Identifier
-
Mp00031:
Dyck paths
—to 312-avoiding permutation⟶
Permutations
Mp00175: Permutations —inverse Foata bijection⟶ Permutations
Mp00204: Permutations —LLPS⟶ Integer partitions
St001918: Integer partitions ⟶ ℤ
Values
[1,0] => [1] => [1] => [1] => 0
[1,0,1,0] => [1,2] => [1,2] => [1,1] => 0
[1,1,0,0] => [2,1] => [2,1] => [2] => 1
[1,0,1,0,1,0] => [1,2,3] => [1,2,3] => [1,1,1] => 0
[1,0,1,1,0,0] => [1,3,2] => [3,1,2] => [2,1] => 1
[1,1,0,0,1,0] => [2,1,3] => [2,1,3] => [2,1] => 1
[1,1,0,1,0,0] => [2,3,1] => [2,3,1] => [2,1] => 1
[1,1,1,0,0,0] => [3,2,1] => [3,2,1] => [3] => 2
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [1,2,3,4] => [1,1,1,1] => 0
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [4,1,2,3] => [2,1,1] => 1
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [3,1,2,4] => [2,1,1] => 1
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [3,4,1,2] => [2,1,1] => 1
[1,0,1,1,1,0,0,0] => [1,4,3,2] => [4,3,1,2] => [3,1] => 2
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [2,1,3,4] => [2,1,1] => 1
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [2,4,1,3] => [2,1,1] => 1
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [2,3,1,4] => [2,1,1] => 1
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [2,3,4,1] => [2,1,1] => 1
[1,1,0,1,1,0,0,0] => [2,4,3,1] => [4,2,3,1] => [3,1] => 2
[1,1,1,0,0,0,1,0] => [3,2,1,4] => [3,2,1,4] => [3,1] => 2
[1,1,1,0,0,1,0,0] => [3,2,4,1] => [3,2,4,1] => [3,1] => 2
[1,1,1,0,1,0,0,0] => [3,4,2,1] => [3,4,2,1] => [3,1] => 2
[1,1,1,1,0,0,0,0] => [4,3,2,1] => [4,3,2,1] => [4] => 3
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [1,2,3,4,5] => [1,1,1,1,1] => 0
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [5,1,2,3,4] => [2,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [4,1,2,3,5] => [2,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [4,5,1,2,3] => [2,1,1,1] => 1
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [5,4,1,2,3] => [3,1,1] => 2
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [3,1,2,4,5] => [2,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [3,5,1,2,4] => [2,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [3,4,1,2,5] => [2,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [3,4,5,1,2] => [2,1,1,1] => 1
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [5,3,4,1,2] => [3,1,1] => 2
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [4,3,1,2,5] => [3,1,1] => 2
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [4,3,5,1,2] => [3,1,1] => 2
[1,0,1,1,1,0,1,0,0,0] => [1,4,5,3,2] => [4,5,3,1,2] => [3,1,1] => 2
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [5,4,3,1,2] => [4,1] => 3
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,1,1] => 1
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [2,5,1,3,4] => [2,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [2,4,1,3,5] => [2,1,1,1] => 1
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [2,4,5,1,3] => [2,1,1,1] => 1
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [5,2,4,1,3] => [3,1,1] => 2
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [2,3,1,4,5] => [2,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [2,3,5,1,4] => [2,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [2,3,4,1,5] => [2,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [2,3,4,5,1] => [2,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [5,2,3,4,1] => [3,1,1] => 2
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [4,2,3,1,5] => [3,1,1] => 2
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [4,2,3,5,1] => [3,1,1] => 2
[1,1,0,1,1,0,1,0,0,0] => [2,4,5,3,1] => [4,5,2,3,1] => [3,1,1] => 2
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [5,4,2,3,1] => [4,1] => 3
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [3,2,1,4,5] => [3,1,1] => 2
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [3,2,5,1,4] => [3,1,1] => 2
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [3,2,4,1,5] => [3,1,1] => 2
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [3,2,4,5,1] => [3,1,1] => 2
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [3,5,2,4,1] => [3,1,1] => 2
[1,1,1,0,1,0,0,0,1,0] => [3,4,2,1,5] => [3,4,2,1,5] => [3,1,1] => 2
[1,1,1,0,1,0,0,1,0,0] => [3,4,2,5,1] => [3,4,2,5,1] => [3,1,1] => 2
[1,1,1,0,1,0,1,0,0,0] => [3,4,5,2,1] => [3,4,5,2,1] => [3,1,1] => 2
[1,1,1,0,1,1,0,0,0,0] => [3,5,4,2,1] => [5,3,4,2,1] => [4,1] => 3
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [4,3,2,1,5] => [4,1] => 3
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [4,3,2,5,1] => [4,1] => 3
[1,1,1,1,0,0,1,0,0,0] => [4,3,5,2,1] => [4,3,5,2,1] => [4,1] => 3
[1,1,1,1,0,1,0,0,0,0] => [4,5,3,2,1] => [4,5,3,2,1] => [4,1] => 3
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [5,4,3,2,1] => [5] => 4
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [6,1,2,3,4,5] => [2,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [5,1,2,3,4,6] => [2,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [5,6,1,2,3,4] => [2,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [6,5,1,2,3,4] => [3,1,1,1] => 2
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [4,1,2,3,5,6] => [2,1,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [4,6,1,2,3,5] => [2,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [4,5,1,2,3,6] => [2,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [4,5,6,1,2,3] => [2,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [6,4,5,1,2,3] => [3,1,1,1] => 2
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [5,4,1,2,3,6] => [3,1,1,1] => 2
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [5,4,6,1,2,3] => [3,1,1,1] => 2
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,4,3] => [5,6,4,1,2,3] => [3,1,1,1] => 2
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [6,5,4,1,2,3] => [4,1,1] => 3
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [3,1,2,4,5,6] => [2,1,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [3,6,1,2,4,5] => [2,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [3,5,1,2,4,6] => [2,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [3,5,6,1,2,4] => [2,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [6,3,5,1,2,4] => [3,1,1,1] => 2
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [3,4,1,2,5,6] => [2,1,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [3,4,6,1,2,5] => [2,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [3,4,5,1,2,6] => [2,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [3,4,5,6,1,2] => [2,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [6,3,4,5,1,2] => [3,1,1,1] => 2
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [5,3,4,1,2,6] => [3,1,1,1] => 2
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [5,3,4,6,1,2] => [3,1,1,1] => 2
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,4,2] => [5,6,3,4,1,2] => [3,1,1,1] => 2
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [6,5,3,4,1,2] => [4,1,1] => 3
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [4,3,1,2,5,6] => [3,1,1,1] => 2
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [4,3,6,1,2,5] => [3,1,1,1] => 2
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [4,3,5,1,2,6] => [3,1,1,1] => 2
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [4,3,5,6,1,2] => [3,1,1,1] => 2
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [4,6,3,5,1,2] => [3,1,1,1] => 2
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,3,2,6] => [4,5,3,1,2,6] => [3,1,1,1] => 2
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,3,6,2] => [4,5,3,6,1,2] => [3,1,1,1] => 2
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,3,2] => [4,5,6,3,1,2] => [3,1,1,1] => 2
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,5,3,2] => [6,4,5,3,1,2] => [4,1,1] => 3
>>> Load all 1927 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [5,4,3,1,2,6] => [4,1,1] => 3
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [5,4,3,6,1,2] => [4,1,1] => 3
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,4,6,3,2] => [5,4,6,3,1,2] => [4,1,1] => 3
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,4,3,2] => [5,6,4,3,1,2] => [4,1,1] => 3
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => [5,1] => 4
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [2,6,1,3,4,5] => [2,1,1,1,1] => 1
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [2,5,1,3,4,6] => [2,1,1,1,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [2,5,6,1,3,4] => [2,1,1,1,1] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [6,2,5,1,3,4] => [3,1,1,1] => 2
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [2,4,1,3,5,6] => [2,1,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [2,4,6,1,3,5] => [2,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [2,4,5,1,3,6] => [2,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [2,4,5,6,1,3] => [2,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [6,2,4,5,1,3] => [3,1,1,1] => 2
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [5,2,4,1,3,6] => [3,1,1,1] => 2
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [5,2,4,6,1,3] => [3,1,1,1] => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,4,3] => [5,6,2,4,1,3] => [3,1,1,1] => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [6,5,2,4,1,3] => [4,1,1] => 3
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [2,3,1,4,5,6] => [2,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [2,3,6,1,4,5] => [2,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [2,3,5,1,4,6] => [2,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [2,3,5,6,1,4] => [2,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [6,2,3,5,1,4] => [3,1,1,1] => 2
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [2,3,4,1,5,6] => [2,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [2,3,4,6,1,5] => [2,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [2,3,4,5,1,6] => [2,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => [2,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [6,2,3,4,5,1] => [3,1,1,1] => 2
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [5,2,3,4,1,6] => [3,1,1,1] => 2
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [5,2,3,4,6,1] => [3,1,1,1] => 2
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,4,1] => [5,6,2,3,4,1] => [3,1,1,1] => 2
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [6,5,2,3,4,1] => [4,1,1] => 3
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [4,2,3,1,5,6] => [3,1,1,1] => 2
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [4,2,3,6,1,5] => [3,1,1,1] => 2
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [4,2,3,5,1,6] => [3,1,1,1] => 2
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [4,2,3,5,6,1] => [3,1,1,1] => 2
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [4,6,2,3,5,1] => [3,1,1,1] => 2
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,3,1,6] => [4,5,2,3,1,6] => [3,1,1,1] => 2
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,3,6,1] => [4,5,2,3,6,1] => [3,1,1,1] => 2
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,6,3,1] => [4,5,6,2,3,1] => [3,1,1,1] => 2
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,5,3,1] => [6,4,5,2,3,1] => [4,1,1] => 3
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [5,4,2,3,1,6] => [4,1,1] => 3
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [5,4,2,3,6,1] => [4,1,1] => 3
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,4,6,3,1] => [5,4,6,2,3,1] => [4,1,1] => 3
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,4,3,1] => [5,6,4,2,3,1] => [4,1,1] => 3
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [6,5,4,2,3,1] => [5,1] => 4
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => [3,1,1,1] => 2
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [3,2,6,1,4,5] => [3,1,1,1] => 2
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [3,2,5,1,4,6] => [3,1,1,1] => 2
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [3,2,5,6,1,4] => [3,1,1,1] => 2
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [3,6,2,5,1,4] => [3,1,1,1] => 2
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [3,2,4,1,5,6] => [3,1,1,1] => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [3,2,4,6,1,5] => [3,1,1,1] => 2
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [3,2,4,5,1,6] => [3,1,1,1] => 2
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [3,2,4,5,6,1] => [3,1,1,1] => 2
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [3,6,2,4,5,1] => [3,1,1,1] => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [3,5,2,4,1,6] => [3,1,1,1] => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [3,5,2,4,6,1] => [3,1,1,1] => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,6,4,1] => [3,5,6,2,4,1] => [3,1,1,1] => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [6,3,5,2,4,1] => [4,1,1] => 3
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,2,1,5,6] => [3,4,2,1,5,6] => [3,1,1,1] => 2
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,2,1,6,5] => [3,4,2,6,1,5] => [3,1,1,1] => 2
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,2,5,1,6] => [3,4,2,5,1,6] => [3,1,1,1] => 2
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,2,5,6,1] => [3,4,2,5,6,1] => [3,1,1,1] => 2
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,2,6,5,1] => [3,4,6,2,5,1] => [3,1,1,1] => 2
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,2,1,6] => [3,4,5,2,1,6] => [3,1,1,1] => 2
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,2,6,1] => [3,4,5,2,6,1] => [3,1,1,1] => 2
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,2,1] => [3,4,5,6,2,1] => [3,1,1,1] => 2
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,5,2,1] => [6,3,4,5,2,1] => [4,1,1] => 3
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,4,2,1,6] => [5,3,4,2,1,6] => [4,1,1] => 3
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,4,2,6,1] => [5,3,4,2,6,1] => [4,1,1] => 3
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,4,6,2,1] => [5,3,4,6,2,1] => [4,1,1] => 3
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,4,2,1] => [5,6,3,4,2,1] => [4,1,1] => 3
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => [6,5,3,4,2,1] => [5,1] => 4
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => [4,1,1] => 3
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [4,3,2,6,1,5] => [4,1,1] => 3
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [4,3,2,5,1,6] => [4,1,1] => 3
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [4,3,2,5,6,1] => [4,1,1] => 3
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [4,3,6,2,5,1] => [4,1,1] => 3
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,3,5,2,1,6] => [4,3,5,2,1,6] => [4,1,1] => 3
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,6,1] => [4,3,5,2,6,1] => [4,1,1] => 3
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,5,6,2,1] => [4,3,5,6,2,1] => [4,1,1] => 3
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,2,1] => [4,6,3,5,2,1] => [4,1,1] => 3
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,3,2,1,6] => [4,5,3,2,1,6] => [4,1,1] => 3
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,3,2,6,1] => [4,5,3,2,6,1] => [4,1,1] => 3
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,3,6,2,1] => [4,5,3,6,2,1] => [4,1,1] => 3
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,3,2,1] => [4,5,6,3,2,1] => [4,1,1] => 3
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => [6,4,5,3,2,1] => [5,1] => 4
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,1] => 4
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [5,4,3,2,6,1] => [5,1] => 4
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => [5,4,3,6,2,1] => [5,1] => 4
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => [5,4,6,3,2,1] => [5,1] => 4
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => [5,6,4,3,2,1] => [5,1] => 4
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6] => 5
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => [7,1,2,3,4,5,6] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [6,1,2,3,4,5,7] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [6,7,1,2,3,4,5] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => [7,6,1,2,3,4,5] => [3,1,1,1,1] => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [5,7,1,2,3,4,6] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [5,6,1,2,3,4,7] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [5,6,7,1,2,3,4] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => [7,5,6,1,2,3,4] => [3,1,1,1,1] => 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => [6,5,1,2,3,4,7] => [3,1,1,1,1] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => [6,5,7,1,2,3,4] => [3,1,1,1,1] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,6,7,5,4] => [6,7,5,1,2,3,4] => [3,1,1,1,1] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => [7,6,5,1,2,3,4] => [4,1,1,1] => 3
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [4,1,2,3,5,6,7] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [4,7,1,2,3,5,6] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [4,6,1,2,3,5,7] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [4,6,7,1,2,3,5] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => [7,4,6,1,2,3,5] => [3,1,1,1,1] => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [4,5,1,2,3,6,7] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [4,5,7,1,2,3,6] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [4,5,6,1,2,3,7] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [4,5,6,7,1,2,3] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => [7,4,5,6,1,2,3] => [3,1,1,1,1] => 2
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => [6,4,5,1,2,3,7] => [3,1,1,1,1] => 2
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => [6,4,5,7,1,2,3] => [3,1,1,1,1] => 2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,7,5,3] => [6,7,4,5,1,2,3] => [3,1,1,1,1] => 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => [7,6,4,5,1,2,3] => [4,1,1,1] => 3
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => [5,4,1,2,3,6,7] => [3,1,1,1,1] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => [5,4,7,1,2,3,6] => [3,1,1,1,1] => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,4,6,3,7] => [5,4,6,1,2,3,7] => [3,1,1,1,1] => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => [5,4,6,7,1,2,3] => [3,1,1,1,1] => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => [5,7,4,6,1,2,3] => [3,1,1,1,1] => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,5,6,4,3,7] => [5,6,4,1,2,3,7] => [3,1,1,1,1] => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,5,6,4,7,3] => [5,6,4,7,1,2,3] => [3,1,1,1,1] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,5,6,7,4,3] => [5,6,7,4,1,2,3] => [3,1,1,1,1] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5,7,6,4,3] => [7,5,6,4,1,2,3] => [4,1,1,1] => 3
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => [6,5,4,1,2,3,7] => [4,1,1,1] => 3
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => [6,5,4,7,1,2,3] => [4,1,1,1] => 3
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,6,5,7,4,3] => [6,5,7,4,1,2,3] => [4,1,1,1] => 3
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,6,7,5,4,3] => [6,7,5,4,1,2,3] => [4,1,1,1] => 3
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => [7,6,5,4,1,2,3] => [5,1,1] => 4
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [3,1,2,4,5,6,7] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [3,7,1,2,4,5,6] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [3,6,1,2,4,5,7] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [3,6,7,1,2,4,5] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => [7,3,6,1,2,4,5] => [3,1,1,1,1] => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [3,5,1,2,4,6,7] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => [3,5,7,1,2,4,6] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [3,5,6,1,2,4,7] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [3,5,6,7,1,2,4] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => [7,3,5,6,1,2,4] => [3,1,1,1,1] => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => [6,3,5,1,2,4,7] => [3,1,1,1,1] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => [6,3,5,7,1,2,4] => [3,1,1,1,1] => 2
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,6,7,5,4] => [6,7,3,5,1,2,4] => [3,1,1,1,1] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => [7,6,3,5,1,2,4] => [4,1,1,1] => 3
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [3,4,1,2,5,6,7] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [3,4,7,1,2,5,6] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [3,4,6,1,2,5,7] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [3,4,6,7,1,2,5] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => [7,3,4,6,1,2,5] => [3,1,1,1,1] => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [3,4,5,1,2,6,7] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [3,4,5,7,1,2,6] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [3,4,5,6,1,2,7] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [3,4,5,6,7,1,2] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => [7,3,4,5,6,1,2] => [3,1,1,1,1] => 2
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => [6,3,4,5,1,2,7] => [3,1,1,1,1] => 2
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => [6,3,4,5,7,1,2] => [3,1,1,1,1] => 2
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,6,7,5,2] => [6,7,3,4,5,1,2] => [3,1,1,1,1] => 2
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => [7,6,3,4,5,1,2] => [4,1,1,1] => 3
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => [5,3,4,1,2,6,7] => [3,1,1,1,1] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => [5,3,4,7,1,2,6] => [3,1,1,1,1] => 2
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => [5,3,4,6,1,2,7] => [3,1,1,1,1] => 2
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => [5,3,4,6,7,1,2] => [3,1,1,1,1] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => [5,7,3,4,6,1,2] => [3,1,1,1,1] => 2
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,5,6,4,2,7] => [5,6,3,4,1,2,7] => [3,1,1,1,1] => 2
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,5,6,4,7,2] => [5,6,3,4,7,1,2] => [3,1,1,1,1] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,6,7,4,2] => [5,6,7,3,4,1,2] => [3,1,1,1,1] => 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,6,4,2] => [7,5,6,3,4,1,2] => [4,1,1,1] => 3
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => [6,5,3,4,1,2,7] => [4,1,1,1] => 3
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => [6,5,3,4,7,1,2] => [4,1,1,1] => 3
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,6,5,7,4,2] => [6,5,7,3,4,1,2] => [4,1,1,1] => 3
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,6,7,5,4,2] => [6,7,5,3,4,1,2] => [4,1,1,1] => 3
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => [7,6,5,3,4,1,2] => [5,1,1] => 4
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => [4,3,1,2,5,6,7] => [3,1,1,1,1] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => [4,3,7,1,2,5,6] => [3,1,1,1,1] => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => [4,3,6,1,2,5,7] => [3,1,1,1,1] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => [4,3,6,7,1,2,5] => [3,1,1,1,1] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => [4,7,3,6,1,2,5] => [3,1,1,1,1] => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => [4,3,5,1,2,6,7] => [3,1,1,1,1] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => [4,3,5,7,1,2,6] => [3,1,1,1,1] => 2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => [4,3,5,6,1,2,7] => [3,1,1,1,1] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => [4,3,5,6,7,1,2] => [3,1,1,1,1] => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => [4,7,3,5,6,1,2] => [3,1,1,1,1] => 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => [4,6,3,5,1,2,7] => [3,1,1,1,1] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => [4,6,3,5,7,1,2] => [3,1,1,1,1] => 2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,6,7,5,2] => [4,6,7,3,5,1,2] => [3,1,1,1,1] => 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => [7,4,6,3,5,1,2] => [4,1,1,1] => 3
