Identifier
-
Mp00023:
Dyck paths
—to non-crossing permutation⟶
Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
St000024: Dyck paths ⟶ ℤ (values match St000443The number of long tunnels of a Dyck path., St001007Number of simple modules with projective dimension 1 in the Nakayama algebra corresponding to the Dyck path., St001187The number of simple modules with grade at least one in the corresponding Nakayama algebra., St001224Let X be the direct sum of all simple modules of the corresponding Nakayama algebra.)
Values
[1,0] => [1] => [1] => [1,0] => 0
[1,0,1,0] => [1,2] => [2] => [1,0,1,0] => 0
[1,1,0,0] => [2,1] => [1,1] => [1,1,0,0] => 1
[1,0,1,0,1,0] => [1,2,3] => [3] => [1,0,1,0,1,0] => 0
[1,0,1,1,0,0] => [1,3,2] => [2,1] => [1,0,1,1,0,0] => 1
[1,1,0,0,1,0] => [2,1,3] => [2,1] => [1,0,1,1,0,0] => 1
[1,1,0,1,0,0] => [2,3,1] => [2,1] => [1,0,1,1,0,0] => 1
[1,1,1,0,0,0] => [3,2,1] => [1,1,1] => [1,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [4] => [1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [3,1] => [1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [3,1] => [1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [3,1] => [1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,0] => [1,4,3,2] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [3,1] => [1,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [2,2] => [1,1,1,0,0,0] => 2
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [3,1] => [1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,0,0,0] => [2,4,3,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,0] => [3,2,1,4] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,1,0,0] => [3,2,4,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,0,0,0] => [4,2,3,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,0] => [4,3,2,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [3,2] => [1,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [3,2] => [1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [3,2] => [1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [3,2] => [1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [2,2,1] => [1,1,1,0,0,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [3,2] => [1,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,0,0] => [2,5,3,4,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [2,2,1] => [1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,0] => [5,3,2,4,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,6,4,5,2] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,5,3,4,2,6] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,6,3,4,5,2] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,6,3,5,4,2] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
>>> Load all 1201 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,6,4,3,5,2] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,6,4,5,3,2] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [3,3] => [1,1,1,0,1,0,0,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,6,4,5,3] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,6,4,5,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,5,3,4,1,6] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,5,3,4,6,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,6,3,4,5,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,6,3,5,4,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,6,4,3,5,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,6,4,5,3,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [2,2,2] => [1,1,1,1,0,0,0,0] => 3
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,6,4,5,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,2,3,1,5,6] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,2,3,1,6,5] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,2,3,5,1,6] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,2,3,6,5,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,3,4,1,6] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,2,3,4,6,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,0] => [6,2,3,4,5,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,0,0] => [6,2,3,5,4,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,2,4,3,1,6] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,4,3,6,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,0] => [6,2,4,3,5,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,0] => [6,2,4,5,3,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,0] => [6,2,5,4,3,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,3,2,4,1,6] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,0,0] => [6,3,2,4,5,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,0,0] => [6,3,2,5,4,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,3,4,2,1,6] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,3,4,2,6,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,0] => [6,3,4,2,5,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,0,0] => [6,3,4,5,2,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,5,4,2,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => [6,4,3,2,5,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => [6,4,3,5,2,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => [6,5,3,4,2,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => [7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,7,5,6,4] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,7,5,6,3] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,4,6,3,7] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,6,4,5,3,7] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,6,4,5,7,3] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,7,4,5,6,3] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,7,4,6,5,3] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,7,5,4,6,3] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,7,5,6,4,3] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,7,5,6,4] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,7,5,6,2] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,6,4,5,2,7] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,6,4,5,7,2] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,7,4,5,6,2] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,7,4,6,5,2] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,7,5,4,6,2] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,7,5,6,4,2] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 3
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,7,5,6,2] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,5,3,4,2,6,7] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,5,3,4,2,7,6] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,5,3,4,6,2,7] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,5,3,4,6,7,2] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,5,3,4,7,6,2] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,6,3,4,5,2,7] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,6,3,4,5,7,2] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,7,3,4,5,6,2] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,7,3,4,6,5,2] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,6,3,5,4,2,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,6,3,5,4,7,2] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,7,3,5,4,6,2] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,7,3,5,6,4,2] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,7,3,6,5,4,2] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,4,3,2,6,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,4,3,6,2,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,6,4,3,5,2,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,6,4,3,5,7,2] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,7,4,3,5,6,2] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,7,4,3,6,5,2] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,6,4,5,3,2,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,6,4,5,3,7,2] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,7,4,5,3,6,2] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,7,4,5,6,3,2] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,7,4,6,5,3,2] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,7,5,4,3,6,2] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,7,5,4,6,3,2] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,7,6,4,5,3,2] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,6,4] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,5,7,4] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,7,5,6,4] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,5,3,7] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,7,5,6,3] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,4,3,6,7] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,4,3,7,6] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,4,6,3,7] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,4,6,7,3] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,4,7,6,3] