Identifier
Mp00025:
Dyck paths
—to 132-avoiding permutation⟶
Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00277: Permutations —catalanization⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00277: Permutations —catalanization⟶ Permutations
Images
[1,0] => [1] => [1] => [1]
[1,0,1,0] => [2,1] => [1,2] => [1,2]
[1,1,0,0] => [1,2] => [2,1] => [2,1]
[1,0,1,0,1,0] => [3,2,1] => [1,2,3] => [1,2,3]
[1,0,1,1,0,0] => [2,3,1] => [2,1,3] => [2,1,3]
[1,1,0,0,1,0] => [3,1,2] => [1,3,2] => [1,3,2]
[1,1,0,1,0,0] => [2,1,3] => [2,3,1] => [2,3,1]
[1,1,1,0,0,0] => [1,2,3] => [3,2,1] => [3,2,1]
[1,0,1,0,1,0,1,0] => [4,3,2,1] => [1,2,3,4] => [1,2,3,4]
[1,0,1,0,1,1,0,0] => [3,4,2,1] => [2,1,3,4] => [2,1,3,4]
[1,0,1,1,0,0,1,0] => [4,2,3,1] => [1,3,2,4] => [1,3,2,4]
[1,0,1,1,0,1,0,0] => [3,2,4,1] => [2,3,1,4] => [2,3,1,4]
[1,0,1,1,1,0,0,0] => [2,3,4,1] => [3,2,1,4] => [3,2,1,4]
[1,1,0,0,1,0,1,0] => [4,3,1,2] => [1,2,4,3] => [1,2,4,3]
[1,1,0,0,1,1,0,0] => [3,4,1,2] => [2,1,4,3] => [2,1,4,3]
[1,1,0,1,0,0,1,0] => [4,2,1,3] => [1,3,4,2] => [1,3,4,2]
[1,1,0,1,0,1,0,0] => [3,2,1,4] => [2,3,4,1] => [2,3,4,1]
[1,1,0,1,1,0,0,0] => [2,3,1,4] => [3,2,4,1] => [3,2,4,1]
[1,1,1,0,0,0,1,0] => [4,1,2,3] => [1,4,3,2] => [1,4,3,2]
[1,1,1,0,0,1,0,0] => [3,1,2,4] => [2,4,3,1] => [2,4,3,1]
[1,1,1,0,1,0,0,0] => [2,1,3,4] => [3,4,2,1] => [3,4,2,1]
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1]
[1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => [1,2,3,4,5] => [1,2,3,4,5]
[1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => [2,1,3,4,5] => [2,1,3,4,5]
[1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => [1,3,2,4,5] => [1,3,2,4,5]
[1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => [2,3,1,4,5] => [2,3,1,4,5]
[1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => [3,2,1,4,5] => [3,2,1,4,5]
[1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => [1,2,4,3,5] => [1,2,4,3,5]
[1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => [2,1,4,3,5] => [2,1,4,3,5]
[1,0,1,1,0,1,0,0,1,0] => [5,3,2,4,1] => [1,3,4,2,5] => [1,3,4,2,5]
[1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => [2,3,4,1,5] => [2,3,4,1,5]
[1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => [3,2,4,1,5] => [3,2,4,1,5]
[1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => [1,4,3,2,5] => [1,4,3,2,5]
[1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => [2,4,3,1,5] => [2,4,3,1,5]
[1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => [3,4,2,1,5] => [3,4,2,1,5]
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [4,3,2,1,5] => [4,3,2,1,5]
[1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => [1,2,3,5,4] => [1,2,3,5,4]
[1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => [2,1,3,5,4] => [2,1,3,5,4]
[1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => [1,3,2,5,4] => [1,3,2,5,4]
[1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => [2,3,1,5,4] => [2,3,1,5,4]
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => [3,2,1,5,4] => [3,2,1,5,4]
[1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,3] => [1,2,4,5,3] => [1,2,4,5,3]
[1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => [2,1,4,5,3] => [2,1,4,5,3]
[1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,4] => [1,3,4,5,2] => [1,3,4,5,2]
[1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,5] => [2,3,4,5,1] => [2,3,4,5,1]
[1,1,0,1,0,1,1,0,0,0] => [3,4,2,1,5] => [3,2,4,5,1] => [3,2,4,5,1]
[1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => [1,4,3,5,2] => [1,4,3,5,2]
[1,1,0,1,1,0,0,1,0,0] => [4,2,3,1,5] => [2,4,3,5,1] => [2,4,3,5,1]
[1,1,0,1,1,0,1,0,0,0] => [3,2,4,1,5] => [3,4,2,5,1] => [3,4,2,5,1]
[1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => [4,3,2,5,1] => [4,3,2,5,1]
[1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => [1,2,5,4,3] => [1,2,5,4,3]
[1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => [2,1,5,4,3] => [2,1,5,4,3]
[1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => [1,3,5,4,2] => [1,3,5,4,2]
[1,1,1,0,0,1,0,1,0,0] => [4,3,1,2,5] => [2,3,5,4,1] => [2,3,5,4,1]
[1,1,1,0,0,1,1,0,0,0] => [3,4,1,2,5] => [3,2,5,4,1] => [3,2,5,4,1]
[1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => [1,4,5,3,2] => [1,4,5,3,2]
[1,1,1,0,1,0,0,1,0,0] => [4,2,1,3,5] => [2,4,5,3,1] => [2,4,5,3,1]
[1,1,1,0,1,0,1,0,0,0] => [3,2,1,4,5] => [3,4,5,2,1] => [3,4,5,2,1]
[1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => [4,3,5,2,1] => [4,3,5,2,1]
[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => [1,5,4,3,2] => [1,5,4,3,2]
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => [2,5,4,3,1] => [2,5,4,3,1]
[1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => [3,5,4,2,1] => [3,5,4,2,1]
[1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => [4,5,3,2,1] => [4,5,3,2,1]
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => [1,2,3,4,5,6] => [1,2,3,4,5,6]
[1,0,1,0,1,0,1,0,1,1,0,0] => [5,6,4,3,2,1] => [2,1,3,4,5,6] => [2,1,3,4,5,6]
[1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,5,3,2,1] => [1,3,2,4,5,6] => [1,3,2,4,5,6]
[1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,6,3,2,1] => [2,3,1,4,5,6] => [2,3,1,4,5,6]
[1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => [3,2,1,4,5,6] => [3,2,1,4,5,6]
[1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,4,2,1] => [1,2,4,3,5,6] => [1,2,4,3,5,6]
[1,0,1,0,1,1,0,0,1,1,0,0] => [5,6,3,4,2,1] => [2,1,4,3,5,6] => [2,1,4,3,5,6]
[1,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,5,2,1] => [1,3,4,2,5,6] => [1,3,4,2,5,6]
[1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,6,2,1] => [2,3,4,1,5,6] => [2,3,4,1,5,6]
[1,0,1,0,1,1,0,1,1,0,0,0] => [4,5,3,6,2,1] => [3,2,4,1,5,6] => [3,2,4,1,5,6]
[1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,4,5,2,1] => [1,4,3,2,5,6] => [1,4,3,2,5,6]
[1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,4,6,2,1] => [2,4,3,1,5,6] => [2,4,3,1,5,6]
[1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => [3,4,2,1,5,6] => [3,4,2,1,5,6]
[1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => [4,3,2,1,5,6] => [4,3,2,1,5,6]
[1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,3,1] => [1,2,3,5,4,6] => [1,2,3,5,4,6]
[1,0,1,1,0,0,1,0,1,1,0,0] => [5,6,4,2,3,1] => [2,1,3,5,4,6] => [2,1,3,5,4,6]
[1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,5,2,3,1] => [1,3,2,5,4,6] => [1,3,2,5,4,6]
[1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,6,2,3,1] => [2,3,1,5,4,6] => [2,3,1,5,4,6]
[1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => [3,2,1,5,4,6] => [3,2,1,5,4,6]
[1,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,4,1] => [1,2,4,5,3,6] => [1,2,4,5,3,6]
[1,0,1,1,0,1,0,0,1,1,0,0] => [5,6,3,2,4,1] => [2,1,4,5,3,6] => [2,1,4,5,3,6]
[1,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,5,1] => [1,3,4,5,2,6] => [1,3,4,5,2,6]
[1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,1] => [2,3,4,5,1,6] => [2,3,4,5,1,6]
[1,0,1,1,0,1,0,1,1,0,0,0] => [4,5,3,2,6,1] => [3,2,4,5,1,6] => [3,2,4,5,1,6]
[1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,4,2,5,1] => [1,4,3,5,2,6] => [1,4,3,5,2,6]
[1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,4,2,6,1] => [2,4,3,5,1,6] => [2,4,3,5,1,6]
[1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,5,2,6,1] => [3,4,2,5,1,6] => [3,4,2,5,1,6]
[1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => [4,3,2,5,1,6] => [4,3,2,5,1,6]
[1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,3,4,1] => [1,2,5,4,3,6] => [1,2,5,4,3,6]
[1,0,1,1,1,0,0,0,1,1,0,0] => [5,6,2,3,4,1] => [2,1,5,4,3,6] => [2,1,5,4,3,6]
[1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,3,5,1] => [1,3,5,4,2,6] => [1,3,5,4,2,6]
[1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,3,6,1] => [2,3,5,4,1,6] => [2,3,5,4,1,6]
[1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => [3,2,5,4,1,6] => [3,2,5,4,1,6]
[1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1] => [1,4,5,3,2,6] => [1,4,5,3,2,6]
[1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [2,4,5,3,1,6] => [2,4,5,3,1,6]
[1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => [3,4,5,2,1,6] => [3,4,5,2,1,6]
[1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => [4,3,5,2,1,6] => [4,3,5,2,1,6]
>>> Load all 727 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => [1,5,4,3,2,6] => [1,5,4,3,2,6]
[1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => [2,5,4,3,1,6] => [2,5,4,3,1,6]
[1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => [3,5,4,2,1,6] => [3,5,4,2,1,6]
[1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => [4,5,3,2,1,6] => [4,5,3,2,1,6]
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [5,4,3,2,1,6] => [5,4,3,2,1,6]
