Identifier
-
Mp00127:
Permutations
—left-to-right-maxima to Dyck path⟶
Dyck paths
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
St000803: Permutations ⟶ ℤ
Values
[1,2] => [1,0,1,0] => [2,1] => [1,2] => 0
[2,1] => [1,1,0,0] => [1,2] => [2,1] => 0
[1,2,3] => [1,0,1,0,1,0] => [3,2,1] => [2,1,3] => 0
[1,3,2] => [1,0,1,1,0,0] => [2,3,1] => [1,2,3] => 0
[2,1,3] => [1,1,0,0,1,0] => [3,1,2] => [3,1,2] => 0
[2,3,1] => [1,1,0,1,0,0] => [2,1,3] => [1,3,2] => 1
[3,1,2] => [1,1,1,0,0,0] => [1,2,3] => [2,3,1] => 0
[3,2,1] => [1,1,1,0,0,0] => [1,2,3] => [2,3,1] => 0
[1,2,3,4] => [1,0,1,0,1,0,1,0] => [4,3,2,1] => [3,2,1,4] => 0
[1,2,4,3] => [1,0,1,0,1,1,0,0] => [3,4,2,1] => [3,1,2,4] => 0
[1,3,2,4] => [1,0,1,1,0,0,1,0] => [4,2,3,1] => [2,3,1,4] => 0
[1,3,4,2] => [1,0,1,1,0,1,0,0] => [3,2,4,1] => [2,1,3,4] => 0
[1,4,2,3] => [1,0,1,1,1,0,0,0] => [2,3,4,1] => [1,2,3,4] => 0
[1,4,3,2] => [1,0,1,1,1,0,0,0] => [2,3,4,1] => [1,2,3,4] => 0
[2,1,3,4] => [1,1,0,0,1,0,1,0] => [4,3,1,2] => [4,2,1,3] => 0
[2,1,4,3] => [1,1,0,0,1,1,0,0] => [3,4,1,2] => [4,1,2,3] => 0
[2,3,1,4] => [1,1,0,1,0,0,1,0] => [4,2,1,3] => [2,4,1,3] => 1
[2,3,4,1] => [1,1,0,1,0,1,0,0] => [3,2,1,4] => [2,1,4,3] => 1
[2,4,1,3] => [1,1,0,1,1,0,0,0] => [2,3,1,4] => [1,2,4,3] => 1
[2,4,3,1] => [1,1,0,1,1,0,0,0] => [2,3,1,4] => [1,2,4,3] => 1
[3,1,2,4] => [1,1,1,0,0,0,1,0] => [4,1,2,3] => [3,4,1,2] => 0
[3,1,4,2] => [1,1,1,0,0,1,0,0] => [3,1,2,4] => [3,1,4,2] => 0
[3,2,1,4] => [1,1,1,0,0,0,1,0] => [4,1,2,3] => [3,4,1,2] => 0
[3,2,4,1] => [1,1,1,0,0,1,0,0] => [3,1,2,4] => [3,1,4,2] => 0
[3,4,1,2] => [1,1,1,0,1,0,0,0] => [2,1,3,4] => [1,3,4,2] => 2
[3,4,2,1] => [1,1,1,0,1,0,0,0] => [2,1,3,4] => [1,3,4,2] => 2
[4,1,2,3] => [1,1,1,1,0,0,0,0] => [1,2,3,4] => [2,3,4,1] => 0
[4,1,3,2] => [1,1,1,1,0,0,0,0] => [1,2,3,4] => [2,3,4,1] => 0
[4,2,1,3] => [1,1,1,1,0,0,0,0] => [1,2,3,4] => [2,3,4,1] => 0
[4,2,3,1] => [1,1,1,1,0,0,0,0] => [1,2,3,4] => [2,3,4,1] => 0
[4,3,1,2] => [1,1,1,1,0,0,0,0] => [1,2,3,4] => [2,3,4,1] => 0
[4,3,2,1] => [1,1,1,1,0,0,0,0] => [1,2,3,4] => [2,3,4,1] => 0
[1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => [4,3,2,1,5] => 0
[1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => [4,3,1,2,5] => 0
[1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => [4,2,3,1,5] => 0
[1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => [4,2,1,3,5] => 0
[1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => [4,1,2,3,5] => 0
[1,2,5,4,3] => [1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => [4,1,2,3,5] => 0
[1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => [3,4,2,1,5] => 0
[1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => [3,4,1,2,5] => 0
[1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0] => [5,3,2,4,1] => [3,2,4,1,5] => 0
[1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => [3,2,1,4,5] => 0
[1,3,5,2,4] => [1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => [3,1,2,4,5] => 0
[1,3,5,4,2] => [1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => [3,1,2,4,5] => 0
[1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => [2,3,4,1,5] => 0
[1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => [2,3,1,4,5] => 0
[1,4,3,2,5] => [1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => [2,3,4,1,5] => 0
[1,4,3,5,2] => [1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => [2,3,1,4,5] => 0
[1,4,5,2,3] => [1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => [2,1,3,4,5] => 0
[1,4,5,3,2] => [1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => [2,1,3,4,5] => 0
[1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [1,2,3,4,5] => 0
[1,5,2,4,3] => [1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [1,2,3,4,5] => 0
[1,5,3,2,4] => [1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [1,2,3,4,5] => 0
[1,5,3,4,2] => [1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [1,2,3,4,5] => 0
[1,5,4,2,3] => [1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [1,2,3,4,5] => 0
[1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [1,2,3,4,5] => 0
[2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => [5,3,2,1,4] => 0
[2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => [5,3,1,2,4] => 0
[2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => [5,2,3,1,4] => 0
[2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => [5,2,1,3,4] => 0
[2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => [5,1,2,3,4] => 0
[2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => [5,1,2,3,4] => 0
[2,3,1,4,5] => [1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,3] => [3,5,2,1,4] => 1
[2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => [3,5,1,2,4] => 1
[2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,4] => [3,2,5,1,4] => 1
[2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,5] => [3,2,1,5,4] => 1
[2,3,5,1,4] => [1,1,0,1,0,1,1,0,0,0] => [3,4,2,1,5] => [3,1,2,5,4] => 1
[2,3,5,4,1] => [1,1,0,1,0,1,1,0,0,0] => [3,4,2,1,5] => [3,1,2,5,4] => 1
[2,4,1,3,5] => [1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => [2,3,5,1,4] => 1
[2,4,1,5,3] => [1,1,0,1,1,0,0,1,0,0] => [4,2,3,1,5] => [2,3,1,5,4] => 1
[2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => [2,3,5,1,4] => 1
[2,4,3,5,1] => [1,1,0,1,1,0,0,1,0,0] => [4,2,3,1,5] => [2,3,1,5,4] => 1
[2,4,5,1,3] => [1,1,0,1,1,0,1,0,0,0] => [3,2,4,1,5] => [2,1,3,5,4] => 1
[2,4,5,3,1] => [1,1,0,1,1,0,1,0,0,0] => [3,2,4,1,5] => [2,1,3,5,4] => 1
[2,5,1,3,4] => [1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => [1,2,3,5,4] => 1
[2,5,1,4,3] => [1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => [1,2,3,5,4] => 1
[2,5,3,1,4] => [1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => [1,2,3,5,4] => 1
[2,5,3,4,1] => [1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => [1,2,3,5,4] => 1
[2,5,4,1,3] => [1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => [1,2,3,5,4] => 1
[2,5,4,3,1] => [1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => [1,2,3,5,4] => 1
[3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => [4,5,2,1,3] => 0
[3,1,2,5,4] => [1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => [4,5,1,2,3] => 0
[3,1,4,2,5] => [1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => [4,2,5,1,3] => 0
[3,1,4,5,2] => [1,1,1,0,0,1,0,1,0,0] => [4,3,1,2,5] => [4,2,1,5,3] => 0
[3,1,5,2,4] => [1,1,1,0,0,1,1,0,0,0] => [3,4,1,2,5] => [4,1,2,5,3] => 0
[3,1,5,4,2] => [1,1,1,0,0,1,1,0,0,0] => [3,4,1,2,5] => [4,1,2,5,3] => 0
[3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => [4,5,2,1,3] => 0
[3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => [4,5,1,2,3] => 0
[3,2,4,1,5] => [1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => [4,2,5,1,3] => 0
[3,2,4,5,1] => [1,1,1,0,0,1,0,1,0,0] => [4,3,1,2,5] => [4,2,1,5,3] => 0
[3,2,5,1,4] => [1,1,1,0,0,1,1,0,0,0] => [3,4,1,2,5] => [4,1,2,5,3] => 0
[3,2,5,4,1] => [1,1,1,0,0,1,1,0,0,0] => [3,4,1,2,5] => [4,1,2,5,3] => 0
[3,4,1,2,5] => [1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => [2,4,5,1,3] => 2
[3,4,1,5,2] => [1,1,1,0,1,0,0,1,0,0] => [4,2,1,3,5] => [2,4,1,5,3] => 2
[3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => [2,4,5,1,3] => 2
[3,4,2,5,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,1,3,5] => [2,4,1,5,3] => 2
[3,4,5,1,2] => [1,1,1,0,1,0,1,0,0,0] => [3,2,1,4,5] => [2,1,4,5,3] => 2
[3,4,5,2,1] => [1,1,1,0,1,0,1,0,0,0] => [3,2,1,4,5] => [2,1,4,5,3] => 2
[3,5,1,2,4] => [1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => [1,2,4,5,3] => 2
[3,5,1,4,2] => [1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => [1,2,4,5,3] => 2
[3,5,2,1,4] => [1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => [1,2,4,5,3] => 2
>>> Load all 1592 entries. <<<[3,5,2,4,1] => [1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => [1,2,4,5,3] => 2
[3,5,4,1,2] => [1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => [1,2,4,5,3] => 2
[3,5,4,2,1] => [1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => [1,2,4,5,3] => 2
[4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => [3,4,5,1,2] => 0
[4,1,2,5,3] => [1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => [3,4,1,5,2] => 0
[4,1,3,2,5] => [1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => [3,4,5,1,2] => 0
[4,1,3,5,2] => [1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => [3,4,1,5,2] => 0
[4,1,5,2,3] => [1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => [3,1,4,5,2] => 0
[4,1,5,3,2] => [1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => [3,1,4,5,2] => 0
[4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => [3,4,5,1,2] => 0
[4,2,1,5,3] => [1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => [3,4,1,5,2] => 0
[4,2,3,1,5] => [1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => [3,4,5,1,2] => 0
[4,2,3,5,1] => [1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => [3,4,1,5,2] => 0
[4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => [3,1,4,5,2] => 0
[4,2,5,3,1] => [1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => [3,1,4,5,2] => 0
[4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => [3,4,5,1,2] => 0
[4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => [3,4,1,5,2] => 0
[4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => [3,4,5,1,2] => 0
[4,3,2,5,1] => [1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => [3,4,1,5,2] => 0
[4,3,5,1,2] => [1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => [3,1,4,5,2] => 0
[4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => [3,1,4,5,2] => 0
[4,5,1,2,3] => [1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => [1,3,4,5,2] => 3
[4,5,1,3,2] => [1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => [1,3,4,5,2] => 3
[4,5,2,1,3] => [1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => [1,3,4,5,2] => 3
[4,5,2,3,1] => [1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => [1,3,4,5,2] => 3
[4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => [1,3,4,5,2] => 3
[4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => [1,3,4,5,2] => 3
[5,1,2,3,4] => [1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [2,3,4,5,1] => 0
[5,1,2,4,3] => [1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [2,3,4,5,1] => 0
[5,1,3,2,4] => [1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [2,3,4,5,1] => 0
[5,1,3,4,2] => [1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [2,3,4,5,1] => 0
[5,1,4,2,3] => [1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [2,3,4,5,1] => 0
[5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [2,3,4,5,1] => 0
[5,2,1,3,4] => [1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [2,3,4,5,1] => 0
[5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [2,3,4,5,1] => 0
[5,2,3,1,4] => [1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [2,3,4,5,1] => 0
[5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [2,3,4,5,1] => 0
[5,2,4,1,3] => [1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [2,3,4,5,1] => 0
[5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [2,3,4,5,1] => 0
[5,3,1,2,4] => [1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [2,3,4,5,1] => 0
[5,3,1,4,2] => [1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [2,3,4,5,1] => 0
[5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [2,3,4,5,1] => 0
[5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [2,3,4,5,1] => 0
[5,3,4,1,2] => [1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [2,3,4,5,1] => 0
[5,3,4,2,1] => [1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [2,3,4,5,1] => 0
[5,4,1,2,3] => [1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [2,3,4,5,1] => 0
[5,4,1,3,2] => [1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [2,3,4,5,1] => 0
[5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [2,3,4,5,1] => 0
[5,4,2,3,1] => [1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [2,3,4,5,1] => 0
[5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [2,3,4,5,1] => 0
[5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [2,3,4,5,1] => 0
[1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => [5,4,3,2,1,6] => 0
[1,2,3,4,6,5] => [1,0,1,0,1,0,1,0,1,1,0,0] => [5,6,4,3,2,1] => [5,4,3,1,2,6] => 0
[1,2,3,5,4,6] => [1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,5,3,2,1] => [5,4,2,3,1,6] => 0
[1,2,3,5,6,4] => [1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,6,3,2,1] => [5,4,2,1,3,6] => 0
[1,2,3,6,4,5] => [1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => [5,4,1,2,3,6] => 0
[1,2,3,6,5,4] => [1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => [5,4,1,2,3,6] => 0
[1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,4,2,1] => [5,3,4,2,1,6] => 0
[1,2,4,3,6,5] => [1,0,1,0,1,1,0,0,1,1,0,0] => [5,6,3,4,2,1] => [5,3,4,1,2,6] => 0
[1,2,4,5,3,6] => [1,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,5,2,1] => [5,3,2,4,1,6] => 0
[1,2,4,5,6,3] => [1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,6,2,1] => [5,3,2,1,4,6] => 0
[1,2,4,6,3,5] => [1,0,1,0,1,1,0,1,1,0,0,0] => [4,5,3,6,2,1] => [5,3,1,2,4,6] => 0
[1,2,4,6,5,3] => [1,0,1,0,1,1,0,1,1,0,0,0] => [4,5,3,6,2,1] => [5,3,1,2,4,6] => 0
[1,2,5,3,4,6] => [1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,4,5,2,1] => [5,2,3,4,1,6] => 0
[1,2,5,3,6,4] => [1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,4,6,2,1] => [5,2,3,1,4,6] => 0
[1,2,5,4,3,6] => [1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,4,5,2,1] => [5,2,3,4,1,6] => 0
[1,2,5,4,6,3] => [1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,4,6,2,1] => [5,2,3,1,4,6] => 0
[1,2,5,6,3,4] => [1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => [5,2,1,3,4,6] => 0
[1,2,5,6,4,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => [5,2,1,3,4,6] => 0
[1,2,6,3,4,5] => [1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => [5,1,2,3,4,6] => 0
[1,2,6,3,5,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => [5,1,2,3,4,6] => 0
[1,2,6,4,3,5] => [1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => [5,1,2,3,4,6] => 0
[1,2,6,4,5,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => [5,1,2,3,4,6] => 0
[1,2,6,5,3,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => [5,1,2,3,4,6] => 0
[1,2,6,5,4,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => [5,1,2,3,4,6] => 0
[1,3,2,4,5,6] => [1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,3,1] => [4,5,3,2,1,6] => 0
[1,3,2,4,6,5] => [1,0,1,1,0,0,1,0,1,1,0,0] => [5,6,4,2,3,1] => [4,5,3,1,2,6] => 0
[1,3,2,5,4,6] => [1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,5,2,3,1] => [4,5,2,3,1,6] => 0
[1,3,2,5,6,4] => [1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,6,2,3,1] => [4,5,2,1,3,6] => 0
[1,3,2,6,4,5] => [1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => [4,5,1,2,3,6] => 0
[1,3,2,6,5,4] => [1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => [4,5,1,2,3,6] => 0
[1,3,4,2,5,6] => [1,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,4,1] => [4,3,5,2,1,6] => 0
[1,3,4,2,6,5] => [1,0,1,1,0,1,0,0,1,1,0,0] => [5,6,3,2,4,1] => [4,3,5,1,2,6] => 0
[1,3,4,5,2,6] => [1,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,5,1] => [4,3,2,5,1,6] => 0
[1,3,4,5,6,2] => [1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,1] => [4,3,2,1,5,6] => 0
[1,3,4,6,2,5] => [1,0,1,1,0,1,0,1,1,0,0,0] => [4,5,3,2,6,1] => [4,3,1,2,5,6] => 0
[1,3,4,6,5,2] => [1,0,1,1,0,1,0,1,1,0,0,0] => [4,5,3,2,6,1] => [4,3,1,2,5,6] => 0
[1,3,5,2,4,6] => [1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,4,2,5,1] => [4,2,3,5,1,6] => 0