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,6,4,5,3,7] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,6,4,5,7,3] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,7,4,5,6,3] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,7,4,6,5,3] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,5,4,3,7] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,5,4,7,3] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,7,5,4,6,3] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,7,5,6,4,3] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,6,5] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,6,4] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,5,4,7] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,5,7,4] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,7,5,6,4] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,6,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,5,7,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,7,5,6,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,6,5,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,4,6,1,7] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,4,6,7,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,4,7,6,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,6,4,5,1,7] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,6,4,5,7,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,7,4,5,6,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,7,4,6,5,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,5,4,7,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,7,5,4,6,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,7,5,6,4,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,3,1,5,7,6] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,7] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3,1,6,7,5] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3,1,7,6,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 3
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,3,5,1,6,7] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,3,5,1,7,6] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,3,5,6,1,7] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,3,5,7,6,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,1,7] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,7,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,3,7,5,6,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,5,3,4,1,6,7] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,5,3,4,1,7,6] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,5,3,4,6,1,7] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,5,3,4,6,7,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,5,3,4,7,6,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,6,3,4,5,1,7] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,6,3,4,5,7,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,7,3,4,5,6,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,7,3,4,6,5,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,6,3,5,4,1,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,6,3,5,4,7,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,7,3,5,4,6,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,7,3,5,6,4,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,7,3,6,5,4,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,4,3,6,1,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,4,3,6,7,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,4,3,7,6,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,6,4,3,5,1,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,6,4,3,5,7,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,7,4,3,5,6,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,7,4,3,6,5,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,6,4,5,3,1,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,6,4,5,3,7,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,7,4,5,3,6,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,7,4,5,6,3,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,7,4,6,5,3,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,7,5,4,3,6,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,7,5,4,6,3,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,7,6,4,5,3,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,7,6] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,2,1,4,6,5,7] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,2,1,4,6,7,5] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,5,4,6,7] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,5,6,4,7] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,5,6,7,4] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,1,5,7,6,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,2,1,6,5,4,7] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,2,1,6,5,7,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,2,1,7,5,6,4] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 3
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,7] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,2,4,1,6,7,5] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,4,1,7,6,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,7,6,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,4,6,5,1,7] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,2,4,6,5,7,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,7,5,6,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,2,4,7,6,5,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,5,4,1,6,7] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,5,4,6,1,7] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,5,4,6,7,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,6,4,5,1,7] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,6,4,5,7,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,7,4,5,6,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,7,4,6,5,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,2,6,5,4,1,7] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,2,6,5,4,7,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,2,7,5,4,6,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,7,5,6,4,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,2,3,1,5,7,6] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,2,3,1,6,5,7] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,2,3,1,6,7,5] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,2,3,1,7,6,5] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,2,3,5,1,6,7] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,2,3,5,1,7,6] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,2,3,5,6,1,7] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,2,3,5,7,6,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,2,3,6,5,1,7] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [4,2,3,6,5,7,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,2,3,7,5,6,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,2,3,7,6,5,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [5,2,3,4,1,6,7] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,2,3,4,1,7,6] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [5,2,3,4,6,1,7] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,2,3,4,6,7,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,2,3,4,7,6,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,2,3,4,5,1,7] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,2,3,4,5,7,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7,2,3,4,5,6,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [7,2,3,4,6,5,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,3,5,4,1,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,2,3,5,4,7,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [7,2,3,5,4,6,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [7,2,3,5,6,4,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [7,2,3,6,5,4,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,2,4,3,1,6,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,2,4,3,1,7,6] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [5,2,4,3,6,1,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,2,4,3,6,7,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,2,4,3,7,6,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,2,4,3,5,1,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,2,4,3,5,7,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7,2,4,3,5,6,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7,2,4,3,6,5,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,4,5,3,1,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,2,4,5,3,7,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7,2,4,5,3,6,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7,2,4,5,6,3,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7,2,4,6,5,3,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,2,5,4,3,1,7] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,5,4,3,7,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [7,2,5,4,3,6,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [7,2,5,4,6,3,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [7,2,6,4,5,3,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [7,2,6,5,4,3,1] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,3,2,1,5,7,6] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,7] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3,2,1,6,7,5] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 3
