Identifier
Mp00020:
Binary trees
—to Tamari-corresponding Dyck path⟶
Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
Images
[.,.] => [1,0] => [] => []
[.,[.,.]] => [1,1,0,0] => [] => []
[[.,.],.] => [1,0,1,0] => [1] => [1]
[.,[.,[.,.]]] => [1,1,1,0,0,0] => [] => []
[.,[[.,.],.]] => [1,1,0,1,0,0] => [1] => [1]
[[.,.],[.,.]] => [1,0,1,1,0,0] => [1,1] => [2]
[[.,[.,.]],.] => [1,1,0,0,1,0] => [2] => [1,1]
[[[.,.],.],.] => [1,0,1,0,1,0] => [2,1] => [2,1]
[.,[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0] => [] => []
[.,[.,[[.,.],.]]] => [1,1,1,0,1,0,0,0] => [1] => [1]
[.,[[.,.],[.,.]]] => [1,1,0,1,1,0,0,0] => [1,1] => [2]
[.,[[.,[.,.]],.]] => [1,1,1,0,0,1,0,0] => [2] => [1,1]
[.,[[[.,.],.],.]] => [1,1,0,1,0,1,0,0] => [2,1] => [2,1]
[[.,.],[.,[.,.]]] => [1,0,1,1,1,0,0,0] => [1,1,1] => [3]
[[.,.],[[.,.],.]] => [1,0,1,1,0,1,0,0] => [2,1,1] => [3,1]
[[.,[.,.]],[.,.]] => [1,1,0,0,1,1,0,0] => [2,2] => [2,2]
[[[.,.],.],[.,.]] => [1,0,1,0,1,1,0,0] => [2,2,1] => [3,2]
[[.,[.,[.,.]]],.] => [1,1,1,0,0,0,1,0] => [3] => [1,1,1]
[[.,[[.,.],.]],.] => [1,1,0,1,0,0,1,0] => [3,1] => [2,1,1]
[[[.,.],[.,.]],.] => [1,0,1,1,0,0,1,0] => [3,1,1] => [3,1,1]
[[[.,[.,.]],.],.] => [1,1,0,0,1,0,1,0] => [3,2] => [2,2,1]
[[[[.,.],.],.],.] => [1,0,1,0,1,0,1,0] => [3,2,1] => [3,2,1]
[.,[.,[.,[.,[.,.]]]]] => [1,1,1,1,1,0,0,0,0,0] => [] => []
[.,[.,[.,[[.,.],.]]]] => [1,1,1,1,0,1,0,0,0,0] => [1] => [1]
[.,[.,[[.,.],[.,.]]]] => [1,1,1,0,1,1,0,0,0,0] => [1,1] => [2]
[.,[.,[[.,[.,.]],.]]] => [1,1,1,1,0,0,1,0,0,0] => [2] => [1,1]
[.,[.,[[[.,.],.],.]]] => [1,1,1,0,1,0,1,0,0,0] => [2,1] => [2,1]
[.,[[.,.],[.,[.,.]]]] => [1,1,0,1,1,1,0,0,0,0] => [1,1,1] => [3]
[.,[[.,.],[[.,.],.]]] => [1,1,0,1,1,0,1,0,0,0] => [2,1,1] => [3,1]
[.,[[.,[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,0] => [2,2] => [2,2]
[.,[[[.,.],.],[.,.]]] => [1,1,0,1,0,1,1,0,0,0] => [2,2,1] => [3,2]
[.,[[.,[.,[.,.]]],.]] => [1,1,1,1,0,0,0,1,0,0] => [3] => [1,1,1]
[.,[[.,[[.,.],.]],.]] => [1,1,1,0,1,0,0,1,0,0] => [3,1] => [2,1,1]
[.,[[[.,.],[.,.]],.]] => [1,1,0,1,1,0,0,1,0,0] => [3,1,1] => [3,1,1]
[.,[[[.,[.,.]],.],.]] => [1,1,1,0,0,1,0,1,0,0] => [3,2] => [2,2,1]
[.,[[[[.,.],.],.],.]] => [1,1,0,1,0,1,0,1,0,0] => [3,2,1] => [3,2,1]
[[.,.],[.,[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => [4]
[[.,.],[.,[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => [4,1]
[[.,.],[[.,.],[.,.]]] => [1,0,1,1,0,1,1,0,0,0] => [2,2,1,1] => [4,2]
[[.,.],[[.,[.,.]],.]] => [1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => [4,1,1]
[[.,.],[[[.,.],.],.]] => [1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => [4,2,1]
[[.,[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,1,0,0,0] => [2,2,2] => [3,3]
[[.,[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,1,0,0] => [3,2,2] => [3,3,1]
[[[.,.],.],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => [4,3]
[[[.,.],.],[[.,.],.]] => [1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => [4,3,1]
[[.,[.,[.,.]]],[.,.]] => [1,1,1,0,0,0,1,1,0,0] => [3,3] => [2,2,2]
[[.,[[.,.],.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0] => [3,3,1] => [3,2,2]
[[[.,.],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0] => [3,3,1,1] => [4,2,2]
[[[.,[.,.]],.],[.,.]] => [1,1,0,0,1,0,1,1,0,0] => [3,3,2] => [3,3,2]
[[[[.,.],.],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => [4,3,2]
[[.,[.,[.,[.,.]]]],.] => [1,1,1,1,0,0,0,0,1,0] => [4] => [1,1,1,1]
[[.,[.,[[.,.],.]]],.] => [1,1,1,0,1,0,0,0,1,0] => [4,1] => [2,1,1,1]
[[.,[[.,.],[.,.]]],.] => [1,1,0,1,1,0,0,0,1,0] => [4,1,1] => [3,1,1,1]
[[.,[[.,[.,.]],.]],.] => [1,1,1,0,0,1,0,0,1,0] => [4,2] => [2,2,1,1]
[[.,[[[.,.],.],.]],.] => [1,1,0,1,0,1,0,0,1,0] => [4,2,1] => [3,2,1,1]
[[[.,.],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => [4,1,1,1]
[[[.,.],[[.,.],.]],.] => [1,0,1,1,0,1,0,0,1,0] => [4,2,1,1] => [4,2,1,1]
[[[.,[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,0] => [4,2,2] => [3,3,1,1]
[[[[.,.],.],[.,.]],.] => [1,0,1,0,1,1,0,0,1,0] => [4,2,2,1] => [4,3,1,1]
[[[.,[.,[.,.]]],.],.] => [1,1,1,0,0,0,1,0,1,0] => [4,3] => [2,2,2,1]
[[[.,[[.,.],.]],.],.] => [1,1,0,1,0,0,1,0,1,0] => [4,3,1] => [3,2,2,1]
[[[[.,.],[.,.]],.],.] => [1,0,1,1,0,0,1,0,1,0] => [4,3,1,1] => [4,2,2,1]
[[[[.,[.,.]],.],.],.] => [1,1,0,0,1,0,1,0,1,0] => [4,3,2] => [3,3,2,1]
[[[[[.,.],.],.],.],.] => [1,0,1,0,1,0,1,0,1,0] => [4,3,2,1] => [4,3,2,1]
[.,[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,1,1,1,0,0,0,0,0,0] => [] => []
[.,[.,[.,[.,[[.,.],.]]]]] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1] => [1]
[.,[.,[.,[[.,.],[.,.]]]]] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1] => [2]
[.,[.,[.,[[.,[.,.]],.]]]] => [1,1,1,1,1,0,0,1,0,0,0,0] => [2] => [1,1]
[.,[.,[.,[[[.,.],.],.]]]] => [1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => [2,1]
[.,[.,[[.,.],[.,[.,.]]]]] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1] => [3]
[.,[.,[[.,.],[[.,.],.]]]] => [1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,1] => [3,1]
[.,[.,[[.,[.,.]],[.,.]]]] => [1,1,1,1,0,0,1,1,0,0,0,0] => [2,2] => [2,2]
[.,[.,[[[.,.],.],[.,.]]]] => [1,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1] => [3,2]
[.,[.,[[.,[.,[.,.]]],.]]] => [1,1,1,1,1,0,0,0,1,0,0,0] => [3] => [1,1,1]
[.,[.,[[.,[[.,.],.]],.]]] => [1,1,1,1,0,1,0,0,1,0,0,0] => [3,1] => [2,1,1]
[.,[.,[[[.,.],[.,.]],.]]] => [1,1,1,0,1,1,0,0,1,0,0,0] => [3,1,1] => [3,1,1]
[.,[.,[[[.,[.,.]],.],.]]] => [1,1,1,1,0,0,1,0,1,0,0,0] => [3,2] => [2,2,1]
[.,[.,[[[[.,.],.],.],.]]] => [1,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1] => [3,2,1]
[.,[[.,.],[.,[.,[.,.]]]]] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1] => [4]
[.,[[.,.],[.,[[.,.],.]]]] => [1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,1] => [4,1]
[.,[[.,.],[[.,.],[.,.]]]] => [1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,1,1] => [4,2]
[.,[[.,.],[[.,[.,.]],.]]] => [1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,1,1] => [4,1,1]
[.,[[.,.],[[[.,.],.],.]]] => [1,1,0,1,1,0,1,0,1,0,0,0] => [3,2,1,1] => [4,2,1]
[.,[[.,[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,0,0] => [2,2,2] => [3,3]
[.,[[.,[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,2] => [3,3,1]
[.,[[[.,.],.],[.,[.,.]]]] => [1,1,0,1,0,1,1,1,0,0,0,0] => [2,2,2,1] => [4,3]
[.,[[[.,.],.],[[.,.],.]]] => [1,1,0,1,0,1,1,0,1,0,0,0] => [3,2,2,1] => [4,3,1]
[.,[[.,[.,[.,.]]],[.,.]]] => [1,1,1,1,0,0,0,1,1,0,0,0] => [3,3] => [2,2,2]
[.,[[.,[[.,.],.]],[.,.]]] => [1,1,1,0,1,0,0,1,1,0,0,0] => [3,3,1] => [3,2,2]
[.,[[[.,.],[.,.]],[.,.]]] => [1,1,0,1,1,0,0,1,1,0,0,0] => [3,3,1,1] => [4,2,2]
[.,[[[.,[.,.]],.],[.,.]]] => [1,1,1,0,0,1,0,1,1,0,0,0] => [3,3,2] => [3,3,2]
[.,[[[[.,.],.],.],[.,.]]] => [1,1,0,1,0,1,0,1,1,0,0,0] => [3,3,2,1] => [4,3,2]
[.,[[.,[.,[.,[.,.]]]],.]] => [1,1,1,1,1,0,0,0,0,1,0,0] => [4] => [1,1,1,1]
[.,[[.,[.,[[.,.],.]]],.]] => [1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => [2,1,1,1]
[.,[[.,[[.,.],[.,.]]],.]] => [1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,1] => [3,1,1,1]
[.,[[.,[[.,[.,.]],.]],.]] => [1,1,1,1,0,0,1,0,0,1,0,0] => [4,2] => [2,2,1,1]
[.,[[.,[[[.,.],.],.]],.]] => [1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => [3,2,1,1]
[.,[[[.,.],[.,[.,.]]],.]] => [1,1,0,1,1,1,0,0,0,1,0,0] => [4,1,1,1] => [4,1,1,1]
[.,[[[.,.],[[.,.],.]],.]] => [1,1,0,1,1,0,1,0,0,1,0,0] => [4,2,1,1] => [4,2,1,1]
[.,[[[.,[.,.]],[.,.]],.]] => [1,1,1,0,0,1,1,0,0,1,0,0] => [4,2,2] => [3,3,1,1]
[.,[[[[.,.],.],[.,.]],.]] => [1,1,0,1,0,1,1,0,0,1,0,0] => [4,2,2,1] => [4,3,1,1]
>>> Load all 1606 entries. <<<
[.,[[[.,[.,[.,.]]],.],.]] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => [2,2,2,1]
[.,[[[.,[[.,.],.]],.],.]] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => [3,2,2,1]
[.,[[[[.,.],[.,.]],.],.]] => [1,1,0,1,1,0,0,1,0,1,0,0] => [4,3,1,1] => [4,2,2,1]
[.,[[[[.,[.,.]],.],.],.]] => [1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => [3,3,2,1]
[.,[[[[[.,.],.],.],.],.]] => [1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => [4,3,2,1]
[[.,.],[.,[.,[.,[.,.]]]]] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => [5]
[[.,.],[.,[.,[[.,.],.]]]] => [1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => [5,1]
[[.,.],[.,[[.,.],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => [5,2]
[[.,.],[.,[[.,[.,.]],.]]] => [1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => [5,1,1]
[[.,.],[.,[[[.,.],.],.]]] => [1,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => [5,2,1]
[[.,.],[[.,.],[.,[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,0,0] => [2,2,2,1,1] => [5,3]
[[.,.],[[.,.],[[.,.],.]]] => [1,0,1,1,0,1,1,0,1,0,0,0] => [3,2,2,1,1] => [5,3,1]
[[.,.],[[.,[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,0] => [3,3,1,1,1] => [5,2,2]
[[.,.],[[[.,.],.],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,0] => [3,3,2,1,1] => [5,3,2]
[[.,.],[[.,[.,[.,.]]],.]] => [1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => [5,1,1,1]
[[.,.],[[.,[[.,.],.]],.]] => [1,0,1,1,1,0,1,0,0,1,0,0] => [4,2,1,1,1] => [5,2,1,1]
[[.,.],[[[.,.],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,1,0,0] => [4,2,2,1,1] => [5,3,1,1]
[[.,.],[[[.,[.,.]],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,0] => [4,3,1,1,1] => [5,2,2,1]
[[.,.],[[[[.,.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,1] => [5,3,2,1]
[[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,2,2] => [4,4]
[[.,[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,1,0,1,0,0,0] => [3,2,2,2] => [4,4,1]
[[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,0] => [3,3,2,2] => [4,4,2]
[[.,[.,.]],[[.,[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,0,0] => [4,2,2,2] => [4,4,1,1]
[[.,[.,.]],[[[.,.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,0] => [4,3,2,2] => [4,4,2,1]
[[[.,.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => [5,4]
[[[.,.],.],[.,[[.,.],.]]] => [1,0,1,0,1,1,1,0,1,0,0,0] => [3,2,2,2,1] => [5,4,1]
[[[.,.],.],[[.,.],[.,.]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => [3,3,2,2,1] => [5,4,2]
[[[.,.],.],[[.,[.,.]],.]] => [1,0,1,0,1,1,1,0,0,1,0,0] => [4,2,2,2,1] => [5,4,1,1]
[[[.,.],.],[[[.,.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,0] => [4,3,2,2,1] => [5,4,2,1]
[[.,[.,[.,.]]],[.,[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => [3,3,3]
[[.,[.,[.,.]]],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,1,0,0] => [4,3,3] => [3,3,3,1]
[[.,[[.,.],.]],[.,[.,.]]] => [1,1,0,1,0,0,1,1,1,0,0,0] => [3,3,3,1] => [4,3,3]
[[.,[[.,.],.]],[[.,.],.]] => [1,1,0,1,0,0,1,1,0,1,0,0] => [4,3,3,1] => [4,3,3,1]
[[[.,.],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => [3,3,3,1,1] => [5,3,3]
[[[.,.],[.,.]],[[.,.],.]] => [1,0,1,1,0,0,1,1,0,1,0,0] => [4,3,3,1,1] => [5,3,3,1]
[[[.,[.,.]],.],[.,[.,.]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => [3,3,3,2] => [4,4,3]
[[[.,[.,.]],.],[[.,.],.]] => [1,1,0,0,1,0,1,1,0,1,0,0] => [4,3,3,2] => [4,4,3,1]
[[[[.,.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => [3,3,3,2,1] => [5,4,3]
[[[[.,.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,1,0,1,0,0] => [4,3,3,2,1] => [5,4,3,1]
[[.,[.,[.,[.,.]]]],[.,.]] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => [2,2,2,2]
[[.,[.,[[.,.],.]]],[.,.]] => [1,1,1,0,1,0,0,0,1,1,0,0] => [4,4,1] => [3,2,2,2]
[[.,[[.,.],[.,.]]],[.,.]] => [1,1,0,1,1,0,0,0,1,1,0,0] => [4,4,1,1] => [4,2,2,2]
[[.,[[.,[.,.]],.]],[.,.]] => [1,1,1,0,0,1,0,0,1,1,0,0] => [4,4,2] => [3,3,2,2]
[[.,[[[.,.],.],.]],[.,.]] => [1,1,0,1,0,1,0,0,1,1,0,0] => [4,4,2,1] => [4,3,2,2]
[[[.,.],[.,[.,.]]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0] => [4,4,1,1,1] => [5,2,2,2]
[[[.,.],[[.,.],.]],[.,.]] => [1,0,1,1,0,1,0,0,1,1,0,0] => [4,4,2,1,1] => [5,3,2,2]
[[[.,[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => [4,4,2,2]
[[[[.,.],.],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0] => [4,4,2,2,1] => [5,4,2,2]
[[[.,[.,[.,.]]],.],[.,.]] => [1,1,1,0,0,0,1,0,1,1,0,0] => [4,4,3] => [3,3,3,2]
[[[.,[[.,.],.]],.],[.,.]] => [1,1,0,1,0,0,1,0,1,1,0,0] => [4,4,3,1] => [4,3,3,2]