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,5,3,2,6,7] => [4,5,3,1,2,6,7] => [3,1,1,1,1] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,5,3,2,7,6] => [4,5,3,7,1,2,6] => [3,1,1,1,1] => 2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,4,5,3,6,2,7] => [4,5,3,6,1,2,7] => [3,1,1,1,1] => 2
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,5,3,6,7,2] => [4,5,3,6,7,1,2] => [3,1,1,1,1] => 2
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,5,3,7,6,2] => [4,5,7,3,6,1,2] => [3,1,1,1,1] => 2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,3,2,7] => [4,5,6,3,1,2,7] => [3,1,1,1,1] => 2
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,3,7,2] => [4,5,6,3,7,1,2] => [3,1,1,1,1] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,3,2] => [4,5,6,7,3,1,2] => [3,1,1,1,1] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,4,5,7,6,3,2] => [7,4,5,6,3,1,2] => [4,1,1,1] => 3
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,4,6,5,3,2,7] => [6,4,5,3,1,2,7] => [4,1,1,1] => 3
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,5,3,7,2] => [6,4,5,3,7,1,2] => [4,1,1,1] => 3
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,4,6,5,7,3,2] => [6,4,5,7,3,1,2] => [4,1,1,1] => 3
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,4,6,7,5,3,2] => [6,7,4,5,3,1,2] => [4,1,1,1] => 3
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,4,7,6,5,3,2] => [7,6,4,5,3,1,2] => [5,1,1] => 4
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,4,3,2,6,7] => [5,4,3,1,2,6,7] => [4,1,1,1] => 3
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => [5,4,3,7,1,2,6] => [4,1,1,1] => 3
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,4,3,6,2,7] => [5,4,3,6,1,2,7] => [4,1,1,1] => 3
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => [5,4,3,6,7,1,2] => [4,1,1,1] => 3
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => [5,4,7,3,6,1,2] => [4,1,1,1] => 3
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,4,6,3,2,7] => [5,4,6,3,1,2,7] => [4,1,1,1] => 3
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,4,6,3,7,2] => [5,4,6,3,7,1,2] => [4,1,1,1] => 3
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,4,6,7,3,2] => [5,4,6,7,3,1,2] => [4,1,1,1] => 3
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,4,7,6,3,2] => [5,7,4,6,3,1,2] => [4,1,1,1] => 3
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,5,6,4,3,2,7] => [5,6,4,3,1,2,7] => [4,1,1,1] => 3
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,6,4,3,7,2] => [5,6,4,3,7,1,2] => [4,1,1,1] => 3
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,5,6,4,7,3,2] => [5,6,4,7,3,1,2] => [4,1,1,1] => 3
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,5,6,7,4,3,2] => [5,6,7,4,3,1,2] => [4,1,1,1] => 3
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,5,7,6,4,3,2] => [7,5,6,4,3,1,2] => [5,1,1] => 4
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => [6,5,4,3,1,2,7] => [5,1,1] => 4
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => [6,5,4,3,7,1,2] => [5,1,1] => 4
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,6,5,4,7,3,2] => [6,5,4,7,3,1,2] => [5,1,1] => 4
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,5,7,4,3,2] => [6,5,7,4,3,1,2] => [5,1,1] => 4
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,6,7,5,4,3,2] => [6,7,5,4,3,1,2] => [5,1,1] => 4
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => [7,6,5,4,3,1,2] => [6,1] => 5
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [2,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => [2,7,1,3,4,5,6] => [2,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => [2,6,1,3,4,5,7] => [2,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => [2,6,7,1,3,4,5] => [2,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => [7,2,6,1,3,4,5] => [3,1,1,1,1] => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => [2,5,1,3,4,6,7] => [2,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => [2,5,7,1,3,4,6] => [2,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => [2,5,6,1,3,4,7] => [2,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [2,5,6,7,1,3,4] => [2,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,6,4] => [7,2,5,6,1,3,4] => [3,1,1,1,1] => 2
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => [6,2,5,1,3,4,7] => [3,1,1,1,1] => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,5,7,4] => [6,2,5,7,1,3,4] => [3,1,1,1,1] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,6,7,5,4] => [6,7,2,5,1,3,4] => [3,1,1,1,1] => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => [7,6,2,5,1,3,4] => [4,1,1,1] => 3
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => [2,4,1,3,5,6,7] => [2,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => [2,4,7,1,3,5,6] => [2,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => [2,4,6,1,3,5,7] => [2,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => [2,4,6,7,1,3,5] => [2,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => [7,2,4,6,1,3,5] => [3,1,1,1,1] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [2,4,5,1,3,6,7] => [2,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [2,4,5,7,1,3,6] => [2,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [2,4,5,6,1,3,7] => [2,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [2,4,5,6,7,1,3] => [2,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => [7,2,4,5,6,1,3] => [3,1,1,1,1] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,5,3,7] => [6,2,4,5,1,3,7] => [3,1,1,1,1] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => [6,2,4,5,7,1,3] => [3,1,1,1,1] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,6,7,5,3] => [6,7,2,4,5,1,3] => [3,1,1,1,1] => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => [7,6,2,4,5,1,3] => [4,1,1,1] => 3
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,4,3,6,7] => [5,2,4,1,3,6,7] => [3,1,1,1,1] => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,4,3,7,6] => [5,2,4,7,1,3,6] => [3,1,1,1,1] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,4,6,3,7] => [5,2,4,6,1,3,7] => [3,1,1,1,1] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,4,6,7,3] => [5,2,4,6,7,1,3] => [3,1,1,1,1] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,4,7,6,3] => [5,7,2,4,6,1,3] => [3,1,1,1,1] => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,5,6,4,3,7] => [5,6,2,4,1,3,7] => [3,1,1,1,1] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,5,6,4,7,3] => [5,6,2,4,7,1,3] => [3,1,1,1,1] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,5,6,7,4,3] => [5,6,7,2,4,1,3] => [3,1,1,1,1] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,5,7,6,4,3] => [7,5,6,2,4,1,3] => [4,1,1,1] => 3
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,5,4,3,7] => [6,5,2,4,1,3,7] => [4,1,1,1] => 3
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,5,4,7,3] => [6,5,2,4,7,1,3] => [4,1,1,1] => 3
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,5,7,4,3] => [6,5,7,2,4,1,3] => [4,1,1,1] => 3
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,6,7,5,4,3] => [6,7,5,2,4,1,3] => [4,1,1,1] => 3
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => [7,6,5,2,4,1,3] => [5,1,1] => 4
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [2,3,1,4,5,6,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [2,3,7,1,4,5,6] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [2,3,6,1,4,5,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [2,3,6,7,1,4,5] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,6,5] => [7,2,3,6,1,4,5] => [3,1,1,1,1] => 2
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [2,3,5,1,4,6,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [2,3,5,7,1,4,6] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [2,3,5,6,1,4,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [2,3,5,6,7,1,4] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,6,4] => [7,2,3,5,6,1,4] => [3,1,1,1,1] => 2
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,5,4,7] => [6,2,3,5,1,4,7] => [3,1,1,1,1] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,5,7,4] => [6,2,3,5,7,1,4] => [3,1,1,1,1] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,6,7,5,4] => [6,7,2,3,5,1,4] => [3,1,1,1,1] => 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => [7,6,2,3,5,1,4] => [4,1,1,1] => 3
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [2,3,4,1,5,6,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [2,3,4,7,1,5,6] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [2,3,4,6,1,5,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [2,3,4,6,7,1,5] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => [7,2,3,4,6,1,5] => [3,1,1,1,1] => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [2,3,4,5,1,6,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [2,3,4,5,7,1,6] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [2,3,4,5,6,1,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [2,3,4,5,6,7,1] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,6,1] => [7,2,3,4,5,6,1] => [3,1,1,1,1] => 2
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => [6,2,3,4,5,1,7] => [3,1,1,1,1] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,5,7,1] => [6,2,3,4,5,7,1] => [3,1,1,1,1] => 2
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,6,7,5,1] => [6,7,2,3,4,5,1] => [3,1,1,1,1] => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,6,5,1] => [7,6,2,3,4,5,1] => [4,1,1,1] => 3
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => [5,2,3,4,1,6,7] => [3,1,1,1,1] => 2
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => [5,2,3,4,7,1,6] => [3,1,1,1,1] => 2
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,4,6,1,7] => [5,2,3,4,6,1,7] => [3,1,1,1,1] => 2
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,4,6,7,1] => [5,2,3,4,6,7,1] => [3,1,1,1,1] => 2
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,4,7,6,1] => [5,7,2,3,4,6,1] => [3,1,1,1,1] => 2
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,5,6,4,1,7] => [5,6,2,3,4,1,7] => [3,1,1,1,1] => 2
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,5,6,4,7,1] => [5,6,2,3,4,7,1] => [3,1,1,1,1] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,6,7,4,1] => [5,6,7,2,3,4,1] => [3,1,1,1,1] => 2
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,7,6,4,1] => [7,5,6,2,3,4,1] => [4,1,1,1] => 3
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => [6,5,2,3,4,1,7] => [4,1,1,1] => 3
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,5,4,7,1] => [6,5,2,3,4,7,1] => [4,1,1,1] => 3
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,6,5,7,4,1] => [6,5,7,2,3,4,1] => [4,1,1,1] => 3
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,6,7,5,4,1] => [6,7,5,2,3,4,1] => [4,1,1,1] => 3
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => [7,6,5,2,3,4,1] => [5,1,1] => 4
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7] => [4,2,3,1,5,6,7] => [3,1,1,1,1] => 2
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,3,1,5,7,6] => [4,2,3,7,1,5,6] => [3,1,1,1,1] => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,7] => [4,2,3,6,1,5,7] => [3,1,1,1,1] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3,1,6,7,5] => [4,2,3,6,7,1,5] => [3,1,1,1,1] => 2
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3,1,7,6,5] => [4,7,2,3,6,1,5] => [3,1,1,1,1] => 2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,3,5,1,6,7] => [4,2,3,5,1,6,7] => [3,1,1,1,1] => 2
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,3,5,1,7,6] => [4,2,3,5,7,1,6] => [3,1,1,1,1] => 2
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,3,5,6,1,7] => [4,2,3,5,6,1,7] => [3,1,1,1,1] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,1] => [4,2,3,5,6,7,1] => [3,1,1,1,1] => 2
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,3,5,7,6,1] => [4,7,2,3,5,6,1] => [3,1,1,1,1] => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,1,7] => [4,6,2,3,5,1,7] => [3,1,1,1,1] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,7,1] => [4,6,2,3,5,7,1] => [3,1,1,1,1] => 2
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,3,6,7,5,1] => [4,6,7,2,3,5,1] => [3,1,1,1,1] => 2
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => [7,4,6,2,3,5,1] => [4,1,1,1] => 3
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,4,5,3,1,6,7] => [4,5,2,3,1,6,7] => [3,1,1,1,1] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,4,5,3,1,7,6] => [4,5,2,3,7,1,6] => [3,1,1,1,1] => 2
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,4,5,3,6,1,7] => [4,5,2,3,6,1,7] => [3,1,1,1,1] => 2
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,4,5,3,6,7,1] => [4,5,2,3,6,7,1] => [3,1,1,1,1] => 2
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,4,5,3,7,6,1] => [4,5,7,2,3,6,1] => [3,1,1,1,1] => 2
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,3,1,7] => [4,5,6,2,3,1,7] => [3,1,1,1,1] => 2
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,3,7,1] => [4,5,6,2,3,7,1] => [3,1,1,1,1] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,3,1] => [4,5,6,7,2,3,1] => [3,1,1,1,1] => 2
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,4,5,7,6,3,1] => [7,4,5,6,2,3,1] => [4,1,1,1] => 3
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,4,6,5,3,1,7] => [6,4,5,2,3,1,7] => [4,1,1,1] => 3
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,4,6,5,3,7,1] => [6,4,5,2,3,7,1] => [4,1,1,1] => 3
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,4,6,5,7,3,1] => [6,4,5,7,2,3,1] => [4,1,1,1] => 3
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,4,6,7,5,3,1] => [6,7,4,5,2,3,1] => [4,1,1,1] => 3
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,4,7,6,5,3,1] => [7,6,4,5,2,3,1] => [5,1,1] => 4
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => [5,4,2,3,1,6,7] => [4,1,1,1] => 3
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => [5,4,2,3,7,1,6] => [4,1,1,1] => 3
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,4,3,6,1,7] => [5,4,2,3,6,1,7] => [4,1,1,1] => 3
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,4,3,6,7,1] => [5,4,2,3,6,7,1] => [4,1,1,1] => 3
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,4,3,7,6,1] => [5,4,7,2,3,6,1] => [4,1,1,1] => 3
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,5,4,6,3,1,7] => [5,4,6,2,3,1,7] => [4,1,1,1] => 3
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,5,4,6,3,7,1] => [5,4,6,2,3,7,1] => [4,1,1,1] => 3
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,5,4,6,7,3,1] => [5,4,6,7,2,3,1] => [4,1,1,1] => 3
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,5,4,7,6,3,1] => [5,7,4,6,2,3,1] => [4,1,1,1] => 3
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,5,6,4,3,1,7] => [5,6,4,2,3,1,7] => [4,1,1,1] => 3
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,5,6,4,3,7,1] => [5,6,4,2,3,7,1] => [4,1,1,1] => 3
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,5,6,4,7,3,1] => [5,6,4,7,2,3,1] => [4,1,1,1] => 3
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,5,6,7,4,3,1] => [5,6,7,4,2,3,1] => [4,1,1,1] => 3
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,5,7,6,4,3,1] => [7,5,6,4,2,3,1] => [5,1,1] => 4
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => [6,5,4,2,3,1,7] => [5,1,1] => 4
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => [6,5,4,2,3,7,1] => [5,1,1] => 4
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,6,5,4,7,3,1] => [6,5,4,7,2,3,1] => [5,1,1] => 4
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,6,5,7,4,3,1] => [6,5,7,4,2,3,1] => [5,1,1] => 4
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,6,7,5,4,3,1] => [6,7,5,4,2,3,1] => [5,1,1] => 4
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => [7,6,5,4,2,3,1] => [6,1] => 5
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => [3,2,1,4,5,6,7] => [3,1,1,1,1] => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,7,6] => [3,2,7,1,4,5,6] => [3,1,1,1,1] => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,2,1,4,6,5,7] => [3,2,6,1,4,5,7] => [3,1,1,1,1] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,2,1,4,6,7,5] => [3,2,6,7,1,4,5] => [3,1,1,1,1] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => [3,7,2,6,1,4,5] => [3,1,1,1,1] => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,5,4,6,7] => [3,2,5,1,4,6,7] => [3,1,1,1,1] => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => [3,2,5,7,1,4,6] => [3,1,1,1,1] => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,5,6,4,7] => [3,2,5,6,1,4,7] => [3,1,1,1,1] => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,5,6,7,4] => [3,2,5,6,7,1,4] => [3,1,1,1,1] => 2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,1,5,7,6,4] => [3,7,2,5,6,1,4] => [3,1,1,1,1] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,2,1,6,5,4,7] => [3,6,2,5,1,4,7] => [3,1,1,1,1] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,2,1,6,5,7,4] => [3,6,2,5,7,1,4] => [3,1,1,1,1] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,2,1,6,7,5,4] => [3,6,7,2,5,1,4] => [3,1,1,1,1] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => [7,3,6,2,5,1,4] => [4,1,1,1] => 3
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => [3,2,4,1,5,6,7] => [3,1,1,1,1] => 2
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => [3,2,4,7,1,5,6] => [3,1,1,1,1] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,7] => [3,2,4,6,1,5,7] => [3,1,1,1,1] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,2,4,1,6,7,5] => [3,2,4,6,7,1,5] => [3,1,1,1,1] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,4,1,7,6,5] => [3,7,2,4,6,1,5] => [3,1,1,1,1] => 2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => [3,2,4,5,1,6,7] => [3,1,1,1,1] => 2
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => [3,2,4,5,7,1,6] => [3,1,1,1,1] => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => [3,2,4,5,6,1,7] => [3,1,1,1,1] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => [3,2,4,5,6,7,1] => [3,1,1,1,1] => 2
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,7,6,1] => [3,7,2,4,5,6,1] => [3,1,1,1,1] => 2
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,4,6,5,1,7] => [3,6,2,4,5,1,7] => [3,1,1,1,1] => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,2,4,6,5,7,1] => [3,6,2,4,5,7,1] => [3,1,1,1,1] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,6,7,5,1] => [3,6,7,2,4,5,1] => [3,1,1,1,1] => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,2,4,7,6,5,1] => [7,3,6,2,4,5,1] => [4,1,1,1] => 3
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,5,4,1,6,7] => [3,5,2,4,1,6,7] => [3,1,1,1,1] => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => [3,5,2,4,7,1,6] => [3,1,1,1,1] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,5,4,6,1,7] => [3,5,2,4,6,1,7] => [3,1,1,1,1] => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,5,4,6,7,1] => [3,5,2,4,6,7,1] => [3,1,1,1,1] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => [3,5,7,2,4,6,1] => [3,1,1,1,1] => 2
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,5,6,4,1,7] => [3,5,6,2,4,1,7] => [3,1,1,1,1] => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,5,6,4,7,1] => [3,5,6,2,4,7,1] => [3,1,1,1,1] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,5,6,7,4,1] => [3,5,6,7,2,4,1] => [3,1,1,1,1] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,5,7,6,4,1] => [7,3,5,6,2,4,1] => [4,1,1,1] => 3
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,2,6,5,4,1,7] => [6,3,5,2,4,1,7] => [4,1,1,1] => 3
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,2,6,5,4,7,1] => [6,3,5,2,4,7,1] => [4,1,1,1] => 3
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,2,6,5,7,4,1] => [6,3,5,7,2,4,1] => [4,1,1,1] => 3
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,6,7,5,4,1] => [6,7,3,5,2,4,1] => [4,1,1,1] => 3
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => [7,6,3,5,2,4,1] => [5,1,1] => 4
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7] => [3,4,2,1,5,6,7] => [3,1,1,1,1] => 2
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,4,2,1,5,7,6] => [3,4,2,7,1,5,6] => [3,1,1,1,1] => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,4,2,1,6,5,7] => [3,4,2,6,1,5,7] => [3,1,1,1,1] => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,2,1,6,7,5] => [3,4,2,6,7,1,5] => [3,1,1,1,1] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,2,1,7,6,5] => [3,4,7,2,6,1,5] => [3,1,1,1,1] => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,2,5,1,6,7] => [3,4,2,5,1,6,7] => [3,1,1,1,1] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,2,5,1,7,6] => [3,4,2,5,7,1,6] => [3,1,1,1,1] => 2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,2,5,6,1,7] => [3,4,2,5,6,1,7] => [3,1,1,1,1] => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,1] => [3,4,2,5,6,7,1] => [3,1,1,1,1] => 2
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [3,4,2,5,7,6,1] => [3,4,7,2,5,6,1] => [3,1,1,1,1] => 2
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,4,2,6,5,1,7] => [3,4,6,2,5,1,7] => [3,1,1,1,1] => 2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [3,4,2,6,5,7,1] => [3,4,6,2,5,7,1] => [3,1,1,1,1] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,2,6,7,5,1] => [3,4,6,7,2,5,1] => [3,1,1,1,1] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,4,2,7,6,5,1] => [7,3,4,6,2,5,1] => [4,1,1,1] => 3
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,2,1,6,7] => [3,4,5,2,1,6,7] => [3,1,1,1,1] => 2
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,2,1,7,6] => [3,4,5,2,7,1,6] => [3,1,1,1,1] => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,2,6,1,7] => [3,4,5,2,6,1,7] => [3,1,1,1,1] => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,2,6,7,1] => [3,4,5,2,6,7,1] => [3,1,1,1,1] => 2
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,2,7,6,1] => [3,4,5,7,2,6,1] => [3,1,1,1,1] => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,2,1,7] => [3,4,5,6,2,1,7] => [3,1,1,1,1] => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,2,7,1] => [3,4,5,6,2,7,1] => [3,1,1,1,1] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,2,1] => [3,4,5,6,7,2,1] => [3,1,1,1,1] => 2
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,7,6,2,1] => [7,3,4,5,6,2,1] => [4,1,1,1] => 3
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,4,6,5,2,1,7] => [6,3,4,5,2,1,7] => [4,1,1,1] => 3
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [3,4,6,5,2,7,1] => [6,3,4,5,2,7,1] => [4,1,1,1] => 3
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,6,5,7,2,1] => [6,3,4,5,7,2,1] => [4,1,1,1] => 3
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,6,7,5,2,1] => [6,7,3,4,5,2,1] => [4,1,1,1] => 3
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,7,6,5,2,1] => [7,6,3,4,5,2,1] => [5,1,1] => 4
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,5,4,2,1,6,7] => [5,3,4,2,1,6,7] => [4,1,1,1] => 3
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,5,4,2,1,7,6] => [5,3,4,2,7,1,6] => [4,1,1,1] => 3
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,5,4,2,6,1,7] => [5,3,4,2,6,1,7] => [4,1,1,1] => 3
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,5,4,2,6,7,1] => [5,3,4,2,6,7,1] => [4,1,1,1] => 3
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,5,4,2,7,6,1] => [5,3,4,7,2,6,1] => [4,1,1,1] => 3
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,5,4,6,2,1,7] => [5,3,4,6,2,1,7] => [4,1,1,1] => 3
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,5,4,6,2,7,1] => [5,3,4,6,2,7,1] => [4,1,1,1] => 3
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,5,4,6,7,2,1] => [5,3,4,6,7,2,1] => [4,1,1,1] => 3
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,5,4,7,6,2,1] => [5,7,3,4,6,2,1] => [4,1,1,1] => 3