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,3,2,5,1,6,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,3,2,5,7,6,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,3,2,6,5,7,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,2,7,5,6,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 3
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,3,2,4,1,6,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,3,2,4,1,7,6] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [5,3,2,4,6,1,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,3,2,4,6,7,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,3,2,4,7,6,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,3,2,4,5,7,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [7,3,2,4,5,6,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [7,3,2,4,6,5,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,3,2,5,4,1,7] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,2,5,4,7,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [7,3,2,5,4,6,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [7,3,2,5,6,4,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [7,3,2,6,5,4,1] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,3,4,2,1,6,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,3,4,2,1,7,6] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,3,4,2,6,1,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,3,4,2,6,7,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,3,4,2,7,6,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,4,2,5,1,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,3,4,2,5,7,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7,3,4,2,5,6,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7,3,4,2,6,5,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,3,4,5,2,1,7] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7,3,4,5,2,6,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7,3,4,5,6,2,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7,3,4,6,5,2,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,3,5,4,2,1,7] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,3,5,4,2,7,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [7,3,5,4,2,6,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [7,3,5,4,6,2,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [7,3,6,4,5,2,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [7,3,6,5,4,2,1] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,4,3,2,7,6,1] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,4,3,2,5,1,7] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [7,4,3,2,5,6,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [7,4,3,2,6,5,1] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,4,3,5,2,1,7] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,4,3,5,2,7,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [7,4,3,5,2,6,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [7,4,3,5,6,2,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [7,4,3,6,5,2,1] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,5,3,4,2,1,7] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,5,3,4,2,7,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [7,5,3,4,2,6,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [7,5,3,4,6,2,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [7,6,3,4,5,2,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7,6,3,5,4,2,1] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,5,4,3,2,7,1] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [7,5,4,3,2,6,1] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [7,5,4,3,6,2,1] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [7,6,4,3,5,2,1] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7,6,4,5,3,2,1] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 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] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,3,5,4,6,8,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3,5,4,7,8,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,7,6] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,5,6,4,8,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,5,4,8,7] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,6,5,8,7,4] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,8,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5,7,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,4,3,5,7,8,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,4,3,5,8,7,6] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,4,3,6,7,5,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4,3,6,7,8,5] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,6,8,5] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,7,6,5] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,4,5,3,7,8,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,4,5,3,8,7,6] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,2,4,5,6,3,8,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,5,4,3,6,8,7] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,5,4,3,7,8,6] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,2,5,4,6,8,7,3] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,2,5,4,7,6,8,3] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,2,5,4,8,7,6,3] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,8,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,7,8,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,8,7,6] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,6,5,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,2,4,6,5,8,7] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,2,4,6,7,8,5] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,2,4,6,8,7,5] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,2,4,7,6,5,8] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,2,4,7,6,8,5] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,7,6,5] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,7,6] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,3,2,5,6,4,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,2,5,6,4,8,7] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,2,5,6,7,4,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,6,7,8,4] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,3,2,5,6,8,7,4] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,2,5,7,6,4,8] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,2,5,8,7,6,4] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,6,5,4,8,7] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,5,7,8,4] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,5,8,7,4] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,2,7,5,6,8,4] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2,8,5,7,6,4] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,6,5,4,8] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,7,6,5,8,4] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,8,6,5,7,4] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,3,2,8,6,7,5,4] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,2,5,6,8,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,5,7,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,2,5,7,8,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4,2,6,7,8,5] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,3,4,2,6,8,7,5] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,6,8,5] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,3,4,2,8,6,7,5] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4,2,8,7,6,5] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,5,2,7,8,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,5,2,8,7,6] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,2,8,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,3,5,4,2,6,8,7] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,3,5,4,2,7,6,8] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,3,5,4,2,7,8,6] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,3,5,4,7,6,2,8] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,5,4,7,6,8,2] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 