Identifier
-
Mp00025:
Dyck paths
—to 132-avoiding permutation⟶
Permutations
Mp00223: Permutations —runsort⟶ Permutations
Mp00204: Permutations —LLPS⟶ Integer partitions
St001214: Integer partitions ⟶ ℤ
Values
[1,0] => [1] => [1] => [1] => 0
[1,0,1,0] => [2,1] => [1,2] => [1,1] => 0
[1,1,0,0] => [1,2] => [1,2] => [1,1] => 0
[1,0,1,0,1,0] => [3,2,1] => [1,2,3] => [1,1,1] => 0
[1,0,1,1,0,0] => [2,3,1] => [1,2,3] => [1,1,1] => 0
[1,1,0,0,1,0] => [3,1,2] => [1,2,3] => [1,1,1] => 0
[1,1,0,1,0,0] => [2,1,3] => [1,3,2] => [2,1] => 1
[1,1,1,0,0,0] => [1,2,3] => [1,2,3] => [1,1,1] => 0
[1,0,1,0,1,0,1,0] => [4,3,2,1] => [1,2,3,4] => [1,1,1,1] => 0
[1,0,1,0,1,1,0,0] => [3,4,2,1] => [1,2,3,4] => [1,1,1,1] => 0
[1,0,1,1,0,0,1,0] => [4,2,3,1] => [1,2,3,4] => [1,1,1,1] => 0
[1,0,1,1,0,1,0,0] => [3,2,4,1] => [1,2,4,3] => [2,1,1] => 1
[1,0,1,1,1,0,0,0] => [2,3,4,1] => [1,2,3,4] => [1,1,1,1] => 0
[1,1,0,0,1,0,1,0] => [4,3,1,2] => [1,2,3,4] => [1,1,1,1] => 0
[1,1,0,0,1,1,0,0] => [3,4,1,2] => [1,2,3,4] => [1,1,1,1] => 0
[1,1,0,1,0,0,1,0] => [4,2,1,3] => [1,3,2,4] => [2,1,1] => 1
[1,1,0,1,0,1,0,0] => [3,2,1,4] => [1,4,2,3] => [2,1,1] => 1
[1,1,0,1,1,0,0,0] => [2,3,1,4] => [1,4,2,3] => [2,1,1] => 1
[1,1,1,0,0,0,1,0] => [4,1,2,3] => [1,2,3,4] => [1,1,1,1] => 0
[1,1,1,0,0,1,0,0] => [3,1,2,4] => [1,2,4,3] => [2,1,1] => 1
[1,1,1,0,1,0,0,0] => [2,1,3,4] => [1,3,4,2] => [2,1,1] => 1
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [1,2,3,4] => [1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => [1,2,3,4,5] => [1,1,1,1,1] => 0
[1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => [1,2,3,4,5] => [1,1,1,1,1] => 0
[1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => [1,2,3,4,5] => [1,1,1,1,1] => 0
[1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => [1,2,3,5,4] => [2,1,1,1] => 1
[1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => [1,2,3,4,5] => [1,1,1,1,1] => 0
[1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => [1,2,3,4,5] => [1,1,1,1,1] => 0
[1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => [1,2,3,4,5] => [1,1,1,1,1] => 0
[1,0,1,1,0,1,0,0,1,0] => [5,3,2,4,1] => [1,2,4,3,5] => [2,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => [1,2,5,3,4] => [2,1,1,1] => 1
[1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => [1,2,5,3,4] => [2,1,1,1] => 1
[1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => [1,2,3,4,5] => [1,1,1,1,1] => 0
[1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => [1,2,3,5,4] => [2,1,1,1] => 1
[1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => [1,2,4,5,3] => [2,1,1,1] => 1
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [1,2,3,4,5] => [1,1,1,1,1] => 0
[1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => [1,2,3,4,5] => [1,1,1,1,1] => 0
[1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => [1,2,3,4,5] => [1,1,1,1,1] => 0
[1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => [1,2,3,4,5] => [1,1,1,1,1] => 0
[1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => [1,2,3,5,4] => [2,1,1,1] => 1
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => [1,2,3,4,5] => [1,1,1,1,1] => 0
[1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,3] => [1,3,2,4,5] => [2,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => [1,3,2,4,5] => [2,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,4] => [1,4,2,3,5] => [2,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,5] => [1,5,2,3,4] => [2,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,0] => [3,4,2,1,5] => [1,5,2,3,4] => [2,1,1,1] => 1
[1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => [1,4,2,3,5] => [2,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,0] => [4,2,3,1,5] => [1,5,2,3,4] => [2,1,1,1] => 1
[1,1,0,1,1,0,1,0,0,0] => [3,2,4,1,5] => [1,5,2,4,3] => [3,1,1] => 2
[1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => [1,5,2,3,4] => [2,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => [1,2,3,4,5] => [1,1,1,1,1] => 0
[1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => [1,2,3,4,5] => [1,1,1,1,1] => 0
[1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => [1,2,4,3,5] => [2,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,0] => [4,3,1,2,5] => [1,2,5,3,4] => [2,1,1,1] => 1
[1,1,1,0,0,1,1,0,0,0] => [3,4,1,2,5] => [1,2,5,3,4] => [2,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => [1,3,4,2,5] => [2,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,0] => [4,2,1,3,5] => [1,3,5,2,4] => [2,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,0] => [3,2,1,4,5] => [1,4,5,2,3] => [2,1,1,1] => 1
[1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => [1,4,5,2,3] => [2,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => [1,2,3,4,5] => [1,1,1,1,1] => 0
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => [1,2,3,5,4] => [2,1,1,1] => 1
[1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => [1,2,4,5,3] => [2,1,1,1] => 1
[1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => [1,3,4,5,2] => [2,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [1,2,3,4,5] => [1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => [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] => [5,6,4,3,2,1] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,5,3,2,1] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,6,3,2,1] => [1,2,3,4,6,5] => [2,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 0
[1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,4,2,1] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 0
[1,0,1,0,1,1,0,0,1,1,0,0] => [5,6,3,4,2,1] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 0
[1,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,5,2,1] => [1,2,3,5,4,6] => [2,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,6,2,1] => [1,2,3,6,4,5] => [2,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => [4,5,3,6,2,1] => [1,2,3,6,4,5] => [2,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,4,5,2,1] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 0
[1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,4,6,2,1] => [1,2,3,4,6,5] => [2,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => [1,2,3,5,6,4] => [2,1,1,1,1] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 0
[1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,3,1] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 0
[1,0,1,1,0,0,1,0,1,1,0,0] => [5,6,4,2,3,1] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 0
[1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,5,2,3,1] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 0
[1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,6,2,3,1] => [1,2,3,4,6,5] => [2,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 0
[1,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,4,1] => [1,2,4,3,5,6] => [2,1,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,0] => [5,6,3,2,4,1] => [1,2,4,3,5,6] => [2,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,5,1] => [1,2,5,3,4,6] => [2,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,1] => [1,2,6,3,4,5] => [2,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,0] => [4,5,3,2,6,1] => [1,2,6,3,4,5] => [2,1,1,1,1] => 1
[1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,4,2,5,1] => [1,2,5,3,4,6] => [2,1,1,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,4,2,6,1] => [1,2,6,3,4,5] => [2,1,1,1,1] => 1
[1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,5,2,6,1] => [1,2,6,3,5,4] => [3,1,1,1] => 2
[1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => [1,2,6,3,4,5] => [2,1,1,1,1] => 1
[1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,3,4,1] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 0
[1,0,1,1,1,0,0,0,1,1,0,0] => [5,6,2,3,4,1] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 0
[1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,3,5,1] => [1,2,3,5,4,6] => [2,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,3,6,1] => [1,2,3,6,4,5] => [2,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => [1,2,3,6,4,5] => [2,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1] => [1,2,4,5,3,6] => [2,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [1,2,4,6,3,5] => [2,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => [1,2,5,6,3,4] => [2,1,1,1,1] => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => [1,2,5,6,3,4] => [2,1,1,1,1] => 1
>>> Load all 1072 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 0
[1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => [1,2,3,4,6,5] => [2,1,1,1,1] => 1
[1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => [1,2,3,5,6,4] => [2,1,1,1,1] => 1
[1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => [1,2,4,5,6,3] => [2,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 0
[1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,2] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 0
[1,1,0,0,1,0,1,0,1,1,0,0] => [5,6,4,3,1,2] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 0
[1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,5,3,1,2] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 0
[1,1,0,0,1,0,1,1,0,1,0,0] => [5,4,6,3,1,2] => [1,2,3,4,6,5] => [2,1,1,1,1] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [4,5,6,3,1,2] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 0
[1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,4,1,2] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 0
[1,1,0,0,1,1,0,0,1,1,0,0] => [5,6,3,4,1,2] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 0
[1,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,5,1,2] => [1,2,3,5,4,6] => [2,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,6,1,2] => [1,2,3,6,4,5] => [2,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => [4,5,3,6,1,2] => [1,2,3,6,4,5] => [2,1,1,1,1] => 1
[1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,4,5,1,2] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 0
[1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,4,6,1,2] => [1,2,3,4,6,5] => [2,1,1,1,1] => 1
[1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,5,6,1,2] => [1,2,3,5,6,4] => [2,1,1,1,1] => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 0
[1,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1,3] => [1,3,2,4,5,6] => [2,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [5,6,4,2,1,3] => [1,3,2,4,5,6] => [2,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [6,4,5,2,1,3] => [1,3,2,4,5,6] => [2,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,6,2,1,3] => [1,3,2,4,6,5] => [2,2,1,1] => 2
[1,1,0,1,0,0,1,1,1,0,0,0] => [4,5,6,2,1,3] => [1,3,2,4,5,6] => [2,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1,4] => [1,4,2,3,5,6] => [2,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,0] => [5,6,3,2,1,4] => [1,4,2,3,5,6] => [2,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,5] => [1,5,2,3,4,6] => [2,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,6] => [1,6,2,3,4,5] => [2,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,0] => [4,5,3,2,1,6] => [1,6,2,3,4,5] => [2,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,4,2,1,5] => [1,5,2,3,4,6] => [2,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,4,2,1,6] => [1,6,2,3,4,5] => [2,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,5,2,1,6] => [1,6,2,3,5,4] => [3,1,1,1] => 2
