- FindStat

Identifier

Mp00103: Dyck paths —peeling map⟶ Dyck paths
Mp00024: Dyck paths —to 321-avoiding permutation⟶ Permutations
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
St001130: Permutations ⟶ ℤ

Values

[1,0,1,0] => [1,0,1,0] => [2,1] => [1,2] => 0

[1,1,0,0] => [1,0,1,0] => [2,1] => [1,2] => 0

[1,0,1,0,1,0] => [1,0,1,0,1,0] => [2,1,3] => [1,3,2] => 0

[1,0,1,1,0,0] => [1,0,1,0,1,0] => [2,1,3] => [1,3,2] => 0

[1,1,0,0,1,0] => [1,0,1,0,1,0] => [2,1,3] => [1,3,2] => 0

[1,1,0,1,0,0] => [1,0,1,0,1,0] => [2,1,3] => [1,3,2] => 0

[1,1,1,0,0,0] => [1,0,1,0,1,0] => [2,1,3] => [1,3,2] => 0

[1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => [2,1,4,3] => [1,4,3,2] => 0

[1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0] => [2,1,4,3] => [1,4,3,2] => 0

[1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0] => [2,1,4,3] => [1,4,3,2] => 0

[1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0] => [2,1,4,3] => [1,4,3,2] => 0

[1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0] => [2,1,4,3] => [1,4,3,2] => 0

[1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => [2,1,4,3] => [1,4,3,2] => 0

[1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0] => [2,1,4,3] => [1,4,3,2] => 0

[1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0] => [2,1,4,3] => [1,4,3,2] => 0

[1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0] => [2,1,4,3] => [1,4,3,2] => 0

[1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0] => [2,1,4,3] => [1,4,3,2] => 0

[1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0] => [2,1,4,3] => [1,4,3,2] => 0

[1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0] => [2,1,4,3] => [1,4,3,2] => 0

[1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0] => [2,1,4,3] => [1,4,3,2] => 0

[1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0] => [2,1,3,4] => [1,3,4,2] => 0

[1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5] => [1,4,3,5,2] => 0

[1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5] => [1,4,3,5,2] => 0

[1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5] => [1,4,3,5,2] => 0

[1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5] => [1,4,3,5,2] => 0

[1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5] => [1,4,3,5,2] => 0

[1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5] => [1,4,3,5,2] => 0

[1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5] => [1,4,3,5,2] => 0

[1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5] => [1,4,3,5,2] => 0

[1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5] => [1,4,3,5,2] => 0

[1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5] => [1,4,3,5,2] => 0

[1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5] => [1,4,3,5,2] => 0

[1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5] => [1,4,3,5,2] => 0

[1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5] => [1,4,3,5,2] => 0

[1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0] => [2,1,4,5,3] => [1,5,3,4,2] => 0

[1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5] => [1,4,3,5,2] => 0

[1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5] => [1,4,3,5,2] => 0

[1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5] => [1,4,3,5,2] => 0

[1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5] => [1,4,3,5,2] => 0

[1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5] => [1,4,3,5,2] => 0

[1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5] => [1,4,3,5,2] => 0

[1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5] => [1,4,3,5,2] => 0

[1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5] => [1,4,3,5,2] => 0

[1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5] => [1,4,3,5,2] => 0

[1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5] => [1,4,3,5,2] => 0

[1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5] => [1,4,3,5,2] => 0

[1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5] => [1,4,3,5,2] => 0

[1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5] => [1,4,3,5,2] => 0

[1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0] => [2,1,4,5,3] => [1,5,3,4,2] => 0

[1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5] => [1,4,3,5,2] => 0

[1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5] => [1,4,3,5,2] => 0

[1,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5] => [1,4,3,5,2] => 0

[1,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5] => [1,4,3,5,2] => 0

[1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5] => [1,4,3,5,2] => 0

[1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5] => [1,4,3,5,2] => 0

[1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5] => [1,4,3,5,2] => 0

[1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5] => [1,4,3,5,2] => 0

[1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0] => [2,1,4,5,3] => [1,5,3,4,2] => 0

[1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => [2,1,5,3,4] => [1,4,5,3,2] => 0

[1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0] => [2,1,5,3,4] => [1,4,5,3,2] => 0

[1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0] => [2,1,5,3,4] => [1,4,5,3,2] => 0