[1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,2] => [1,2,3,4,6,5] => [1,2,3,4,6,5]
[1,1,0,0,1,0,1,0,1,1,0,0] => [5,6,4,3,1,2] => [2,1,3,4,6,5] => [2,1,3,4,6,5]
[1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,5,3,1,2] => [1,3,2,4,6,5] => [1,3,2,4,6,5]
[1,1,0,0,1,0,1,1,0,1,0,0] => [5,4,6,3,1,2] => [2,3,1,4,6,5] => [2,3,1,4,6,5]
[1,1,0,0,1,0,1,1,1,0,0,0] => [4,5,6,3,1,2] => [3,2,1,4,6,5] => [3,2,1,4,6,5]
[1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,4,1,2] => [1,2,4,3,6,5] => [1,2,4,3,6,5]
[1,1,0,0,1,1,0,0,1,1,0,0] => [5,6,3,4,1,2] => [2,1,4,3,6,5] => [2,1,4,3,6,5]
[1,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,5,1,2] => [1,3,4,2,6,5] => [1,3,4,2,6,5]
[1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,6,1,2] => [2,3,4,1,6,5] => [2,3,4,1,6,5]
[1,1,0,0,1,1,0,1,1,0,0,0] => [4,5,3,6,1,2] => [3,2,4,1,6,5] => [3,2,4,1,6,5]
[1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,4,5,1,2] => [1,4,3,2,6,5] => [1,4,3,2,6,5]
[1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,4,6,1,2] => [2,4,3,1,6,5] => [2,4,3,1,6,5]
[1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,5,6,1,2] => [3,4,2,1,6,5] => [3,4,2,1,6,5]
[1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => [4,3,2,1,6,5] => [4,3,2,1,6,5]
[1,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1,3] => [1,2,3,5,6,4] => [1,2,3,5,6,4]
[1,1,0,1,0,0,1,0,1,1,0,0] => [5,6,4,2,1,3] => [2,1,3,5,6,4] => [2,1,3,5,6,4]
[1,1,0,1,0,0,1,1,0,0,1,0] => [6,4,5,2,1,3] => [1,3,2,5,6,4] => [1,3,2,5,6,4]
[1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,6,2,1,3] => [2,3,1,5,6,4] => [2,3,1,5,6,4]
[1,1,0,1,0,0,1,1,1,0,0,0] => [4,5,6,2,1,3] => [3,2,1,5,6,4] => [3,2,1,5,6,4]
[1,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1,4] => [1,2,4,5,6,3] => [1,2,4,5,6,3]
[1,1,0,1,0,1,0,0,1,1,0,0] => [5,6,3,2,1,4] => [2,1,4,5,6,3] => [2,1,4,5,6,3]
[1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,5] => [1,3,4,5,6,2] => [1,3,4,5,6,2]
[1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,6] => [2,3,4,5,6,1] => [2,3,4,5,6,1]
[1,1,0,1,0,1,0,1,1,0,0,0] => [4,5,3,2,1,6] => [3,2,4,5,6,1] => [3,2,4,5,6,1]
[1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,4,2,1,5] => [1,4,3,5,6,2] => [1,4,3,5,6,2]
[1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,4,2,1,6] => [2,4,3,5,6,1] => [2,4,3,5,6,1]
[1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,5,2,1,6] => [3,4,2,5,6,1] => [3,4,2,5,6,1]
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,2,1,6] => [4,3,2,5,6,1] => [4,3,2,5,6,1]
[1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,3,1,4] => [1,2,5,4,6,3] => [1,2,5,4,6,3]
[1,1,0,1,1,0,0,0,1,1,0,0] => [5,6,2,3,1,4] => [2,1,5,4,6,3] => [2,1,5,4,6,3]
[1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,3,1,5] => [1,3,5,4,6,2] => [1,3,5,4,6,2]
[1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,3,1,6] => [2,3,5,4,6,1] => [2,3,5,4,6,1]
[1,1,0,1,1,0,0,1,1,0,0,0] => [4,5,2,3,1,6] => [3,2,5,4,6,1] => [3,2,5,4,6,1]
[1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,4,1,5] => [1,4,5,3,6,2] => [1,4,5,3,6,2]
[1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,4,1,6] => [2,4,5,3,6,1] => [2,4,5,3,6,1]
[1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,5,1,6] => [3,4,5,2,6,1] => [3,4,5,2,6,1]
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,4,2,5,1,6] => [4,3,5,2,6,1] => [4,3,5,2,6,1]
[1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,3,4,1,5] => [1,5,4,3,6,2] => [1,5,4,3,6,2]
[1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,3,4,1,6] => [2,5,4,3,6,1] => [2,5,4,3,6,1]
[1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,3,5,1,6] => [3,5,4,2,6,1] => [3,5,4,2,6,1]
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,5,1,6] => [4,5,3,2,6,1] => [4,5,3,2,6,1]
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [5,4,3,2,6,1] => [5,4,3,2,6,1]
[1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,2,3] => [1,2,3,6,5,4] => [1,2,3,6,5,4]
[1,1,1,0,0,0,1,0,1,1,0,0] => [5,6,4,1,2,3] => [2,1,3,6,5,4] => [2,1,3,6,5,4]
[1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,5,1,2,3] => [1,3,2,6,5,4] => [1,3,2,6,5,4]
[1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,6,1,2,3] => [2,3,1,6,5,4] => [2,3,1,6,5,4]
[1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => [3,2,1,6,5,4]
[1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,2,4] => [1,2,4,6,5,3] => [1,2,4,6,5,3]
[1,1,1,0,0,1,0,0,1,1,0,0] => [5,6,3,1,2,4] => [2,1,4,6,5,3] => [2,1,4,6,5,3]
[1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,2,5] => [1,3,4,6,5,2] => [1,3,4,6,5,2]
[1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,2,6] => [2,3,4,6,5,1] => [2,3,4,6,5,1]
[1,1,1,0,0,1,0,1,1,0,0,0] => [4,5,3,1,2,6] => [3,2,4,6,5,1] => [3,2,4,6,5,1]
[1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,4,1,2,5] => [1,4,3,6,5,2] => [1,4,3,6,5,2]
[1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,4,1,2,6] => [2,4,3,6,5,1] => [2,4,3,6,5,1]
[1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,5,1,2,6] => [3,4,2,6,5,1] => [3,4,2,6,5,1]
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => [4,3,2,6,5,1] => [4,3,2,6,5,1]
[1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,3,4] => [1,2,5,6,4,3] => [1,2,5,6,4,3]
[1,1,1,0,1,0,0,0,1,1,0,0] => [5,6,2,1,3,4] => [2,1,5,6,4,3] => [2,1,5,6,4,3]
[1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,3,5] => [1,3,5,6,4,2] => [1,3,5,6,4,2]
[1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,3,6] => [2,3,5,6,4,1] => [2,3,5,6,4,1]
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,5,2,1,3,6] => [3,2,5,6,4,1] => [3,2,5,6,4,1]
[1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,4,5] => [1,4,5,6,3,2] => [1,4,5,6,3,2]
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,4,6] => [2,4,5,6,3,1] => [2,4,5,6,3,1]
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,5,6] => [3,4,5,6,2,1] => [3,4,5,6,2,1]
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,2,1,5,6] => [4,3,5,6,2,1] => [4,3,5,6,2,1]
[1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,3,1,4,5] => [1,5,4,6,3,2] => [1,5,4,6,3,2]
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,3,1,4,6] => [2,5,4,6,3,1] => [2,5,4,6,3,1]
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,3,1,5,6] => [3,5,4,6,2,1] => [3,5,4,6,2,1]
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,4,1,5,6] => [4,5,3,6,2,1] => [4,5,3,6,2,1]
[1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [5,4,3,6,2,1] => [5,4,3,6,2,1]
[1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => [1,2,6,5,4,3] => [1,2,6,5,4,3]
[1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => [2,1,6,5,4,3] => [2,1,6,5,4,3]
[1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,2,3,5] => [1,3,6,5,4,2] => [1,3,6,5,4,2]
[1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,2,3,6] => [2,3,6,5,4,1] => [2,3,6,5,4,1]
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => [3,2,6,5,4,1] => [3,2,6,5,4,1]
[1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,2,4,5] => [1,4,6,5,3,2] => [1,4,6,5,3,2]
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,2,4,6] => [2,4,6,5,3,1] => [2,4,6,5,3,1]
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,2,5,6] => [3,4,6,5,2,1] => [3,4,6,5,2,1]
[1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => [4,3,6,5,2,1] => [4,3,6,5,2,1]
[1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => [1,5,6,4,3,2] => [1,5,6,4,3,2]
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,3,4,6] => [2,5,6,4,3,1] => [2,5,6,4,3,1]
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,3,5,6] => [3,5,6,4,2,1] => [3,5,6,4,2,1]
[1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,4,5,6] => [4,5,6,3,2,1] => [4,5,6,3,2,1]
[1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [5,4,6,3,2,1] => [5,4,6,3,2,1]
[1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [1,6,5,4,3,2] => [1,6,5,4,3,2]
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [2,6,5,4,3,1] => [2,6,5,4,3,1]
[1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [3,6,5,4,2,1] => [3,6,5,4,2,1]
[1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [4,6,5,3,2,1] => [4,6,5,3,2,1]
[1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [5,6,4,3,2,1] => [5,6,4,3,2,1]