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,2,1,6] => [1,6,2,3,4,5] => [2,1,1,1,1] => 1
[1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,3,1,4] => [1,4,2,3,5,6] => [2,1,1,1,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,0] => [5,6,2,3,1,4] => [1,4,2,3,5,6] => [2,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,3,1,5] => [1,5,2,3,4,6] => [2,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,3,1,6] => [1,6,2,3,4,5] => [2,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,0] => [4,5,2,3,1,6] => [1,6,2,3,4,5] => [2,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,4,1,5] => [1,5,2,4,3,6] => [3,1,1,1] => 2
[1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,4,1,6] => [1,6,2,4,3,5] => [3,1,1,1] => 2
[1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,5,1,6] => [1,6,2,5,3,4] => [3,1,1,1] => 2
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,4,2,5,1,6] => [1,6,2,5,3,4] => [3,1,1,1] => 2
[1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,3,4,1,5] => [1,5,2,3,4,6] => [2,1,1,1,1] => 1
[1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,3,4,1,6] => [1,6,2,3,4,5] => [2,1,1,1,1] => 1
[1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,3,5,1,6] => [1,6,2,3,5,4] => [3,1,1,1] => 2
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,5,1,6] => [1,6,2,4,5,3] => [3,1,1,1] => 2
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [1,6,2,3,4,5] => [2,1,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,2,3] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 0
[1,1,1,0,0,0,1,0,1,1,0,0] => [5,6,4,1,2,3] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 0
[1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,5,1,2,3] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 0
[1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,6,1,2,3] => [1,2,3,4,6,5] => [2,1,1,1,1] => 1
[1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 0
[1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,2,4] => [1,2,4,3,5,6] => [2,1,1,1,1] => 1
[1,1,1,0,0,1,0,0,1,1,0,0] => [5,6,3,1,2,4] => [1,2,4,3,5,6] => [2,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,2,5] => [1,2,5,3,4,6] => [2,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,2,6] => [1,2,6,3,4,5] => [2,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,1,0,0,0] => [4,5,3,1,2,6] => [1,2,6,3,4,5] => [2,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,4,1,2,5] => [1,2,5,3,4,6] => [2,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,4,1,2,6] => [1,2,6,3,4,5] => [2,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,5,1,2,6] => [1,2,6,3,5,4] => [3,1,1,1] => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => [1,2,6,3,4,5] => [2,1,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,3,4] => [1,3,4,2,5,6] => [2,1,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [5,6,2,1,3,4] => [1,3,4,2,5,6] => [2,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,3,5] => [1,3,5,2,4,6] => [2,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,3,6] => [1,3,6,2,4,5] => [2,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,5,2,1,3,6] => [1,3,6,2,4,5] => [2,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,4,5] => [1,4,5,2,3,6] => [2,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,4,6] => [1,4,6,2,3,5] => [2,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,5,6] => [1,5,6,2,3,4] => [2,1,1,1,1] => 1
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,2,1,5,6] => [1,5,6,2,3,4] => [2,1,1,1,1] => 1
[1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,3,1,4,5] => [1,4,5,2,3,6] => [2,1,1,1,1] => 1
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,3,1,4,6] => [1,4,6,2,3,5] => [2,1,1,1,1] => 1
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,3,1,5,6] => [1,5,6,2,3,4] => [2,1,1,1,1] => 1
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,4,1,5,6] => [1,5,6,2,4,3] => [3,1,1,1] => 2
[1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [1,5,6,2,3,4] => [2,1,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 0
[1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 0
[1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,2,3,5] => [1,2,3,5,4,6] => [2,1,1,1,1] => 1
[1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,2,3,6] => [1,2,3,6,4,5] => [2,1,1,1,1] => 1
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => [1,2,3,6,4,5] => [2,1,1,1,1] => 1
[1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,2,4,5] => [1,2,4,5,3,6] => [2,1,1,1,1] => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,2,4,6] => [1,2,4,6,3,5] => [2,1,1,1,1] => 1
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,2,5,6] => [1,2,5,6,3,4] => [2,1,1,1,1] => 1
[1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => [1,2,5,6,3,4] => [2,1,1,1,1] => 1
[1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => [1,3,4,5,2,6] => [2,1,1,1,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,3,4,6] => [1,3,4,6,2,5] => [2,1,1,1,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,3,5,6] => [1,3,5,6,2,4] => [2,1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,4,5,6] => [1,4,5,6,2,3] => [2,1,1,1,1] => 1
[1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [1,4,5,6,2,3] => [2,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 0
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [1,2,3,4,6,5] => [2,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [1,2,3,5,6,4] => [2,1,1,1,1] => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [1,2,4,5,6,3] => [2,1,1,1,1] => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [1,3,4,5,6,2] => [2,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1] => [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] => [6,7,5,4,3,2,1] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,2,1] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,2,1] => [1,2,3,4,5,7,6] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,2,1] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,2,1] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,2,1] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,2,1] => [1,2,3,4,6,5,7] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,2,1] => [1,2,3,4,7,5,6] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,2,1] => [1,2,3,4,7,5,6] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,2,1] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,2,1] => [1,2,3,4,5,7,6] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,2,1] => [1,2,3,4,6,7,5] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,2,1] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,2,1] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,2,1] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,2,1] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,2,1] => [1,2,3,4,5,7,6] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,2,1] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,2,1] => [1,2,3,5,4,6,7] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,2,1] => [1,2,3,5,4,6,7] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,2,1] => [1,2,3,6,4,5,7] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,2,1] => [1,2,3,7,4,5,6] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,2,1] => [1,2,3,7,4,5,6] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,2,1] => [1,2,3,6,4,5,7] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,2,1] => [1,2,3,7,4,5,6] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,2,1] => [1,2,3,7,4,6,5] => [3,1,1,1,1] => 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,2,1] => [1,2,3,7,4,5,6] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,2,1] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,2,1] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,2,1] => [1,2,3,4,6,5,7] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,2,1] => [1,2,3,4,7,5,6] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,2,1] => [1,2,3,4,7,5,6] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,2,1] => [1,2,3,5,6,4,7] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,2,1] => [1,2,3,5,7,4,6] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => [1,2,3,6,7,4,5] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,2,1] => [1,2,3,6,7,4,5] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,2,1] => [1,2,3,4,5,7,6] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,2,1] => [1,2,3,4,6,7,5] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,2,1] => [1,2,3,5,6,7,4] => [2,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,2,1] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,3,1] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,3,1] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,3,1] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,3,1] => [1,2,3,4,5,7,6] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,3,1] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,3,1] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,3,1] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,3,1] => [1,2,3,4,6,5,7] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,3,1] => [1,2,3,4,7,5,6] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,3,1] => [1,2,3,4,7,5,6] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,3,1] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,3,1] => [1,2,3,4,5,7,6] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,3,1] => [1,2,3,4,6,7,5] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,3,1] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,4,1] => [1,2,4,3,5,6,7] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,4,1] => [1,2,4,3,5,6,7] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,4,1] => [1,2,4,3,5,6,7] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,4,1] => [1,2,4,3,5,7,6] => [2,2,1,1,1] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,4,1] => [1,2,4,3,5,6,7] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,5,1] => [1,2,5,3,4,6,7] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,5,1] => [1,2,5,3,4,6,7] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,6,1] => [1,2,6,3,4,5,7] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,1] => [1,2,7,3,4,5,6] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,7,1] => [1,2,7,3,4,5,6] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,6,1] => [1,2,6,3,4,5,7] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,7,1] => [1,2,7,3,4,5,6] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,7,1] => [1,2,7,3,4,6,5] => [3,1,1,1,1] => 2
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,7,1] => [1,2,7,3,4,5,6] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,5,1] => [1,2,5,3,4,6,7] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,5,1] => [1,2,5,3,4,6,7] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,6,1] => [1,2,6,3,4,5,7] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,7,1] => [1,2,7,3,4,5,6] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,7,1] => [1,2,7,3,4,5,6] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1] => [1,2,6,3,5,4,7] => [3,1,1,1,1] => 2