[[[[.,.],[.,.]],.],[.,.]] => [1,0,1,1,0,0,1,0,1,1,0,0] => [4,4,3,1,1] => [5,3,3,2]
[[[[.,[.,.]],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,1,0,0] => [4,4,3,2] => [4,4,3,2]
[[[[[.,.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0] => [4,4,3,2,1] => [5,4,3,2]
[[.,[.,[.,[.,[.,.]]]]],.] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5] => [1,1,1,1,1]
[[.,[.,[.,[[.,.],.]]]],.] => [1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => [2,1,1,1,1]
[[.,[.,[[.,.],[.,.]]]],.] => [1,1,1,0,1,1,0,0,0,0,1,0] => [5,1,1] => [3,1,1,1,1]
[[.,[.,[[.,[.,.]],.]]],.] => [1,1,1,1,0,0,1,0,0,0,1,0] => [5,2] => [2,2,1,1,1]
[[.,[.,[[[.,.],.],.]]],.] => [1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,1] => [3,2,1,1,1]
[[.,[[.,.],[.,[.,.]]]],.] => [1,1,0,1,1,1,0,0,0,0,1,0] => [5,1,1,1] => [4,1,1,1,1]
[[.,[[.,.],[[.,.],.]]],.] => [1,1,0,1,1,0,1,0,0,0,1,0] => [5,2,1,1] => [4,2,1,1,1]
[[.,[[.,[.,.]],[.,.]]],.] => [1,1,1,0,0,1,1,0,0,0,1,0] => [5,2,2] => [3,3,1,1,1]
[[.,[[[.,.],.],[.,.]]],.] => [1,1,0,1,0,1,1,0,0,0,1,0] => [5,2,2,1] => [4,3,1,1,1]
[[.,[[.,[.,[.,.]]],.]],.] => [1,1,1,1,0,0,0,1,0,0,1,0] => [5,3] => [2,2,2,1,1]
[[.,[[.,[[.,.],.]],.]],.] => [1,1,1,0,1,0,0,1,0,0,1,0] => [5,3,1] => [3,2,2,1,1]
[[.,[[[.,.],[.,.]],.]],.] => [1,1,0,1,1,0,0,1,0,0,1,0] => [5,3,1,1] => [4,2,2,1,1]
[[.,[[[.,[.,.]],.],.]],.] => [1,1,1,0,0,1,0,1,0,0,1,0] => [5,3,2] => [3,3,2,1,1]
[[.,[[[[.,.],.],.],.]],.] => [1,1,0,1,0,1,0,1,0,0,1,0] => [5,3,2,1] => [4,3,2,1,1]
[[[.,.],[.,[.,[.,.]]]],.] => [1,0,1,1,1,1,0,0,0,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1]
[[[.,.],[.,[[.,.],.]]],.] => [1,0,1,1,1,0,1,0,0,0,1,0] => [5,2,1,1,1] => [5,2,1,1,1]
[[[.,.],[[.,.],[.,.]]],.] => [1,0,1,1,0,1,1,0,0,0,1,0] => [5,2,2,1,1] => [5,3,1,1,1]
[[[.,.],[[.,[.,.]],.]],.] => [1,0,1,1,1,0,0,1,0,0,1,0] => [5,3,1,1,1] => [5,2,2,1,1]
[[[.,.],[[[.,.],.],.]],.] => [1,0,1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,1] => [5,3,2,1,1]
[[[.,[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,1,0,0,0,1,0] => [5,2,2,2] => [4,4,1,1,1]
[[[.,[.,.]],[[.,.],.]],.] => [1,1,0,0,1,1,0,1,0,0,1,0] => [5,3,2,2] => [4,4,2,1,1]
[[[[.,.],.],[.,[.,.]]],.] => [1,0,1,0,1,1,1,0,0,0,1,0] => [5,2,2,2,1] => [5,4,1,1,1]
[[[[.,.],.],[[.,.],.]],.] => [1,0,1,0,1,1,0,1,0,0,1,0] => [5,3,2,2,1] => [5,4,2,1,1]
[[[.,[.,[.,.]]],[.,.]],.] => [1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => [3,3,3,1,1]
[[[.,[[.,.],.]],[.,.]],.] => [1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,3,1] => [4,3,3,1,1]
[[[[.,.],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,0] => [5,3,3,1,1] => [5,3,3,1,1]
[[[[.,[.,.]],.],[.,.]],.] => [1,1,0,0,1,0,1,1,0,0,1,0] => [5,3,3,2] => [4,4,3,1,1]
[[[[[.,.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,1,0,0,1,0] => [5,3,3,2,1] => [5,4,3,1,1]
[[[.,[.,[.,[.,.]]]],.],.] => [1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => [2,2,2,2,1]
[[[.,[.,[[.,.],.]]],.],.] => [1,1,1,0,1,0,0,0,1,0,1,0] => [5,4,1] => [3,2,2,2,1]
[[[.,[[.,.],[.,.]]],.],.] => [1,1,0,1,1,0,0,0,1,0,1,0] => [5,4,1,1] => [4,2,2,2,1]
[[[.,[[.,[.,.]],.]],.],.] => [1,1,1,0,0,1,0,0,1,0,1,0] => [5,4,2] => [3,3,2,2,1]
[[[.,[[[.,.],.],.]],.],.] => [1,1,0,1,0,1,0,0,1,0,1,0] => [5,4,2,1] => [4,3,2,2,1]
[[[[.,.],[.,[.,.]]],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0] => [5,4,1,1,1] => [5,2,2,2,1]
[[[[.,.],[[.,.],.]],.],.] => [1,0,1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,1] => [5,3,2,2,1]
[[[[.,[.,.]],[.,.]],.],.] => [1,1,0,0,1,1,0,0,1,0,1,0] => [5,4,2,2] => [4,4,2,2,1]
[[[[[.,.],.],[.,.]],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0] => [5,4,2,2,1] => [5,4,2,2,1]
[[[[.,[.,[.,.]]],.],.],.] => [1,1,1,0,0,0,1,0,1,0,1,0] => [5,4,3] => [3,3,3,2,1]
[[[[.,[[.,.],.]],.],.],.] => [1,1,0,1,0,0,1,0,1,0,1,0] => [5,4,3,1] => [4,3,3,2,1]
[[[[[.,.],[.,.]],.],.],.] => [1,0,1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,1] => [5,3,3,2,1]
[[[[[.,[.,.]],.],.],.],.] => [1,1,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2] => [4,4,3,2,1]
[[[[[[.,.],.],.],.],.],.] => [1,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => [5,4,3,2,1]
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [] => []
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1] => [1]
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1] => [2]
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => [1,1]
[.,[.,[.,[.,[[[.,.],.],.]]]]] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => [2,1]
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1] => [3]
[.,[.,[.,[[.,.],[[.,.],.]]]]] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,1,1] => [3,1]
[.,[.,[.,[[.,[.,.]],[.,.]]]]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,2] => [2,2]
[.,[.,[.,[[[.,.],.],[.,.]]]]] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,2,1] => [3,2]
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => [1,1,1]
[.,[.,[.,[[.,[[.,.],.]],.]]]] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,1] => [2,1,1]
[.,[.,[.,[[[.,.],[.,.]],.]]]] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [3,1,1] => [3,1,1]
[.,[.,[.,[[[.,[.,.]],.],.]]]] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,2] => [2,2,1]
[.,[.,[.,[[[[.,.],.],.],.]]]] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => [3,2,1]
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1] => [4]
[.,[.,[[.,.],[.,[[.,.],.]]]]] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1] => [4,1]
[.,[.,[[.,.],[[.,.],[.,.]]]]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1] => [4,2]
[.,[.,[[.,.],[[.,[.,.]],.]]]] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1] => [4,1,1]
[.,[.,[[.,.],[[[.,.],.],.]]]] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => [4,2,1]
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,2,2] => [3,3]
[.,[.,[[.,[.,.]],[[.,.],.]]]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2] => [3,3,1]
[.,[.,[[[.,.],.],[.,[.,.]]]]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1] => [4,3]
[.,[.,[[[.,.],.],[[.,.],.]]]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => [4,3,1]
[.,[.,[[.,[.,[.,.]]],[.,.]]]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,3] => [2,2,2]
[.,[.,[[.,[[.,.],.]],[.,.]]]] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [3,3,1] => [3,2,2]
[.,[.,[[[.,.],[.,.]],[.,.]]]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1] => [4,2,2]
[.,[.,[[[.,[.,.]],.],[.,.]]]] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,3,2] => [3,3,2]
[.,[.,[[[[.,.],.],.],[.,.]]]] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1] => [4,3,2]
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [4] => [1,1,1,1]
[.,[.,[[.,[.,[[.,.],.]]],.]]] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [4,1] => [2,1,1,1]
[.,[.,[[.,[[.,.],[.,.]]],.]]] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,1,1] => [3,1,1,1]
[.,[.,[[.,[[.,[.,.]],.]],.]]] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [4,2] => [2,2,1,1]
[.,[.,[[.,[[[.,.],.],.]],.]]] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,2,1] => [3,2,1,1]
[.,[.,[[[.,.],[.,[.,.]]],.]]] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1] => [4,1,1,1]
[.,[.,[[[.,.],[[.,.],.]],.]]] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1] => [4,2,1,1]
[.,[.,[[[.,[.,.]],[.,.]],.]]] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,2] => [3,3,1,1]
[.,[.,[[[[.,.],.],[.,.]],.]]] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1] => [4,3,1,1]
[.,[.,[[[.,[.,[.,.]]],.],.]]] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [4,3] => [2,2,2,1]
[.,[.,[[[.,[[.,.],.]],.],.]]] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,3,1] => [3,2,2,1]
[.,[.,[[[[.,.],[.,.]],.],.]]] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1] => [4,2,2,1]
[.,[.,[[[[.,[.,.]],.],.],.]]] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,2] => [3,3,2,1]
[.,[.,[[[[[.,.],.],.],.],.]]] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1] => [4,3,2,1]
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => [5]
[.,[[.,.],[.,[.,[[.,.],.]]]]] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1] => [5,1]
[.,[[.,.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1] => [5,2]
[.,[[.,.],[.,[[.,[.,.]],.]]]] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1] => [5,1,1]
[.,[[.,.],[.,[[[.,.],.],.]]]] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => [5,2,1]
[.,[[.,.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => [5,3]
[.,[[.,.],[[.,.],[[.,.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => [5,3,1]
[.,[[.,.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => [5,2,2]
[.,[[.,.],[[[.,.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1] => [5,3,2]
[.,[[.,.],[[.,[.,[.,.]]],.]]] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1] => [5,1,1,1]
[.,[[.,.],[[.,[[.,.],.]],.]]] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1] => [5,2,1,1]
[.,[[.,.],[[[.,.],[.,.]],.]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1] => [5,3,1,1]
[.,[[.,.],[[[.,[.,.]],.],.]]] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1] => [5,2,2,1]
[.,[[.,.],[[[[.,.],.],.],.]]] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1] => [5,3,2,1]
[.,[[.,[.,.]],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => [4,4]
[.,[[.,[.,.]],[.,[[.,.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2] => [4,4,1]
[.,[[.,[.,.]],[[.,.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => [4,4,2]
[.,[[.,[.,.]],[[.,[.,.]],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2] => [4,4,1,1]
[.,[[.,[.,.]],[[[.,.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2] => [4,4,2,1]
[.,[[[.,.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1] => [5,4]
[.,[[[.,.],.],[.,[[.,.],.]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1] => [5,4,1]
[.,[[[.,.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => [5,4,2]
[.,[[[.,.],.],[[.,[.,.]],.]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1] => [5,4,1,1]
[.,[[[.,.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1] => [5,4,2,1]
[.,[[.,[.,[.,.]]],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,3,3] => [3,3,3]
[.,[[.,[.,[.,.]]],[[.,.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,3] => [3,3,3,1]
[.,[[.,[[.,.],.]],[.,[.,.]]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1] => [4,3,3]
[.,[[.,[[.,.],.]],[[.,.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1] => [4,3,3,1]
[.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => [5,3,3]
[.,[[[.,.],[.,.]],[[.,.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1] => [5,3,3,1]
[.,[[[.,[.,.]],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2] => [4,4,3]
[.,[[[.,[.,.]],.],[[.,.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2] => [4,4,3,1]
[.,[[[[.,.],.],.],[.,[.,.]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1] => [5,4,3]
[.,[[[[.,.],.],.],[[.,.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1] => [5,4,3,1]
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,4] => [2,2,2,2]
[.,[[.,[.,[[.,.],.]]],[.,.]]] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,4,1] => [3,2,2,2]
[.,[[.,[[.,.],[.,.]]],[.,.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1] => [4,2,2,2]
[.,[[.,[[.,[.,.]],.]],[.,.]]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,4,2] => [3,3,2,2]
[.,[[.,[[[.,.],.],.]],[.,.]]] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1] => [4,3,2,2]
[.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1] => [5,2,2,2]
[.,[[[.,.],[[.,.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1] => [5,3,2,2]
[.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2] => [4,4,2,2]
[.,[[[[.,.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1] => [5,4,2,2]
[.,[[[.,[.,[.,.]]],.],[.,.]]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,4,3] => [3,3,3,2]
[.,[[[.,[[.,.],.]],.],[.,.]]] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1] => [4,3,3,2]
[.,[[[[.,.],[.,.]],.],[.,.]]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1] => [5,3,3,2]
[.,[[[[.,[.,.]],.],.],[.,.]]] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2] => [4,4,3,2]