[1,3,5,2,6,4] => [1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,4,2,6,1] => [4,2,3,1,5,6] => 0
[1,3,5,4,2,6] => [1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,4,2,5,1] => [4,2,3,5,1,6] => 0
[1,3,5,4,6,2] => [1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,4,2,6,1] => [4,2,3,1,5,6] => 0
[1,3,5,6,2,4] => [1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,5,2,6,1] => [4,2,1,3,5,6] => 0
[1,3,5,6,4,2] => [1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,5,2,6,1] => [4,2,1,3,5,6] => 0
[1,3,6,2,4,5] => [1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => [4,1,2,3,5,6] => 0
[1,3,6,2,5,4] => [1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => [4,1,2,3,5,6] => 0
[1,3,6,4,2,5] => [1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => [4,1,2,3,5,6] => 0
[1,3,6,4,5,2] => [1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => [4,1,2,3,5,6] => 0
[1,3,6,5,2,4] => [1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => [4,1,2,3,5,6] => 0
[1,3,6,5,4,2] => [1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => [4,1,2,3,5,6] => 0
[1,4,2,3,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,3,4,1] => [3,4,5,2,1,6] => 0
[1,4,2,3,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0] => [5,6,2,3,4,1] => [3,4,5,1,2,6] => 0
[1,4,2,5,3,6] => [1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,3,5,1] => [3,4,2,5,1,6] => 0
[1,4,2,5,6,3] => [1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,3,6,1] => [3,4,2,1,5,6] => 0
[1,4,2,6,3,5] => [1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => [3,4,1,2,5,6] => 0
[1,4,2,6,5,3] => [1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => [3,4,1,2,5,6] => 0
[1,4,3,2,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,3,4,1] => [3,4,5,2,1,6] => 0
[1,4,3,2,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0] => [5,6,2,3,4,1] => [3,4,5,1,2,6] => 0
[1,4,3,5,2,6] => [1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,3,5,1] => [3,4,2,5,1,6] => 0
[1,4,3,5,6,2] => [1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,3,6,1] => [3,4,2,1,5,6] => 0
[1,4,3,6,2,5] => [1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => [3,4,1,2,5,6] => 0
[1,4,3,6,5,2] => [1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => [3,4,1,2,5,6] => 0
[1,4,5,2,3,6] => [1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1] => [3,2,4,5,1,6] => 0
[1,4,5,2,6,3] => [1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [3,2,4,1,5,6] => 0
[1,4,5,3,2,6] => [1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1] => [3,2,4,5,1,6] => 0
[1,4,5,3,6,2] => [1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [3,2,4,1,5,6] => 0
[1,4,5,6,2,3] => [1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => [3,2,1,4,5,6] => 0
[1,4,5,6,3,2] => [1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => [3,2,1,4,5,6] => 0
[1,4,6,2,3,5] => [1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => [3,1,2,4,5,6] => 0
[1,4,6,2,5,3] => [1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => [3,1,2,4,5,6] => 0
[1,4,6,3,2,5] => [1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => [3,1,2,4,5,6] => 0
[1,4,6,3,5,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => [3,1,2,4,5,6] => 0
[1,4,6,5,2,3] => [1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => [3,1,2,4,5,6] => 0
[1,4,6,5,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => [3,1,2,4,5,6] => 0
[1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => [2,3,4,5,1,6] => 0
[1,5,2,3,6,4] => [1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => [2,3,4,1,5,6] => 0
[1,5,2,4,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => [2,3,4,5,1,6] => 0
[1,5,2,4,6,3] => [1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => [2,3,4,1,5,6] => 0
[1,5,2,6,3,4] => [1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => [2,3,1,4,5,6] => 0
[1,5,2,6,4,3] => [1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => [2,3,1,4,5,6] => 0
[1,5,3,2,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => [2,3,4,5,1,6] => 0
[1,5,3,2,6,4] => [1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => [2,3,4,1,5,6] => 0
[1,5,3,4,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => [2,3,4,5,1,6] => 0
[1,5,3,4,6,2] => [1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => [2,3,4,1,5,6] => 0
[1,5,3,6,2,4] => [1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => [2,3,1,4,5,6] => 0
[1,5,3,6,4,2] => [1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => [2,3,1,4,5,6] => 0
[1,5,4,2,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => [2,3,4,5,1,6] => 0
[1,5,4,2,6,3] => [1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => [2,3,4,1,5,6] => 0
[1,5,4,3,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => [2,3,4,5,1,6] => 0
[1,5,4,3,6,2] => [1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => [2,3,4,1,5,6] => 0
[1,5,4,6,2,3] => [1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => [2,3,1,4,5,6] => 0
[1,5,4,6,3,2] => [1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => [2,3,1,4,5,6] => 0
[1,5,6,2,3,4] => [1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => [2,1,3,4,5,6] => 0
[1,5,6,2,4,3] => [1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => [2,1,3,4,5,6] => 0
[1,5,6,3,2,4] => [1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => [2,1,3,4,5,6] => 0
[1,5,6,3,4,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => [2,1,3,4,5,6] => 0
[1,5,6,4,2,3] => [1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => [2,1,3,4,5,6] => 0
[1,5,6,4,3,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => [2,1,3,4,5,6] => 0
[1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => 0
[1,6,2,3,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => 0
[1,6,2,4,3,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => 0
[1,6,2,4,5,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => 0
[1,6,2,5,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => 0
[1,6,2,5,4,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => 0
[1,6,3,2,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => 0
[1,6,3,2,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => 0
[1,6,3,4,2,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => 0
[1,6,3,4,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => 0
[1,6,3,5,2,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => 0
[1,6,3,5,4,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => 0
[1,6,4,2,3,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => 0
[1,6,4,2,5,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => 0
[1,6,4,3,2,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => 0
[1,6,4,3,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => 0
[1,6,4,5,2,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => 0
[1,6,4,5,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => 0
[1,6,5,2,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => 0
[1,6,5,2,4,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => 0
[1,6,5,3,2,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => 0
[1,6,5,3,4,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => 0
[1,6,5,4,2,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => 0
[1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => 0
[2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,2] => [6,4,3,2,1,5] => 0
[2,1,3,4,6,5] => [1,1,0,0,1,0,1,0,1,1,0,0] => [5,6,4,3,1,2] => [6,4,3,1,2,5] => 0
[2,1,3,5,4,6] => [1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,5,3,1,2] => [6,4,2,3,1,5] => 0
[2,1,3,5,6,4] => [1,1,0,0,1,0,1,1,0,1,0,0] => [5,4,6,3,1,2] => [6,4,2,1,3,5] => 0
[2,1,3,6,4,5] => [1,1,0,0,1,0,1,1,1,0,0,0] => [4,5,6,3,1,2] => [6,4,1,2,3,5] => 0
[2,1,3,6,5,4] => [1,1,0,0,1,0,1,1,1,0,0,0] => [4,5,6,3,1,2] => [6,4,1,2,3,5] => 0
[2,1,4,3,5,6] => [1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,4,1,2] => [6,3,4,2,1,5] => 0
[2,1,4,3,6,5] => [1,1,0,0,1,1,0,0,1,1,0,0] => [5,6,3,4,1,2] => [6,3,4,1,2,5] => 0
[2,1,4,5,3,6] => [1,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,5,1,2] => [6,3,2,4,1,5] => 0
[2,1,4,5,6,3] => [1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,6,1,2] => [6,3,2,1,4,5] => 0
[2,1,4,6,3,5] => [1,1,0,0,1,1,0,1,1,0,0,0] => [4,5,3,6,1,2] => [6,3,1,2,4,5] => 0
[2,1,4,6,5,3] => [1,1,0,0,1,1,0,1,1,0,0,0] => [4,5,3,6,1,2] => [6,3,1,2,4,5] => 0
[2,1,5,3,4,6] => [1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,4,5,1,2] => [6,2,3,4,1,5] => 0
[2,1,5,3,6,4] => [1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,4,6,1,2] => [6,2,3,1,4,5] => 0
[2,1,5,4,3,6] => [1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,4,5,1,2] => [6,2,3,4,1,5] => 0
[2,1,5,4,6,3] => [1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,4,6,1,2] => [6,2,3,1,4,5] => 0
[2,1,5,6,3,4] => [1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,5,6,1,2] => [6,2,1,3,4,5] => 0
[2,1,5,6,4,3] => [1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,5,6,1,2] => [6,2,1,3,4,5] => 0
[2,1,6,3,4,5] => [1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[2,1,6,3,5,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[2,1,6,4,3,5] => [1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[2,1,6,4,5,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[2,1,6,5,3,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => 0
[2,3,1,4,5,6] => [1,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1,3] => [4,6,3,2,1,5] => 1
[2,3,1,4,6,5] => [1,1,0,1,0,0,1,0,1,1,0,0] => [5,6,4,2,1,3] => [4,6,3,1,2,5] => 1
[2,3,1,5,4,6] => [1,1,0,1,0,0,1,1,0,0,1,0] => [6,4,5,2,1,3] => [4,6,2,3,1,5] => 1
[2,3,1,5,6,4] => [1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,6,2,1,3] => [4,6,2,1,3,5] => 1
[2,3,1,6,4,5] => [1,1,0,1,0,0,1,1,1,0,0,0] => [4,5,6,2,1,3] => [4,6,1,2,3,5] => 1
[2,3,1,6,5,4] => [1,1,0,1,0,0,1,1,1,0,0,0] => [4,5,6,2,1,3] => [4,6,1,2,3,5] => 1
[2,3,4,1,5,6] => [1,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1,4] => [4,3,6,2,1,5] => 1
[2,3,4,1,6,5] => [1,1,0,1,0,1,0,0,1,1,0,0] => [5,6,3,2,1,4] => [4,3,6,1,2,5] => 1
[2,3,4,5,1,6] => [1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,5] => [4,3,2,6,1,5] => 1
[2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,6] => [4,3,2,1,6,5] => 1
[2,3,4,6,1,5] => [1,1,0,1,0,1,0,1,1,0,0,0] => [4,5,3,2,1,6] => [4,3,1,2,6,5] => 1
[2,3,4,6,5,1] => [1,1,0,1,0,1,0,1,1,0,0,0] => [4,5,3,2,1,6] => [4,3,1,2,6,5] => 1
[2,3,5,1,4,6] => [1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,4,2,1,5] => [4,2,3,6,1,5] => 1
[2,3,5,1,6,4] => [1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,4,2,1,6] => [4,2,3,1,6,5] => 1
[2,3,5,4,1,6] => [1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,4,2,1,5] => [4,2,3,6,1,5] => 1
[2,3,5,4,6,1] => [1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,4,2,1,6] => [4,2,3,1,6,5] => 1
[2,3,5,6,1,4] => [1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,5,2,1,6] => [4,2,1,3,6,5] => 1
[2,3,5,6,4,1] => [1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,5,2,1,6] => [4,2,1,3,6,5] => 1
[2,3,6,1,4,5] => [1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,2,1,6] => [4,1,2,3,6,5] => 1
[2,3,6,1,5,4] => [1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,2,1,6] => [4,1,2,3,6,5] => 1
[2,3,6,4,1,5] => [1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,2,1,6] => [4,1,2,3,6,5] => 1
[2,3,6,4,5,1] => [1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,2,1,6] => [4,1,2,3,6,5] => 1
[2,3,6,5,1,4] => [1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,2,1,6] => [4,1,2,3,6,5] => 1
[2,3,6,5,4,1] => [1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,2,1,6] => [4,1,2,3,6,5] => 1
[2,4,1,3,5,6] => [1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,3,1,4] => [3,4,6,2,1,5] => 1
[2,4,1,3,6,5] => [1,1,0,1,1,0,0,0,1,1,0,0] => [5,6,2,3,1,4] => [3,4,6,1,2,5] => 1
[2,4,1,5,3,6] => [1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,3,1,5] => [3,4,2,6,1,5] => 1
[2,4,1,5,6,3] => [1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,3,1,6] => [3,4,2,1,6,5] => 1
[2,4,1,6,3,5] => [1,1,0,1,1,0,0,1,1,0,0,0] => [4,5,2,3,1,6] => [3,4,1,2,6,5] => 1
[2,4,1,6,5,3] => [1,1,0,1,1,0,0,1,1,0,0,0] => [4,5,2,3,1,6] => [3,4,1,2,6,5] => 1
[2,4,3,1,5,6] => [1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,3,1,4] => [3,4,6,2,1,5] => 1
[2,4,3,1,6,5] => [1,1,0,1,1,0,0,0,1,1,0,0] => [5,6,2,3,1,4] => [3,4,6,1,2,5] => 1
[2,4,3,5,1,6] => [1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,3,1,5] => [3,4,2,6,1,5] => 1
[2,4,3,5,6,1] => [1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,3,1,6] => [3,4,2,1,6,5] => 1
[2,4,3,6,1,5] => [1,1,0,1,1,0,0,1,1,0,0,0] => [4,5,2,3,1,6] => [3,4,1,2,6,5] => 1
[2,4,3,6,5,1] => [1,1,0,1,1,0,0,1,1,0,0,0] => [4,5,2,3,1,6] => [3,4,1,2,6,5] => 1
[2,4,5,1,3,6] => [1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,4,1,5] => [3,2,4,6,1,5] => 1
[2,4,5,1,6,3] => [1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,4,1,6] => [3,2,4,1,6,5] => 1
[2,4,5,3,1,6] => [1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,4,1,5] => [3,2,4,6,1,5] => 1
[2,4,5,3,6,1] => [1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,4,1,6] => [3,2,4,1,6,5] => 1
[2,4,5,6,1,3] => [1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,5,1,6] => [3,2,1,4,6,5] => 1
[2,4,5,6,3,1] => [1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,5,1,6] => [3,2,1,4,6,5] => 1
[2,4,6,1,3,5] => [1,1,0,1,1,0,1,1,0,0,0,0] => [3,4,2,5,1,6] => [3,1,2,4,6,5] => 1
[2,4,6,1,5,3] => [1,1,0,1,1,0,1,1,0,0,0,0] => [3,4,2,5,1,6] => [3,1,2,4,6,5] => 1
[2,4,6,3,1,5] => [1,1,0,1,1,0,1,1,0,0,0,0] => [3,4,2,5,1,6] => [3,1,2,4,6,5] => 1
[2,4,6,3,5,1] => [1,1,0,1,1,0,1,1,0,0,0,0] => [3,4,2,5,1,6] => [3,1,2,4,6,5] => 1
[2,4,6,5,1,3] => [1,1,0,1,1,0,1,1,0,0,0,0] => [3,4,2,5,1,6] => [3,1,2,4,6,5] => 1
[2,4,6,5,3,1] => [1,1,0,1,1,0,1,1,0,0,0,0] => [3,4,2,5,1,6] => [3,1,2,4,6,5] => 1
[2,5,1,3,4,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,3,4,1,5] => [2,3,4,6,1,5] => 1
[2,5,1,3,6,4] => [1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,3,4,1,6] => [2,3,4,1,6,5] => 1
[2,5,1,4,3,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,3,4,1,5] => [2,3,4,6,1,5] => 1
[2,5,1,4,6,3] => [1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,3,4,1,6] => [2,3,4,1,6,5] => 1
[2,5,1,6,3,4] => [1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,3,5,1,6] => [2,3,1,4,6,5] => 1
[2,5,1,6,4,3] => [1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,3,5,1,6] => [2,3,1,4,6,5] => 1
[2,5,3,1,4,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,3,4,1,5] => [2,3,4,6,1,5] => 1
[2,5,3,1,6,4] => [1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,3,4,1,6] => [2,3,4,1,6,5] => 1
[2,5,3,4,1,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,3,4,1,5] => [2,3,4,6,1,5] => 1
[2,5,3,4,6,1] => [1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,3,4,1,6] => [2,3,4,1,6,5] => 1
[2,5,3,6,1,4] => [1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,3,5,1,6] => [2,3,1,4,6,5] => 1
[2,5,3,6,4,1] => [1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,3,5,1,6] => [2,3,1,4,6,5] => 1
[2,5,4,1,3,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,3,4,1,5] => [2,3,4,6,1,5] => 1
[2,5,4,1,6,3] => [1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,3,4,1,6] => [2,3,4,1,6,5] => 1
[2,5,4,3,1,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,3,4,1,5] => [2,3,4,6,1,5] => 1
[2,5,4,3,6,1] => [1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,3,4,1,6] => [2,3,4,1,6,5] => 1