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,7,1] => [1,2,7,3,5,4,6] => [3,1,1,1,1] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,7,1] => [1,2,7,3,6,4,5] => [3,1,1,1,1] => 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,7,1] => [1,2,7,3,6,4,5] => [3,1,1,1,1] => 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,6,1] => [1,2,6,3,4,5,7] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [1,2,7,3,4,5,6] => [2,1,1,1,1,1] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,7,1] => [1,2,7,3,4,6,5] => [3,1,1,1,1] => 2
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,7,1] => [1,2,7,3,5,6,4] => [3,1,1,1,1] => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,7,1] => [1,2,7,3,4,5,6] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,4,1] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,4,1] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,4,1] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,4,1] => [1,2,3,4,5,7,6] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,4,1] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,5,1] => [1,2,3,5,4,6,7] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,5,1] => [1,2,3,5,4,6,7] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,6,1] => [1,2,3,6,4,5,7] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,7,1] => [1,2,3,7,4,5,6] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,7,1] => [1,2,3,7,4,5,6] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,6,1] => [1,2,3,6,4,5,7] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,7,1] => [1,2,3,7,4,5,6] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,7,1] => [1,2,3,7,4,6,5] => [3,1,1,1,1] => 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,7,1] => [1,2,3,7,4,5,6] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,5,1] => [1,2,4,5,3,6,7] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,5,1] => [1,2,4,5,3,6,7] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,6,1] => [1,2,4,6,3,5,7] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,7,1] => [1,2,4,7,3,5,6] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,7,1] => [1,2,4,7,3,5,6] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,6,1] => [1,2,5,6,3,4,7] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [1,2,5,7,3,4,6] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,7,1] => [1,2,6,7,3,4,5] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,7,1] => [1,2,6,7,3,4,5] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,6,1] => [1,2,5,6,3,4,7] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,7,1] => [1,2,5,7,3,4,6] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,7,1] => [1,2,6,7,3,4,5] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,7,1] => [1,2,6,7,3,5,4] => [3,1,1,1,1] => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,7,1] => [1,2,6,7,3,4,5] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,5,1] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,5,1] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,6,1] => [1,2,3,4,6,5,7] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,7,1] => [1,2,3,4,7,5,6] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,7,1] => [1,2,3,4,7,5,6] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,6,1] => [1,2,3,5,6,4,7] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,7,1] => [1,2,3,5,7,4,6] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,7,1] => [1,2,3,6,7,4,5] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,7,1] => [1,2,3,6,7,4,5] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,6,1] => [1,2,4,5,6,3,7] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,7,1] => [1,2,4,5,7,3,6] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,7,1] => [1,2,4,6,7,3,5] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,7,1] => [1,2,5,6,7,3,4] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,7,1] => [1,2,5,6,7,3,4] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,6,1] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,7,1] => [1,2,3,4,5,7,6] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,7,1] => [1,2,3,4,6,7,5] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,7,1] => [1,2,3,5,6,7,4] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,7,1] => [1,2,4,5,6,7,3] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,1,2] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,1,2] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,1,2] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,1,2] => [1,2,3,4,5,7,6] => [2,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,1,2] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,1,2] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,1,2] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,1,2] => [1,2,3,4,6,5,7] => [2,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,1,2] => [1,2,3,4,7,5,6] => [2,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,1,2] => [1,2,3,4,7,5,6] => [2,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,1,2] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,1,2] => [1,2,3,4,5,7,6] => [2,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,1,2] => [1,2,3,4,6,7,5] => [2,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,1,2] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,1,2] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,1,2] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,1,2] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,1,2] => [1,2,3,4,5,7,6] => [2,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,1,2] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,1,2] => [1,2,3,5,4,6,7] => [2,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,1,2] => [1,2,3,5,4,6,7] => [2,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,1,2] => [1,2,3,6,4,5,7] => [2,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,1,2] => [1,2,3,7,4,5,6] => [2,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,1,2] => [1,2,3,7,4,5,6] => [2,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,1,2] => [1,2,3,6,4,5,7] => [2,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,1,2] => [1,2,3,7,4,5,6] => [2,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,1,2] => [1,2,3,7,4,6,5] => [3,1,1,1,1] => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,1,2] => [1,2,3,7,4,5,6] => [2,1,1,1,1,1] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,1,2] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,1,2] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,1,2] => [1,2,3,4,6,5,7] => [2,1,1,1,1,1] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,1,2] => [1,2,3,4,7,5,6] => [2,1,1,1,1,1] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,1,2] => [1,2,3,4,7,5,6] => [2,1,1,1,1,1] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,1,2] => [1,2,3,5,6,4,7] => [2,1,1,1,1,1] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,1,2] => [1,2,3,5,7,4,6] => [2,1,1,1,1,1] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,1,2] => [1,2,3,6,7,4,5] => [2,1,1,1,1,1] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,1,2] => [1,2,3,6,7,4,5] => [2,1,1,1,1,1] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,1,2] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,1,2] => [1,2,3,4,5,7,6] => [2,1,1,1,1,1] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,1,2] => [1,2,3,4,6,7,5] => [2,1,1,1,1,1] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,1,2] => [1,2,3,5,6,7,4] => [2,1,1,1,1,1] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,1,3] => [1,3,2,4,5,6,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,1,3] => [1,3,2,4,5,6,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,1,3] => [1,3,2,4,5,6,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,1,3] => [1,3,2,4,5,7,6] => [2,2,1,1,1] => 2
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,1,3] => [1,3,2,4,5,6,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,1,3] => [1,3,2,4,5,6,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,1,3] => [1,3,2,4,5,6,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,1,3] => [1,3,2,4,6,5,7] => [2,2,1,1,1] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,1,3] => [1,3,2,4,7,5,6] => [2,2,1,1,1] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,1,3] => [1,3,2,4,7,5,6] => [2,2,1,1,1] => 2
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,1,3] => [1,3,2,4,5,6,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,1,3] => [1,3,2,4,5,7,6] => [2,2,1,1,1] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,1,3] => [1,3,2,4,6,7,5] => [2,2,1,1,1] => 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,1,3] => [1,3,2,4,5,6,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,1,4] => [1,4,2,3,5,6,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,1,4] => [1,4,2,3,5,6,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,1,4] => [1,4,2,3,5,6,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,1,4] => [1,4,2,3,5,7,6] => [2,2,1,1,1] => 2
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,1,4] => [1,4,2,3,5,6,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,1,5] => [1,5,2,3,4,6,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,1,5] => [1,5,2,3,4,6,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,1,6] => [1,6,2,3,4,5,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,7] => [1,7,2,3,4,5,6] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,1,7] => [1,7,2,3,4,5,6] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,1,6] => [1,6,2,3,4,5,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,1,7] => [1,7,2,3,4,5,6] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,1,7] => [1,7,2,3,4,6,5] => [3,1,1,1,1] => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,1,7] => [1,7,2,3,4,5,6] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,1,5] => [1,5,2,3,4,6,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,1,5] => [1,5,2,3,4,6,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,1,6] => [1,6,2,3,4,5,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,1,7] => [1,7,2,3,4,5,6] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,1,7] => [1,7,2,3,4,5,6] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,1,6] => [1,6,2,3,5,4,7] => [3,1,1,1,1] => 2
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,1,7] => [1,7,2,3,5,4,6] => [3,1,1,1,1] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,1,7] => [1,7,2,3,6,4,5] => [3,1,1,1,1] => 2
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,1,7] => [1,7,2,3,6,4,5] => [3,1,1,1,1] => 2
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,1,6] => [1,6,2,3,4,5,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,1,7] => [1,7,2,3,4,5,6] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,1,7] => [1,7,2,3,4,6,5] => [3,1,1,1,1] => 2
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,1,7] => [1,7,2,3,5,6,4] => [3,1,1,1,1] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,1,7] => [1,7,2,3,4,5,6] => [2,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,1,4] => [1,4,2,3,5,6,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,1,4] => [1,4,2,3,5,6,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,1,4] => [1,4,2,3,5,6,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,1,4] => [1,4,2,3,5,7,6] => [2,2,1,1,1] => 2
