- FindStat

Identifier

Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00012: Binary trees —to Dyck path: up step, left tree, down step, right tree⟶ Dyck paths
St001253: Dyck paths ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 625 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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$F_{1} = 1$

$F_{2} = 2$

$F_{3} = 4 + q$

$F_{4} = 9 + 4\ q + q^{2}$

$F_{5} = 21 + 15\ q + 5\ q^{2} + q^{3}$

$F_{6} = 51 + 50\ q + 24\ q^{2} + 6\ q^{3} + q^{4}$

$F_{7} = 127 + 161\ q + 98\ q^{2} + 35\ q^{3} + 7\ q^{4} + q^{5}$

Description

The number of non-projective indecomposable reflexive modules in the corresponding Nakayama algebra.
For the first 196 values the statistic coincides also with the number of fixed points of

$\tau \Omega^2$ composed with its inverse, see theorem 5.8. in the reference for more details.
The number of Dyck paths of length n where the statistics returns zero seems to be 2^(n-1).

Map

to Dyck path: up step, left tree, down step, right tree

Description

Return the associated Dyck path, using the bijection 1L0R.
This is given recursively as follows:

a leaf is associated to the empty Dyck Word
a tree with children $l,r$ is associated with the Dyck path described by 1L0R where $L$ and $R$ are respectively the Dyck words associated with the trees $l$ and $r$ .

Map

to 312-avoiding permutation

Description

Return a 312-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.

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.