[2,5,4,6,1,3] => [1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,3,5,1,6] => [2,3,1,4,6,5] => 1
[2,5,4,6,3,1] => [1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,3,5,1,6] => [2,3,1,4,6,5] => 1
[2,5,6,1,3,4] => [1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,5,1,6] => [2,1,3,4,6,5] => 1
[2,5,6,1,4,3] => [1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,5,1,6] => [2,1,3,4,6,5] => 1
[2,5,6,3,1,4] => [1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,5,1,6] => [2,1,3,4,6,5] => 1
[2,5,6,3,4,1] => [1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,5,1,6] => [2,1,3,4,6,5] => 1
[2,5,6,4,1,3] => [1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,5,1,6] => [2,1,3,4,6,5] => 1
[2,5,6,4,3,1] => [1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,5,1,6] => [2,1,3,4,6,5] => 1
[2,6,1,3,4,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [1,2,3,4,6,5] => 1
[2,6,1,3,5,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [1,2,3,4,6,5] => 1
[2,6,1,4,3,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [1,2,3,4,6,5] => 1
[2,6,1,4,5,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [1,2,3,4,6,5] => 1
[2,6,1,5,3,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [1,2,3,4,6,5] => 1
[2,6,1,5,4,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [1,2,3,4,6,5] => 1
[2,6,3,1,4,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [1,2,3,4,6,5] => 1
[2,6,3,1,5,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [1,2,3,4,6,5] => 1
[2,6,3,4,1,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [1,2,3,4,6,5] => 1
[2,6,3,4,5,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [1,2,3,4,6,5] => 1
[2,6,3,5,1,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [1,2,3,4,6,5] => 1
[2,6,3,5,4,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [1,2,3,4,6,5] => 1
[2,6,4,1,3,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [1,2,3,4,6,5] => 1
[2,6,4,1,5,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [1,2,3,4,6,5] => 1
[2,6,4,3,1,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [1,2,3,4,6,5] => 1
[2,6,4,3,5,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [1,2,3,4,6,5] => 1
[2,6,4,5,1,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [1,2,3,4,6,5] => 1
[2,6,4,5,3,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [1,2,3,4,6,5] => 1
[2,6,5,1,3,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [1,2,3,4,6,5] => 1
[2,6,5,1,4,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [1,2,3,4,6,5] => 1
[2,6,5,3,1,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [1,2,3,4,6,5] => 1
[2,6,5,3,4,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [1,2,3,4,6,5] => 1
[2,6,5,4,1,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [1,2,3,4,6,5] => 1
[2,6,5,4,3,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [1,2,3,4,6,5] => 1
[3,1,2,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,2,3] => [5,6,3,2,1,4] => 0
[3,1,2,4,6,5] => [1,1,1,0,0,0,1,0,1,1,0,0] => [5,6,4,1,2,3] => [5,6,3,1,2,4] => 0
[3,1,2,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,5,1,2,3] => [5,6,2,3,1,4] => 0
[3,1,2,5,6,4] => [1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,6,1,2,3] => [5,6,2,1,3,4] => 0
[3,1,2,6,4,5] => [1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[3,1,2,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[3,1,4,2,5,6] => [1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,2,4] => [5,3,6,2,1,4] => 0
[3,1,4,2,6,5] => [1,1,1,0,0,1,0,0,1,1,0,0] => [5,6,3,1,2,4] => [5,3,6,1,2,4] => 0
[3,1,4,5,2,6] => [1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,2,5] => [5,3,2,6,1,4] => 0
[3,1,4,5,6,2] => [1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,2,6] => [5,3,2,1,6,4] => 0
[3,1,4,6,2,5] => [1,1,1,0,0,1,0,1,1,0,0,0] => [4,5,3,1,2,6] => [5,3,1,2,6,4] => 0
[3,1,4,6,5,2] => [1,1,1,0,0,1,0,1,1,0,0,0] => [4,5,3,1,2,6] => [5,3,1,2,6,4] => 0
[3,1,5,2,4,6] => [1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,4,1,2,5] => [5,2,3,6,1,4] => 0
[3,1,5,2,6,4] => [1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,4,1,2,6] => [5,2,3,1,6,4] => 0
[3,1,5,4,2,6] => [1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,4,1,2,5] => [5,2,3,6,1,4] => 0
[3,1,5,4,6,2] => [1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,4,1,2,6] => [5,2,3,1,6,4] => 0
[3,1,5,6,2,4] => [1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,5,1,2,6] => [5,2,1,3,6,4] => 0
[3,1,5,6,4,2] => [1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,5,1,2,6] => [5,2,1,3,6,4] => 0
[3,1,6,2,4,5] => [1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => [5,1,2,3,6,4] => 0
[3,1,6,2,5,4] => [1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => [5,1,2,3,6,4] => 0
[3,1,6,4,2,5] => [1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => [5,1,2,3,6,4] => 0
[3,1,6,4,5,2] => [1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => [5,1,2,3,6,4] => 0
[3,1,6,5,2,4] => [1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => [5,1,2,3,6,4] => 0
[3,1,6,5,4,2] => [1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => [5,1,2,3,6,4] => 0
[3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,2,3] => [5,6,3,2,1,4] => 0
[3,2,1,4,6,5] => [1,1,1,0,0,0,1,0,1,1,0,0] => [5,6,4,1,2,3] => [5,6,3,1,2,4] => 0
[3,2,1,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,5,1,2,3] => [5,6,2,3,1,4] => 0
[3,2,1,5,6,4] => [1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,6,1,2,3] => [5,6,2,1,3,4] => 0
[3,2,1,6,4,5] => [1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => 0
[3,2,4,1,5,6] => [1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,2,4] => [5,3,6,2,1,4] => 0
[3,2,4,1,6,5] => [1,1,1,0,0,1,0,0,1,1,0,0] => [5,6,3,1,2,4] => [5,3,6,1,2,4] => 0
[3,2,4,5,1,6] => [1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,2,5] => [5,3,2,6,1,4] => 0
[3,2,4,5,6,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,2,6] => [5,3,2,1,6,4] => 0
[3,2,4,6,1,5] => [1,1,1,0,0,1,0,1,1,0,0,0] => [4,5,3,1,2,6] => [5,3,1,2,6,4] => 0
[3,2,4,6,5,1] => [1,1,1,0,0,1,0,1,1,0,0,0] => [4,5,3,1,2,6] => [5,3,1,2,6,4] => 0
[3,2,5,1,4,6] => [1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,4,1,2,5] => [5,2,3,6,1,4] => 0
[3,2,5,1,6,4] => [1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,4,1,2,6] => [5,2,3,1,6,4] => 0
[3,2,5,4,1,6] => [1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,4,1,2,5] => [5,2,3,6,1,4] => 0
[3,2,5,4,6,1] => [1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,4,1,2,6] => [5,2,3,1,6,4] => 0
[3,2,5,6,1,4] => [1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,5,1,2,6] => [5,2,1,3,6,4] => 0
[3,2,5,6,4,1] => [1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,5,1,2,6] => [5,2,1,3,6,4] => 0
[3,2,6,1,4,5] => [1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => [5,1,2,3,6,4] => 0
[3,2,6,1,5,4] => [1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => [5,1,2,3,6,4] => 0
[3,2,6,4,1,5] => [1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => [5,1,2,3,6,4] => 0
[3,2,6,4,5,1] => [1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => [5,1,2,3,6,4] => 0
[3,2,6,5,1,4] => [1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => [5,1,2,3,6,4] => 0
[3,2,6,5,4,1] => [1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => [5,1,2,3,6,4] => 0
[3,4,1,2,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,3,4] => [3,5,6,2,1,4] => 2
[3,4,1,2,6,5] => [1,1,1,0,1,0,0,0,1,1,0,0] => [5,6,2,1,3,4] => [3,5,6,1,2,4] => 2
[3,4,1,5,2,6] => [1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,3,5] => [3,5,2,6,1,4] => 2
[3,4,1,5,6,2] => [1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,3,6] => [3,5,2,1,6,4] => 2
[3,4,1,6,2,5] => [1,1,1,0,1,0,0,1,1,0,0,0] => [4,5,2,1,3,6] => [3,5,1,2,6,4] => 2
[3,4,1,6,5,2] => [1,1,1,0,1,0,0,1,1,0,0,0] => [4,5,2,1,3,6] => [3,5,1,2,6,4] => 2
[3,4,2,1,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,3,4] => [3,5,6,2,1,4] => 2
[3,4,2,1,6,5] => [1,1,1,0,1,0,0,0,1,1,0,0] => [5,6,2,1,3,4] => [3,5,6,1,2,4] => 2
[3,4,2,5,1,6] => [1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,3,5] => [3,5,2,6,1,4] => 2
[3,4,2,5,6,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,3,6] => [3,5,2,1,6,4] => 2
[3,4,2,6,1,5] => [1,1,1,0,1,0,0,1,1,0,0,0] => [4,5,2,1,3,6] => [3,5,1,2,6,4] => 2
[3,4,2,6,5,1] => [1,1,1,0,1,0,0,1,1,0,0,0] => [4,5,2,1,3,6] => [3,5,1,2,6,4] => 2
[3,4,5,1,2,6] => [1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,4,5] => [3,2,5,6,1,4] => 2
[3,4,5,1,6,2] => [1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,4,6] => [3,2,5,1,6,4] => 2
[3,4,5,2,1,6] => [1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,4,5] => [3,2,5,6,1,4] => 2
[3,4,5,2,6,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,4,6] => [3,2,5,1,6,4] => 2
[3,4,5,6,1,2] => [1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,5,6] => [3,2,1,5,6,4] => 2
[3,4,5,6,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,5,6] => [3,2,1,5,6,4] => 2
[3,4,6,1,2,5] => [1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,2,1,5,6] => [3,1,2,5,6,4] => 2
[3,4,6,1,5,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,2,1,5,6] => [3,1,2,5,6,4] => 2
[3,4,6,2,1,5] => [1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,2,1,5,6] => [3,1,2,5,6,4] => 2
[3,4,6,2,5,1] => [1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,2,1,5,6] => [3,1,2,5,6,4] => 2
[3,4,6,5,1,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,2,1,5,6] => [3,1,2,5,6,4] => 2
[3,4,6,5,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,2,1,5,6] => [3,1,2,5,6,4] => 2
[3,5,1,2,4,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,3,1,4,5] => [2,3,5,6,1,4] => 2
[3,5,1,2,6,4] => [1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,3,1,4,6] => [2,3,5,1,6,4] => 2
[3,5,1,4,2,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,3,1,4,5] => [2,3,5,6,1,4] => 2
[3,5,1,4,6,2] => [1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,3,1,4,6] => [2,3,5,1,6,4] => 2
[3,5,1,6,2,4] => [1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,3,1,5,6] => [2,3,1,5,6,4] => 2
[3,5,1,6,4,2] => [1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,3,1,5,6] => [2,3,1,5,6,4] => 2
[3,5,2,1,4,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,3,1,4,5] => [2,3,5,6,1,4] => 2
[3,5,2,1,6,4] => [1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,3,1,4,6] => [2,3,5,1,6,4] => 2
[3,5,2,4,1,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,3,1,4,5] => [2,3,5,6,1,4] => 2
[3,5,2,4,6,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,3,1,4,6] => [2,3,5,1,6,4] => 2
[3,5,2,6,1,4] => [1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,3,1,5,6] => [2,3,1,5,6,4] => 2
[3,5,2,6,4,1] => [1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,3,1,5,6] => [2,3,1,5,6,4] => 2
[3,5,4,1,2,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,3,1,4,5] => [2,3,5,6,1,4] => 2
[3,5,4,1,6,2] => [1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,3,1,4,6] => [2,3,5,1,6,4] => 2
[3,5,4,2,1,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,3,1,4,5] => [2,3,5,6,1,4] => 2
[3,5,4,2,6,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,3,1,4,6] => [2,3,5,1,6,4] => 2
[3,5,4,6,1,2] => [1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,3,1,5,6] => [2,3,1,5,6,4] => 2
[3,5,4,6,2,1] => [1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,3,1,5,6] => [2,3,1,5,6,4] => 2
[3,5,6,1,2,4] => [1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,4,1,5,6] => [2,1,3,5,6,4] => 2
[3,5,6,1,4,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,4,1,5,6] => [2,1,3,5,6,4] => 2
[3,5,6,2,1,4] => [1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,4,1,5,6] => [2,1,3,5,6,4] => 2
[3,5,6,2,4,1] => [1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,4,1,5,6] => [2,1,3,5,6,4] => 2
[3,5,6,4,1,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,4,1,5,6] => [2,1,3,5,6,4] => 2
[3,5,6,4,2,1] => [1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,4,1,5,6] => [2,1,3,5,6,4] => 2
[3,6,1,2,4,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [1,2,3,5,6,4] => 2
[3,6,1,2,5,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [1,2,3,5,6,4] => 2
[3,6,1,4,2,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [1,2,3,5,6,4] => 2
[3,6,1,4,5,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [1,2,3,5,6,4] => 2
[3,6,1,5,2,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [1,2,3,5,6,4] => 2
[3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [1,2,3,5,6,4] => 2
[3,6,2,1,4,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [1,2,3,5,6,4] => 2
[3,6,2,1,5,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [1,2,3,5,6,4] => 2
[3,6,2,4,1,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [1,2,3,5,6,4] => 2
[3,6,2,4,5,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [1,2,3,5,6,4] => 2
[3,6,2,5,1,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [1,2,3,5,6,4] => 2
[3,6,2,5,4,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [1,2,3,5,6,4] => 2
[3,6,4,1,2,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [1,2,3,5,6,4] => 2
[3,6,4,1,5,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [1,2,3,5,6,4] => 2
[3,6,4,2,1,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [1,2,3,5,6,4] => 2
[3,6,4,2,5,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [1,2,3,5,6,4] => 2
[3,6,4,5,1,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [1,2,3,5,6,4] => 2
[3,6,4,5,2,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [1,2,3,5,6,4] => 2
[3,6,5,1,2,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [1,2,3,5,6,4] => 2
[3,6,5,1,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [1,2,3,5,6,4] => 2
[3,6,5,2,1,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [1,2,3,5,6,4] => 2
[3,6,5,2,4,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [1,2,3,5,6,4] => 2
[3,6,5,4,1,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [1,2,3,5,6,4] => 2
[3,6,5,4,2,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [1,2,3,5,6,4] => 2
[4,1,2,3,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => [4,5,6,2,1,3] => 0
[4,1,2,3,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => [4,5,6,1,2,3] => 0
[4,1,2,5,3,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,2,3,5] => [4,5,2,6,1,3] => 0
[4,1,2,5,6,3] => [1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,2,3,6] => [4,5,2,1,6,3] => 0
[4,1,2,6,3,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => [4,5,1,2,6,3] => 0
[4,1,2,6,5,3] => [1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => [4,5,1,2,6,3] => 0
[4,1,3,2,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => [4,5,6,2,1,3] => 0
[4,1,3,2,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => [4,5,6,1,2,3] => 0
[4,1,3,5,2,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,2,3,5] => [4,5,2,6,1,3] => 0
[4,1,3,5,6,2] => [1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,2,3,6] => [4,5,2,1,6,3] => 0
[4,1,3,6,2,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => [4,5,1,2,6,3] => 0
[4,1,3,6,5,2] => [1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => [4,5,1,2,6,3] => 0
[4,1,5,2,3,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,2,4,5] => [4,2,5,6,1,3] => 0
[4,1,5,2,6,3] => [1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,2,4,6] => [4,2,5,1,6,3] => 0
[4,1,5,3,2,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,2,4,5] => [4,2,5,6,1,3] => 0
[4,1,5,3,6,2] => [1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,2,4,6] => [4,2,5,1,6,3] => 0