[.,[[[[[.,.],.],.],.],[.,.]]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1] => [5,4,3,2]
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => [1,1,1,1,1]
[.,[[.,[.,[.,[[.,.],.]]]],.]] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1] => [2,1,1,1,1]
[.,[[.,[.,[[.,.],[.,.]]]],.]] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,1] => [3,1,1,1,1]
[.,[[.,[.,[[.,[.,.]],.]]],.]] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => [2,2,1,1,1]
[.,[[.,[.,[[[.,.],.],.]]],.]] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => [3,2,1,1,1]
[.,[[.,[[.,.],[.,[.,.]]]],.]] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1] => [4,1,1,1,1]
[.,[[.,[[.,.],[[.,.],.]]],.]] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1] => [4,2,1,1,1]
[.,[[.,[[.,[.,.]],[.,.]]],.]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [5,2,2] => [3,3,1,1,1]
[.,[[.,[[[.,.],.],[.,.]]],.]] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1] => [4,3,1,1,1]
[.,[[.,[[.,[.,[.,.]]],.]],.]] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,3] => [2,2,2,1,1]
[.,[[.,[[.,[[.,.],.]],.]],.]] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,3,1] => [3,2,2,1,1]
[.,[[.,[[[.,.],[.,.]],.]],.]] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1] => [4,2,2,1,1]
[.,[[.,[[[.,[.,.]],.],.]],.]] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [5,3,2] => [3,3,2,1,1]
[.,[[.,[[[[.,.],.],.],.]],.]] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1] => [4,3,2,1,1]
[.,[[[.,.],[.,[.,[.,.]]]],.]] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1] => [5,1,1,1,1]
[.,[[[.,.],[.,[[.,.],.]]],.]] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1] => [5,2,1,1,1]
[.,[[[.,.],[[.,.],[.,.]]],.]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1] => [5,3,1,1,1]
[.,[[[.,.],[[.,[.,.]],.]],.]] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1] => [5,2,2,1,1]
[.,[[[.,.],[[[.,.],.],.]],.]] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1] => [5,3,2,1,1]
[.,[[[.,[.,.]],[.,[.,.]]],.]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2] => [4,4,1,1,1]
[.,[[[.,[.,.]],[[.,.],.]],.]] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2] => [4,4,2,1,1]
[.,[[[[.,.],.],[.,[.,.]]],.]] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1] => [5,4,1,1,1]
[.,[[[[.,.],.],[[.,.],.]],.]] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1] => [5,4,2,1,1]
[.,[[[.,[.,[.,.]]],[.,.]],.]] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [5,3,3] => [3,3,3,1,1]
[.,[[[.,[[.,.],.]],[.,.]],.]] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1] => [4,3,3,1,1]
[.,[[[[.,.],[.,.]],[.,.]],.]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1] => [5,3,3,1,1]
[.,[[[[.,[.,.]],.],[.,.]],.]] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2] => [4,4,3,1,1]
[.,[[[[[.,.],.],.],[.,.]],.]] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1] => [5,4,3,1,1]
[.,[[[.,[.,[.,[.,.]]]],.],.]] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4] => [2,2,2,2,1]
[.,[[[.,[.,[[.,.],.]]],.],.]] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,4,1] => [3,2,2,2,1]
[.,[[[.,[[.,.],[.,.]]],.],.]] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1] => [4,2,2,2,1]
[.,[[[.,[[.,[.,.]],.]],.],.]] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,4,2] => [3,3,2,2,1]
[.,[[[.,[[[.,.],.],.]],.],.]] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1] => [4,3,2,2,1]
[.,[[[[.,.],[.,[.,.]]],.],.]] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1] => [5,2,2,2,1]
[.,[[[[.,.],[[.,.],.]],.],.]] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,1] => [5,3,2,2,1]
[.,[[[[.,[.,.]],[.,.]],.],.]] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2] => [4,4,2,2,1]
[.,[[[[[.,.],.],[.,.]],.],.]] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2,1] => [5,4,2,2,1]
[.,[[[[.,[.,[.,.]]],.],.],.]] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [5,4,3] => [3,3,3,2,1]
[.,[[[[.,[[.,.],.]],.],.],.]] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1] => [4,3,3,2,1]
[.,[[[[[.,.],[.,.]],.],.],.]] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,1] => [5,3,3,2,1]
[.,[[[[[.,[.,.]],.],.],.],.]] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2] => [4,4,3,2,1]
[.,[[[[[[.,.],.],.],.],.],.]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1] => [5,4,3,2,1]
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => [6]
[[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => [6,1]
[[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1,1] => [6,2]
[[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1,1] => [6,1,1]
[[.,.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1] => [6,2,1]
[[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => [6,3]
[[.,.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => [6,3,1]
[[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1,1] => [6,2,2]
[[.,.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1,1] => [6,3,2]
[[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1,1] => [6,1,1,1]
[[.,.],[.,[[.,[[.,.],.]],.]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1,1] => [6,2,1,1]
[[.,.],[.,[[[.,.],[.,.]],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1,1] => [6,3,1,1]
[[.,.],[.,[[[.,[.,.]],.],.]]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1,1] => [6,2,2,1]
[[.,.],[.,[[[[.,.],.],.],.]]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1,1] => [6,3,2,1]
[[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => [6,4]
[[.,.],[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1,1] => [6,4,1]
[[.,.],[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => [6,4,2]
[[.,.],[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1,1] => [6,4,1,1]
[[.,.],[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1,1] => [6,4,2,1]
[[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => [6,3,3]
[[.,.],[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1,1] => [6,3,3,1]
[[.,.],[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => [6,4,3]
[[.,.],[[[.,.],.],[[.,.],.]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1,1] => [6,4,3,1]
[[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1,1] => [6,2,2,2]
[[.,.],[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1,1] => [6,3,2,2]
[[.,.],[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => [6,4,2,2]
[[.,.],[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1,1] => [6,3,3,2]
[[.,.],[[[[.,.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1,1] => [6,4,3,2]
[[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1,1] => [6,1,1,1,1]
[[.,.],[[.,[.,[[.,.],.]]],.]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1,1] => [6,2,1,1,1]
[[.,.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1,1] => [6,3,1,1,1]
[[.,.],[[.,[[.,[.,.]],.]],.]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1,1] => [6,2,2,1,1]
[[.,.],[[.,[[[.,.],.],.]],.]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1,1] => [6,3,2,1,1]
[[.,.],[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1,1] => [6,4,1,1,1]
[[.,.],[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1,1] => [6,4,2,1,1]
[[.,.],[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1,1] => [6,3,3,1,1]
[[.,.],[[[[.,.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1,1] => [6,4,3,1,1]
[[.,.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1,1] => [6,2,2,2,1]
[[.,.],[[[.,[[.,.],.]],.],.]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,1,1] => [6,3,2,2,1]
[[.,.],[[[[.,.],[.,.]],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2,1,1] => [6,4,2,2,1]
[[.,.],[[[[.,[.,.]],.],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,1,1] => [6,3,3,2,1]
[[.,.],[[[[[.,.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,1] => [6,4,3,2,1]
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => [5,5]
[[.,[.,.]],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2] => [5,5,1]
[[.,[.,.]],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => [5,5,2]
[[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2] => [5,5,1,1]
[[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2] => [5,5,2,1]
[[.,[.,.]],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => [5,5,3]
[[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => [5,5,3,1]
[[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => [5,5,2,2]
[[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => [5,5,3,2]
[[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2] => [5,5,1,1,1]
[[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2] => [5,5,2,1,1]
[[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2] => [5,5,3,1,1]
[[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2] => [5,5,2,2,1]
[[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2] => [5,5,3,2,1]
[[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2,1] => [6,5]
[[[.,.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2,1] => [6,5,1]
[[[.,.],.],[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2,1] => [6,5,2]
[[[.,.],.],[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2,1] => [6,5,1,1]
[[[.,.],.],[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2,1] => [6,5,2,1]
[[[.,.],.],[[.,.],[.,[.,.]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => [6,5,3]
[[[.,.],.],[[.,.],[[.,.],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => [6,5,3,1]
[[[.,.],.],[[.,[.,.]],[.,.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => [6,5,2,2]
[[[.,.],.],[[[.,.],.],[.,.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => [6,5,3,2]
[[[.,.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2,1] => [6,5,1,1,1]
[[[.,.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2,1] => [6,5,2,1,1]
[[[.,.],.],[[[.,.],[.,.]],.]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2,1] => [6,5,3,1,1]
[[[.,.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2,1] => [6,5,2,2,1]
[[[.,.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2,1] => [6,5,3,2,1]
[[.,[.,[.,.]]],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => [4,4,4]
[[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3] => [4,4,4,1]
[[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => [4,4,4,2]
[[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3] => [4,4,4,1,1]
[[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3] => [4,4,4,2,1]
[[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1] => [5,4,4]
[[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1] => [5,4,4,1]
[[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => [5,4,4,2]
[[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1] => [5,4,4,1,1]
[[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1] => [5,4,4,2,1]
[[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => [6,4,4]
[[[.,.],[.,.]],[.,[[.,.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => [6,4,4,1]
[[[.,.],[.,.]],[[.,.],[.,.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => [6,4,4,2]
[[[.,.],[.,.]],[[.,[.,.]],.]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => [6,4,4,1,1]
[[[.,.],[.,.]],[[[.,.],.],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => [6,4,4,2,1]
[[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2] => [5,5,4]
[[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2] => [5,5,4,1]
[[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => [5,5,4,2]
[[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2] => [5,5,4,1,1]
[[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2] => [5,5,4,2,1]
[[[[.,.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2,1] => [6,5,4]
[[[[.,.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2,1] => [6,5,4,1]
[[[[.,.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => [6,5,4,2]
[[[[.,.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2,1] => [6,5,4,1,1]
[[[[.,.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2,1] => [6,5,4,2,1]
[[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => [3,3,3,3]
[[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,4,4] => [3,3,3,3,1]
[[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1] => [4,3,3,3]