[1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,4] => [1,3,5,4,2] => 0

[1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0] => [2,1,3,4,5] => [1,3,4,5,2] => 1

[1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,6,3,5] => [1,5,3,6,4,2] => 0

[1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,6,3,5] => [1,5,3,6,4,2] => 0

[1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,6,3,5] => [1,5,3,6,4,2] => 0

[1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [1,4,3,5,6,2] => 0

>>> Load all 552 entries. <<<

[1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [1,4,3,5,6,2] => 0

[1,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [1,4,3,5,6,2] => 0

[1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [1,5,3,4,6,2] => 0

[1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,4,5,6,3] => [1,6,3,4,5,2] => 1

[1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,6,3,5] => [1,5,3,6,4,2] => 0

[1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,6,3,5] => [1,5,3,6,4,2] => 0

[1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,6,3,5] => [1,5,3,6,4,2] => 0

[1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [1,4,3,5,6,2] => 0

[1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [1,4,3,5,6,2] => 0

[1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [1,4,3,5,6,2] => 0

[1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [1,5,3,4,6,2] => 0

[1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,4,5,6,3] => [1,6,3,4,5,2] => 1

[1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,6,3,5] => [1,5,3,6,4,2] => 0

[1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 0

[1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,6,3,5] => [1,5,3,6,4,2] => 0

[1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [1,4,3,5,6,2] => 0

[1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [1,4,3,5,6,2] => 0

[1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [1,4,3,5,6,2] => 0

[1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [1,5,3,4,6,2] => 0

[1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,4,5,6,3] => [1,6,3,4,5,2] => 1

[1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,5,3,6,4] => [1,4,6,3,5,2] => 0

[1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,5,3,6,4] => [1,4,6,3,5,2] => 0

[1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,5,3,6,4] => [1,4,6,3,5,2] => 0

[1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,5,3,6,4] => [1,4,6,3,5,2] => 0

[1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,5,3,6,4] => [1,4,6,3,5,2] => 0

[1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,5,3,6,4] => [1,4,6,3,5,2] => 0

[1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,5,3,6,4] => [1,4,6,3,5,2] => 0

[1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,5,3,6,4] => [1,4,6,3,5,2] => 0

[1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,5,6,3,4] => [1,5,6,3,4,2] => 0

[1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,5,3,4,6] => [1,4,5,3,6,2] => 0

[1,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,5,3,4,6] => [1,4,5,3,6,2] => 0

[1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,5,3,4,6] => [1,4,5,3,6,2] => 0

[1,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,3,5,4,6] => [1,3,5,4,6,2] => 0

[1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => [2,1,3,5,6,4] => [1,3,6,4,5,2] => 0

[1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,6,3,4,5] => [1,4,5,6,3,2] => 1

[1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,6,3,4,5] => [1,4,5,6,3,2] => 1

[1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,6,3,4,5] => [1,4,5,6,3,2] => 1

[1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,3,6,4,5] => [1,3,5,6,4,2] => 0

[1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,3,4,6,5] => [1,3,4,6,5,2] => 0

[1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,3,4,5,6] => [1,3,4,5,6,2] => 2

[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => [1,4,3,7,5,6,2] => 0

[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => [1,4,3,7,5,6,2] => 0

[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => [1,4,3,7,5,6,2] => 0

[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => [1,4,3,7,5,6,2] => 0

[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => [1,4,3,7,5,6,2] => 0

[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => [1,4,3,7,5,6,2] => 0

[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => [1,4,3,7,5,6,2] => 0

[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => [1,4,3,7,5,6,2] => 0

[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => [1,4,3,7,5,6,2] => 0

[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,7,5,6] => [1,4,3,6,7,5,2] => 0

[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,7,5,6] => [1,4,3,6,7,5,2] => 0

[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,7,5,6] => [1,4,3,6,7,5,2] => 0

[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,7,5,6] => [1,4,3,6,7,5,2] => 0

[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,7,5,6] => [1,4,3,6,7,5,2] => 0

[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,7,5,6] => [1,4,3,6,7,5,2] => 0

[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,7,5,6] => [1,4,3,6,7,5,2] => 0

[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,7,5,6] => [1,4,3,6,7,5,2] => 0

[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,3,5,7,6] => [1,4,3,5,7,6,2] => 0

[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,3,5,7,6] => [1,4,3,5,7,6,2] => 0