[4,1,5,6,2,3] => [1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,2,5,6] => [4,2,1,5,6,3] => 0
[4,1,5,6,3,2] => [1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,2,5,6] => [4,2,1,5,6,3] => 0
[4,1,6,2,3,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => [4,1,2,5,6,3] => 0
[4,1,6,2,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => [4,1,2,5,6,3] => 0
[4,1,6,3,2,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => [4,1,2,5,6,3] => 0
[4,1,6,3,5,2] => [1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => [4,1,2,5,6,3] => 0
[4,1,6,5,2,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => [4,1,2,5,6,3] => 0
[4,1,6,5,3,2] => [1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => [4,1,2,5,6,3] => 0
[4,2,1,3,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => [4,5,6,2,1,3] => 0
[4,2,1,3,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => [4,5,6,1,2,3] => 0
[4,2,1,5,3,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,2,3,5] => [4,5,2,6,1,3] => 0
[4,2,1,5,6,3] => [1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,2,3,6] => [4,5,2,1,6,3] => 0
[4,2,1,6,3,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => [4,5,1,2,6,3] => 0
[4,2,1,6,5,3] => [1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => [4,5,1,2,6,3] => 0
[4,2,3,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => [4,5,6,2,1,3] => 0
[4,2,3,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => [4,5,6,1,2,3] => 0
[4,2,3,5,1,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,2,3,5] => [4,5,2,6,1,3] => 0
[4,2,3,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,2,3,6] => [4,5,2,1,6,3] => 0
[4,2,3,6,1,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => [4,5,1,2,6,3] => 0
[4,2,3,6,5,1] => [1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => [4,5,1,2,6,3] => 0
[4,2,5,1,3,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,2,4,5] => [4,2,5,6,1,3] => 0
[4,2,5,1,6,3] => [1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,2,4,6] => [4,2,5,1,6,3] => 0
[4,2,5,3,1,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,2,4,5] => [4,2,5,6,1,3] => 0
[4,2,5,3,6,1] => [1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,2,4,6] => [4,2,5,1,6,3] => 0
[4,2,5,6,1,3] => [1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,2,5,6] => [4,2,1,5,6,3] => 0
[4,2,5,6,3,1] => [1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,2,5,6] => [4,2,1,5,6,3] => 0
[4,2,6,1,3,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => [4,1,2,5,6,3] => 0
[4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => [4,1,2,5,6,3] => 0
[4,2,6,3,1,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => [4,1,2,5,6,3] => 0
[4,2,6,3,5,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => [4,1,2,5,6,3] => 0
[4,2,6,5,1,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => [4,1,2,5,6,3] => 0
[4,2,6,5,3,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => [4,1,2,5,6,3] => 0
[4,3,1,2,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => [4,5,6,2,1,3] => 0
[4,3,1,2,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => [4,5,6,1,2,3] => 0
[4,3,1,5,2,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,2,3,5] => [4,5,2,6,1,3] => 0
[4,3,1,5,6,2] => [1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,2,3,6] => [4,5,2,1,6,3] => 0
[4,3,1,6,2,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => [4,5,1,2,6,3] => 0
[4,3,1,6,5,2] => [1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => [4,5,1,2,6,3] => 0
[4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => [4,5,6,2,1,3] => 0
[4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => [4,5,6,1,2,3] => 0
[4,3,2,5,1,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,2,3,5] => [4,5,2,6,1,3] => 0
[4,3,2,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,2,3,6] => [4,5,2,1,6,3] => 0
[4,3,2,6,1,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => [4,5,1,2,6,3] => 0
[4,3,2,6,5,1] => [1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => [4,5,1,2,6,3] => 0
[4,3,5,1,2,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,2,4,5] => [4,2,5,6,1,3] => 0
[4,3,5,1,6,2] => [1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,2,4,6] => [4,2,5,1,6,3] => 0
[4,3,5,2,1,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,2,4,5] => [4,2,5,6,1,3] => 0
[4,3,5,2,6,1] => [1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,2,4,6] => [4,2,5,1,6,3] => 0
[4,3,5,6,1,2] => [1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,2,5,6] => [4,2,1,5,6,3] => 0
[4,3,5,6,2,1] => [1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,2,5,6] => [4,2,1,5,6,3] => 0
[4,3,6,1,2,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => [4,1,2,5,6,3] => 0
[4,3,6,1,5,2] => [1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => [4,1,2,5,6,3] => 0
[4,3,6,2,1,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => [4,1,2,5,6,3] => 0
[4,3,6,2,5,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => [4,1,2,5,6,3] => 0
[4,3,6,5,1,2] => [1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => [4,1,2,5,6,3] => 0
[4,3,6,5,2,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => [4,1,2,5,6,3] => 0
[4,5,1,2,3,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => [2,4,5,6,1,3] => 3
[4,5,1,2,6,3] => [1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,3,4,6] => [2,4,5,1,6,3] => 3
[4,5,1,3,2,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => [2,4,5,6,1,3] => 3
[4,5,1,3,6,2] => [1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,3,4,6] => [2,4,5,1,6,3] => 3
[4,5,1,6,2,3] => [1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,3,5,6] => [2,4,1,5,6,3] => 3
[4,5,1,6,3,2] => [1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,3,5,6] => [2,4,1,5,6,3] => 3
[4,5,2,1,3,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => [2,4,5,6,1,3] => 3
[4,5,2,1,6,3] => [1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,3,4,6] => [2,4,5,1,6,3] => 3
[4,5,2,3,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => [2,4,5,6,1,3] => 3
[4,5,2,3,6,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,3,4,6] => [2,4,5,1,6,3] => 3
[4,5,2,6,1,3] => [1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,3,5,6] => [2,4,1,5,6,3] => 3
[4,5,2,6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,3,5,6] => [2,4,1,5,6,3] => 3
[4,5,3,1,2,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => [2,4,5,6,1,3] => 3
[4,5,3,1,6,2] => [1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,3,4,6] => [2,4,5,1,6,3] => 3
[4,5,3,2,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => [2,4,5,6,1,3] => 3
[4,5,3,2,6,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,3,4,6] => [2,4,5,1,6,3] => 3
[4,5,3,6,1,2] => [1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,3,5,6] => [2,4,1,5,6,3] => 3
[4,5,3,6,2,1] => [1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,3,5,6] => [2,4,1,5,6,3] => 3
[4,5,6,1,2,3] => [1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,4,5,6] => [2,1,4,5,6,3] => 3
[4,5,6,1,3,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,4,5,6] => [2,1,4,5,6,3] => 3
[4,5,6,2,1,3] => [1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,4,5,6] => [2,1,4,5,6,3] => 3
[4,5,6,2,3,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,4,5,6] => [2,1,4,5,6,3] => 3
[4,5,6,3,1,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,4,5,6] => [2,1,4,5,6,3] => 3
[4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,4,5,6] => [2,1,4,5,6,3] => 3
[4,6,1,2,3,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [1,2,4,5,6,3] => 3
[4,6,1,2,5,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [1,2,4,5,6,3] => 3
[4,6,1,3,2,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [1,2,4,5,6,3] => 3
[4,6,1,3,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [1,2,4,5,6,3] => 3
[4,6,1,5,2,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [1,2,4,5,6,3] => 3
[4,6,1,5,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [1,2,4,5,6,3] => 3
[4,6,2,1,3,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [1,2,4,5,6,3] => 3
[4,6,2,1,5,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [1,2,4,5,6,3] => 3
[4,6,2,3,1,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [1,2,4,5,6,3] => 3
[4,6,2,3,5,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [1,2,4,5,6,3] => 3
[4,6,2,5,1,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [1,2,4,5,6,3] => 3
[4,6,2,5,3,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [1,2,4,5,6,3] => 3
[4,6,3,1,2,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [1,2,4,5,6,3] => 3
[4,6,3,1,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [1,2,4,5,6,3] => 3
[4,6,3,2,1,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [1,2,4,5,6,3] => 3
[4,6,3,2,5,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [1,2,4,5,6,3] => 3
[4,6,3,5,1,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [1,2,4,5,6,3] => 3
[4,6,3,5,2,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [1,2,4,5,6,3] => 3
[4,6,5,1,2,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [1,2,4,5,6,3] => 3
[4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [1,2,4,5,6,3] => 3
[4,6,5,2,1,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [1,2,4,5,6,3] => 3
[4,6,5,2,3,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [1,2,4,5,6,3] => 3
[4,6,5,3,1,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [1,2,4,5,6,3] => 3
[4,6,5,3,2,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [1,2,4,5,6,3] => 3
[5,1,2,3,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [3,4,5,6,1,2] => 0
[5,1,2,3,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [3,4,5,1,6,2] => 0
[5,1,2,4,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [3,4,5,6,1,2] => 0
[5,1,2,4,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [3,4,5,1,6,2] => 0
[5,1,2,6,3,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [3,4,1,5,6,2] => 0
[5,1,2,6,4,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [3,4,1,5,6,2] => 0
[5,1,3,2,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [3,4,5,6,1,2] => 0
[5,1,3,2,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [3,4,5,1,6,2] => 0
[5,1,3,4,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [3,4,5,6,1,2] => 0
[5,1,3,4,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [3,4,5,1,6,2] => 0
[5,1,3,6,2,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [3,4,1,5,6,2] => 0
[5,1,3,6,4,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [3,4,1,5,6,2] => 0
[5,1,4,2,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [3,4,5,6,1,2] => 0
[5,1,4,2,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [3,4,5,1,6,2] => 0
[5,1,4,3,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [3,4,5,6,1,2] => 0
[5,1,4,3,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [3,4,5,1,6,2] => 0
[5,1,4,6,2,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [3,4,1,5,6,2] => 0
[5,1,4,6,3,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [3,4,1,5,6,2] => 0
[5,1,6,2,3,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [3,1,4,5,6,2] => 0
[5,1,6,2,4,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [3,1,4,5,6,2] => 0
[5,1,6,3,2,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [3,1,4,5,6,2] => 0
[5,1,6,3,4,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [3,1,4,5,6,2] => 0
[5,1,6,4,2,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [3,1,4,5,6,2] => 0
[5,1,6,4,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [3,1,4,5,6,2] => 0
[5,2,1,3,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [3,4,5,6,1,2] => 0
[5,2,1,3,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [3,4,5,1,6,2] => 0
[5,2,1,4,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [3,4,5,6,1,2] => 0
[5,2,1,4,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [3,4,5,1,6,2] => 0
[5,2,1,6,3,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [3,4,1,5,6,2] => 0
[5,2,1,6,4,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [3,4,1,5,6,2] => 0
[5,2,3,1,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [3,4,5,6,1,2] => 0
[5,2,3,1,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [3,4,5,1,6,2] => 0
[5,2,3,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [3,4,5,6,1,2] => 0
[5,2,3,4,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [3,4,5,1,6,2] => 0
[5,2,3,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [3,4,1,5,6,2] => 0
[5,2,3,6,4,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [3,4,1,5,6,2] => 0
[5,2,4,1,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [3,4,5,6,1,2] => 0
[5,2,4,1,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [3,4,5,1,6,2] => 0
[5,2,4,3,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [3,4,5,6,1,2] => 0
[5,2,4,3,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [3,4,5,1,6,2] => 0
[5,2,4,6,1,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [3,4,1,5,6,2] => 0
[5,2,4,6,3,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [3,4,1,5,6,2] => 0
[5,2,6,1,3,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [3,1,4,5,6,2] => 0
[5,2,6,1,4,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [3,1,4,5,6,2] => 0
[5,2,6,3,1,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [3,1,4,5,6,2] => 0
[5,2,6,3,4,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [3,1,4,5,6,2] => 0
[5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [3,1,4,5,6,2] => 0
[5,2,6,4,3,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [3,1,4,5,6,2] => 0
[5,3,1,2,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [3,4,5,6,1,2] => 0
[5,3,1,2,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [3,4,5,1,6,2] => 0
[5,3,1,4,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [3,4,5,6,1,2] => 0
[5,3,1,4,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [3,4,5,1,6,2] => 0
[5,3,1,6,2,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [3,4,1,5,6,2] => 0
[5,3,1,6,4,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [3,4,1,5,6,2] => 0
[5,3,2,1,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [3,4,5,6,1,2] => 0
[5,3,2,1,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [3,4,5,1,6,2] => 0
[5,3,2,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [3,4,5,6,1,2] => 0
[5,3,2,4,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [3,4,5,1,6,2] => 0
[5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [3,4,1,5,6,2] => 0
[5,3,2,6,4,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [3,4,1,5,6,2] => 0
[5,3,4,1,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [3,4,5,6,1,2] => 0
[5,3,4,1,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [3,4,5,1,6,2] => 0
[5,3,4,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [3,4,5,6,1,2] => 0
[5,3,4,2,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [3,4,5,1,6,2] => 0
[5,3,4,6,1,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [3,4,1,5,6,2] => 0
[5,3,4,6,2,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [3,4,1,5,6,2] => 0
[5,3,6,1,2,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [3,1,4,5,6,2] => 0
[5,3,6,1,4,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [3,1,4,5,6,2] => 0
[5,3,6,2,1,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [3,1,4,5,6,2] => 0
[5,3,6,2,4,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [3,1,4,5,6,2] => 0
[5,3,6,4,1,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [3,1,4,5,6,2] => 0
[5,3,6,4,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [3,1,4,5,6,2] => 0