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [6,5,4,3,2,1] => [6,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,2,1] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,2,1] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,2,1] => [2,3,1,4,5,6,7] => [2,3,1,4,5,6,7]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,2,1] => [3,2,1,4,5,6,7] => [3,2,1,4,5,6,7]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,2,1] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,2,1] => [2,1,4,3,5,6,7] => [2,1,4,3,5,6,7]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,2,1] => [1,3,4,2,5,6,7] => [1,3,4,2,5,6,7]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,2,1] => [2,3,4,1,5,6,7] => [2,3,4,1,5,6,7]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,2,1] => [3,2,4,1,5,6,7] => [3,2,4,1,5,6,7]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,2,1] => [1,4,3,2,5,6,7] => [1,4,3,2,5,6,7]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,2,1] => [2,4,3,1,5,6,7] => [2,4,3,1,5,6,7]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,2,1] => [3,4,2,1,5,6,7] => [3,4,2,1,5,6,7]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,2,1] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6,7]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,2,1] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,2,1] => [2,1,3,5,4,6,7] => [2,1,3,5,4,6,7]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,2,1] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,2,1] => [2,3,1,5,4,6,7] => [2,3,1,5,4,6,7]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,2,1] => [3,2,1,5,4,6,7] => [3,2,1,5,4,6,7]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,2,1] => [1,2,4,5,3,6,7] => [1,2,4,5,3,6,7]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,2,1] => [2,1,4,5,3,6,7] => [2,1,4,5,3,6,7]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,2,1] => [1,3,4,5,2,6,7] => [1,3,4,5,2,6,7]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,2,1] => [2,3,4,5,1,6,7] => [2,3,4,5,1,6,7]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,2,1] => [3,2,4,5,1,6,7] => [3,2,4,5,1,6,7]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,2,1] => [1,4,3,5,2,6,7] => [1,4,3,5,2,6,7]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,2,1] => [2,4,3,5,1,6,7] => [2,4,3,5,1,6,7]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,2,1] => [3,4,2,5,1,6,7] => [3,4,2,5,1,6,7]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,2,1] => [4,3,2,5,1,6,7] => [4,3,2,5,1,6,7]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,2,1] => [1,2,5,4,3,6,7] => [1,2,5,4,3,6,7]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,2,1] => [2,1,5,4,3,6,7] => [2,1,5,4,3,6,7]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,2,1] => [1,3,5,4,2,6,7] => [1,3,5,4,2,6,7]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,2,1] => [2,3,5,4,1,6,7] => [2,3,5,4,1,6,7]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,2,1] => [3,2,5,4,1,6,7] => [3,2,5,4,1,6,7]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,2,1] => [1,4,5,3,2,6,7] => [1,4,5,3,2,6,7]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,2,1] => [2,4,5,3,1,6,7] => [2,4,5,3,1,6,7]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => [3,4,5,2,1,6,7] => [3,4,5,2,1,6,7]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,2,1] => [4,3,5,2,1,6,7] => [4,3,5,2,1,6,7]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1] => [1,5,4,3,2,6,7] => [1,5,4,3,2,6,7]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,2,1] => [2,5,4,3,1,6,7] => [2,5,4,3,1,6,7]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,2,1] => [3,5,4,2,1,6,7] => [3,5,4,2,1,6,7]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,2,1] => [4,5,3,2,1,6,7] => [4,5,3,2,1,6,7]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,2,1] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,3,1] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,3,1] => [2,1,3,4,6,5,7] => [2,1,3,4,6,5,7]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,3,1] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,3,1] => [2,3,1,4,6,5,7] => [2,3,1,4,6,5,7]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,3,1] => [3,2,1,4,6,5,7] => [3,2,1,4,6,5,7]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,3,1] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,3,1] => [2,1,4,3,6,5,7] => [2,1,4,3,6,5,7]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,3,1] => [1,3,4,2,6,5,7] => [1,3,4,2,6,5,7]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,3,1] => [2,3,4,1,6,5,7] => [2,3,4,1,6,5,7]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,3,1] => [3,2,4,1,6,5,7] => [3,2,4,1,6,5,7]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,3,1] => [1,4,3,2,6,5,7] => [1,4,3,2,6,5,7]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,3,1] => [2,4,3,1,6,5,7] => [2,4,3,1,6,5,7]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,3,1] => [3,4,2,1,6,5,7] => [3,4,2,1,6,5,7]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,3,1] => [4,3,2,1,6,5,7] => [4,3,2,1,6,5,7]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,4,1] => [1,2,3,5,6,4,7] => [1,2,3,5,6,4,7]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,4,1] => [2,1,3,5,6,4,7] => [2,1,3,5,6,4,7]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,4,1] => [1,3,2,5,6,4,7] => [1,3,2,5,6,4,7]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,4,1] => [2,3,1,5,6,4,7] => [2,3,1,5,6,4,7]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,4,1] => [3,2,1,5,6,4,7] => [3,2,1,5,6,4,7]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,5,1] => [1,2,4,5,6,3,7] => [1,2,4,5,6,3,7]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,5,1] => [2,1,4,5,6,3,7] => [2,1,4,5,6,3,7]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,6,1] => [1,3,4,5,6,2,7] => [1,3,4,5,6,2,7]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,1] => [2,3,4,5,6,1,7] => [2,3,4,5,6,1,7]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,7,1] => [3,2,4,5,6,1,7] => [3,2,4,5,6,1,7]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,6,1] => [1,4,3,5,6,2,7] => [1,4,3,5,6,2,7]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,7,1] => [2,4,3,5,6,1,7] => [2,4,3,5,6,1,7]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,7,1] => [3,4,2,5,6,1,7] => [3,4,2,5,6,1,7]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,7,1] => [4,3,2,5,6,1,7] => [4,3,2,5,6,1,7]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,5,1] => [1,2,5,4,6,3,7] => [1,2,5,4,6,3,7]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,5,1] => [2,1,5,4,6,3,7] => [2,1,5,4,6,3,7]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,6,1] => [1,3,5,4,6,2,7] => [1,3,5,4,6,2,7]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,7,1] => [2,3,5,4,6,1,7] => [2,3,5,4,6,1,7]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,7,1] => [3,2,5,4,6,1,7] => [3,2,5,4,6,1,7]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1] => [1,4,5,3,6,2,7] => [1,4,5,3,6,2,7]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,7,1] => [2,4,5,3,6,1,7] => [2,4,5,3,6,1,7]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,7,1] => [3,4,5,2,6,1,7] => [3,4,5,2,6,1,7]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,7,1] => [4,3,5,2,6,1,7] => [4,3,5,2,6,1,7]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,6,1] => [1,5,4,3,6,2,7] => [1,5,4,3,6,2,7]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [2,5,4,3,6,1,7] => [2,5,4,3,6,1,7]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,7,1] => [3,5,4,2,6,1,7] => [3,5,4,2,6,1,7]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,7,1] => [4,5,3,2,6,1,7] => [4,5,3,2,6,1,7]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,7,1] => [5,4,3,2,6,1,7] => [5,4,3,2,6,1,7]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,4,1] => [1,2,3,6,5,4,7] => [1,2,3,6,5,4,7]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,4,1] => [2,1,3,6,5,4,7] => [2,1,3,6,5,4,7]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,4,1] => [1,3,2,6,5,4,7] => [1,3,2,6,5,4,7]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,4,1] => [2,3,1,6,5,4,7] => [2,3,1,6,5,4,7]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,4,1] => [3,2,1,6,5,4,7] => [3,2,1,6,5,4,7]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,5,1] => [1,2,4,6,5,3,7] => [1,2,4,6,5,3,7]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,5,1] => [2,1,4,6,5,3,7] => [2,1,4,6,5,3,7]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,6,1] => [1,3,4,6,5,2,7] => [1,3,4,6,5,2,7]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,7,1] => [2,3,4,6,5,1,7] => [2,3,4,6,5,1,7]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,7,1] => [3,2,4,6,5,1,7] => [3,2,4,6,5,1,7]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,6,1] => [1,4,3,6,5,2,7] => [1,4,3,6,5,2,7]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,7,1] => [2,4,3,6,5,1,7] => [2,4,3,6,5,1,7]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,7,1] => [3,4,2,6,5,1,7] => [3,4,2,6,5,1,7]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,7,1] => [4,3,2,6,5,1,7] => [4,3,2,6,5,1,7]