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] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,3,6,5,4,2,8,7] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,4,3,2,5,6,8,7] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,4,3,2,5,7,6,8] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,4,3,2,5,7,8,6] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,3,2,5,8,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,4,3,2,6,7,5,8] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,4,3,2,6,7,8,5] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,4,3,2,6,8,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,4,3,2,7,6,8,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,3,2,8,7,6,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,3,5,7,6,2,8] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,3,5,8,6,7,2] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,3,6,5,2,7,8] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,3,6,5,7,8,2] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,2] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,3,8,5,6,7,2] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,3,8,5,7,6,2] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,5,3,4,2,7,8,6] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,5,3,4,2,8,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,5,3,4,6,2,8,7] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,6,3,4,5,8,7,2] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,4,3,2,7,6,8] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,4,3,2,8,7,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,4,3,6,8,7,2] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,5,4,3,8,7,6,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,6,4,3,5,8,7,2] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,8,4,3,5,7,6,2] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,8,4,3,6,7,5,2] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,5,4,3,2,8,7] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,8,5,4,3,7,6,2] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,7,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,7,8,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,8,7,6] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,4,6,5,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,4,6,5,8,7] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,4,6,7,8,5] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,4,7,6,8,5] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,4,8,6,7,5] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,7,6,5] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,3,5,4,7,8,6] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,3,5,4,8,7,6] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,5,6,4,8,7] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,4] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,1,3,5,8,6,7,4] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,3,6,5,8,7,4] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,8,5,6,7,4] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,1,3,8,5,7,6,4] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,3,8,6,5,7,4] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,3,8,6,7,5,4] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,7,6,5,4] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,3,5,7,8,6] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,3,5,8,7,6] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,5] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,7,5] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,6,8,5] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,8,6,7,5] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 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] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6,8,7] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,1,4,5,3,8,7,6] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,4,5,6,3,8,7] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,3,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,3] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,1,4,5,6,8,7,3] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,4,5,8,6,7,3] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,4,5,8,7,6,3] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,1,4,6,5,8,7,3] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,1,4,8,5,6,7,3] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,1,4,8,5,7,6,3] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,1,4,7,6,5,8,3] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,1,4,8,6,5,7,3] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,5,4,3,7,6,8] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,4,6,7,8,3] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,5,4,6,8,7,3] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,8,3] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,4,8,6,7,3] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,4,8,7,6,3] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,6,4,5,3,8,7] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,1,6,4,5,7,8,3] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,1,6,4,5,8,7,3] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,1,8,4,5,6,7,3] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,1,8,4,5,7,6,3] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,1,7,4,6,5,8,3] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,1,8,4,6,5,7,3] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,8,4,6,7,5,3] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,1,6,5,4,8,7,3] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 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] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,8,5,6,7,4,3] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,1,8,5,7,6,4,3] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,6,5,4,3,8] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,8,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,3,1,4,5,7,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,4,6,5,8,7] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,3,1,4,6,7,5,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,1,4,6,7,8,5] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,7,6,8,5] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,8,7,6,5] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 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] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,5,6,4,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,3,1,5,6,7,4,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,4] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,7,6,8,4] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,6,5,4,7,8] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,1,6,5,4,8,7] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,5,8,7,4] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,3,1,7,5,6,4,8] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,8,5,6,7,4] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,7,6,5,8,4] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5,6,8,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,4,1,5,7,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,4,1,5,7,8,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,8,7,6] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,5,7,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,4,1,6,7,5,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,4,1,6,8,7,5] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,4,1,7,6,5,8] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,6,8,5] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,4,1,8,6,7,5] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,8,7,6,5] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,5,1,6,8,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,8] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,1,7,8,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,8,7,6] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,4,6,5,8,7,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,3,5,4,1,6,8,7] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,4,1,8,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,3,5,4,7,6,8,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,3,5,4,8,6,7,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,3,6,4,5,1,8,7] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,3,6,4,5,8,7,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,4,3,1,5,8,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,4,3,1,6,5,7,8] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,4,3,1,6,7,8,5] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,8,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,3,1,7,6,8,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,4,3,1,8,7,6,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,4,3,5,1,7,8,6] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,4,3,5,1,8,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,4,3,5,6,1,8,7] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,4,3,5,6,8,7,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,4,3,5,8,6,7,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,4,3,6,5,1,7,8] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,3,6,5,1,8,7] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,4,3,6,5,7,1,8] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,4,3,6,5,7,8,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,1] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,4,3,7,5,6,8,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,4,3,8,5,6,7,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,4,3,8,5,7,6,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,4,3,8,6,5,7,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,5,3,4,1,8,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,5,3,4,6,8,7,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [2,5,3,4,7,6,8,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,5,3,4,8,6,7,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,6,3,4,5,8,7,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,5,4,3,1,6,8,7] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,5,4,3,1,8,7,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,5,4,3,6,1,8,7] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,5,4,3,8,7,6,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,6,4,3,5,1,8,7] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [2,6,4,3,5,8,7,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,7,4,3,6,5,8,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,6,8,7] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,2,1,4,5,7,8,6] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,2,1,4,5,8,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,2,1,4,6,7,8,5] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,2,1,4,6,8,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,2,1,4,7,6,5,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [3,2,1,4,7,6,8,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,2,1,4,8,6,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,2,1,4,8,7,6,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,1,5,4,7,6,8] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,2,1,5,6,4,7,8] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,2,1,5,6,7,8,4] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,2,1,5,6,8,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,2,1,5,7,6,4,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [3,2,1,5,7,6,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,2,1,5,8,6,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,2,1,5,8,7,6,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,2,1,6,5,7,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,2,1,6,5,8,7,4] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,2,1,7,5,6,8,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,8,5,6,7,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,2,1,8,5,7,6,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,2,1,7,6,5,4,8] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [3,2,1,7,6,5,8,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,2,1,8,6,5,7,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,1,8,6,7,5,4] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [3,2,4,1,5,6,8,7] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [3,2,4,1,5,7,6,8] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [3,2,4,1,5,7,8,6] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [3,2,4,1,5,8,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [3,2,4,1,6,5,7,8] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [3,2,4,1,6,7,5,8] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [3,2,4,1,6,7,8,5] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,2,4,1,6,8,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [3,2,4,1,7,6,5,8] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,7,6,8,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,2,4,1,8,6,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,2,4,1,8,7,6,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [3,2,4,5,1,8,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,6,8,7,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [3,2,4,5,7,6,8,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,2,4,5,8,6,7,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [3,2,4,6,5,8,7,1] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [3,2,4,7,5,6,8,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [3,2,4,8,5,6,7,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [3,2,5,4,1,6,8,7] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,2,5,4,1,7,6,8] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [3,2,5,4,1,7,8,6] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,2,5,4,1,8,7,6] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,6,1,8,7] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [3,2,5,4,6,7,8,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [3,2,5,4,6,8,7,1] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,7,6,1,8] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,8,1] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,4,8,6,7,1] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [3,2,6,4,5,1,8,7] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [3,2,7,4,5,6,1,8] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [3,2,8,4,5,6,7,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [3,2,7,4,6,5,1,8] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,2,7,4,6,5,8,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [3,2,6,5,4,1,8,7] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [3,2,6,5,4,7,1,8] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [3,2,8,5,4,6,7,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,8,7,5,6,4,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,2,8,7,6,5,4,1] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [4,2,3,1,5,7,8,6] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [4,2,3,1,6,5,8,7] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [4,2,3,1,6,7,8,5] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [4,2,3,1,6,8,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [4,2,3,1,7,6,8,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [4,2,3,1,8,6,7,5] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,2,3,1,8,7,6,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [4,2,3,5,1,8,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [4,2,3,5,6,1,8,7] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [4,2,3,5,6,8,7,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [4,2,3,5,8,7,6,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [4,2,3,6,5,8,7,1] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [4,2,3,7,5,6,8,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [4,2,3,8,5,6,7,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,2,3,8,5,7,6,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [5,2,3,4,1,6,8,7] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [5,2,3,4,1,7,8,6] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [5,2,3,4,1,8,7,6] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [5,2,3,4,6,1,8,7] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [5,2,3,4,7,6,1,8] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [5,2,3,4,8,6,7,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [6,2,3,4,5,1,8,7] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [6,2,3,4,5,8,7,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [6,2,3,5,4,1,8,7] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [5,2,4,3,6,1,8,7] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [5,2,4,3,8,7,6,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [6,2,4,3,5,1,8,7] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [6,2,5,4,3,1,8,7] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [8,2,5,4,3,7,6,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,3,2,1,7,6,8,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,2,1,8,6,7,5] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 3