[[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1] => [4,3,3,3,1]
[[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1] => [5,3,3,3]
[[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1] => [5,3,3,3,1]
[[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2] => [4,4,3,3]
[[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2] => [4,4,3,3,1]
[[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1] => [5,4,3,3]
[[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1] => [5,4,3,3,1]
[[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => [6,3,3,3]
[[[.,.],[.,[.,.]]],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => [6,3,3,3,1]
[[[.,.],[[.,.],.]],[.,[.,.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => [6,4,3,3]
[[[.,.],[[.,.],.]],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => [6,4,3,3,1]
[[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => [5,5,3,3]
[[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => [5,5,3,3,1]
[[[[.,.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => [6,5,3,3]
[[[[.,.],.],[.,.]],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2,1] => [6,5,3,3,1]
[[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3] => [4,4,4,3]
[[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3] => [4,4,4,3,1]
[[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1] => [5,4,4,3]
[[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3,1] => [5,4,4,3,1]
[[[[.,.],[.,.]],.],[.,[.,.]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1,1] => [6,4,4,3]
[[[[.,.],[.,.]],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3,1,1] => [6,4,4,3,1]
[[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2] => [5,5,4,3]
[[[[.,[.,.]],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [5,4,4,3,2] => [5,5,4,3,1]
[[[[[.,.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2,1] => [6,5,4,3]
[[[[[.,.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,4,3,2,1] => [6,5,4,3,1]
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => [2,2,2,2,2]
[[.,[.,[.,[[.,.],.]]]],[.,.]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,5,1] => [3,2,2,2,2]
[[.,[.,[[.,.],[.,.]]]],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1] => [4,2,2,2,2]
[[.,[.,[[.,[.,.]],.]]],[.,.]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,5,2] => [3,3,2,2,2]
[[.,[.,[[[.,.],.],.]]],[.,.]] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1] => [4,3,2,2,2]
[[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1] => [5,2,2,2,2]
[[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1] => [5,3,2,2,2]
[[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2] => [4,4,2,2,2]
[[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1] => [5,4,2,2,2]
[[.,[[.,[.,[.,.]]],.]],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [5,5,3] => [3,3,3,2,2]
[[.,[[.,[[.,.],.]],.]],[.,.]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1] => [4,3,3,2,2]
[[.,[[[.,.],[.,.]],.]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1] => [5,3,3,2,2]
[[.,[[[.,[.,.]],.],.]],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2] => [4,4,3,2,2]
[[.,[[[[.,.],.],.],.]],[.,.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1] => [5,4,3,2,2]
[[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1,1] => [6,2,2,2,2]
[[[.,.],[.,[[.,.],.]]],[.,.]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1,1] => [6,3,2,2,2]
[[[.,.],[[.,.],[.,.]]],[.,.]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => [6,4,2,2,2]
[[[.,.],[[.,[.,.]],.]],[.,.]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1,1] => [6,3,3,2,2]
[[[.,.],[[[.,.],.],.]],[.,.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1,1] => [6,4,3,2,2]
[[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => [5,5,2,2,2]
[[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2] => [5,5,3,2,2]
[[[[.,.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => [6,5,2,2,2]
[[[[.,.],.],[[.,.],.]],[.,.]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2,1] => [6,5,3,2,2]
[[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => [4,4,4,2,2]
[[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1] => [5,4,4,2,2]
[[[[.,.],[.,.]],[.,.]],[.,.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => [6,4,4,2,2]
[[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => [5,5,4,2,2]
[[[[[.,.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2,1] => [6,5,4,2,2]
[[[.,[.,[.,[.,.]]]],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,5,4] => [3,3,3,3,2]
[[[.,[.,[[.,.],.]]],.],[.,.]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1] => [4,3,3,3,2]
[[[.,[[.,.],[.,.]]],.],[.,.]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1] => [5,3,3,3,2]
[[[.,[[.,[.,.]],.]],.],[.,.]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [5,5,4,2] => [4,4,3,3,2]
[[[.,[[[.,.],.],.]],.],[.,.]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [5,5,4,2,1] => [5,4,3,3,2]
[[[[.,.],[.,[.,.]]],.],[.,.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1,1] => [6,3,3,3,2]
[[[[.,.],[[.,.],.]],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [5,5,4,2,1,1] => [6,4,3,3,2]
[[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => [5,5,3,3,2]
[[[[[.,.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2,1] => [6,5,3,3,2]
[[[[.,[.,[.,.]]],.],.],[.,.]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3] => [4,4,4,3,2]
[[[[.,[[.,.],.]],.],.],[.,.]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3,1] => [5,4,4,3,2]
[[[[[.,.],[.,.]],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3,1,1] => [6,4,4,3,2]
[[[[[.,[.,.]],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [5,5,4,3,2] => [5,5,4,3,2]
[[[[[[.,.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [5,5,4,3,2,1] => [6,5,4,3,2]
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => [1,1,1,1,1,1]
[[.,[.,[.,[.,[[.,.],.]]]]],.] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => [2,1,1,1,1,1]
[[.,[.,[.,[[.,.],[.,.]]]]],.] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,1,1] => [3,1,1,1,1,1]
[[.,[.,[.,[[.,[.,.]],.]]]],.] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,2] => [2,2,1,1,1,1]
[[.,[.,[.,[[[.,.],.],.]]]],.] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,2,1] => [3,2,1,1,1,1]
[[.,[.,[[.,.],[.,[.,.]]]]],.] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1] => [4,1,1,1,1,1]
[[.,[.,[[.,.],[[.,.],.]]]],.] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1] => [4,2,1,1,1,1]
[[.,[.,[[.,[.,.]],[.,.]]]],.] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,2,2] => [3,3,1,1,1,1]
[[.,[.,[[[.,.],.],[.,.]]]],.] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1] => [4,3,1,1,1,1]
[[.,[.,[[.,[.,[.,.]]],.]]],.] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,3] => [2,2,2,1,1,1]
[[.,[.,[[.,[[.,.],.]],.]]],.] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,1] => [3,2,2,1,1,1]
[[.,[.,[[[.,.],[.,.]],.]]],.] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1] => [4,2,2,1,1,1]
[[.,[.,[[[.,[.,.]],.],.]]],.] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2] => [3,3,2,1,1,1]
[[.,[.,[[[[.,.],.],.],.]]],.] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1] => [4,3,2,1,1,1]
[[.,[[.,.],[.,[.,[.,.]]]]],.] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1] => [5,1,1,1,1,1]
[[.,[[.,.],[.,[[.,.],.]]]],.] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1] => [5,2,1,1,1,1]
[[.,[[.,.],[[.,.],[.,.]]]],.] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1] => [5,3,1,1,1,1]
[[.,[[.,.],[[.,[.,.]],.]]],.] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1,1] => [5,2,2,1,1,1]
[[.,[[.,.],[[[.,.],.],.]]],.] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,1] => [5,3,2,1,1,1]
[[.,[[.,[.,.]],[.,[.,.]]]],.] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2] => [4,4,1,1,1,1]
[[.,[[.,[.,.]],[[.,.],.]]],.] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2] => [4,4,2,1,1,1]
[[.,[[[.,.],.],[.,[.,.]]]],.] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2,1] => [5,4,1,1,1,1]
[[.,[[[.,.],.],[[.,.],.]]],.] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2,1] => [5,4,2,1,1,1]
[[.,[[.,[.,[.,.]]],[.,.]]],.] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [6,3,3] => [3,3,3,1,1,1]
[[.,[[.,[[.,.],.]],[.,.]]],.] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1] => [4,3,3,1,1,1]
[[.,[[[.,.],[.,.]],[.,.]]],.] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1,1] => [5,3,3,1,1,1]
[[.,[[[.,[.,.]],.],[.,.]]],.] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2] => [4,4,3,1,1,1]
[[.,[[[[.,.],.],.],[.,.]]],.] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2,1] => [5,4,3,1,1,1]
[[.,[[.,[.,[.,[.,.]]]],.]],.] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,4] => [2,2,2,2,1,1]
[[.,[[.,[.,[[.,.],.]]],.]],.] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [6,4,1] => [3,2,2,2,1,1]
[[.,[[.,[[.,.],[.,.]]],.]],.] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1] => [4,2,2,2,1,1]
[[.,[[.,[[.,[.,.]],.]],.]],.] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [6,4,2] => [3,3,2,2,1,1]
[[.,[[.,[[[.,.],.],.]],.]],.] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1] => [4,3,2,2,1,1]
[[.,[[[.,.],[.,[.,.]]],.]],.] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1,1] => [5,2,2,2,1,1]
[[.,[[[.,.],[[.,.],.]],.]],.] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,1] => [5,3,2,2,1,1]
[[.,[[[.,[.,.]],[.,.]],.]],.] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [6,4,2,2] => [4,4,2,2,1,1]
[[.,[[[[.,.],.],[.,.]],.]],.] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,2,1] => [5,4,2,2,1,1]
[[.,[[[.,[.,[.,.]]],.],.]],.] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [6,4,3] => [3,3,3,2,1,1]
[[.,[[[.,[[.,.],.]],.],.]],.] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1] => [4,3,3,2,1,1]
[[.,[[[[.,.],[.,.]],.],.]],.] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,1] => [5,3,3,2,1,1]
[[.,[[[[.,[.,.]],.],.],.]],.] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2] => [4,4,3,2,1,1]
[[.,[[[[[.,.],.],.],.],.]],.] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1] => [5,4,3,2,1,1]
[[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1,1] => [6,1,1,1,1,1]
[[[.,.],[.,[.,[[.,.],.]]]],.] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1,1] => [6,2,1,1,1,1]
[[[.,.],[.,[[.,.],[.,.]]]],.] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1,1] => [6,3,1,1,1,1]
[[[.,.],[.,[[.,[.,.]],.]]],.] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1,1,1] => [6,2,2,1,1,1]
[[[.,.],[.,[[[.,.],.],.]]],.] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,1,1] => [6,3,2,1,1,1]
[[[.,.],[[.,.],[.,[.,.]]]],.] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2,1,1] => [6,4,1,1,1,1]
[[[.,.],[[.,.],[[.,.],.]]],.] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2,1,1] => [6,4,2,1,1,1]
[[[.,.],[[.,[.,.]],[.,.]]],.] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1,1,1] => [6,3,3,1,1,1]
[[[.,.],[[[.,.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2,1,1] => [6,4,3,1,1,1]
[[[.,.],[[.,[.,[.,.]]],.]],.] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1,1,1] => [6,2,2,2,1,1]
[[[.,.],[[.,[[.,.],.]],.]],.] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,1,1] => [6,3,2,2,1,1]
[[[.,.],[[[.,.],[.,.]],.]],.] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,2,1,1] => [6,4,2,2,1,1]
[[[.,.],[[[.,[.,.]],.],.]],.] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,1,1] => [6,3,3,2,1,1]
[[[.,.],[[[[.,.],.],.],.]],.] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,1] => [6,4,3,2,1,1]
[[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => [5,5,1,1,1,1]
[[[.,[.,.]],[.,[[.,.],.]]],.] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,2,2] => [5,5,2,1,1,1]
[[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2] => [5,5,3,1,1,1]
[[[.,[.,.]],[[.,[.,.]],.]],.] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,2,2] => [5,5,2,2,1,1]
[[[.,[.,.]],[[[.,.],.],.]],.] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,2] => [5,5,3,2,1,1]
[[[[.,.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2,1] => [6,5,1,1,1,1]
