- FindStat

Identifier

Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00020: Binary trees —to Tamari-corresponding Dyck path⟶ Dyck paths
St001418: Dyck paths ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 624 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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$F_{2} = 1 + q$

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

$F_{4} = 1 + 7\ q + 5\ q^{2} + q^{3}$

$F_{5} = 1 + 15\ q + 18\ q^{2} + 7\ q^{3} + q^{4}$

$F_{6} = 1 + 31\ q + 56\ q^{2} + 34\ q^{3} + 9\ q^{4} + q^{5}$

$F_{7} = 1 + 63\ q + 160\ q^{2} + 138\ q^{3} + 55\ q^{4} + 11\ q^{5} + q^{6}$

Description

Half of the global dimension of the stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path.
The stable Auslander algebra is by definition the stable endomorphism ring of the direct sum of all indecomposable modules.

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

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..

Map

to Tamari-corresponding Dyck path

Description

Return the Dyck path associated with a binary tree in consistency with the Tamari order on Dyck words and binary trees.
The bijection is defined recursively as follows:

a leaf is associated with an empty Dyck path,
a tree with children $l,r$ is associated with the Dyck word $T(l) 1 T(r) 0$ where $T(l)$ and $T(r)$ are the images of this bijection to $l$ and $r$ .