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,5,1] => [1,2,5,6,4,3,7] => [1,2,5,6,4,3,7]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,5,1] => [2,1,5,6,4,3,7] => [2,1,5,6,4,3,7]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,6,1] => [1,3,5,6,4,2,7] => [1,3,5,6,4,2,7]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,7,1] => [2,3,5,6,4,1,7] => [2,3,5,6,4,1,7]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,7,1] => [3,2,5,6,4,1,7] => [3,2,5,6,4,1,7]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,6,1] => [1,4,5,6,3,2,7] => [1,4,5,6,3,2,7]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [2,4,5,6,3,1,7] => [2,4,5,6,3,1,7]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,7,1] => [3,4,5,6,2,1,7] => [3,4,5,6,2,1,7]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,7,1] => [4,3,5,6,2,1,7] => [4,3,5,6,2,1,7]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,6,1] => [1,5,4,6,3,2,7] => [1,5,4,6,3,2,7]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,7,1] => [2,5,4,6,3,1,7] => [2,5,4,6,3,1,7]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,7,1] => [3,5,4,6,2,1,7] => [3,5,4,6,2,1,7]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,7,1] => [4,5,3,6,2,1,7] => [4,5,3,6,2,1,7]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,7,1] => [5,4,3,6,2,1,7] => [5,4,3,6,2,1,7]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,5,1] => [1,2,6,5,4,3,7] => [1,2,6,5,4,3,7]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,5,1] => [2,1,6,5,4,3,7] => [2,1,6,5,4,3,7]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,6,1] => [1,3,6,5,4,2,7] => [1,3,6,5,4,2,7]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,7,1] => [2,3,6,5,4,1,7] => [2,3,6,5,4,1,7]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,7,1] => [3,2,6,5,4,1,7] => [3,2,6,5,4,1,7]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,6,1] => [1,4,6,5,3,2,7] => [1,4,6,5,3,2,7]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,7,1] => [2,4,6,5,3,1,7] => [2,4,6,5,3,1,7]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,7,1] => [3,4,6,5,2,1,7] => [3,4,6,5,2,1,7]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,7,1] => [4,3,6,5,2,1,7] => [4,3,6,5,2,1,7]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,6,1] => [1,5,6,4,3,2,7] => [1,5,6,4,3,2,7]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,7,1] => [2,5,6,4,3,1,7] => [2,5,6,4,3,1,7]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,7,1] => [3,5,6,4,2,1,7] => [3,5,6,4,2,1,7]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,7,1] => [4,5,6,3,2,1,7] => [4,5,6,3,2,1,7]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,7,1] => [5,4,6,3,2,1,7] => [5,4,6,3,2,1,7]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,6,1] => [1,6,5,4,3,2,7] => [1,6,5,4,3,2,7]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,7,1] => [2,6,5,4,3,1,7] => [2,6,5,4,3,1,7]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,7,1] => [3,6,5,4,2,1,7] => [3,6,5,4,2,1,7]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,7,1] => [4,6,5,3,2,1,7] => [4,6,5,3,2,1,7]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,7,1] => [5,6,4,3,2,1,7] => [5,6,4,3,2,1,7]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,1,2] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,1,2] => [2,1,3,4,5,7,6] => [2,1,3,4,5,7,6]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,1,2] => [1,3,2,4,5,7,6] => [1,3,2,4,5,7,6]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,1,2] => [2,3,1,4,5,7,6] => [2,3,1,4,5,7,6]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,1,2] => [3,2,1,4,5,7,6] => [3,2,1,4,5,7,6]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,1,2] => [1,2,4,3,5,7,6] => [1,2,4,3,5,7,6]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,1,2] => [2,1,4,3,5,7,6] => [2,1,4,3,5,7,6]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,1,2] => [1,3,4,2,5,7,6] => [1,3,4,2,5,7,6]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,1,2] => [2,3,4,1,5,7,6] => [2,3,4,1,5,7,6]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,1,2] => [3,2,4,1,5,7,6] => [3,2,4,1,5,7,6]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,1,2] => [1,4,3,2,5,7,6] => [1,4,3,2,5,7,6]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,1,2] => [2,4,3,1,5,7,6] => [2,4,3,1,5,7,6]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,1,2] => [3,4,2,1,5,7,6] => [3,4,2,1,5,7,6]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,1,2] => [4,3,2,1,5,7,6] => [4,3,2,1,5,7,6]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,1,2] => [1,2,3,5,4,7,6] => [1,2,3,5,4,7,6]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,1,2] => [2,1,3,5,4,7,6] => [2,1,3,5,4,7,6]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,1,2] => [1,3,2,5,4,7,6] => [1,3,2,5,4,7,6]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,1,2] => [2,3,1,5,4,7,6] => [2,3,1,5,4,7,6]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,1,2] => [3,2,1,5,4,7,6] => [3,2,1,5,4,7,6]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,1,2] => [1,2,4,5,3,7,6] => [1,2,4,5,3,7,6]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,1,2] => [2,1,4,5,3,7,6] => [2,1,4,5,3,7,6]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,1,2] => [1,3,4,5,2,7,6] => [1,3,4,5,2,7,6]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,1,2] => [2,3,4,5,1,7,6] => [2,3,4,5,1,7,6]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,1,2] => [3,2,4,5,1,7,6] => [3,2,4,5,1,7,6]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,1,2] => [1,4,3,5,2,7,6] => [1,4,3,5,2,7,6]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,1,2] => [2,4,3,5,1,7,6] => [2,4,3,5,1,7,6]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,1,2] => [3,4,2,5,1,7,6] => [3,4,2,5,1,7,6]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,1,2] => [4,3,2,5,1,7,6] => [4,3,2,5,1,7,6]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,1,2] => [1,2,5,4,3,7,6] => [1,2,5,4,3,7,6]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,1,2] => [2,1,5,4,3,7,6] => [2,1,5,4,3,7,6]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,1,2] => [1,3,5,4,2,7,6] => [1,3,5,4,2,7,6]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,1,2] => [2,3,5,4,1,7,6] => [2,3,5,4,1,7,6]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,1,2] => [3,2,5,4,1,7,6] => [3,2,5,4,1,7,6]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,1,2] => [1,4,5,3,2,7,6] => [1,4,5,3,2,7,6]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,1,2] => [2,4,5,3,1,7,6] => [2,4,5,3,1,7,6]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,1,2] => [3,4,5,2,1,7,6] => [3,4,5,2,1,7,6]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,1,2] => [4,3,5,2,1,7,6] => [4,3,5,2,1,7,6]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,1,2] => [1,5,4,3,2,7,6] => [1,5,4,3,2,7,6]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,1,2] => [2,5,4,3,1,7,6] => [2,5,4,3,1,7,6]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,1,2] => [3,5,4,2,1,7,6] => [3,5,4,2,1,7,6]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,1,2] => [4,5,3,2,1,7,6] => [4,5,3,2,1,7,6]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2] => [5,4,3,2,1,7,6] => [5,4,3,2,1,7,6]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,1,3] => [1,2,3,4,6,7,5] => [1,2,3,4,6,7,5]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,1,3] => [2,1,3,4,6,7,5] => [2,1,3,4,6,7,5]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,1,3] => [1,3,2,4,6,7,5] => [1,3,2,4,6,7,5]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,1,3] => [2,3,1,4,6,7,5] => [2,3,1,4,6,7,5]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,1,3] => [3,2,1,4,6,7,5] => [3,2,1,4,6,7,5]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,1,3] => [1,2,4,3,6,7,5] => [1,2,4,3,6,7,5]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,1,3] => [2,1,4,3,6,7,5] => [2,1,4,3,6,7,5]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,1,3] => [1,3,4,2,6,7,5] => [1,3,4,2,6,7,5]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,1,3] => [2,3,4,1,6,7,5] => [2,3,4,1,6,7,5]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,1,3] => [3,2,4,1,6,7,5] => [3,2,4,1,6,7,5]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,1,3] => [1,4,3,2,6,7,5] => [1,4,3,2,6,7,5]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,1,3] => [2,4,3,1,6,7,5] => [2,4,3,1,6,7,5]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,1,3] => [3,4,2,1,6,7,5] => [3,4,2,1,6,7,5]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,1,3] => [4,3,2,1,6,7,5] => [4,3,2,1,6,7,5]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,1,4] => [1,2,3,5,6,7,4] => [1,2,3