[[[[.,.],.],[.,[[.,.],.]]],.] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,2,2,1] => [6,5,2,1,1,1]
[[[[.,.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2,1] => [6,5,3,1,1,1]
[[[[.,.],.],[[.,[.,.]],.]],.] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,2,2,1] => [6,5,2,2,1,1]
[[[[.,.],.],[[[.,.],.],.]],.] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,2,1] => [6,5,3,2,1,1]
[[[.,[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => [4,4,4,1,1,1]
[[[.,[.,[.,.]]],[[.,.],.]],.] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3] => [4,4,4,2,1,1]
[[[.,[[.,.],.]],[.,[.,.]]],.] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1] => [5,4,4,1,1,1]
[[[.,[[.,.],.]],[[.,.],.]],.] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3,1] => [5,4,4,2,1,1]
[[[[.,.],[.,.]],[.,[.,.]]],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1,1] => [6,4,4,1,1,1]
[[[[.,.],[.,.]],[[.,.],.]],.] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3,1,1] => [6,4,4,2,1,1]
[[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2] => [5,5,4,1,1,1]
[[[[.,[.,.]],.],[[.,.],.]],.] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,3,2] => [5,5,4,2,1,1]
[[[[[.,.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2,1] => [6,5,4,1,1,1]
[[[[[.,.],.],.],[[.,.],.]],.] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,3,2,1] => [6,5,4,2,1,1]
[[[.,[.,[.,[.,.]]]],[.,.]],.] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => [3,3,3,3,1,1]
[[[.,[.,[[.,.],.]]],[.,.]],.] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1] => [4,3,3,3,1,1]
[[[.,[[.,.],[.,.]]],[.,.]],.] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1] => [5,3,3,3,1,1]
[[[.,[[.,[.,.]],.]],[.,.]],.] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [6,4,4,2] => [4,4,3,3,1,1]
[[[.,[[[.,.],.],.]],[.,.]],.] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [6,4,4,2,1] => [5,4,3,3,1,1]
[[[[.,.],[.,[.,.]]],[.,.]],.] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1,1] => [6,3,3,3,1,1]
[[[[.,.],[[.,.],.]],[.,.]],.] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [6,4,4,2,1,1] => [6,4,3,3,1,1]
[[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => [5,5,3,3,1,1]
[[[[[.,.],.],[.,.]],[.,.]],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2,1] => [6,5,3,3,1,1]
[[[[.,[.,[.,.]]],.],[.,.]],.] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3] => [4,4,4,3,1,1]
[[[[.,[[.,.],.]],.],[.,.]],.] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3,1] => [5,4,4,3,1,1]
[[[[[.,.],[.,.]],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3,1,1] => [6,4,4,3,1,1]
[[[[[.,[.,.]],.],.],[.,.]],.] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [6,4,4,3,2] => [5,5,4,3,1,1]
[[[[[[.,.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,4,3,2,1] => [6,5,4,3,1,1]
[[[.,[.,[.,[.,[.,.]]]]],.],.] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => [2,2,2,2,2,1]
[[[.,[.,[.,[[.,.],.]]]],.],.] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [6,5,1] => [3,2,2,2,2,1]
[[[.,[.,[[.,.],[.,.]]]],.],.] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1] => [4,2,2,2,2,1]
[[[.,[.,[[.,[.,.]],.]]],.],.] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [6,5,2] => [3,3,2,2,2,1]
[[[.,[.,[[[.,.],.],.]]],.],.] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1] => [4,3,2,2,2,1]
[[[.,[[.,.],[.,[.,.]]]],.],.] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1,1] => [5,2,2,2,2,1]
[[[.,[[.,.],[[.,.],.]]],.],.] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,1] => [5,3,2,2,2,1]
[[[.,[[.,[.,.]],[.,.]]],.],.] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [6,5,2,2] => [4,4,2,2,2,1]
[[[.,[[[.,.],.],[.,.]]],.],.] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,2,1] => [5,4,2,2,2,1]
[[[.,[[.,[.,[.,.]]],.]],.],.] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [6,5,3] => [3,3,3,2,2,1]
[[[.,[[.,[[.,.],.]],.]],.],.] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1] => [4,3,3,2,2,1]
[[[.,[[[.,.],[.,.]],.]],.],.] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,1] => [5,3,3,2,2,1]
[[[.,[[[.,[.,.]],.],.]],.],.] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2] => [4,4,3,2,2,1]
[[[.,[[[[.,.],.],.],.]],.],.] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1] => [5,4,3,2,2,1]
[[[[.,.],[.,[.,[.,.]]]],.],.] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1,1,1] => [6,2,2,2,2,1]
[[[[.,.],[.,[[.,.],.]]],.],.] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,1,1] => [6,3,2,2,2,1]
[[[[.,.],[[.,.],[.,.]]],.],.] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,2,1,1] => [6,4,2,2,2,1]
[[[[.,.],[[.,[.,.]],.]],.],.] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,1,1] => [6,3,3,2,2,1]
[[[[.,.],[[[.,.],.],.]],.],.] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1,1] => [6,4,3,2,2,1]
[[[[.,[.,.]],[.,[.,.]]],.],.] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => [5,5,2,2,2,1]
[[[[.,[.,.]],[[.,.],.]],.],.] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,2] => [5,5,3,2,2,1]
[[[[[.,.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2,1] => [6,5,2,2,2,1]
[[[[[.,.],.],[[.,.],.]],.],.] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,2,1] => [6,5,3,2,2,1]
[[[[.,[.,[.,.]]],[.,.]],.],.] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => [4,4,4,2,2,1]
[[[[.,[[.,.],.]],[.,.]],.],.] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3,1] => [5,4,4,2,2,1]
[[[[[.,.],[.,.]],[.,.]],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3,1,1] => [6,4,4,2,2,1]
[[[[[.,[.,.]],.],[.,.]],.],.] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,3,2] => [5,5,4,2,2,1]
[[[[[[.,.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,3,2,1] => [6,5,4,2,2,1]
[[[[.,[.,[.,[.,.]]]],.],.],.] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [6,5,4] => [3,3,3,3,2,1]
[[[[.,[.,[[.,.],.]]],.],.],.] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1] => [4,3,3,3,2,1]
[[[[.,[[.,.],[.,.]]],.],.],.] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,1] => [5,3,3,3,2,1]
[[[[.,[[.,[.,.]],.]],.],.],.] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2] => [4,4,3,3,2,1]
[[[[.,[[[.,.],.],.]],.],.],.] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1] => [5,4,3,3,2,1]
[[[[[.,.],[.,[.,.]]],.],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,1,1] => [6,3,3,3,2,1]
[[[[[.,.],[[.,.],.]],.],.],.] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1,1] => [6,4,3,3,2,1]
[[[[[.,[.,.]],[.,.]],.],.],.] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2] => [5,5,3,3,2,1]
[[[[[[.,.],.],[.,.]],.],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2,1] => [6,5,3,3,2,1]
[[[[[.,[.,[.,.]]],.],.],.],.] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3] => [4,4,4,3,2,1]
[[[[[.,[[.,.],.]],.],.],.],.] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1] => [5,4,4,3,2,1]
[[[[[[.,.],[.,.]],.],.],.],.] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,1] => [6,4,4,3,2,1]
[[[[[[.,[.,.]],.],.],.],.],.] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2] => [5,5,4,3,2,1]
[[[[[[[.,.],.],.],.],.],.],.] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => [6,5,4,3,2,1]
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [] => []
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1] => [1]
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1] => [2]
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => [1,1]
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => [2,1]
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1] => [3]
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,1,1] => [3,1]
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,2] => [2,2]
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [2,2,1] => [3,2]
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => [1,1,1]
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => [2,1,1]
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]] => [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [3,1,1] => [3,1,1]
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => [2,2,1]
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => [3,2,1]
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1] => [4]
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1] => [4,1]
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1] => [4,2]
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]] => [1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1] => [4,1,1]
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]] => [1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1] => [4,2,1]
[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [2,2,2] => [3,3]
[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [3,2,2] => [3,3,1]
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1] => [4,3]
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]] => [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => [4,3,1]
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [3,3] => [2,2,2]
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]] => [1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [3,3,1] => [3,2,2]
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]] => [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1] => [4,2,2]
[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]] => [1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [3,3,2] => [3,3,2]
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1] => [4,3,2]
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => [1,1,1,1]
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,1] => [2,1,1,1]
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [4,1,1] => [3,1,1,1]
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [4,2] => [2,2,1,1]
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]] => [1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [4,2,1] => [3,2,1,1]
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1] => [4,1,1,1]
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]] => [1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1] => [4,2,1,1]
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]] => [1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [4,2,2] => [3,3,1,1]
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]] => [1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1] => [4,3,1,1]
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [4,3] => [2,2,2,1]
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [4,3,1] => [3,2,2,1]
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]] => [1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1] => [4,2,2,1]
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [4,3,2] => [3,3,2,1]
[.,[.,[.,[[[[[.,.],.],.],.],.]]]] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1] => [4,3,2,1]
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1] => [5]
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1] => [5,1]
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => [5,2]
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]] => [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1] => [5,1,1]
[.,[.,[[.,.],[.,[[[.,.],.],.]]]]] => [1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1] => [5,2,1]
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1] => [5,3]
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => [5,3,1]
[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]] => [1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1] => [5,2,2]
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]] => [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1] => [5,3,2]
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1] => [5,1,1,1]
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1] => [5,2,1,1]
[.,[.,[[.,.],[[[.,.],[.,.]],.]]]] => [1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1] => [5,3,1,1]
[.,[.,[[.,.],[[[.,[.,.]],.],.]]]] => [1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1] => [5,2,2,1]
[.,[.,[[.,.],[[[[.,.],.],.],.]]]] => [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1] => [5,3,2,1]
