- FindStat

Identifier

Mp00132: Dyck paths —switch returns and last double rise⟶ Dyck paths
Mp00129: Dyck paths —to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶ Permutations
Mp00252: Permutations —restriction⟶ Permutations
St000155: Permutations ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 624 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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$F_{2} = 2$

$F_{3} = 3 + 2\ q$

$F_{4} = 4 + 8\ q + 2\ q^{2}$

$F_{5} = 5 + 20\ q + 15\ q^{2} + 2\ q^{3}$

$F_{6} = 6 + 40\ q + 60\ q^{2} + 24\ q^{3} + 2\ q^{4}$

$F_{7} = 7 + 70\ q + 175\ q^{2} + 140\ q^{3} + 35\ q^{4} + 2\ q^{5}$

Description

The number of exceedances (also excedences) of a permutation.
This is defined as

$exc(\sigma) = \#\{ i : \sigma(i) > i \}$ .
It is known that the number of exceedances is equidistributed with the number of descents, and that the bistatistic

$(exc,den)$ is Euler-Mahonian. Here,

$den$ is the Denert index of a permutation, see St000156The Denert index of a permutation..

Map

to 321-avoiding permutation (Billey-Jockusch-Stanley)

Description

The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.

Map

switch returns and last double rise

Description

An alternative to the Adin-Bagno-Roichman transformation of a Dyck path.
This is a bijection preserving the number of up steps before each peak and exchanging the number of components with the position of the last double rise.

Map

restriction

Description

The permutation obtained by removing the largest letter.
This map is undefined for the empty permutation.