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,5,6,4,2,1,7] => [5,6,3,4,2,1,7] => [4,1,1,1] => 3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,5,6,4,2,7,1] => [5,6,3,4,2,7,1] => [4,1,1,1] => 3
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [3,5,6,4,7,2,1] => [5,6,3,4,7,2,1] => [4,1,1,1] => 3
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,5,6,7,4,2,1] => [5,6,7,3,4,2,1] => [4,1,1,1] => 3
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,5,7,6,4,2,1] => [7,5,6,3,4,2,1] => [5,1,1] => 4
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,6,5,4,2,1,7] => [6,5,3,4,2,1,7] => [5,1,1] => 4
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [3,6,5,4,2,7,1] => [6,5,3,4,2,7,1] => [5,1,1] => 4
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,6,5,4,7,2,1] => [6,5,3,4,7,2,1] => [5,1,1] => 4
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,6,5,7,4,2,1] => [6,5,7,3,4,2,1] => [5,1,1] => 4
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,6,7,5,4,2,1] => [6,7,5,3,4,2,1] => [5,1,1] => 4
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,7,6,5,4,2,1] => [7,6,5,3,4,2,1] => [6,1] => 5
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6,7] => [4,1,1,1] => 3
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,3,2,1,5,7,6] => [4,3,2,7,1,5,6] => [4,1,1,1] => 3
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,7] => [4,3,2,6,1,5,7] => [4,1,1,1] => 3
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3,2,1,6,7,5] => [4,3,2,6,7,1,5] => [4,1,1,1] => 3
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => [4,3,7,2,6,1,5] => [4,1,1,1] => 3
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,3,2,5,1,6,7] => [4,3,2,5,1,6,7] => [4,1,1,1] => 3
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => [4,3,2,5,7,1,6] => [4,1,1,1] => 3
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => [4,3,2,5,6,1,7] => [4,1,1,1] => 3
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => [4,3,2,5,6,7,1] => [4,1,1,1] => 3
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,3,2,5,7,6,1] => [4,3,7,2,5,6,1] => [4,1,1,1] => 3
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => [4,3,6,2,5,1,7] => [4,1,1,1] => 3
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,3,2,6,5,7,1] => [4,3,6,2,5,7,1] => [4,1,1,1] => 3
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,2,6,7,5,1] => [4,3,6,7,2,5,1] => [4,1,1,1] => 3
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,1] => [4,7,3,6,2,5,1] => [4,1,1,1] => 3
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [4,3,5,2,1,6,7] => [4,3,5,2,1,6,7] => [4,1,1,1] => 3
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [4,3,5,2,1,7,6] => [4,3,5,2,7,1,6] => [4,1,1,1] => 3
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [4,3,5,2,6,1,7] => [4,3,5,2,6,1,7] => [4,1,1,1] => 3
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [4,3,5,2,6,7,1] => [4,3,5,2,6,7,1] => [4,1,1,1] => 3
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,3,5,2,7,6,1] => [4,3,5,7,2,6,1] => [4,1,1,1] => 3
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [4,3,5,6,2,1,7] => [4,3,5,6,2,1,7] => [4,1,1,1] => 3
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [4,3,5,6,2,7,1] => [4,3,5,6,2,7,1] => [4,1,1,1] => 3
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,5,6,7,2,1] => [4,3,5,6,7,2,1] => [4,1,1,1] => 3
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,3,5,7,6,2,1] => [4,7,3,5,6,2,1] => [4,1,1,1] => 3
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [4,3,6,5,2,1,7] => [4,6,3,5,2,1,7] => [4,1,1,1] => 3
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [4,3,6,5,2,7,1] => [4,6,3,5,2,7,1] => [4,1,1,1] => 3
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,3,6,5,7,2,1] => [4,6,3,5,7,2,1] => [4,1,1,1] => 3
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,6,7,5,2,1] => [4,6,7,3,5,2,1] => [4,1,1,1] => 3
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,3,7,6,5,2,1] => [7,4,6,3,5,2,1] => [5,1,1] => 4
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [4,5,3,2,1,6,7] => [4,5,3,2,1,6,7] => [4,1,1,1] => 3
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [4,5,3,2,1,7,6] => [4,5,3,2,7,1,6] => [4,1,1,1] => 3
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [4,5,3,2,6,1,7] => [4,5,3,2,6,1,7] => [4,1,1,1] => 3
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [4,5,3,2,6,7,1] => [4,5,3,2,6,7,1] => [4,1,1,1] => 3
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,5,3,2,7,6,1] => [4,5,3,7,2,6,1] => [4,1,1,1] => 3
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [4,5,3,6,2,1,7] => [4,5,3,6,2,1,7] => [4,1,1,1] => 3
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [4,5,3,6,2,7,1] => [4,5,3,6,2,7,1] => [4,1,1,1] => 3
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,5,3,6,7,2,1] => [4,5,3,6,7,2,1] => [4,1,1,1] => 3
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,3,7,6,2,1] => [4,5,7,3,6,2,1] => [4,1,1,1] => 3
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,3,2,1,7] => [4,5,6,3,2,1,7] => [4,1,1,1] => 3
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,3,2,7,1] => [4,5,6,3,2,7,1] => [4,1,1,1] => 3
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,3,7,2,1] => [4,5,6,3,7,2,1] => [4,1,1,1] => 3
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,3,2,1] => [4,5,6,7,3,2,1] => [4,1,1,1] => 3
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,7,6,3,2,1] => [7,4,5,6,3,2,1] => [5,1,1] => 4
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [4,6,5,3,2,1,7] => [6,4,5,3,2,1,7] => [5,1,1] => 4
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [4,6,5,3,2,7,1] => [6,4,5,3,2,7,1] => [5,1,1] => 4
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,6,5,3,7,2,1] => [6,4,5,3,7,2,1] => [5,1,1] => 4
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,6,5,7,3,2,1] => [6,4,5,7,3,2,1] => [5,1,1] => 4
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,6,7,5,3,2,1] => [6,7,4,5,3,2,1] => [5,1,1] => 4
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [4,7,6,5,3,2,1] => [7,6,4,5,3,2,1] => [6,1] => 5
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [5,1,1] => 4
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => [5,4,3,2,7,1,6] => [5,1,1] => 4
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => [5,4,3,2,6,1,7] => [5,1,1] => 4
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => [5,4,3,2,6,7,1] => [5,1,1] => 4
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,4,3,2,7,6,1] => [5,4,3,7,2,6,1] => [5,1,1] => 4
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [5,4,3,6,2,1,7] => [5,4,3,6,2,1,7] => [5,1,1] => 4
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,4,3,6,2,7,1] => [5,4,3,6,2,7,1] => [5,1,1] => 4
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => [5,4,3,6,7,2,1] => [5,1,1] => 4
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,4,3,7,6,2,1] => [5,4,7,3,6,2,1] => [5,1,1] => 4
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,4,6,3,2,1,7] => [5,4,6,3,2,1,7] => [5,1,1] => 4
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,4,6,3,2,7,1] => [5,4,6,3,2,7,1] => [5,1,1] => 4
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,4,6,3,7,2,1] => [5,4,6,3,7,2,1] => [5,1,1] => 4
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,6,7,3,2,1] => [5,4,6,7,3,2,1] => [5,1,1] => 4
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [5,4,7,6,3,2,1] => [5,7,4,6,3,2,1] => [5,1,1] => 4
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [5,6,4,3,2,1,7] => [5,6,4,3,2,1,7] => [5,1,1] => 4
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,6,4,3,2,7,1] => [5,6,4,3,2,7,1] => [5,1,1] => 4
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,6,4,3,7,2,1] => [5,6,4,3,7,2,1] => [5,1,1] => 4
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,6,4,7,3,2,1] => [5,6,4,7,3,2,1] => [5,1,1] => 4
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [5,6,7,4,3,2,1] => [5,6,7,4,3,2,1] => [5,1,1] => 4
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [5,7,6,4,3,2,1] => [7,5,6,4,3,2,1] => [6,1] => 5
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => [6,1] => 5
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,5,4,3,2,7,1] => [6,5,4,3,2,7,1] => [6,1] => 5
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,5,4,3,7,2,1] => [6,5,4,3,7,2,1] => [6,1] => 5
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [6,5,4,7,3,2,1] => [6,5,4,7,3,2,1] => [6,1] => 5
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [6,5,7,4,3,2,1] => [6,5,7,4,3,2,1] => [6,1] => 5
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [6,7,5,4,3,2,1] => [6,7,5,4,3,2,1] => [6,1] => 5
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => [7] => 6
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => [8,1,2,3,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => [7,1,2,3,4,5,6,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,7,8,6] => [7,8,1,2,3,4,5,6] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,7,6] => [8,7,1,2,3,4,5,6] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,6,5,7,8] => [6,1,2,3,4,5,7,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => [6,8,1,2,3,4,5,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,6,7,5,8] => [6,7,1,2,3,4,5,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,5] => [6,7,8,1,2,3,4,5] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,6,8,7,5] => [8,6,7,1,2,3,4,5] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,7,6,5,8] => [7,6,1,2,3,4,5,8] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,7,6,8,5] => [7,6,8,1,2,3,4,5] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,7,8,6,5] => [7,8,6,1,2,3,4,5] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,7,6,5] => [8,7,6,1,2,3,4,5] => [4,1,1,1,1] => 3
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8] => [5,1,2,3,4,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,3,5,4,6,8,7] => [5,8,1,2,3,4,6,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => [5,7,1,2,3,4,6,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3,5,4,7,8,6] => [5,7,8,1,2,3,4,6] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,7,6] => [8,5,7,1,2,3,4,6] => [3,1,1,1,1,1] => 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] => [5,6,8,1,2,3,4,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,5,6,7,4,8] => [5,6,7,1,2,3,4,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => [5,6,7,8,1,2,3,4] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,8,7,4] => [8,5,6,7,1,2,3,4] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,3,5,7,6,4,8] => [7,5,6,1,2,3,4,8] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,3,5,7,6,8,4] => [7,5,6,8,1,2,3,4] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,5,7,8,6,4] => [7,8,5,6,1,2,3,4] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,5,8,7,6,4] => [8,7,5,6,1,2,3,4] => [4,1,1,1,1] => 3
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,5,4,8,7] => [6,5,8,1,2,3,4,7] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,3,6,5,7,4,8] => [6,5,7,1,2,3,4,8] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,6,5,7,8,4] => [6,5,7,8,1,2,3,4] => [3,1,1,1,1,1] => 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] => [6,8,5,7,1,2,3,4] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,3,6,7,5,4,8] => [6,7,5,1,2,3,4,8] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,6,7,5,8,4] => [6,7,5,8,1,2,3,4] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,6,7,8,5,4] => [6,7,8,5,1,2,3,4] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,6,8,7,5,4] => [8,6,7,5,1,2,3,4] => [4,1,1,1,1] => 3
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,7,6,5,4,8] => [7,6,5,1,2,3,4,8] => [4,1,1,1,1] => 3
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,3,7,6,5,8,4] => [7,6,5,8,1,2,3,4] => [4,1,1,1,1] => 3
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,7,6,8,5,4] => [7,6,8,5,1,2,3,4] => [4,1,1,1,1] => 3
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,7,8,6,5,4] => [7,8,6,5,1,2,3,4] => [4,1,1,1,1] => 3
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,7,6,5,4] => [8,7,6,5,1,2,3,4] => [5,1,1,1] => 4
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8] => [4,1,2,3,5,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,8,7] => [4,8,1,2,3,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5,7,6,8] => [4,7,1,2,3,5,6,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,4,3,5,7,8,6] => [4,7,8,1,2,3,5,6] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,4,3,5,8,7,6] => [8,4,7,1,2,3,5,6] => [3,1,1,1,1,1] => 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] => [4,6,1,2,3,5,7,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => [4,6,8,1,2,3,5,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,4,3,6,7,5,8] => [4,6,7,1,2,3,5,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4,3,6,7,8,5] => [4,6,7,8,1,2,3,5] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,4,3,6,8,7,5] => [8,4,6,7,1,2,3,5] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,4,3,7,6,5,8] => [7,4,6,1,2,3,5,8] => [3,1,1,1,1,1] => 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] => [7,4,6,8,1,2,3,5] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,4,3,7,8,6,5] => [7,8,4,6,1,2,3,5] => [3,1,1,1,1,1] => 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] => [8,7,4,6,1,2,3,5] => [4,1,1,1,1] => 3
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,2,4,5,3,6,7,8] => [4,5,1,2,3,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,2,4,5,3,6,8,7] => [4,5,8,1,2,3,6,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,4,5,3,7,8,6] => [4,5,7,8,1,2,3,6] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,4,5,6,3,7,8] => [4,5,6,1,2,3,7,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,2,4,5,6,3,8,7] => [4,5,6,8,1,2,3,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,7,3,8] => [4,5,6,7,1,2,3,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,3] => [4,5,6,7,8,1,2,3] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,4,5,6,8,7,3] => [8,4,5,6,7,1,2,3] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,2,4,5,7,6,3,8] => [7,4,5,6,1,2,3,8] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,4,5,7,8,6,3] => [7,8,4,5,6,1,2,3] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,4,5,8,7,6,3] => [8,7,4,5,6,1,2,3] => [4,1,1,1,1] => 3
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,2,4,6,5,3,8,7] => [6,4,5,8,1,2,3,7] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,2,4,6,5,8,7,3] => [6,8,4,5,7,1,2,3] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,2,4,6,7,5,8,3] => [6,7,4,5,8,1,2,3] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,2,4,6,7,8,5,3] => [6,7,8,4,5,1,2,3] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,2,4,6,8,7,5,3] => [8,6,7,4,5,1,2,3] => [4,1,1,1,1] => 3
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,2,4,7,6,5,3,8] => [7,6,4,5,1,2,3,8] => [4,1,1,1,1] => 3
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4,8,7,6,5,3] => [8,7,6,4,5,1,2,3] => [5,1,1,1] => 4
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,5,4,3,6,7,8] => [5,4,1,2,3,6,7,8] => [3,1,1,1,1,1] => 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] => [5,4,8,1,2,3,6,7] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,2,5,4,3,7,6,8] => [5,4,7,1,2,3,6,8] => [3,1,1,1,1,1] => 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] => [5,4,7,8,1,2,3,6] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,4,3,8,7,6] => [5,8,4,7,1,2,3,6] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,3] => [5,4,6,7,8,1,2,3] => [3,1,1,1,1,1] => 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] => [5,8,4,6,7,1,2,3] => [3,1,1,1,1,1] => 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] => [5,7,4,6,8,1,2,3] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,2,5,6,4,7,8,3] => [5,6,4,7,8,1,2,3] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,2,5,6,7,4,3,8] => [5,6,7,4,1,2,3,8] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,2,5,6,7,4,8,3] => [5,6,7,4,8,1,2,3] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,5,6,7,8,4,3] => [5,6,7,8,4,1,2,3] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,2,5,6,8,7,4,3] => [8,5,6,7,4,1,2,3] => [4,1,1,1,1] => 3
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,2,5,7,6,4,3,8] => [7,5,6,4,1,2,3,8] => [4,1,1,1,1] => 3
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,2,5,7,6,8,4,3] => [7,5,6,8,4,1,2,3] => [4,1,1,1,1] => 3
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,2,5,7,8,6,4,3] => [7,8,5,6,4,1,2,3] => [4,1,1,1,1] => 3
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,6,5,4,3,7,8] => [6,5,4,1,2,3,7,8] => [4,1,1,1,1] => 3
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,6,5,4,3,8,7] => [6,5,4,8,1,2,3,7] => [4,1,1,1,1] => 3
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,6,5,4,7,8,3] => [6,5,4,7,8,1,2,3] => [4,1,1,1,1] => 3
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,2,6,5,7,4,8,3] => [6,5,7,4,8,1,2,3] => [4,1,1,1,1] => 3
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,6,5,7,8,4,3] => [6,5,7,8,4,1,2,3] => [4,1,1,1,1] => 3
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,6,5,8,7,4,3] => [6,8,5,7,4,1,2,3] => [4,1,1,1,1] => 3
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,2,6,7,5,4,8,3] => [6,7,5,4,8,1,2,3] => [4,1,1,1,1] => 3
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,2,6,7,5,8,4,3] => [6,7,5,8,4,1,2,3] => [4,1,1,1,1] => 3
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,6,7,8,5,4,3] => [6,7,8,5,4,1,2,3] => [4,1,1,1,1] => 3
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,7,6,5,4,3,8] => [7,6,5,4,1,2,3,8] => [5,1,1,1] => 4
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,7,6,5,4,8,3] => [7,6,5,4,8,1,2,3] => [5,1,1,1] => 4
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,7,6,5,8,4,3] => [7,6,5,8,4,1,2,3] => [5,1,1,1] => 4
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,7,6,8,5,4,3] => [7,6,8,5,4,1,2,3] => [5,1,1,1] => 4
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,7,8,6,5,4,3] => [7,8,6,5,4,1,2,3] => [5,1,1,1] => 4
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,7,6,5,4,3] => [8,7,6,5,4,1,2,3] => [6,1,1] => 5
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => [3,1,2,4,5,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,8,7] => [3,8,1,2,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => [3,7,1,2,4,5,6,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,7,8,6] => [3,7,8,1,2,4,5,6] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,8,7,6] => [8,3,7,1,2,4,5,6] => [3,1,1,1,1,1] => 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] => [3,6,1,2,4,5,7,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,2,4,6,5,8,7] => [3,6,8,1,2,4,5,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,3,2,4,6,7,5,8] => [3,6,7,1,2,4,5,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,2,4,6,7,8,5] => [3,6,7,8,1,2,4,5] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,2,4,7,6,5,8] => [7,3,6,1,2,4,5,8] => [3,1,1,1,1,1] => 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] => [8,7,3,6,1,2,4,5] => [4,1,1,1,1] => 3
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => [3,5,1,2,4,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => [3,5,7,1,2,4,6,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => [3,5,7,8,1,2,4,6] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,7,6] => [8,3,5,7,1,2,4,6] => [3,1,1,1,1,1] => 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] => [3,5,6,1,2,4,7,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,2,5,6,4,8,7] => [3,5,6,8,1,2,4,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,2,5,6,7,4,8] => [3,5,6,7,1,2,4,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,6,7,8,4] => [3,5,6,7,8,1,2,4] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,3,2,5,6,8,7,4] => [8,3,5,6,7,1,2,4] => [3,1,1,1,1,1] => 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] => [7,3,5,6,1,2,4,8] => [3,1,1,1,1,1] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,3,2,5,7,6,8,4] => [7,3,5,6,8,1,2,4] => [3,1,1,1,1,1] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,3,2,5,7,8,6,4] => [7,8,3,5,6,1,2,4] => [3,1,1,1,1,1] => 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] => [8,7,3,5,6,1,2,4] => [4,1,1,1,1] => 3
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,6,5,4,7,8] => [6,3,5,1,2,4,7,8] => [3,1,1,1,1,1] => 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] => [6,3,5,8,1,2,4,7] => [3,1,1,1,1,1] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,5,7,4,8] => [6,3,5,7,1,2,4,8] => [3,1,1,1,1,1] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,5,8,7,4] => [6,8,3,5,7,1,2,4] => [3,1,1,1,1,1] => 2
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,2,6,7,5,8,4] => [6,7,3,5,8,1,2,4] => [3,1,1,1,1,1] => 2
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,3,2,6,7,8,5,4] => [6,7,8,3,5,1,2,4] => [3,1,1,1,1,1] => 2
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2,6,8,7,5,4] => [8,6,7,3,5,1,2,4] => [4,1,1,1,1] => 3
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,6,5,4,8] => [7,6,3,5,1,2,4,8] => [4,1,1,1,1] => 3
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,7,6,5,8,4] => [7,6,3,5,8,1,2,4] => [4,1,1,1,1] => 3
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,7,6,8,5,4] => [7,6,8,3,5,1,2,4] => [4,1,1,1,1] => 3
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,3,2,7,8,6,5,4] => [7,8,6,3,5,1,2,4] => [4,1,1,1,1] => 3
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,7,6,5,4] => [8,7,6,3,5,1,2,4] => [5,1,1,1] => 4
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8] => [3,4,1,2,5,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,2,5,6,8,7] => [3,4,8,1,2,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,2,5,7,8,6] => [3,4,7,8,1,2,5,6] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7] => [3,4,6,8,1,2,5,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => [3,4,6,7,1,2,5,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4,2,6,7,8,5] => [3,4,6,7,8,1,2,5] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,3,4,2,7,6,5,8] => [7,3,4,6,1,2,5,8] => [3,1,1,1,1,1] => 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] => [7,3,4,6,8,1,2,5] => [3,1,1,1,1,1] => 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] => [8,7,3,4,6,1,2,5] => [4,1,1,1,1] => 3
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8] => [3,4,5,1,2,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,5,2,6,8,7] => [3,4,5,8,1,2,6,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6,8] => [3,4,5,7,1,2,6,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,5,2,7,8,6] => [3,4,5,7,8,1,2,6] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,5,2,8,7,6] => [8,3,4,5,7,1,2,6] => [3,1,1,1,1,1] => 2
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,2,7,8] => [3,4,5,6,1,2,7,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,2,8,7] => [3,4,5,6,8,1,2,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,2,8] => [3,4,5,6,7,1,2,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,2] => [3,4,5,6,7,8,1,2] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,8,7,2] => [8,3,4,5,6,7,1,2] => [3,1,1,1,1,1] => 2
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,5,7,6,8,2] => [7,3,4,5,6,8,1,2] => [3,1,1,1,1,1] => 2
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,5,7,8,6,2] => [7,8,3,4,5,6,1,2] => [3,1,1,1,1,1] => 2
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,5,8,7,6,2] => [8,7,3,4,5,6,1,2] => [4,1,1,1,1] => 3
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,3,4,6,5,2,8,7] => [6,3,4,5,8,1,2,7] => [3,1,1,1,1,1] => 2
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,3,4,6,5,7,2,8] => [6,3,4,5,7,1,2,8] => [3,1,1,1,1,1] => 2
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,4,6,5,7,8,2] => [6,3,4,5,7,8,1,2] => [3,1,1,1,1,1] => 2
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,3,4,6,5,8,7,2] => [6,8,3,4,5,7,1,2] => [3,1,1,1,1,1] => 2