[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,3,5,7,6] => [1,4,3,5,7,6,2] => 0

[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,4,3,5,6,7] => [1,4,3,5,6,7,2] => 1

[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,4,3,5,6,7] => [1,4,3,5,6,7,2] => 1

[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,4,3,5,6,7] => [1,4,3,5,6,7,2] => 1

[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => [1,4,3,7,5,6,2] => 0

[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => [1,4,3,7,5,6,2] => 0

[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => [1,4,3,7,5,6,2] => 0

[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => [1,4,3,7,5,6,2] => 0

[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => [1,4,3,7,5,6,2] => 0

[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => [1,4,3,7,5,6,2] => 0

[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => [1,4,3,7,5,6,2] => 0

[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => [1,4,3,7,5,6,2] => 0

[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => [1,4,3,7,5,6,2] => 0

[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,7,5,6] => [1,4,3,6,7,5,2] => 0

[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,7,5,6] => [1,4,3,6,7,5,2] => 0

[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,7,5,6] => [1,4,3,6,7,5,2] => 0

[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,7,5,6] => [1,4,3,6,7,5,2] => 0

[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,7,5,6] => [1,4,3,6,7,5,2] => 0

[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,7,5,6] => [1,4,3,6,7,5,2] => 0

[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,7,5,6] => [1,4,3,6,7,5,2] => 0

[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,7,5,6] => [1,4,3,6,7,5,2] => 0

[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,3,5,7,6] => [1,4,3,5,7,6,2] => 0

[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,3,5,7,6] => [1,4,3,5,7,6,2] => 0

[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,3,5,7,6] => [1,4,3,5,7,6,2] => 0

[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,4,3,5,6,7] => [1,4,3,5,6,7,2] => 1

[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,4,3,5,6,7] => [1,4,3,5,6,7,2] => 1

[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,4,3,5,6,7] => [1,4,3,5,6,7,2] => 1

[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => [1,4,3,7,5,6,2] => 0

[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => [1,4,3,7,5,6,2] => 0

[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => [1,4,3,7,5,6,2] => 0

[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [1,4,3,6,5,7,2] => 0

[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => [1,4,3,7,5,6,2] => 0

[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => [1,4,3,7,5,6,2] => 0

[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => [1,4,3,7,5,6,2] => 0

[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,7,5,6] => [1,4,3,6,7,5,2] => 0

[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,7,5,6] => [1,4,3,6,7,5,2] => 0

[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,7,5,6] => [1,4,3,6,7,5,2] => 0

[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,7,5,6] => [1,4,3,6,7,5,2] => 0

[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,7,5,6] => [1,4,3,6,7,5,2] => 0

[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,7,5,6] => [1,4,3,6,7,5,2] => 0

[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,7,5,6] => [1,4,3,6,7,5,2] => 0

[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,7,5,6] => [1,4,3,6,7,5,2] => 0

[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,3,5,7,6] => [1,4,3,5,7,6,2] => 0

[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,3,5,7,6] => [1,4,3,5,7,6,2] => 0

[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,3,5,7,6] => [1,4,3,5,7,6,2] => 0

[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,4,3,5,6,7] => [1,4,3,5,6,7,2] => 1

[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,4,3,5,6,7] => [1,4,3,5,6,7,2] => 1

[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,4,3,5,6,7] => [1,4,3,5,6,7,2] => 1

[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,5,3,6,4,7] => [1,4,6,3,5,7,2] => 0

[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,5,3,6,4,7] => [1,4,6,3,5,7,2] => 0

[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,5,3,6,4,7] => [1,4,6,3,5,7,2] => 0

[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,5,3,6,4,7] => [1,4,6,3,5,7,2] => 0

[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,5,3,6,4,7] => [1,4,6,3,5,7,2] => 0

[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,5,3,6,4,7] => [1,4,6,3,5,7,2] => 0

[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,5,3,6,4,7] => [1,4,6,3,5,7,2] => 0

[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,5,3,6,4,7] => [1,4,6,3,5,7,2] => 0

[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,5,3,6,4,7] => [1,4,6,3,5,7,2] => 0

[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,5,3,6,4,7] => [1,4,6,3,5,7,2] => 0

[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,5,3,6,4,7] => [1,4,6,3,5,7,2] => 0

[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,5,3,6,4,7] => [1,4,6,3,5,7,2] => 0