[5,4,1,2,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [3,4,5,6,1,2] => 0
[5,4,1,2,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [3,4,5,1,6,2] => 0
[5,4,1,3,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [3,4,5,6,1,2] => 0
[5,4,1,3,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [3,4,5,1,6,2] => 0
[5,4,1,6,2,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [3,4,1,5,6,2] => 0
[5,4,1,6,3,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [3,4,1,5,6,2] => 0
[5,4,2,1,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [3,4,5,6,1,2] => 0
[5,4,2,1,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [3,4,5,1,6,2] => 0
[5,4,2,3,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [3,4,5,6,1,2] => 0
[5,4,2,3,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [3,4,5,1,6,2] => 0
[5,4,2,6,1,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [3,4,1,5,6,2] => 0
[5,4,2,6,3,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [3,4,1,5,6,2] => 0
[5,4,3,1,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [3,4,5,6,1,2] => 0
[5,4,3,1,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [3,4,5,1,6,2] => 0
[5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [3,4,5,6,1,2] => 0
[5,4,3,2,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [3,4,5,1,6,2] => 0
[5,4,3,6,1,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [3,4,1,5,6,2] => 0
[5,4,3,6,2,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [3,4,1,5,6,2] => 0
[5,4,6,1,2,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [3,1,4,5,6,2] => 0
[5,4,6,1,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [3,1,4,5,6,2] => 0
[5,4,6,2,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [3,1,4,5,6,2] => 0
[5,4,6,2,3,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [3,1,4,5,6,2] => 0
[5,4,6,3,1,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [3,1,4,5,6,2] => 0
[5,4,6,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [3,1,4,5,6,2] => 0
[5,6,1,2,3,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [1,3,4,5,6,2] => 4
[5,6,1,2,4,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [1,3,4,5,6,2] => 4
[5,6,1,3,2,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [1,3,4,5,6,2] => 4
[5,6,1,3,4,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [1,3,4,5,6,2] => 4
[5,6,1,4,2,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [1,3,4,5,6,2] => 4
[5,6,1,4,3,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [1,3,4,5,6,2] => 4
[5,6,2,1,3,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [1,3,4,5,6,2] => 4
[5,6,2,1,4,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [1,3,4,5,6,2] => 4
[5,6,2,3,1,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [1,3,4,5,6,2] => 4
[5,6,2,3,4,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [1,3,4,5,6,2] => 4
[5,6,2,4,1,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [1,3,4,5,6,2] => 4
[5,6,2,4,3,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [1,3,4,5,6,2] => 4
[5,6,3,1,2,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [1,3,4,5,6,2] => 4
[5,6,3,1,4,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [1,3,4,5,6,2] => 4
[5,6,3,2,1,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [1,3,4,5,6,2] => 4
[5,6,3,2,4,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [1,3,4,5,6,2] => 4
[5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [1,3,4,5,6,2] => 4
[5,6,3,4,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [1,3,4,5,6,2] => 4
[5,6,4,1,2,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [1,3,4,5,6,2] => 4
[5,6,4,1,3,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [1,3,4,5,6,2] => 4
[5,6,4,2,1,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [1,3,4,5,6,2] => 4
[5,6,4,2,3,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [1,3,4,5,6,2] => 4
[5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [1,3,4,5,6,2] => 4
[5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [1,3,4,5,6,2] => 4
[6,1,2,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,1,2,3,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,1,2,4,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,1,2,4,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,1,2,5,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,1,2,5,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,1,3,2,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,1,3,2,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,1,3,4,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,1,3,4,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,1,3,5,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,1,3,5,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,1,4,2,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,1,4,2,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,1,4,3,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,1,4,3,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,1,4,5,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,1,4,5,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,1,5,2,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,1,5,2,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,1,5,3,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,1,5,3,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,1,5,4,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,1,5,4,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,2,1,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,2,1,3,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,2,1,4,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,2,1,4,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,2,1,5,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,2,1,5,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,2,3,1,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,2,3,1,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,2,3,4,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,2,3,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,2,3,5,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,2,3,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,2,4,1,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,2,4,1,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,2,4,3,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,2,4,3,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,2,4,5,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,2,4,5,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,2,5,1,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,2,5,1,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,2,5,3,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,2,5,3,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,2,5,4,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,3,1,2,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,3,1,2,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,3,1,4,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,3,1,4,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,3,1,5,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,3,1,5,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,3,2,1,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,3,2,1,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,3,2,4,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,3,2,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,3,2,5,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,3,2,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,3,4,1,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,3,4,1,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,3,4,2,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,3,4,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,3,4,5,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,3,4,5,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,3,5,1,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,3,5,1,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,3,5,2,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,3,5,2,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,3,5,4,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,3,5,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,4,1,2,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,4,1,2,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,4,1,3,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,4,1,3,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,4,1,5,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,4,1,5,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,4,2,1,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,4,2,1,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,4,2,3,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,4,2,3,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,4,2,5,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,4,2,5,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,4,3,1,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,4,3,1,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,4,3,2,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,4,3,5,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,4,3,5,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,4,5,1,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,4,5,1,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,4,5,2,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,4,5,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,4,5,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,4,5,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,5,1,2,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,5,1,2,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,5,1,3,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,5,1,3,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,5,1,4,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,5,1,4,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,5,2,1,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,5,2,1,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,5,2,3,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,5,2,3,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,5,2,4,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,5,2,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,5,3,1,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,5,3,1,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,5,3,2,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,5,3,2,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,5,3,4,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,5,4,1,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,5,4,1,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,5,4,2,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,5,4,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,5,4,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0
[1,7,2,3,4,5,6] => [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] => 0
[1,7,2,3,4,6,5] => [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] => 0
[1,7,2,3,5,4,6] => [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] => 0
[1,7,2,3,5,6,4] => [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] => 0
[1,7,2,3,6,4,5] => [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] => 0
[1,7,2,3,6,5,4] => [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] => 0
[1,7,2,4,3,5,6] => [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] => 0
[1,7,2,4,3,6,5] => [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] => 0
[1,7,2,4,5,3,6] => [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] => 0
[1,7,2,4,5,6,3] => [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] => 0
[1,7,2,4,6,3,5] => [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] => 0
[1,7,2,4,6,5,3] => [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] => 0
[1,7,2,5,3,4,6] => [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] => 0
[1,7,2,5,3,6,4] => [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] => 0
[1,7,2,5,4,3,6] => [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] => 0
[1,7,2,5,4,6,3] => [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] => 0
[1,7,2,5,6,3,4] => [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] => 0
[1,7,2,5,6,4,3] => [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] => 0
[1,7,2,6,3,4,5] => [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] => 0
[1,7,2,6,3,5,4] => [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] => 0
[1,7,2,6,4,3,5] => [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] => 0
[1,7,2,6,4,5,3] => [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] => 0
[1,7,2,6,5,3,4] => [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] => 0
[1,7,2,6,5,4,3] => [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] => 0
[1,7,3,2,4,5,6] => [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] => 0
[1,7,3,2,4,6,5] => [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] => 0
[1,7,3,2,5,4,6] => [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] => 0
[1,7,3,2,5,6,4] => [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] => 0
[1,7,3,2,6,4,5] => [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] => 0
[1,7,3,2,6,5,4] => [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] => 0
[1,7,3,4,2,5,6] => [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] => 0
[1,7,3,4,2,6,5] => [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] => 0
[1,7,3,4,5,2,6] => [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] => 0
[1,7,3,4,5,6,2] => [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] => 0
[1,7,3,4,6,2,5] => [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] => 0
[1,7,3,4,6,5,2] => [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] => 0
[1,7,3,5,2,4,6] => [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] => 0
[1,7,3,5,2,6,4] => [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] => 0
[1,7,3,5,4,2,6] => [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] => 0
[1,7,3,5,4,6,2] => [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] => 0
[1,7,3,5,6,2,4] => [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] => 0
[1,7,3,5,6,4,2] => [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] => 0
[1,7,3,6,2,4,5] => [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] => 0
[1,7,3,6,2,5,4] => [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] => 0
[1,7,3,6,4,2,5] => [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] => 0
[1,7,3,6,4,5,2] => [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] => 0
[1,7,3,6,5,2,4] => [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] => 0
[1,7,3,6,5,4,2] => [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] => 0
[1,7,4,2,3,5,6] => [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] => 0
[1,7,4,2,3,6,5] => [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] => 0
[1,7,4,2,5,3,6] => [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] => 0
[1,7,4,2,5,6,3] => [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] => 0
[1,7,4,2,6,3,5] => [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] => 0
[1,7,4,2,6,5,3] => [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] => 0
[1,7,4,3,2,5,6] => [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] => 0
[1,7,4,3,2,6,5] => [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] => 0