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,3,4,6,7,5,2,8] => [6,7,3,4,5,1,2,8] => [3,1,1,1,1,1] => 2
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,6,7,8,5,2] => [6,7,8,3,4,5,1,2] => [3,1,1,1,1,1] => 2
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,3,4,6,8,7,5,2] => [8,6,7,3,4,5,1,2] => [4,1,1,1,1] => 3
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,4,7,6,5,8,2] => [7,6,3,4,5,8,1,2] => [4,1,1,1,1] => 3
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,8,7,6,5,2] => [8,7,6,3,4,5,1,2] => [5,1,1,1] => 4
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,3,5,4,2,6,7,8] => [5,3,4,1,2,6,7,8] => [3,1,1,1,1,1] => 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] => [5,3,4,7,1,2,6,8] => [3,1,1,1,1,1] => 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] => [5,3,4,7,8,1,2,6] => [3,1,1,1,1,1] => 2
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,3,5,4,6,7,8,2] => [5,3,4,6,7,8,1,2] => [3,1,1,1,1,1] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,3,5,4,7,6,2,8] => [5,7,3,4,6,1,2,8] => [3,1,1,1,1,1] => 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] => [5,7,3,4,6,8,1,2] => [3,1,1,1,1,1] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,3,5,4,7,8,6,2] => [5,7,8,3,4,6,1,2] => [3,1,1,1,1,1] => 2
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,3,5,6,4,2,7,8] => [5,6,3,4,1,2,7,8] => [3,1,1,1,1,1] => 2
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,3,5,6,4,7,8,2] => [5,6,3,4,7,8,1,2] => [3,1,1,1,1,1] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,5,6,7,8,4,2] => [5,6,7,8,3,4,1,2] => [3,1,1,1,1,1] => 2
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,3,5,6,8,7,4,2] => [8,5,6,7,3,4,1,2] => [4,1,1,1,1] => 3
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,3,5,7,6,4,2,8] => [7,5,6,3,4,1,2,8] => [4,1,1,1,1] => 3
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,3,5,7,6,4,8,2] => [7,5,6,3,4,8,1,2] => [4,1,1,1,1] => 3
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,3,5,7,6,8,4,2] => [7,5,6,8,3,4,1,2] => [4,1,1,1,1] => 3
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,5,7,8,6,4,2] => [7,8,5,6,3,4,1,2] => [4,1,1,1,1] => 3
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,3,5,8,7,6,4,2] => [8,7,5,6,3,4,1,2] => [5,1,1,1] => 4
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,6,5,7,8,4,2] => [6,5,7,8,3,4,1,2] => [4,1,1,1,1] => 3
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,3,6,5,8,7,4,2] => [6,8,5,7,3,4,1,2] => [4,1,1,1,1] => 3
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,3,6,7,5,8,4,2] => [6,7,5,8,3,4,1,2] => [4,1,1,1,1] => 3
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,6,7,8,5,4,2] => [6,7,8,5,3,4,1,2] => [4,1,1,1,1] => 3
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,3,7,6,5,4,2,8] => [7,6,5,3,4,1,2,8] => [5,1,1,1] => 4
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,3,7,6,5,8,4,2] => [7,6,5,8,3,4,1,2] => [5,1,1,1] => 4
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,7,6,8,5,4,2] => [7,6,8,5,3,4,1,2] => [5,1,1,1] => 4
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,7,8,6,5,4,2] => [7,8,6,5,3,4,1,2] => [5,1,1,1] => 4
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,8,7,6,5,4,2] => [8,7,6,5,3,4,1,2] => [6,1,1] => 5
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8] => [4,3,1,2,5,6,7,8] => [3,1,1,1,1,1] => 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] => [4,3,7,8,1,2,5,6] => [3,1,1,1,1,1] => 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] => [4,8,3,7,1,2,5,6] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,3,2,6,5,8,7] => [4,3,6,8,1,2,5,7] => [3,1,1,1,1,1] => 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] => [4,3,6,7,8,1,2,5] => [3,1,1,1,1,1] => 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] => [4,8,3,6,7,1,2,5] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => [4,7,3,6,1,2,5,8] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,4,3,2,7,6,8,5] => [4,7,3,6,8,1,2,5] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,3,2,8,7,6,5] => [8,4,7,3,6,1,2,5] => [4,1,1,1,1] => 3
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,4,3,5,2,6,7,8] => [4,3,5,1,2,6,7,8] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,3,5,2,7,6,8] => [4,3,5,7,1,2,6,8] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,4,3,5,2,8,7,6] => [4,8,3,5,7,1,2,6] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,3,5,6,2,7,8] => [4,3,5,6,1,2,7,8] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,4,3,5,6,7,2,8] => [4,3,5,6,7,1,2,8] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,2] => [4,3,5,6,7,8,1,2] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,4,3,5,6,8,7,2] => [4,8,3,5,6,7,1,2] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,3,5,7,6,2,8] => [4,7,3,5,6,1,2,8] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,3,5,7,8,6,2] => [4,7,8,3,5,6,1,2] => [3,1,1,1,1,1] => 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] => [4,6,3,5,1,2,7,8] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,3,6,5,7,2,8] => [4,6,3,5,7,1,2,8] => [3,1,1,1,1,1] => 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] => [4,6,8,3,5,7,1,2] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,4,3,6,7,5,8,2] => [4,6,7,3,5,8,1,2] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,3,6,7,8,5,2] => [4,6,7,8,3,5,1,2] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,3,7,6,8,5,2] => [7,4,6,8,3,5,1,2] => [4,1,1,1,1] => 3
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,3,7,8,6,5,2] => [7,8,4,6,3,5,1,2] => [4,1,1,1,1] => 3
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,3,8,7,6,5,2] => [8,7,4,6,3,5,1,2] => [5,1,1,1] => 4
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,4,5,3,2,7,6,8] => [4,5,3,7,1,2,6,8] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,4,5,3,2,7,8,6] => [4,5,3,7,8,1,2,6] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,4,5,3,2,8,7,6] => [4,5,8,3,7,1,2,6] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,4,5,3,6,7,8,2] => [4,5,3,6,7,8,1,2] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,4,5,3,6,8,7,2] => [4,5,8,3,6,7,1,2] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,4,5,3,8,7,6,2] => [8,4,5,7,3,6,1,2] => [4,1,1,1,1] => 3
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,4,5,6,3,7,8,2] => [4,5,6,3,7,8,1,2] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,7,3,2,8] => [4,5,6,7,3,1,2,8] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,7,3,8,2] => [4,5,6,7,3,8,1,2] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,8,3,2] => [4,5,6,7,8,3,1,2] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,4,5,7,6,3,2,8] => [7,4,5,6,3,1,2,8] => [4,1,1,1,1] => 3
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,4,6,5,3,2,7,8] => [6,4,5,3,1,2,7,8] => [4,1,1,1,1] => 3
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,4,6,5,3,7,2,8] => [6,4,5,3,7,1,2,8] => [4,1,1,1,1] => 3
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,4,6,5,3,8,7,2] => [6,4,5,8,3,7,1,2] => [4,1,1,1,1] => 3
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,4,6,7,5,3,8,2] => [6,7,4,5,3,8,1,2] => [4,1,1,1,1] => 3
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,4,6,7,5,8,3,2] => [6,7,4,5,8,3,1,2] => [4,1,1,1,1] => 3
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,4,6,7,8,5,3,2] => [6,7,8,4,5,3,1,2] => [4,1,1,1,1] => 3
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,4,6,8,7,5,3,2] => [8,6,7,4,5,3,1,2] => [5,1,1,1] => 4
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,4,7,6,5,3,2,8] => [7,6,4,5,3,1,2,8] => [5,1,1,1] => 4
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,4,7,6,5,8,3,2] => [7,6,4,5,8,3,1,2] => [5,1,1,1] => 4
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,4,7,8,6,5,3,2] => [7,8,6,4,5,3,1,2] => [5,1,1,1] => 4
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,4,8,7,6,5,3,2] => [8,7,6,4,5,3,1,2] => [6,1,1] => 5
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,5,4,3,2,6,7,8] => [5,4,3,1,2,6,7,8] => [4,1,1,1,1] => 3
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,5,4,3,2,7,8,6] => [5,4,3,7,8,1,2,6] => [4,1,1,1,1] => 3
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,4,3,2,8,7,6] => [5,4,8,3,7,1,2,6] => [4,1,1,1,1] => 3
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,5,4,3,6,2,7,8] => [5,4,3,6,1,2,7,8] => [4,1,1,1,1] => 3
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,4,3,6,7,8,2] => [5,4,3,6,7,8,1,2] => [4,1,1,1,1] => 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] => [5,4,8,3,6,7,1,2] => [4,1,1,1,1] => 3
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,5,4,3,7,6,8,2] => [5,4,7,3,6,8,1,2] => [4,1,1,1,1] => 3
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,5,4,3,7,8,6,2] => [5,4,7,8,3,6,1,2] => [4,1,1,1,1] => 3
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,5,4,3,8,7,6,2] => [5,8,4,7,3,6,1,2] => [4,1,1,1,1] => 3
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,5,4,6,3,7,8,2] => [5,4,6,3,7,8,1,2] => [4,1,1,1,1] => 3
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,5,4,6,7,3,2,8] => [5,4,6,7,3,1,2,8] => [4,1,1,1,1] => 3
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,5,4,6,7,3,8,2] => [5,4,6,7,3,8,1,2] => [4,1,1,1,1] => 3
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,5,4,6,7,8,3,2] => [5,4,6,7,8,3,1,2] => [4,1,1,1,1] => 3
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,5,4,7,6,3,8,2] => [5,7,4,6,3,8,1,2] => [4,1,1,1,1] => 3
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,5,6,4,3,8,7,2] => [5,6,4,8,3,7,1,2] => [4,1,1,1,1] => 3
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,5,6,4,7,3,8,2] => [5,6,4,7,3,8,1,2] => [4,1,1,1,1] => 3
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,5,6,4,7,8,3,2] => [5,6,4,7,8,3,1,2] => [4,1,1,1,1] => 3
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,5,6,7,4,3,8,2] => [5,6,7,4,3,8,1,2] => [4,1,1,1,1] => 3
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,5,6,7,8,4,3,2] => [5,6,7,8,4,3,1,2] => [4,1,1,1,1] => 3
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,5,7,6,4,3,2,8] => [7,5,6,4,3,1,2,8] => [5,1,1,1] => 4
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,5,7,6,8,4,3,2] => [7,5,6,8,4,3,1,2] => [5,1,1,1] => 4
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,5,7,8,6,4,3,2] => [7,8,5,6,4,3,1,2] => [5,1,1,1] => 4
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,5,8,7,6,4,3,2] => [8,7,5,6,4,3,1,2] => [6,1,1] => 5
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,6,5,4,3,2,7,8] => [6,5,4,3,1,2,7,8] => [5,1,1,1] => 4
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,5,4,3,2,8,7] => [6,5,4,3,8,1,2,7] => [5,1,1,1] => 4
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,6,5,4,3,7,2,8] => [6,5,4,3,7,1,2,8] => [5,1,1,1] => 4
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,6,5,4,3,7,8,2] => [6,5,4,3,7,8,1,2] => [5,1,1,1] => 4
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,5,4,3,8,7,2] => [6,5,4,8,3,7,1,2] => [5,1,1,1] => 4
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,6,5,4,7,3,8,2] => [6,5,4,7,3,8,1,2] => [5,1,1,1] => 4
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,6,5,4,7,8,3,2] => [6,5,4,7,8,3,1,2] => [5,1,1,1] => 4
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,5,7,4,3,8,2] => [6,5,7,4,3,8,1,2] => [5,1,1,1] => 4
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,6,5,7,4,8,3,2] => [6,5,7,4,8,3,1,2] => [5,1,1,1] => 4
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,6,5,7,8,4,3,2] => [6,5,7,8,4,3,1,2] => [5,1,1,1] => 4
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,6,7,5,4,3,2,8] => [6,7,5,4,3,1,2,8] => [5,1,1,1] => 4
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,6,7,5,8,4,3,2] => [6,7,5,8,4,3,1,2] => [5,1,1,1] => 4
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,6,7,8,5,4,3,2] => [6,7,8,5,4,3,1,2] => [5,1,1,1] => 4
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,6,8,7,5,4,3,2] => [8,6,7,5,4,3,1,2] => [6,1,1] => 5
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,6,5,4,3,2,8] => [7,6,5,4,3,1,2,8] => [6,1,1] => 5
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,6,5,4,3,8,2] => [7,6,5,4,3,8,1,2] => [6,1,1] => 5
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,7,6,5,4,8,3,2] => [7,6,5,4,8,3,1,2] => [6,1,1] => 5
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,7,6,5,8,4,3,2] => [7,6,5,8,4,3,1,2] => [6,1,1] => 5
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7,6,8,5,4,3,2] => [7,6,8,5,4,3,1,2] => [6,1,1] => 5
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,7,8,6,5,4,3,2] => [7,8,6,5,4,3,1,2] => [6,1,1] => 5
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => [8,7,6,5,4,3,1,2] => [7,1] => 6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => [2,8,1,3,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,7,6,8] => [2,7,1,3,4,5,6,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,7,8,6] => [2,7,8,1,3,4,5,6] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,4,6,5,7,8] => [2,6,1,3,4,5,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,4,6,5,8,7] => [2,6,8,1,3,4,5,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,4,6,7,5,8] => [2,6,7,1,3,4,5,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,4,6,7,8,5] => [2,6,7,8,1,3,4,5] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,4,6,8,7,5] => [8,2,6,7,1,3,4,5] => [3,1,1,1,1,1] => 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] => [8,7,2,6,1,3,4,5] => [4,1,1,1,1] => 3
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,3,5,4,6,7,8] => [2,5,1,3,4,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4,6,8,7] => [2,5,8,1,3,4,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,3,5,4,7,8,6] => [2,5,7,8,1,3,4,6] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,5,6,4,8,7] => [2,5,6,8,1,3,4,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,4] => [2,5,6,7,8,1,3,4] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,1,3,5,6,8,7,4] => [8,2,5,6,7,1,3,4] => [3,1,1,1,1,1] => 2
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,1,3,5,7,6,8,4] => [7,2,5,6,8,1,3,4] => [3,1,1,1,1,1] => 2
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,1,3,5,7,8,6,4] => [7,8,2,5,6,1,3,4] => [3,1,1,1,1,1] => 2
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,1,3,5,8,7,6,4] => [8,7,2,5,6,1,3,4] => [4,1,1,1,1] => 3
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,3,6,5,7,8,4] => [6,2,5,7,8,1,3,4] => [3,1,1,1,1,1] => 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] => [6,8,2,5,7,1,3,4] => [3,1,1,1,1,1] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,3,6,7,5,4,8] => [6,7,2,5,1,3,4,8] => [3,1,1,1,1,1] => 2
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,1,3,6,8,7,5,4] => [8,6,7,2,5,1,3,4] => [4,1,1,1,1] => 3
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,3,7,6,8,5,4] => [7,6,8,2,5,1,3,4] => [4,1,1,1,1] => 3
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,3,7,8,6,5,4] => [7,8,6,2,5,1,3,4] => [4,1,1,1,1] => 3
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,7,6,5,4] => [8,7,6,2,5,1,3,4] => [5,1,1,1] => 4
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => [2,4,1,3,5,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,3,5,6,8,7] => [2,4,8,1,3,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,3,5,7,8,6] => [2,4,7,8,1,3,5,6] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => [2,4,6,1,3,5,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => [2,4,6,8,1,3,5,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,3,6,7,5,8] => [2,4,6,7,1,3,5,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,5] => [2,4,6,7,8,1,3,5] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,7,5] => [8,2,4,6,7,1,3,5] => [3,1,1,1,1,1] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,4,3,7,6,5,8] => [7,2,4,6,1,3,5,8] => [3,1,1,1,1,1] => 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] => [7,2,4,6,8,1,3,5] => [3,1,1,1,1,1] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,7,8,6,5] => [7,8,2,4,6,1,3,5] => [3,1,1,1,1,1] => 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] => [8,7,2,4,6,1,3,5] => [4,1,1,1,1] => 3
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8] => [2,4,5,1,3,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3,7,8,6] => [2,4,5,7,8,1,3,6] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,1,4,5,6,3,7,8] => [2,4,5,6,1,3,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,4,5,6,3,8,7] => [2,4,5,6,8,1,3,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,3,8] => [2,4,5,6,7,1,3,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,3] => [2,4,5,6,7,8,1,3] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,1,4,5,7,6,8,3] => [7,2,4,5,6,8,1,3] => [3,1,1,1,1,1] => 2
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,4,5,7,8,6,3] => [7,8,2,4,5,6,1,3] => [3,1,1,1,1,1] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,4,6,5,3,7,8] => [6,2,4,5,1,3,7,8] => [3,1,1,1,1,1] => 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] => [6,2,4,5,8,1,3,7] => [3,1,1,1,1,1] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,1,4,6,5,7,8,3] => [6,2,4,5,7,8,1,3] => [3,1,1,1,1,1] => 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] => [6,8,2,4,5,7,1,3] => [3,1,1,1,1,1] => 2
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,1,4,6,8,7,5,3] => [8,6,7,2,4,5,1,3] => [4,1,1,1,1] => 3
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,1,4,7,6,5,8,3] => [7,6,2,4,5,8,1,3] => [4,1,1,1,1] => 3
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4,8,7,6,5,3] => [8,7,6,2,4,5,1,3] => [5,1,1,1] => 4
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,4,3,6,7,8] => [5,2,4,1,3,6,7,8] => [3,1,1,1,1,1] => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,5,4,3,6,8,7] => [5,2,4,8,1,3,6,7] => [3,1,1,1,1,1] => 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] => [5,2,4,7,1,3,6,8] => [3,1,1,1,1,1] => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,1,5,4,3,7,8,6] => [5,2,4,7,8,1,3,6] => [3,1,1,1,1,1] => 2
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,5,4,3,8,7,6] => [5,8,2,4,7,1,3,6] => [3,1,1,1,1,1] => 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] => [5,2,4,6,8,1,3,7] => [3,1,1,1,1,1] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,5,4,6,7,3,8] => [5,2,4,6,7,1,3,8] => [3,1,1,1,1,1] => 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] => [5,8,2,4,6,7,1,3] => [3,1,1,1,1,1] => 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] => [5,7,2,4,6,8,1,3] => [3,1,1,1,1,1] => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,5,6,4,3,8,7] => [5,6,2,4,8,1,3,7] => [3,1,1,1,1,1] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,1,5,6,4,7,8,3] => [5,6,2,4,7,8,1,3] => [3,1,1,1,1,1] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,1,5,6,7,8,4,3] => [5,6,7,8,2,4,1,3] => [3,1,1,1,1,1] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,1,5,7,6,8,4,3] => [7,5,6,8,2,4,1,3] => [4,1,1,1,1] => 3
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,5,7,8,6,4,3] => [7,8,5,6,2,4,1,3] => [4,1,1,1,1] => 3
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,1,5,8,7,6,4,3] => [8,7,5,6,2,4,1,3] => [5,1,1,1] => 4
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => [6,5,2,4,8,1,3,7] => [4,1,1,1,1] => 3
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,1,6,5,4,7,3,8] => [6,5,2,4,7,1,3,8] => [4,1,1,1,1] => 3
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,1,6,5,4,7,8,3] => [6,5,2,4,7,8,1,3] => [4,1,1,1,1] => 3
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,6,5,7,4,8,3] => [6,5,7,2,4,8,1,3] => [4,1,1,1,1] => 3
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,6,5,7,8,4,3] => [6,5,7,8,2,4,1,3] => [4,1,1,1,1] => 3
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,6,5,8,7,4,3] => [6,8,5,7,2,4,1,3] => [4,1,1,1,1] => 3
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,1,6,7,5,8,4,3] => [6,7,5,8,2,4,1,3] => [4,1,1,1,1] => 3
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,6,7,8,5,4,3] => [6,7,8,5,2,4,1,3] => [4,1,1,1,1] => 3
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,7,6,5,4,8,3] => [7,6,5,2,4,8,1,3] => [5,1,1,1] => 4
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,7,6,5,8,4,3] => [7,6,5,8,2,4,1,3] => [5,1,1,1] => 4
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,7,6,8,5,4,3] => [7,6,8,5,2,4,1,3] => [5,1,1,1] => 4
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => [8,7,6,5,2,4,1,3] => [6,1,1] => 5
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8] => [2,3,1,4,5,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,8,7] => [2,3,8,1,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,3,1,4,5,7,6,8] => [2,3,7,1,4,5,6,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => [2,3,7,8,1,4,5,6] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,3,1,4,5,8,7,6] => [8,2,3,7,1,4,5,6] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,3,1,4,6,5,7,8] => [2,3,6,1,4,5,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,4,6,5,8,7] => [2,3,6,8,1,4,5,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,3,1,4,6,7,5,8] => [2,3,6,7,1,4,5,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,1,4,6,7,8,5] => [2,3,6,7,8,1,4,5] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,3,1,4,6,8,7,5] => [8,2,3,6,7,1,4,5] => [3,1,1,1,1,1] => 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] => [7,2,3,6,8,1,4,5] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,3,1,4,7,8,6,5] => [7,8,2,3,6,1,4,5] => [3,1,1,1,1,1] => 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] => [8,7,2,3,6,1,4,5] => [4,1,1,1,1] => 3
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8] => [2,3,5,1,4,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,8] => [2,3,5,7,1,4,6,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,3,1,5,4,7,8,6] => [2,3,5,7,8,1,4,6] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,5,6,4,7,8] => [2,3,5,6,1,4,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,6,4,8,7] => [2,3,5,6,8,1,4,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,3,1,5,6,7,4,8] => [2,3,5,6,7,1,4,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,4] => [2,3,5,6,7,8,1,4] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,3,1,5,6,8,7,4] => [8,2,3,5,6,7,1,4] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,3,1,5,7,8,6,4] => [7,8,2,3,5,6,1,4] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,5,7,4,8] => [6,2,3,5,7,1,4,8] => [3,1,1,1,1,1] => 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] => [6,8,2,3,5,7,1,4] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,3,1,7,6,5,4,8] => [7,6,2,3,5,1,4,8] => [4,1,1,1,1] => 3
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,7,6,5,8,4] => [7,6,2,3,5,8,1,4] => [4,1,1,1,1] => 3
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,3,1,7,6,8,5,4] => [7,6,8,2,3,5,1,4] => [4,1,1,1,1] => 3
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,1,7,8,6,5,4] => [7,8,6,2,3,5,1,4] => [4,1,1,1,1] => 3
