Identifier
Mp00014:
Binary trees
—to 132-avoiding permutation⟶
Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00020: Binary trees —to Tamari-corresponding Dyck path⟶ Dyck paths
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00020: Binary trees —to Tamari-corresponding Dyck path⟶ Dyck paths
Images
[.,.] => [1] => [.,.] => [1,0]
[.,[.,.]] => [2,1] => [[.,.],.] => [1,0,1,0]
[[.,.],.] => [1,2] => [.,[.,.]] => [1,1,0,0]
[.,[.,[.,.]]] => [3,2,1] => [[[.,.],.],.] => [1,0,1,0,1,0]
[.,[[.,.],.]] => [2,3,1] => [[.,[.,.]],.] => [1,1,0,0,1,0]
[[.,.],[.,.]] => [3,1,2] => [[.,.],[.,.]] => [1,0,1,1,0,0]
[[.,[.,.]],.] => [2,1,3] => [[.,.],[.,.]] => [1,0,1,1,0,0]
[[[.,.],.],.] => [1,2,3] => [.,[.,[.,.]]] => [1,1,1,0,0,0]
[.,[.,[.,[.,.]]]] => [4,3,2,1] => [[[[.,.],.],.],.] => [1,0,1,0,1,0,1,0]
[.,[.,[[.,.],.]]] => [3,4,2,1] => [[[.,[.,.]],.],.] => [1,1,0,0,1,0,1,0]
[.,[[.,.],[.,.]]] => [4,2,3,1] => [[[.,.],[.,.]],.] => [1,0,1,1,0,0,1,0]
[.,[[.,[.,.]],.]] => [3,2,4,1] => [[[.,.],[.,.]],.] => [1,0,1,1,0,0,1,0]
[.,[[[.,.],.],.]] => [2,3,4,1] => [[.,[.,[.,.]]],.] => [1,1,1,0,0,0,1,0]
[[.,.],[.,[.,.]]] => [4,3,1,2] => [[[.,.],.],[.,.]] => [1,0,1,0,1,1,0,0]
[[.,.],[[.,.],.]] => [3,4,1,2] => [[.,[.,.]],[.,.]] => [1,1,0,0,1,1,0,0]
[[.,[.,.]],[.,.]] => [4,2,1,3] => [[[.,.],.],[.,.]] => [1,0,1,0,1,1,0,0]
[[[.,.],.],[.,.]] => [4,1,2,3] => [[.,.],[.,[.,.]]] => [1,0,1,1,1,0,0,0]
[[.,[.,[.,.]]],.] => [3,2,1,4] => [[[.,.],.],[.,.]] => [1,0,1,0,1,1,0,0]
[[.,[[.,.],.]],.] => [2,3,1,4] => [[.,[.,.]],[.,.]] => [1,1,0,0,1,1,0,0]
[[[.,.],[.,.]],.] => [3,1,2,4] => [[.,.],[.,[.,.]]] => [1,0,1,1,1,0,0,0]
[[[.,[.,.]],.],.] => [2,1,3,4] => [[.,.],[.,[.,.]]] => [1,0,1,1,1,0,0,0]
[[[[.,.],.],.],.] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0]
[.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => [[[[[.,.],.],.],.],.] => [1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => [[[[.,[.,.]],.],.],.] => [1,1,0,0,1,0,1,0,1,0]
[.,[.,[[.,.],[.,.]]]] => [5,3,4,2,1] => [[[[.,.],[.,.]],.],.] => [1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => [[[[.,.],[.,.]],.],.] => [1,0,1,1,0,0,1,0,1,0]
[.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => [[[.,[.,[.,.]]],.],.] => [1,1,1,0,0,0,1,0,1,0]
[.,[[.,.],[.,[.,.]]]] => [5,4,2,3,1] => [[[[.,.],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[[.,.],.]]] => [4,5,2,3,1] => [[[.,[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,0]
[.,[[.,[.,.]],[.,.]]] => [5,3,2,4,1] => [[[[.,.],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0]
[.,[[[.,.],.],[.,.]]] => [5,2,3,4,1] => [[[.,.],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,0]
[.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => [[[[.,.],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0]
[.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => [[[.,[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,0]
[.,[[[.,.],[.,.]],.]] => [4,2,3,5,1] => [[[.,.],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,0]
[.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => [[[.,.],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,0]
[.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => [[.,[.,[.,[.,.]]]],.] => [1,1,1,1,0,0,0,0,1,0]
[[.,.],[.,[.,[.,.]]]] => [5,4,3,1,2] => [[[[.,.],.],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[[.,.],.]]] => [4,5,3,1,2] => [[[.,[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0]
[[.,.],[[.,.],[.,.]]] => [5,3,4,1,2] => [[[.,.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[.,.]],.]] => [4,3,5,1,2] => [[[.,.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0]
[[.,.],[[[.,.],.],.]] => [3,4,5,1,2] => [[.,[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,0,0]
[[.,[.,.]],[.,[.,.]]] => [5,4,2,1,3] => [[[[.,.],.],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0]
[[.,[.,.]],[[.,.],.]] => [4,5,2,1,3] => [[[.,[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0]
[[[.,.],.],[.,[.,.]]] => [5,4,1,2,3] => [[[.,.],.],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[[.,.],.]] => [4,5,1,2,3] => [[.,[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0]
[[.,[.,[.,.]]],[.,.]] => [5,3,2,1,4] => [[[[.,.],.],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0]
[[.,[[.,.],.]],[.,.]] => [5,2,3,1,4] => [[[.,.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0]
[[[.,.],[.,.]],[.,.]] => [5,3,1,2,4] => [[[.,.],.],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[.,.]] => [5,2,1,3,4] => [[[.,.],.],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0]
[[[[.,.],.],.],[.,.]] => [5,1,2,3,4] => [[.,.],[.,[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,0]
[[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => [[[[.,.],.],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0]
[[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => [[[.,[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0]
[[.,[[.,.],[.,.]]],.] => [4,2,3,1,5] => [[[.,.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => [[[.,.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0]
[[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => [[.,[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,0,0]
[[[.,.],[.,[.,.]]],.] => [4,3,1,2,5] => [[[.,.],.],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0]
[[[.,.],[[.,.],.]],.] => [3,4,1,2,5] => [[.,[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0]
[[[.,[.,.]],[.,.]],.] => [4,2,1,3,5] => [[[.,.],.],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0]
[[[[.,.],.],[.,.]],.] => [4,1,2,3,5] => [[.,.],[.,[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,0]
[[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => [[[.,.],.],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => [[.,[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0]
[[[[.,.],[.,.]],.],.] => [3,1,2,4,5] => [[.,.],[.,[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,0]
[[[[[.,.],.],.],.],.] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => [1,1,1,1,1,0,0,0,0,0]
[.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],.] => [1,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => [[[[[.,[.,.]],.],.],.],.] => [1,1,0,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[[.,.],[.,.]]]]] => [6,4,5,3,2,1] => [[[[[.,.],[.,.]],.],.],.] => [1,0,1,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => [[[[[.,.],[.,.]],.],.],.] => [1,0,1,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => [[[[.,[.,[.,.]]],.],.],.] => [1,1,1,0,0,0,1,0,1,0,1,0]
[.,[.,[[.,.],[.,[.,.]]]]] => [6,5,3,4,2,1] => [[[[[.,.],.],[.,.]],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,.],[[.,.],.]]]] => [5,6,3,4,2,1] => [[[[.,[.,.]],[.,.]],.],.] => [1,1,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[.,.]],[.,.]]]] => [6,4,3,5,2,1] => [[[[[.,.],.],[.,.]],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[[.,.],.],[.,.]]]] => [6,3,4,5,2,1] => [[[[.,.],[.,[.,.]]],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => [[[[[.,.],.],[.,.]],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => [[[[.,[.,.]],[.,.]],.],.] => [1,1,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[[.,.],[.,.]],.]]] => [5,3,4,6,2,1] => [[[[.,.],[.,[.,.]]],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => [[[[.,.],[.,[.,.]]],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => [[[.,[.,[.,[.,.]]]],.],.] => [1,1,1,1,0,0,0,0,1,0,1,0]
[.,[[.,.],[.,[.,[.,.]]]]] => [6,5,4,2,3,1] => [[[[[.,.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[.,[[.,.],.]]]] => [5,6,4,2,3,1] => [[[[.,[.,.]],.],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[[.,.],[.,.]]]] => [6,4,5,2,3,1] => [[[[.,.],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[.,[.,.]],.]]] => [5,4,6,2,3,1] => [[[[.,.],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[[.,.],.],.]]] => [4,5,6,2,3,1] => [[[.,[.,[.,.]]],[.,.]],.] => [1,1,1,0,0,0,1,1,0,0,1,0]
[.,[[.,[.,.]],[.,[.,.]]]] => [6,5,3,2,4,1] => [[[[[.,.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,.]],[[.,.],.]]] => [5,6,3,2,4,1] => [[[[.,[.,.]],.],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,0]
[.,[[[.,.],.],[.,[.,.]]]] => [6,5,2,3,4,1] => [[[[.,.],.],[.,[.,.]]],.] => [1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[[.,.],.]]] => [5,6,2,3,4,1] => [[[.,[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[.,[.,[.,.]]],[.,.]]] => [6,4,3,2,5,1] => [[[[[.,.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[[.,.],.]],[.,.]]] => [6,3,4,2,5,1] => [[[[.,.],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[[.,.],[.,.]],[.,.]]] => [6,4,2,3,5,1] => [[[[.,.],.],[.,[.,.]]],.] => [1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,[.,.]],.],[.,.]]] => [6,3,2,4,5,1] => [[[[.,.],.],[.,[.,.]]],.] => [1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[[.,.],.],.],[.,.]]] => [6,2,3,4,5,1] => [[[.,.],[.,[.,[.,.]]]],.] => [1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => [[[[[.,.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => [[[[.,[.,.]],.],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,0]
[.,[[.,[[.,.],[.,.]]],.]] => [5,3,4,2,6,1] => [[[[.,.],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => [[[[.,.],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => [[[.,[.,[.,.]]],[.,.]],.] => [1,1,1,0,0,0,1,1,0,0,1,0]
[.,[[[.,.],[.,[.,.]]],.]] => [5,4,2,3,6,1] => [[[[.,.],.],[.,[.,.]]],.] => [1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],[[.,.],.]],.]] => [4,5,2,3,6,1] => [[[.,[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,[.,.]],[.,.]],.]] => [5,3,2,4,6,1] => [[[[.,.],.],[.,[.,.]]],.] => [1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[[.,.],.],[.,.]],.]] => [5,2,3,4,6,1] => [[[.,.],[.,[.,[.,.]]]],.] => [1,0,1,1,1,1,0,0,0,0,1,0]
>>> Load all 1709 entries. <<<
[.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => [[[[.,.],.],[.,[.,.]]],.] => [1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => [[[.,[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[[.,.],[.,.]],.],.]] => [4,2,3,5,6,1] => [[[.,.],[.,[.,[.,.]]]],.] => [1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => [[[.,.],[.,[.,[.,.]]]],.] => [1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.] => [1,1,1,1,1,0,0,0,0,0,1,0]
[[.,.],[.,[.,[.,[.,.]]]]] => [6,5,4,3,1,2] => [[[[[.,.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[[.,.],.]]]] => [5,6,4,3,1,2] => [[[[.,[.,.]],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[[.,.],[.,.]]]] => [6,4,5,3,1,2] => [[[[.,.],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[.,[.,.]],.]]] => [5,4,6,3,1,2] => [[[[.,.],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[.,.],.],.]]] => [4,5,6,3,1,2] => [[[.,[.,[.,.]]],.],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0]
[[.,.],[[.,.],[.,[.,.]]]] => [6,5,3,4,1,2] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[[.,.],.]]] => [5,6,3,4,1,2] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[.,.]],[.,.]]] => [6,4,3,5,1,2] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[[.,.],.],[.,.]]] => [6,3,4,5,1,2] => [[[.,.],[.,[.,.]]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[.,[.,[.,.]]],.]] => [5,4,3,6,1,2] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[[.,.],.]],.]] => [4,5,3,6,1,2] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[[.,.],[.,.]],.]] => [5,3,4,6,1,2] => [[[.,.],[.,[.,.]]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,[.,.]],.],.]] => [4,3,5,6,1,2] => [[[.,.],[.,[.,.]]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[[.,.],.],.],.]] => [3,4,5,6,1,2] => [[.,[.,[.,[.,.]]]],[.,.]] => [1,1,1,1,0,0,0,0,1,1,0,0]
[[.,[.,.]],[.,[.,[.,.]]]] => [6,5,4,2,1,3] => [[[[[.,.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,.]],[.,[[.,.],.]]] => [5,6,4,2,1,3] => [[[[.,[.,.]],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,.]],[[.,.],[.,.]]] => [6,4,5,2,1,3] => [[[[.,.],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[.,[.,.]],.]] => [5,4,6,2,1,3] => [[[[.,.],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[[.,.],.],.]] => [4,5,6,2,1,3] => [[[.,[.,[.,.]]],.],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0]
[[[.,.],.],[.,[.,[.,.]]]] => [6,5,4,1,2,3] => [[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[[.,.],.]]] => [5,6,4,1,2,3] => [[[.,[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,[.,.]],.]] => [5,4,6,1,2,3] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[.,.],.],.]] => [4,5,6,1,2,3] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,0]
[[.,[.,[.,.]]],[.,[.,.]]] => [6,5,3,2,1,4] => [[[[[.,.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,.]]],[[.,.],.]] => [5,6,3,2,1,4] => [[[[.,[.,.]],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[[.,.],.]],[.,[.,.]]] => [6,5,2,3,1,4] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],.]],[[.,.],.]] => [5,6,2,3,1,4] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0]
[[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => [[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => [[[.,[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[.,[.,.]]] => [6,5,2,1,3,4] => [[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[[.,.],.]] => [5,6,2,1,3,4] => [[[.,[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,0]
[[[[.,.],.],.],[.,[.,.]]] => [6,5,1,2,3,4] => [[[.,.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[[.,.],.]] => [5,6,1,2,3,4] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,0,0]
[[.,[.,[.,[.,.]]]],[.,.]] => [6,4,3,2,1,5] => [[[[[.,.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[[.,.],.]]],[.,.]] => [6,3,4,2,1,5] => [[[[.,.],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[[.,.],[.,.]]],[.,.]] => [6,4,2,3,1,5] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[.,.]],.]],[.,.]] => [6,3,2,4,1,5] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[[.,.],.],.]],[.,.]] => [6,2,3,4,1,5] => [[[.,.],[.,[.,.]]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0]
[[[.,.],[.,[.,.]]],[.,.]] => [6,4,3,1,2,5] => [[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],[[.,.],.]],[.,.]] => [6,3,4,1,2,5] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[.,.]],[.,.]],[.,.]] => [6,4,2,1,3,5] => [[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0]
[[[[.,.],.],[.,.]],[.,.]] => [6,4,1,2,3,5] => [[[.,.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0]
[[[.,[.,[.,.]]],.],[.,.]] => [6,3,2,1,4,5] => [[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],.],[.,.]] => [6,2,3,1,4,5] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0]
[[[[.,.],[.,.]],.],[.,.]] => [6,3,1,2,4,5] => [[[.,.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],.],.],[.,.]] => [6,2,1,3,4,5] => [[[.,.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0]
[[[[[.,.],.],.],.],[.,.]] => [6,1,2,3,4,5] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => [[[[[.,.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => [[[[.,[.,.]],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[[.,.],[.,.]]]],.] => [5,3,4,2,1,6] => [[[[.,.],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => [[[[.,.],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => [[[.,[.,[.,.]]],.],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0]
[[.,[[.,.],[.,[.,.]]]],.] => [5,4,2,3,1,6] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[[.,.],.]]],.] => [4,5,2,3,1,6] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,[.,.]],[.,.]]],.] => [5,3,2,4,1,6] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[[.,.],.],[.,.]]],.] => [5,2,3,4,1,6] => [[[.,.],[.,[.,.]]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => [[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[[.,.],[.,.]],.]],.] => [4,2,3,5,1,6] => [[[.,.],[.,[.,.]]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => [[[.,.],[.,[.,.]]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => [[.,[.,[.,[.,.]]]],[.,.]] => [1,1,1,1,0,0,0,0,1,1,0,0]
[[[.,.],[.,[.,[.,.]]]],.] => [5,4,3,1,2,6] => [[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,[[.,.],.]]],.] => [4,5,3,1,2,6] => [[[.,[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,.],[[.,.],[.,.]]],.] => [5,3,4,1,2,6] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],[[.,[.,.]],.]],.] => [4,3,5,1,2,6] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],[[[.,.],.],.]],.] => [3,4,5,1,2,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,[.,.]],[.,[.,.]]],.] => [5,4,2,1,3,6] => [[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],[[.,.],.]],.] => [4,5,2,1,3,6] => [[[.,[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,0]
[[[[.,.],.],[.,[.,.]]],.] => [5,4,1,2,3,6] => [[[.,.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[[.,.],.]],.] => [4,5,1,2,3,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,0,0]
[[[.,[.,[.,.]]],[.,.]],.] => [5,3,2,1,4,6] => [[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],[.,.]],.] => [5,2,3,1,4,6] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0]
[[[[.,.],[.,.]],[.,.]],.] => [5,3,1,2,4,6] => [[[.,.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],.],[.,.]],.] => [5,2,1,3,4,6] => [[[.,.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0]
[[[[[.,.],.],.],[.,.]],.] => [5,1,2,3,4,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,0,1,1,1,1,1,0,0,0,0,0]
[[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => [[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => [[[.,[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[[.,.],[.,.]]],.],.] => [4,2,3,1,5,6] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => [[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,0]
[[[[.,.],[.,[.,.]]],.],.] => [4,3,1,2,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],[[.,.],.]],.],.] => [3,4,1,2,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],[.,.]],.],.] => [4,2,1,3,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0]
[[[[[.,.],.],[.,.]],.],.] => [4,1,2,3,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,0,1,1,1,1,1,0,0,0,0,0]
[[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,0,0]
[[[[[.,.],[.,.]],.],.],.] => [3,1,2,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,1,1,1,0,0,0,0,0,0]