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2] => [4,4]
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2] => [4,4,1]
[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => [4,4,2]
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]] => [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2] => [4,4,1,1]
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2] => [4,4,2,1]
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1] => [5,4]
[.,[.,[[[.,.],.],[.,[[.,.],.]]]]] => [1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1] => [5,4,1]
[.,[.,[[[.,.],.],[[.,.],[.,.]]]]] => [1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1] => [5,4,2]
[.,[.,[[[.,.],.],[[.,[.,.]],.]]]] => [1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1] => [5,4,1,1]
[.,[.,[[[.,.],.],[[[.,.],.],.]]]] => [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1] => [5,4,2,1]
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => [3,3,3]
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [4,3,3] => [3,3,3,1]
[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]] => [1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1] => [4,3,3]
[.,[.,[[.,[[.,.],.]],[[.,.],.]]]] => [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1] => [4,3,3,1]
[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1] => [5,3,3]
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]] => [1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1] => [5,3,3,1]
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]] => [1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2] => [4,4,3]
[.,[.,[[[.,[.,.]],.],[[.,.],.]]]] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2] => [4,4,3,1]
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => [1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1] => [5,4,3]
[.,[.,[[[[.,.],.],.],[[.,.],.]]]] => [1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1] => [5,4,3,1]
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [4,4] => [2,2,2,2]
[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]] => [1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [4,4,1] => [3,2,2,2]
[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]] => [1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1] => [4,2,2,2]
[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]] => [1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [4,4,2] => [3,3,2,2]
[.,[.,[[.,[[[.,.],.],.]],[.,.]]]] => [1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1] => [4,3,2,2]
[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]] => [1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1] => [5,2,2,2]
[.,[.,[[[.,.],[[.,.],.]],[.,.]]]] => [1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1] => [5,3,2,2]
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2] => [4,4,2,2]
[.,[.,[[[[.,.],.],[.,.]],[.,.]]]] => [1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1] => [5,4,2,2]
[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]] => [1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [4,4,3] => [3,3,3,2]
[.,[.,[[[.,[[.,.],.]],.],[.,.]]]] => [1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1] => [4,3,3,2]
[.,[.,[[[[.,.],[.,.]],.],[.,.]]]] => [1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1] => [5,3,3,2]
[.,[.,[[[[.,[.,.]],.],.],[.,.]]]] => [1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2] => [4,4,3,2]
[.,[.,[[[[[.,.],.],.],.],[.,.]]]] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1] => [5,4,3,2]
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => [1,1,1,1,1]
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]] => [1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [5,1] => [2,1,1,1,1]
[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]] => [1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,1,1] => [3,1,1,1,1]
[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]] => [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [5,2] => [2,2,1,1,1]
[.,[.,[[.,[.,[[[.,.],.],.]]],.]]] => [1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,2,1] => [3,2,1,1,1]
[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]] => [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1] => [4,1,1,1,1]
[.,[.,[[.,[[.,.],[[.,.],.]]],.]]] => [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1] => [4,2,1,1,1]
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]] => [1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,2,2] => [3,3,1,1,1]
[.,[.,[[.,[[[.,.],.],[.,.]]],.]]] => [1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1] => [4,3,1,1,1]
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]] => [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [5,3] => [2,2,2,1,1]
[.,[.,[[.,[[.,[[.,.],.]],.]],.]]] => [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,3,1] => [3,2,2,1,1]
[.,[.,[[.,[[[.,.],[.,.]],.]],.]]] => [1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1] => [4,2,2,1,1]
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]] => [1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,3,2] => [3,3,2,1,1]
[.,[.,[[.,[[[[.,.],.],.],.]],.]]] => [1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1] => [4,3,2,1,1]
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1] => [5,1,1,1,1]
[.,[.,[[[.,.],[.,[[.,.],.]]],.]]] => [1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1] => [5,2,1,1,1]
[.,[.,[[[.,.],[[.,.],[.,.]]],.]]] => [1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1] => [5,3,1,1,1]
[.,[.,[[[.,.],[[.,[.,.]],.]],.]]] => [1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1] => [5,2,2,1,1]
[.,[.,[[[.,.],[[[.,.],.],.]],.]]] => [1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1] => [5,3,2,1,1]
[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]] => [1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2] => [4,4,1,1,1]
[.,[.,[[[.,[.,.]],[[.,.],.]],.]]] => [1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2] => [4,4,2,1,1]
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]] => [1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1] => [5,4,1,1,1]
[.,[.,[[[[.,.],.],[[.,.],.]],.]]] => [1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1] => [5,4,2,1,1]
[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]] => [1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,3,3] => [3,3,3,1,1]
[.,[.,[[[.,[[.,.],.]],[.,.]],.]]] => [1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1] => [4,3,3,1,1]
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]] => [1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1] => [5,3,3,1,1]
[.,[.,[[[[.,[.,.]],.],[.,.]],.]]] => [1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2] => [4,4,3,1,1]
[.,[.,[[[[[.,.],.],.],[.,.]],.]]] => [1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1] => [5,4,3,1,1]
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [5,4] => [2,2,2,2,1]
[.,[.,[[[.,[.,[[.,.],.]]],.],.]]] => [1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,4,1] => [3,2,2,2,1]
[.,[.,[[[.,[[.,.],[.,.]]],.],.]]] => [1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1] => [4,2,2,2,1]
[.,[.,[[[.,[[.,[.,.]],.]],.],.]]] => [1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [5,4,2] => [3,3,2,2,1]
[.,[.,[[[.,[[[.,.],.],.]],.],.]]] => [1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1] => [4,3,2,2,1]
[.,[.,[[[[.,.],[.,[.,.]]],.],.]]] => [1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1] => [5,2,2,2,1]
[.,[.,[[[[.,.],[[.,.],.]],.],.]]] => [1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1] => [5,3,2,2,1]
[.,[.,[[[[.,[.,.]],[.,.]],.],.]]] => [1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2] => [4,4,2,2,1]
[.,[.,[[[[[.,.],.],[.,.]],.],.]]] => [1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1] => [5,4,2,2,1]
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3] => [3,3,3,2,1]
[.,[.,[[[[.,[[.,.],.]],.],.],.]]] => [1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1] => [4,3,3,2,1]
[.,[.,[[[[[.,.],[.,.]],.],.],.]]] => [1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1] => [5,3,3,2,1]
[.,[.,[[[[[.,[.,.]],.],.],.],.]]] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2] => [4,4,3,2,1]
[.,[.,[[[[[[.,.],.],.],.],.],.]]] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1] => [5,4,3,2,1]
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => [6]
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1] => [6,1]
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1] => [6,2]
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1] => [6,1,1]
[.,[[.,.],[.,[.,[[[.,.],.],.]]]]] => [1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1] => [6,2,1]
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1] => [6,3]
[.,[[.,.],[.,[[.,.],[[.,.],.]]]]] => [1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1] => [6,3,1]
[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]] => [1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1] => [6,2,2]
[.,[[.,.],[.,[[[.,.],.],[.,.]]]]] => [1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1] => [6,3,2]
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]] => [1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1] => [6,1,1,1]
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]] => [1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1] => [6,2,1,1]
[.,[[.,.],[.,[[[.,.],[.,.]],.]]]] => [1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1,1] => [6,3,1,1]
[.,[[.,.],[.,[[[.,[.,.]],.],.]]]] => [1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1,1] => [6,2,2,1]
[.,[[.,.],[.,[[[[.,.],.],.],.]]]] => [1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1,1] => [6,3,2,1]
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1] => [6,4]
[.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => [1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1] => [6,4,1]
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => [6,4,2]
[.,[[.,.],[[.,.],[[.,[.,.]],.]]]] => [1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1] => [6,4,1,1]
[.,[[.,.],[[.,.],[[[.,.],.],.]]]] => [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1,1] => [6,4,2,1]
[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1] => [6,3,3]
[.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1] => [6,3,3,1]
[.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1] => [6,4,3]
[.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1] => [6,4,3,1]
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => [1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1] => [6,2,2,2]
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]] => [1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1,1] => [6,3,2,2]
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1] => [6,4,2,2]
[.,[[.,.],[[[.,[.,.]],.],[.,.]]]] => [1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1,1] => [6,3,3,2]
[.,[[.,.],[[[[.,.],.],.],[.,.]]]] => [1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1,1] => [6,4,3,2]
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]] => [1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1] => [6,1,1,1,1]
[.,[[.,.],[[.,[.,[[.,.],.]]],.]]] => [1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1,1] => [6,2,1,1,1]
[.,[[.,.],[[.,[[.,.],[.,.]]],.]]] => [1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1] => [6,3,1,1,1]
[.,[[.,.],[[.,[[.,[.,.]],.]],.]]] => [1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1,1] => [6,2,2,1,1]
[.,[[.,.],[[.,[[[.,.],.],.]],.]]] => [1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1,1] => [6,3,2,1,1]
[.,[[.,.],[[[.,.],[.,[.,.]]],.]]] => [1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1,1] => [6,4,1,1,1]
[.,[[.,.],[[[.,.],[[.,.],.]],.]]] => [1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1] => [6,4,2,1,1]
[.,[[.,.],[[[.,[.,.]],[.,.]],.]]] => [1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1,1] => [6,3,3,1,1]
[.,[[.,.],[[[[.,.],.],[.,.]],.]]] => [1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1,1] => [6,4,3,1,1]
[.,[[.,.],[[[.,[.,[.,.]]],.],.]]] => [1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1,1] => [6,2,2,2,1]