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,3,2,5,1,7,8,6] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [4,3,2,5,6,1,8,7] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [4,3,2,5,7,6,1,8] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [4,3,2,5,7,6,8,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,3,2,5,8,7,6,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [4,3,2,6,5,1,7,8] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [4,3,2,6,5,1,8,7] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [4,3,2,6,5,8,7,1] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [4,3,2,7,6,5,8,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,2,8,6,7,5,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,3,2,8,7,6,5,1] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [5,3,2,4,1,6,8,7] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [5,3,2,4,1,7,6,8] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,3,2,4,1,8,7,6] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [5,3,2,4,7,6,1,8] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [8,3,2,4,6,5,7,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [8,3,2,4,7,6,5,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [7,3,2,5,4,6,1,8] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [8,3,2,5,6,7,4,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [8,3,2,5,7,6,4,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [5,3,4,2,6,1,8,7] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [5,3,4,2,7,6,1,8] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [7,3,4,2,6,5,8,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [6,3,4,5,2,8,7,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [8,3,4,5,2,7,6,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [6,3,5,4,2,8,7,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [8,3,5,4,2,7,6,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,4,3,2,1,6,8,7] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,4,3,2,6,1,8,7] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,4,3,2,8,7,6,1] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,4,3,2,5,1,8,7] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [6,4,3,2,5,8,7,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,4,3,5,2,1,8,7] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [8,4,3,7,6,5,2,1] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,5,4,3,2,8,7,1] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [8,5,4,3,2,7,6,1] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [8,5,4,3,7,6,2,1] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [8,7,4,3,6,5,2,1] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[] => [] => [] => [] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,9,8,1] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 2
[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] => [6,3] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2
[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] => [6,3] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2
[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] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => 2
[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] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => 2
[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] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,2,1,9,8,7,6,5,4] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,3,2,1,9,8,7,6,5] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,4,3,2,1,9,8,7,6] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,5,4,3,2,1,9,8,7] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[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] => [6,4] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 2
[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] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 2
[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] => [4,4,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 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] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 3
[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] => [5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 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] => [4,4,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 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] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 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] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 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] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 3
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1,10,9,8,7,6] => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 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] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,2,3,1,9,8,7,6,5] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,3,4,2,1,9,8,7,6] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => [6,5,3,4,2,1,9,8,7] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,2,1,9,5,8,7,6,4] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,3,5,4,2,1,9,8,7] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,2,1,9,7,8,6,5] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,3,2,1,9,7,8,6] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,1,9,8,6,7,5,4] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,8,7,1,9] => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 2
[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] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => 2
[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] => [5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 2
[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] => [5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 2
[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] => [6,4] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 2
[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] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8,11,10] => [6,5] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,8,7,9] => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,5,4,6,1,8,7,9] => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 2
[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] => [5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 2
[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] => [5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,7,6,9,8,1,10] => [5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 2
[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] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 3
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,8,7,9,2] => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,6,9,10,8] => [6,4] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,9,5] => [6,3] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,9,8,3] => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,10,9,2] => [5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[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] => [4,4,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 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] => [6,4] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 2
[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] => [5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 2
[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] => [5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 2
[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] => [5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 2
[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] => [5,3,2] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3
[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] => [5,3,2] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3
[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] => [5,3,2] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3
[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] => [6,3] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2
[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] => [6,4] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 2
[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] => [6,3] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6,9,8] => [6,3] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6,9,8] => [6,3] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2
[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] => [6,3] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2
[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] => [4,4,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 2
[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] => [6,4] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 2
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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 number of double up and double down steps of a Dyck path.
In other words, this is the number of double rises (and, equivalently, the number of double falls) of a Dyck path.
In other words, this is the number of double rises (and, equivalently, the number of double falls) of a Dyck path.
Map
parallelogram polyomino
Description
Return the Dyck path corresponding to the partition interpreted as a parallogram polyomino.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
Map
Robinson-Schensted tableau shape
Description
Sends a permutation to its Robinson-Schensted tableau shape.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to the shape of its corresponding insertion and recording tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to the shape of its corresponding insertion and recording tableau.
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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