10] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,4,6,7,9,8,5] => [1,2,3,4,8,9,5,6,7] => [2,1,1,1,1,1,1,1] => 1
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [10,3,2,5,4,7,6,9,8,1] => [3,2,5,4,7,6,9,8,10,1] => [3,2,2,2,1] => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7,10,9] => [1,4,2,3,6,5,8,7,10,9] => [2,2,2,2,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,5,1,7,8,9,6] => [5,1,2,3,4,9,6,7,8] => [2,2,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7,10,9] => [2,1,5,6,3,4,8,7,10,9] => [2,2,2,2,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,3,6,8,7,5,10,9] => [2,1,4,3,7,8,5,6,10,9] => [2,2,2,2,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,5,8,10,9,7] => [2,1,4,3,6,5,9,10,7,8] => [2,2,2,2,1,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3,8,10,9,7] => [2,1,5,6,3,4,9,10,7,8] => [2,2,2,1,1,1,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,5,8,10,9,7] => [3,4,1,2,6,5,9,10,7,8] => [2,2,2,1,1,1,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,8,7,5,10,9] => [3,4,1,2,7,8,5,6,10,9] => [2,2,2,1,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,8,7,9] => [1,4,2,3,6,5,8,7,9] => [2,2,2,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,6,7,1,9,10,8] => [7,1,2,3,4,5,6,10,8,9] => [2,2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,5,8,9,10,7] => [4,1,2,3,6,5,10,7,8,9] => [2,2,2,1,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,9,10,5] => [2,1,4,3,10,5,6,7,8,9] => [2,2,2,1,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,5,8,9,10,7] => [2,1,4,3,6,5,10,7,8,9] => [2,2,2,2,1,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,2,3,1,6,5,10,8,9,7] => [2,3,4,1,6,5,8,9,10,7] => [2,2,2,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,8,7,9] => [4,1,2,3,6,5,8,7,9] => [2,2,2,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,4,6,5,8,7,9] => [3,1,2,4,6,5,8,7,9] => [2,2,2,1,1,1] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0] => [10,9,6,5,4,3,8,7,2,1] => [5,4,6,3,8,7,9,2,10,1] => [5,2,1,1,1] => 4
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [6,3,2,5,4,1,8,7,10,9] => [3,2,5,4,6,1,8,7,10,9] => [3,2,2,2,1] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,3,10,4,5,6,7,8,9,2] => [1,4,5,6,7,8,9,10,2,3] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7,10,9] => [6,1,2,3,4,5,8,7,10,9] => [2,2,2,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7,10,9] => [4,1,2,3,6,5,8,7,10,9] => [2,2,2,2,1,1] => 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:
1,1 1,4 1,12,1 1,33,8 1,88,42,1 1,232,184,12
$F_{1} = 1$
$F_{2} = 1 + q$
$F_{3} = 1 + 4\ q$
$F_{4} = 1 + 12\ q + q^{2}$
$F_{5} = 1 + 33\ q + 8\ q^{2}$
$F_{6} = 1 + 88\ q + 42\ q^{2} + q^{3}$
$F_{7} = 1 + 232\ q + 184\ q^{2} + 12\ q^{3}$
Description
The dinv adjustment of an integer partition.
The Ferrers shape of an integer partition $\lambda = (\lambda_1,\ldots,\lambda_k)$ can be decomposed into border strips. For $0 \leq j < \lambda_1$ let $n_j$ be the length of the border strip starting at $(\lambda_1-j,0)$.
The dinv adjustment is then defined by
$$\sum_{j:n_j > 0}(\lambda_1-1-j).$$
The following example is taken from Appendix B in [2]: Let $\lambda=(5,5,4,4,2,1)$. Removing the border strips successively yields the sequence of partitions
$$(5,5,4,4,2,1),(4,3,3,1),(2,2),(1),(),$$
and we obtain $(n_0,\ldots,n_4) = (10,7,0,3,1)$.
The dinv adjustment is thus $4+3+1+0 = 8$.