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,1,4] => [1,4,2,3,5,6,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,1,5] => [1,5,2,3,4,6,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,1,5] => [1,5,2,3,4,6,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,1,6] => [1,6,2,3,4,5,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,1,7] => [1,7,2,3,4,5,6] => [2,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,1,7] => [1,7,2,3,4,5,6] => [2,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,1,6] => [1,6,2,3,4,5,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,1,7] => [1,7,2,3,4,5,6] => [2,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,1,7] => [1,7,2,3,4,6,5] => [3,1,1,1,1] => 2
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,1,7] => [1,7,2,3,4,5,6] => [2,1,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,1,5] => [1,5,2,4,3,6,7] => [3,1,1,1,1] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,1,5] => [1,5,2,4,3,6,7] => [3,1,1,1,1] => 2
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,1,6] => [1,6,2,4,3,5,7] => [3,1,1,1,1] => 2
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,1,7] => [1,7,2,4,3,5,6] => [3,1,1,1,1] => 2
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,1,7] => [1,7,2,4,3,5,6] => [3,1,1,1,1] => 2
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,1,6] => [1,6,2,5,3,4,7] => [3,1,1,1,1] => 2
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,1,7] => [1,7,2,5,3,4,6] => [3,1,1,1,1] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,1,7] => [1,7,2,6,3,4,5] => [3,1,1,1,1] => 2
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,1,7] => [1,7,2,6,3,4,5] => [3,1,1,1,1] => 2
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,1,6] => [1,6,2,5,3,4,7] => [3,1,1,1,1] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,1,7] => [1,7,2,5,3,4,6] => [3,1,1,1,1] => 2
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,1,7] => [1,7,2,6,3,4,5] => [3,1,1,1,1] => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,1,7] => [1,7,2,6,3,5,4] => [4,1,1,1] => 3
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,1,7] => [1,7,2,6,3,4,5] => [3,1,1,1,1] => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,1,5] => [1,5,2,3,4,6,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,1,5] => [1,5,2,3,4,6,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,1,6] => [1,6,2,3,4,5,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,1,7] => [1,7,2,3,4,5,6] => [2,1,1,1,1,1] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,1,7] => [1,7,2,3,4,5,6] => [2,1,1,1,1,1] => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,1,6] => [1,6,2,3,5,4,7] => [3,1,1,1,1] => 2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,1,7] => [1,7,2,3,5,4,6] => [3,1,1,1,1] => 2
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,1,7] => [1,7,2,3,6,4,5] => [3,1,1,1,1] => 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,1,7] => [1,7,2,3,6,4,5] => [3,1,1,1,1] => 2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,1,6] => [1,6,2,4,5,3,7] => [3,1,1,1,1] => 2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,1,7] => [1,7,2,4,5,3,6] => [3,1,1,1,1] => 2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,1,7] => [1,7,2,4,6,3,5] => [3,1,1,1,1] => 2
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,1,7] => [1,7,2,5,6,3,4] => [3,1,1,1,1] => 2
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,1,7] => [1,7,2,5,6,3,4] => [3,1,1,1,1] => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,1,6] => [1,6,2,3,4,5,7] => [2,1,1,1,1,1] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,1,7] => [1,7,2,3,4,5,6] => [2,1,1,1,1,1] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,1,7] => [1,7,2,3,4,6,5] => [3,1,1,1,1] => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,1,7] => [1,7,2,3,5,6,4] => [3,1,1,1,1] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,1,7] => [1,7,2,4,5,6,3] => [3,1,1,1,1] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,7,2,3,4,5,6] => [2,1,1,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1,2,3] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,1,2,3] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,1,2,3] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,1,2,3] => [1,2,3,4,5,7,6] => [2,1,1,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,1,2,3] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,1,2,3] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,1,2,3] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,1,2,3] => [1,2,3,4,6,5,7] => [2,1,1,1,1,1] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,1,2,3] => [1,2,3,4,7,5,6] => [2,1,1,1,1,1] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,1,2,3] => [1,2,3,4,7,5,6] => [2,1,1,1,1,1] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,1,2,3] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,1,2,3] => [1,2,3,4,5,7,6] => [2,1,1,1,1,1] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,1,2,3] => [1,2,3,4,6,7,5] => [2,1,1,1,1,1] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,1,2,3] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,1,2,4] => [1,2,4,3,5,6,7] => [2,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,1,2,4] => [1,2,4,3,5,6,7] => [2,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,1,2,4] => [1,2,4,3,5,6,7] => [2,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,1,2,4] => [1,2,4,3,5,7,6] => [2,2,1,1,1] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,1,2,4] => [1,2,4,3,5,6,7] => [2,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,1,2,5] => [1,2,5,3,4,6,7] => [2,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,1,2,5] => [1,2,5,3,4,6,7] => [2,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,1,2,6] => [1,2,6,3,4,5,7] => [2,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,2,7] => [1,2,7,3,4,5,6] => [2,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,1,2,7] => [1,2,7,3,4,5,6] => [2,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,1,2,6] => [1,2,6,3,4,5,7] => [2,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,1,2,7] => [1,2,7,3,4,5,6] => [2,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,1,2,7] => [1,2,7,3,4,6,5] => [3,1,1,1,1] => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,1,2,7] => [1,2,7,3,4,5,6] => [2,1,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,1,2,5] => [1,2,5,3,4,6,7] => [2,1,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,1,2,5] => [1,2,5,3,4,6,7] => [2,1,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,1,2,6] => [1,2,6,3,4,5,7] => [2,1,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,1,2,7] => [1,2,7,3,4,5,6] => [2,1,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,1,2,7] => [1,2,7,3,4,5,6] => [2,1,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,1,2,6] => [1,2,6,3,5,4,7] => [3,1,1,1,1] => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,1,2,7] => [1,2,7,3,5,4,6] => [3,1,1,1,1] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,1,2,7] => [1,2,7,3,6,4,5] => [3,1,1,1,1] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,1,2,7] => [1,2,7,3,6,4,5] => [3,1,1,1,1] => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,1,2,6] => [1,2,6,3,4,5,7] => [2,1,1,1,1,1] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,1,2,7] => [1,2,7,3,4,5,6] => [2,1,1,1,1,1] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,1,2,7] => [1,2,7,3,4,6,5] => [3,1,1,1,1] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,1,2,7] => [1,2,7,3,5,6,4] => [3,1,1,1,1] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,1,2,7] => [1,2,7,3,4,5,6] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,1,3,4] => [1,3,4,2,5,6,7] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,1,3,4] => [1,3,4,2,5,6,7] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,1,3,4] => [1,3,4,2,5,6,7] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,1,3,4] => [1,3,4,2,5,7,6] => [2,2,1,1,1] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,1,3,4] => [1,3,4,2,5,6,7] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,1,3,5] => [1,3,5,2,4,6,7] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,1,3,5] => [1,3,5,2,4,6,7] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,1,3,6] => [1,3,6,2,4,5,7] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,3,7] => [1,3,7,2,4,5,6] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,1,3,7] => [1,3,7,2,4,5,6] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,1,3,6] => [1,3,6,2,4,5,7] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,1,3,7] => [1,3,7,2,4,5,6] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,1,3,7] => [1,3,7,2,4,6,5] => [3,1,1,1,1] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,1,3,7] => [1,3,7,2,4,5,6] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,1,4,5] => [1,4,5,2,3,6,7] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,1,4,5] => [1,4,5,2,3,6,7] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,1,4,6] => [1,4,6,2,3,5,7] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1,4,7] => [1,4,7,2,3,5,6] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,1,4,7] => [1,4,7,2,3,5,6] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,1,5,6] => [1,5,6,2,3,4,7] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,5,7] => [1,5,7,2,3,4,6] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,6,7] => [1,6,7,2,3,4,5] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,1,6,7] => [1,6,7,2,3,4,5] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,1,5,6] => [1,5,6,2,3,4,7] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,1,5,7] => [1,5,7,2,3,4,6] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,1,6,7] => [1,6,7,2,3,4,5] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,1,6,7] => [1,6,7,2,3,5,4] => [3,1,1,1,1] => 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,1,6,7] => [1,6,7,2,3,4,5] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,1,4,5] => [1,4,5,2,3,6,7] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,1,4,5] => [1,4,5,2,3,6,7] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,1,4,6] => [1,4,6,2,3,5,7] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,1,4,7] => [1,4,7,2,3,5,6] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,1,4,7] => [1,4,7,2,3,5,6] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,1,5,6] => [1,5,6,2,3,4,7] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,1,5,7] => [1,5,7,2,3,4,6] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,1,6,7] => [1,6,7,2,3,4,5] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,1,6,7] => [1,6,7,2,3,4,5] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,1,5,6] => [1,5,6,2,4,3,7] => [3,1,1,1,1] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,1,5,7] => [1,5,7,2,4,3,6] => [3,1,1,1,1] => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,1,6,7] => [1,6,7,2,4,3,5] => [3,1,1,1,1] => 2
