- FindStat

Identifier

Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00066: Permutations —inverse⟶ Permutations
St000141: Permutations ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 470 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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$F_{1} = 1$

$F_{2} = 1 + q$

$F_{3} = 1 + 2\ q + 2\ q^{2}$

$F_{4} = 1 + 3\ q + 5\ q^{2} + 5\ q^{3}$

$F_{5} = 1 + 4\ q + 9\ q^{2} + 14\ q^{3} + 14\ q^{4}$

$F_{6} = 1 + 5\ q + 14\ q^{2} + 28\ q^{3} + 42\ q^{4} + 42\ q^{5}$

Description

The maximum drop size of a permutation.
The maximum drop size of a permutation

$\pi$ of

$[n]=\{1,2,\ldots, n\}$ is defined to be the maximum value of

$i-\pi(i)$ .

Map

to 132-avoiding permutation

Description

Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].

Map

inverse

Description

Sends a permutation to its inverse.