The Ferrers shape of an integer partition $\lambda = (\lambda_1,\ldots,\lambda_k)$ can be decomposed into border strips. For $0 \leq j < \lambda_1$ let $n_j$ be the length of the border strip starting at $(\lambda_1-j,0)$.
The dinv adjustment is then defined by
$$\sum_{j:n_j > 0}(\lambda_1-1-j).$$
The following example is taken from Appendix B in [2]: Let $\lambda=(5,5,4,4,2,1)$. Removing the border strips successively yields the sequence of partitions
$$(5,5,4,4,2,1),(4,3,3,1),(2,2),(1),(),$$
and we obtain $(n_0,\ldots,n_4) = (10,7,0,3,1)$.
The dinv adjustment is thus $4+3+1+0 = 8$.
Map
inverse first fundamental transformation
Description
Let $\sigma = (i_{11}\cdots i_{1k_1})\cdots(i_{\ell 1}\cdots i_{\ell k_\ell})$ be a permutation given by cycle notation such that every cycle starts with its maximal entry, and all cycles are ordered increasingly by these maximal entries.
Maps $\sigma$ to the permutation $[i_{11},\ldots,i_{1k_1},\ldots,i_{\ell 1},\ldots,i_{\ell k_\ell}]$ in one-line notation.
In other words, this map sends the maximal entries of the cycles to the left-to-right maxima, and the sequences between two left-to-right maxima are given by the cycles.
Maps $\sigma$ to the permutation $[i_{11},\ldots,i_{1k_1},\ldots,i_{\ell 1},\ldots,i_{\ell k_\ell}]$ in one-line notation.
In other words, this map sends the maximal entries of the cycles to the left-to-right maxima, and the sequences between two left-to-right maxima are given by the cycles.
Map
LLPS
Description
The Lewis-Lyu-Pylyavskyy-Sen shape of a permutation.
An ascent in a sequence $u = (u_1, u_2, \ldots)$ is an index $i$ such that $u_i < u_{i+1}$. Let $\mathrm{asc}(u)$ denote the number of ascents of $u$, and let
$$\mathrm{asc}^{*}(u) := \begin{cases} 0 &\textrm{if u is empty}, \\ 1 + \mathrm{asc}(u) &\textrm{otherwise}.\end{cases}$$
Given a permutation $w$ in the symmetric group $\mathfrak{S}_n$, define
$A'_k := \max_{u_1, \ldots, u_k} (\mathrm{asc}^{*}(u_1) + \cdots + \mathrm{asc}^{*}(u_k))$
where the maximum is taken over disjoint subsequences ${u_i}$ of $w$.
Then $A'_1, A'_2-A'_1, A'_3-A'_2,\dots$ is a partition of $n$. Its conjugate is the Lewis-Lyu-Pylyavskyy-Sen shape of a permutation.
An ascent in a sequence $u = (u_1, u_2, \ldots)$ is an index $i$ such that $u_i < u_{i+1}$. Let $\mathrm{asc}(u)$ denote the number of ascents of $u$, and let
$$\mathrm{asc}^{*}(u) := \begin{cases} 0 &\textrm{if u is empty}, \\ 1 + \mathrm{asc}(u) &\textrm{otherwise}.\end{cases}$$
Given a permutation $w$ in the symmetric group $\mathfrak{S}_n$, define
$A'_k := \max_{u_1, \ldots, u_k} (\mathrm{asc}^{*}(u_1) + \cdots + \mathrm{asc}^{*}(u_k))$
where the maximum is taken over disjoint subsequences ${u_i}$ of $w$.
Then $A'_1, A'_2-A'_1, A'_3-A'_2,\dots$ is a partition of $n$. Its conjugate is the Lewis-Lyu-Pylyavskyy-Sen shape of a permutation.
Map
to non-crossing permutation
Description
Sends a Dyck path $D$ with valley at positions $\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation $\pi$ having descents $\{i_1,\ldots,i_k\}$ and whose inverse has descents $\{j_1,\ldots,j_k\}$.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
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