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,1,6,7] => [1,6,7,2,5,3,4] => [3,1,1,1,1] => 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,1,6,7] => [1,6,7,2,5,3,4] => [3,1,1,1,1] => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,1,5,6] => [1,5,6,2,3,4,7] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,1,5,7] => [1,5,7,2,3,4,6] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,1,6,7] => [1,6,7,2,3,4,5] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,1,6,7] => [1,6,7,2,3,5,4] => [3,1,1,1,1] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,1,6,7] => [1,6,7,2,4,5,3] => [3,1,1,1,1] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,6,7,2,3,4,5] => [2,1,1,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [7,6,5,1,2,3,4] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [6,7,5,1,2,3,4] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [7,5,6,1,2,3,4] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [6,5,7,1,2,3,4] => [1,2,3,4,5,7,6] => [2,1,1,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [7,6,4,1,2,3,5] => [1,2,3,5,4,6,7] => [2,1,1,1,1,1] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [6,7,4,1,2,3,5] => [1,2,3,5,4,6,7] => [2,1,1,1,1,1] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [7,5,4,1,2,3,6] => [1,2,3,6,4,5,7] => [2,1,1,1,1,1] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,2,3,7] => [1,2,3,7,4,5,6] => [2,1,1,1,1,1] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,6,4,1,2,3,7] => [1,2,3,7,4,5,6] => [2,1,1,1,1,1] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [7,4,5,1,2,3,6] => [1,2,3,6,4,5,7] => [2,1,1,1,1,1] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,5,1,2,3,7] => [1,2,3,7,4,5,6] => [2,1,1,1,1,1] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,6,1,2,3,7] => [1,2,3,7,4,6,5] => [3,1,1,1,1] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => [1,2,3,7,4,5,6] => [2,1,1,1,1,1] => 1
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [7,6,3,1,2,4,5] => [1,2,4,5,3,6,7] => [2,1,1,1,1,1] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [6,7,3,1,2,4,5] => [1,2,4,5,3,6,7] => [2,1,1,1,1,1] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1,2,4,6] => [1,2,4,6,3,5,7] => [2,1,1,1,1,1] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,2,4,7] => [1,2,4,7,3,5,6] => [2,1,1,1,1,1] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,6,3,1,2,4,7] => [1,2,4,7,3,5,6] => [2,1,1,1,1,1] => 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,2,5,6] => [1,2,5,6,3,4,7] => [2,1,1,1,1,1] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,2,5,7] => [1,2,5,7,3,4,6] => [2,1,1,1,1,1] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,2,6,7] => [1,2,6,7,3,4,5] => [2,1,1,1,1,1] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,5,3,1,2,6,7] => [1,2,6,7,3,4,5] => [2,1,1,1,1,1] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,4,1,2,5,6] => [1,2,5,6,3,4,7] => [2,1,1,1,1,1] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,4,1,2,5,7] => [1,2,5,7,3,4,6] => [2,1,1,1,1,1] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,4,1,2,6,7] => [1,2,6,7,3,4,5] => [2,1,1,1,1,1] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,5,1,2,6,7] => [1,2,6,7,3,5,4] => [3,1,1,1,1] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,4,5,1,2,6,7] => [1,2,6,7,3,4,5] => [2,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [7,6,2,1,3,4,5] => [1,3,4,5,2,6,7] => [2,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,7,2,1,3,4,5] => [1,3,4,5,2,6,7] => [2,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,3,4,6] => [1,3,4,6,2,5,7] => [2,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,3,4,7] => [1,3,4,7,2,5,6] => [2,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,6,2,1,3,4,7] => [1,3,4,7,2,5,6] => [2,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,3,5,6] => [1,3,5,6,2,4,7] => [2,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,3,5,7] => [1,3,5,7,2,4,6] => [2,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,3,6,7] => [1,3,6,7,2,4,5] => [2,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,2,1,3,6,7] => [1,3,6,7,2,4,5] => [2,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,4,5,6] => [1,4,5,6,2,3,7] => [2,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,4,5,7] => [1,4,5,7,2,3,6] => [2,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,4,6,7] => [1,4,6,7,2,3,5] => [2,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,5,6,7] => [1,5,6,7,2,3,4] => [2,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,4,2,1,5,6,7] => [1,5,6,7,2,3,4] => [2,1,1,1,1,1] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,3,1,4,5,6] => [1,4,5,6,2,3,7] => [2,1,1,1,1,1] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,3,1,4,5,7] => [1,4,5,7,2,3,6] => [2,1,1,1,1,1] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,3,1,4,6,7] => [1,4,6,7,2,3,5] => [2,1,1,1,1,1] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,3,1,5,6,7] => [1,5,6,7,2,3,4] => [2,1,1,1,1,1] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,4,1,5,6,7] => [1,5,6,7,2,4,3] => [3,1,1,1,1] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,5,6,7,2,3,4] => [2,1,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,2,3,4,5] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,2,3,4,6] => [1,2,3,4,6,5,7] => [2,1,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,2,3,4,7] => [1,2,3,4,7,5,6] => [2,1,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,6,1,2,3,4,7] => [1,2,3,4,7,5,6] => [2,1,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,2,3,5,6] => [1,2,3,5,6,4,7] => [2,1,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,2,3,5,7] => [1,2,3,5,7,4,6] => [2,1,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,2,3,6,7] => [1,2,3,6,7,4,5] => [2,1,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,5,1,2,3,6,7] => [1,2,3,6,7,4,5] => [2,1,1,1,1,1] => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,2,4,5,6] => [1,2,4,5,6,3,7] => [2,1,1,1,1,1] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,2,4,5,7] => [1,2,4,5,7,3,6] => [2,1,1,1,1,1] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,2,4,6,7] => [1,2,4,6,7,3,5] => [2,1,1,1,1,1] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,2,5,6,7] => [1,2,5,6,7,3,4] => [2,1,1,1,1,1] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,4,1,2,5,6,7] => [1,2,5,6,7,3,4] => [2,1,1,1,1,1] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,3,4,5,6] => [1,3,4,5,6,2,7] => [2,1,1,1,1,1] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,3,4,5,7] => [1,3,4,5,7,2,6] => [2,1,1,1,1,1] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,3,4,6,7] => [1,3,4,6,7,2,5] => [2,1,1,1,1,1] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,3,5,6,7] => [1,3,5,6,7,2,4] => [2,1,1,1,1,1] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,4,5,6,7] => [1,4,5,6,7,2,3] => [2,1,1,1,1,1] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,4,5,6,7,2,3] => [2,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,5,7] => [1,2,3,4,5,7,6] => [2,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,2,3,4,6,7] => [1,2,3,4,6,7,5] => [2,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,2,3,5,6,7] => [1,2,3,5,6,7,4] => [2,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,2,4,5,6,7] => [1,2,4,5,6,7,3] => [2,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => [1,3,4,5,6,7,2] => [2,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,2,1] => [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] => [7,8,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,3,2,1] => [1,2,3,4,5,6,8,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,3,2,1] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,3,2,1] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,3,2,1] => [1,2,3,4,5,8,6,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,3,2,1] => [1,2,3,4,5,6,8,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,3,2,1] => [1,2,3,4,5,7,8,6] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,2,1] => [1,2,3,4,5,6,7,8] => [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] => [8,7,6,4,5,3,2,1] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,2,1] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,3,2,1] => [1,2,3,4,5,6,7,8] => [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] => [7,6,5,4,8,3,2,1] => [1,2,3,4,8,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,3,2,1] => [1,2,3,4,8,5,7,6] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,3,2,1] => [1,2,3,4,5,8,6,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,3,2,1] => [1,2,3,4,6,8,5,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,3,2,1] => [1,2,3,4,5,6,8,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,2,1] => [1,2,3,4,5,6,7,8] => [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] => [8,7,6,5,3,4,2,1] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,4,2,1] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,4,2,1] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,2,1] => [1,2,3,4,5,6,7,8] => [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] => [5,6,7,8,3,4,2,1] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,6,2,1] => [1,2,3,6,4,5,7,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,8,2,1] => [1,2,3,8,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,8,2,1] => [1,2,3,8,4,5,7,6] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,8,2,1] => [1,2,3,8,4,6,7,5] => [3,1,1,1,1,1] => 2
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,8,2,1] => [1,2,3,8,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,5,2,1] => [1,2,3,4,5,6,7,8] => [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] => [7,6,5,3,4,8,2,1] => [1,2,3,4,8,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,8,2,1] => [1,2,3,5,8,4,6,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,8,2,1] => [1,2,3,4,5,8,6,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,8,2,1] => [1,2,3,4,5,7,8,6] => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,8,2,1] => [1,2,3,5,6,7,8,4] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2,3,1] => [1,2,3,4,5,6,7,8] => [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] => [7,8,6,5,4,2,3,1] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,3,1] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,2,3,1] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,3,1] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,2,3,1] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,2,3,1] => [1,2,3,4,5,6,7,8] => [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] => [4,5,6,7,8,2,3,1] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,2,4,1] => [1,2,4,3,5,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,2,4,1] => [1,2,4,3,5,7,6,8] => [2,2,1,1,1,1] => 2
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,2,4,1] => [1,2,4,3,5,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,8,1] => [1,2,8,3,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,2,8,1] => [1,2,8,3,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,8,1] => [1,2,8,3,4,5,7,6] => [3,1,1,1,1,1] => 2
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,2,8,1] => [1,2,8,3,4,5,7,6] => [3,1,1,1,1,1] => 2
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,2,8,1] => [1,2,8,3,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,2,8,1] => [1,2,8,3,7,4,5,6] => [3,1,1,1,1,1] => 2