[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,5,3,6,4,7] => [1,4,6,3,5,7,2] => 0

[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,5,3,6,4,7] => [1,4,6,3,5,7,2] => 0

[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,5,3,6,4,7] => [1,4,6,3,5,7,2] => 0

[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,5,3,6,4,7] => [1,4,6,3,5,7,2] => 0

[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,5,3,6,4,7] => [1,4,6,3,5,7,2] => 0

[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,5,3,6,4,7] => [1,4,6,3,5,7,2] => 0

[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,5,3,6,4,7] => [1,4,6,3,5,7,2] => 0

[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,5,3,6,4,7] => [1,4,6,3,5,7,2] => 0

[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,5,3,6,4,7] => [1,4,6,3,5,7,2] => 0

[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,5,3,7,4,6] => [1,4,6,3,7,5,2] => 0

[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,5,3,7,4,6] => [1,4,6,3,7,5,2] => 0

[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,5,3,7,4,6] => [1,4,6,3,7,5,2] => 0

[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,5,3,7,4,6] => [1,4,6,3,7,5,2] => 0

[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,5,3,7,4,6] => [1,4,6,3,7,5,2] => 0

[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,5,3,7,4,6] => [1,4,6,3,7,5,2] => 0

[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,5,3,7,4,6] => [1,4,6,3,7,5,2] => 0

[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,5,3,7,4,6] => [1,4,6,3,7,5,2] => 0

[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,1,5,3,4,7,6] => [1,4,5,3,7,6,2] => 0

[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,1,5,3,4,7,6] => [1,4,5,3,7,6,2] => 0

[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,1,5,3,4,7,6] => [1,4,5,3,7,6,2] => 0

[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,3,5,4,7,6] => [1,3,5,4,7,6,2] => 0

[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,1,3,5,7,4,6] => [1,3,6,4,7,5,2] => 0

[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,5,3,4,6,7] => [1,4,5,3,6,7,2] => 0

[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,5,3,4,6,7] => [1,4,5,3,6,7,2] => 0

[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,5,3,4,6,7] => [1,4,5,3,6,7,2] => 0

[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,1,3,5,4,6,7] => [1,3,5,4,6,7,2] => 0

[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,1,3,5,6,4,7] => [1,3,6,4,5,7,2] => 0

[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,1,3,5,6,7,4] => [1,3,7,4,5,6,2] => 1

[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,1,6,3,4,7,5] => [1,4,5,7,3,6,2] => 0

[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,1,6,3,4,7,5] => [1,4,5,7,3,6,2] => 0

[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,1,6,3,4,7,5] => [1,4,5,7,3,6,2] => 0

[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,3,6,4,7,5] => [1,3,5,7,4,6,2] => 0

[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,1,3,6,7,4,5] => [1,3,6,7,4,5,2] => 0

[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,1,6,3,4,5,7] => [1,4,5,6,3,7,2] => 1

[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,1,6,3,4,5,7] => [1,4,5,6,3,7,2] => 1

[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,1,6,3,4,5,7] => [1,4,5,6,3,7,2] => 1

[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,1,3,6,4,5,7] => [1,3,5,6,4,7,2] => 0

[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,1,3,4,6,5,7] => [1,3,4,6,5,7,2] => 0

[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,1,3,4,6,7,5] => [1,3,4,7,5,6,2] => 0

[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,1,7,3,4,5,6] => [1,4,5,6,7,3,2] => 2

[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,1,7,3,4,5,6] => [1,4,5,6,7,3,2] => 2

[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,1,7,3,4,5,6] => [1,4,5,6,7,3,2] => 2

[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,1,3,7,4,5,6] => [1,3,5,6,7,4,2] => 1

[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,1,3,4,7,5,6] => [1,3,4,6,7,5,2] => 0

[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,1,3,4,5,7,6] => [1,3,4,5,7,6,2] => 1

[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7] => [1,3,4,5,6,7,2] => 3

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$F_{2} = 2$

$F_{3} = 5$

$F_{4} = 14$

$F_{5} = 41 + q$

$F_{6} = 125 + 6\ q + q^{2}$

Description

The number of two successive successions in a 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

to 321-avoiding permutation

Description

Sends a Dyck path to a 321-avoiding permutation.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.

Map

peeling map

Description

Send a Dyck path to its peeled Dyck path.