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8] => [2,3,4,1,5,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5,6,8,7] => [2,3,4,8,1,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,4,1,5,7,6,8] => [2,3,4,7,1,5,6,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,4,1,5,7,8,6] => [2,3,4,7,8,1,5,6] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,5,7,8] => [2,3,4,6,1,5,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7] => [2,3,4,6,8,1,5,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,4,1,6,7,5,8] => [2,3,4,6,7,1,5,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => [2,3,4,6,7,8,1,5] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,4,1,6,8,7,5] => [8,2,3,4,6,7,1,5] => [3,1,1,1,1,1] => 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] => [7,2,3,4,6,8,1,5] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,4,1,7,8,6,5] => [7,8,2,3,4,6,1,5] => [3,1,1,1,1,1] => 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] => [8,7,2,3,4,6,1,5] => [4,1,1,1,1] => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => [2,3,4,5,1,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,5,1,6,8,7] => [2,3,4,5,8,1,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,8] => [2,3,4,5,7,1,6,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,1,7,8,6] => [2,3,4,5,7,8,1,6] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,8,7,6] => [8,2,3,4,5,7,1,6] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => [2,3,4,5,6,1,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => [2,3,4,5,6,8,1,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => [2,3,4,5,6,7,1,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => [2,3,4,5,6,7,8,1] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,8,7,1] => [8,2,3,4,5,6,7,1] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,7,6,1,8] => [7,2,3,4,5,6,1,8] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,7,6,8,1] => [7,2,3,4,5,6,8,1] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,7,8,6,1] => [7,8,2,3,4,5,6,1] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,8,7,6,1] => [8,7,2,3,4,5,6,1] => [4,1,1,1,1] => 3
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,6,5,1,7,8] => [6,2,3,4,5,1,7,8] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,4,6,5,1,8,7] => [6,2,3,4,5,8,1,7] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,4,6,5,7,1,8] => [6,2,3,4,5,7,1,8] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,4,6,5,7,8,1] => [6,2,3,4,5,7,8,1] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,4,6,7,5,1,8] => [6,7,2,3,4,5,1,8] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,4,6,7,5,8,1] => [6,7,2,3,4,5,8,1] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,6,7,8,5,1] => [6,7,8,2,3,4,5,1] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,4,6,8,7,5,1] => [8,6,7,2,3,4,5,1] => [4,1,1,1,1] => 3
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,4,7,6,5,1,8] => [7,6,2,3,4,5,1,8] => [4,1,1,1,1] => 3
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,4,7,6,5,8,1] => [7,6,2,3,4,5,8,1] => [4,1,1,1,1] => 3
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,7,6,8,5,1] => [7,6,8,2,3,4,5,1] => [4,1,1,1,1] => 3
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,7,8,6,5,1] => [7,8,6,2,3,4,5,1] => [4,1,1,1,1] => 3
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,8,7,6,5,1] => [8,7,6,2,3,4,5,1] => [5,1,1,1] => 4
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,5,4,1,6,7,8] => [5,2,3,4,1,6,7,8] => [3,1,1,1,1,1] => 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] => [5,2,3,4,8,1,6,7] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,4,1,7,6,8] => [5,2,3,4,7,1,6,8] => [3,1,1,1,1,1] => 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] => [5,8,2,3,4,7,1,6] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,3,5,4,6,1,7,8] => [5,2,3,4,6,1,7,8] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,3,5,4,6,7,1,8] => [5,2,3,4,6,7,1,8] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,5,4,6,7,8,1] => [5,2,3,4,6,7,8,1] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,3,5,4,7,6,8,1] => [5,7,2,3,4,6,8,1] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,3,5,6,4,1,7,8] => [5,6,2,3,4,1,7,8] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,3,5,6,4,8,7,1] => [5,6,8,2,3,4,7,1] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,3,5,6,7,4,1,8] => [5,6,7,2,3,4,1,8] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,3,5,6,7,4,8,1] => [5,6,7,2,3,4,8,1] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,5,6,7,8,4,1] => [5,6,7,8,2,3,4,1] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,3,5,6,8,7,4,1] => [8,5,6,7,2,3,4,1] => [4,1,1,1,1] => 3
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,3,5,7,6,4,8,1] => [7,5,6,2,3,4,8,1] => [4,1,1,1,1] => 3
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,3,5,7,8,6,4,1] => [7,8,5,6,2,3,4,1] => [4,1,1,1,1] => 3
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,3,5,8,7,6,4,1] => [8,7,5,6,2,3,4,1] => [5,1,1,1] => 4
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,3,6,5,4,1,7,8] => [6,5,2,3,4,1,7,8] => [4,1,1,1,1] => 3
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,6,5,4,1,8,7] => [6,5,2,3,4,8,1,7] => [4,1,1,1,1] => 3
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,3,6,5,4,7,8,1] => [6,5,2,3,4,7,8,1] => [4,1,1,1,1] => 3
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,3,6,5,7,8,4,1] => [6,5,7,8,2,3,4,1] => [4,1,1,1,1] => 3
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,3,6,7,5,8,4,1] => [6,7,5,8,2,3,4,1] => [4,1,1,1,1] => 3
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,6,7,8,5,4,1] => [6,7,8,5,2,3,4,1] => [4,1,1,1,1] => 3
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,3,6,8,7,5,4,1] => [8,6,7,5,2,3,4,1] => [5,1,1,1] => 4
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,3,7,6,5,4,1,8] => [7,6,5,2,3,4,1,8] => [5,1,1,1] => 4
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,3,7,6,5,4,8,1] => [7,6,5,2,3,4,8,1] => [5,1,1,1] => 4
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,3,7,6,5,8,4,1] => [7,6,5,8,2,3,4,1] => [5,1,1,1] => 4
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,3,7,6,8,5,4,1] => [7,6,8,5,2,3,4,1] => [5,1,1,1] => 4
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,8,7,6,5,4,1] => [8,7,6,5,2,3,4,1] => [6,1,1] => 5
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8] => [4,2,3,1,5,6,7,8] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [2,4,3,1,5,6,8,7] => [4,2,3,8,1,5,6,7] => [3,1,1,1,1,1] => 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] => [4,2,3,6,8,1,5,7] => [3,1,1,1,1,1] => 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] => [4,2,3,6,7,8,1,5] => [3,1,1,1,1,1] => 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] => [4,8,2,3,6,7,1,5] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,3,1,7,6,8,5] => [4,7,2,3,6,8,1,5] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,4,3,1,8,7,6,5] => [8,4,7,2,3,6,1,5] => [4,1,1,1,1] => 3
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,4,3,5,1,6,7,8] => [4,2,3,5,1,6,7,8] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,4,3,5,1,6,8,7] => [4,2,3,5,8,1,6,7] => [3,1,1,1,1,1] => 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] => [4,8,2,3,5,7,1,6] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [2,4,3,5,6,1,7,8] => [4,2,3,5,6,1,7,8] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,4,3,5,6,1,8,7] => [4,2,3,5,6,8,1,7] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,4,3,5,6,7,1,8] => [4,2,3,5,6,7,1,8] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,8,1] => [4,2,3,5,6,7,8,1] => [3,1,1,1,1,1] => 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] => [4,8,2,3,5,6,7,1] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [2,4,3,5,7,6,1,8] => [4,7,2,3,5,6,1,8] => [3,1,1,1,1,1] => 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] => [4,6,2,3,5,1,7,8] => [3,1,1,1,1,1] => 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] => [4,6,2,3,5,8,1,7] => [3,1,1,1,1,1] => 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] => [4,6,2,3,5,7,1,8] => [3,1,1,1,1,1] => 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] => [4,6,8,2,3,5,7,1] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,4,3,6,7,5,8,1] => [4,6,7,2,3,5,8,1] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,4,3,6,7,8,5,1] => [4,6,7,8,2,3,5,1] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,4,3,6,8,7,5,1] => [8,4,6,7,2,3,5,1] => [4,1,1,1,1] => 3
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [2,4,3,7,6,5,1,8] => [7,4,6,2,3,5,1,8] => [4,1,1,1,1] => 3
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,4,3,7,6,5,8,1] => [7,4,6,2,3,5,8,1] => [4,1,1,1,1] => 3
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,4,5,3,1,6,7,8] => [4,5,2,3,1,6,7,8] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,4,5,3,1,8,7,6] => [4,5,8,2,3,7,1,6] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,4,5,3,6,7,1,8] => [4,5,2,3,6,7,1,8] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,4,5,3,6,7,8,1] => [4,5,2,3,6,7,8,1] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,4,5,3,6,8,7,1] => [4,5,8,2,3,6,7,1] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [2,4,5,3,7,6,8,1] => [4,5,7,2,3,6,8,1] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [2,4,5,6,3,1,8,7] => [4,5,6,2,3,8,1,7] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,4,5,6,3,7,8,1] => [4,5,6,2,3,7,8,1] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,4,5,6,3,8,7,1] => [4,5,6,8,2,3,7,1] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,7,3,1,8] => [4,5,6,7,2,3,1,8] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,7,3,8,1] => [4,5,6,7,2,3,8,1] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,8,3,1] => [4,5,6,7,8,2,3,1] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [2,4,5,6,8,7,3,1] => [8,4,5,6,7,2,3,1] => [4,1,1,1,1] => 3
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [2,4,5,7,6,3,1,8] => [7,4,5,6,2,3,1,8] => [4,1,1,1,1] => 3
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [2,4,5,7,6,3,8,1] => [7,4,5,6,2,3,8,1] => [4,1,1,1,1] => 3
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [2,4,5,7,8,6,3,1] => [7,8,4,5,6,2,3,1] => [4,1,1,1,1] => 3
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,4,6,5,3,1,8,7] => [6,4,5,2,3,8,1,7] => [4,1,1,1,1] => 3
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,4,6,5,3,7,8,1] => [6,4,5,2,3,7,8,1] => [4,1,1,1,1] => 3
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,4,6,5,3,8,7,1] => [6,4,5,8,2,3,7,1] => [4,1,1,1,1] => 3
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,4,6,5,7,3,8,1] => [6,4,5,7,2,3,8,1] => [4,1,1,1,1] => 3
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,4,6,5,8,7,3,1] => [6,8,4,5,7,2,3,1] => [4,1,1,1,1] => 3
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [2,4,6,7,5,3,1,8] => [6,7,4,5,2,3,1,8] => [4,1,1,1,1] => 3
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,4,6,7,5,3,8,1] => [6,7,4,5,2,3,8,1] => [4,1,1,1,1] => 3
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,4,6,7,8,5,3,1] => [6,7,8,4,5,2,3,1] => [4,1,1,1,1] => 3
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,4,6,8,7,5,3,1] => [8,6,7,4,5,2,3,1] => [5,1,1,1] => 4
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [2,4,7,6,5,3,1,8] => [7,6,4,5,2,3,1,8] => [5,1,1,1] => 4
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [2,4,7,6,5,3,8,1] => [7,6,4,5,2,3,8,1] => [5,1,1,1] => 4
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,4,8,7,6,5,3,1] => [8,7,6,4,5,2,3,1] => [6,1,1] => 5
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,5,4,3,1,6,7,8] => [5,4,2,3,1,6,7,8] => [4,1,1,1,1] => 3
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,5,4,3,1,6,8,7] => [5,4,2,3,8,1,6,7] => [4,1,1,1,1] => 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] => [5,4,2,3,6,8,1,7] => [4,1,1,1,1] => 3
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,5,4,3,6,7,1,8] => [5,4,2,3,6,7,1,8] => [4,1,1,1,1] => 3
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,5,4,3,6,7,8,1] => [5,4,2,3,6,7,8,1] => [4,1,1,1,1] => 3
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,5,4,3,6,8,7,1] => [5,4,8,2,3,6,7,1] => [4,1,1,1,1] => 3
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,5,4,3,7,6,8,1] => [5,4,7,2,3,6,8,1] => [4,1,1,1,1] => 3
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,5,4,3,7,8,6,1] => [5,4,7,8,2,3,6,1] => [4,1,1,1,1] => 3
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,5,4,3,8,7,6,1] => [5,8,4,7,2,3,6,1] => [4,1,1,1,1] => 3
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,5,4,6,3,1,7,8] => [5,4,6,2,3,1,7,8] => [4,1,1,1,1] => 3
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,5,4,6,3,7,1,8] => [5,4,6,2,3,7,1,8] => [4,1,1,1,1] => 3
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,5,4,6,7,3,1,8] => [5,4,6,7,2,3,1,8] => [4,1,1,1,1] => 3
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,5,4,6,7,3,8,1] => [5,4,6,7,2,3,8,1] => [4,1,1,1,1] => 3
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,5,4,7,6,3,1,8] => [5,7,4,6,2,3,1,8] => [4,1,1,1,1] => 3
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,5,4,8,7,6,3,1] => [8,5,7,4,6,2,3,1] => [5,1,1,1] => 4
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [2,5,6,4,7,3,1,8] => [5,6,4,7,2,3,1,8] => [4,1,1,1,1] => 3
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [2,5,6,4,7,3,8,1] => [5,6,4,7,2,3,8,1] => [4,1,1,1,1] => 3
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,5,6,7,4,3,8,1] => [5,6,7,4,2,3,8,1] => [4,1,1,1,1] => 3
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,5,6,7,8,4,3,1] => [5,6,7,8,4,2,3,1] => [4,1,1,1,1] => 3
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,5,6,8,7,4,3,1] => [8,5,6,7,4,2,3,1] => [5,1,1,1] => 4
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [2,5,7,6,4,3,1,8] => [7,5,6,4,2,3,1,8] => [5,1,1,1] => 4
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [2,5,7,6,4,3,8,1] => [7,5,6,4,2,3,8,1] => [5,1,1,1] => 4
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [2,5,7,6,4,8,3,1] => [7,5,6,4,8,2,3,1] => [5,1,1,1] => 4
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [2,5,7,6,8,4,3,1] => [7,5,6,8,4,2,3,1] => [5,1,1,1] => 4
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,6,5,4,3,7,8,1] => [6,5,4,2,3,7,8,1] => [5,1,1,1] => 4
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,6,5,4,8,7,3,1] => [6,5,8,4,7,2,3,1] => [5,1,1,1] => 4
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,6,5,7,4,3,8,1] => [6,5,7,4,2,3,8,1] => [5,1,1,1] => 4
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [2,6,5,7,4,8,3,1] => [6,5,7,4,8,2,3,1] => [5,1,1,1] => 4
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,6,5,8,7,4,3,1] => [6,8,5,7,4,2,3,1] => [5,1,1,1] => 4
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,6,7,5,4,3,1,8] => [6,7,5,4,2,3,1,8] => [5,1,1,1] => 4
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,6,8,7,5,4,3,1] => [8,6,7,5,4,2,3,1] => [6,1,1] => 5
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,7,6,5,4,3,1,8] => [7,6,5,4,2,3,1,8] => [6,1,1] => 5
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,7,6,5,4,3,8,1] => [7,6,5,4,2,3,8,1] => [6,1,1] => 5
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,7,6,5,4,8,3,1] => [7,6,5,4,8,2,3,1] => [6,1,1] => 5
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,7,6,5,8,4,3,1] => [7,6,5,8,4,2,3,1] => [6,1,1] => 5
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,7,6,8,5,4,3,1] => [7,6,8,5,4,2,3,1] => [6,1,1] => 5
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,7,8,6,5,4,3,1] => [7,8,6,5,4,2,3,1] => [6,1,1] => 5
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,8,7,6,5,4,3,1] => [8,7,6,5,4,2,3,1] => [7,1] => 6
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8] => [3,2,1,4,5,6,7,8] => [3,1,1,1,1,1] => 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] => [3,2,8,1,4,5,6,7] => [3,1,1,1,1,1] => 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] => [3,2,7,8,1,4,5,6] => [3,1,1,1,1,1] => 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] => [3,8,2,7,1,4,5,6] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [3,2,1,4,6,5,7,8] => [3,2,6,1,4,5,7,8] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,2,1,4,6,7,8,5] => [3,2,6,7,8,1,4,5] => [3,1,1,1,1,1] => 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] => [3,8,2,6,7,1,4,5] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,2,1,4,7,6,5,8] => [3,7,2,6,1,4,5,8] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [3,2,1,4,7,6,8,5] => [3,7,2,6,8,1,4,5] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,2,1,4,7,8,6,5] => [3,7,8,2,6,1,4,5] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,2,1,4,8,7,6,5] => [8,3,7,2,6,1,4,5] => [4,1,1,1,1] => 3
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,5,4,6,7,8] => [3,2,5,1,4,6,7,8] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,1,5,4,7,6,8] => [3,2,5,7,1,4,6,8] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [3,2,1,5,4,8,7,6] => [3,8,2,5,7,1,4,6] => [3,1,1,1,1,1] => 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] => [3,2,5,6,1,4,7,8] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [3,2,1,5,6,4,8,7] => [3,2,5,6,8,1,4,7] => [3,1,1,1,1,1] => 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] => [3,2,5,6,7,8,1,4] => [3,1,1,1,1,1] => 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] => [3,8,2,5,6,7,1,4] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,2,1,5,7,8,6,4] => [3,7,8,2,5,6,1,4] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,2,1,5,8,7,6,4] => [8,3,7,2,5,6,1,4] => [4,1,1,1,1] => 3
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [3,2,1,6,5,4,7,8] => [3,6,2,5,1,4,7,8] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,2,1,6,5,4,8,7] => [3,6,2,5,8,1,4,7] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,2,1,6,5,7,8,4] => [3,6,2,5,7,8,1,4] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,2,1,6,5,8,7,4] => [3,6,8,2,5,7,1,4] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [3,2,1,6,7,5,4,8] => [3,6,7,2,5,1,4,8] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,2,1,6,7,5,8,4] => [3,6,7,2,5,8,1,4] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,2,1,7,6,5,4,8] => [7,3,6,2,5,1,4,8] => [4,1,1,1,1] => 3
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,1,7,8,6,5,4] => [7,8,3,6,2,5,1,4] => [4,1,1,1,1] => 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] => [8,7,3,6,2,5,1,4] => [5,1,1,1] => 4
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8] => [3,2,4,1,5,6,7,8] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [3,2,4,1,5,6,8,7] => [3,2,4,8,1,5,6,7] => [3,1,1,1,1,1] => 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] => [3,2,4,7,8,1,5,6] => [3,1,1,1,1,1] => 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] => [3,8,2,4,7,1,5,6] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [3,2,4,1,6,5,7,8] => [3,2,4,6,1,5,7,8] => [3,1,1,1,1,1] => 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] => [3,2,4,6,8,1,5,7] => [3,1,1,1,1,1] => 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] => [3,2,4,6,7,8,1,5] => [3,1,1,1,1,1] => 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] => [3,8,2,4,6,7,1,5] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,7,6,8,5] => [3,7,2,4,6,8,1,5] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,2,4,1,7,8,6,5] => [3,7,8,2,4,6,1,5] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,2,4,1,8,7,6,5] => [8,3,7,2,4,6,1,5] => [4,1,1,1,1] => 3
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,2,4,5,1,6,7,8] => [3,2,4,5,1,6,7,8] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [3,2,4,5,1,6,8,7] => [3,2,4,5,8,1,6,7] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,6,1,7,8] => [3,2,4,5,6,1,7,8] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,1,8] => [3,2,4,5,6,7,1,8] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,1] => [3,2,4,5,6,7,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,6,8,7,1] => [3,8,2,4,5,6,7,1] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [3,2,4,5,7,6,1,8] => [3,7,2,4,5,6,1,8] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [3,2,4,6,5,7,1,8] => [3,6,2,4,5,7,1,8] => [3,1,1,1,1,1] => 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] => [3,6,8,2,4,5,7,1] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [3,2,4,6,7,5,8,1] => [3,6,7,2,4,5,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [3,2,4,7,6,5,8,1] => [7,3,6,2,4,5,8,1] => [4,1,1,1,1] => 3
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [3,2,4,7,6,8,5,1] => [7,3,6,8,2,4,5,1] => [4,1,1,1,1] => 3
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,7,8,6,5,1] => [7,8,3,6,2,4,5,1] => [4,1,1,1,1] => 3
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [3,2,5,4,1,6,7,8] => [3,5,2,4,1,6,7,8] => [3,1,1,1,1,1] => 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] => [3,5,2,4,8,1,6,7] => [3,1,1,1,1,1] => 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] => [3,5,2,4,7,1,6,8] => [3,1,1,1,1,1] => 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] => [3,5,8,2,4,7,1,6] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,6,1,8,7] => [3,5,2,4,6,8,1,7] => [3,1,1,1,1,1] => 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] => [3,5,2,4,6,7,8,1] => [3,1,1,1,1,1] => 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] => [3,5,8,2,4,6,7,1] => [3,1,1,1,1,1] => 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] => [3,5,7,2,4,6,1,8] => [3,1,1,1,1,1] => 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] => [3,5,7,2,4,6,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,4,7,8,6,1] => [3,5,7,8,2,4,6,1] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [3,2,5,6,4,1,8,7] => [3,5,6,2,4,8,1,7] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [3,2,5,6,4,7,8,1] => [3,5,6,2,4,7,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [3,2,5,6,7,4,1,8] => [3,5,6,7,2,4,1,8] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [3,2,5,6,7,4,8,1] => [3,5,6,7,2,4,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [3,2,5,6,7,8,4,1] => [3,5,6,7,8,2,4,1] => [3,1,1,1,1,1] => 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] => [6,3,5,2,4,8,1,7] => [4,1,1,1,1] => 3
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,2,6,5,4,8,7,1] => [6,3,5,8,2,4,7,1] => [4,1,1,1,1] => 3
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,2,6,5,7,4,8,1] => [6,3,5,7,2,4,8,1] => [4,1,1,1,1] => 3
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [3,2,6,5,7,8,4,1] => [6,3,5,7,8,2,4,1] => [4,1,1,1,1] => 3
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [3,2,6,5,8,7,4,1] => [6,8,3,5,7,2,4,1] => [4,1,1,1,1] => 3
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,2,6,7,5,4,1,8] => [6,7,3,5,2,4,1,8] => [4,1,1,1,1] => 3
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [3,2,6,7,5,4,8,1] => [6,7,3,5,2,4,8,1] => [4,1,1,1,1] => 3
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,2,6,8,7,5,4,1] => [8,6,7,3,5,2,4,1] => [5,1,1,1] => 4
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,2,7,6,5,4,1,8] => [7,6,3,5,2,4,1,8] => [5,1,1,1] => 4
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [3,2,7,6,5,4,8,1] => [7,6,3,5,2,4,8,1] => [5,1,1,1] => 4
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [3,2,7,6,5,8,4,1] => [7,6,3,5,8,2,4,1] => [5,1,1,1] => 4
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [3,2,7,6,8,5,4,1] => [7,6,8,3,5,2,4,1] => [5,1,1,1] => 4
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,2,8,7,6,5,4,1] => [8,7,6,3,5,2,4,1] => [6,1,1] => 5
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7,8] => [3,4,2,1,5,6,7,8] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [3,4,2,1,5,6,8,7] => [3,4,2,8,1,5,6,7] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [3,4,2,1,5,7,6,8] => [3,4,2,7,1,5,6,8] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [3,4,2,1,5,7,8,6] => [3,4,2,7,8,1,5,6] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [3,4,2,1,5,8,7,6] => [3,4,8,2,7,1,5,6] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [3,4,2,1,6,5,8,7] => [3,4,2,6,8,1,5,7] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [3,4,2,1,6,7,8,5] => [3,4,2,6,7,8,1,5] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [3,4,2,1,6,8,7,5] => [3,4,8,2,6,7,1,5] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [3,4,2,1,7,8,6,5] => [3,4,7,8,2,6,1,5] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [3,4,2,1,8,7,6,5] => [8,3,4,7,2,6,1,5] => [4,1,1,1,1] => 3