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,2,8,1] => [1,2,8,3,7,4,6,5] => [4,1,1,1,1] => 3
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,3,4,1] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,3,4,1] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,3,4,1] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,4,1] => [1,2,3,4,5,6,7,8] => [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] => [7,6,5,4,2,3,8,1] => [1,2,3,8,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,8,1] => [1,2,3,8,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,2,3,8,1] => [1,2,3,8,4,5,7,6] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,3,8,1] => [1,2,3,8,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,4,8,1] => [1,2,4,8,3,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,8,1] => [1,2,3,4,8,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,4,5,6,1] => [1,2,4,5,6,3,7,8] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,7,8,1] => [1,2,6,7,8,3,4,5] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,7,8,1] => [1,2,6,7,8,3,4,5] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,5,8,1] => [1,2,3,4,5,8,6,7] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,7,8,1] => [1,2,5,6,7,8,3,4] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,7,8,1] => [1,2,5,6,7,8,3,4] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,7,8,1] => [1,2,3,4,6,7,8,5] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,7,8,1] => [1,2,3,5,6,7,8,4] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,8,1] => [1,2,4,5,6,7,8,3] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => [1,2,3,4,5,6,7,8] => [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] => [8,7,6,5,4,3,1,2] => [1,2,3,4,5,6,7,8] => [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] => [7,8,6,5,4,3,1,2] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,3,1,2] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,3,1,2] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,3,1,2] => [1,2,3,4,5,7,8,6] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,1,2] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,3,1,2] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,1,2] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,1,2] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,4,1,2] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,1,2] => [1,2,3,4,5,6,7,8] => [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] => [7,8,5,6,3,4,1,2] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,4,1,2] => [1,2,3,4,5,8,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,4,1,2] => [1,2,3,4,5,8,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,4,1,2] => [1,2,3,4,5,6,8,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,4,1,2] => [1,2,3,4,5,7,8,6] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,1,2] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,6,1,2] => [1,2,3,6,4,5,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,8,1,2] => [1,2,3,8,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,8,1,2] => [1,2,3,8,4,5,7,6] => [3,1,1,1,1,1] => 2
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,8,1,2] => [1,2,3,8,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,3,6,1,2] => [1,2,3,6,4,5,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,8,1,2] => [1,2,3,8,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,3,8,1,2] => [1,2,3,8,4,7,5,6] => [3,1,1,1,1,1] => 2
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,8,1,2] => [1,2,3,8,4,6,7,5] => [3,1,1,1,1,1] => 2
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,8,1,2] => [1,2,3,8,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,6,1,2] => [1,2,3,4,6,5,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,6,1,2] => [1,2,3,5,6,4,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,8,1,2] => [1,2,3,7,8,4,6,5] => [3,1,1,1,1,1] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,6,1,2] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,8,1,2] => [1,2,3,4,7,8,5,6] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,7,1,2] => [1,2,3,5,6,7,4,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,8,1,2] => [1,2,3,5,7,8,4,6] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,8,1,2] => [1,2,3,6,7,8,4,5] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,8,1,2] => [1,2,3,6,7,8,4,5] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,7,1,2] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,8,1,2] => [1,2,3,4,5,7,8,6] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,8,1,2] => [1,2,3,5,6,7,8,4] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2,1,3] => [1,3,2,4,5,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,2,1,3] => [1,3,2,4,5,6,8,7] => [2,2,1,1,1,1] => 2
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,1,3] => [1,3,2,4,5,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,2,1,3] => [1,3,2,4,5,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,2,1,4] => [1,4,2,3,5,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,2,1,4] => [1,4,2,3,5,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,2,1,4] => [1,4,2,3,5,8,6,7] => [2,2,1,1,1,1] => 2
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,2,1,4] => [1,4,2,3,5,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,2,1,5] => [1,5,2,3,4,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,2,1,5] => [1,5,2,3,4,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,2,1,6] => [1,6,2,3,4,5,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,2,1,7] => [1,7,2,3,4,5,6,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,1,8] => [1,8,2,3,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,2,1,8] => [1,8,2,3,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,1,8] => [1,8,2,3,4,5,7,6] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,2,1,8] => [1,8,2,3,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,2,1,8] => [1,8,2,3,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,2,1,8] => [1,8,2,3,4,7,5,6] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,3,2,1,7] => [1,7,2,3,4,5,6,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,2,1,8] => [1,8,2,3,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,2,1,8] => [1,8,2,3,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,2,1,5] => [1,5,2,3,4,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,2,1,5] => [1,5,2,3,4,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,2,1,8] => [1,8,2,3,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,2,1,8] => [1,8,2,3,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,2,1,8] => [1,8,2,3,5,4,6,7] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,2,1,8] => [1,8,2,3,6,4,5,7] => [3,1,1,1,1,1] => 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,2,1,8] => [1,8,2,3,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,3,1,4] => [1,4,2,3,5,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,3,1,4] => [1,4,2,3,5,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,3,1,4] => [1,4,2,3,5,8,6,7] => [2,2,1,1,1,1] => 2
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,2,3,1,4] => [1,4,2,3,5,6,8,7] => [2,2,1,1,1,1] => 2
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,1,4] => [1,4,2,3,5,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,3,1,5] => [1,5,2,3,4,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,3,1,5] => [1,5,2,3,4,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,2,3,1,8] => [1,8,2,3,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,2,3,1,8] => [1,8,2,3,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,2,3,1,6] => [1,6,2,3,4,5,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,3,1,8] => [1,8,2,3,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,1,8] => [1,8,2,3,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,2,3,1,8] => [1,8,2,3,4,7,5,6] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,2,3,1,8] => [1,8,2,3,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,3,1,8] => [1,8,2,3,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,4,1,5] => [1,5,2,4,3,6,7,8] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,4,1,5] => [1,5,2,4,3,6,7,8] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,2,4,1,8] => [1,8,2,4,3,5,6,7] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,2,5,1,6] => [1,6,2,5,3,4,7,8] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,2,5,1,8] => [1,8,2,5,3,4,6,7] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,2,7,1,8] => [1,8,2,7,3,4,5,6] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,2,7,1,8] => [1,8,2,7,3,6,4,5] => [4,1,1,1,1] => 3
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,4,1,5] => [1,5,2,3,4,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,4,1,5] => [1,5,2,3,4,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,1,8] => [1,8,2,3,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,3,4,1,8] => [1,8,2,3,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,4,1,8] => [1,8,2,3,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [6,5,7,2,3,4,1,8] => [1,8,2,3,4,5,7,6] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,4,1,8] => [1,8,2,3,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,3,6,1,8] => [1,8,2,3,6,4,5,7] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,7,1,8] => [1,8,2,6,7,3,4,5] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,1,8] => [1,8,2,4,5,6,7,3] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8] => [1,8,2,3,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,1,2,3] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,1,2,3] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,1,2,3] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,1,2,3] => [1,2,3,4,5,7,8,6] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,1,2,3] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,1,2,3] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,1,2,3] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,1,2,3] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,1,2,3] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,1,2,3] => [1,2,3,4,5,8,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,1,2,3] => [1,2,3,4,7,8,5,6] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,1,2,3] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,1,2,4] => [1,2,4,3,5,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,1,2,4] => [1,2,4,3,5,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,1,2,4] => [1,2,4,3,5,8,6,7] => [2,2,1,1,1,1] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,1,2,4] => [1,2,4,3,5,6,8,7] => [2,2,1,1,1,1] => 2