[1,7,4,3,5,2,6] => [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] => 0
[1,7,4,3,5,6,2] => [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] => 0
[1,7,4,3,6,2,5] => [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] => 0
[1,7,4,3,6,5,2] => [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] => 0
[1,7,4,5,2,3,6] => [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] => 0
[1,7,4,5,2,6,3] => [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] => 0
[1,7,4,5,3,2,6] => [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] => 0
[1,7,4,5,3,6,2] => [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] => 0
[1,7,4,5,6,2,3] => [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] => 0
[1,7,4,5,6,3,2] => [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] => 0
[1,7,4,6,2,3,5] => [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] => 0
[1,7,4,6,2,5,3] => [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] => 0
[1,7,4,6,3,2,5] => [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] => 0
[1,7,4,6,3,5,2] => [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] => 0
[1,7,4,6,5,2,3] => [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] => 0
[1,7,4,6,5,3,2] => [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] => 0
[1,7,5,2,3,4,6] => [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] => 0
[1,7,5,2,3,6,4] => [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] => 0
[1,7,5,2,4,3,6] => [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] => 0
[1,7,5,2,4,6,3] => [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] => 0
[1,7,5,2,6,3,4] => [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] => 0
[1,7,5,2,6,4,3] => [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] => 0
[1,7,5,3,2,4,6] => [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] => 0
[1,7,5,3,2,6,4] => [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] => 0
[1,7,5,3,4,2,6] => [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] => 0
[1,7,5,3,4,6,2] => [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] => 0
[1,7,5,3,6,2,4] => [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] => 0
[1,7,5,3,6,4,2] => [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] => 0
[1,7,5,4,2,3,6] => [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] => 0
[1,7,5,4,2,6,3] => [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] => 0
[1,7,5,4,3,2,6] => [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] => 0
[1,7,5,4,3,6,2] => [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] => 0
[1,7,5,4,6,2,3] => [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] => 0
[1,7,5,4,6,3,2] => [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] => 0
[1,7,5,6,2,3,4] => [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] => 0
[1,7,5,6,2,4,3] => [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] => 0
[1,7,5,6,3,2,4] => [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] => 0
[1,7,5,6,3,4,2] => [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] => 0
[1,7,5,6,4,2,3] => [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] => 0
[1,7,5,6,4,3,2] => [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] => 0
[1,7,6,2,3,4,5] => [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] => 0
[1,7,6,2,3,5,4] => [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] => 0
[1,7,6,2,4,3,5] => [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] => 0
[1,7,6,2,4,5,3] => [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] => 0
[1,7,6,2,5,3,4] => [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] => 0
[1,7,6,2,5,4,3] => [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] => 0
[1,7,6,3,2,4,5] => [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] => 0
[1,7,6,3,2,5,4] => [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] => 0
[1,7,6,3,4,2,5] => [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] => 0
[1,7,6,3,4,5,2] => [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] => 0
[1,7,6,3,5,2,4] => [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] => 0
[1,7,6,3,5,4,2] => [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] => 0
[1,7,6,4,2,3,5] => [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] => 0
[1,7,6,4,2,5,3] => [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] => 0
[1,7,6,4,3,2,5] => [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] => 0
[1,7,6,4,3,5,2] => [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] => 0
[1,7,6,4,5,2,3] => [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] => 0
[1,7,6,4,5,3,2] => [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] => 0
[1,7,6,5,2,3,4] => [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] => 0
[1,7,6,5,2,4,3] => [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] => 0
[1,7,6,5,3,2,4] => [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] => 0
[1,7,6,5,3,4,2] => [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] => 0
[1,7,6,5,4,2,3] => [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] => 0
[1,7,6,5,4,3,2] => [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] => 0
[2,7,1,3,4,5,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,1,3,4,6,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,1,3,5,4,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,1,3,5,6,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,1,3,6,4,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,1,3,6,5,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,1,4,3,5,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,1,4,3,6,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,1,4,5,3,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,1,4,5,6,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,1,4,6,3,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,1,4,6,5,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,1,5,3,4,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,1,5,3,6,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,1,5,4,3,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,1,5,4,6,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,1,5,6,3,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,1,5,6,4,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,1,6,3,4,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,1,6,3,5,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,1,6,4,3,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,1,6,4,5,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,1,6,5,3,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,1,6,5,4,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,3,1,4,5,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,3,1,4,6,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,3,1,5,4,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,3,1,5,6,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,3,1,6,4,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,3,1,6,5,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,3,4,1,5,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,3,4,1,6,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,3,4,5,1,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,3,4,5,6,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,3,4,6,1,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,3,4,6,5,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,3,5,1,4,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,3,5,1,6,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,3,5,4,1,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,3,5,4,6,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,3,5,6,1,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,3,5,6,4,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,3,6,1,4,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,3,6,1,5,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,3,6,4,1,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,3,6,4,5,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,3,6,5,1,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,3,6,5,4,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,4,1,3,5,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,4,1,3,6,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,4,1,5,3,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,4,1,5,6,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,4,1,6,3,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,4,1,6,5,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,4,3,1,5,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,4,3,1,6,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,4,3,5,1,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,4,3,5,6,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,4,3,6,1,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,4,3,6,5,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,4,5,1,3,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,4,5,1,6,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,4,5,3,1,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,4,5,3,6,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,4,5,6,1,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,4,5,6,3,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,4,6,1,3,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,4,6,1,5,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,4,6,3,1,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,4,6,3,5,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,4,6,5,1,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,4,6,5,3,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,5,1,3,4,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,5,1,3,6,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,5,1,4,3,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,5,1,4,6,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,5,1,6,3,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,5,1,6,4,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,5,3,1,4,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,5,3,1,6,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,5,3,4,1,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,5,3,4,6,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,5,3,6,1,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,5,3,6,4,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,5,4,1,3,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,5,4,1,6,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,5,4,3,1,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,5,4,3,6,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,5,4,6,1,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,5,4,6,3,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,5,6,1,3,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,5,6,1,4,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,5,6,3,1,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,5,6,3,4,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,5,6,4,1,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,5,6,4,3,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,6,1,3,4,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,6,1,3,5,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,6,1,4,3,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,6,1,4,5,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,6,1,5,3,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,6,1,5,4,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,6,3,1,4,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,6,3,1,5,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,6,3,4,1,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,6,3,4,5,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,6,3,5,1,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,6,3,5,4,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,6,4,1,3,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,6,4,1,5,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,6,4,3,1,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,6,4,3,5,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,6,4,5,1,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,6,4,5,3,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,6,5,1,3,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,6,5,1,4,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,6,5,3,1,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,6,5,3,4,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,6,5,4,1,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[2,7,6,5,4,3,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => 1
[3,7,1,2,4,5,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,1,2,4,6,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,1,2,5,4,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,1,2,5,6,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,1,2,6,4,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,1,2,6,5,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,1,4,2,5,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,1,4,2,6,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,1,4,5,2,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,1,4,5,6,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,1,4,6,2,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,1,4,6,5,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,1,5,2,4,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,1,5,2,6,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,1,5,4,2,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,1,5,4,6,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,1,5,6,2,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,1,5,6,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,1,6,2,4,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,1,6,2,5,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,1,6,4,2,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,1,6,4,5,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,1,6,5,2,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,1,6,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,2,1,4,5,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,2,1,4,6,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,2,1,5,4,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,2,1,5,6,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,2,1,6,4,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,2,1,6,5,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,2,4,1,5,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,2,4,1,6,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,2,4,5,1,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,2,4,5,6,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,2,4,6,1,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,2,4,6,5,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,2,5,1,4,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,2,5,1,6,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,2,5,4,1,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,2,5,4,6,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,2,5,6,1,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,2,5,6,4,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,2,6,1,4,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,2,6,1,5,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,2,6,4,1,