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [3,4,2,5,1,6,7,8] => [3,4,2,5,1,6,7,8] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [3,4,2,5,6,1,7,8] => [3,4,2,5,6,1,7,8] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [3,4,2,5,6,1,8,7] => [3,4,2,5,6,8,1,7] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [3,4,2,5,6,7,1,8] => [3,4,2,5,6,7,1,8] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,8,1] => [3,4,2,5,6,7,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [3,4,2,5,6,8,7,1] => [3,4,8,2,5,6,7,1] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [3,4,2,5,7,6,8,1] => [3,4,7,2,5,6,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [3,4,2,5,7,8,6,1] => [3,4,7,8,2,5,6,1] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [3,4,2,5,8,7,6,1] => [8,3,4,7,2,5,6,1] => [4,1,1,1,1] => 3
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [3,4,2,6,5,1,7,8] => [3,4,6,2,5,1,7,8] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [3,4,2,6,5,7,1,8] => [3,4,6,2,5,7,1,8] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [3,4,2,6,5,8,7,1] => [3,4,6,8,2,5,7,1] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [3,4,2,6,7,5,8,1] => [3,4,6,7,2,5,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [3,4,2,6,7,8,5,1] => [3,4,6,7,8,2,5,1] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,5,2,1,6,7,8] => [3,4,5,2,1,6,7,8] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [3,4,5,2,1,7,6,8] => [3,4,5,2,7,1,6,8] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,5,2,1,7,8,6] => [3,4,5,2,7,8,1,6] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,5,2,1,8,7,6] => [3,4,5,8,2,7,1,6] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,5,2,6,1,7,8] => [3,4,5,2,6,1,7,8] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,5,2,6,7,8,1] => [3,4,5,2,6,7,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [3,4,5,2,6,8,7,1] => [3,4,5,8,2,6,7,1] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [3,4,5,2,7,6,8,1] => [3,4,5,7,2,6,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,5,2,7,8,6,1] => [3,4,5,7,8,2,6,1] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,6,2,7,1,8] => [3,4,5,6,2,7,1,8] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,6,2,7,8,1] => [3,4,5,6,2,7,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,6,2,8,7,1] => [3,4,5,6,8,2,7,1] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,7,2,1,8] => [3,4,5,6,7,2,1,8] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,7,2,8,1] => [3,4,5,6,7,2,8,1] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,2,1] => [3,4,5,6,7,8,2,1] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,6,8,7,2,1] => [8,3,4,5,6,7,2,1] => [4,1,1,1,1] => 3
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,5,7,6,8,2,1] => [7,3,4,5,6,8,2,1] => [4,1,1,1,1] => 3
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,5,7,8,6,2,1] => [7,8,3,4,5,6,2,1] => [4,1,1,1,1] => 3
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,8,7,6,2,1] => [8,7,3,4,5,6,2,1] => [5,1,1,1] => 4
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [3,4,6,5,2,7,1,8] => [6,3,4,5,2,7,1,8] => [4,1,1,1,1] => 3
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [3,4,6,5,7,2,8,1] => [6,3,4,5,7,2,8,1] => [4,1,1,1,1] => 3
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [3,4,6,5,7,8,2,1] => [6,3,4,5,7,8,2,1] => [4,1,1,1,1] => 3
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [3,4,6,5,8,7,2,1] => [6,8,3,4,5,7,2,1] => [4,1,1,1,1] => 3
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [3,4,6,7,8,5,2,1] => [6,7,8,3,4,5,2,1] => [4,1,1,1,1] => 3
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,4,6,8,7,5,2,1] => [8,6,7,3,4,5,2,1] => [5,1,1,1] => 4
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [3,4,7,6,5,2,1,8] => [7,6,3,4,5,2,1,8] => [5,1,1,1] => 4
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [3,4,7,6,5,2,8,1] => [7,6,3,4,5,2,8,1] => [5,1,1,1] => 4
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [3,4,7,6,5,8,2,1] => [7,6,3,4,5,8,2,1] => [5,1,1,1] => 4
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [3,4,7,6,8,5,2,1] => [7,6,8,3,4,5,2,1] => [5,1,1,1] => 4
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,4,7,8,6,5,2,1] => [7,8,6,3,4,5,2,1] => [5,1,1,1] => 4
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,8,7,6,5,2,1] => [8,7,6,3,4,5,2,1] => [6,1,1] => 5
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [3,5,4,2,1,6,7,8] => [5,3,4,2,1,6,7,8] => [4,1,1,1,1] => 3
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [3,5,4,2,1,7,6,8] => [5,3,4,2,7,1,6,8] => [4,1,1,1,1] => 3
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [3,5,4,2,6,8,7,1] => [5,3,4,8,2,6,7,1] => [4,1,1,1,1] => 3
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [3,5,4,2,7,6,1,8] => [5,3,4,7,2,6,1,8] => [4,1,1,1,1] => 3
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [3,5,4,6,2,1,8,7] => [5,3,4,6,2,8,1,7] => [4,1,1,1,1] => 3
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [3,5,4,6,2,7,1,8] => [5,3,4,6,2,7,1,8] => [4,1,1,1,1] => 3
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [3,5,4,6,2,8,7,1] => [5,3,4,6,8,2,7,1] => [4,1,1,1,1] => 3
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [3,5,4,6,8,7,2,1] => [5,8,3,4,6,7,2,1] => [4,1,1,1,1] => 3
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [3,5,4,7,6,2,8,1] => [5,7,3,4,6,2,8,1] => [4,1,1,1,1] => 3
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [3,5,4,7,6,8,2,1] => [5,7,3,4,6,8,2,1] => [4,1,1,1,1] => 3
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [3,5,4,7,8,6,2,1] => [5,7,8,3,4,6,2,1] => [4,1,1,1,1] => 3
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,5,4,8,7,6,2,1] => [8,5,7,3,4,6,2,1] => [5,1,1,1] => 4
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [3,5,6,4,2,1,7,8] => [5,6,3,4,2,1,7,8] => [4,1,1,1,1] => 3
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [3,5,6,4,2,1,8,7] => [5,6,3,4,2,8,1,7] => [4,1,1,1,1] => 3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [3,5,6,4,2,7,1,8] => [5,6,3,4,2,7,1,8] => [4,1,1,1,1] => 3
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [3,5,6,4,2,8,7,1] => [5,6,3,4,8,2,7,1] => [4,1,1,1,1] => 3
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [3,5,6,4,7,2,8,1] => [5,6,3,4,7,2,8,1] => [4,1,1,1,1] => 3
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [3,5,6,7,8,4,2,1] => [5,6,7,8,3,4,2,1] => [4,1,1,1,1] => 3
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,5,6,8,7,4,2,1] => [8,5,6,7,3,4,2,1] => [5,1,1,1] => 4
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [3,5,7,6,4,2,1,8] => [7,5,6,3,4,2,1,8] => [5,1,1,1] => 4
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [3,5,7,6,4,2,8,1] => [7,5,6,3,4,2,8,1] => [5,1,1,1] => 4
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,5,7,8,6,4,2,1] => [7,8,5,6,3,4,2,1] => [5,1,1,1] => 4
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [3,5,8,7,6,4,2,1] => [8,7,5,6,3,4,2,1] => [6,1,1] => 5
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [3,6,5,4,2,1,7,8] => [6,5,3,4,2,1,7,8] => [5,1,1,1] => 4
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [3,6,5,4,2,7,8,1] => [6,5,3,4,2,7,8,1] => [5,1,1,1] => 4
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [3,6,5,4,2,8,7,1] => [6,5,3,4,8,2,7,1] => [5,1,1,1] => 4
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [3,6,5,4,7,2,8,1] => [6,5,3,4,7,2,8,1] => [5,1,1,1] => 4
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [3,6,5,4,7,8,2,1] => [6,5,3,4,7,8,2,1] => [5,1,1,1] => 4
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [3,6,5,7,4,2,8,1] => [6,5,7,3,4,2,8,1] => [5,1,1,1] => 4
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [3,6,5,7,8,4,2,1] => [6,5,7,8,3,4,2,1] => [5,1,1,1] => 4
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [3,6,8,7,5,4,2,1] => [8,6,7,5,3,4,2,1] => [6,1,1] => 5
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [3,7,6,5,4,2,1,8] => [7,6,5,3,4,2,1,8] => [6,1,1] => 5
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [3,7,6,5,4,2,8,1] => [7,6,5,3,4,2,8,1] => [6,1,1] => 5
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [3,7,6,5,4,8,2,1] => [7,6,5,3,4,8,2,1] => [6,1,1] => 5
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [3,7,6,5,8,4,2,1] => [7,6,5,8,3,4,2,1] => [6,1,1] => 5
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,7,6,8,5,4,2,1] => [7,6,8,5,3,4,2,1] => [6,1,1] => 5
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,7,8,6,5,4,2,1] => [7,8,6,5,3,4,2,1] => [6,1,1] => 5
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,8,7,6,5,4,2,1] => [8,7,6,5,3,4,2,1] => [7,1] => 6
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8] => [4,3,2,1,5,6,7,8] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,3,2,1,5,6,8,7] => [4,3,2,8,1,5,6,7] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,3,2,1,5,7,6,8] => [4,3,2,7,1,5,6,8] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,3,2,1,5,7,8,6] => [4,3,2,7,8,1,5,6] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,3,2,1,5,8,7,6] => [4,3,8,2,7,1,5,6] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,3,2,1,6,5,7,8] => [4,3,2,6,1,5,7,8] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => [4,3,2,6,8,1,5,7] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,3,2,1,6,7,5,8] => [4,3,2,6,7,1,5,8] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,3,2,1,6,7,8,5] => [4,3,2,6,7,8,1,5] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,3,2,1,6,8,7,5] => [4,3,8,2,6,7,1,5] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,3,2,1,7,6,5,8] => [4,3,7,2,6,1,5,8] => [4,1,1,1,1] => 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] => [4,3,7,2,6,8,1,5] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,2,1,7,8,6,5] => [4,3,7,8,2,6,1,5] => [4,1,1,1,1] => 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] => [4,8,3,7,2,6,1,5] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,3,2,5,1,6,7,8] => [4,3,2,5,1,6,7,8] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [4,3,2,5,1,6,8,7] => [4,3,2,5,8,1,6,7] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [4,3,2,5,1,7,6,8] => [4,3,2,5,7,1,6,8] => [4,1,1,1,1] => 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] => [4,3,2,5,7,8,1,6] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,3,2,5,1,8,7,6] => [4,3,8,2,5,7,1,6] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [4,3,2,5,6,1,7,8] => [4,3,2,5,6,1,7,8] => [4,1,1,1,1] => 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] => [4,3,2,5,6,8,1,7] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,3,2,5,6,7,1,8] => [4,3,2,5,6,7,1,8] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,1] => [4,3,2,5,6,7,8,1] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [4,3,2,5,6,8,7,1] => [4,3,8,2,5,6,7,1] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [4,3,2,5,7,6,1,8] => [4,3,7,2,5,6,1,8] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [4,3,2,5,7,6,8,1] => [4,3,7,2,5,6,8,1] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,3,2,5,8,7,6,1] => [4,8,3,7,2,5,6,1] => [4,1,1,1,1] => 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] => [4,3,6,2,5,1,7,8] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [4,3,2,6,5,7,1,8] => [4,3,6,2,5,7,1,8] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [4,3,2,6,5,7,8,1] => [4,3,6,2,5,7,8,1] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,6,7,8,5,1] => [4,3,6,7,8,2,5,1] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,3,2,6,8,7,5,1] => [4,8,3,6,7,2,5,1] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [4,3,2,7,6,5,1,8] => [4,7,3,6,2,5,1,8] => [4,1,1,1,1] => 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] => [4,7,3,6,2,5,8,1] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,2,7,8,6,5,1] => [4,7,8,3,6,2,5,1] => [4,1,1,1,1] => 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] => [8,4,7,3,6,2,5,1] => [5,1,1,1] => 4
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [4,3,5,2,1,6,7,8] => [4,3,5,2,1,6,7,8] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [4,3,5,2,1,6,8,7] => [4,3,5,2,8,1,6,7] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [4,3,5,2,1,7,6,8] => [4,3,5,2,7,1,6,8] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [4,3,5,2,6,1,7,8] => [4,3,5,2,6,1,7,8] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,3,5,2,6,1,8,7] => [4,3,5,2,6,8,1,7] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [4,3,5,2,6,7,8,1] => [4,3,5,2,6,7,8,1] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,3,5,2,7,6,8,1] => [4,3,5,7,2,6,8,1] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,3,5,2,8,7,6,1] => [4,8,3,5,7,2,6,1] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [4,3,5,6,2,1,8,7] => [4,3,5,6,2,8,1,7] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [4,3,5,6,2,7,1,8] => [4,3,5,6,2,7,1,8] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [4,3,5,6,2,7,8,1] => [4,3,5,6,2,7,8,1] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [4,3,5,6,7,8,2,1] => [4,3,5,6,7,8,2,1] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,3,5,6,8,7,2,1] => [4,8,3,5,6,7,2,1] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [4,3,5,7,6,2,1,8] => [4,7,3,5,6,2,1,8] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [4,3,5,7,6,2,8,1] => [4,7,3,5,6,2,8,1] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [4,3,5,7,6,8,2,1] => [4,7,3,5,6,8,2,1] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,5,7,8,6,2,1] => [4,7,8,3,5,6,2,1] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [4,3,5,8,7,6,2,1] => [8,4,7,3,5,6,2,1] => [5,1,1,1] => 4
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [4,3,6,5,2,1,8,7] => [4,6,3,5,2,8,1,7] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [4,3,6,5,2,7,1,8] => [4,6,3,5,2,7,1,8] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [4,3,6,5,2,8,7,1] => [4,6,3,5,8,2,7,1] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,3,6,5,7,2,8,1] => [4,6,3,5,7,2,8,1] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [4,3,6,5,7,8,2,1] => [4,6,3,5,7,8,2,1] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,8,7,2,1] => [4,6,8,3,5,7,2,1] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [4,3,6,7,5,8,2,1] => [4,6,7,3,5,8,2,1] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,6,7,8,5,2,1] => [4,6,7,8,3,5,2,1] => [4,1,1,1,1] => 3
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [4,3,6,8,7,5,2,1] => [8,4,6,7,3,5,2,1] => [5,1,1,1] => 4
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [4,3,7,6,5,2,1,8] => [7,4,6,3,5,2,1,8] => [5,1,1,1] => 4
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [4,3,7,6,5,2,8,1] => [7,4,6,3,5,2,8,1] => [5,1,1,1] => 4
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [4,3,8,7,6,5,2,1] => [8,7,4,6,3,5,2,1] => [6,1,1] => 5
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [4,5,3,2,1,6,7,8] => [4,5,3,2,1,6,7,8] => [4,1,1,1,1] => 3
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [4,5,3,2,1,7,8,6] => [4,5,3,2,7,8,1,6] => [4,1,1,1,1] => 3
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [4,5,3,2,1,8,7,6] => [4,5,3,8,2,7,1,6] => [4,1,1,1,1] => 3
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [4,5,3,2,6,1,7,8] => [4,5,3,2,6,1,7,8] => [4,1,1,1,1] => 3
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [4,5,3,2,6,7,8,1] => [4,5,3,2,6,7,8,1] => [4,1,1,1,1] => 3
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [4,5,3,2,7,6,1,8] => [4,5,3,7,2,6,1,8] => [4,1,1,1,1] => 3
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [4,5,3,2,7,8,6,1] => [4,5,3,7,8,2,6,1] => [4,1,1,1,1] => 3
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,5,3,2,8,7,6,1] => [4,5,8,3,7,2,6,1] => [4,1,1,1,1] => 3
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [4,5,3,6,2,1,8,7] => [4,5,3,6,2,8,1,7] => [4,1,1,1,1] => 3
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [4,5,3,6,2,7,1,8] => [4,5,3,6,2,7,1,8] => [4,1,1,1,1] => 3
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [4,5,3,6,2,8,7,1] => [4,5,3,6,8,2,7,1] => [4,1,1,1,1] => 3
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [4,5,3,6,7,2,8,1] => [4,5,3,6,7,2,8,1] => [4,1,1,1,1] => 3
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,5,3,6,8,7,2,1] => [4,5,8,3,6,7,2,1] => [4,1,1,1,1] => 3
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [4,5,3,7,6,2,8,1] => [4,5,7,3,6,2,8,1] => [4,1,1,1,1] => 3
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [4,5,3,7,6,8,2,1] => [4,5,7,3,6,8,2,1] => [4,1,1,1,1] => 3
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,5,3,7,8,6,2,1] => [4,5,7,8,3,6,2,1] => [4,1,1,1,1] => 3
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,5,3,8,7,6,2,1] => [8,4,5,7,3,6,2,1] => [5,1,1,1] => 4
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [4,5,6,3,2,1,7,8] => [4,5,6,3,2,1,7,8] => [4,1,1,1,1] => 3
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [4,5,6,3,2,1,8,7] => [4,5,6,3,2,8,1,7] => [4,1,1,1,1] => 3
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [4,5,6,3,2,7,8,1] => [4,5,6,3,2,7,8,1] => [4,1,1,1,1] => 3
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [4,5,6,3,2,8,7,1] => [4,5,6,3,8,2,7,1] => [4,1,1,1,1] => 3
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [4,5,6,3,7,2,8,1] => [4,5,6,3,7,2,8,1] => [4,1,1,1,1] => 3
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,5,6,3,8,7,2,1] => [4,5,6,8,3,7,2,1] => [4,1,1,1,1] => 3
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,7,3,2,1,8] => [4,5,6,7,3,2,1,8] => [4,1,1,1,1] => 3
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,7,3,2,8,1] => [4,5,6,7,3,2,8,1] => [4,1,1,1,1] => 3
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,7,3,8,2,1] => [4,5,6,7,3,8,2,1] => [4,1,1,1,1] => 3
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,3,2,1] => [4,5,6,7,8,3,2,1] => [4,1,1,1,1] => 3
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,6,8,7,3,2,1] => [8,4,5,6,7,3,2,1] => [5,1,1,1] => 4
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [4,5,7,6,3,2,1,8] => [7,4,5,6,3,2,1,8] => [5,1,1,1] => 4
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [4,5,7,6,3,2,8,1] => [7,4,5,6,3,2,8,1] => [5,1,1,1] => 4
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [4,5,7,6,3,8,2,1] => [7,4,5,6,3,8,2,1] => [5,1,1,1] => 4
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,5,7,6,8,3,2,1] => [7,4,5,6,8,3,2,1] => [5,1,1,1] => 4
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [4,5,8,7,6,3,2,1] => [8,7,4,5,6,3,2,1] => [6,1,1] => 5
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [4,6,5,3,2,1,8,7] => [6,4,5,3,2,8,1,7] => [5,1,1,1] => 4
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [4,6,5,3,2,8,7,1] => [6,4,5,3,8,2,7,1] => [5,1,1,1] => 4
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [4,6,5,3,7,2,8,1] => [6,4,5,3,7,2,8,1] => [5,1,1,1] => 4
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,6,5,3,8,7,2,1] => [6,4,5,8,3,7,2,1] => [5,1,1,1] => 4
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [4,6,5,7,3,2,8,1] => [6,4,5,7,3,2,8,1] => [5,1,1,1] => 4
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [4,6,5,7,3,8,2,1] => [6,4,5,7,3,8,2,1] => [5,1,1,1] => 4
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,6,5,7,8,3,2,1] => [6,4,5,7,8,3,2,1] => [5,1,1,1] => 4
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [4,6,7,5,3,2,1,8] => [6,7,4,5,3,2,1,8] => [5,1,1,1] => 4
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [4,6,7,5,3,2,8,1] => [6,7,4,5,3,2,8,1] => [5,1,1,1] => 4
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [4,6,7,5,3,8,2,1] => [6,7,4,5,3,8,2,1] => [5,1,1,1] => 4
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,6,7,5,8,3,2,1] => [6,7,4,5,8,3,2,1] => [5,1,1,1] => 4
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,6,7,8,5,3,2,1] => [6,7,8,4,5,3,2,1] => [5,1,1,1] => 4
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [4,6,8,7,5,3,2,1] => [8,6,7,4,5,3,2,1] => [6,1,1] => 5
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [4,7,6,5,3,2,1,8] => [7,6,4,5,3,2,1,8] => [6,1,1] => 5
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [4,7,6,5,3,2,8,1] => [7,6,4,5,3,2,8,1] => [6,1,1] => 5
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,7,6,5,8,3,2,1] => [7,6,4,5,8,3,2,1] => [6,1,1] => 5
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [4,7,6,8,5,3,2,1] => [7,6,8,4,5,3,2,1] => [6,1,1] => 5
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [4,7,8,6,5,3,2,1] => [7,8,6,4,5,3,2,1] => [6,1,1] => 5
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [4,8,7,6,5,3,2,1] => [8,7,6,4,5,3,2,1] => [7,1] => 6
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8] => [5,4,3,2,1,6,7,8] => [5,1,1,1] => 4
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,4,3,2,1,6,8,7] => [5,4,3,2,8,1,6,7] => [5,1,1,1] => 4
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,4,3,2,1,7,6,8] => [5,4,3,2,7,1,6,8] => [5,1,1,1] => 4
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,4,3,2,1,7,8,6] => [5,4,3,2,7,8,1,6] => [5,1,1,1] => 4
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => [5,4,3,8,2,7,1,6] => [5,1,1,1] => 4
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [5,4,3,2,6,1,7,8] => [5,4,3,2,6,1,7,8] => [5,1,1,1] => 4
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,4,3,2,6,1,8,7] => [5,4,3,2,6,8,1,7] => [5,1,1,1] => 4
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [5,4,3,2,6,7,1,8] => [5,4,3,2,6,7,1,8] => [5,1,1,1] => 4
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,1] => [5,4,3,2,6,7,8,1] => [5,1,1,1] => 4
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,4,3,2,6,8,7,1] => [5,4,3,8,2,6,7,1] => [5,1,1,1] => 4
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [5,4,3,2,7,6,1,8] => [5,4,3,7,2,6,1,8] => [5,1,1,1] => 4
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,3,2,7,8,6,1] => [5,4,3,7,8,2,6,1] => [5,1,1,1] => 4
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,4,3,2,8,7,6,1] => [5,4,8,3,7,2,6,1] => [5,1,1,1] => 4
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [5,4,3,6,2,1,7,8] => [5,4,3,6,2,1,7,8] => [5,1,1,1] => 4
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [5,4,3,6,2,7,1,8] => [5,4,3,6,2,7,1,8] => [5,1,1,1] => 4
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [5,4,3,6,2,7,8,1] => [5,4,3,6,2,7,8,1] => [5,1,1,1] => 4
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,4,3,6,2,8,7,1] => [5,4,3,6,8,2,7,1] => [5,1,1,1] => 4
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [5,4,3,6,7,2,1,8] => [5,4,3,6,7,2,1,8] => [5,1,1,1] => 4
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [5,4,3,6,7,2,8,1] => [5,4,3,6,7,2,8,1] => [5,1,1,1] => 4
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3,6,7,8,2,1] => [5,4,3,6,7,8,2,1] => [5,1,1,1] => 4
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [5,4,3,7,6,2,1,8] => [5,4,7,3,6,2,1,8] => [5,1,1,1] => 4
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [5,4,3,7,6,2,8,1] => [5,4,7,3,6,2,8,1] => [5,1,1,1] => 4
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [5,4,3,7,8,6,2,1] => [5,4,7,8,3,6,2,1] => [5,1,1,1] => 4
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [5,4,3,8,7,6,2,1] => [5,8,4,7,3,6,2,1] => [5,1,1,1] => 4
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [5,4,6,3,2,1,7,8] => [5,4,6,3,2,1,7,8] => [5,1,1,1] => 4
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [5,4,6,3,2,7,1,8] => [5,4,6,3,2,7,1,8] => [5,1,1,1] => 4
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [5,4,6,3,2,7,8,1] => [5,4,6,3,2,7,8,1] => [5,1,1,1] => 4
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,4,6,3,2,8,7,1] => [5,4,6,3,8,2,7,1] => [5,1,1,1] => 4
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [5,4,6,3,7,2,1,8] => [5,4,6,3,7,2,1,8] => [5,1,1,1] => 4
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,4,6,3,7,2,8,1] => [5,4,6,3,7,2,8,1] => [5,1,1,1] => 4
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [5,4,6,7,3,2,1,8] => [5,4,6,7,3,2,1,8] => [5,1,1,1] => 4
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,4,6,7,3,8,2,1] => [5,4,6,7,3,8,2,1] => [5,1,1,1] => 4
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,6,7,8,3,2,1] => [5,4,6,7,8,3,2,1] => [5,1,1,1] => 4
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [5,4,7,6,3,2,1,8] => [5,7,4,6,3,2,1,8] => [5,1,1,1] => 4