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,1,2,4] => [1,2,4,3,5,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,1,2,5] => [1,2,5,3,4,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,1,2,5] => [1,2,5,3,4,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,1,2,7] => [1,2,7,3,4,5,6,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,1,2,8] => [1,2,8,3,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,1,2,8] => [1,2,8,3,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,1,2,8] => [1,2,8,3,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,1,2,8] => [1,2,8,3,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,1,2,5] => [1,2,5,3,4,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,1,2,5] => [1,2,5,3,4,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,1,2,7] => [1,2,7,3,4,5,6,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,1,2,7] => [1,2,7,3,4,5,6,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,1,3,4] => [1,3,4,2,5,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,2,1,3,4] => [1,3,4,2,5,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,1,3,4] => [1,3,4,2,5,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,1,3,4] => [1,3,4,2,5,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,1,3,4] => [1,3,4,2,5,7,8,6] => [2,2,1,1,1,1] => 2
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,1,3,4] => [1,3,4,2,5,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,1,3,5] => [1,3,5,2,4,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,1,3,5] => [1,3,5,2,4,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,2,1,3,6] => [1,3,6,2,4,5,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,1,3,7] => [1,3,7,2,4,5,6,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,1,3,8] => [1,3,8,2,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,2,1,3,8] => [1,3,8,2,4,5,7,6] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,1,3,8] => [1,3,8,2,4,6,5,7] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,2,1,3,8] => [1,3,8,2,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,1,3,8] => [1,3,8,2,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,1,4,5] => [1,4,5,2,3,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,1,4,5] => [1,4,5,2,3,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,1,5,6] => [1,5,6,2,3,4,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,1,5,6] => [1,5,6,2,3,4,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,2,1,5,7] => [1,5,7,2,3,4,6,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,1,5,8] => [1,5,8,2,3,4,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,1,7,8] => [1,7,8,2,3,4,5,6] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,2,1,5,7] => [1,5,7,2,3,4,6,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,1,4,5] => [1,4,5,2,3,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,1,4,5] => [1,4,5,2,3,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,3,1,4,7] => [1,4,7,2,3,5,6,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,3,1,4,7] => [1,4,7,2,3,5,6,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,1,5,6] => [1,5,6,2,3,4,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,1,7,8] => [1,7,8,2,3,5,6,4] => [3,1,1,1,1,1] => 2
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8] => [1,7,8,2,3,4,5,6] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,1,2,3,4] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,1,2,3,4] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,1,2,3,4] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,1,2,3,4] => [1,2,3,4,5,6,8,7] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,1,2,3,4] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,1,2,3,4] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,1,2,3,4] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,1,2,3,4] => [1,2,3,4,5,7,6,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,1,2,3,4] => [1,2,3,4,5,8,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,1,2,3,4] => [1,2,3,4,5,8,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,1,2,3,4] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,1,2,3,4] => [1,2,3,4,5,6,8,7] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,1,2,3,4] => [1,2,3,4,5,7,8,6] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,1,2,3,5] => [1,2,3,5,4,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,1,2,3,5] => [1,2,3,5,4,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,1,2,3,6] => [1,2,3,6,4,5,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,1,2,3,8] => [1,2,3,8,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,1,2,3,8] => [1,2,3,8,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,1,2,3,6] => [1,2,3,6,4,5,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,1,2,3,7] => [1,2,3,7,4,5,6,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,1,2,3,8] => [1,2,3,8,4,7,5,6] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,1,2,3,8] => [1,2,3,8,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,1,2,3,8] => [1,2,3,8,4,6,7,5] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,1,2,3,8] => [1,2,3,8,4,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,1,2,4,8] => [1,2,4,8,3,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,1,2,5,8] => [1,2,5,8,3,4,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,1,2,7,8] => [1,2,7,8,3,4,5,6] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,1,2,7,8] => [1,2,7,8,3,4,6,5] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,1,2,5,6] => [1,2,5,6,3,4,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,1,2,7,8] => [1,2,7,8,3,4,5,6] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,1,2,7,8] => [1,2,7,8,3,6,4,5] => [3,1,1,1,1,1] => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,1,3,4,5] => [1,3,4,5,2,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,1,3,4,5] => [1,3,4,5,2,6,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [8,7,5,2,1,3,4,6] => [1,3,4,6,2,5,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [7,8,5,2,1,3,4,6] => [1,3,4,6,2,5,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,1,3,4,7] => [1,3,4,7,2,5,6,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,1,3,4,8] => [1,3,4,8,2,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,1,3,5,6] => [1,3,5,6,2,4,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,1,3,5,7] => [1,3,5,7,2,4,6,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [5,6,4,2,1,3,7,8] => [1,3,7,8,2,4,5,6] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [8,7,3,2,1,4,5,6] => [1,4,5,6,2,3,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,1,4,5,6] => [1,4,5,6,2,3,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [5,6,3,2,1,4,7,8] => [1,4,7,8,2,3,5,6] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [8,4,3,2,1,5,6,7] => [1,5,6,7,2,3,4,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,1,5,6,8] => [1,5,6,8,2,3,4,7] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,1,5,7,8] => [1,5,7,8,2,3,4,6] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1,6,7,8] => [1,6,7,8,2,3,4,5] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,1,6,7,8] => [1,6,7,8,2,3,4,5] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,1,5,6,7] => [1,5,6,7,2,3,4,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,1,6,7,8] => [1,6,7,8,2,3,4,5] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8] => [1,6,7,8,2,3,4,5] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [8,7,6,1,2,3,4,5] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [7,8,6,1,2,3,4,5] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [8,6,7,1,2,3,4,5] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [7,6,8,1,2,3,4,5] => [1,2,3,4,5,6,8,7] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,7,8,1,2,3,4,5] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [8,7,5,1,2,3,4,6] => [1,2,3,4,6,5,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [7,8,5,1,2,3,4,6] => [1,2,3,4,6,5,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [8,6,5,1,2,3,4,7] => [1,2,3,4,7,5,6,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [7,6,5,1,2,3,4,8] => [1,2,3,4,8,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [6,7,5,1,2,3,4,8] => [1,2,3,4,8,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [8,5,6,1,2,3,4,7] => [1,2,3,4,7,5,6,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [7,5,6,1,2,3,4,8] => [1,2,3,4,8,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [6,5,7,1,2,3,4,8] => [1,2,3,4,8,5,7,6] => [3,1,1,1,1,1] => 2
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,6,7,1,2,3,4,8] => [1,2,3,4,8,5,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [8,7,4,1,2,3,5,6] => [1,2,3,5,6,4,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [4,5,6,1,2,3,7,8] => [1,2,3,7,8,4,5,6] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [7,5,3,1,2,4,6,8] => [1,2,4,6,8,3,5,7] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [6,4,3,1,2,5,7,8] => [1,2,5,7,8,3,4,6] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [7,8,2,1,3,4,5,6] => [1,3,4,5,6,2,7,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2,1,4,5,6,7] => [1,4,5,6,7,2,3,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,5,6,7,8] => [1,5,6,7,8,2,3,4] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [8,2,3,1,4,5,6,7] => [1,4,5,6,7,2,3,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [6,2,3,1,4,5,7,8] => [1,4,5,7,8,2,3,6] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,4,1,5,6,7,8] => [1,5,6,7,8,2,4,3] => [3,1,1,1,1,1] => 2
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8] => [1,5,6,7,8,2,3,4] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [8,7,1,2,3,4,5,6] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,8,1,2,3,4,5,6] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,7,1,2,3,4,5,8] => [1,2,3,4,5,8,6,7] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [7,5,1,2,3,4,6,8] => [1,2,3,4,6,8,5,7] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [8,4,1,2,3,5,6,7] => [1,2,3,5,6,7,4,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,4,1,2,3,5,7,8] => [1,2,3,5,7,8,4,6] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1,2,4,5,6,7] => [1,2,4,5,6,7,3,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [7,3,1,2,4,5,6,8] => [1,2,4,5,6,8,3,7] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1,2,4,6,7,8] => [1,2,4,6,7,8,3,5] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8] => [1,2,5,6,7,8,3,4] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1,3,4,5,6,7] => [1,3,4,5,6,7,2,8] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1,3,4,5,6,8] => [1,3,4,5,6,8,2,7] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8] => [1,4,5,6,7,8,2,3] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,2,3,4,5,6,8] => [1,2,3,4,5,6,8,7] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,2,3,4,5,7,8] => [1,2,3,4,5,7,8,6] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,2,3,4,6,7,8] => [1,2,3,4,6,7,8,5] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,2,3,5,6,7,8] => [1,2,3,5,6,7,8,4] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8] => [1,2,4,5,6,7,8,3] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8] => [1,3,4,5,6,7,8,2] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1] => 0
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => [1,2,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [9,2,1,3,4,5,6,7,8] => [1,3,4,5,6,7,8,2,9] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,9,1] => [1,2,4,5,6,7,8,9,3] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1] => [1,2,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [10,2,1,3,4,5,6,7,8,9] => [1,3,4,5,6,7,8,9,2,10] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [4,2,3,5,6,7,8,9,1] => [1,2,3,5,6,7,8,9,4] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,9,10,1] => [1,2,4,5,6,7,8,9,10,3] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [8,9,1,2,3,4,5,6,7] => [1,2,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1] => 0
