- FindStat

Identifier

Mp00222: Dyck paths —peaks-to-valleys⟶ Dyck paths
Mp00031: Dyck paths —to 312-avoiding permutation⟶ Permutations
Mp00252: Permutations —restriction⟶ Permutations
St000672: Permutations ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 753 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 0

[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1] => 0

[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => [6,5,4,3,2,1,7] => 1

[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,5,4,3,2,1,7,8] => [6,5,4,3,2,1,7] => 1

[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,6,5,4,3,2,8,1] => [7,6,5,4,3,2,1] => 0

[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => [5,4,3,2,1,7,6] => 1

[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,4,3,2,1,7,6,8] => [5,4,3,2,1,7,6] => 1

[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,4,3,2,1,6,8,7] => [5,4,3,2,1,6,7] => 2

[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8] => [5,4,3,2,1,6,7] => 2

[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,4,3,2,1,7,8,6] => [5,4,3,2,1,7,6] => 1

[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [7,6,5,4,3,8,2,1] => [7,6,5,4,3,2,1] => 0

[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,3,2,1,5,6,8,7] => [4,3,2,1,5,6,7] => 3

[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8] => [4,3,2,1,5,6,7] => 3

[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,4,3,2,6,1,8,7] => [5,4,3,2,6,1,7] => 2

[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [5,4,3,2,6,1,7,8] => [5,4,3,2,6,1,7] => 2

[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [7,6,5,4,8,3,2,1] => [7,6,5,4,3,2,1] => 0

[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8] => [3,2,1,4,5,6,7] => 4

[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,1] => [4,3,2,5,6,7,1] => 3

[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [5,4,3,6,2,1,8,7] => [5,4,3,6,2,1,7] => 2

[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [7,6,5,8,4,3,2,1] => [7,6,5,4,3,2,1] => 0

[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => [2,1,7,6,5,4,3] => 1

[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,7,6,5,8,4,3] => [2,1,7,6,5,4,3] => 1

[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,7] => 5

[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7] => 5

[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,1,8] => [3,2,4,5,6,7,1] => 4

[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,1] => [3,2,4,5,6,7,1] => 4

[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [4,3,6,5,2,1,8,7] => [4,3,6,5,2,1,7] => 2

[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [7,6,8,5,4,3,2,1] => [7,6,5,4,3,2,1] => 0

[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => 1

[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,5,4,3,8,7,2] => [1,6,5,4,3,7,2] => 2

[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,7,6,5,8,4,3,2] => [1,7,6,5,4,3,2] => 1

[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7] => 5

[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7,6,8,5,4,3,2] => [1,7,6,5,4,3,2] => 1

[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,7,6] => [1,2,3,4,5,7,6] => 5

[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => [1,2,3,4,5,7,6] => 5

[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,7] => 6

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7] => 6

[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,7,8,6] => [1,2,3,4,5,7,6] => 5

[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,4,8,7,6,5,3,2] => [1,4,7,6,5,3,2] => 2

[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,4,7,8,6,5,3,2] => [1,4,7,6,5,3,2] => 2

[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,5,8,7,6,4,3,2] => [1,5,7,6,4,3,2] => 2

[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,5,6,7,8,4,3,2] => [1,5,6,7,4,3,2] => 3

[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,6,8,7,5,4,3,2] => [1,6,7,5,4,3,2] => 2

[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,6,7,8,5,4,3,2] => [1,6,7,5,4,3,2] => 2

[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,7,8,6,5,4,3,2] => [1,7,6,5,4,3,2] => 1

[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,8,7,6] => [2,3,4,1,5,7,6] => 4

[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,4,1,5,7,6,8] => [2,3,4,1,5,7,6] => 4

[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5,6,8,7] => [2,3,4,1,5,6,7] => 5

[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8] => [2,3,4,1,5,6,7] => 5

[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,4,1,5,7,8,6] => [2,3,4,1,5,7,6] => 4

[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,8,7,6] => [2,3,4,5,1,7,6] => 4

[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => [2,3,4,5,1,6,7] => 5

[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => [2,3,4,5,6,1,7] => 5

[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => [2,3,4,5,6,1,7] => 5

[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,8,7,1] => [2,3,4,5,6,7,1] => 5

[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => [2,3,4,5,6,7,1] => 5

[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => [2,3,4,5,6,7,1] => 5

[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [3,6,5,4,2,1,8,7] => [3,6,5,4,2,1,7] => 2

[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,8,1] => [3,4,2,5,6,7,1] => 4

[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,5,2,6,7,8,1] => [3,4,5,2,6,7,1] => 4

[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [4,5,3,6,2,1,8,7] => [4,5,3,6,2,1,7] => 3

[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [4,5,6,3,2,1,8,7] => [4,5,6,3,2,1,7] => 3

[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [5,6,4,3,2,1,8,7] => [5,6,4,3,2,1,7] => 2

[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [7,8,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 0

[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [8,7,9,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0

[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [9,8,10,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 0

[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,7,9,8,6,5,4,3,2] => [1,7,8,6,5,4,3,2] => 2

[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [7,6,8,5,4,3,2,1,9] => [7,6,8,5,4,3,2,1] => 1

[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,8,7,9,6,5,4,3,2] => [1,8,7,6,5,4,3,2] => 1