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,4,7,6,3,8,2,1] => [5,7,4,6,3,8,2,1] => [5,1,1,1] => 4
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [5,4,7,6,8,3,2,1] => [5,7,4,6,8,3,2,1] => [5,1,1,1] => 4
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [5,4,7,8,6,3,2,1] => [5,7,8,4,6,3,2,1] => [5,1,1,1] => 4
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [5,4,8,7,6,3,2,1] => [8,5,7,4,6,3,2,1] => [6,1,1] => 5
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [5,6,4,3,2,1,7,8] => [5,6,4,3,2,1,7,8] => [5,1,1,1] => 4
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [5,6,4,3,2,7,1,8] => [5,6,4,3,2,7,1,8] => [5,1,1,1] => 4
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [5,6,4,3,2,8,7,1] => [5,6,4,3,8,2,7,1] => [5,1,1,1] => 4
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [5,6,4,3,7,2,1,8] => [5,6,4,3,7,2,1,8] => [5,1,1,1] => 4
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [5,6,4,3,8,7,2,1] => [5,6,4,8,3,7,2,1] => [5,1,1,1] => 4
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [5,6,4,7,3,2,1,8] => [5,6,4,7,3,2,1,8] => [5,1,1,1] => 4
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,6,4,7,8,3,2,1] => [5,6,4,7,8,3,2,1] => [5,1,1,1] => 4
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [5,6,4,8,7,3,2,1] => [5,6,8,4,7,3,2,1] => [5,1,1,1] => 4
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [5,6,7,4,3,2,1,8] => [5,6,7,4,3,2,1,8] => [5,1,1,1] => 4
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,6,7,4,3,8,2,1] => [5,6,7,4,3,8,2,1] => [5,1,1,1] => 4
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,6,7,4,8,3,2,1] => [5,6,7,4,8,3,2,1] => [5,1,1,1] => 4
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,4,3,2,1] => [5,6,7,8,4,3,2,1] => [5,1,1,1] => 4
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [5,6,8,7,4,3,2,1] => [8,5,6,7,4,3,2,1] => [6,1,1] => 5
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [5,7,6,4,3,2,1,8] => [7,5,6,4,3,2,1,8] => [6,1,1] => 5
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [5,7,6,4,3,2,8,1] => [7,5,6,4,3,2,8,1] => [6,1,1] => 5
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,7,6,4,3,8,2,1] => [7,5,6,4,3,8,2,1] => [6,1,1] => 5
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,7,6,4,8,3,2,1] => [7,5,6,4,8,3,2,1] => [6,1,1] => 5
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [5,7,6,8,4,3,2,1] => [7,5,6,8,4,3,2,1] => [6,1,1] => 5
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [5,7,8,6,4,3,2,1] => [7,8,5,6,4,3,2,1] => [6,1,1] => 5
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [5,8,7,6,4,3,2,1] => [8,7,5,6,4,3,2,1] => [7,1] => 6
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,5,4,3,2,1,7,8] => [6,5,4,3,2,1,7,8] => [6,1,1] => 5
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => [6,5,4,3,2,8,1,7] => [6,1,1] => 5
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,5,4,3,2,7,1,8] => [6,5,4,3,2,7,1,8] => [6,1,1] => 5
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5,4,3,2,7,8,1] => [6,5,4,3,2,7,8,1] => [6,1,1] => 5
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,5,4,3,2,8,7,1] => [6,5,4,3,8,2,7,1] => [6,1,1] => 5
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [6,5,4,3,7,2,1,8] => [6,5,4,3,7,2,1,8] => [6,1,1] => 5
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,5,4,3,7,2,8,1] => [6,5,4,3,7,2,8,1] => [6,1,1] => 5
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,4,3,7,8,2,1] => [6,5,4,3,7,8,2,1] => [6,1,1] => 5
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [6,5,4,3,8,7,2,1] => [6,5,4,8,3,7,2,1] => [6,1,1] => 5
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [6,5,4,7,3,2,1,8] => [6,5,4,7,3,2,1,8] => [6,1,1] => 5
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,5,4,7,3,8,2,1] => [6,5,4,7,3,8,2,1] => [6,1,1] => 5
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [6,5,4,7,8,3,2,1] => [6,5,4,7,8,3,2,1] => [6,1,1] => 5
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [6,5,4,8,7,3,2,1] => [6,5,8,4,7,3,2,1] => [6,1,1] => 5
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [6,5,7,4,3,2,1,8] => [6,5,7,4,3,2,1,8] => [6,1,1] => 5
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,5,7,4,3,2,8,1] => [6,5,7,4,3,2,8,1] => [6,1,1] => 5
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [6,5,7,4,8,3,2,1] => [6,5,7,4,8,3,2,1] => [6,1,1] => 5
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [6,5,7,8,4,3,2,1] => [6,5,7,8,4,3,2,1] => [6,1,1] => 5
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [6,5,8,7,4,3,2,1] => [6,8,5,7,4,3,2,1] => [6,1,1] => 5
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [6,7,5,4,3,2,1,8] => [6,7,5,4,3,2,1,8] => [6,1,1] => 5
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,7,5,4,3,2,8,1] => [6,7,5,4,3,2,8,1] => [6,1,1] => 5
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [6,7,5,4,3,8,2,1] => [6,7,5,4,3,8,2,1] => [6,1,1] => 5
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [6,7,5,4,8,3,2,1] => [6,7,5,4,8,3,2,1] => [6,1,1] => 5
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [6,7,5,8,4,3,2,1] => [6,7,5,8,4,3,2,1] => [6,1,1] => 5
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,5,4,3,2,1] => [6,7,8,5,4,3,2,1] => [6,1,1] => 5
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [6,8,7,5,4,3,2,1] => [8,6,7,5,4,3,2,1] => [7,1] => 6
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8] => [7,1] => 6
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,6,5,4,3,2,8,1] => [7,6,5,4,3,2,8,1] => [7,1] => 6
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [7,6,5,4,3,8,2,1] => [7,6,5,4,3,8,2,1] => [7,1] => 6
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [7,6,5,4,8,3,2,1] => [7,6,5,4,8,3,2,1] => [7,1] => 6
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [7,6,5,8,4,3,2,1] => [7,6,5,8,4,3,2,1] => [7,1] => 6
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [7,6,8,5,4,3,2,1] => [7,6,8,5,4,3,2,1] => [7,1] => 6
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [7,8,6,5,4,3,2,1] => [7,8,6,5,4,3,2,1] => [7,1] => 6
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => [8] => 7
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,7,6,5,4,3,2,1,9] => [8,7,6,5,4,3,2,1,9] => [8,1] => 7
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,8,7,6,5,4,3,2] => [9,8,7,6,5,4,3,1,2] => [8,1] => 7
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,8,7,6,5,4,3,2,1,10] => [9,8,7,6,5,4,3,2,1,10] => [9,1] => 8
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [7,8,6,5,4,3,2,1,9] => [7,8,6,5,4,3,2,1,9] => [7,1,1] => 6
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,8,9,7,6,5,4,3,2] => [8,9,7,6,5,4,3,1,2] => [7,1,1] => 6
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,9,8,7,6,5,4,3,2] => [10,9,8,7,6,5,4,3,1,2] => [9,1] => 8
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10,9,8,7,6,5,4,3,2,1,11] => [10,9,8,7,6,5,4,3,2,1,11] => [10,1] => 9
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [8,9,7,6,5,4,3,2,1,10] => [8,9,7,6,5,4,3,2,1,10] => [8,1,1] => 7
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [7,6,8,5,4,3,2,1,9] => [7,6,8,5,4,3,2,1,9] => [7,1,1] => 6
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [6,8,7,5,4,3,2,1,9] => [8,6,7,5,4,3,2,1,9] => [7,1,1] => 6
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,8,7,9,6,5,4,3,2] => [8,7,9,6,5,4,3,1,2] => [7,1,1] => 6
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,7,9,8,6,5,4,3,2] => [9,7,8,6,5,4,3,1,2] => [7,1,1] => 6
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,9,10,8,7,6,5,4,3,2] => [9,10,8,7,6,5,4,3,1,2] => [8,1,1] => 7
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,10,9,8,7,6,5,4,3,2] => [11,10,9,8,7,6,5,4,3,1,2] => [10,1] => 9
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0] => [11,10,9,8,7,6,5,4,3,2,1,12] => [11,10,9,8,7,6,5,4,3,2,1,12] => [11,1] => 10
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0] => [8,7,9,6,5,4,3,2,1,10] => [8,7,9,6,5,4,3,2,1,10] => [8,1,1] => 7
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [7,6,5,8,4,3,2,1,9] => [7,6,5,8,4,3,2,1,9] => [7,1,1] => 6
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [6,7,8,5,4,3,2,1,9] => [6,7,8,5,4,3,2,1,9] => [6,1,1,1] => 5
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => [5,8,7,6,4,3,2,1,9] => [8,7,5,6,4,3,2,1,9] => [7,1,1] => 6
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0] => [9,8,10,7,6,5,4,3,2,1,11] => [9,8,10,7,6,5,4,3,2,1,11] => [9,1,1] => 8
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0] => [8,7,6,9,5,4,3,2,1,10] => [8,7,6,9,5,4,3,2,1,10] => [8,1,1] => 7
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0] => [7,8,9,6,5,4,3,2,1,10] => [7,8,9,6,5,4,3,2,1,10] => [7,1,1,1] => 6
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => [6,7,5,8,4,3,2,1,9] => [6,7,5,8,4,3,2,1,9] => [6,1,1,1] => 5
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [4,8,7,6,5,3,2,1,9] => [8,7,6,4,5,3,2,1,9] => [7,1,1] => 6
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [5,9,8,7,6,4,3,2,1,10] => [9,8,7,5,6,4,3,2,1,10] => [8,1,1] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [7,6,5,4,3,8,2,1,9] => [7,6,5,4,3,8,2,1,9] => [7,1,1] => 6
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0] => [6,5,7,8,4,3,2,1,9] => [6,5,7,8,4,3,2,1,9] => [6,1,1,1] => 5
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0] => [8,7,6,5,4,9,3,2,1,10] => [8,7,6,5,4,9,3,2,1,10] => [8,1,1] => 7
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,1,0] => [7,6,8,9,5,4,3,2,1,10] => [7,6,8,9,5,4,3,2,1,10] => [7,1,1,1] => 6
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [4,9,8,7,6,5,3,2,1,10] => [9,8,7,6,4,5,3,2,1,10] => [8,1,1] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [7,6,5,4,3,2,8,1,9] => [7,6,5,4,3,2,8,1,9] => [7,1,1] => 6
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,6,5,4,3,2,1,9,8] => [7,6,5,4,3,2,9,1,8] => [7,1,1] => 6
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,8,7,6,5,4,3] => [9,8,7,6,5,2,4,1,3] => [7,1,1] => 6
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,9,8,7,6,5,4,2] => [9,8,7,6,5,3,4,1,2] => [7,1,1] => 6
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0] => [8,7,6,5,4,3,9,2,1,10] => [8,7,6,5,4,3,9,2,1,10] => [8,1,1] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9] => [7,6,5,4,3,2,1,8,9] => [7,1,1] => 6
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,8,7,6,5,4,3,2,9] => [8,7,6,5,4,3,1,2,9] => [7,1,1] => 6
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,9,8,7,6,5,4,3] => [9,8,7,6,5,4,1,2,3] => [7,1,1] => 6
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => [8,7,6,5,4,3,2,9,1,10] => [8,7,6,5,4,3,2,9,1,10] => [8,1,1] => 7
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,7,6,5,4,3,2,1,10,9] => [8,7,6,5,4,3,2,10,1,9] => [8,1,1] => 7
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [6,7,5,4,3,2,1,8,9] => [6,7,5,4,3,2,1,8,9] => [6,1,1,1] => 5
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,9,8,7,6,5,4,3] => [10,9,8,7,6,5,2,4,1,3] => [8,1,1] => 7
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [8,7,6,5,4,3,2,1,9,10] => [8,7,6,5,4,3,2,1,9,10] => [8,1,1] => 7
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,9,8,7,6,5,4,3,2,10] => [9,8,7,6,5,4,3,1,2,10] => [8,1,1] => 7
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,0] => [6,5,4,3,7,8,2,1,9] => [6,5,4,3,7,8,2,1,9] => [6,1,1,1] => 5
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,10,9,8,7,6,5,4,3] => [10,9,8,7,6,5,4,1,2,3] => [8,1,1] => 7
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,1] => [2,3,4,5,6,7,8,9,1] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,9,8,1] => [9,2,3,4,5,6,7,8,1] => [3,1,1,1,1,1,1] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,6,8,7,9,1] => [8,2,3,4,5,6,7,9,1] => [3,1,1,1,1,1,1] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,6,8,9,7,1] => [8,9,2,3,4,5,6,7,1] => [3,1,1,1,1,1,1] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,6,9,8,7,1] => [9,8,2,3,4,5,6,7,1] => [4,1,1,1,1,1] => 3
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,4,6,7,8,9,5,1] => [6,7,8,9,2,3,4,5,1] => [3,1,1,1,1,1,1] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,3,5,6,7,4,8,9,1] => [5,6,7,2,3,4,8,9,1] => [3,1,1,1,1,1,1] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,5,6,7,8,9,4,1] => [5,6,7,8,9,2,3,4,1] => [3,1,1,1,1,1,1] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,8,9,1] => [4,2,3,5,6,7,8,9,1] => [3,1,1,1,1,1,1] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,8,9,3,1] => [4,5,6,7,8,9,2,3,1] => [3,1,1,1,1,1,1] => 2
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [2,8,7,6,5,4,3,9,1] => [8,7,6,5,4,2,3,9,1] => [7,1,1] => 6
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,9,8,7,6,5,4,3,1] => [9,8,7,6,5,4,2,3,1] => [8,1] => 7
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,1] => [3,2,4,5,6,7,8,9,1] => [3,1,1,1,1,1,1] => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,8,9,1] => [3,4,2,5,6,7,8,9,1] => [3,1,1,1,1,1,1] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,7,8,2,9,1] => [3,4,5,6,7,8,2,9,1] => [3,1,1,1,1,1,1] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,9,2,1] => [3,4,5,6,7,8,9,2,1] => [3,1,1,1,1,1,1] => 2
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [3,5,6,7,8,9,4,2,1] => [5,6,7,8,9,3,4,2,1] => [4,1,1,1,1,1] => 3
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [3,8,7,6,5,4,9,2,1] => [8,7,6,5,3,4,9,2,1] => [7,1,1] => 6
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,9,8,7,6,5,4,2,1] => [9,8,7,6,5,3,4,2,1] => [8,1] => 7
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,9,1] => [4,3,2,5,6,7,8,9,1] => [4,1,1,1,1,1] => 3
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,9,3,2,1] => [4,5,6,7,8,9,3,2,1] => [4,1,1,1,1,1] => 3
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,6,7,8,9,5,3,2,1] => [6,7,8,9,4,5,3,2,1] => [5,1,1,1,1] => 4
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4,8,7,6,5,9,3,2,1] => [8,7,6,4,5,9,3,2,1] => [7,1,1] => 6
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [4,9,8,7,6,5,3,2,1] => [9,8,7,6,4,5,3,2,1] => [8,1] => 7
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,9,1] => [5,4,3,2,6,7,8,9,1] => [5,1,1,1,1] => 4
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [5,6,4,7,3,8,2,9,1] => [5,6,4,7,3,8,2,9,1] => [5,1,1,1,1] => 4
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,9,4,3,2,1] => [5,6,7,8,9,4,3,2,1] => [5,1,1,1,1] => 4
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [5,7,8,9,6,4,3,2,1] => [7,8,9,5,6,4,3,2,1] => [6,1,1,1] => 5
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [5,8,7,6,9,4,3,2,1] => [8,7,5,6,9,4,3,2,1] => [7,1,1] => 6
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [5,9,8,7,6,4,3,2,1] => [9,8,7,5,6,4,3,2,1] => [8,1] => 7
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,8,9,1] => [6,5,4,3,2,7,8,9,1] => [6,1,1,1] => 5
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,9,5,4,3,2,1] => [6,7,8,9,5,4,3,2,1] => [6,1,1,1] => 5
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [6,7,9,8,5,4,3,2,1] => [9,6,7,8,5,4,3,2,1] => [7,1,1] => 6
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [6,8,7,9,5,4,3,2,1] => [8,6,7,9,5,4,3,2,1] => [7,1,1] => 6
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [6,8,9,7,5,4,3,2,1] => [8,9,6,7,5,4,3,2,1] => [7,1,1] => 6
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [7,6,5,4,3,2,8,9,1] => [7,6,5,4,3,2,8,9,1] => [7,1,1] => 6
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [7,6,5,4,3,2,9,8,1] => [7,6,5,4,3,9,2,8,1] => [7,1,1] => 6
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [7,6,9,8,5,4,3,2,1] => [7,9,6,8,5,4,3,2,1] => [7,1,1] => 6
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [7,8,9,6,5,4,3,2,1] => [7,8,9,6,5,4,3,2,1] => [7,1,1] => 6
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [7,9,8,6,5,4,3,2,1] => [9,7,8,6,5,4,3,2,1] => [8,1] => 7
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,7,6,5,4,3,2,9,1] => [8,7,6,5,4,3,2,9,1] => [8,1] => 7
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [8,7,6,5,4,3,9,2,1] => [8,7,6,5,4,3,9,2,1] => [8,1] => 7
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [8,7,6,5,4,9,3,2,1] => [8,7,6,5,4,9,3,2,1] => [8,1] => 7
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [8,7,6,5,9,4,3,2,1] => [8,7,6,5,9,4,3,2,1] => [8,1] => 7
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [8,7,6,9,5,4,3,2,1] => [8,7,6,9,5,4,3,2,1] => [8,1] => 7
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [8,7,9,6,5,4,3,2,1] => [8,7,9,6,5,4,3,2,1] => [8,1] => 7
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [8,9,7,6,5,4,3,2,1] => [8,9,7,6,5,4,3,2,1] => [8,1] => 7
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => [9] => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8] => [9,1,2,3,4,5,6,7,8] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,8,9,7] => [8,9,1,2,3,4,5,6,7] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,6] => [7,8,9,1,2,3,4,5,6] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,5] => [6,7,8,9,1,2,3,4,5] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,4] => [5,6,7,8,9,1,2,3,4] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,3] => [4,5,6,7,8,9,1,2,3] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,2] => [3,4,5,6,7,8,9,1,2] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9] => [10,1,2,3,4,5,6,7,8,9] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,9,8,7] => [9,8,1,2,3,4,5,6,7] => [3,1,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,7,9,10,8] => [9,10,1,2,3,4,5,6,7,8] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,5,8,7,9,6] => [8,7,9,1,2,3,4,5,6] => [3,1,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,6,8,9,10,7] => [8,9,10,1,2,3,4,5,6,7] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,4,7,6,8,9,5] => [7,6,8,9,1,2,3,4,5] => [3,1,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,10,6] => [7,8,9,10,1,2,3,4,5,6] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,3,6,5,7,8,9,4] => [6,5,7,8,9,1,2,3,4] => [3,1,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,10,5] => [6,7,8,9,10,1,2,3,4,5] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,9,3] => [5,4,6,7,8,9,1,2,3] => [3,1,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,10,4] => [5,6,7,8,9,10,1,2,3,4] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,9,2] => [4,3,5,6,7,8,9,1,2] => [3,1,1,1,1,1,1] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,10,3] => [4,5,6,7,8,9,10,1,2,3] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,2] => [3,4,5,6,7,8,9,10,1,2] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,1] => [2,3,4,5,6,7,8,9,10,1] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10,11] => [1,2,3,4,5,6,7,8,9,10,11] => [1,1,1,1,1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,9,11,10] => [11,1,2,3,4,5,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,10,9,8] => [10,9,1,2,3,4,5,6,7,8] => [3,1,1,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,7,8,10,11,9] => [10,11,1,2,3,4,5,6,7,8,9] => [2,1,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,9,8,7,6] => [9,8,7,1,2,3,4,5,6] => [4,1,1,1,1,1] => 3
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,5,3,6,7,8,9,2] => [4,5,3,6,7,8,9,1,2] => [3,1,1,1,1,1,1] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,9,10,2] => [4,3,5,6,7,8,9,10,1,2] => [3,1,1,1,1,1,1,1] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,10,1] => [3,2,4,5,6,7,8,9,10,1] => [3,1,1,1,1,1,1,1] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,11,2] => [3,4,5,6,7,8,9,10,11,1,2] => [2,1,1,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => [2,3,4,5,6,7,8,9,10,11,1] => [2,1,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,8,11,10,9] => [11,10,1,2,3,4,5,6,7,8,9] => [3,1,1,1,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,7,8,9,11,12,10] => [11,12,1,2,3,4,5,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,6,10,9,8,7] => [10,9,8,1,2,3,4,5,6,7] => [4,1,1,1,1,1,1] => 3
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,9,10,1] => [4,3,2,5,6,7,8,9,10,1] => [4,1,1,1,1,1,1] => 3
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,10,11,1] => [3,2,4,5,6,7,8,9,10,11,1] => [3,1,1,1,1,1,1,1,1] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,11,12,2] => [3,4,5,6,7,8,9,10,11,12,1,2] => [2,1,1,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,9,8,7,6,5] => [9,8,7,6,1,2,3,4,5] => [5,1,1,1,1] => 4
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5,10,9,8,7,6] => [10,9,8,7,1,2,3,4,5,6] => [5,1,1,1,1,1] => 4
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,9,10,1] => [5,4,3,2,6,7,8,9,10,1] => [5,1,1,1,1,1] => 4
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,8,9,3,2] => [4,5,6,7,8,9,3,1,2] => [3,1,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,9,8,7,6,5,4] => [9,8,7,6,5,1,2,3,4] => [6,1,1,1] => 5
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,10,9,8,7,6,5] => [10,9,8,7,6,1,2,3,4,5] => [6,1,1,1,1] => 5
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,8,9,10,1] => [6,5,4,3,2,7,8,9,10,1] => [6,1,1,1,1] => 5
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,8,7,9] => [8,1,2,3,4,5,6,7,9] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9] => [7,1,2,3,4,5,6,8,9] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,7,6,9,8] => [7,9,1,2,3,4,5,6,8] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9] => [6,1,2,3,4,5,7,8,9] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,4,6,5,9,8,7] => [9,6,8,1,2,3,4,5,7] => [3,1,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9] => [5,1,2,3,4,6,7,8,9] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6,9,8] => [5,7,9,1,2,3,4,6,8] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,3,5,4,9,8,7,6] => [9,8,5,7,1,2,3,4,6] => [4,1,1,1,1,1] => 3
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,3,6,5,4,9,8,7] => [6,9,5,8,1,2,3,4,7] => [3,1,1,1,1,1,1] => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9] => [4,1,2,3,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,7,9,8] => [4,9,1,2,3,5,6,7,8] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,4,3,9,8,7,6,5] => [9,8,7,4,6,1,2,3,5] => [5,1,1,1,1] => 4
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,2,8,7,6,5,4,3,9] => [8,7,6,5,4,1,2,3,9] => [6,1,1,1] => 5
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9] => [3,1,2,4,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,7,9,8] => [3,9,1,2,4,5,6,7,8] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => [3,5,7,9,1,2,4,6,8] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,3,2,9,8,7,6,5,4] => [9,8,7,6,3,5,1,2,4] => [6,1,1,1] => 5
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8,9] => [4,3,1,2,5,6,7,8,9] => [3,1,1,1,1,1,1] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2,9,8,7,6] => [5,9,4,8,3,7,1,2,6] => [4,1,1,1,1,1] => 3
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,9,8] => [2,9,1,3,4,5,6,7,8] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,6,8,7,9] => [2,8,1,3,4,5,6,7,9] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8,9] => [2,4,1,3,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,9] => [2,4,6,8,1,3,5,7,9] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,6,5,9,8,7] => [9,2,4,6,8,1,3,5,7] => [3,1,1,1,1,1,1] => 2
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,4,3,9,8,7,6,5] => [9,8,7,2,4,6,1,3,5] => [5,1,1,1,1] => 4
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9] => [3,2,1,4,5,6,7,8,9] => [3,1,1,1,1,1,1] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,6,7,9,8] => [3,2,9,1,4,5,6,7,8] => [3,1,1,1,1,1,1] => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,2,1,5,4,6,7,8,9] => [3,2,5,1,4,6,7,8,9] => [3,1,1,1,1,1,1] => 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] => [3,2,5,7,9,1,4,6,8] => [3,1,1,1,1,1,1] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,6,5,4,7,8,9] => [3,6,2,5,1,4,7,8,9] => [3,1,1,1,1,1,1] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4,9,8,7] => [3,6,9,2,5,8,1,4,7] => [3,1,1,1,1,1,1] => 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] => [9,8,7,3,6,2,5,1,4] => [6,1,1,1] => 5