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],.] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => [6,7,5,4,3,2,1] => [[[[[[.,[.,.]],.],.],.],.],.] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => [7,5,6,4,3,2,1] => [[[[[[.,.],[.,.]],.],.],.],.] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => [6,5,7,4,3,2,1] => [[[[[[.,.],[.,.]],.],.],.],.] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[[[.,.],.],.]]]]] => [5,6,7,4,3,2,1] => [[[[[.,[.,[.,.]]],.],.],.],.] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => [7,6,4,5,3,2,1] => [[[[[[.,.],.],[.,.]],.],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[.,.],[[.,.],.]]]]] => [6,7,4,5,3,2,1] => [[[[[.,[.,.]],[.,.]],.],.],.] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[.,[.,.]],[.,.]]]]] => [7,5,4,6,3,2,1] => [[[[[[.,.],.],[.,.]],.],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[.,.],.],[.,.]]]]] => [7,4,5,6,3,2,1] => [[[[[.,.],[.,[.,.]]],.],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => [6,5,4,7,3,2,1] => [[[[[[.,.],.],[.,.]],.],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[.,[[.,.],.]],.]]]] => [5,6,4,7,3,2,1] => [[[[[.,[.,.]],[.,.]],.],.],.] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[.,.],[.,.]],.]]]] => [6,4,5,7,3,2,1] => [[[[[.,.],[.,[.,.]]],.],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[.,[.,.]],.],.]]]] => [5,4,6,7,3,2,1] => [[[[[.,.],[.,[.,.]]],.],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[[.,.],.],.],.]]]] => [4,5,6,7,3,2,1] => [[[[.,[.,[.,[.,.]]]],.],.],.] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => [7,6,5,3,4,2,1] => [[[[[[.,.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,.],[.,[[.,.],.]]]]] => [6,7,5,3,4,2,1] => [[[[[.,[.,.]],.],[.,.]],.],.] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,.],[[.,.],[.,.]]]]] => [7,5,6,3,4,2,1] => [[[[[.,.],[.,.]],[.,.]],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,.],[[.,[.,.]],.]]]] => [6,5,7,3,4,2,1] => [[[[[.,.],[.,.]],[.,.]],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,.],[[[.,.],.],.]]]] => [5,6,7,3,4,2,1] => [[[[.,[.,[.,.]]],[.,.]],.],.] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => [7,6,4,3,5,2,1] => [[[[[[.,.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[.,.]],[[.,.],.]]]] => [6,7,4,3,5,2,1] => [[[[[.,[.,.]],.],[.,.]],.],.] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[[.,.],.],[.,[.,.]]]]] => [7,6,3,4,5,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[[.,.],.],[[.,.],.]]]] => [6,7,3,4,5,2,1] => [[[[.,[.,.]],[.,[.,.]]],.],.] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[.,[.,[.,.]]],[.,.]]]] => [7,5,4,3,6,2,1] => [[[[[[.,.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[[.,.],.]],[.,.]]]] => [7,4,5,3,6,2,1] => [[[[[.,.],[.,.]],[.,.]],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[[.,.],[.,.]],[.,.]]]] => [7,5,3,4,6,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[[.,[.,.]],.],[.,.]]]] => [7,4,3,5,6,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[[[.,.],.],.],[.,.]]]] => [7,3,4,5,6,2,1] => [[[[.,.],[.,[.,[.,.]]]],.],.] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => [6,5,4,3,7,2,1] => [[[[[[.,.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[.,[[.,.],.]]],.]]] => [5,6,4,3,7,2,1] => [[[[[.,[.,.]],.],[.,.]],.],.] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[[.,.],[.,.]]],.]]] => [6,4,5,3,7,2,1] => [[[[[.,.],[.,.]],[.,.]],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[[.,[.,.]],.]],.]]] => [5,4,6,3,7,2,1] => [[[[[.,.],[.,.]],[.,.]],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[[[.,.],.],.]],.]]] => [4,5,6,3,7,2,1] => [[[[.,[.,[.,.]]],[.,.]],.],.] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[[.,.],[.,[.,.]]],.]]] => [6,5,3,4,7,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[[.,.],[[.,.],.]],.]]] => [5,6,3,4,7,2,1] => [[[[.,[.,.]],[.,[.,.]]],.],.] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[[.,[.,.]],[.,.]],.]]] => [6,4,3,5,7,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[[[.,.],.],[.,.]],.]]] => [6,3,4,5,7,2,1] => [[[[.,.],[.,[.,[.,.]]]],.],.] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[.,[.,[[[.,[.,[.,.]]],.],.]]] => [5,4,3,6,7,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[[.,[[.,.],.]],.],.]]] => [4,5,3,6,7,2,1] => [[[[.,[.,.]],[.,[.,.]]],.],.] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[[[.,.],[.,.]],.],.]]] => [5,3,4,6,7,2,1] => [[[[.,.],[.,[.,[.,.]]]],.],.] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[.,[.,[[[[.,[.,.]],.],.],.]]] => [4,3,5,6,7,2,1] => [[[[.,.],[.,[.,[.,.]]]],.],.] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[.,[.,[[[[[.,.],.],.],.],.]]] => [3,4,5,6,7,2,1] => [[[.,[.,[.,[.,[.,.]]]]],.],.] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => [7,6,5,4,2,3,1] => [[[[[[.,.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[.,[.,[[.,.],.]]]]] => [6,7,5,4,2,3,1] => [[[[[.,[.,.]],.],.],[.,.]],.] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[.,[[.,.],[.,.]]]]] => [7,5,6,4,2,3,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[.,[[.,[.,.]],.]]]] => [6,5,7,4,2,3,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[.,[[[.,.],.],.]]]] => [5,6,7,4,2,3,1] => [[[[.,[.,[.,.]]],.],[.,.]],.] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[[.,.],[.,[.,.]]]]] => [7,6,4,5,2,3,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[.,.],[[.,.],.]]]] => [6,7,4,5,2,3,1] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[.,[.,.]],[.,.]]]] => [7,5,4,6,2,3,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[[.,.],.],[.,.]]]] => [7,4,5,6,2,3,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[.,[[.,.],[[.,[.,[.,.]]],.]]] => [6,5,4,7,2,3,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[.,[[.,.],.]],.]]] => [5,6,4,7,2,3,1] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[[.,.],[.,.]],.]]] => [6,4,5,7,2,3,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[.,[[.,.],[[[.,[.,.]],.],.]]] => [5,4,6,7,2,3,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[.,[[.,.],[[[[.,.],.],.],.]]] => [4,5,6,7,2,3,1] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[.,[[.,[.,.]],[.,[.,[.,.]]]]] => [7,6,5,3,2,4,1] => [[[[[[.,.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,.]],[.,[[.,.],.]]]] => [6,7,5,3,2,4,1] => [[[[[.,[.,.]],.],.],[.,.]],.] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,.]],[[.,.],[.,.]]]] => [7,5,6,3,2,4,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,.]],[[.,[.,.]],.]]] => [6,5,7,3,2,4,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,.]],[[[.,.],.],.]]] => [5,6,7,3,2,4,1] => [[[[.,[.,[.,.]]],.],[.,.]],.] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[.,[[[.,.],.],[.,[.,[.,.]]]]] => [7,6,5,2,3,4,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[.,[[.,.],.]]]] => [6,7,5,2,3,4,1] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[[.,.],[.,.]]]] => [7,5,6,2,3,4,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[[.,[.,.]],.]]] => [6,5,7,2,3,4,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[[[.,.],.],.]]] => [5,6,7,2,3,4,1] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[.,[[.,[.,[.,.]]],[.,[.,.]]]] => [7,6,4,3,2,5,1] => [[[[[[.,.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,[.,.]]],[[.,.],.]]] => [6,7,4,3,2,5,1] => [[[[[.,[.,.]],.],.],[.,.]],.] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[[.,.],.]],[.,[.,.]]]] => [7,6,3,4,2,5,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[.,.],.]],[[.,.],.]]] => [6,7,3,4,2,5,1] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[[.,.],[.,.]],[.,[.,.]]]] => [7,6,4,2,3,5,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],[.,.]],[[.,.],.]]] => [6,7,4,2,3,5,1] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,[.,.]],.],[.,[.,.]]]] => [7,6,3,2,4,5,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,[.,.]],.],[[.,.],.]]] => [6,7,3,2,4,5,1] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[[.,.],.],.],[.,[.,.]]]] => [7,6,2,3,4,5,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,.],.],.],[[.,.],.]]] => [6,7,2,3,4,5,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => [7,5,4,3,2,6,1] => [[[[[[.,.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,[[.,.],.]]],[.,.]]] => [7,4,5,3,2,6,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[.,[[.,[[.,.],[.,.]]],[.,.]]] => [7,5,3,4,2,6,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[.,[.,.]],.]],[.,.]]] => [7,4,3,5,2,6,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[[.,.],.],.]],[.,.]]] => [7,3,4,5,2,6,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[.,[[[.,.],[.,[.,.]]],[.,.]]] => [7,5,4,2,3,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],[[.,.],.]],[.,.]]] => [7,4,5,2,3,6,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,[.,.]],[.,.]],[.,.]]] => [7,5,3,2,4,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[[.,.],.],[.,.]],[.,.]]] => [7,5,2,3,4,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[.,[.,[.,.]]],.],[.,.]]] => [7,4,3,2,5,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,[[.,.],.]],.],[.,.]]] => [7,3,4,2,5,6,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[[.,.],[.,.]],.],[.,.]]] => [7,4,2,3,5,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,[.,.]],.],.],[.,.]]] => [7,3,2,4,5,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[[.,.],.],.],.],[.,.]]] => [7,2,3,4,5,6,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => [6,5,4,3,2,7,1] => [[[[[[.,.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,[.,[[.,.],.]]]],.]] => [5,6,4,3,2,7,1] => [[[[[.,[.,.]],.],.],[.,.]],.] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,[[.,.],[.,.]]]],.]] => [6,4,5,3,2,7,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,[[.,[.,.]],.]]],.]] => [5,4,6,3,2,7,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,[[[.,.],.],.]]],.]] => [4,5,6,3,2,7,1] => [[[[.,[.,[.,.]]],.],[.,.]],.] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[.,[[.,[[.,.],[.,[.,.]]]],.]] => [6,5,3,4,2,7,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[.,.],[[.,.],.]]],.]] => [5,6,3,4,2,7,1] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[.,[.,.]],[.,.]]],.]] => [6,4,3,5,2,7,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[[.,.],.],[.,.]]],.]] => [6,3,4,5,2,7,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[.,[[.,[[.,[.,[.,.]]],.]],.]] => [5,4,3,6,2,7,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[.,[[.,.],.]],.]],.]] => [4,5,3,6,2,7,1] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[[.,.],[.,.]],.]],.]] => [5,3,4,6,2,7,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[.,[[.,[[[.,[.,.]],.],.]],.]] => [4,3,5,6,2,7,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[.,[[.,[[[[.,.],.],.],.]],.]] => [3,4,5,6,2,7,1] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[.,[[[.,.],[.,[.,[.,.]]]],.]] => [6,5,4,2,3,7,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],[.,[[.,.],.]]],.]] => [5,6,4,2,3,7,1] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],[[.,.],[.,.]]],.]] => [6,4,5,2,3,7,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],[[.,[.,.]],.]],.]] => [5,4,6,2,3,7,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],[[[.,.],.],.]],.]] => [4,5,6,2,3,7,1] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,[.,.]],[.,[.,.]]],.]] => [6,5,3,2,4,7,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,[.,.]],[[.,.],.]],.]] => [5,6,3,2,4,7,1] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[[.,.],.],[.,[.,.]]],.]] => [6,5,2,3,4,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,.],.],[[.,.],.]],.]] => [5,6,2,3,4,7,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[.,[.,[.,.]]],[.,.]],.]] => [6,4,3,2,5,7,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,[[.,.],.]],[.,.]],.]] => [6,3,4,2,5,7,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[[.,.],[.,.]],[.,.]],.]] => [6,4,2,3,5,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,[.,.]],.],[.,.]],.]] => [6,3,2,4,5,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[[.,.],.],.],[.,.]],.]] => [6,2,3,4,5,7,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[.,[[[.,[.,[.,[.,.]]]],.],.]] => [5,4,3,2,6,7,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,[.,[[.,.],.]]],.],.]] => [4,5,3,2,6,7,1] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,[[.,.],[.,.]]],.],.]] => [5,3,4,2,6,7,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,[[.,[.,.]],.]],.],.]] => [4,3,5,2,6,7,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,[[[.,.],.],.]],.],.]] => [3,4,5,2,6,7,1] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[.,[[[[.,.],[.,[.,.]]],.],.]] => [5,4,2,3,6,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,.],[[.,.],.]],.],.]] => [4,5,2,3,6,7,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,[.,.]],[.,.]],.],.]] => [5,3,2,4,6,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[[.,.],.],[.,.]],.],.]] => [5,2,3,4,6,7,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[.,[[[[.,[.,[.,.]]],.],.],.]] => [4,3,2,5,6,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,[[.,.],.]],.],.],.]] => [3,4,2,5,6,7,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[[.,.],[.,.]],.],.],.]] => [4,2,3,5,6,7,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[.,[[[[[.,[.,.]],.],.],.],.]] => [3,2,4,5,6,7,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[.,[[[[[[.,.],.],.],.],.],.]] => [2,3,4,5,6,7,1] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => [7,6,5,4,3,1,2] => [[[[[[.,.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[.,[[.,.],.]]]]] => [6,7,5,4,3,1,2] => [[[[[.,[.,.]],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[[.,.],[.,.]]]]] => [7,5,6,4,3,1,2] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[[.,[.,.]],.]]]] => [6,5,7,4,3,1,2] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[[[.,.],.],.]]]] => [5,6,7,4,3,1,2] => [[[[.,[.,[.,.]]],.],.],[.,.]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[[.,.],[.,[.,.]]]]] => [7,6,4,5,3,1,2] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[.,.],[[.,.],.]]]] => [6,7,4,5,3,1,2] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[.,[.,.]],[.,.]]]] => [7,5,4,6,3,1,2] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[.,.],.],[.,.]]]] => [7,4,5,6,3,1,2] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,.],[.,[[.,[.,[.,.]]],.]]] => [6,5,4,7,3,1,2] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[.,[[.,.],.]],.]]] => [5,6,4,7,3,1,2] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[.,.],[.,.]],.]]] => [6,4,5,7,3,1,2] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[.,[.,.]],.],.]]] => [5,4,6,7,3,1,2] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[[.,.],.],.],.]]] => [4,5,6,7,3,1,2] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[.,.],[[.,.],[.,[.,[.,.]]]]] => [7,6,5,3,4,1,2] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[.,[[.,.],.]]]] => [6,7,5,3,4,1,2] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[[.,.],[.,.]]]] => [7,5,6,3,4,1,2] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[[.,[.,.]],.]]] => [6,5,7,3,4,1,2] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[[[.,.],.],.]]] => [5,6,7,3,4,1,2] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[.,.]],[.,[.,.]]]] => [7,6,4,3,5,1,2] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[.,.]],[[.,.],.]]] => [6,7,4,3,5,1,2] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[[.,.],.],[.,[.,.]]]] => [7,6,3,4,5,1,2] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,.],.],[[.,.],.]]] => [6,7,3,4,5,1,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[.,[.,[.,.]]],[.,.]]] => [7,5,4,3,6,1,2] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[[.,.],.]],[.,.]]] => [7,4,5,3,6,1,2] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[[.,.],[.,.]],[.,.]]] => [7,5,3,4,6,1,2] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,[.,.]],.],[.,.]]] => [7,4,3,5,6,1,2] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[[.,.],.],.],[.,.]]] => [7,3,4,5,6,1,2] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,.],[[.,[.,[.,[.,.]]]],.]] => [6,5,4,3,7,1,2] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[.,[[.,.],.]]],.]] => [5,6,4,3,7,1,2] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[[.,.],[.,.]]],.]] => [6,4,5,3,7,1,2] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[[.,[.,.]],.]],.]] => [5,4,6,3,7,1,2] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[[[.,.],.],.]],.]] => [4,5,6,3,7,1,2] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[[.,.],[.,[.,.]]],.]] => [6,5,3,4,7,1,2] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,.],[[.,.],.]],.]] => [5,6,3,4,7,1,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,[.,.]],[.,.]],.]] => [6,4,3,5,7,1,2] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[[.,.],.],[.,.]],.]] => [6,3,4,5,7,1,2] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,.],[[[.,[.,[.,.]]],.],.]] => [5,4,3,6,7,1,2] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,[[.,.],.]],.],.]] => [4,5,3,6,7,1,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[[.,.],[.,.]],.],.]] => [5,3,4,6,7,1,2] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,.],[[[[.,[.,.]],.],.],.]] => [4,3,5,6,7,1,2] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,.],[[[[[.,.],.],.],.],.]] => [3,4,5,6,7,1,2] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => [7,6,5,4,2,1,3] => [[[[[[.,.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,.]],[.,[.,[[.,.],.]]]] => [6,7,5,4,2,1,3] => [[[[[.,[.,.]],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,.]],[.,[[.,.],[.,.]]]] => [7,5,6,4,2,1,3] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,.]],[.,[[.,[.,.]],.]]] => [6,5,7,4,2,1,3] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,.]],[.,[[[.,.],.],.]]] => [5,6,7,4,2,1,3] => [[[[.,[.,[.,.]]],.],.],[.,.]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[.,[.,.]],[[.,.],[.,[.,.]]]] => [7,6,4,5,2,1,3] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[.,.],[[.,.],.]]] => [6,7,4,5,2,1,3] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[.,[.,.]],[.,.]]] => [7,5,4,6,2,1,3] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[[.,.],.],[.,.]]] => [7,4,5,6,2,1,3] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[.,[.,[.,.]]],.]] => [6,5,4,7,2,1,3] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[.,[[.,.],.]],.]] => [5,6,4,7,2,1,3] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[[.,.],[.,.]],.]] => [6,4,5,7,2,1,3] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[[.,[.,.]],.],.]] => [5,4,6,7,2,1,3] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[[[.,.],.],.],.]] => [4,5,6,7,2,1,3] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[[.,.],.],[.,[.,[.,[.,.]]]]] => [7,6,5,4,1,2,3] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[.,[[.,.],.]]]] => [6,7,5,4,1,2,3] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[[.,.],[.,.]]]] => [7,5,6,4,1,2,3] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[[.,[.,.]],.]]] => [6,5,7,4,1,2,3] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[[[.,.],.],.]]] => [5,6,7,4,1,2,3] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[[.,.],[.,[.,.]]]] => [7,6,4,5,1,2,3] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,.],[[.,.],.]]] => [6,7,4,5,1,2,3] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,[.,.]],[.,.]]] => [7,5,4,6,1,2,3] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[.,.],.],[.,.]]] => [7,4,5,6,1,2,3] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,[.,[.,.]]],.]] => [6,5,4,7,1,2,3] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,[[.,.],.]],.]] => [5,6,4,7,1,2,3] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[.,.],[.,.]],.]] => [6,4,5,7,1,2,3] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[.,[.,.]],.],.]] => [5,4,6,7,1,2,3] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[[.,.],.],.],.]] => [4,5,6,7,1,2,3] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[.,[.,[.,.]]],[.,[.,[.,.]]]] => [7,6,5,3,2,1,4] => [[[[[[.,.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,.]]],[.,[[.,.],.]]] => [6,7,5,3,2,1,4] => [[[[[.,[.,.]],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,.]]],[[.,.],[.,.]]] => [7,5,6,3,2,1,4] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,.]]],[[.,[.,.]],.]] => [6,5,7,3,2,1,4] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,.]]],[[[.,.],.],.]] => [5,6,7,3,2,1,4] => [[[[.,[.,[.,.]]],.],.],[.,.]