,5,6,7,4]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,1,4] => [2,1,3,5,6,7,4] => [2,1,3,5,6,7,4]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,1,4] => [1,3,2,5,6,7,4] => [1,3,2,5,6,7,4]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,1,4] => [2,3,1,5,6,7,4] => [2,3,1,5,6,7,4]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,1,4] => [3,2,1,5,6,7,4] => [3,2,1,5,6,7,4]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,1,5] => [1,2,4,5,6,7,3] => [1,2,4,5,6,7,3]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,1,5] => [2,1,4,5,6,7,3] => [2,1,4,5,6,7,3]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,1,6] => [1,3,4,5,6,7,2] => [1,3,4,5,6,7,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,7] => [2,3,4,5,6,7,1] => [2,3,4,5,6,7,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,1,7] => [3,2,4,5,6,7,1] => [3,2,4,5,6,7,1]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,1,6] => [1,4,3,5,6,7,2] => [1,4,3,5,6,7,2]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,1,7] => [2,4,3,5,6,7,1] => [2,4,3,5,6,7,1]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,1,7] => [3,4,2,5,6,7,1] => [3,4,2,5,6,7,1]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,1,7] => [4,3,2,5,6,7,1] => [4,3,2,5,6,7,1]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,1,5] => [1,2,5,4,6,7,3] => [1,2,5,4,6,7,3]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,1,5] => [2,1,5,4,6,7,3] => [2,1,5,4,6,7,3]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,1,6] => [1,3,5,4,6,7,2] => [1,3,5,4,6,7,2]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,1,7] => [2,3,5,4,6,7,1] => [2,3,5,4,6,7,1]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,1,7] => [3,2,5,4,6,7,1] => [3,2,5,4,6,7,1]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,1,6] => [1,4,5,3,6,7,2] => [1,4,5,3,6,7,2]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,1,7] => [2,4,5,3,6,7,1] => [2,4,5,3,6,7,1]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,1,7] => [3,4,5,2,6,7,1] => [3,4,5,2,6,7,1]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,1,7] => [4,3,5,2,6,7,1] => [4,3,5,2,6,7,1]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,1,6] => [1,5,4,3,6,7,2] => [1,5,4,3,6,7,2]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,1,7] => [2,5,4,3,6,7,1] => [2,5,4,3,6,7,1]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,1,7] => [3,5,4,2,6,7,1] => [3,5,4,2,6,7,1]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,1,7] => [4,5,3,2,6,7,1] => [4,5,3,2,6,7,1]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,1,7] => [5,4,3,2,6,7,1] => [5,4,3,2,6,7,1]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,1,4] => [1,2,3,6,5,7,4] => [1,2,3,6,5,7,4]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,1,4] => [2,1,3,6,5,7,4] => [2,1,3,6,5,7,4]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,1,4] => [1,3,2,6,5,7,4] => [1,3,2,6,5,7,4]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,1,4] => [2,3,1,6,5,7,4] => [2,3,1,6,5,7,4]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,1,4] => [3,2,1,6,5,7,4] => [3,2,1,6,5,7,4]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,1,5] => [1,2,4,6,5,7,3] => [1,2,4,6,5,7,3]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,1,5] => [2,1,4,6,5,7,3] => [2,1,4,6,5,7,3]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,1,6] => [1,3,4,6,5,7,2] => [1,3,4,6,5,7,2]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,1,7] => [2,3,4,6,5,7,1] => [2,3,4,6,5,7,1]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,1,7] => [3,2,4,6,5,7,1] => [3,2,4,6,5,7,1]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,1,6] => [1,4,3,6,5,7,2] => [1,4,3,6,5,7,2]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,1,7] => [2,4,3,6,5,7,1] => [2,4,3,6,5,7,1]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,1,7] => [3,4,2,6,5,7,1] => [3,4,2,6,5,7,1]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,1,7] => [4,3,2,6,5,7,1] => [4,3,2,6,5,7,1]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,1,5] => [1,2,5,6,4,7,3] => [1,2,5,6,4,7,3]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,1,5] => [2,1,5,6,4,7,3] => [2,1,5,6,4,7,3]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,1,6] => [1,3,5,6,4,7,2] => [1,3,5,6,4,7,2]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,1,7] => [2,3,5,6,4,7,1] => [2,3,5,6,4,7,1]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,1,7] => [3,2,5,6,4,7,1] => [3,2,5,6,4,7,1]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,1,6] => [1,4,5,6,3,7,2] => [1,4,5,6,3,7,2]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,1,7] => [2,4,5,6,3,7,1] => [2,4,5,6,3,7,1]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,1,7] => [3,4,5,6,2,7,1] => [3,4,5,6,2,7,1]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,1,7] => [4,3,5,6,2,7,1] => [4,3,5,6,2,7,1]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,1,6] => [1,5,4,6,3,7,2] => [1,5,4,6,3,7,2]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,1,7] => [2,5,4,6,3,7,1] => [2,5,4,6,3,7,1]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,1,7] => [3,5,4,6,2,7,1] => [3,5,4,6,2,7,1]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,1,7] => [4,5,3,6,2,7,1] => [4,5,3,6,2,7,1]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,1,7] => [5,4,3,6,2,7,1] => [5,4,3,6,2,7,1]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,1,5] => [1,2,6,5,4,7,3] => [1,2,6,5,4,7,3]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,1,5] => [2,1,6,5,4,7,3] => [2,1,6,5,4,7,3]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,1,6] => [1,3,6,5,4,7,2] => [1,3,6,5,4,7,2]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,1,7] => [2,3,6,5,4,7,1] => [2,3,6,5,4,7,1]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,1,7] => [3,2,6,5,4,7,1] => [3,2,6,5,4,7,1]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,1,6] => [1,4,6,5,3,7,2] => [1,4,6,5,3,7,2]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,1,7] => [2,4,6,5,3,7,1] => [2,4,6,5,3,7,1]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,1,7] => [3,4,6,5,2,7,1] => [3,4,6,5,2,7,1]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,1,7] => [4,3,6,5,2,7,1] => [4,3,6,5,2,7,1]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,1,6] => [1,5,6,4,3,7,2] => [1,5,6,4,3,7,2]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,1,7] => [2,5,6,4,3,7,1] => [2,5,6,4,3,7,1]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,1,7] => [3,5,6,4,2,7,1] => [3,5,6,4,2,7,1]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,1,7] => [4,5,6,3,2,7,1] => [4,5,6,3,2,7,1]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,1,7] => [5,4,6,3,2,7,1] => [5,4,6,3,2,7,1]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,1,6] => [1,6,5,4,3,7,2] => [1,6,5,4,3,7,2]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,1,7] => [2,6,5,4,3,7,1] => [2,6,5,4,3,7,1]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,1,7] => [3,6,5,4,2,7,1] => [3,6,5,4,2,7,1]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,1,7] => [4,6,5,3,2,7,1] => [4,6,5,3,2,7,1]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,1,7] => [5,6,4,3,2,7,1] => [5,6,4,3,2,7,1]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [6,5,4,3,2,7,1] => [6,5,4,3,2,7,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1,2,3] => [1,2,3,4,7,6,5] => [1,2,3,4,7,6,5]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,1,2,3] => [2,1,3,4,7,6,5] => [2,1,3,4,7,6,5]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,1,2,3] => [1,3,2,4,7,6,5] => [1,3,2,4,7,6,5]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,1,2,3] => [2,3,1,4,7,6,5] => [2,3,1,4,7,6,5]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,1,2,3] => [3,2,1,4,7,6,5] => [3,2,1,4,7,6,5]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,1,2,3] => [1,2,4,3,7,6,5] => [1,2,4,3,7,6,5]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,1,2,3] => [2,1,4,3,7,6,5] => [2,1,4,3,7,6,5]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,1,2,3] => [1,3,4,2,7,6,5] => [1,3,4,2,7,6,5]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,1,2,3] => [2,3,4,1,7,6,5] => [2,3,4,1,7,6,5]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,1,2,3] => [3,2,4,1,7,6,5] => [3,2,4,1,7,6,5]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,1,2,3] => [1,4,3,2,7,6,5] => [1,4,3,2,7,6,5]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,1,2,3] => [2,4,3,1,7,6,5] => [2,4,3,1,7,6,5]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,1,2,3] => [3,4,2,1,7,6,5] => [3,4,2,1,7,6,5]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,1,2,3] => [4,3,2,1,7,6,5] => [4,3,2,1,7,6,5]