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9] => [4,3,2,1,5,6,7,8,9] => [4,1,1,1,1,1] => 3
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0] => [4,3,2,1,6,5,7,8,9] => [4,3,2,6,1,5,7,8,9] => [4,1,1,1,1,1] => 3
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,8,7,9] => [4,3,2,6,8,1,5,7,9] => [4,1,1,1,1,1] => 3
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0] => [4,3,2,1,7,6,5,8,9] => [4,3,7,2,6,1,5,8,9] => [4,1,1,1,1,1] => 3
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0] => [4,3,2,1,7,6,5,9,8] => [4,3,7,2,6,9,1,5,8] => [4,1,1,1,1,1] => 3
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,8,7,6,5,9] => [4,8,3,7,2,6,1,5,9] => [4,1,1,1,1,1] => 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] => [9,4,8,3,7,2,6,1,5] => [5,1,1,1,1] => 4
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9] => [5,4,3,2,1,6,7,8,9] => [5,1,1,1,1] => 4
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [5,4,3,2,1,7,6,8,9] => [5,4,3,2,7,1,6,8,9] => [5,1,1,1,1] => 4
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [5,4,3,2,1,8,7,6,9] => [5,4,3,8,2,7,1,6,9] => [5,1,1,1,1] => 4
[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] => [5,4,9,3,8,2,7,1,6] => [5,1,1,1,1] => 4
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9] => [6,5,4,3,2,1,7,8,9] => [6,1,1,1] => 5
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [6,5,4,3,2,1,8,7,9] => [6,5,4,3,2,8,1,7,9] => [6,1,1,1] => 5
[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] => [6,5,4,3,9,2,8,1,7] => [6,1,1,1] => 5
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,9,8,10] => [9,1,2,3,4,5,6,7,8,10] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,6,8,7,9,10] => [8,1,2,3,4,5,6,7,9,10] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,6,8,7,10,9] => [8,10,1,2,3,4,5,6,7,9] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9,10] => [7,1,2,3,4,5,6,8,9,10] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9,10] => [6,1,2,3,4,5,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9,10] => [5,1,2,3,4,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,10,9,8,7,6,5,4] => [10,9,8,7,6,5,1,2,3,4] => [7,1,1,1] => 6
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9,10] => [4,1,2,3,5,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7,10,9] => [4,6,8,10,1,2,3,5,7,9] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3,10,9,8,7] => [6,10,5,9,4,8,1,2,3,7] => [4,1,1,1,1,1,1] => 3
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9,10] => [3,1,2,4,5,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8,10] => [3,5,7,9,1,2,4,6,8,10] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,7,6,10,9,8] => [10,3,5,7,9,1,2,4,6,8] => [3,1,1,1,1,1,1,1] => 2
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,2,10,9,8,7,6,5,4] => [10,9,8,7,6,3,5,1,2,4] => [7,1,1,1] => 6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,8,10,9] => [2,10,1,3,4,5,6,7,8,9] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8,9,10] => [2,4,1,3,5,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => [2,4,6,8,10,1,3,5,7,9] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5,10,9,8] => [7,10,2,4,6,9,1,3,5,8] => [3,1,1,1,1,1,1,1] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3,10,9,8,7] => [6,10,5,9,2,4,8,1,3,7] => [4,1,1,1,1,1,1] => 3
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,1,8,7,6,5,4,3,10,9] => [8,7,6,5,2,4,10,1,3,9] => [6,1,1,1,1] => 5
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9,10] => [3,2,1,4,5,6,7,8,9,10] => [3,1,1,1,1,1,1,1] => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,5,4,6,7,8,9,10] => [3,2,5,1,4,6,7,8,9,10] => [3,1,1,1,1,1,1,1] => 2
[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] => [3,2,5,7,9,1,4,6,8,10] => [3,1,1,1,1,1,1,1] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,6,5,4,8,7,10,9] => [3,6,2,5,8,10,1,4,7,9] => [3,1,1,1,1,1,1,1] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,6,5,4,10,9,8,7] => [10,3,6,9,2,5,8,1,4,7] => [4,1,1,1,1,1,1] => 3
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,2,1,10,9,8,7,6,5,4] => [10,9,8,7,3,6,2,5,1,4] => [7,1,1,1] => 6
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9,10] => [4,3,2,1,5,6,7,8,9,10] => [4,1,1,1,1,1,1] => 3
[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] => [4,3,2,6,8,10,1,5,7,9] => [4,1,1,1,1,1,1] => 3
[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] => [4,10,3,9,2,6,8,1,5,7] => [4,1,1,1,1,1,1] => 3
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5,10,9,8] => [4,3,7,10,2,6,9,1,5,8] => [4,1,1,1,1,1,1] => 3
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,8,7,6,5,9,10] => [4,8,3,7,2,6,1,5,9,10] => [4,1,1,1,1,1,1] => 3
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,8,7,6,5,10,9] => [4,8,3,7,2,6,10,1,5,9] => [4,1,1,1,1,1,1] => 3
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,3,2,1,10,9,8,7,6,5] => [10,9,4,8,3,7,2,6,1,5] => [6,1,1,1,1] => 5
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9,10] => [5,4,3,2,1,6,7,8,9,10] => [5,1,1,1,1,1] => 4
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [5,4,3,2,1,7,6,9,8,10] => [5,4,3,2,7,9,1,6,8,10] => [5,1,1,1,1,1] => 4
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [5,4,3,2,1,9,8,7,6,10] => [5,4,9,3,8,2,7,1,6,10] => [5,1,1,1,1,1] => 4
[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] => [5,10,4,9,3,8,2,7,1,6] => [5,1,1,1,1,1] => 4
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9,10] => [6,5,4,3,2,1,7,8,9,10] => [6,1,1,1,1] => 5
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0] => [6,5,4,3,2,1,9,8,7,10] => [6,5,4,3,9,2,8,1,7,10] => [6,1,1,1,1] => 5
[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] => [6,5,4,10,3,9,2,8,1,7] => [6,1,1,1,1] => 5
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9,10] => [7,6,5,4,3,2,1,8,9,10] => [7,1,1,1] => 6
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [7,6,5,4,3,2,1,9,8,10] => [7,6,5,4,3,2,9,1,8,10] => [7,1,1,1] => 6
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [7,6,5,4,3,2,1,10,9,8] => [7,6,5,4,3,10,2,9,1,8] => [7,1,1,1] => 6
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [10,9,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => [10] => 9
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9] => [2,3,1,4,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8,9] => [2,3,4,1,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9] => [2,3,4,5,1,6,7,8,9] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,1,7,8,9] => [2,3,4,5,6,1,7,8,9] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9] => [2,3,4,5,6,7,1,8,9] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,1,9] => [2,3,4,5,6,7,8,1,9] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9,10] => [2,3,1,4,5,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8,9,10] => [2,3,4,1,5,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9,10] => [2,3,4,5,1,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1,7,8,9,10] => [2,3,4,5,6,1,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,5,7,6,1,8,9] => [7,2,3,4,5,6,1,8,9] => [3,1,1,1,1,1,1] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9,10] => [2,3,4,5,6,7,1,8,9,10] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,6,8,7,1,9] => [8,2,3,4,5,6,7,1,9] => [3,1,1,1,1,1,1] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,8,1,9,10] => [2,3,4,5,6,7,8,1,9,10] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,9,1,10] => [2,3,4,5,6,7,8,9,1,10] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10,11] => [2,1,3,4,5,6,7,8,9,10,11] => [2,1,1,1,1,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,6,8,9,7] => [2,8,9,1,3,4,5,6,7] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,8,10,9,1] => [10,2,3,4,5,6,7,8,9,1] => [3,1,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [8,10,9,7,6,5,4,3,2,1] => [10,8,9,7,6,5,4,3,2,1] => [9,1] => 8
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [9,8,10,7,6,5,4,3,2,1] => [9,8,10,7,6,5,4,3,2,1] => [9,1] => 8
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [9,11,10,8,7,6,5,4,3,2,1] => [11,9,10,8,7,6,5,4,3,2,1] => [10,1] => 9
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,6,7,9,10,8] => [2,9,10,1,3,4,5,6,7,8] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,7,9,8] => [2,3,9,1,4,5,6,7,8] => [2,1,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,7,8,2,1,9] => [3,4,5,6,7,8,2,1,9] => [3,1,1,1,1,1,1] => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [3,4,5,2,1,6,7,8,9] => [3,4,5,2,1,6,7,8,9] => [3,1,1,1,1,1,1] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7,8,9] => [3,4,2,1,5,6,7,8,9] => [3,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,8,7,6,5,4,3,2,10,1] => [9,8,7,6,5,4,3,2,10,1] => [9,1] => 8
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [10,9,8,7,6,5,4,3,2,11,1] => [10,9,8,7,6,5,4,3,2,11,1] => [10,1] => 9
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [6,5,4,3,2,7,1,8,9] => [6,5,4,3,2,7,1,8,9] => [6,1,1,1] => 5
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [5,4,3,2,6,1,7,8,9] => [5,4,3,2,6,1,7,8,9] => [5,1,1,1,1] => 4
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [4,3,2,5,1,6,7,8,9] => [4,3,2,5,1,6,7,8,9] => [4,1,1,1,1,1] => 3
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8,9] => [3,2,4,1,5,6,7,8,9] => [3,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [9,10,8,7,6,5,4,3,2,1] => [9,10,8,7,6,5,4,3,2,1] => [9,1] => 8
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [6,10,9,8,7,5,4,3,2,1] => [10,9,8,6,7,5,4,3,2,1] => [9,1] => 8
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [5,10,9,8,7,6,4,3,2,1] => [10,9,8,7,5,6,4,3,2,1] => [9,1] => 8
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,8,9,10,3,1] => [4,5,6,7,8,9,10,2,3,1] => [3,1,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [10,11,9,8,7,6,5,4,3,2,1] => [10,11,9,8,7,6,5,4,3,2,1] => [10,1] => 9
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8,9] => [3,4,5,1,2,6,7,8,9] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,5,1,6,7,9,8] => [2,3,4,5,9,1,6,7,8] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,3,4,6,5,7,8,9,10,1] => [6,2,3,4,5,7,8,9,10,1] => [3,1,1,1,1,1,1,1] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,8,1,9] => [3,2,4,5,6,7,8,1,9] => [3,1,1,1,1,1,1] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,7,9,8,2] => [9,3,4,5,6,7,8,1,2] => [3,1,1,1,1,1,1] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,1,9,8] => [2,3,4,5,6,7,9,1,8] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,9,3] => [2,4,5,6,7,8,9,1,3] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,6,7,10,9,8,1] => [10,9,2,3,4,5,6,7,8,1] => [4,1,1,1,1,1,1] => 3
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,9,10,3,2,1] => [4,5,6,7,8,9,10,3,2,1] => [4,1,1,1,1,1,1] => 3
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [9,8,7,6,5,4,3,10,2,1] => [9,8,7,6,5,4,3,10,2,1] => [9,1] => 8
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [9,8,7,6,5,4,10,3,2,1] => [9,8,7,6,5,4,10,3,2,1] => [9,1] => 8
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [9,8,7,6,5,10,4,3,2,1] => [9,8,7,6,5,10,4,3,2,1] => [9,1] => 8
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [9,8,7,6,10,5,4,3,2,1] => [9,8,7,6,10,5,4,3,2,1] => [9,1] => 8
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [9,8,7,10,6,5,4,3,2,1] => [9,8,7,10,6,5,4,3,2,1] => [9,1] => 8
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,4,6,7,8,5,9] => [6,7,8,1,2,3,4,5,9] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,6,1,8,7,9] => [2,3,4,5,6,8,1,7,9] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,5,1,7,6,8,9] => [2,3,4,5,7,1,6,8,9] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,4,1,6,5,7,8,9] => [2,3,4,6,1,5,7,8,9] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8,9] => [2,3,5,1,4,6,7,8,9] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6,9,8] => [2,3,5,7,9,1,4,6,8] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,9,8,10] => [2,3,5,7,9,1,4,6,8,10] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,4,1,5,7,8,9,6] => [2,3,4,7,8,9,1,5,6] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,4,6,7,8,9,10,5,1] => [6,7,8,9,10,2,3,4,5,1] => [3,1,1,1,1,1,1,1] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,5,6,7,8,9,10,4,1] => [5,6,7,8,9,10,2,3,4,1] => [3,1,1,1,1,1,1,1] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,9,10,2,1] => [3,4,5,6,7,8,9,10,2,1] => [3,1,1,1,1,1,1,1] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,8,9,11,10,1] => [11,2,3,4,5,6,7,8,9,10,1] => [3,1,1,1,1,1,1,1,1] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,9,10,11,2,1] => [3,4,5,6,7,8,9,10,11,2,1] => [3,1,1,1,1,1,1,1,1] => 2
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,3,5,7,9,10,8,6,4,2] => [9,10,7,8,5,6,3,4,1,2] => [5,1,1,1,1,1] => 4
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [5,6,4,7,3,8,2,9,1,10] => [5,6,4,7,3,8,2,9,1,10] => [5,1,1,1,1,1] => 4
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,3,5,7,9,11,12,10,8,6,4,2] => [11,12,9,10,7,8,5,6,3,4,1,2] => [6,1,1,1,1,1,1] => 5
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [11,10,9,8,7,6,5,4,3,2,1] => [11,10,9,8,7,6,5,4,3,2,1] => [11] => 10
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [7,9,10,8,6,5,4,3,2,1] => [9,10,7,8,6,5,4,3,2,1] => [8,1,1] => 7
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9,10,11] => [2,3,1,4,5,6,7,8,9,10,11] => [2,1,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,2,4,9,8,7,6,5,3] => [9,8,7,6,4,5,1,2,3] => [6,1,1,1] => 5
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,3,5,9,8,7,6,4] => [9,8,7,5,6,1,2,3,4] => [5,1,1,1,1] => 4
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,4,6,9,8,7,5] => [9,8,6,7,1,2,3,4,5] => [4,1,1,1,1,1] => 3
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,5,7,9,8,6] => [9,7,8,1,2,3,4,5,6] => [3,1,1,1,1,1,1] => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [3,2,1,5,6,7,8,9,4] => [3,2,5,6,7,8,9,1,4] => [3,1,1,1,1,1,1] => 2
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,9,10,4,3,2,1] => [5,6,7,8,9,10,4,3,2,1] => [5,1,1,1,1,1] => 4
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0] => [5,6,4,3,2,1,7,8,9] => [5,6,4,3,2,1,7,8,9] => [5,1,1,1,1] => 4
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,5,3,2,1,6,7,8,9] => [4,5,3,2,1,6,7,8,9] => [4,1,1,1,1,1] => 3
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8,9] => [3,4,1,2,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,9,10,3] => [2,4,5,6,7,8,9,10,1,3] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,9,4] => [2,3,5,6,7,8,9,1,4] => [2,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [8,9,10,7,6,5,4,3,2,1] => [8,9,10,7,6,5,4,3,2,1] => [8,1,1] => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9,11] => [10,1,2,3,4,5,6,7,8,9,11] => [2,1,1,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,5,6,1,8,9,10,7] => [2,3,4,5,6,8,9,10,1,7] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,5,7,8,6,9] => [7,8,1,2,3,4,5,6,9] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,5,6,8,9,7,10] => [8,9,1,2,3,4,5,6,7,10] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,7,8,2,9,10] => [3,4,5,6,7,8,1,2,9,10] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,4,2,5,1,6,7,8,9] => [3,4,2,5,1,6,7,8,9] => [3,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,9,10,5,4,3,2,1] => [6,7,8,9,10,5,4,3,2,1] => [6,1,1,1,1] => 5
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [7,8,9,10,6,5,4,3,2,1] => [7,8,9,10,6,5,4,3,2,1] => [7,1,1,1] => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,9,10,1,11] => [2,3,4,5,6,7,8,9,10,1,11] => [2,1,1,1,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,8,2,9] => [3,4,5,6,7,8,1,2,9] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,5,6,2,8,9,7] => [3,4,5,6,8,9,1,2,7] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9,10,11] => [3,1,2,4,5,6,7,8,9,10,11] => [2,1,1,1,1,1,1,1,1,1] => 1
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,2,10,9,8,7,6,5,4,1] => [10,9,8,7,6,3,5,2,4,1] => [8,1,1] => 7
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,9,4] => [2,5,6,7,8,9,1,3,4] => [2,1,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,4,5,2,1,6,7,8,9,10] => [3,4,5,2,1,6,7,8,9,10] => [3,1,1,1,1,1,1,1] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7,8,9,10] => [3,4,2,1,5,6,7,8,9,10] => [3,1,1,1,1,1,1,1] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,8,1,10,9] => [2,3,4,5,6,7,8,10,1,9] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [5,6,4,3,2,1,7,8,9,10] => [5,6,4,3,2,1,7,8,9,10] => [5,1,1,1,1,1] => 4
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0] => [5,6,4,3,2,7,1,8,9] => [5,6,4,3,2,7,1,8,9] => [5,1,1,1,1] => 4
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,7,5,4,3,2,1,8,9,10] => [6,7,5,4,3,2,1,8,9,10] => [6,1,1,1,1] => 5
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,7,5,4,3,2,1,8,9,10,11] => [6,7,5,4,3,2,1,8,9,10,11] => [6,1,1,1,1,1] => 5
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,4,2,1,6,5,8,7,10,9] => [3,4,2,6,8,10,1,5,7,9] => [3,1,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0] => [9,8,7,6,5,4,3,2,1,10,11] => [9,8,7,6,5,4,3,2,1,10,11] => [9,1,1] => 8
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,8,9,2,10] => [3,4,5,6,7,8,9,1,2,10] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,9,5] => [2,3,4,6,7,8,9,1,5] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,7,8,10,9,2] => [10,3,4,5,6,7,8,9,1,2] => [3,1,1,1,1,1,1,1] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,8,3,9] => [2,4,5,6,7,8,1,3,9] => [2,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0] => [8,7,6,5,4,3,2,9,10,1] => [8,7,6,5,4,3,2,9,10,1] => [8,1,1] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,8,9,10,1] => [7,6,5,4,3,2,8,9,10,1] => [7,1,1,1] => 6
[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] => [3,5,7,9,10,1,2,4,6,8] => [2,1,1,1,1,1,1,1,1] => 1
[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] => [2,4,6,7,8,9,1,3,5] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,6,7,8,9,4] => [3,5,6,7,8,9,1,2,4] => [2,1,1,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8,9,10] => [3,2,4,1,5,6,7,8,9,10] => [3,1,1,1,1,1,1,1] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,7,2,8,9] => [3,4,5,6,7,1,2,8,9] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,6,7,9,8,1,10] => [9,2,3,4,5,6,7,8,1,10] => [3,1,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [6,5,7,4,8,3,9,2,10,1] => [6,5,7,4,8,3,9,2,10,1] => [6,1,1,1,1] => 5
[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] => [2,4,6,8,10,12,1,3,5,7,9,11] => [2,1,1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [7,6,8,5,9,4,10,3,11,2,12,1] => [7,6,8,5,9,4,10,3,11,2,12,1] => [7,1,1,1,1,1] => 6
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,8,9,10,2,11] => [3,4,5,6,7,8,9,10,1,2,11] => [2,1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0] => [10,9,8,7,6,5,4,3,2,1,12,11] => [10,9,8,7,6,5,4,3,2,12,1,11] => [10,1,1] => 9
[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] => [3,4,6,8,10,1,2,5,7,9] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,8,9,11,10] => [2,11,1,3,4,5,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9,10,11,12] => [3,1,2,4,5,6,7,8,9,10,11,12] => [2,1,1,1,1,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,5,6,9,8,7,2] => [9,8,3,4,5,6,7,1,2] => [4,1,1,1,1,1] => 3
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [5,4,6,3,7,2,8,1,9] => [5,4,6,3,7,2,8,1,9] => [5,1,1,1,1] => 4
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [2,1,7,8,9,10,6,5,4,3] => [7,8,9,10,6,5,2,4,1,3] => [5,1,1,1,1,1] => 4
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [3,4,2,1,6,5,9,10,8,7] => [3,4,9,10,2,6,8,1,5,7] => [3,1,1,1,1,1,1,1] => 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] => [2,3,4,5,7,9,1,6,8] => [2,1,1,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0] => [4,5,3,6,2,7,1,8,9] => [4,5,3,6,2,7,1,8,9] => [4,1,1,1,1,1] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,6,9,8,11,12,10] => [3,5,7,9,11,12,1,2,4,6,8,10] => [2,1,1,1,1,1,1,1,1,1,1] => 1
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,3,1 1,7,5,1 1,15,18,7,1 1,31,57,33,9,1 1,63,169,132,52,11,1
$F_{1} = 1$
$F_{2} = 1 + q$
$F_{3} = 1 + 3\ q + q^{2}$
$F_{4} = 1 + 7\ q + 5\ q^{2} + q^{3}$
$F_{5} = 1 + 15\ q + 18\ q^{2} + 7\ q^{3} + q^{4}$
$F_{6} = 1 + 31\ q + 57\ q^{2} + 33\ q^{3} + 9\ q^{4} + q^{5}$
$F_{7} = 1 + 63\ q + 169\ q^{2} + 132\ q^{3} + 52\ q^{4} + 11\ q^{5} + q^{6}$
Description
The degree of the cyclic sieving polynomial corresponding to an integer partition.
Let $\lambda$ be an integer partition of $n$ and let $N$ be the least common multiple of the parts of $\lambda$. Fix an arbitrary permutation $\pi$ of cycle type $\lambda$. Then $\pi$ induces a cyclic action of order $N$ on $\{1,\dots,n\}$.
The corresponding character can be identified with the cyclic sieving polynomial $C_\lambda(q)$ of this action, modulo $q^N-1$. Explicitly, it is
$$ \sum_{p\in\lambda} [p]_{q^{N/p}}, $$
where $[p]_q = 1+\dots+q^{p-1}$ is the $q$-integer.
This statistic records the degree of $C_\lambda(q)$. Equivalently, it equals
$$ \left(1 - \frac{1}{\lambda_1}\right) N, $$
where $\lambda_1$ is the largest part of $\lambda$.
The statistic is undefined for the empty partition.
Let $\lambda$ be an integer partition of $n$ and let $N$ be the least common multiple of the parts of $\lambda$. Fix an arbitrary permutation $\pi$ of cycle type $\lambda$. Then $\pi$ induces a cyclic action of order $N$ on $\{1,\dots,n\}$.
The corresponding character can be identified with the cyclic sieving polynomial $C_\lambda(q)$ of this action, modulo $q^N-1$. Explicitly, it is
$$ \sum_{p\in\lambda} [p]_{q^{N/p}}, $$
where $[p]_q = 1+\dots+q^{p-1}$ is the $q$-integer.
This statistic records the degree of $C_\lambda(q)$. Equivalently, it equals
$$ \left(1 - \frac{1}{\lambda_1}\right) N, $$
where $\lambda_1$ is the largest part of $\lambda$.
The statistic is undefined for the empty partition.
Map
LLPS
Description
The Lewis-Lyu-Pylyavskyy-Sen shape of a permutation.
An ascent in a sequence $u = (u_1, u_2, \ldots)$ is an index $i$ such that $u_i < u_{i+1}$. Let $\mathrm{asc}(u)$ denote the number of ascents of $u$, and let
$$\mathrm{asc}^{*}(u) := \begin{cases} 0 &\textrm{if u is empty}, \\ 1 + \mathrm{asc}(u) &\textrm{otherwise}.\end{cases}$$
Given a permutation $w$ in the symmetric group $\mathfrak{S}_n$, define
$A'_k := \max_{u_1, \ldots, u_k} (\mathrm{asc}^{*}(u_1) + \cdots + \mathrm{asc}^{*}(u_k))$
where the maximum is taken over disjoint subsequences ${u_i}$ of $w$.
Then $A'_1, A'_2-A'_1, A'_3-A'_2,\dots$ is a partition of $n$. Its conjugate is the Lewis-Lyu-Pylyavskyy-Sen shape of a permutation.
An ascent in a sequence $u = (u_1, u_2, \ldots)$ is an index $i$ such that $u_i < u_{i+1}$. Let $\mathrm{asc}(u)$ denote the number of ascents of $u$, and let
$$\mathrm{asc}^{*}(u) := \begin{cases} 0 &\textrm{if u is empty}, \\ 1 + \mathrm{asc}(u) &\textrm{otherwise}.\end{cases}$$
Given a permutation $w$ in the symmetric group $\mathfrak{S}_n$, define
$A'_k := \max_{u_1, \ldots, u_k} (\mathrm{asc}^{*}(u_1) + \cdots + \mathrm{asc}^{*}(u_k))$
where the maximum is taken over disjoint subsequences ${u_i}$ of $w$.
Then $A'_1, A'_2-A'_1, A'_3-A'_2,\dots$ is a partition of $n$. Its conjugate is the Lewis-Lyu-Pylyavskyy-Sen shape of a permutation.
Map
to 312-avoiding permutation
Description
Map
inverse Foata bijection
Description
The inverse of Foata's bijection.
See Mp00067Foata bijection.
See Mp00067Foata bijection.
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