- FindStat

Identifier

Mp00124: Dyck paths —Adin-Bagno-Roichman transformation⟶ Dyck paths
Mp00031: Dyck paths —to 312-avoiding permutation⟶ Permutations
Mp00252: Permutations —restriction⟶ Permutations
St000062: Permutations ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 624 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [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] => 5

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

[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [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] => 5

[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [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] => 5

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

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

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

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

[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [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] => 5

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [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] => 5

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [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] => 5

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

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

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

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

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

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

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

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

[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [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] => 5

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

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

[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [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] => 5

[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [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] => 5

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

search for individual values

searching the database for the individual values of this statistic

/ search for generating function

searching the database for statistics with the same generating function

click to show known generating functions

$F_{2} = 2\ q$

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

$F_{4} = 4\ q + 8\ q^{2} + 2\ q^{3}$

$F_{5} = 5\ q + 20\ q^{2} + 15\ q^{3} + 2\ q^{4}$

$F_{6} = 6\ q + 40\ q^{2} + 60\ q^{3} + 24\ q^{4} + 2\ q^{5}$

$F_{7} = 7\ q + 70\ q^{2} + 175\ q^{3} + 140\ q^{4} + 35\ q^{5} + 2\ q^{6}$

Description

The length of the longest increasing subsequence of the permutation.

Map

Adin-Bagno-Roichman transformation

Description

The Adin-Bagno-Roichman transformation of a Dyck path.
This is a bijection preserving the number of up steps before each peak and sending the number of returns to the number of up steps after the last double up step.

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.