[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [8,7,6,9,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0

[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [9,8,7,10,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 0

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8] => 7

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,8,9,7] => [1,2,3,4,5,6,8,7] => 6

[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,4] => [1,2,3,5,6,7,8,4] => 6

[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,8,9,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2] => 1

[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9] => [2,3,4,5,6,7,1,8] => 6

[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,1,9] => [2,3,4,5,6,7,8,1] => 6

[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,1] => [2,3,4,5,6,7,8,1] => 6

[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,8,9,1] => [3,4,2,5,6,7,8,1] => 5

[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [8,9,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [9,8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,7,6,5,4,3,2,1,9] => [8,7,6,5,4,3,2,1] => 0

[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9] => [7,6,5,4,3,2,1,8] => 1

[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9] => [6,5,4,3,2,1,7,8] => 2

[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9] => [5,4,3,2,1,6,7,8] => 3

[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9] => [4,3,2,1,5,6,7,8] => 4

[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9] => [3,2,1,4,5,6,7,8] => 5

[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8] => 6

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [10,9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 0

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,8,7,6,5,4,3,2,1,10] => [9,8,7,6,5,4,3,2,1] => 0

[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,7,6,5,4,3,2,9,1] => [8,7,6,5,4,3,2,1] => 0

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [8,7,6,5,4,3,2,1,9,10] => [8,7,6,5,4,3,2,1,9] => 1

[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9,10] => [7,6,5,4,3,2,1,8,9] => 2

[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9,10] => [6,5,4,3,2,1,7,8,9] => 3

[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9,10] => [5,4,3,2,1,6,7,8,9] => 4

[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9,10] => [4,3,2,1,5,6,7,8,9] => 5

[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9,10] => [3,2,1,4,5,6,7,8,9] => 6

[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9] => 7

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9] => 8

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10,9,8,7,6,5,4,3,2,1,11] => [10,9,8,7,6,5,4,3,2,1] => 0

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,8,7,6,5,4,3,2,10,1] => [9,8,7,6,5,4,3,2,1] => 0

[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [8,7,6,5,4,3,9,2,1] => [8,7,6,5,4,3,2,1] => 0

[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10,11] => [2,1,3,4,5,6,7,8,9,10] => 8

[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [9,8,7,6,5,4,3,10,2,1] => [9,8,7,6,5,4,3,2,1] => 0

[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [8,7,6,5,4,9,3,2,1] => [8,7,6,5,4,3,2,1] => 0

[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [9,8,7,6,5,4,10,3,2,1] => [9,8,7,6,5,4,3,2,1] => 0

[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,1] => [3,2,4,5,6,7,8,1] => 5

[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [8,7,6,5,9,4,3,2,1] => [8,7,6,5,4,3,2,1] => 0

[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [9,8,7,6,5,10,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 0

[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,10,1] => [3,2,4,5,6,7,8,9,1] => 6

[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,9,1,10] => [2,3,4,5,6,7,8,9,1] => 7

[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,9] => [2,1,4,3,6,5,8,7] => 3

[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,8,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2] => 1

[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => [1,3,2,5,4,7,6,8] => 4

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,7,6,5,4,3,2,1,10,9] => [8,7,6,5,4,3,2,1,9] => 1

[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [9,8,7,6,10,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 0

[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,9,8,7,6,5,4,3,2] => [1,9,8,7,6,5,4,3,2] => 1

[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [9,10,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 0

[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,9,8,7] => [1,2,3,4,5,6,8,7] => 6

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,8] => 7

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,9] => 8

[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,10,9,8,7,6,5,4,3,2] => [1,10,9,8,7,6,5,4,3,2] => 1

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,7,9,10,8] => [1,2,3,4,5,6,7,9,8] => 7

[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,9,10,8,7,6,5,4,3,2] => [1,9,8,7,6,5,4,3,2] => 1

[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,1] => [2,3,4,5,6,7,8,9,1] => 7

[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => [2,3,4,5,6,7,8,9,10,1] => 8

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,9,11,10] => [1,2,3,4,5,6,7,8,9,10] => 9

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0] => [10,9,8,7,6,5,4,3,2,1,12,11] => [10,9,8,7,6,5,4,3,2,1,11] => 1

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$F_{1} = 1$

$F_{2} = 2$

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

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

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

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

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

Description

The number of minimal elements in Bruhat order not less than the permutation.
The minimal elements in question are biGrassmannian, that is

$1\dots r\ \ a+1\dots b\ \ r+1\dots a\ \ b+1\dots$
for some

$(r,a,b)$ .
This is also the size of Fulton's essential set of the reverse permutation, according to [ex.4.7, 2].

Map

peaks-to-valleys

Description

Return the path that has a valley wherever the original path has a peak of height at least one.
More precisely, the height of a valley in the image is the height of the corresponding peak minus

$2$ .
This is also (the inverse of) rowmotion on Dyck paths regarded as order ideals in the triangular poset.

Map

to 312-avoiding permutation

Description

Sends a Dyck path to the 312-avoiding permutation according to Bandlow-Killpatrick.
This map is defined in [1] and sends the area (St000012The area of a Dyck path.) to the inversion number (St000018The number of inversions of a permutation.).

Map

restriction

Description

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