[.,[[.,.],[[[.,[[.,.],.]],.],.]]] => [1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1,1] => [6,3,2,2,1]
[.,[[.,.],[[[[.,.],[.,.]],.],.]]] => [1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1,1] => [6,4,2,2,1]
[.,[[.,.],[[[[.,[.,.]],.],.],.]]] => [1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1,1] => [6,3,3,2,1]
[.,[[.,.],[[[[[.,.],.],.],.],.]]] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,1] => [6,4,3,2,1]
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2] => [5,5]
[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2] => [5,5,1]
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2] => [5,5,2]
[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2] => [5,5,1,1]
[.,[[.,[.,.]],[.,[[[.,.],.],.]]]] => [1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2] => [5,5,2,1]
[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2] => [5,5,3]
[.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2] => [5,5,3,1]
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => [5,5,2,2]
[.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2] => [5,5,3,2]
[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] => [1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2] => [5,5,1,1,1]
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]] => [1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2] => [5,5,2,1,1]
[.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2] => [5,5,3,1,1]
[.,[[.,[.,.]],[[[.,[.,.]],.],.]]] => [1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2] => [5,5,2,2,1]
[.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2] => [5,5,3,2,1]
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1] => [6,5]
[.,[[[.,.],.],[.,[.,[[.,.],.]]]]] => [1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1] => [6,5,1]
[.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => [1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1] => [6,5,2]
[.,[[[.,.],.],[.,[[.,[.,.]],.]]]] => [1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,1] => [6,5,1,1]
[.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1] => [6,5,2,1]
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1] => [6,5,3]
[.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1] => [6,5,3,1]
[.,[[[.,.],.],[[.,[.,.]],[.,.]]]] => [1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1] => [6,5,2,2]
[.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1] => [6,5,3,2]
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]] => [1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1] => [6,5,1,1,1]
[.,[[[.,.],.],[[.,[[.,.],.]],.]]] => [1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1] => [6,5,2,1,1]
[.,[[[.,.],.],[[[.,.],[.,.]],.]]] => [1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1] => [6,5,3,1,1]
[.,[[[.,.],.],[[[.,[.,.]],.],.]]] => [1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1] => [6,5,2,2,1]
[.,[[[.,.],.],[[[[.,.],.],.],.]]] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2,1] => [6,5,3,2,1]
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3] => [4,4,4]
[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3] => [4,4,4,1]
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3] => [4,4,4,2]
[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]] => [1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3] => [4,4,4,1,1]
[.,[[.,[.,[.,.]]],[[[.,.],.],.]]] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3] => [4,4,4,2,1]
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]] => [1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1] => [5,4,4]
[.,[[.,[[.,.],.]],[.,[[.,.],.]]]] => [1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1] => [5,4,4,1]
[.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1] => [5,4,4,2]
[.,[[.,[[.,.],.]],[[.,[.,.]],.]]] => [1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1] => [5,4,4,1,1]
[.,[[.,[[.,.],.]],[[[.,.],.],.]]] => [1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1] => [5,4,4,2,1]
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1] => [6,4,4]
[.,[[[.,.],[.,.]],[.,[[.,.],.]]]] => [1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1] => [6,4,4,1]
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => [6,4,4,2]
[.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1] => [6,4,4,1,1]
[.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1,1] => [6,4,4,2,1]
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2] => [5,5,4]
[.,[[[.,[.,.]],.],[.,[[.,.],.]]]] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2] => [5,5,4,1]
[.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2] => [5,5,4,2]
[.,[[[.,[.,.]],.],[[.,[.,.]],.]]] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2] => [5,5,4,1,1]
[.,[[[.,[.,.]],.],[[[.,.],.],.]]] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2] => [5,5,4,2,1]
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1] => [6,5,4]
[.,[[[[.,.],.],.],[.,[[.,.],.]]]] => [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1] => [6,5,4,1]
[.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2,1] => [6,5,4,2]
[.,[[[[.,.],.],.],[[.,[.,.]],.]]] => [1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2,1] => [6,5,4,1,1]
[.,[[[[.,.],.],.],[[[.,.],.],.]]] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2,1] => [6,5,4,2,1]
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [4,4,4] => [3,3,3,3]
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,4] => [3,3,3,3,1]
[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]] => [1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1] => [4,3,3,3]
[.,[[.,[.,[[.,.],.]]],[[.,.],.]]] => [1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1] => [4,3,3,3,1]
[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]] => [1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1] => [5,3,3,3]
[.,[[.,[[.,.],[.,.]]],[[.,.],.]]] => [1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1] => [5,3,3,3,1]
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]] => [1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2] => [4,4,3,3]
[.,[[.,[[.,[.,.]],.]],[[.,.],.]]] => [1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2] => [4,4,3,3,1]
[.,[[.,[[[.,.],.],.]],[.,[.,.]]]] => [1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1] => [5,4,3,3]
[.,[[.,[[[.,.],.],.]],[[.,.],.]]] => [1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1] => [5,4,3,3,1]
[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1] => [6,3,3,3]
[.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1] => [6,3,3,3,1]
[.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1] => [6,4,3,3]
[.,[[[.,.],[[.,.],.]],[[.,.],.]]] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1,1] => [6,4,3,3,1]
[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2] => [5,5,3,3]
[.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2] => [5,5,3,3,1]
[.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,1] => [6,5,3,3]
[.,[[[[.,.],.],[.,.]],[[.,.],.]]] => [1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2,1] => [6,5,3,3,1]
[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3] => [4,4,4,3]
[.,[[[.,[.,[.,.]]],.],[[.,.],.]]] => [1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3] => [4,4,4,3,1]
[.,[[[.,[[.,.],.]],.],[.,[.,.]]]] => [1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1] => [5,4,4,3]
[.,[[[.,[[.,.],.]],.],[[.,.],.]]] => [1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,1] => [5,4,4,3,1]
[.,[[[[.,.],[.,.]],.],[.,[.,.]]]] => [1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1,1] => [6,4,4,3]
[.,[[[[.,.],[.,.]],.],[[.,.],.]]] => [1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,1,1] => [6,4,4,3,1]
[.,[[[[.,[.,.]],.],.],[.,[.,.]]]] => [1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,2] => [5,5,4,3]
[.,[[[[.,[.,.]],.],.],[[.,.],.]]] => [1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,2] => [5,5,4,3,1]
[.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,2,1] => [6,5,4,3]
[.,[[[[[.,.],.],.],.],[[.,.],.]]] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,2,1] => [6,5,4,3,1]
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [5,5] => [2,2,2,2,2]
[.,[[.,[.,[.,[[.,.],.]]]],[.,.]]] => [1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [5,5,1] => [3,2,2,2,2]
[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]] => [1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1] => [4,2,2,2,2]
[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]] => [1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,5,2] => [3,3,2,2,2]
[.,[[.,[.,[[[.,.],.],.]]],[.,.]]] => [1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1] => [4,3,2,2,2]
[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]] => [1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1] => [5,2,2,2,2]
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]] => [1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1] => [5,3,2,2,2]
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2] => [4,4,2,2,2]
[.,[[.,[[[.,.],.],[.,.]]],[.,.]]] => [1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1] => [5,4,2,2,2]
[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]] => [1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,5,3] => [3,3,3,2,2]
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]] => [1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1] => [4,3,3,2,2]
[.,[[.,[[[.,.],[.,.]],.]],[.,.]]] => [1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1] => [5,3,3,2,2]
[.,[[.,[[[.,[.,.]],.],.]],[.,.]]] => [1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2] => [4,4,3,2,2]
[.,[[.,[[[[.,.],.],.],.]],[.,.]]] => [1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,1] => [5,4,3,2,2]
[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1] => [6,2,2,2,2]
[.,[[[.,.],[.,[[.,.],.]]],[.,.]]] => [1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1,1] => [6,3,2,2,2]
[.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1] => [6,4,2,2,2]
[.,[[[.,.],[[.,[.,.]],.]],[.,.]]] => [1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1] => [6,3,3,2,2]
[.,[[[.,.],[[[.,.],.],.]],[.,.]]] => [1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,1,1] => [6,4,3,2,2]
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2] => [5,5,2,2,2]
[.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,2] => [5,5,3,2,2]
[.,[[[[.,.],.],[.,[.,.]]],[.,.]]] => [1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2,1] => [6,5,2,2,2]
[.,[[[[.,.],.],[[.,.],.]],[.,.]]] => [1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,2,1] => [6,5,3,2,2]
[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3] => [4,4,4,2,2]
[.,[[[.,[[.,.],.]],[.,.]],[.,.]]] => [1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1] => [5,4,4,2,2]
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1,1] => [6,4,4,2,2]
[.,[[[[.,[.,.]],.],[.,.]],[.,.]]] => [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2] => [5,5,4,2,2]
[.,[[[[[.,.],.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2,1] => [6,5,4,2,2]
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]] => [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,5,4] => [3,3,3,3,2]
[.,[[[.,[.,[[.,.],.]]],.],[.,.]]] => [1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1] => [4,3,3,3,2]
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]] => [1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1] => [5,3,3,3,2]
[.,[[[.,[[.,[.,.]],.]],.],[.,.]]] => [1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2] => [4,4,3,3,2]
[.,[[[.,[[[.,.],.],.]],.],[.,.]]] => [1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,1] => [5,4,3,3,2]
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]] => [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1,1] => [6,3,3,3,2]
[.,[[[[.,.],[[.,.],.]],.],[.,.]]] => [1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,1,1] => [6,4,3,3,2]
[.,[[[[.,[.,.]],[.,.]],.],[.,.]]] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,2] => [5,5,3,3,2]