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,1,2] => [1,2,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [9,8,1,2,3,4,5,6,7] => [1,2,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [9,10,1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1] => 0
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,1,2] => [1,2,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [10,9,1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8,9,10] => [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] => [8,7,6,5,4,3,2,1,9] => [1,9,2,3,4,5,6,7,8] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7,8,6,5,4,3,2,1,9] => [1,9,2,3,4,5,6,7,8] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [7,6,8,5,4,3,2,1,9] => [1,9,2,3,4,5,6,8,7] => [3,1,1,1,1,1,1] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [8,7,6,4,5,3,2,1,9] => [1,9,2,3,4,5,6,7,8] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1,9] => [1,9,2,3,4,5,6,7,8] => [2,1,1,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,1,2,9] => [1,2,9,3,4,5,6,7,8] => [2,1,1,1,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [7,8,5,6,3,4,1,2,9] => [1,2,9,3,4,5,6,7,8] => [2,1,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,2,1,8,9] => [1,8,9,2,3,4,5,6,7] => [2,1,1,1,1,1,1,1] => 1
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8,9] => [1,8,9,2,3,4,5,6,7] => [2,1,1,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,1,7,8,9] => [1,7,8,9,2,3,4,5,6] => [2,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [5,6,7,8,1,2,3,4,9] => [1,2,3,4,9,5,6,7,8] => [2,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,1,6,7,8,9] => [1,6,7,8,9,2,3,4,5] => [2,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1,5,6,7,8,9] => [1,5,6,7,8,9,2,3,4] => [2,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [7,8,1,2,3,4,5,6,9] => [1,2,3,4,5,6,9,7,8] => [2,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8,9] => [1,4,5,6,7,8,9,2,3] => [2,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,2,3,4,5,6,7,9] => [1,2,3,4,5,6,7,9,8] => [2,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [7,1,2,3,4,5,6,8,9] => [1,2,3,4,5,6,8,9,7] => [2,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9] => [1,3,4,5,6,7,8,9,2] => [2,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [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
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,3,2,1] => [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] => [8,9,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,7,9,6,5,4,3,2,1] => [1,2,3,4,5,6,7,9,8] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [8,7,6,9,5,4,3,2,1] => [1,2,3,4,5,6,9,7,8] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [8,7,6,5,9,4,3,2,1] => [1,2,3,4,5,9,6,7,8] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,9,3,2,1] => [1,2,3,4,9,5,6,7,8] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,9,2,1] => [1,2,3,9,4,5,6,7,8] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,2,9,1] => [1,2,9,3,4,5,6,7,8] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,3,2,1] => [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] => [9,10,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [7,8,9,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [9,8,10,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,10,9] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [8,6,7,9,5,4,3,2,1] => [1,2,3,4,5,6,7,9,8] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [9,8,7,10,6,5,4,3,2,1] => [1,2,3,4,5,6,7,10,8,9] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [8,7,5,6,9,4,3,2,1] => [1,2,3,4,5,6,9,7,8] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [9,8,7,6,10,5,4,3,2,1] => [1,2,3,4,5,6,10,7,8,9] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [8,7,6,4,5,9,3,2,1] => [1,2,3,4,5,9,6,7,8] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,10,4,3,2,1] => [1,2,3,4,5,10,6,7,8,9] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,3,4,9,2,1] => [1,2,3,4,9,5,6,7,8] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,10,3,2,1] => [1,2,3,4,10,5,6,7,8,9] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,2,3,9,1] => [1,2,3,9,4,5,6,7,8] => [2,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,10,2,1] => [1,2,3,10,4,5,6,7,8,9] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,2,10,1] => [1,2,10,3,4,5,6,7,8,9] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,2,1,10] => [1,10,2,3,4,5,6,7,8,9] => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [6,7,8,9,10,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9,10] => [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] => [9,8,7,6,5,4,3,1,2] => [1,2,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1] => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,3,4,1,2] => [1,2,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [9,8,7,5,6,3,4,1,2] => [1,2,3,4,5,6,7,8,9] => [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] => [9,7,8,5,6,3,4,1,2] => [1,2,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,1,2,3] => [1,2,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1] => 0
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,5,1,2,3] => [1,2,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1] => 0
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [8,9,6,7,4,5,1,2,3] => [1,2,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1] => 0
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [9,8,7,4,5,6,1,2,3] => [1,2,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1] => 0
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [7,8,9,4,5,6,1,2,3] => [1,2,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,1,2,3,4] => [1,2,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0] => [9,8,7,5,6,1,2,3,4] => [1,2,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [9,7,8,5,6,1,2,3,4] => [1,2,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0] => [9,8,5,6,7,1,2,3,4] => [1,2,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0] => [8,9,5,6,7,1,2,3,4] => [1,2,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [9,5,6,7,8,1,2,3,4] => [1,2,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,1,2,3,4,5] => [1,2,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [9,8,6,7,1,2,3,4,5] => [1,2,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [9,6,7,8,1,2,3,4,5] => [1,2,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,1,2,3,4,5] => [1,2,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [9,8,7,1,2,3,4,5,6] => [1,2,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [9,7,8,1,2,3,4,5,6] => [1,2,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [7,8,9,1,2,3,4,5,6] => [1,2,3,4,5,6,7,8,9] => [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] => [10,9,8,7,6,5,4,3,1,2] => [1,2,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1] => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,3,4,1,2] => [1,2,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [10,9,8,7,5,6,3,4,1,2] => [1,2,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [10,9,7,8,5,6,3,4,1,2] => [1,2,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,5,6,3,4,1,2] => [1,2,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,1,2,3] => [1,2,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,4,5,1,2,3] => [1,2,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [10,8,9,6,7,4,5,1,2,3] => [1,2,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,4,5,6,1,2,3] => [1,2,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,1,2,3,4] => [1,2,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,5,6,1,2,3,4] => [1,2,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [8,9,10,5,6,7,1,2,3,4] => [1,2,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [10,9,5,6,7,8,1,2,3,4] => [1,2,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [9,10,5,6,7,8,1,2,3,4] => [1,2,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,1,2,3,4,5] => [1,2,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [10,8,9,6,7,1,2,3,4,5] => [1,2,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [10,6,7,8,9,1,2,3,4,5] => [1,2,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [6,7,8,9,10,1,2,3,4,5] => [1,2,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [10,9,8,7,1,2,3,4,5,6] => [1,2,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0] => [10,7,8,9,1,2,3,4,5,6] => [1,2,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,1,2,3,4,5,6] => [1,2,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [10,9,8,1,2,3,4,5,6,7] => [1,2,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [10,8,9,1,2,3,4,5,6,7] => [1,2,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [8,9,10,1,2,3,4,5,6,7] => [1,2,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [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
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [8,9,7,6,5,4,3,2,1,10] => [1,10,2,3,4,5,6,7,8,9] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1,10] => [1,10,2,3,4,5,6,7,8,9] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,1,2,3,4,5,6,7,8,10] => [1,2,3,4,5,6,7,8,10,9] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10] => [1,3,4,5,6,7,8,9,10,2] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,3,2,1,8,9,10] => [1,8,9,10,2,3,4,5,6,7] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [9,8,7,5,6,4,3,2,1,10] => [1,10,2,3,4,5,6,7,8,9] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,6,5,4,3,2,1,9,10] => [1,9,10,2,3,4,5,6,7,8] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,5,4,3,2,1,7,8,9,10] => [1,7,8,9,10,2,3,4,5,6] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8,9,10] => [1,4,5,6,7,8,9,10,2,3] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,4,3,2,1,6,7,8,9,10] => [1,6,7,8,9,10,2,3,4,5] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [4,3,2,1,5,6,7,8,9,10] => [1,5,6,7,8,9,10,2,3,4] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [8,9,1,2,3,4,5,6,7,10] => [1,2,3,4,5,6,7,10,8,9] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [7,8,9,4,5,6,1,2,3,10] => [1,2,3,10,4,5,6,7,8,9] => [2,1,1,1,1,1,1,1,1] => 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:
4,1 8,6 16,25,1 32,89,11 64,290,74,1
$F_{1} = 1$
$F_{2} = 2$
$F_{3} = 4 + q$
$F_{4} = 8 + 6\ q$
$F_{5} = 16 + 25\ q + q^{2}$
$F_{6} = 32 + 89\ q + 11\ q^{2}$
$F_{7} = 64 + 290\ q + 74\ q^{2} + q^{3}$
Description
The aft of an integer partition.
The aft is the size of the partition minus the length of the first row or column, whichever is larger.
See also St000784The maximum of the length and the largest part of the integer partition..
The aft is the size of the partition minus the length of the first row or column, whichever is larger.
See also St000784The maximum of the length and the largest part of the integer partition..
Map
runsort
Description
The permutation obtained by sorting the increasing runs lexicographically.
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 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
This bijection is defined in [1, Section 2].
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