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,2,6,4,5,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,2,6,5,1,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,2,6,5,4,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,4,1,2,5,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,4,1,2,6,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,4,1,5,2,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,4,1,5,6,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,4,1,6,2,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,4,1,6,5,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,4,2,1,5,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,4,2,1,6,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,4,2,5,1,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,4,2,5,6,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,4,2,6,1,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,4,2,6,5,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,4,5,1,2,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,4,5,1,6,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,4,5,2,1,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,4,5,2,6,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,4,5,6,1,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,4,5,6,2,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,4,6,1,2,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,4,6,1,5,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,4,6,2,1,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,4,6,2,5,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,4,6,5,1,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,4,6,5,2,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,5,1,2,4,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,5,1,2,6,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,5,1,4,2,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,5,1,4,6,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,5,1,6,2,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,5,1,6,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,5,2,1,4,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,5,2,1,6,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,5,2,4,1,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,5,2,4,6,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,5,2,6,1,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,5,2,6,4,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,5,4,1,2,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,5,4,1,6,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,5,4,2,1,6] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,5,4,2,6,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,5,4,6,1,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,5,4,6,2,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,5,6,1,2,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,5,6,1,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,5,6,2,1,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,5,6,2,4,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,5,6,4,1,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,5,6,4,2,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,6,1,2,4,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,6,1,2,5,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,6,1,4,2,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,6,1,4,5,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,6,1,5,2,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,6,1,5,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,6,2,1,4,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,6,2,1,5,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,6,2,4,1,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,6,2,4,5,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,6,2,5,1,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,6,2,5,4,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,6,4,1,2,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,6,4,1,5,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,6,4,2,1,5] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,6,4,2,5,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,6,4,5,1,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,6,4,5,2,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,6,5,1,2,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,6,5,1,4,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,6,5,2,1,4] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,6,5,2,4,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,6,5,4,1,2] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[3,7,6,5,4,2,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => 2
[4,7,1,2,3,5,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,1,2,3,6,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,1,2,5,3,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,1,2,5,6,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,1,2,6,3,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,1,2,6,5,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,1,3,2,5,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,1,3,2,6,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,1,3,5,2,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,1,3,5,6,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,1,3,6,2,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,1,3,6,5,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,1,5,2,3,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,1,5,2,6,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,1,5,3,2,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,1,5,3,6,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,1,5,6,2,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,1,5,6,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,1,6,2,3,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,1,6,2,5,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,1,6,3,2,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,1,6,3,5,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,1,6,5,2,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,1,6,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,2,1,3,5,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,2,1,3,6,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,2,1,5,3,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,2,1,5,6,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,2,1,6,3,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,2,1,6,5,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,2,3,1,5,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,2,3,1,6,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,2,3,5,1,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,2,3,5,6,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,2,3,6,1,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,2,3,6,5,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,2,5,1,3,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,2,5,1,6,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,2,5,3,1,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,2,5,3,6,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,2,5,6,1,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,2,5,6,3,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,2,6,1,3,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,2,6,1,5,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,2,6,3,1,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,2,6,3,5,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,2,6,5,1,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,2,6,5,3,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,3,1,2,5,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,3,1,2,6,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,3,1,5,2,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,3,1,5,6,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,3,1,6,2,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,3,1,6,5,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,3,2,1,5,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,3,2,1,6,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,3,2,5,1,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,3,2,5,6,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,3,2,6,1,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,3,2,6,5,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,3,5,1,2,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,3,5,1,6,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,3,5,2,1,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,3,5,2,6,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,3,5,6,1,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,3,5,6,2,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,3,6,1,2,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,3,6,1,5,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,3,6,2,1,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,3,6,2,5,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,3,6,5,1,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,3,6,5,2,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,5,1,2,3,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,5,1,2,6,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,5,1,3,2,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,5,1,3,6,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,5,1,6,2,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,5,1,6,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,5,2,1,3,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,5,2,1,6,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,5,2,3,1,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,5,2,3,6,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,5,2,6,1,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,5,2,6,3,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,5,3,1,2,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,5,3,1,6,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,5,3,2,1,6] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,5,3,2,6,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,5,3,6,1,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,5,3,6,2,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,5,6,1,2,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,5,6,1,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,5,6,2,1,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,5,6,2,3,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,5,6,3,1,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,5,6,3,2,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,6,1,2,3,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,6,1,2,5,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,6,1,3,2,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,6,1,3,5,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,6,1,5,2,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,6,1,5,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,6,2,1,3,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,6,2,1,5,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,6,2,3,1,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,6,2,3,5,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,6,2,5,1,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,6,2,5,3,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,6,3,1,2,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,6,3,1,5,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,6,3,2,1,5] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,6,3,2,5,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,6,3,5,1,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,6,3,5,2,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,6,5,1,2,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,6,5,1,3,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,6,5,2,1,3] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,6,5,2,3,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,6,5,3,1,2] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[4,7,6,5,3,2,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => 3
[5,7,1,2,3,4,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,1,2,3,6,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,1,2,4,3,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,1,2,4,6,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,1,2,6,3,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,1,2,6,4,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,1,3,2,4,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,1,3,2,6,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,1,3,4,2,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,1,3,4,6,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,1,3,6,2,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,1,3,6,4,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,1,4,2,3,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,1,4,2,6,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,1,4,3,2,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,1,4,3,6,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,1,4,6,2,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,1,4,6,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,1,6,2,3,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,1,6,2,4,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,1,6,3,2,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,1,6,3,4,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,1,6,4,2,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,1,6,4,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,2,1,3,4,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,2,1,3,6,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,2,1,4,3,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,2,1,4,6,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,2,1,6,3,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,2,1,6,4,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,2,3,1,4,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,2,3,1,6,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,2,3,4,1,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,2,3,4,6,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,2,3,6,1,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,2,3,6,4,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,2,4,1,3,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,2,4,1,6,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,2,4,3,1,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,2,4,3,6,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,2,4,6,1,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,2,4,6,3,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,2,6,1,3,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,2,6,1,4,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,2,6,3,1,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,2,6,3,4,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,2,6,4,1,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,2,6,4,3,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,3,1,2,4,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,3,1,2,6,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,3,1,4,2,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