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[.,[[.,.],.]],[.,[.,[.,.]]]] => [7,6,5,2,3,1,4] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],.]],[.,[[.,.],.]]] => [6,7,5,2,3,1,4] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],.]],[[.,.],[.,.]]] => [7,5,6,2,3,1,4] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],.]],[[.,[.,.]],.]] => [6,5,7,2,3,1,4] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],.]],[[[.,.],.],.]] => [5,6,7,2,3,1,4] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[[.,.],[.,.]],[.,[.,[.,.]]]] => [7,6,5,3,1,2,4] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,.]],[.,[[.,.],.]]] => [6,7,5,3,1,2,4] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,.]],[[.,.],[.,.]]] => [7,5,6,3,1,2,4] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,.]],[[.,[.,.]],.]] => [6,5,7,3,1,2,4] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,.]],[[[.,.],.],.]] => [5,6,7,3,1,2,4] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[.,[.,[.,.]]]] => [7,6,5,2,1,3,4] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[.,[[.,.],.]]] => [6,7,5,2,1,3,4] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[[.,.],[.,.]]] => [7,5,6,2,1,3,4] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[[.,[.,.]],.]] => [6,5,7,2,1,3,4] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[[[.,.],.],.]] => [5,6,7,2,1,3,4] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[[.,.],.],.],[.,[.,[.,.]]]] => [7,6,5,1,2,3,4] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[.,[[.,.],.]]] => [6,7,5,1,2,3,4] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[[.,.],[.,.]]] => [7,5,6,1,2,3,4] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[[.,[.,.]],.]] => [6,5,7,1,2,3,4] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[[[.,.],.],.]] => [5,6,7,1,2,3,4] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[.,[.,[.,[.,.]]]],[.,[.,.]]] => [7,6,4,3,2,1,5] => [[[[[[.,.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[.,.]]]],[[.,.],.]] => [6,7,4,3,2,1,5] => [[[[[.,[.,.]],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[[.,.],.]]],[.,[.,.]]] => [7,6,3,4,2,1,5] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[.,.],.]]],[[.,.],.]] => [6,7,3,4,2,1,5] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,[[.,.],[.,.]]],[.,[.,.]]] => [7,6,4,2,3,1,5] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[.,.]]],[[.,.],.]] => [6,7,4,2,3,1,5] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[.,.]],.]],[.,[.,.]]] => [7,6,3,2,4,1,5] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[.,.]],.]],[[.,.],.]] => [6,7,3,2,4,1,5] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[[.,.],.],.]],[.,[.,.]]] => [7,6,2,3,4,1,5] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,.],.],.]],[[.,.],.]] => [6,7,2,3,4,1,5] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[[.,.],[.,[.,.]]],[.,[.,.]]] => [7,6,4,3,1,2,5] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,[.,.]]],[[.,.],.]] => [6,7,4,3,1,2,5] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],[[.,.],.]],[.,[.,.]]] => [7,6,3,4,1,2,5] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],[[.,.],.]],[[.,.],.]] => [6,7,3,4,1,2,5] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[.,.]],[.,.]],[.,[.,.]]] => [7,6,4,2,1,3,5] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],[.,.]],[[.,.],.]] => [6,7,4,2,1,3,5] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[[.,.],.],[.,.]],[.,[.,.]]] => [7,6,4,1,2,3,5] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[.,.]],[[.,.],.]] => [6,7,4,1,2,3,5] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[.,[.,[.,.]]],.],[.,[.,.]]] => [7,6,3,2,1,4,5] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[.,.]]],.],[[.,.],.]] => [6,7,3,2,1,4,5] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],.],[.,[.,.]]] => [7,6,2,3,1,4,5] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],.],[[.,.],.]] => [6,7,2,3,1,4,5] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[[.,.],[.,.]],.],[.,[.,.]]] => [7,6,3,1,2,4,5] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],[.,.]],.],[[.,.],.]] => [6,7,3,1,2,4,5] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],.],.],[.,[.,.]]] => [7,6,2,1,3,4,5] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],.],.],[[.,.],.]] => [6,7,2,1,3,4,5] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[[.,.],.],.],.],[.,[.,.]]] => [7,6,1,2,3,4,5] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,.],.],.],.],[[.,.],.]] => [6,7,1,2,3,4,5] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => [7,5,4,3,2,1,6] => [[[[[[.,.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[[.,.],.]]]],[.,.]] => [7,4,5,3,2,1,6] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[[.,.],[.,.]]]],[.,.]] => [7,5,3,4,2,1,6] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[.,[.,.]],.]]],[.,.]] => [7,4,3,5,2,1,6] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[[.,.],.],.]]],[.,.]] => [7,3,4,5,2,1,6] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,[[.,.],[.,[.,.]]]],[.,.]] => [7,5,4,2,3,1,6] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[[.,.],.]]],[.,.]] => [7,4,5,2,3,1,6] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,[.,.]],[.,.]]],[.,.]] => [7,5,3,2,4,1,6] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[[.,.],.],[.,.]]],[.,.]] => [7,5,2,3,4,1,6] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[.,[.,[.,.]]],.]],[.,.]] => [7,4,3,2,5,1,6] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[[.,.],.]],.]],[.,.]] => [7,3,4,2,5,1,6] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[[.,.],[.,.]],.]],[.,.]] => [7,4,2,3,5,1,6] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,[.,.]],.],.]],[.,.]] => [7,3,2,4,5,1,6] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[[.,.],.],.],.]],[.,.]] => [7,2,3,4,5,1,6] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[[.,.],[.,[.,[.,.]]]],[.,.]] => [7,5,4,3,1,2,6] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,[[.,.],.]]],[.,.]] => [7,4,5,3,1,2,6] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,.],[[.,.],[.,.]]],[.,.]] => [7,5,3,4,1,2,6] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],[[.,[.,.]],.]],[.,.]] => [7,4,3,5,1,2,6] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],[[[.,.],.],.]],[.,.]] => [7,3,4,5,1,2,6] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,[.,.]],[.,[.,.]]],[.,.]] => [7,5,4,2,1,3,6] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],[[.,.],.]],[.,.]] => [7,4,5,2,1,3,6] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[[.,.],.],[.,[.,.]]],[.,.]] => [7,5,4,1,2,3,6] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[[.,.],.]],[.,.]] => [7,4,5,1,2,3,6] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[.,[.,[.,.]]],[.,.]],[.,.]] => [7,5,3,2,1,4,6] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],[.,.]],[.,.]] => [7,5,2,3,1,4,6] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[[.,.],[.,.]],[.,.]],[.,.]] => [7,5,3,1,2,4,6] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],.],[.,.]],[.,.]] => [7,5,2,1,3,4,6] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[[.,.],.],.],[.,.]],[.,.]] => [7,5,1,2,3,4,6] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[.,[.,[.,[.,.]]]],.],[.,.]] => [7,4,3,2,1,5,6] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[[.,.],.]]],.],[.,.]] => [7,3,4,2,1,5,6] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[[.,.],[.,.]]],.],[.,.]] => [7,4,2,3,1,5,6] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,[.,.]],.]],.],[.,.]] => [7,3,2,4,1,5,6] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[[.,.],.],.]],.],[.,.]] => [7,2,3,4,1,5,6] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[[.,.],[.,[.,.]]],.],[.,.]] => [7,4,3,1,2,5,6] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],[[.,.],.]],.],[.,.]] => [7,3,4,1,2,5,6] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],[.,.]],.],[.,.]] => [7,4,2,1,3,5,6] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[[.,.],.],[.,.]],.],[.,.]] => [7,4,1,2,3,5,6] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[.,[.,[.,.]]],.],.],[.,.]] => [7,3,2,1,4,5,6] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[[.,.],.]],.],.],[.,.]] => [7,2,3,1,4,5,6] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[[.,.],[.,.]],.],.],[.,.]] => [7,3,1,2,4,5,6] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,[.,.]],.],.],.],[.,.]] => [7,2,1,3,4,5,6] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[[.,.],.],.],.],.],[.,.]] => [7,1,2,3,4,5,6] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => [[[[[[.,.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[.,[[.,.],.]]]]],.] => [5,6,4,3,2,1,7] => [[[[[.,[.,.]],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[[.,.],[.,.]]]]],.] => [6,4,5,3,2,1,7] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[[.,[.,.]],.]]]],.] => [5,4,6,3,2,1,7] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[[[.,.],.],.]]]],.] => [4,5,6,3,2,1,7] => [[[[.,[.,[.,.]]],.],.],[.,.]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[[.,.],[.,[.,.]]]]],.] => [6,5,3,4,2,1,7] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[.,.],[[.,.],.]]]],.] => [5,6,3,4,2,1,7] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[.,[.,.]],[.,.]]]],.] => [6,4,3,5,2,1,7] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[[.,.],.],[.,.]]]],.] => [6,3,4,5,2,1,7] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,[.,[[.,[.,[.,.]]],.]]],.] => [5,4,3,6,2,1,7] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[.,[[.,.],.]],.]]],.] => [4,5,3,6,2,1,7] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[[.,.],[.,.]],.]]],.] => [5,3,4,6,2,1,7] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,[.,[[[.,[.,.]],.],.]]],.] => [4,3,5,6,2,1,7] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,[.,[[[[.,.],.],.],.]]],.] => [3,4,5,6,2,1,7] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[.,[[.,.],[.,[.,[.,.]]]]],.] => [6,5,4,2,3,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[.,[[.,.],.]]]],.] => [5,6,4,2,3,1,7] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[[.,.],[.,.]]]],.] => [6,4,5,2,3,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[[.,[.,.]],.]]],.] => [5,4,6,2,3,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[[[.,.],.],.]]],.] => [4,5,6,2,3,1,7] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,[.,.]],[.,[.,.]]]],.] => [6,5,3,2,4,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[.,.]],[[.,.],.]]],.] => [5,6,3,2,4,1,7] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[[.,.],.],[.,[.,.]]]],.] => [6,5,2,3,4,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,.],.],[[.,.],.]]],.] => [5,6,2,3,4,1,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[.,[.,[.,.]]],[.,.]]],.] => [6,4,3,2,5,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[[.,.],.]],[.,.]]],.] => [6,3,4,2,5,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[[.,.],[.,.]],[.,.]]],.] => [6,4,2,3,5,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,[.,.]],.],[.,.]]],.] => [6,3,2,4,5,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[[.,.],.],.],[.,.]]],.] => [6,2,3,4,5,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,[[.,[.,[.,[.,.]]]],.]],.] => [5,4,3,2,6,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[.,[[.,.],.]]],.]],.] => [4,5,3,2,6,1,7] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[[.,.],[.,.]]],.]],.] => [5,3,4,2,6,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,[[.,[.,.]],.]],.]],.] => [4,3,5,2,6,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,[[[.,.],.],.]],.]],.] => [3,4,5,2,6,1,7] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[.,[[[.,.],[.,[.,.]]],.]],.] => [5,4,2,3,6,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,.],[[.,.],.]],.]],.] => [4,5,2,3,6,1,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,[.,.]],[.,.]],.]],.] => [5,3,2,4,6,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[[.,.],.],[.,.]],.]],.] => [5,2,3,4,6,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,[[[.,[.,[.,.]]],.],.]],.] => [4,3,2,5,6,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,[[.,.],.]],.],.]],.] => [3,4,2,5,6,1,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[[.,.],[.,.]],.],.]],.] => [4,2,3,5,6,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,[[[[.,[.,.]],.],.],.]],.] => [3,2,4,5,6,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,[[[[[.,.],.],.],.],.]],.] => [2,3,4,5,6,1,7] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[[.,.],[.,[.,[.,[.,.]]]]],.] => [6,5,4,3,1,2,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,[.,[[.,.],.]]]],.] => [5,6,4,3,1,2,7] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,[[.,.],[.,.]]]],.] => [6,4,5,3,1,2,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,[[.,[.,.]],.]]],.] => [5,4,6,3,1,2,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,[[[.,.],.],.]]],.] => [4,5,6,3,1,2,7] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,.],[[.,.],[.,[.,.]]]],.] => [6,5,3,4,1,2,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],[[.,.],[[.,.],.]]],.] => [5,6,3,4,1,2,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],[[.,[.,.]],[.,.]]],.] => [6,4,3,5,1,2,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],[[[.,.],.],[.,.]]],.] => [6,3,4,5,1,2,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],[[.,[.,[.,.]]],.]],.] => [5,4,3,6,1,2,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],[[.,[[.,.],.]],.]],.] => [4,5,3,6,1,2,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],[[[.,.],[.,.]],.]],.] => [5,3,4,6,1,2,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],[[[.,[.,.]],.],.]],.] => [4,3,5,6,1,2,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],[[[[.,.],.],.],.]],.] => [3,4,5,6,1,2,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[[.,[.,.]],[.,[.,[.,.]]]],.] => [6,5,4,2,1,3,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],[.,[[.,.],.]]],.] => [5,6,4,2,1,3,7] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],[[.,.],[.,.]]],.] => [6,4,5,2,1,3,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],[[.,[.,.]],.]],.] => [5,4,6,2,1,3,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],[[[.,.],.],.]],.] => [4,5,6,2,1,3,7] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[[.,.],.],[.,[.,[.,.]]]],.] => [6,5,4,1,2,3,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[.,[[.,.],.]]],.] => [5,6,4,1,2,3,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[[.,.],[.,.]]],.] => [6,4,5,1,2,3,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[[.,[.,.]],.]],.] => [5,4,6,1,2,3,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[[[.,.],.],.]],.] => [4,5,6,1,2,3,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[.,[.,[.,.]]],[.,[.,.]]],.] => [6,5,3,2,1,4,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[.,.]]],[[.,.],.]],.] => [5,6,3,2,1,4,7] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],[.,[.,.]]],.] => [6,5,2,3,1,4,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],[[.,.],.]],.] => [5,6,2,3,1,4,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[[.,.],[.,.]],[.,[.,.]]],.] => [6,5,3,1,2,4,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],[.,.]],[[.,.],.]],.] => [5,6,3,1,2,4,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],.],[.,[.,.]]],.] => [6,5,2,1,3,4,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],.],[[.,.],.]],.] => [5,6,2,1,3,4,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[[.,.],.],.],[.,[.,.]]],.] => [6,5,1,2,3,4,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,.],.],.],[[.,.],.]],.] => [5,6,1,2,3,4,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[.,[.,[.,[.,.]]]],[.,.]],.] => [6,4,3,2,1,5,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[[.,.],.]]],[.,.]],.] => [6,3,4,2,1,5,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[[.,.],[.,.]]],[.,.]],.] => [6,4,2,3,1,5,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,[.,.]],.]],[.,.]],.] => [6,3,2,4,1,5,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[[.,.],.],.]],[.,.]],.] => [6,2,3,4,1,5,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[[.,.],[.,[.,.]]],[.,.]],.] => [6,4,3,1,2,5,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],[[.,.],.]],[.,.]],.] => [6,3,4,1,2,5,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],[.,.]],[.,.]],.] => [6,4,2,1,3,5,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[[.,.],.],[.,.]],[.,.]],.] => [6,4,1,2,3,5,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[.,[.,[.,.]]],.],[.,.]],.] => [6,3,2,1,4,5,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[[.,.],.]],.],[.,.]],.] => [6,2,3,1,4,5,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[[.,.],[.,.]],.],[.,.]],.] => [6,3,1,2,4,5,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,[.,.]],.],.],[.,.]],.] => [6,2,1,3,4,5,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[[.,.],.],.],.],[.,.]],.] => [6,1,2,3,4,5,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[.,[[.,.],.]]]],.],.] => [4,5,3,2,1,6,7] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[[.,.],[.,.]]]],.],.] => [5,3,4,2,1,6,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,[[.,[.,.]],.]]],.],.] => [4,3,5,2,1,6,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,[[[.,.],.],.]]],.],.] => [3,4,5,2,1,6,7] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,[[.,.],[.,[.,.]]]],.],.] => [5,4,2,3,1,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,.],[[.,.],.]]],.],.] => [4,5,2,3,1,6,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,[.,.]],[.,.]]],.],.] => [5,3,2,4,1,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[[.,.],.],[.,.]]],.],.] => [5,2,3,4,1,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,[[.,[.,[.,.]]],.]],.],.] => [4,3,2,5,1,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,[[.,.],.]],.]],.],.] => [3,4,2,5,1,6,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[[.,.],[.,.]],.]],.],.] => [4,2,3,5,1,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,[[[.,[.,.]],.],.]],.],.] => [3,2,4,5,1,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,[[[[.,.],.],.],.]],.],.] => [2,3,4,5,1,6,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[[[.,.],[.,[.,[.,.]]]],.],.] => [5,4,3,1,2,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],[.,[[.,.],.]]],.],.] => [4,5,3,1,2,6,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],[[.,.],[.,.]]],.],.] => [5,3,4,1,2,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],[[.,[.,.]],.]],.],.] => [4,3,5,1,2,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],[[[.,.],.],.]],.],.] => [3,4,5,1,2,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],[.,[.,.]]],.],.] => [5,4,2,1,3,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],[[.,.],.]],.],.] => [4,5,2,1,3,6,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[[.,.],.],[.,[.,.]]],.],.] => [5,4,1,2,3,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,.],.],[[.,.],.]],.],.] => [4,5,1,2,3,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[[.,[.,[.,.]]],[.,.]],.],.] => [5,3,2,1,4,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[[.,.],.]],[.,.]],.],.] => [5,2,3,1,4,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[[.,.],[.,.]],[.,.]],.],.] => [5,3,1,2,4,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,[.,.]],.],[.,.]],.],.] => [5,2,1,3,4,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[[.,.],.],.],[.,.]],.],.] => [5,1,2,3,4,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,[[.,.],.]]],.],.],.] => [3,4,2,1,5,6,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[[.,.],[.,.]]],.],.],.] => [4,2,3,1,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,[[.,[.,.]],.]],.],.],.] => [3,2,4,1,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,[[[.,.],.],.]],.],.],.] => [2,3,4,1,5,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[[[.,.],[.,[.,.]]],.],.],.] => [4,3,1,2,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,.],[[.,.],.]],.],.],.] => [3,4,1,2,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,[.,.]],[.,.]],.],.],.] => [4,2,1,3,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[[.,.],.],[.,.]],.],.],.] => [4,1,2,3,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,[[.,.],.]],.],.],.],.] => [2,3,1,4,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[[[[.,.],[.,.]],.],.],.],.] => [3,1,2,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [8,7,6,5,4,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],.] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [7,8,6,5,4,3,2,1] => [[[[[[[.,[.,.]],.],.],.],.],.],.] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [8,6,7,5,4,3,2,1] => [[[[[[[.,.],[.,.]],.],.],.],.],.] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [7,6,8,5,4,3,2,1] => [[[[[[[.,.],[.,.]],.],.],.],.],.] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] => [6,7,8,5,4,3,2,1] => [[[[[[.,[.,[.,.]]],.],.],.],.],.] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => [8,7,5,6,4,3,2,1] => [[[[[[[.,.],.],[.,.]],.],.],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [7,8,5,6,4,3,2,1] => [[[[[[.,[.,.]],[.,.]],.],.],.],.] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [8,6,5,7,4,3,2,1] => [[[[[[[.,.],.],[.,.]],.],.],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] => [8,5,6,7,4,3,2,1] => [[[[[[.,.],[.,[.,.]]],.],.],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => [7,6,5,8,4,3,2,1] => [[[[[[[.,.],.],[.,.]],.],.],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]] => [6,7,5,8,4,3,2,1] => [[[[[[.,[.,.]],[.,.]],.],.],.],.] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]] => [7,5,6,8,4,3,2,1] => [[[[[[.,.],[.,[.,.]]],.],.],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]] => [6,5,7,8,4,3,2,1] => [[[[[[.,.],[.,[.,.]]],.],.],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => [5,6,7,8,4,3,2,1] => [[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [8,7,6,4,5,3,2,1] => [[[[[[[.,.],.],.],[.,.]],.],.],.] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [7,8,6,4,5,3,2,1] => [[[[[[.,[.,.]],.],[.,.]],.],.],.] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [8,6,7,4,5,3,2,1] => [[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => [8,7,5,4,6,3,2,1] => [[[[[[[.,.],.],.],[.,.]],.],.],.] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => [8,7,4,5,6,3,2,1] => [[[[[[.,.],.],[.,[.,.]]],.],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]] => [8,5,6,4,7,3,2,1] => [[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]] => [8,6,4,5,7,3,2,1] => [[[[[[.,.],.],[.,[.,.]]],.],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => [8,4,5,6,7,3,2,1] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => [7,6,5,4,8,3,2,1] => [[[[[[[.,.],.],.],[.,.]],.],.],.] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]] => [6,7,5,4,8,3,2,1] => [[[[[[.,[.,.]],.],[.,.]],.],.],.] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]] => [7,5,6,4,8,3,2,1] => [[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]] => [6,5,7,4,8,3,2,1] => [[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]] => [5,6,7,4,8,3,2,1] => [[[[[.,[.,[.,.]]],[.,.]],.],.],.] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]] => [7,6,4,5,8,3,2,1] => [[[[[[.,.],.],[.,[.,.]]],.],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]] => [6,7,4,5,8,3,2,1] => [[[[[.,[.,.]],[.,[.,.]]],.],.],.] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]] => [7,5,4,6,8,3,2,1] => [[[[[[.,.],.],[.,[.,.]]],.],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]] => [7,4,5,6,8,3,2,1] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]] => [6,5,4,7,8,3,2,1] => [[[[[[.,.],.],[.,[.,.]]],.],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]] => [5,6,4,7,8,3,2,1] => [[[[[.,[.,.]],[.,[.,.]]],.],.],.] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]] => [6,4,5,7,8,3,2,1] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]] => [5,4,6,7,8,3,2,1] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[[[.,.],.],.],.],.]]]] => [4,5,6,7,8,3,2,1] => [[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,3,4,2,1] => [[[[[[[.,.],.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [7,8,6,5,3,4,2,1] => [[[[[[.,[.,.]],.],.],[.,.]],.],.] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [8,6,7,5,3,4,2,1] => [[[[[[.,.],[.,.]],.],[.,.]],.],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]] => [7,6,8,5,3,4,2,1] => [[[[[[.,.],[.,.]],.],[.,.]],.],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [8,7,5,6,3,4,2,1] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [7,8,5,6,3,4,2,1] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]] => [8,5,6,7,3,4,2,1] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]] => [7,6,5,8,3,4,2,1] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]] => [6,7,5,8,3,4,2,1] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,.],[[[.,[.,.]],.],.]]]] => [6,5,7,8,3,4,2,1] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,.],[[[[.,.],.],.],.]]]] => [5,6,7,8,3,4,2,1] => [[[[.,[.,[.,[.,.]]]],[.,.]],.],.] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [8,7,6,4,3,5,2,1] => [[[[[[[.,.],.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => [7,8,6,4,3,5,2,1] => [[[[[[.,[.,.]],.],.],[.,.]],.],.] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]] => [7,6,8,4,3,5,2,1] => [[[[[[.,.],[.,.]],.],[.,.]],.],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => [6,7,8,4,3,5,2,1] => [[[[[.,[.,[.,.]]],.],[.,.]],.],.] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => [8,7,6,3,4,5,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[[.,.],.],[.,[[.,.],.]]]]] => [7,8,6,3,4,5,2,1] => [[[[[.,[.,.]],.],[.,[.,.]]],.],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[[.,.],.],[[.,.],[.,.]]]]] => [8,6,7,3,4,5,2,1] => [[[[[.,.],[.,.]],[.,[.,.]]],.],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[[.,.],.],[[.,[.,.]],.]]]] => [7,6,8,3,4,5,2,1] => [[[[[.,.],[.,.]],[.,[.,.]]],.],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[[.,.],.],[[[.,.],.],.]]]] => [6,7,8,3,4,5,2,1] => [[[[.,[.,[.,.]]],[.,[.,.]]],.],.] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [8,7,5,4,3,6,2,1] => [[[[[[[.,.],.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => [7,8,5,4,3,6,2,1] => [[[[[[.,[.,.]],.],.],[.,.]],.],.] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]] => [8,7,5,3,4,6,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]] => [7,8,5,3,4,6,2,1] => [[[[[.,[.,.]],.],[.,[.,.]]],.],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]] => [8,7,4,3,5,6,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => [8,7,3,4,5,6,2,1] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[.,[.,[[[[.,.],.],.],[[.,.],.]]]] => [7,8,3,4,5,6,2,1] => [[[[.,[.,.]],[.,[.,[.,.]]]],.],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => [8,6,5,4,3,7,2,1] => [[[[[[[.,.],.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]] => [8,5,4,6,3,7,2,1] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [8,6,4,3,5,7,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[[[.,.],[.,.]],.],[.,.]]]] => [8,5,3,4,6,7,2,1] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[.,[.,[[[[.,[.,.]],.],.],[.,.]]]] => [8,4,3,5,6,7,2,1] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[.,[.,[[[[[.,.],.],.],.],[.,.]]]] => [8,3,4,5,6,7,2,1] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => [7,6,5,4,3,8,2,1] => [[[[[[[.,.],.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]] => [6,7,5,4,3,8,2,1] => [[[[[[.,[.,.]],.],.],[.,.]],.],.] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]] => [7,5,6,4,3,8,2,1] => [[[[[[.,.],[.,.]],.],[.,.]],.],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[.,[[[.,.],.],.]]],.]]] => [5,6,7,4,3,8,2,1] => [[[[[.,[.,[.,.]]],.],[.,.]],.],.] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]] => [7,6,4,5,3,8,2,1] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[[.,.],[[.,.],.]]],.]]] => [6,7,4,5,3,8,2,1] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]] => [7,5,4,6,3,8,2,1] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[[[.,.],.],[.,.]]],.]]] => [7,4,5,6,3,8,2,1] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]] => [6,5,4,7,3,8,2,1] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[[[.,.],[.,.]],.]],.]]] => [6,4,5,7,3,8,2,1] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]] => [5,4,6,7,3,8,2,1] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[[[[.,.],.],.],.]],.]]] => [4,5,6,7,3,8,2,1] => [[[[.,[.,[.,[.,.]]]],[.,.]],.],.] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]] => [7,6,5,3,4,8,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]] => [7,6,4,3,5,8,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]] => [7,6,3,4,5,8,2,1] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]] => [7,5,4,3,6,8,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]] => [7,5,3,4,6,8,2,1] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[.,[.,[[[[[.,.],.],.],[.,.]],.]]] => [7,3,4,5,6,8,2,1] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]] => [6,5,4,3,7,8,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[[[.,.],[.,[.,.]]],.],.]]] => [6,5,3,4,7,8,2,1] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[.,[.,[[[[[.,.],.],[.,.]],.],.]]] => [6,3,4,5,7,8,2,1] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]] => [5,4,3,6,7,8,2,1] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[.,[.,[[[[[.,.],[.,.]],.],.],.]]] => [5,3,4,6,7,8,2,1] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[.,[.,[[[[[.,[.,.]],.],.],.],.]]] => [4,3,5,6,7,8,2,1] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[.,[.,[[[[[[.,.],.],.],.],.],.]]] => [3,4,5,6,7,8,2,1] => [[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,4,2,3,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [7,8,6,5,4,2,3,1] => [[[[[[.,[.,.]],.],.],.],[.,.]],.] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,2,3,1] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] => [7,6,8,5,4,2,3,1] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,2,3,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]] => [8,6,5,7,4,2,3,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[.,[[[.,.],.],[.,.]]]]] => [8,5,6,7,4,2,3,1] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]] => [7,6,5,8,4,2,3,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]] => [6,7,5,8,4,2,3,1] => [[[[[.,[.,.]],[.,.]],.],[.,.]],.] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[.,[[[.,.],[.,.]],.]]]] => [7,5,6,8,4,2,3,1] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[.,[[[[.,.],.],.],.]]]] => [5,6,7,8,4,2,3,1] => [[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,2,3,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [8,6,7,4,5,2,3,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[.,.],[[.,[.,.]],.]]]] => [7,6,8,4,5,2,3,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[.,.],[[[.,.],.],.]]]] => [6,7,8,4,5,2,3,1] => [[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [8,7,4,5,6,2,3,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [7,8,4,5,6,2,3,1] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]] => [8,5,6,4,7,2,3,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [8,6,4,5,7,2,3,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[.,[[.,.],[[[[.,.],.],.],[.,.]]]] => [8,4,5,6,7,2,3,1] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[.,[[.,.],[[.,[[.,.],[.,.]]],.]]] => [7,5,6,4,8,2,3,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[.,[[.,[.,.]],.]],.]]] => [6,5,7,4,8,2,3,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[[.,.],[.,[.,.]]],.]]] => [7,6,4,5,8,2,3,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[.,[[.,.],[[[.,.],[[.,.],.]],.]]] => [6,7,4,5,8,2,3,1] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[.,[[.,.],[[[[[.,.],.],.],.],.]]] => [4,5,6,7,8,2,3,1] => [[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,3,2,4,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [7,8,6,5,3,2,4,1] => [[[[[[.,[.,.]],.],.],.],[.,.]],.] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [8,6,7,5,3,2,4,1] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [7,6,8,5,3,2,4,1] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,.]],[.,[[[.,.],.],.]]]] => [6,7,8,5,3,2,4,1] => [[[[[.,[.,[.,.]]],.],.],[.,.]],.] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [8,7,5,6,3,2,4,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [8,6,5,7,3,2,4,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [8,5,6,7,3,2,4,1] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] => [7,6,5,8,3,2,4,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]] => [6,7,5,8,3,2,4,1] => [[[[[.,[.,.]],[.,.]],.],[.,.]],.] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [5,6,7,8,3,2,4,1] => [[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,2,3,4,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => [8,6,7,5,2,3,4,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[.,[[.,[.,.]],.]]]] => [7,6,8,5,2,3,4,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [6,7,8,5,2,3,4,1] => [[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [8,7,5,6,2,3,4,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [7,8,5,6,2,3,4,1] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[[.,[.,.]],[.,.]]]] => [8,6,5,7,2,3,4,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [8,5,6,7,2,3,4,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]] => [7,6,5,8,2,3,4,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[[.,[[.,.],.]],.]]] => [6,7,5,8,2,3,4,1] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[[[.,[.,.]],.],.]]] => [6,5,7,8,2,3,4,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[[[[.,.],.],.],.]]] => [5,6,7,8,2,3,4,1] => [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [8,7,6,4,3,2,5,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]] => [7,6,8,4,3,2,5,1] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]] => [8,7,6,3,4,2,5,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[.,.],.]],[.,[[.,.],.]]]] => [7,8,6,3,4,2,5,1] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => [8,6,7,3,4,2,5,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[.,.],.]],[[.,[.,.]],.]]] => [7,6,8,3,4,2,5,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[.,.],.]],[[[.,.],.],.]]] => [6,7,8,3,4,2,5,1] => [[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [6,7,8,4,2,3,5,1] => [[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [8,7,6,3,2,4,5,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,[.,.]],.],[.,[[.,.],.]]]] => [7,8,6,3,2,4,5,1] => [[[[[.,[.,.]],.],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [8,6,7,3,2,4,5,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,[.,.]],.],[[[.,.],.],.]]] => [6,7,8,3,2,4,5,1] => [[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [8,7,6,2,3,4,5,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,.],.],.],[.,[[.,.],.]]]] => [7,8,6,2,3,4,5,1] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [8,6,7,2,3,4,5,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,.],.],.],[[.,[.,.]],.]]] => [7,6,8,2,3,4,5,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,.],.],.],[[[.,.],.],.]]] => [6,7,8,2,3,4,5,1] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [7,8,5,4,3,2,6,1] => [[[[[[.,[.,.]],.],.],.],[.,.]],.] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]] => [8,7,5,3,4,2,6,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[.,.],[.,.]]],[[.,.],.]]] => [7,8,5,3,4,2,6,1] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]] => [8,7,4,3,5,2,6,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[.,[.,.]],.]],[[.,.],.]]] => [7,8,4,3,5,2,6,1] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [8,7,5,4,2,3,6,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [8,7,5,3,2,4,6,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => [8,7,4,3,2,5,6,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,[.,[.,.]]],.],[[.,.],.]]] => [7,8,4,3,2,5,6,1] => [[[[[.,[.,.]],.],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,[[.,.],.]],.],[[.,.],.]]] => [7,8,3,4,2,5,6,1] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[[.,.],[.,.]],.],[[.,.],.]]] => [7,8,4,2,3,5,6,1] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,[.,.]],.],.],[[.,.],.]]] => [7,8,3,2,4,5,6,1] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [8,7,2,3,4,5,6,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[.,[[[[[.,.],.],.],.],[[.,.],.]]] => [7,8,2,3,4,5,6,1] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [8,6,5,4,3,2,7,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]] => [8,5,4,6,3,2,7,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]] => [8,5,6,3,4,2,7,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [8,6,4,3,5,2,7,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[[.,.],.],[.,.]]],[.,.]]] => [8,6,3,4,5,2,7,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]] => [8,4,5,3,6,2,7,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[[.,[.,.]],.],.]],[.,.]]] => [8,4,3,5,6,2,7,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [8,6,5,4,2,3,7,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],[.,[[.,.],.]]],[.,.]]] => [8,5,6,4,2,3,7,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [8,6,5,3,2,4,7,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [8,6,4,2,3,5,7,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[[.,.],.],.],[.,.]],[.,.]]] => [8,6,2,3,4,5,7,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]] => [8,5,4,3,2,6,7,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,[.,[[.,.],.]]],.],[.,.]]] => [8,4,5,3,2,6,7,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]] => [8,5,3,4,2,6,7,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,[[[.,.],.],.]],.],[.,.]]] => [8,3,4,5,2,6,7,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]] => [8,5,4,2,3,6,7,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,[.,[.,.]]],.],.],[.,.]]] => [8,4,3,2,5,6,7,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,[[.,.],.]],.],.],[.,.]]] => [8,3,4,2,5,6,7,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[[.,.],[.,.]],.],.],[.,.]]] => [8,4,2,3,5,6,7,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[.,[[[[[.,[.,.]],.],.],.],[.,.]]] => [8,3,2,4,5,6,7,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[.,[[[[[[.,.],.],.],.],.],[.,.]]] => [8,2,3,4,5,6,7,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [7,6,5,4,3,2,8,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]] => [6,7,5,4,3,2,8,1] => [[[[[[.,[.,.]],.],.],.],[.,.]],.] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]] => [6,5,7,4,3,2,8,1] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]] => [7,6,4,5,3,2,8,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,[[.,.],[[.,.],.]]]],.]] => [6,7,4,5,3,2,8,1] => [[[[[.,[.,.]],[.,.]],.],[.,.]],.] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,[[[.,.],.],[.,.]]]],.]] => [7,4,5,6,3,2,8,1] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]] => [6,4,5,7,3,2,8,1] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[.,[[.,[.,[[[[.,.],.],.],.]]],.]] => [4,5,6,7,3,2,8,1] => [[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]] => [7,6,5,3,4,2,8,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]] => [7,5,6,3,4,2,8,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[.,.],[[.,[.,.]],.]]],.]] => [6,5,7,3,4,2,8,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]] => [7,6,4,3,5,2,8,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[[.,.],.],[.,[.,.]]]],.]] => [7,6,3,4,5,2,8,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]] => [7,5,4,3,6,2,8,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]] => [7,4,5,3,6,2,8,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[[.,.],[.,.]],[.,.]]],.]] => [7,5,3,4,6,2,8,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[.,[[.,[[[[.,.],.],.],[.,.]]],.]] => [7,3,4,5,6,2,8,1] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]] => [6,5,4,3,7,2,8,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => [6,4,5,3,7,2,8,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => [5,4,6,3,7,2,8,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[.,[[[.,.],.],.]],.]],.]] => [4,5,6,3,7,2,8,1] => [[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]] => [6,5,3,4,7,2,8,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[.,[[.,[[[.,.],[[.,.],.]],.]],.]] => [5,6,3,4,7,2,8,1] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => [6,4,3,5,7,2,8,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[.,[[.,[[[[.,.],.],[.,.]],.]],.]] => [6,3,4,5,7,2,8,1] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[.,[[.,[[[.,[[.,.],.]],.],.]],.]] => [4,5,3,6,7,2,8,1] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[.,[[.,[[[[[.,.],.],.],.],.]],.]] => [3,4,5,6,7,2,8,1] => [[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [7,6,5,4,2,3,8,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],[.,[.,[[.,.],.]]]],.]] => [6,7,5,4,2,3,8,1] => [[[[[.,[.,.]],.],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],[.,[[.,.],[.,.]]]],.]] => [7,5,6,4,2,3,8,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],[.,[[.,[.,.]],.]]],.]] => [6,5,7,4,2,3,8,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],[.,[[[.,.],.],.]]],.]] => [5,6,7,4,2,3,8,1] => [[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],[[.,.],[.,[.,.]]]],.]] => [7,6,4,5,2,3,8,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],[[.,.],[[.,.],.]]],.]] => [6,7,4,5,2,3,8,1] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],[[[.,.],.],[.,.]]],.]] => [7,4,5,6,2,3,8,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],[[.,[.,[.,.]]],.]],.]] => [6,5,4,7,2,3,8,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],[[.,[[.,.],.]],.]],.]] => [5,6,4,7,2,3,8,1] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],[[[.,[.,.]],.],.]],.]] => [5,4,6,7,2,3,8,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],[[[[.,.],.],.],.]],.]] => [4,5,6,7,2,3,8,1] => [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => [7,6,5,3,2,4,8,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,[.,.]],[.,[[.,.],.]]],.]] => [6,7,5,3,2,4,8,1] => [[[[[.,[.,.]],.],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [6,5,7,3,2,4,8,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => [7,6,5,2,3,4,8,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,.],.],[[.,.],[.,.]]],.]] => [7,5,6,2,3,4,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,.],.],[[[.,.],.],.]],.]] => [5,6,7,2,3,4,8,1] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[.,[.,[.,.]]],[[.,.],.]],.]] => [6,7,4,3,2,5,8,1] => [[[[[.,[.,.]],.],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]] => [7,6,4,2,3,5,8,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]] => [7,6,3,2,4,5,8,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,[.,.]],.],[[.,.],.]],.]] => [6,7,3,2,4,5,8,1] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[[.,.],.],.],[.,[.,.]]],.]] => [7,6,2,3,4,5,8,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[.,[[[[[.,.],.],.],[[.,.],.]],.]] => [6,7,2,3,4,5,8,1] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]] => [7,5,4,3,2,6,8,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => [7,4,3,5,2,6,8,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]] => [7,5,4,2,3,6,8,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,.],[[.,.],.]],[.,.]],.]] => [7,4,5,2,3,6,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [7,5,3,2,4,6,8,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[[.,.],.],[.,.]],[.,.]],.]] => [7,5,2,3,4,6,8,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[.,[[[[.,[.,[.,.]]],.],[.,.]],.]] => [7,4,3,2,5,6,8,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[[.,[.,.]],.],.],[.,.]],.]] => [7,3,2,4,5,6,8,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[.,[[[[[[.,.],.],.],.],[.,.]],.]] => [7,2,3,4,5,6,8,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]] => [6,5,4,3,2,7,8,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,[.,[[[.,.],.],.]]],.],.]] => [4,5,6,3,2,7,8,1] => [[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,[[.,.],[.,[.,.]]]],.],.]] => [6,5,3,4,2,7,8,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,[[[.,.],.],[.,.]]],.],.]] => [6,3,4,5,2,7,8,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]] => [5,4,3,6,2,7,8,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,[[[.,[.,.]],.],.]],.],.]] => [4,3,5,6,2,7,8,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,[[[[.,.],.],.],.]],.],.]] => [3,4,5,6,2,7,8,1] => [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]] => [6,5,4,2,3,7,8,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,.],[[.,.],[.,.]]],.],.]] => [6,4,5,2,3,7,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,.],[[[.,.],.],.]],.],.]] => [4,5,6,2,3,7,8,1] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,[.,.]],[.,[.,.]]],.],.]] => [6,5,3,2,4,7,8,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[[.,.],.],[.,[.,.]]],.],.]] => [6,5,2,3,4,7,8,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[.,[[[[[[.,.],.],.],[.,.]],.],.]] => [6,2,3,4,5,7,8,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]] => [5,4,3,2,6,7,8,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,[.,[[.,.],.]]],.],.],.]] => [4,5,3,2,6,7,8,1] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,[[.,.],[.,.]]],.],.],.]] => [5,3,4,2,6,7,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,[[.,[.,.]],.]],.],.],.]] => [4,3,5,2,6,7,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,[[[.,.],.],.]],.],.],.]] => [3,4,5,2,6,7,8,1] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[[.,.],[.,[.,.]]],.],.],.]] => [5,4,2,3,6,7,8,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[.,[[[[[.,.],[[.,.],.]],.],.],.]] => [4,5,2,3,6,7,8,1] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[.,[[[[[.,[.,.]],[.,.]],.],.],.]] => [5,3,2,4,6,7,8,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[.,[[[[[[.,.],.],[.,.]],.],.],.]] => [5,2,3,4,6,7,8,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [4,3,2,5,6,7,8,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[.,[[[[[.,[[.,.],.]],.],.],.],.]] => [3,4,2,5,6,7,8,1] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[.,[[[[[[.,.],[.,.]],.],.],.],.]] => [4,2,3,5,6,7,8,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[.,[[[[[[.,[.,.]],.],.],.],.],.]] => [3,2,4,5,6,7,8,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[.,[[[[[[[.,.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,1] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,4,3,1,2] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [7,8,6,5,4,3,1,2] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,3,1,2] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [7,6,8,5,4,3,1,2] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [6,7,8,5,4,3,1,2] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,3,1,2] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [7,8,5,6,4,3,1,2] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [8,6,5,7,4,3,1,2] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [7,6,5,8,4,3,1,2] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]] => [6,7,5,8,4,3,1,2] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [7,5,6,8,4,3,1,2] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => [6,5,7,8,4,3,1,2] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [5,6,7,8,4,3,1,2] => [[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,3,1,2] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [7,8,6,4,5,3,1,2] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [8,6,7,4,5,3,1,2] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [6,7,8,4,5,3,1,2] => [[[[.,[.,[.,.]]],[.,.]],.],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [8,7,5,4,6,3,1,2] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [7,8,4,5,6,3,1,2] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,.],[.,[[.,[[.,.],.]],[.,.]]]] => [8,5,6,4,7,3,1,2] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [8,6,4,5,7,3,1,2] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[.,[.,.]],.],[.,.]]]] => [8,5,4,6,7,3,1,2] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [7,6,5,4,8,3,1,2] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[.,[[.,.],[.,.]]],.]]] => [7,5,6,4,8,3,1,2] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[.,[[.,[.,.]],.]],.]]] => [6,5,7,4,8,3,1,2] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [7,6,4,5,8,3,1,2] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [6,7,4,5,8,3,1,2] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]] => [6,5,4,7,8,3,1,2] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[.,[[.,.],.]],.],.]]] => [5,6,4,7,8,3,1,2] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[[.,[.,.]],.],.],.]]] => [5,4,6,7,8,3,1,2] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[[[.,.],.],.],.],.]]] => [4,5,6,7,8,3,1,2] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,3,4,1,2] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [7,8,6,5,3,4,1,2] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [7,6,8,5,3,4,1,2] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [6,7,8,5,3,4,1,2] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [8,7,5,6,3,4,1,2] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [7,8,5,6,3,4,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [8,6,5,7,3,4,1,2] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [8,5,6,7,3,4,1,2] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [7,6,5,8,3,4,1,2] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [6,7,5,8,3,4,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [7,5,6,8,3,4,1,2] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [6,5,7,8,3,4,1,2] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[[[[.,.],.],.],.]]] => [5,6,7,8,3,4,1,2] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [6,7,8,4,3,5,1,2] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [8,7,6,3,4,5,1,2] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [7,8,6,3,4,5,1,2] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [8,6,7,3,4,5,1,2] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [7,8,5,4,3,6,1,2] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [8,7,4,5,3,6,1,2] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [7,8,4,5,3,6,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [7,8,5,3,4,6,1,2] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [8,7,4,3,5,6,1,2] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [7,8,4,3,5,6,1,2] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [8,7,3,4,5,6,1,2] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,.],[[[[.,.],.],.],[[.,.],.]]] => [7,8,3,4,5,6,1,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [8,6,5,4,3,7,1,2] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]] => [8,5,4,3,6,7,1,2] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [8,5,3,4,6,7,1,2] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [8,4,3,5,6,7,1,2] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,.],[[[[[.,.],.],.],.],[.,.]]] => [8,3,4,5,6,7,1,2] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [7,6,5,4,3,8,1,2] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[.,[[.,.],[.,.]]]],.]] => [7,5,6,4,3,8,1,2] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[.,[[[.,.],.],.]]],.]] => [5,6,7,4,3,8,1,2] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [6,7,4,5,3,8,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[[.,[[.,.],.]],.]],.]] => [5,6,4,7,3,8,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[[[.,.],[.,.]],.]],.]] => [6,4,5,7,3,8,1,2] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[[[[.,.],.],.],.]],.]] => [4,5,6,7,3,8,1,2] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [7,6,5,3,4,8,1,2] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,[.,.]],[.,[.,.]]],.]] => [7,6,4,3,5,8,1,2] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [7,6,3,4,5,8,1,2] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,.],[[[.,[.,[.,.]]],[.,.]],.]] => [7,5,4,3,6,8,1,2] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [7,5,3,4,6,8,1,2] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,.],[[[[[.,.],.],.],[.,.]],.]] => [7,3,4,5,6,8,1,2] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => [6,5,4,3,7,8,1,2] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,[.,[[.,.],.]]],.],.]] => [5,6,4,3,7,8,1,2] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,[[.,[.,.]],.]],.],.]] => [5,4,6,3,7,8,1,2] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,[[[.,.],.],.]],.],.]] => [4,5,6,3,7,8,1,2] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[[.,.],[[.,.],.]],.],.]] => [5,6,3,4,7,8,1,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [6,4,3,5,7,8,1,2] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,.],[[[[[.,.],.],[.,.]],.],.]] => [6,3,4,5,7,8,1,2] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[.,.],[[[[.,[.,[.,.]]],.],.],.]] => [5,4,3,6,7,8,1,2] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,.],[[[[.,[[.,.],.]],.],.],.]] => [4,5,3,6,7,8,1,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,.],[[[[[.,.],[.,.]],.],.],.]] => [5,3,4,6,7,8,1,2] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[.,.],[[[[[.,[.,.]],.],.],.],.]] => [4,3,5,6,7,8,1,2] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[.,.],[[[[[[.,.],.],.],.],.],.]] => [3,4,5,6,7,8,1,2] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [8,7,6,5,4,2,1,3] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [7,8,6,5,4,2,1,3] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [8,6,7,5,4,2,1,3] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [7,6,8,5,4,2,1,3] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [6,7,8,5,4,2,1,3] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [8,7,5,6,4,2,1,3] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [7,8,5,6,4,2,1,3] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [7,6,5,8,4,2,1,3] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [6,7,5,8,4,2,1,3] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [7,5,6,8,4,2,1,3] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [6,5,7,8,4,2,1,3] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [5,6,7,8,4,2,1,3] => [[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [8,7,6,4,5,2,1,3] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [7,6,8,4,5,2,1,3] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [8,4,5,6,7,2,1,3] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [7,6,5,4,8,2,1,3] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [6,7,5,4,8,2,1,3] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [6,5,7,4,8,2,1,3] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[.,[[[.,.],.],.]],.]] => [5,6,7,4,8,2,1,3] => [[[[.,[.,[.,.]]],[.,.]],.],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [7,6,4,5,8,2,1,3] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [7,5,4,6,8,2,1,3] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [7,4,5,6,8,2,1,3] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [5,4,6,7,8,2,1,3] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[[[[.,.],.],.],.],.]] => [4,5,6,7,8,2,1,3] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [8,7,6,5,4,1,2,3] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [7,8,6,5,4,1,2,3] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [7,6,8,5,4,1,2,3] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [6,7,8,5,4,1,2,3] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [7,8,5,6,4,1,2,3] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [8,6,5,7,4,1,2,3] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [8,5,6,7,4,1,2,3] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [7,6,5,8,4,1,2,3] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[[.,[[.,.],.]],.]]] => [6,7,5,8,4,1,2,3] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [7,5,6,8,4,1,2,3] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[[[.,[.,.]],.],.]]] => [6,5,7,8,4,1,2,3] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[[[[.,.],.],.],.]]] => [5,6,7,8,4,1,2,3] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [8,7,6,4,5,1,2,3] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [8,6,7,4,5,1,2,3] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,.],[[[.,.],.],.]]] => [6,7,8,4,5,1,2,3] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [8,7,5,4,6,1,2,3] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [7,8,5,4,6,1,2,3] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [8,7,4,5,6,1,2,3] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[.,.],.],[[.,.],.]]] => [7,8,4,5,6,1,2,3] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [8,5,6,4,7,1,2,3] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [8,6,4,5,7,1,2,3] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[[.,.],.],.],[.,.]]] => [8,4,5,6,7,1,2,3] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [7,6,5,4,8,1,2,3] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,[.,[[.,.],.]]],.]] => [6,7,5,4,8,1,2,3] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,[[.,.],[.,.]]],.]] => [7,5,6,4,8,1,2,3] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,[[.,[.,.]],.]],.]] => [6,5,7,4,8,1,2,3] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,[[[.,.],.],.]],.]] => [5,6,7,4,8,1,2,3] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [7,6,4,5,8,1,2,3] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[.,.],[[.,.],.]],.]] => [6,7,4,5,8,1,2,3] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [7,5,4,6,8,1,2,3] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[[.,.],.],[.,.]],.]] => [7,4,5,6,8,1,2,3] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [6,5,4,7,8,1,2,3] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[.,[[.,.],.]],.],.]] => [5,6,4,7,8,1,2,3] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[[.,.],[.,.]],.],.]] => [6,4,5,7,8,1,2,3] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[[.,[.,.]],.],.],.]] => [5,4,6,7,8,1,2,3] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[[[.,.],.],.],.],.]] => [4,5,6