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,1,2,4] => [1,2,3,5,7,6,4] => [1,2,3,5,7,6,4]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,1,2,4] => [2,1,3,5,7,6,4] => [2,1,3,5,7,6,4]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,1,2,4] => [1,3,2,5,7,6,4] => [1,3,2,5,7,6,4]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,1,2,4] => [2,3,1,5,7,6,4] => [2,3,1,5,7,6,4]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,1,2,4] => [3,2,1,5,7,6,4] => [3,2,1,5,7,6,4]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,1,2,5] => [1,2,4,5,7,6,3] => [1,2,4,5,7,6,3]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,1,2,5] => [2,1,4,5,7,6,3] => [2,1,4,5,7,6,3]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,1,2,6] => [1,3,4,5,7,6,2] => [1,3,4,5,7,6,2]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,2,7] => [2,3,4,5,7,6,1] => [2,3,4,5,7,6,1]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,1,2,7] => [3,2,4,5,7,6,1] => [3,2,4,5,7,6,1]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,1,2,6] => [1,4,3,5,7,6,2] => [1,4,3,5,7,6,2]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,1,2,7] => [2,4,3,5,7,6,1] => [2,4,3,5,7,6,1]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,1,2,7] => [3,4,2,5,7,6,1] => [3,4,2,5,7,6,1]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,1,2,7] => [4,3,2,5,7,6,1] => [4,3,2,5,7,6,1]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,1,2,5] => [1,2,5,4,7,6,3] => [1,2,5,4,7,6,3]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,1,2,5] => [2,1,5,4,7,6,3] => [2,1,5,4,7,6,3]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,1,2,6] => [1,3,5,4,7,6,2] => [1,3,5,4,7,6,2]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,1,2,7] => [2,3,5,4,7,6,1] => [2,3,5,4,7,6,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,1,2,7] => [3,2,5,4,7,6,1] => [3,2,5,4,7,6,1]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,1,2,6] => [1,4,5,3,7,6,2] => [1,4,5,3,7,6,2]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,1,2,7] => [2,4,5,3,7,6,1] => [2,4,5,3,7,6,1]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,1,2,7] => [3,4,5,2,7,6,1] => [3,4,5,2,7,6,1]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,1,2,7] => [4,3,5,2,7,6,1] => [4,3,5,2,7,6,1]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,1,2,6] => [1,5,4,3,7,6,2] => [1,5,4,3,7,6,2]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,1,2,7] => [2,5,4,3,7,6,1] => [2,5,4,3,7,6,1]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,1,2,7] => [3,5,4,2,7,6,1] => [3,5,4,2,7,6,1]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,1,2,7] => [4,5,3,2,7,6,1] => [4,5,3,2,7,6,1]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,1,2,7] => [5,4,3,2,7,6,1] => [5,4,3,2,7,6,1]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,1,3,4] => [1,2,3,6,7,5,4] => [1,2,3,6,7,5,4]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,1,3,4] => [2,1,3,6,7,5,4] => [2,1,3,6,7,5,4]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,1,3,4] => [1,3,2,6,7,5,4] => [1,3,2,6,7,5,4]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,1,3,4] => [2,3,1,6,7,5,4] => [2,3,1,6,7,5,4]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,1,3,4] => [3,2,1,6,7,5,4] => [3,2,1,6,7,5,4]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,1,3,5] => [1,2,4,6,7,5,3] => [1,2,4,6,7,5,3]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,1,3,5] => [2,1,4,6,7,5,3] => [2,1,4,6,7,5,3]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,1,3,6] => [1,3,4,6,7,5,2] => [1,3,4,6,7,5,2]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,3,7] => [2,3,4,6,7,5,1] => [2,3,4,6,7,5,1]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,1,3,7] => [3,2,4,6,7,5,1] => [3,2,4,6,7,5,1]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,1,3,6] => [1,4,3,6,7,5,2] => [1,4,3,6,7,5,2]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,1,3,7] => [2,4,3,6,7,5,1] => [2,4,3,6,7,5,1]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,1,3,7] => [3,4,2,6,7,5,1] => [3,4,2,6,7,5,1]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,1,3,7] => [4,3,2,6,7,5,1] => [4,3,2,6,7,5,1]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,1,4,5] => [1,2,5,6,7,4,3] => [1,2,5,6,7,4,3]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,1,4,5] => [2,1,5,6,7,4,3] => [2,1,5,6,7,4,3]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,1,4,6] => [1,3,5,6,7,4,2] => [1,3,5,6,7,4,2]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1,4,7] => [2,3,5,6,7,4,1] => [2,3,5,6,7,4,1]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,1,4,7] => [3,2,5,6,7,4,1] => [3,2,5,6,7,4,1]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,1,5,6] => [1,4,5,6,7,3,2] => [1,4,5,6,7,3,2]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,5,7] => [2,4,5,6,7,3,1] => [2,4,5,6,7,3,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,6,7] => [3,4,5,6,7,2,1] => [3,4,5,6,7,2,1]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,1,6,7] => [4,3,5,6,7,2,1] => [4,3,5,6,7,2,1]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,1,5,6] => [1,5,4,6,7,3,2] => [1,5,4,6,7,3,2]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,1,5,7] => [2,5,4,6,7,3,1] => [2,5,4,6,7,3,1]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,1,6,7] => [3,5,4,6,7,2,1] => [3,5,4,6,7,2,1]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,1,6,7] => [4,5,3,6,7,2,1] => [4,5,3,6,7,2,1]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,1,6,7] => [5,4,3,6,7,2,1] => [5,4,3,6,7,2,1]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,1,4,5] => [1,2,6,5,7,4,3] => [1,2,6,5,7,4,3]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,1,4,5] => [2,1,6,5,7,4,3] => [2,1,6,5,7,4,3]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,1,4,6] => [1,3,6,5,7,4,2] => [1,3,6,5,7,4,2]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,1,4,7] => [2,3,6,5,7,4,1] => [2,3,6,5,7,4,1]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,1,4,7] => [3,2,6,5,7,4,1] => [3,2,6,5,7,4,1]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,1,5,6] => [1,4,6,5,7,3,2] => [1,4,6,5,7,3,2]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,1,5,7] => [2,4,6,5,7,3,1] => [2,4,6,5,7,3,1]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,1,6,7] => [3,4,6,5,7,2,1] => [3,4,6,5,7,2,1]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,1,6,7] => [4,3,6,5,7,2,1] => [4,3,6,5,7,2,1]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,1,5,6] => [1,5,6,4,7,3,2] => [1,5,6,4,7,3,2]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,1,5,7] => [2,5,6,4,7,3,1] => [2,5,6,4,7,3,1]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,1,6,7] => [3,5,6,4,7,2,1] => [3,5,6,4,7,2,1]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,1,6,7] => [4,5,6,3,7,2,1] => [4,5,6,3,7,2,1]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,1,6,7] => [5,4,6,3,7,2,1] => [5,4,6,3,7,2,1]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,1,5,6] => [1,6,5,4,7,3,2] => [1,6,5,4,7,3,2]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,1,5,7] => [2,6,5,4,7,3,1] => [2,6,5,4,7,3,1]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,1,6,7] => [3,6,5,4,7,2,1] => [3,6,5,4,7,2,1]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,1,6,7] => [4,6,5,3,7,2,1] => [4,6,5,3,7,2,1]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,1,6,7] => [5,6,4,3,7,2,1] => [5,6,4,3,7,2,1]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [6,5,4,3,7,2,1] => [6,5,4,3,7,2,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [7,6,5,1,2,3,4] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [6,7,5,1,2,3,4] => [2,1,3,7,6,5,4] => [2,1,3,7,6,5,4]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [7,5,6,1,2,3,4] => [1,3,2,7,6,5,4] => [1,3,2,7,6,5,4]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [6,5,7,1,2,3,4] => [2,3,1,7,6,5,4] => [2,3,1,7,6,5,4]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4] => [3,2,1,7,6,5,4] => [3,2,1,7,6,5,4]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [7,6,4,1,2,3,5] => [1,2,4,7,6,5,3] => [1,2,4,7,6,5,3]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [6,7,4,1,2,3,5] => [2,1,4,7,6,5,3] => [2,1,4,7,6,5,3]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [7,5,4,1,2,3,6] => [1,3,4,7,6,5,2] => [1,3,4,7,6,5,2]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,2,3,7] => [2,3,4,7,6,5,1] => [2,3,4,7,6,5,1]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,6,4,1,2,3,7] => [3,2,4,7,6,5,1] => [3,2,4,7,6,5,1]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [7,4,5,1,2,3,6] => [1,4,3,7,6,5,2] => [1,4,3,7,6,5,2]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,5,1,2,3