,3,1,4,6,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,3,1,6,2,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,3,1,6,4,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,3,2,1,4,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,3,2,1,6,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,3,2,4,1,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,3,2,4,6,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,3,2,6,1,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,3,2,6,4,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,3,4,1,2,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,3,4,1,6,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,3,4,2,1,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,3,4,2,6,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,3,4,6,1,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,3,4,6,2,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,3,6,1,2,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,3,6,1,4,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,3,6,2,1,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,3,6,2,4,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,3,6,4,1,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,3,6,4,2,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,4,1,2,3,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,4,1,2,6,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,4,1,3,2,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,4,1,3,6,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,4,1,6,2,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,4,1,6,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,4,2,1,3,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,4,2,1,6,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,4,2,3,1,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,4,2,3,6,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,4,2,6,1,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,4,2,6,3,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,4,3,1,2,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,4,3,1,6,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,4,3,2,1,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,4,3,2,6,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,4,3,6,1,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,4,3,6,2,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,4,6,1,2,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,4,6,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,4,6,2,1,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,4,6,2,3,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,4,6,3,1,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,4,6,3,2,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,6,1,2,3,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,6,1,2,4,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,6,1,3,2,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,6,1,3,4,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,6,1,4,2,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,6,1,4,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,6,2,1,3,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,6,2,1,4,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,6,2,3,1,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,6,2,3,4,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,6,2,4,1,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,6,2,4,3,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,6,3,1,2,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,6,3,1,4,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,6,3,2,1,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,6,3,2,4,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,6,3,4,1,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,6,3,4,2,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,6,4,1,2,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,6,4,1,3,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,6,4,2,1,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,6,4,2,3,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,6,4,3,1,2] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[5,7,6,4,3,2,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [1,2,4,5,6,7,3] => 4
[6,7,1,2,3,4,5] => [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] => 5
[6,7,1,2,3,5,4] => [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] => 5
[6,7,1,2,4,3,5] => [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] => 5
[6,7,1,2,4,5,3] => [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] => 5
[6,7,1,2,5,3,4] => [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] => 5
[6,7,1,2,5,4,3] => [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] => 5
[6,7,1,3,2,4,5] => [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] => 5
[6,7,1,3,2,5,4] => [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] => 5
[6,7,1,3,4,2,5] => [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] => 5
[6,7,1,3,4,5,2] => [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] => 5
[6,7,1,3,5,2,4] => [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] => 5
[6,7,1,3,5,4,2] => [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] => 5
[6,7,1,4,2,3,5] => [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] => 5
[6,7,1,4,2,5,3] => [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] => 5
[6,7,1,4,3,2,5] => [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] => 5
[6,7,1,4,3,5,2] => [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] => 5
[6,7,1,4,5,2,3] => [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] => 5
[6,7,1,4,5,3,2] => [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] => 5
[6,7,1,5,2,3,4] => [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] => 5
[6,7,1,5,2,4,3] => [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] => 5
[6,7,1,5,3,2,4] => [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] => 5
[6,7,1,5,3,4,2] => [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] => 5
[6,7,1,5,4,2,3] => [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] => 5
[6,7,1,5,4,3,2] => [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] => 5
[6,7,2,1,3,4,5] => [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] => 5
[6,7,2,1,3,5,4] => [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] => 5
[6,7,2,1,4,3,5] => [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] => 5
[6,7,2,1,4,5,3] => [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] => 5
[6,7,2,1,5,3,4] => [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] => 5
[6,7,2,1,5,4,3] => [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] => 5
[6,7,2,3,1,4,5] => [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] => 5
[6,7,2,3,1,5,4] => [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] => 5
[6,7,2,3,4,1,5] => [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] => 5
[6,7,2,3,4,5,1] => [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] => 5
[6,7,2,3,5,1,4] => [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] => 5
[6,7,2,3,5,4,1] => [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] => 5
[6,7,2,4,1,3,5] => [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] => 5
[6,7,2,4,1,5,3] => [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] => 5
[6,7,2,4,3,1,5] => [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] => 5
[6,7,2,4,3,5,1] => [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] => 5
[6,7,2,4,5,1,3] => [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] => 5
[6,7,2,4,5,3,1] => [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] => 5
[6,7,2,5,1,3,4] => [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] => 5
[6,7,2,5,1,4,3] => [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] => 5
[6,7,2,5,3,1,4] => [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] => 5
[6,7,2,5,3,4,1] => [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] => 5
[6,7,2,5,4,1,3] => [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] => 5
[6,7,2,5,4,3,1] => [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] => 5
[6,7,3,1,2,4,5] => [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] => 5
[6,7,3,1,2,5,4] => [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] => 5
[6,7,3,1,4,2,5] => [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] => 5
[6,7,3,1,4,5,2] => [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] => 5
[6,7,3,1,5,2,4] => [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] => 5
[6,7,3,1,5,4,2] => [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] => 5
[6,7,3,2,1,4,5] => [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] => 5
[6,7,3,2,1,5,4] => [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] => 5
[6,7,3,2,4,1,5] => [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] => 5
[6,7,3,2,4,5,1] => [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] => 5
[6,7,3,2,5,1,4] => [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] => 5
[6,7,3,2,5,4,1] => [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] => 5
[6,7,3,4,1,2,5] => [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] => 5
[6,7,3,4,1,5,2] => [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] => 5
[6,7,3,4,2,1,5] => [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] => 5
[6,7,3,4,2,5,1] => [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] => 5
[6,7,3,4,5,1,2] => [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] => 5
[6,7,3,4,5,2,1] => [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] => 5
[6,7,3,5,1,2,4] => [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] => 5
[6,7,3,5,1,4,2] => [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] => 5
[6,7,3,5,2,1,4] => [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] => 5
[6,7,3,5,2,4,1] => [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] => 5
[6,7,3,5,4,1,2] => [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] => 5
[6,7,3,5,4,2,1] => [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] => 5
[6,7,4,1,2,3,5] => [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] => 5
[6,7,4,1,2,5,3] => [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] => 5
[6,7,4,1,3,2,5] => [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] => 5
[6,7,4,1,3,5,2] => [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] => 5
[6,7,4,1,5,2,3] => [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] => 5
[6,7,4,1,5,3,2] => [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] => 5
[6,7,4,2,1,3,5] => [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] => 5
[6,7,4,2,1,5,3] => [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] => 5
[6,7,4,2,3,1,5] => [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] => 5
[6,7,4,2,3,5,1] => [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] => 5
[6,7,4,2,5,1,3] => [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] => 5
[6,7,4,2,5,3,1] => [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] => 5
[6,7,4,3,1,2,5] => [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] => 5
[6,7,4,3,1,5,2] => [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] => 5
[6,7,4,3,2,1,5] => [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] => 5
[6,7,4,3,2,5,1] => [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] => 5
[6,7,4,3,5,1,2] => [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] => 5
[6,7,4,3,5,2,1] => [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] => 5
[6,7,4,5,1,2,3] => [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] => 5
[6,7,4,5,1,3,2] => [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] => 5
[6,7,4,5,2,1,3] => [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] => 5
[6,7,4,5,2,3,1] => [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] => 5
[6,7,4,5,3,1,2] => [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] => 5
[6,7,4,5,3,2,1] => [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] => 5
[6,7,5,1,2,3,4] => [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] => 5
[6,7,5,1,2,4,3] => [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] => 5
[6,7,5,1,3,2,4] => [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] => 5
[6,7,5,1,3,4,2] => [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] => 5
[6,7,5,1,4,2,3] => [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] => 5
[6,7,5,1,4,3,2] => [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] => 5
[6,7,5,2,1,3,4] => [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] => 5
[6,7,5,2,1,4,3] => [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] => 5
[6,7,5,2,3,1,4] => [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] => 5
[6,7,5,2,3,4,1] => [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] => 5
[6,7,5,2,4,1,3] => [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] => 5
[6,7,5,2,4,3,1] => [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] => 5
[6,7,5,3,1,2,4] => [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] => 5
[6,7,5,3,1,4,2] => [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] => 5
[6,7,5,3,2,1,4] => [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] => 5
[6,7,5,3,2,4,1] => [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] => 5
[6,7,5,3,4,1,2] => [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] => 5
[6,7,5,3,4,2,1] => [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] => 5
[6,7,5,4,1,2,3] => [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] => 5
[6,7,5,4,1,3,2] => [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] => 5
[6,7,5,4,2,1,3] => [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] => 5
[6,7,5,4,2,3,1] => [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] => 5
[6,7,5,4,3,1,2] => [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] => 5
[6,7,5,4,3,2,1] => [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] => 5
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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:
5,1 18,4,2 84,18,12,6 480,96,72,48,24
$F_{2} = 2$
$F_{3} = 5 + q$
$F_{4} = 18 + 4\ q + 2\ q^{2}$
$F_{5} = 84 + 18\ q + 12\ q^{2} + 6\ q^{3}$
$F_{6} = 480 + 96\ q + 72\ q^{2} + 48\ q^{3} + 24\ q^{4}$
Description
The number of occurrences of the vincular pattern |132 in a permutation.
This is the number of occurrences of the pattern $(1,3,2)$, such that the letter matched by $1$ is the first entry of the permutation.
This is the number of occurrences of the pattern $(1,3,2)$, such that the letter matched by $1$ is the first entry of the permutation.
Map
Inverse Kreweras complement
Description
Sends the permutation $\pi \in \mathfrak{S}_n$ to the permutation $c\pi^{-1}$ where $c = (1,\ldots,n)$ is the long cycle.
Map
left-to-right-maxima to Dyck path
Description
The left-to-right maxima of a permutation as a Dyck path.
Let $(c_1, \dots, c_k)$ be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are $c_1, c_1+c_2, \dots, c_1+\dots+c_k$.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
Let $(c_1, \dots, c_k)$ be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are $c_1, c_1+c_2, \dots, c_1+\dots+c_k$.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
Map
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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