,7,8,1,2,3] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [8,7,6,5,3,2,1,4] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [7,8,6,5,3,2,1,4] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [8,6,7,5,3,2,1,4] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [7,6,8,5,3,2,1,4] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [6,7,8,5,3,2,1,4] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [8,7,5,6,3,2,1,4] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [7,8,5,6,3,2,1,4] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [8,6,5,7,3,2,1,4] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [8,5,6,7,3,2,1,4] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [7,6,5,8,3,2,1,4] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [6,7,5,8,3,2,1,4] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [7,5,6,8,3,2,1,4] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]] => [6,5,7,8,3,2,1,4] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [5,6,7,8,3,2,1,4] => [[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [8,7,6,5,2,3,1,4] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],.]],[.,[.,[[.,.],.]]]] => [7,8,6,5,2,3,1,4] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]] => [8,6,7,5,2,3,1,4] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]] => [7,6,8,5,2,3,1,4] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],.]],[.,[[[.,.],.],.]]] => [6,7,8,5,2,3,1,4] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],.]],[[.,.],[.,[.,.]]]] => [8,7,5,6,2,3,1,4] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],.]],[[.,.],[[.,.],.]]] => [7,8,5,6,2,3,1,4] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]] => [8,6,5,7,2,3,1,4] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],.]],[[[.,.],.],[.,.]]] => [8,5,6,7,2,3,1,4] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]] => [7,6,5,8,2,3,1,4] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],.]],[[.,[[.,.],.]],.]] => [6,7,5,8,2,3,1,4] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],.]],[[[.,.],[.,.]],.]] => [7,5,6,8,2,3,1,4] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],.]],[[[.,[.,.]],.],.]] => [6,5,7,8,2,3,1,4] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],.]],[[[[.,.],.],.],.]] => [5,6,7,8,2,3,1,4] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [8,7,6,5,3,1,2,4] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [7,8,6,5,3,1,2,4] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [8,6,7,5,3,1,2,4] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [7,6,8,5,3,1,2,4] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [8,7,5,6,3,1,2,4] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [7,8,5,6,3,1,2,4] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [8,6,5,7,3,1,2,4] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [7,6,5,8,3,1,2,4] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [6,7,5,8,3,1,2,4] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [7,5,6,8,3,1,2,4] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [6,5,7,8,3,1,2,4] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,.]],[[[[.,.],.],.],.]] => [5,6,7,8,3,1,2,4] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [8,7,6,5,2,1,3,4] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [7,8,6,5,2,1,3,4] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[.,[[.,[.,.]],.]]] => [7,6,8,5,2,1,3,4] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [6,7,8,5,2,1,3,4] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [8,7,5,6,2,1,3,4] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [7,8,5,6,2,1,3,4] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [8,6,5,7,2,1,3,4] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [8,5,6,7,2,1,3,4] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[[.,[.,[.,.]]],.]] => [7,6,5,8,2,1,3,4] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[[.,[[.,.],.]],.]] => [6,7,5,8,2,1,3,4] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [7,5,6,8,2,1,3,4] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [6,5,7,8,2,1,3,4] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[[[[.,.],.],.],.]] => [5,6,7,8,2,1,3,4] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [8,7,6,5,1,2,3,4] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [7,8,6,5,1,2,3,4] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [8,6,7,5,1,2,3,4] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [7,6,8,5,1,2,3,4] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[.,[[[.,.],.],.]]] => [6,7,8,5,1,2,3,4] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [8,7,5,6,1,2,3,4] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[[.,.],[[.,.],.]]] => [7,8,5,6,1,2,3,4] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [8,6,5,7,1,2,3,4] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[[[.,.],.],[.,.]]] => [8,5,6,7,1,2,3,4] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [7,6,5,8,1,2,3,4] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[[.,[[.,.],.]],.]] => [6,7,5,8,1,2,3,4] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[[[.,.],[.,.]],.]] => [7,5,6,8,1,2,3,4] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[[[.,[.,.]],.],.]] => [6,5,7,8,1,2,3,4] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[[[[.,.],.],.],.]] => [5,6,7,8,1,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [8,7,6,4,3,2,1,5] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [7,8,6,4,3,2,1,5] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [8,6,7,4,3,2,1,5] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [7,6,8,4,3,2,1,5] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [6,7,8,4,3,2,1,5] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [8,7,6,3,4,2,1,5] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => [7,8,6,3,4,2,1,5] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[.,.],.]]],[[[.,.],.],.]] => [6,7,8,3,4,2,1,5] => [[[[.,[.,[.,.]]],[.,.]],.],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [8,7,6,4,2,3,1,5] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[.,.]]],[[[.,.],.],.]] => [6,7,8,4,2,3,1,5] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [8,7,6,3,2,4,1,5] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [8,6,7,3,2,4,1,5] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[.,.]],.]],[[[.,.],.],.]] => [6,7,8,3,2,4,1,5] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]] => [8,7,6,2,3,4,1,5] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,.],.],.]],[[.,.],[.,.]]] => [8,6,7,2,3,4,1,5] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,.],.],.]],[[.,[.,.]],.]] => [7,6,8,2,3,4,1,5] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,.],.],.]],[[[.,.],.],.]] => [6,7,8,2,3,4,1,5] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [8,7,6,4,3,1,2,5] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [6,7,8,4,3,1,2,5] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [8,7,6,3,4,1,2,5] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [7,8,6,3,4,1,2,5] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [8,6,7,3,4,1,2,5] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],[[.,.],.]],[[[.,.],.],.]] => [6,7,8,3,4,1,2,5] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [8,7,6,4,2,1,3,5] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [7,8,6,4,2,1,3,5] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [8,6,7,4,2,1,3,5] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [6,7,8,4,2,1,3,5] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [8,7,6,4,1,2,3,5] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [7,8,6,4,1,2,3,5] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [7,6,8,4,1,2,3,5] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[.,.]],[[[.,.],.],.]] => [6,7,8,4,1,2,3,5] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [8,7,6,3,2,1,4,5] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [7,8,6,3,2,1,4,5] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [8,6,7,3,2,1,4,5] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [7,6,8,3,2,1,4,5] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [6,7,8,3,2,1,4,5] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [8,7,6,2,3,1,4,5] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],.],[.,[[.,.],.]]] => [7,8,6,2,3,1,4,5] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],.],[[.,.],[.,.]]] => [8,6,7,2,3,1,4,5] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],.],[[.,[.,.]],.]] => [7,6,8,2,3,1,4,5] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],.],[[[.,.],.],.]] => [6,7,8,2,3,1,4,5] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [8,7,6,3,1,2,4,5] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [7,8,6,3,1,2,4,5] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [8,6,7,3,1,2,4,5] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [7,6,8,3,1,2,4,5] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],[.,.]],.],[[[.,.],.],.]] => [6,7,8,3,1,2,4,5] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [8,7,6,2,1,3,4,5] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [7,8,6,2,1,3,4,5] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [8,6,7,2,1,3,4,5] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],.],.],[[[.,.],.],.]] => [6,7,8,2,1,3,4,5] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [8,7,6,1,2,3,4,5] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,.],.],.],.],[.,[[.,.],.]]] => [7,8,6,1,2,3,4,5] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,.],.],.],.],[[.,.],[.,.]]] => [8,6,7,1,2,3,4,5] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,.],.],.],.],[[.,[.,.]],.]] => [7,6,8,1,2,3,4,5] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,.],.],.],.],[[[.,.],.],.]] => [6,7,8,1,2,3,4,5] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [8,7,5,4,3,2,1,6] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [7,8,5,4,3,2,1,6] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]] => [8,7,4,5,3,2,1,6] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[[.,.],.]]]],[[.,.],.]] => [7,8,4,5,3,2,1,6] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => [8,7,5,3,4,2,1,6] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]] => [8,7,3,4,5,2,1,6] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,[.,[[[.,.],.],.]]],[[.,.],.]] => [7,8,3,4,5,2,1,6] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]] => [8,7,4,5,2,3,1,6] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[[.,.],.]]],[[.,.],.]] => [7,8,4,5,2,3,1,6] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [8,7,5,3,2,4,1,6] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[[.,.],.],[.,.]]],[[.,.],.]] => [7,8,5,2,3,4,1,6] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]] => [8,7,4,3,2,5,1,6] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]] => [7,8,4,3,2,5,1,6] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]] => [8,7,3,4,2,5,1,6] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,[[.,.],.]],.]],[[.,.],.]] => [7,8,3,4,2,5,1,6] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[[[.,.],.],.],.]],[.,[.,.]]] => [8,7,2,3,4,5,1,6] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,[[[[.,.],.],.],.]],[[.,.],.]] => [7,8,2,3,4,5,1,6] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [8,7,5,4,3,1,2,6] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [7,8,5,4,3,1,2,6] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [8,7,5,3,4,1,2,6] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [8,7,3,4,5,1,2,6] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],[[[.,.],.],.]],[[.,.],.]] => [7,8,3,4,5,1,2,6] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [7,8,5,4,2,1,3,6] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [8,7,5,4,1,2,3,6] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [7,8,5,4,1,2,3,6] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[[.,.],.]],[[.,.],.]] => [7,8,4,5,1,2,3,6] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [8,7,5,3,2,1,4,6] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [7,8,5,3,2,1,4,6] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [8,7,5,3,1,2,4,6] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [7,8,5,3,1,2,4,6] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [8,7,5,2,1,3,4,6] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [7,8,5,2,1,3,4,6] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [8,7,5,1,2,3,4,6] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,.],.],.],[.,.]],[[.,.],.]] => [7,8,5,1,2,3,4,6] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [8,7,4,3,2,1,5,6] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [7,8,4,3,2,1,5,6] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]] => [8,7,3,4,2,1,5,6] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,[[.,.],.]]],.],[[.,.],.]] => [7,8,3,4,2,1,5,6] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[[.,.],[.,.]]],.],[[.,.],.]] => [7,8,4,2,3,1,5,6] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]] => [8,7,3,2,4,1,5,6] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,[.,.]],.]],.],[[.,.],.]] => [7,8,3,2,4,1,5,6] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[[.,.],.],.]],.],[.,[.,.]]] => [8,7,2,3,4,1,5,6] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,[[[.,.],.],.]],.],[[.,.],.]] => [7,8,2,3,4,1,5,6] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [7,8,4,3,1,2,5,6] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [8,7,3,4,1,2,5,6] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],[[.,.],.]],.],[[.,.],.]] => [7,8,3,4,1,2,5,6] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [8,7,4,2,1,3,5,6] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [7,8,4,2,1,3,5,6] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [8,7,4,1,2,3,5,6] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [8,7,3,2,1,4,5,6] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,[.,.]]],.],.],[[.,.],.]] => [7,8,3,2,1,4,5,6] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[[.,.],.]],.],.],[.,[.,.]]] => [8,7,2,3,1,4,5,6] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,[[.,.],.]],.],.],[[.,.],.]] => [7,8,2,3,1,4,5,6] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[[.,.],[.,.]],.],.],[[.,.],.]] => [7,8,3,1,2,4,5,6] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [8,7,2,1,3,4,5,6] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,[.,.]],.],.],.],[[.,.],.]] => [7,8,2,1,3,4,5,6] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[[.,.],.],.],.],.],[.,[.,.]]] => [8,7,1,2,3,4,5,6] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[[[.,.],.],.],.],.],[[.,.],.]] => [7,8,1,2,3,4,5,6] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [8,6,5,4,3,2,1,7] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]] => [8,5,6,4,3,2,1,7] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]] => [8,6,4,5,3,2,1,7] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => [8,4,5,6,3,2,1,7] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]] => [8,6,5,3,4,2,1,7] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]] => [8,5,6,3,4,2,1,7] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]] => [8,4,5,3,6,2,1,7] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]] => [8,4,3,5,6,2,1,7] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,[.,[[[[.,.],.],.],.]]],[.,.]] => [8,3,4,5,6,2,1,7] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [8,6,5,4,2,3,1,7] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[.,[[.,.],.]]]],[.,.]] => [8,5,6,4,2,3,1,7] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[[[.,.],.],.]]],[.,.]] => [8,4,5,6,2,3,1,7] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [8,6,5,3,2,4,1,7] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]] => [8,6,5,2,3,4,1,7] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,.],.],[[.,.],.]]],[.,.]] => [8,5,6,2,3,4,1,7] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]] => [8,6,4,2,3,5,1,7] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,[.,.]],.],[.,.]]],[.,.]] => [8,6,3,2,4,5,1,7] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]] => [8,5,4,3,2,6,1,7] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => [8,4,3,5,2,6,1,7] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[[.,.],[.,[.,.]]],.]],[.,.]] => [8,5,4,2,3,6,1,7] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,.],[[.,.],.]],.]],[.,.]] => [8,4,5,2,3,6,1,7] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [8,5,3,2,4,6,1,7] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[[.,.],.],[.,.]],.]],[.,.]] => [8,5,2,3,4,6,1,7] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,[[[[.,[.,.]],.],.],.]],[.,.]] => [8,3,2,4,5,6,1,7] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,[[[[[.,.],.],.],.],.]],[.,.]] => [8,2,3,4,5,6,1,7] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [8,6,5,4,3,1,2,7] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,[[.,.],[.,.]]]],[.,.]] => [8,6,4,5,3,1,2,7] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [8,6,5,3,4,1,2,7] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [8,5,6,3,4,1,2,7] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],[[.,[.,[.,.]]],.]],[.,.]] => [8,5,4,3,6,1,2,7] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [8,5,3,4,6,1,2,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],[[[.,[.,.]],.],.]],[.,.]] => [8,4,3,5,6,1,2,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],[[[[.,.],.],.],.]],[.,.]] => [8,3,4,5,6,1,2,7] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [8,6,5,4,2,1,3,7] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [8,5,6,4,2,1,3,7] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [8,4,5,6,2,1,3,7] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [8,6,5,4,1,2,3,7] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [8,5,6,4,1,2,3,7] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [8,6,4,5,1,2,3,7] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[[[.,.],.],.]],[.,.]] => [8,4,5,6,1,2,3,7] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [8,6,5,3,2,1,4,7] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [8,5,6,3,2,1,4,7] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]] => [8,6,5,2,3,1,4,7] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],[[.,.],.]],[.,.]] => [8,5,6,2,3,1,4,7] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [8,5,6,3,1,2,4,7] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [8,6,5,2,1,3,4,7] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [8,5,6,2,1,3,4,7] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [8,6,5,1,2,3,4,7] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,.],.],.],[[.,.],.]],[.,.]] => [8,5,6,1,2,3,4,7] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [8,6,4,3,2,1,5,7] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]] => [8,6,3,4,2,1,5,7] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]] => [8,6,4,2,3,1,5,7] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [8,6,3,2,4,1,5,7] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[[.,.],.],.]],[.,.]],[.,.]] => [8,6,2,3,4,1,5,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [8,6,4,3,1,2,5,7] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [8,6,3,4,1,2,5,7] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [8,6,4,2,1,3,5,7] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [8,6,4,1,2,3,5,7] