- FindStat

Identifier

Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
St000203: Binary trees ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 629 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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$F_{1} = q$

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

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

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

$F_{5} = 5\ q^{2} + 9\ q^{3} + 12\ q^{4} + 16\ q^{5}$

$F_{6} = 14\ q^{2} + 24\ q^{3} + 30\ q^{4} + 32\ q^{5} + 32\ q^{6}$

$F_{7} = 42\ q^{2} + 70\ q^{3} + 85\ q^{4} + 88\ q^{5} + 80\ q^{6} + 64\ q^{7}$

Description

The number of external nodes of a binary tree.
That is, the number of nodes that can be reached from the root by only left steps or only right steps, plus

$1$ for the root node itself. A counting formula for the number of external node in all binary trees of size

$n$ can be found in [1].

Map

binary search tree: left to right

Description

Return the shape of the binary search tree of the permutation as a non labelled binary tree.

Map

cycle-as-one-line notation

Description

Return the permutation obtained by concatenating the cycles of a permutation, each written with minimal element first, sorted by minimal element.

Map

to non-crossing permutation

Description

Sends a Dyck path

$D$ with valley at positions

$\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation

$\pi$ having descents

$\{i_1,\ldots,i_k\}$ and whose inverse has descents

$\{j_1,\ldots,j_k\}$ .
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to

$n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..