,7] => [2,4,3,7,6,5,1] => [2,4,3,7,6,5,1]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,6,1,2,3,7] => [3,4,2,7,6,5,1] => [3,4,2,7,6,5,1]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => [4,3,2,7,6,5,1] => [4,3,2,7,6,5,1]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [7,6,3,1,2,4,5] => [1,2,5,7,6,4,3] => [1,2,5,7,6,4,3]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [6,7,3,1,2,4,5] => [2,1,5,7,6,4,3] => [2,1,5,7,6,4,3]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1,2,4,6] => [1,3,5,7,6,4,2] => [1,3,5,7,6,4,2]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,2,4,7] => [2,3,5,7,6,4,1] => [2,3,5,7,6,4,1]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,6,3,1,2,4,7] => [3,2,5,7,6,4,1] => [3,2,5,7,6,4,1]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,2,5,6] => [1,4,5,7,6,3,2] => [1,4,5,7,6,3,2]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,2,5,7] => [2,4,5,7,6,3,1] => [2,4,5,7,6,3,1]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,2,6,7] => [3,4,5,7,6,2,1] => [3,4,5,7,6,2,1]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,5,3,1,2,6,7] => [4,3,5,7,6,2,1] => [4,3,5,7,6,2,1]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,4,1,2,5,6] => [1,5,4,7,6,3,2] => [1,5,4,7,6,3,2]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,4,1,2,5,7] => [2,5,4,7,6,3,1] => [2,5,4,7,6,3,1]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,4,1,2,6,7] => [3,5,4,7,6,2,1] => [3,5,4,7,6,2,1]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,5,1,2,6,7] => [4,5,3,7,6,2,1] => [4,5,3,7,6,2,1]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,4,5,1,2,6,7] => [5,4,3,7,6,2,1] => [5,4,3,7,6,2,1]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [7,6,2,1,3,4,5] => [1,2,6,7,5,4,3] => [1,2,6,7,5,4,3]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,7,2,1,3,4,5] => [2,1,6,7,5,4,3] => [2,1,6,7,5,4,3]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,3,4,6] => [1,3,6,7,5,4,2] => [1,3,6,7,5,4,2]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,3,4,7] => [2,3,6,7,5,4,1] => [2,3,6,7,5,4,1]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,6,2,1,3,4,7] => [3,2,6,7,5,4,1] => [3,2,6,7,5,4,1]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,3,5,6] => [1,4,6,7,5,3,2] => [1,4,6,7,5,3,2]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,3,5,7] => [2,4,6,7,5,3,1] => [2,4,6,7,5,3,1]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,3,6,7] => [3,4,6,7,5,2,1] => [3,4,6,7,5,2,1]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,2,1,3,6,7] => [4,3,6,7,5,2,1] => [4,3,6,7,5,2,1]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,4,5,6] => [1,5,6,7,4,3,2] => [1,5,6,7,4,3,2]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,4,5,7] => [2,5,6,7,4,3,1] => [2,5,6,7,4,3,1]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,4,6,7] => [3,5,6,7,4,2,1] => [3,5,6,7,4,2,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,5,6,7] => [4,5,6,7,3,2,1] => [4,5,6,7,3,2,1]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,4,2,1,5,6,7] => [5,4,6,7,3,2,1] => [5,4,6,7,3,2,1]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,3,1,4,5,6] => [1,6,5,7,4,3,2] => [1,6,5,7,4,3,2]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,3,1,4,5,7] => [2,6,5,7,4,3,1] => [2,6,5,7,4,3,1]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,3,1,4,6,7] => [3,6,5,7,4,2,1] => [3,6,5,7,4,2,1]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,3,1,5,6,7] => [4,6,5,7,3,2,1] => [4,6,5,7,3,2,1]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,4,1,5,6,7] => [5,6,4,7,3,2,1] => [5,6,4,7,3,2,1]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [6,5,4,7,3,2,1] => [6,5,4,7,3,2,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,2,3,4,5] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,2,3,4,6] => [1,3,7,6,5,4,2] => [1,3,7,6,5,4,2]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,2,3,4,7] => [2,3,7,6,5,4,1] => [2,3,7,6,5,4,1]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,6,1,2,3,4,7] => [3,2,7,6,5,4,1] => [3,2,7,6,5,4,1]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,2,3,5,6] => [1,4,7,6,5,3,2] => [1,4,7,6,5,3,2]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,2,3,5,7] => [2,4,7,6,5,3,1] => [2,4,7,6,5,3,1]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,2,3,6,7] => [3,4,7,6,5,2,1] => [3,4,7,6,5,2,1]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,5,1,2,3,6,7] => [4,3,7,6,5,2,1] => [4,3,7,6,5,2,1]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,2,4,5,6] => [1,5,7,6,4,3,2] => [1,5,7,6,4,3,2]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,2,4,5,7] => [2,5,7,6,4,3,1] => [2,5,7,6,4,3,1]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,2,4,6,7] => [3,5,7,6,4,2,1] => [3,5,7,6,4,2,1]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,2,5,6,7] => [4,5,7,6,3,2,1] => [4,5,7,6,3,2,1]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,4,1,2,5,6,7] => [5,4,7,6,3,2,1] => [5,4,7,6,3,2,1]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,3,4,5,6] => [1,6,7,5,4,3,2] => [1,6,7,5,4,3,2]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,3,4,5,7] => [2,6,7,5,4,3,1] => [2,6,7,5,4,3,1]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,3,4,6,7] => [3,6,7,5,4,2,1] => [3,6,7,5,4,2,1]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,3,5,6,7] => [4,6,7,5,3,2,1] => [4,6,7,5,3,2,1]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,4,5,6,7] => [5,6,7,4,3,2,1] => [5,6,7,4,3,2,1]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [6,5,7,4,3,2,1] => [6,5,7,4,3,2,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,5,7] => [2,7,6,5,4,3,1] => [2,7,6,5,4,3,1]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,2,3,4,6,7] => [3,7,6,5,4,2,1] => [3,7,6,5,4,2,1]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,2,3,5,6,7] => [4,7,6,5,3,2,1] => [4,7,6,5,3,2,1]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,2,4,5,6,7] => [5,7,6,4,3,2,1] => [5,7,6,4,3,2,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => [6,7,5,4,3,2,1] => [6,7,5,4,3,2,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,2,1] => [4,3,2,1,5,6,7,8] => [4,3,2,1,5,6,7,8]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,2,1] => [1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7,8]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,2,1] => [4,3,2,1,6,5,7,8] => [4,3,2,1,6,5,7,8]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,3,1] => [1,3,2,4,5,7,6,8] => [1,3,2,4,5,7,6,8]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,3,1] => [4,3,2,1,5,7,6,8] => [4,3,2,1,5,7,6,8]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,2,4,1] => [1,3,4,2,6,7,5,8] => [1,3,4,2,6,7,5,8]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,2,4,1] => [4,3,2,1,6,7,5,8] => [4,3,2,1,6,7,5,8]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,3,4,1] => [1,4,3,2,7,6,5,8] => [1,4,3,2,7,6,5,8]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,4,1] => [4,3,2,1,7,6,5,8] => [4,3,2,1,7,6,5,8]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,8,1] => [3,2,5,4,7,6,1,8] => [3,2,5,4,7,6,1,8]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,3,8,1] => [5,4,3,2,7,6,1,8] => [5,4,3,2,7,6,1,8]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,5,8,1] => [3,2,7,6,5,4,1,8] => [3,2,7,6,5,4,1,8]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,1,2] => [2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,8,7]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,1,2] => [4,3,2,1,5,6,8,7] => [4,3,2,1,5,6,8,7]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,4,1,2] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,4,1,2] => [2,3,4,1,6,5,8,7] => [2,3,4,1,6,5,8,7]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,4,1,2] => [3,2,4,1,6,5,8,7] => [3,2,4,1,6,5,8,7]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,4,1,2] => [2,4,3,1,6,5,8,7] => [2,4,3,1,6,5,8,7]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,4,1,2] => [3,4,2,1,6,5,8,7] => [3,4,2,1,6,5,8,7]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,1,2] => [4,3,2,1,6,5,8,7] => [4,3,2,1,6,5,8,7]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,6,1,2] => [2,1,4,5,6,3,8,7] => [2,1,4,5,6,3,8,7]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,8,1,2] => [2,3,4,5,6,1,8,7] => [2,3,4,5,6,1,8,7]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,3,6,1,2] => [2,1,5,4,6,3,8,7] => [2,1,5,4,6,3,8,7]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,8,1,2] => [3,2,5,4,6,1,8,7] => [3,2,5,4,6,1,8,7]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,3,8,1,2] => [4,3,5,2,6,1,8,7] => [4,3,5,2,6,1,8,7]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