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [8,6,3,2,1,4,5,7] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[[[.,.],.],.],.],[.,.]],[.,.]] => [8,6,1,2,3,4,5,7] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => [8,5,4,3,2,1,6,7] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[.,[[.,.],.]]]],.],[.,.]] => [8,4,5,3,2,1,6,7] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[[.,[.,.]],.]]],.],[.,.]] => [8,4,3,5,2,1,6,7] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,[[[.,.],.],.]]],.],[.,.]] => [8,3,4,5,2,1,6,7] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,[[.,.],[[.,.],.]]],.],[.,.]] => [8,4,5,2,3,1,6,7] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[[.,.],.],[.,.]]],.],[.,.]] => [8,5,2,3,4,1,6,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,[[[.,.],[.,.]],.]],.],[.,.]] => [8,4,2,3,5,1,6,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,[[[[.,.],.],.],.]],.],[.,.]] => [8,2,3,4,5,1,6,7] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [8,5,3,4,1,2,6,7] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],[[[.,.],.],.]],.],[.,.]] => [8,3,4,5,1,2,6,7] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [8,5,4,2,1,3,6,7] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [8,5,4,1,2,3,6,7] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,.],.],[[.,.],.]],.],[.,.]] => [8,4,5,1,2,3,6,7] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[[.,[.,[.,.]]],[.,.]],.],[.,.]] => [8,5,3,2,1,4,6,7] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [8,5,3,1,2,4,6,7] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [8,5,2,1,3,4,6,7] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[[.,.],.],.],[.,.]],.],[.,.]] => [8,5,1,2,3,4,6,7] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [8,4,3,2,1,5,6,7] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,[[.,.],.]]],.],.],[.,.]] => [8,3,4,2,1,5,6,7] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[[.,.],[.,.]]],.],.],[.,.]] => [8,4,2,3,1,5,6,7] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,[[[.,.],.],.]],.],.],[.,.]] => [8,2,3,4,1,5,6,7] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[[[.,.],[[.,.],.]],.],.],[.,.]] => [8,3,4,1,2,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [8,4,2,1,3,5,6,7] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[[.,.],.],[.,.]],.],.],[.,.]] => [8,4,1,2,3,5,6,7] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [8,3,2,1,4,5,6,7] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,[[.,.],.]],.],.],.],[.,.]] => [8,2,3,1,4,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[[[[.,.],[.,.]],.],.],.],[.,.]] => [8,3,1,2,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[[[.,[.,.]],.],.],.],.],[.,.]] => [8,2,1,3,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[[[[.,.],.],.],.],.],.],[.,.]] => [8,1,2,3,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [7,6,5,4,3,2,1,8] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => [6,7,5,4,3,2,1,8] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => [7,5,6,4,3,2,1,8] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => [6,5,7,4,3,2,1,8] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => [5,6,7,4,3,2,1,8] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => [7,6,4,5,3,2,1,8] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.] => [6,7,4,5,3,2,1,8] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.] => [7,5,4,6,3,2,1,8] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.] => [7,4,5,6,3,2,1,8] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [6,5,4,7,3,2,1,8] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[[.,[[.,.],.]],.]]]],.] => [5,6,4,7,3,2,1,8] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[[[.,[.,.]],.],.]]]],.] => [5,4,6,7,3,2,1,8] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[[[[.,.],.],.],.]]]],.] => [4,5,6,7,3,2,1,8] => [[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.] => [7,6,5,3,4,2,1,8] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[.,.],[.,[[.,.],.]]]]],.] => [6,7,5,3,4,2,1,8] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.] => [7,5,6,3,4,2,1,8] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[.,.],[[.,[.,.]],.]]]],.] => [6,5,7,3,4,2,1,8] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[.,.],[[[.,.],.],.]]]],.] => [5,6,7,3,4,2,1,8] => [[[[.,[.,[.,.]]],[.,.]],.],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.] => [7,6,4,3,5,2,1,8] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[.,[.,.]],[[.,.],.]]]],.] => [6,7,4,3,5,2,1,8] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.] => [7,6,3,4,5,2,1,8] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.] => [7,5,4,3,6,2,1,8] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.] => [6,5,4,3,7,2,1,8] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[.,[.,[[.,.],.]]],.]]],.] => [5,6,4,3,7,2,1,8] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.] => [5,4,6,3,7,2,1,8] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.] => [5,4,3,6,7,2,1,8] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,[.,[[[[[.,.],.],.],.],.]]],.] => [3,4,5,6,7,2,1,8] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.] => [7,6,5,4,2,3,1,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.] => [6,7,5,4,2,3,1,8] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[.,[[.,.],[.,.]]]]],.] => [7,5,6,4,2,3,1,8] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[.,[[[.,.],.],.]]]],.] => [5,6,7,4,2,3,1,8] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.] => [7,6,4,5,2,3,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[[.,.],[[.,.],.]]]],.] => [6,7,4,5,2,3,1,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[[.,[.,.]],[.,.]]]],.] => [7,5,4,6,2,3,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[[.,[.,[.,.]]],.]]],.] => [6,5,4,7,2,3,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[[.,[[.,.],.]],.]]],.] => [5,6,4,7,2,3,1,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[[[.,[.,.]],.],.]]],.] => [5,4,6,7,2,3,1,8] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[[[[.,.],.],.],.]]],.] => [4,5,6,7,2,3,1,8] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [7,6,5,3,2,4,1,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.] => [6,5,7,3,2,4,1,8] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[.,.]],[[[.,.],.],.]]],.] => [5,6,7,3,2,4,1,8] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.] => [7,6,5,2,3,4,1,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,.],.],[.,[[.,.],.]]]],.] => [6,7,5,2,3,4,1,8] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,.],.],[[.,.],[.,.]]]],.] => [7,5,6,2,3,4,1,8] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,.],.],[[.,[.,.]],.]]],.] => [6,5,7,2,3,4,1,8] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,.],.],[[[.,.],.],.]]],.] => [5,6,7,2,3,4,1,8] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[.,[.,[.,.]]],[[.,.],.]]],.] => [6,7,4,3,2,5,1,8] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[[.,.],.]],[[.,.],.]]],.] => [6,7,3,4,2,5,1,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[[.,.],[.,.]],[.,[.,.]]]],.] => [7,6,4,2,3,5,1,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,.],[.,.]],[[.,.],.]]],.] => [6,7,4,2,3,5,1,8] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,[.,.]],.],[.,[.,.]]]],.] => [7,6,3,2,4,5,1,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,[.,.]],.],[[.,.],.]]],.] => [6,7,3,2,4,5,1,8] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[[.,.],.],.],[.,[.,.]]]],.] => [7,6,2,3,4,5,1,8] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,[[[[.,.],.],.],[[.,.],.]]],.] => [6,7,2,3,4,5,1,8] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.] => [7,5,4,3,2,6,1,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.] => [7,4,5,3,2,6,1,8] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.] => [7,5,3,4,2,6,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.] => [7,4,3,5,2,6,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => [7,5,3,2,4,6,1,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[[.,.],[.,.]],.],[.,.]]],.] => [7,4,2,3,5,6,1,8] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,[[[[[.,.],.],.],.],[.,.]]],.] => [7,2,3,4,5,6,1,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.] => [6,5,4,3,2,7,1,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[.,[.,[[.,.],.]]]],.]],.] => [5,6,4,3,2,7,1,8] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[.,[[.,.],[[.,.],.]]],.]],.] => [5,6,3,4,2,7,1,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,[[[.,.],.],[.,.]]],.]],.] => [6,3,4,5,2,7,1,8] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.] => [5,4,3,6,2,7,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,[[.,[[.,.],.]],.]],.]],.] => [4,5,3,6,2,7,1,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,[[[.,.],[.,.]],.]],.]],.] => [5,3,4,6,2,7,1,8] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,[[[.,[.,.]],.],.]],.]],.] => [4,3,5,6,2,7,1,8] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,[[[[.,.],.],.],.]],.]],.] => [3,4,5,6,2,7,1,8] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[[.,[[[.,.],[[.,[.,.]],.]],.]],.] => [5,4,6,2,3,7,1,8] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.] => [6,5,3,2,4,7,1,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[[.,.],[.,.]],[.,.]],.]],.] => [6,4,2,3,5,7,1,8] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.] => [5,4,3,2,6,7,1,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,[[[[.,.],[[.,.],.]],.],.]],.] => [4,5,2,3,6,7,1,8] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,[[[[[.,.],.],[.,.]],.],.]],.] => [5,2,3,4,6,7,1,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[.,[[[[.,[.,[.,.]]],.],.],.]],.] => [4,3,2,5,6,7,1,8] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,[[[[.,[[.,.],.]],.],.],.]],.] => [3,4,2,5,6,7,1,8] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,[[[[[.,.],[.,.]],.],.],.]],.] => [4,2,3,5,6,7,1,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[.,[[[[[.,[.,.]],.],.],.],.]],.] => [3,2,4,5,6,7,1,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[.,[[[[[[.,.],.],.],.],.],.]],.] => [2,3,4,5,6,7,1,8] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [7,6,5,4,3,1,2,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,[.,[.,[[.,.],.]]]]],.] => [6,7,5,4,3,1,2,8] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,[.,[[.,.],[.,.]]]]],.] => [7,5,6,4,3,1,2,8] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,[[.,.],[.,[.,.]]]]],.] => [7,6,4,5,3,1,2,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,[[[.,[.,.]],.],.]]],.] => [5,4,6,7,3,1,2,8] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,[[[[.,.],.],.],.]]],.] => [4,5,6,7,3,1,2,8] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[[[.,.],[[.,.],[.,[.,[.,.]]]]],.] => [7,6,5,3,4,1,2,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],[[.,.],[[.,[.,.]],.]]],.] => [6,5,7,3,4,1,2,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],[[[.,.],.],[[.,.],.]]],.] => [6,7,3,4,5,1,2,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],[[.,[.,[.,[.,.]]]],.]],.] => [6,5,4,3,7,1,2,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],[[[.,.],[[.,.],.]],.]],.] => [5,6,3,4,7,1,2,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],[[[[.,.],.],[.,.]],.]],.] => [6,3,4,5,7,1,2,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[[.,.],[[[[.,[.,.]],.],.],.]],.] => [4,3,5,6,7,1,2,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[[.,.],[[[[[.,.],.],.],.],.]],.] => [3,4,5,6,7,1,2,8] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [7,6,5,4,2,1,3,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],[.,[[.,[.,.]],.]]],.] => [6,5,7,4,2,1,3,8] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],[[.,.],[.,[.,.]]]],.] => [7,6,4,5,2,1,3,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [7,5,4,6,2,1,3,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],[[[.,[.,.]],.],.]],.] => [5,4,6,7,2,1,3,8] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],[[[[.,.],.],.],.]],.] => [4,5,6,7,2,1,3,8] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [7,6,5,4,1,2,3,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[.,[[[.,.],.],.]]],.] => [5,6,7,4,1,2,3,8] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[[[.,.],.],[.,.]]],.] => [7,4,5,6,1,2,3,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[[.,[[.,.],.]],.]],.] => [5,6,4,7,1,2,3,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[[[.,[.,.]],.],.]],.] => [5,4,6,7,1,2,3,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[[[[.,.],.],.],.]],.] => [4,5,6,7,1,2,3,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [7,6,5,3,2,1,4,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],[.,[.,[.,.]]]],.] => [7,6,5,2,3,1,4,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],[.,[[.,.],.]]],.] => [6,7,5,2,3,1,4,8] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],[[.,.],[.,.]]],.] => [7,5,6,2,3,1,4,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],[[.,[.,.]],.]],.] => [6,5,7,2,3,1,4,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],[[[.,.],.],.]],.] => [5,6,7,2,3,1,4,8] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[[[[.,.],[.,.]],[[[.,.],.],.]],.] => [5,6,7,3,1,2,4,8] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => [7,6,5,2,1,3,4,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [7,5,6,2,1,3,4,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],.],[[[.,.],.],.]],.] => [5,6,7,2,1,3,4,8] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [7,6,5,1,2,3,4,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,.],.],.],[.,[[.,.],.]]],.] => [6,7,5,1,2,3,4,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,.],.],.],[[.,.],[.,.]]],.] => [7,5,6,1,2,3,4,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,.],.],.],[[.,[.,.]],.]],.] => [6,5,7,1,2,3,4,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,.],.],.],[[[.,.],.],.]],.] => [5,6,7,1,2,3,4,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [7,6,4,3,2,1,5,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.] => [6,7,4,3,2,1,5,8] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[[.,.],.]]],[.,[.,.]]],.] => [7,6,3,4,2,1,5,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,[[.,.],.]]],[[.,.],.]],.] => [6,7,3,4,2,1,5,8] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[[.,.],[.,.]]],[.,[.,.]]],.] => [7,6,4,2,3,1,5,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,.],[.,.]]],[[.,.],.]],.] => [6,7,4,2,3,1,5,8] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.] => [7,6,3,2,4,1,5,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[[.,.],.],.]],[.,[.,.]]],.] => [7,6,2,3,4,1,5,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,[[[.,.],.],.]],[[.,.],.]],.] => [6,7,2,3,4,1,5,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [7,6,4,3,1,2,5,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [7,6,4,2,1,3,5,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [7,6,3,2,1,4,5,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,[.,.]]],.],[[.,.],.]],.] => [6,7,3,2,1,4,5,8] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[[.,.],.]],.],[.,[.,.]]],.] => [7,6,2,3,1,4,5,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,[[.,.],.]],.],[[.,.],.]],.] => [6,7,2,3,1,4,5,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[[.,.],[.,.]],.],[[.,.],.]],.] => [6,7,3,1,2,4,5,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[[.,.],.],.],.],[.,[.,.]]],.] => [7,6,1,2,3,4,5,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[[[.,.],.],.],.],[[.,.],.]],.] => [6,7,1,2,3,4,5,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] => [7,5,4,3,2,1,6,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[.,[[.,.],.]]]],[.,.]],.] => [7,4,5,3,2,1,6,8] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[[.,[.,.]],.]]],[.,.]],.] => [7,4,3,5,2,1,6,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,[[[.,.],.],.]]],[.,.]],.] => [7,3,4,5,2,1,6,8] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,[[.,.],[.,[.,.]]]],[.,.]],.] => [7,5,4,2,3,1,6,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.] => [7,5,3,2,4,1,6,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[[.,.],.],[.,.]]],[.,.]],.] => [7,5,2,3,4,1,6,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,[[[.,.],[.,.]],.]],[.,.]],.] => [7,4,2,3,5,1,6,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,[[[[.,.],.],.],.]],[.,.]],.] => [7,2,3,4,5,1,6,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [7,5,4,3,1,2,6,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[[.,.],.],[[.,.],.]],[.,.]],.] => [7,4,5,1,2,3,6,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [7,5,3,2,1,4,6,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[[.,.],.]],[.,.]],[.,.]],.] => [7,5,2,3,1,4,6,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [7,5,3,1,2,4,6,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[[.,.],.],.],[.,.]],[.,.]],.] => [7,5,1,2,3,4,6,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => [7,4,3,2,1,5,6,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[[[.,.],.],.]],.],[.,.]],.] => [7,2,3,4,1,5,6,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [7,4,3,1,2,5,6,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,.],[[.,.],.]],.],[.,.]],.] => [7,3,4,1,2,5,6,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[[[[.,.],.],[.,.]],.],[.,.]],.] => [7,4,1,2,3,5,6,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[[.,[.,[.,.]]],.],.],[.,.]],.] => [7,3,2,1,4,5,6,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,[[.,.],.]],.],.],[.,.]],.] => [7,2,3,1,4,5,6,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[[[[.,.],[.,.]],.],.],[.,.]],.] => [7,3,1,2,4,5,6,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[[[.,[.,.]],.],.],.],[.,.]],.] => [7,2,1,3,4,5,6,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[[[[.,.],.],.],.],.],[.,.]],.] => [7,1,2,3,4,5,6,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [6,5,4,3,2,1,7,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.] => [5,6,4,3,2,1,7,8] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[.,[[.,[.,.]],.]]]],.],.] => [5,4,6,3,2,1,7,8] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[.,[[[.,.],.],.]]]],.],.] => [4,5,6,3,2,1,7,8] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.] => [6,5,3,4,2,1,7,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,[[.,.],[[.,.],.]]]],.],.] => [5,6,3,4,2,1,7,8] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,[[[.,.],.],[.,.]]]],.],.] => [6,3,4,5,2,1,7,8] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,[[[[.,.],.],.],.]]],.],.] => [3,4,5,6,2,1,7,8] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[[[.,[[.,.],[[.,[.,.]],.]]],.],.] => [5,4,6,2,3,1,7,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,[.,.]],[[.,.],.]]],.],.] => [5,6,3,2,4,1,7,8] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[[.,.],.],[.,[.,.]]]],.],.] => [6,5,2,3,4,1,7,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,[[[.,.],.],[[.,.],.]]],.],.] => [5,6,2,3,4,1,7,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,[[.,[.,[.,.]]],[.,.]]],.],.] => [6,4,3,2,5,1,7,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[[[.,.],.],.],[.,.]]],.],.] => [6,2,3,4,5,1,7,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.] => [5,4,3,2,6,1,7,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,[.,[[.,.],.]]],.]],.],.] => [4,5,3,2,6,1,7,8] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,[[.,[.,.]],.]],.]],.],.] => [4,3,5,2,6,1,7,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,[[[.,.],.],.]],.]],.],.] => [3,4,5,2,6,1,7,8] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[[[.,.],.],[.,.]],.]],.],.] => [5,2,3,4,6,1,7,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[[.,[[[.,[.,[.,.]]],.],.]],.],.] => [4,3,2,5,6,1,7,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,[[[.,[[.,.],.]],.],.]],.],.] => [3,4,2,5,6,1,7,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,[[[[.,.],[.,.]],.],.]],.],.] => [4,2,3,5,6,1,7,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[[.,[[[[.,[.,.]],.],.],.]],.],.] => [3,2,4,5,6,1,7,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[[.,[[[[[.,.],.],.],.],.]],.],.] => [2,3,4,5,6,1,7,8] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [6,5,4,3,1,2,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],[.,[.,[[.,.],.]]]],.],.] => [5,6,4,3,1,2,7,8] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],[.,[[.,[.,.]],.]]],.],.] => [5,4,6,3,1,2,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],[[.,.],[[.,.],.]]],.],.] => [5,6,3,4,1,2,7,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [6,4,3,5,1,2,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],[[.,[.,[.,.]]],.]],.],.] => [5,4,3,6,1,2,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],[[[.,[.,.]],.],.]],.],.] => [4,3,5,6,1,2,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],[[[[.,.],.],.],.]],.],.] => [3,4,5,6,1,2,7,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],[.,[.,[.,.]]]],.],.] => [6,5,4,2,1,3,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],[.,[[.,.],.]]],.],.] => [5,6,4,2,1,3,7,8] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [6,4,5,2,1,3,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],[[.,[.,.]],.]],.],.] => [5,4,6,2,1,3,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],[[[.,.],.],.]],.],.] => [4,5,6,2,1,3,7,8] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [6,5,4,1,2,3,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,.],.],[[[.,.],.],.]],.],.] => [4,5,6,1,2,3,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[[[[.,[.,[.,.]]],[[.,.],.]],.],.] => [5,6,3,2,1,4,7,8] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[[.,[.,.]],.],[[.,.],.]],.],.] => [5,6,2,1,3,4,7,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[[.,.],.],.],[.,[.,.]]],.],.] => [6,5,1,2,3,4,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.] => [6,4,3,2,1,5,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,[[.,.],.]]],[.,.]],.],.] => [6,3,4,2,1,5,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [6,4,3,1,2,5,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [6,4,2,1,3,5,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[[.,.],.],[.,.]],[.,.]],.],.] => [6,4,1,2,3,5,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[[.,[[.,.],.]],.],[.,.]],.],.] => [6,2,3,1,4,5,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[[[[.,.],[.,.]],.],[.,.]],.],.] => [6,3,1,2,4,5,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[[[[.,.],.],.],.],[.,.]],.],.] => [6,1,2,3,4,5,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [5,4,3,2,1,6,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,[.,[[.,.],.]]]],.],.],.] => [4,5,3,2,1,6,7,8] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,[[.,.],[.,.]]]],.],.],.] => [5,3,4,2,1,6,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,[[.,[.,.]],.]]],.],.],.] => [4,3,5,2,1,6,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,[[[.,.],.],.]]],.],.],.] => [3,4,5,2,1,6,7,8] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[[.,.],[.,[.,.]]]],.],.],.] => [5,4,2,3,1,6,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,[[.,.],[[.,.],.]]],.],.],.] => [4,5,2,3,1,6,7,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,[[.,[.,.]],[.,.]]],.],.],.] => [5,3,2,4,1,6,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,[[[.,.],.],[.,.]]],.],.],.] => [5,2,3,4,1,6,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[[.,[[.,[.,[.,.]]],.]],.],.],.] => [4,3,2,5,1,6,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,[[.,[[.,.],.]],.]],.],.],.] => [3,4,2,5,1,6,7,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,[[[.,.],[.,.]],.]],.],.],.] => [4,2,3,5,1,6,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[[.,[[[.,[.,.]],.],.]],.],.],.] => [3,2,4,5,1,6,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[[.,[[[[.,.],.],.],.]],.],.],.] => [2,3,4,5,1,6,7,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [5,4,3,1,2,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,.],[[.,[.,.]],.]],.],.],.] => [4,3,5,1,2,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,.],[[[.,.],.],.]],.],.],.] => [3,4,5,1,2,6,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,[.,.]],[.,[.,.]]],.],.],.] => [5,4,2,1,3,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,[.,.]],[[.,.],.]],.],.],.] => [4,5,2,1,3,6,7,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[[.,.],.],[.,[.,.]]],.],.],.] => [5,4,1,2,3,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[[[.,.],.],[[.,.],.]],.],.],.] => [4,5,1,2,3,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[[.,[.,[.,.]]],[.,.]],.],.],.] => [5,3,2,1,4,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,[[.,.],.]],[.,.]],.],.],.] => [5,2,3,1,4,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[[[[.,.],[.,.]],[.,.]],.],.],.] => [5,3,1,2,4,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[[[.,[.,.]],.],[.,.]],.],.],.] => [5,2,1,3,4,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[[[[.,.],.],.],[.,.]],.],.],.] => [5,1,2,3,4,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [4,3,2,1,5,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,[.,[[.,.],.]]],.],.],.],.] => [3,4,2,1,5,6,7,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,[[.,.],[.,.]]],.],.],.],.] => [4,2,3,1,5,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,[[.,[.,.]],.]],.],.],.],.] => [3,2,4,1,5,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,[[[.,.],.],.]],.],.],.],.] => [2,3,4,1,5,6,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[[[[[[.,.],[.,[.,.]]],.],.],.],.] => [4,3,1,2,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[[[.,.],[[.,.],.]],.],.],.],.] => [3,4,1,2,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[[[.,[.,.]],[.,.]],.],.],.],.] => [4,2,1,3,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[[[[.,.],.],[.,.]],.],.],.],.] => [4,1,2,3,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[[[[.,[.,[.,.]]],.],.],.],.],.] => [3,2,1,4,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[[[.,[[.,.],.]],.],.],.],.],.] => [2,3,1,4,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[[[[.,.],[.,.]],.],.],.],.],.] => [3,1,2,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[[[[[.,[.,.]],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[[[[[[.,.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [9,8,7,6,5,4,3,2,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],.] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [8,9,7,6,5,4,3,2,1] => [[[[[[[[.,[.,.]],.],.],.],.],.],.],.] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]] => [7,8,9,6,5,4,3,2,1] => [[[[[[[.,[.,[.,.]]],.],.],.],.],.],.] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]] => [6,7,8,9,5,4,3,2,1] => [[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]] => [5,6,7,8,9,4,3,2,1] => [[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]] => [4,5,6,7,8,9,3,2,1] => [[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]
[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]] => [3,4,5,6,7,8,9,2,1] => [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,1] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
[[[[[[[[[.,.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9] => [.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [10,9,8,7,6,5,4,3,2,1] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]] => [9,10,8,7,6,5,4,3,2,1] => [[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]] => [9,7,8,6,5,4,3,2,1] => [[[[[[[[.,.],[.,.]],.],.],.],.],.],.] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]] => [8,9,10,7,6,5,4,3,2,1] => [[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]] => [8,9,6,7,5,4,3,2,1] => [[[[[[[.,[.,.]],[.,.]],.],.],.],.],.] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]] => [7,8,9,10,6,5,4,3,2,1] => [[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]] => [6,7,8,9,10,5,4,3,2,1] => [[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]] => [5,6,7,8,9,10,4,3,2,1] => [[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]] => [4,5,6,7,8,9,10,3,2,1] => [[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]
[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]] => [4,5,6,7,8,9,2,3,1] => [[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]
[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]] => [3,4,5,6,7,8,9,10,2,1] => [[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]
[[.,.],[[[[[[[.,.],.],.],.],.],.],.]] => [3,4,5,6,7,8,9,1,2] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,1] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]] => [8,7,9,6,5,4,3,2,1] => [[[[[[[[.,.],[.,.]],.],.],.],.],.],.] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]] => [8,7,6,9,5,4,3,2,1] => [[[[[[[[.,.],.],[.,.]],.],.],.],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]] => [8,7,6,5,9,4,3,2,1] => [[[[[[[[.,.],.],.],[.,.]],.],.],.],.] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]] => [8,7,6,5,4,9,3,2,1] => [[[[[[[[.,.],.],.],.],[.,.]],.],.],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]] => [8,7,6,5,4,3,9,2,1] => [[[[[[[[.,.],.],.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]] => [8,7,6,5,4,3,2,9,1] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [8,7,6,5,4,3,2,1,9] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]] => [9,8,10,7,6,5,4,3,2,1] => [[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]] => [8,6,7,9,5,4,3,2,1] => [[[[[[[.,.],[.,[.,.]]],.],.],.],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]] => [9,8,7,10,6,5,4,3,2,1] => [[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]] => [9,8,7,6,10,5,4,3,2,1] => [[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]] => [9,8,7,6,5,10,4,3,2,1] => [[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]] => [9,8,7,6,5,4,10,3,2,1] => [[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]] => [9,8,7,6,5,4,3,10,2,1] => [[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]] => [9,8,7,6,5,4,3,2,10,1] => [[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [9,8,7,6,5,4,3,2,1,10] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [9,10,7,8,5,6,3,4,1,2] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]] => [9,10,6,7,4,5,2,3,1,8] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => [5,6,4,7,3,8,2,9,1,10] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => [11,12,9,10,7,8,5,6,3,4,1,2] => [[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [9,1,2,3,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [10,1,2,3,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]] => [9,2,1,3,4,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,1] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]] => [10,2,1,3,4,5,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => [9,3,1,2,4,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]] => [4,2,3,5,6,7,8,9,1] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,11,1] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]] => [8,9,1,2,3,4,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[[[[.,.],.],.],.],.],[[[.,.],.],.]] => [7,8,9,1,2,3,4,5,6] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[[.,.],.],.],.],[[[[.,.],.],.],.]] => [6,7,8,9,1,2,3,4,5] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]
[[[[.,.],.],.],[[[[[.,.],.],.],.],.]] => [5,6,7,8,9,1,2,3,4] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]
[[[.,.],.],[[[[[[.,.],.],.],.],.],.]] => [4,5,6,7,8,9,1,2,3] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [9,8,1,2,3,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,.],[[[[[[.,[.,.]],.],.],.],.],.]] => [4,3,5,6,7,8,9,1,2] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,5,4,3,1,2] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [10,9,8,7,6,5,4,3,1,2] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => [7,6,8,5,4,3,2,1,9] => [[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.] => [8,6,7,5,4,3,2,1,9] => [[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [8,7,9,6,5,4,3,1,2] => [[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [9,7,8,6,5,4,3,1,2] => [[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [9,8,7,6,5,4,2,1,3] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [9,8,7,6,5,3,2,1,4] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [9,8,7,6,4,3,2,1,5] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [9,8,7,5,4,3,2,1,6] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [9,8,6,5,4,3,2,1,7] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [9,7,6,5,4,3,2,1,8] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [10,9,8,7,6,5,4,2,1,3] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]] => [9,8,7,6,5,2,3,1,4] => [[[[[[[.,.],.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [10,9,8,7,6,5,3,2,1,4] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]] => [10,9,8,7,6,4,3,2,1,5] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]] => [10,9,8,7,5,4,3,2,1,6] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]] => [10,9,8,6,5,4,3,2,1,7] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]] => [9,6,7,5,4,3,2,1,8] => [[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]] => [10,9,7,6,5,4,3,2,1,8] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]] => [10,8,7,6,5,4,3,2,1,9] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.] => [4,3,1,2,5,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9,10] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[[[[[.,.],[.,.]],.],.],.],.],.],.] => [3,1,2,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]] => [9,8,7,5,6,4,3,2,1] => [[[[[[[[.,.],.],.],[.,.]],.],.],.],.] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,4,5,3,2,1] => [[[[[[[[.,.],.],.],.],[.,.]],.],.],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,5,3,4,2,1] => [[[[[[[[.,.],.],.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,5,4,2,3,1] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]] => [10,8,9,7,6,5,4,3,2,1] => [[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]] => [10,9,8,6,7,5,4,3,2,1] => [[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]] => [10,9,8,7,5,6,4,3,2,1] => [[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [10,9,8,7,6,5,4,2,3,1] => [[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]] => [9,2,3,4,5,6,7,8,1] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[[[[[[.,[.,.]],.],.],.],.],[.,.]],.] => [8,2,1,3,4,5,6,7,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[[[[[[.,.],.],.],.],.],[.,.]],.]] => [8,2,3,4,5,6,7,9,1] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]] => [3,4,5,6,7,8,2,9,1] => [[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,1,9] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]
[[[[[[[.,[[.,.],.]],.],.],.],.],.],.] => [2,3,1,4,5,6,7,8,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[[[.,[[[[.,.],.],.],.]],.],.],.],.] => [2,3,4,5,1,6,7,8,9] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]
[[[.,[[[[[[.,.],.],.],.],.],.]],.],.] => [2,3,4,5,6,7,1,8,9] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]
[[.,[[[[[[.,.],.],.],.],.],[.,.]]],.] => [8,2,3,4,5,6,7,1,9] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[[[[[[[[.,.],.],[.,.]],.],.],.],.],.] => [4,1,2,3,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[[[[[.,.],.],.],[.,.]],.],.],.],.] => [5,1,2,3,4,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[[[[[.,.],.],.],.],[.,.]],.],.],.] => [6,1,2,3,4,5,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[[[[[.,.],.],.],.],.],[.,.]],.],.] => [7,1,2,3,4,5,6,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.] => [8,1,2,3,4,5,6,7,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.] => [3,1,2,4,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.] => [4,1,2,3,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.] => [5,1,2,3,4,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.] => [6,1,2,3,4,5,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.] => [7,1,2,3,4,5,6,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.] => [8,1,2,3,4,5,6,7,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.] => [9,1,2,3,4,5,6,7,8,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[[.,.],[[[[[[.,.],.],.],.],.],[.,.]]] => [9,3,4,5,6,7,8,1,2] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]] => [9,7,6,5,4,3,2,8,1] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[[[[[[.,.],[[[.,.],.],.]],.],.],.],.] => [3,4,5,1,2,6,7,8,9] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[[[[.,.],[.,.]],[.,.]],.],.],.],.] => [5,3,1,2,4,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]] => [10,8,7,6,5,4,3,2,9,1] => [[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[[[.,.],[[[[[[.,.],.],.],.],.],.]],.] => [3,4,5,6,7,8,1,2,9] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [10,9,1,2,3,4,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]] => [9,7,1,2,3,4,5,6,8] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]] => [9,8,10,7,6,5,4,3,1,2] => [[[[[[[[.,.],[.,.]],.],.],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.] => [7,6,5,4,3,2,8,1,9] => [[[[[[[.,.],.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[[[[[.,[.,.]],.],.],.],.],.]],.] => [3,2,4,5,6,7,8,1,9] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]] => [9,6,7,8,5,4,3,2,1] => [[[[[[[.,.],[.,[.,.]]],.],.],.],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.] => [8,7,6,5,4,2,3,1,9] => [[[[[[[.,.],.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,[[[[[[.,.],.],.],.],.],.]],[.,.]] => [9,2,3,4,5,6,7,1,8] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[[[[[[[.,.],[[.,.],.]],.],.],.],.],.] => [3,4,1,2,5,6,7,8,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]] => [4,5,6,7,8,9,10,2,3,1] => [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0]
[[[[[[[[.,.],[.,.]],.],.],.],.],.],[.,.]] => [10,3,1,2,4,5,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[.,[[[[[[.,.],.],.],.],.],[.,.]]]] => [9,3,4,5,6,7,8,2,1] => [[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
Map
to 132-avoiding permutation
Description
Return a 132-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 maximal element of the Sylvester class.
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 maximal element of the Sylvester class.
Map
to increasing tree
Description
Sends a permutation to its associated increasing tree.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.
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:
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 $r$.
searching the database
Sorry, this map was not found in the database.