,6,1,2] => [2,1,4,6,5,3,8,7] => [2,1,4,6,5,3,8,7]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,6,1,2] => [2,1,5,6,4,3,8,7] => [2,1,5,6,4,3,8,7]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,8,1,2] => [4,5,3,6,2,1,8,7] => [4,5,3,6,2,1,8,7]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,6,1,2] => [2,1,6,5,4,3,8,7] => [2,1,6,5,4,3,8,7]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,8,1,2] => [4,5,6,3,2,1,8,7] => [4,5,6,3,2,1,8,7]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2] => [6,5,4,3,2,1,8,7] => [6,5,4,3,2,1,8,7]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,2,1,3] => [2,3,1,4,5,7,8,6] => [2,3,1,4,5,7,8,6]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,1,3] => [4,3,2,1,5,7,8,6] => [4,3,2,1,5,7,8,6]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,2,1,4] => [2,1,4,3,6,7,8,5] => [2,1,4,3,6,7,8,5]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,2,1,4] => [2,3,4,1,6,7,8,5] => [2,3,4,1,6,7,8,5]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,2,1,4] => [4,3,2,1,6,7,8,5] => [4,3,2,1,6,7,8,5]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,2,1,5] => [1,2,3,5,6,7,8,4] => [1,2,3,5,6,7,8,4]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,2,1,6] => [2,1,4,5,6,7,8,3] => [2,1,4,5,6,7,8,3]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,1,8] => [2,3,4,5,6,7,8,1] => [2,3,4,5,6,7,8,1]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,3,1,4] => [2,1,4,3,7,6,8,5] => [2,1,4,3,7,6,8,5]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,3,1,4] => [3,2,4,1,7,6,8,5] => [3,2,4,1,7,6,8,5]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,2,3,1,4] => [2,4,3,1,7,6,8,5] => [2,4,3,1,7,6,8,5]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,1,4] => [4,3,2,1,7,6,8,5] => [4,3,2,1,7,6,8,5]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,2,3,1,6] => [2,1,5,4,7,6,8,3] => [2,1,5,4,7,6,8,3]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,1,8] => [3,2,5,4,7,6,8,1] => [3,2,5,4,7,6,8,1]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,2,3,1,8] => [4,3,5,2,7,6,8,1] => [4,3,5,2,7,6,8,1]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,2,5,1,6] => [2,1,6,5,7,4,8,3] => [2,1,6,5,7,4,8,3]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,2,5,1,8] => [3,2,6,5,7,4,8,1] => [3,2,6,5,7,4,8,1]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,2,7,1,8] => [4,3,6,5,7,2,8,1] => [4,3,6,5,7,2,8,1]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,2,7,1,8] => [5,4,6,3,7,2,8,1] => [5,4,6,3,7,2,8,1]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,1,2,3] => [3,2,1,4,5,8,7,6] => [3,2,1,4,5,8,7,6]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,1,2,3] => [4,3,2,1,5,8,7,6] => [4,3,2,1,5,8,7,6]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,1,2,3] => [3,2,5,4,1,8,7,6] => [3,2,5,4,1,8,7,6]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,1,2,3] => [5,4,3,2,1,8,7,6] => [5,4,3,2,1,8,7,6]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,1,2,4] => [2,1,4,3,6,8,7,5] => [2,1,4,3,6,8,7,5]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,1,2,4] => [3,2,4,1,6,8,7,5] => [3,2,4,1,6,8,7,5]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,1,2,4] => [2,4,3,1,6,8,7,5] => [2,4,3,1,6,8,7,5]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,1,2,4] => [4,3,2,1,6,8,7,5] => [4,3,2,1,6,8,7,5]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,1,2,5] => [3,2,1,6,5,8,7,4] => [3,2,1,6,5,8,7,4]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,1,2,7] => [1,4,3,6,5,8,7,2] => [1,4,3,6,5,8,7,2]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,1,2,7] => [1,6,5,4,3,8,7,2] => [1,6,5,4,3,8,7,2]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,1,3,4] => [2,1,4,3,7,8,6,5] => [2,1,4,3,7,8,6,5]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,1,3,4] => [3,4,2,1,7,8,6,5] => [3,4,2,1,7,8,6,5]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,1,3,4] => [4,3,2,1,7,8,6,5] => [4,3,2,1,7,8,6,5]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,2,1,3,8] => [3,4,2,5,7,8,6,1] => [3,4,2,5,7,8,6,1]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,1,5,6] => [1,2,5,6,7,8,4,3] => [1,2,5,6,7,8,4,3]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,1,5,6] => [2,1,5,6,7,8,4,3] => [2,1,5,6,7,8,4,3]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,2,1,5,7] => [1,3,5,6,7,8,4,2] => [1,3,5,6,7,8,4,2]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,1,5,8] => [2,3,5,6,7,8,4,1] => [2,3,5,6,7,8,4,1]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,4,1,5,6] => [2,1,6,7,5,8,4,3] => [2,1,6,7,5,8,4,3]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,1,2,3,4] => [1,2,3,4,8,7,6,5] => [1,2,3,4,8,7,6,5]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,1,2,3,4] => [2,1,3,4,8,7,6,5] => [2,1,3,4,8,7,6,5]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,1,2,3,4] => [1,3,2,4,8,7,6,5] => [1,3,2,4,8,7,6,5]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,1,2,3,4] => [2,3,1,4,8,7,6,5] => [2,3,1,4,8,7,6,5]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,1,2,3,4] => [3,2,1,4,8,7,6,5] => [3,2,1,4,8,7,6,5]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,1,2,3,4] => [1,2,4,3,8,7,6,5] => [1,2,4,3,8,7,6,5]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,1,2,3,4] => [2,1,4,3,8,7,6,5] => [2,1,4,3,8,7,6,5]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,1,2,3,4] => [1,3,4,2,8,7,6,5] => [1,3,4,2,8,7,6,5]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,1,2,3,4] => [2,3,4,1,8,7,6,5] => [2,3,4,1,8,7,6,5]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,1,2,3,4] => [3,2,4,1,8,7,6,5] => [3,2,4,1,8,7,6,5]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,1,2,3,4] => [1,4,3,2,8,7,6,5] => [1,4,3,2,8,7,6,5]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,1,2,3,4] => [2,4,3,1,8,7,6,5] => [2,4,3,1,8,7,6,5]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,1,2,3,4] => [3,4,2,1,8,7,6,5] => [3,4,2,1,8,7,6,5]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => [4,3,2,1,8,7,6,5] => [4,3,2,1,8,7,6,5]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,1,2,5,8] => [2,3,5,6,8,7,4,1] => [2,3,5,6,8,7,4,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,1,3,5,7] => [1,3,5,7,8,6,4,2] => [1,3,5,7,8,6,4,2]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [8,7,3,2,1,4,5,6] => [1,2,6,7,8,5,4,3] => [1,2,6,7,8,5,4,3]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,1,4,5,6] => [2,1,6,7,8,5,4,3] => [2,1,6,7,8,5,4,3]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [8,4,3,2,1,5,6,7] => [1,5,6,7,8,4,3,2] => [1,5,6,7,8,4,3,2]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,1,5,6,8] => [2,5,6,7,8,4,3,1] => [2,5,6,7,8,4,3,1]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,1,5,7,8] => [3,5,6,7,8,4,2,1] => [3,5,6,7,8,4,2,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,7,8,1,2,3,4,5] => [3,2,1,8,7,6,5,4] => [3,2,1,8,7,6,5,4]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [8,5,6,1,2,3,4,7] => [1,4,3,8,7,6,5,2] => [1,4,3,8,7,6,5,2]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,5,6,7,8] => [5,6,7,8,4,3,2,1] => [5,6,7,8,4,3,2,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,8,1,2,3,4,5,6] => [2,1,8,7,6,5,4,3] => [2,1,8,7,6,5,4,3]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,4,1,2,3,5,7,8] => [3,5,8,7,6,4,2,1] => [3,5,8,7,6,4,2,1]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [7,3,1,2,4,5,6,8] => [2,6,8,7,5,4,3,1] => [2,6,8,7,5,4,3,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1,3,4,5,6,7] => [1,7,8,6,5,4,3,2] => [1,7,8,6,5,4,3,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7] => [1,8,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1]
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].
Map
complement
Description
Sents a permutation to its complement.
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
Map
catalanization
Description
The catalanization of a permutation.
For a permutation $\sigma$, this is the product of the reflections corresponding to the inversions of $\sigma$ in lex-order.
A permutation is $231$-avoiding if and only if it is a fixpoint of this map. Also, for every permutation there exists an index $k$ such that the $k$-fold application of this map is $231$-avoiding.
For a permutation $\sigma$, this is the product of the reflections corresponding to the inversions of $\sigma$ in lex-order.
A permutation is $231$-avoiding if and only if it is a fixpoint of this map. Also, for every permutation there exists an index $k$ such that the $k$-fold application of this map is $231$-avoiding.
searching the database
Sorry, this map was not found in the database.