[.,[[[[[.,.],.],[.,.]],.],[.,.]]] => [1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,2,1] => [6,5,3,3,2]
[.,[[[[.,[.,[.,.]]],.],.],[.,.]]] => [1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3] => [4,4,4,3,2]
[.,[[[[.,[[.,.],.]],.],.],[.,.]]] => [1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,1] => [5,4,4,3,2]
[.,[[[[[.,.],[.,.]],.],.],[.,.]]] => [1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,1,1] => [6,4,4,3,2]
[.,[[[[[.,[.,.]],.],.],.],[.,.]]] => [1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,2] => [5,5,4,3,2]
[.,[[[[[[.,.],.],.],.],.],[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,2,1] => [6,5,4,3,2]
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => [1,1,1,1,1,1]
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1] => [2,1,1,1,1,1]
[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [6,1,1] => [3,1,1,1,1,1]
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,2] => [2,2,1,1,1,1]
[.,[[.,[.,[.,[[[.,.],.],.]]]],.]] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [6,2,1] => [3,2,1,1,1,1]
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1] => [4,1,1,1,1,1]
[.,[[.,[.,[[.,.],[[.,.],.]]]],.]] => [1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1] => [4,2,1,1,1,1]
[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [6,2,2] => [3,3,1,1,1,1]
[.,[[.,[.,[[[.,.],.],[.,.]]]],.]] => [1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1] => [4,3,1,1,1,1]
[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,3] => [2,2,2,1,1,1]
[.,[[.,[.,[[.,[[.,.],.]],.]]],.]] => [1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [6,3,1] => [3,2,2,1,1,1]
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]] => [1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1] => [4,2,2,1,1,1]
[.,[[.,[.,[[[.,[.,.]],.],.]]],.]] => [1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [6,3,2] => [3,3,2,1,1,1]
[.,[[.,[.,[[[[.,.],.],.],.]]],.]] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1] => [4,3,2,1,1,1]
[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]] => [1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1] => [5,1,1,1,1,1]
[.,[[.,[[.,.],[.,[[.,.],.]]]],.]] => [1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1] => [5,2,1,1,1,1]
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1] => [5,3,1,1,1,1]
[.,[[.,[[.,.],[[.,[.,.]],.]]],.]] => [1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1] => [5,2,2,1,1,1]
[.,[[.,[[.,.],[[[.,.],.],.]]],.]] => [1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,1] => [5,3,2,1,1,1]
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2] => [4,4,1,1,1,1]
[.,[[.,[[.,[.,.]],[[.,.],.]]],.]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2] => [4,4,2,1,1,1]
[.,[[.,[[[.,.],.],[.,[.,.]]]],.]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1] => [5,4,1,1,1,1]
[.,[[.,[[[.,.],.],[[.,.],.]]],.]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1] => [5,4,2,1,1,1]
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [6,3,3] => [3,3,3,1,1,1]
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]] => [1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1] => [4,3,3,1,1,1]
[.,[[.,[[[.,.],[.,.]],[.,.]]],.]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1] => [5,3,3,1,1,1]
[.,[[.,[[[.,[.,.]],.],[.,.]]],.]] => [1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2] => [4,4,3,1,1,1]
[.,[[.,[[[[.,.],.],.],[.,.]]],.]] => [1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1] => [5,4,3,1,1,1]
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]] => [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,4] => [2,2,2,2,1,1]
[.,[[.,[[.,[.,[[.,.],.]]],.]],.]] => [1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [6,4,1] => [3,2,2,2,1,1]
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => [1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1] => [4,2,2,2,1,1]
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [6,4,2] => [3,3,2,2,1,1]
[.,[[.,[[.,[[[.,.],.],.]],.]],.]] => [1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1] => [4,3,2,2,1,1]
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]] => [1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1,1] => [5,2,2,2,1,1]
[.,[[.,[[[.,.],[[.,.],.]],.]],.]] => [1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,1] => [5,3,2,2,1,1]
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => [1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2] => [4,4,2,2,1,1]
[.,[[.,[[[[.,.],.],[.,.]],.]],.]] => [1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,1] => [5,4,2,2,1,1]
[.,[[.,[[[.,[.,[.,.]]],.],.]],.]] => [1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [6,4,3] => [3,3,3,2,1,1]
[.,[[.,[[[.,[[.,.],.]],.],.]],.]] => [1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1] => [4,3,3,2,1,1]
[.,[[.,[[[[.,.],[.,.]],.],.]],.]] => [1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,1] => [5,3,3,2,1,1]
[.,[[.,[[[[.,[.,.]],.],.],.]],.]] => [1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2] => [4,4,3,2,1,1]
[.,[[.,[[[[[.,.],.],.],.],.]],.]] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1] => [5,4,3,2,1,1]
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1] => [6,1,1,1,1,1]
[.,[[[.,.],[.,[.,[[.,.],.]]]],.]] => [1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1,1] => [6,2,1,1,1,1]
[.,[[[.,.],[.,[[.,.],[.,.]]]],.]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1,1] => [6,3,1,1,1,1]
[.,[[[.,.],[.,[[.,[.,.]],.]]],.]] => [1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1,1] => [6,2,2,1,1,1]
[.,[[[.,.],[.,[[[.,.],.],.]]],.]] => [1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,1,1] => [6,3,2,1,1,1]
[.,[[[.,.],[[.,.],[.,[.,.]]]],.]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1,1] => [6,4,1,1,1,1]
[.,[[[.,.],[[.,.],[[.,.],.]]],.]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1,1] => [6,4,2,1,1,1]
[.,[[[.,.],[[.,[.,.]],[.,.]]],.]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1] => [6,3,3,1,1,1]
[.,[[[.,.],[[[.,.],.],[.,.]]],.]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1,1] => [6,4,3,1,1,1]
[.,[[[.,.],[[.,[.,[.,.]]],.]],.]] => [1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1,1,1] => [6,2,2,2,1,1]
[.,[[[.,.],[[.,[[.,.],.]],.]],.]] => [1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,1,1] => [6,3,2,2,1,1]
[.,[[[.,.],[[[.,.],[.,.]],.]],.]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,1,1] => [6,4,2,2,1,1]
[.,[[[.,.],[[[.,[.,.]],.],.]],.]] => [1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,1,1] => [6,3,3,2,1,1]
[.,[[[.,.],[[[[.,.],.],.],.]],.]] => [1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,1] => [6,4,3,2,1,1]
[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2] => [5,5,1,1,1,1]
[.,[[[.,[.,.]],[.,[[.,.],.]]],.]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2] => [5,5,2,1,1,1]
[.,[[[.,[.,.]],[[.,.],[.,.]]],.]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2] => [5,5,3,1,1,1]
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,2] => [5,5,2,2,1,1]
[.,[[[.,[.,.]],[[[.,.],.],.]],.]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,2] => [5,5,3,2,1,1]
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1] => [6,5,1,1,1,1]
[.,[[[[.,.],.],[.,[[.,.],.]]],.]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,1] => [6,5,2,1,1,1]
[.,[[[[.,.],.],[[.,.],[.,.]]],.]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2,1] => [6,5,3,1,1,1]
[.,[[[[.,.],.],[[.,[.,.]],.]],.]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,2,1] => [6,5,2,2,1,1]
[.,[[[[.,.],.],[[[.,.],.],.]],.]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,2,1] => [6,5,3,2,1,1]
[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3] => [4,4,4,1,1,1]
[.,[[[.,[.,[.,.]]],[[.,.],.]],.]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3] => [4,4,4,2,1,1]
[.,[[[.,[[.,.],.]],[.,[.,.]]],.]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,1] => [5,4,4,1,1,1]
[.,[[[.,[[.,.],.]],[[.,.],.]],.]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3,1] => [5,4,4,2,1,1]
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,1,1] => [6,4,4,1,1,1]
[.,[[[[.,.],[.,.]],[[.,.],.]],.]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3,1,1] => [6,4,4,2,1,1]
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,2] => [5,5,4,1,1,1]
[.,[[[[.,[.,.]],.],[[.,.],.]],.]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3,2] => [5,5,4,2,1,1]
[.,[[[[[.,.],.],.],[.,[.,.]]],.]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,2,1] => [6,5,4,1,1,1]
[.,[[[[[.,.],.],.],[[.,.],.]],.]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3,2,1] => [6,5,4,2,1,1]
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [6,4,4] => [3,3,3,3,1,1]
[.,[[[.,[.,[[.,.],.]]],[.,.]],.]] => [1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1] => [4,3,3,3,1,1]
[.,[[[.,[[.,.],[.,.]]],[.,.]],.]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1,1] => [5,3,3,3,1,1]
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2] => [4,4,3,3,1,1]
[.,[[[.,[[[.,.],.],.]],[.,.]],.]] => [1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,1] => [5,4,3,3,1,1]
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1,1,1] => [6,3,3,3,1,1]
[.,[[[[.,.],[[.,.],.]],[.,.]],.]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,1,1] => [6,4,3,3,1,1]
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,2] => [5,5,3,3,1,1]
[.,[[[[[.,.],.],[.,.]],[.,.]],.]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,2,1] => [6,5,3,3,1,1]
[.,[[[[.,[.,[.,.]]],.],[.,.]],.]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3] => [4,4,4,3,1,1]
[.,[[[[.,[[.,.],.]],.],[.,.]],.]] => [1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,1] => [5,4,4,3,1,1]
[.,[[[[[.,.],[.,.]],.],[.,.]],.]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,1,1] => [6,4,4,3,1,1]
[.,[[[[[.,[.,.]],.],.],[.,.]],.]] => [1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,2] => [5,5,4,3,1,1]
[.,[[[[[[.,.],.],.],.],[.,.]],.]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,2,1] => [6,5,4,3,1,1]
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5] => [2,2,2,2,2,1]
[.,[[[.,[.,[.,[[.,.],.]]]],.],.]] => [1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [6,5,1] => [3,2,2,2,2,1]
[.,[[[.,[.,[[.,.],[.,.]]]],.],.]] => [1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1] => [4,2,2,2,2,1]
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]] => [1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [6,5,2] => [3,3,2,2,2,1]
[.,[[[.,[.,[[[.,.],.],.]]],.],.]] => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1] => [4,3,2,2,2,1]
[.,[[[.,[[.,.],[.,[.,.]]]],.],.]] => [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1,1] => [5,2,2,2,2,1]
[.,[[[.,[[.,.],[[.,.],.]]],.],.]] => [1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,1] => [5,3,2,2,2,1]
[.,[[[.,[[.,[.,.]],[.,.]]],.],.]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2] => [4,4,2,2,2,1]
[.,[[[.,[[[.,.],.],[.,.]]],.],.]] => [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,1] => [5,4,2,2,2,1]
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]] => [1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [6,5,3] => [3,3,3,2,2,1]
[.,[[[.,[[.,[[.,.],.]],.]],.],.]] => [1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1] => [4,3,3,2,2,1]
[.,[[[.,[[[.,.],[.,.]],.]],.],.]] => [1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,1] => [5,3,3,2,2,1]
[.,[[[.,[[[.,[.,.]],.],.]],.],.]] => [1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2] => [4,4,3,2,2,1]
[.,[[[.,[[[[.,.],.],.],.]],.],.]] => [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1] => [5,4,3,2,2,1]
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]] => [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1,1,1] => [6,2,2,2,2,1]
[.,[[[[.,.],[.,[[.,.],.]]],.],.]] => [1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,1,1] => [6,3,2,2,2,1]
[.,[[[[.,.],[[.,.],[.,.]]],.],.]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,1,1] => [6,4,2,2,2,1]
[.,[[[[.,.],[[.,[.,.]],.]],.],.]] => [1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,1,1] => [6,3,3,2,2,1]
[.,[[[[.,.],[[[.,.],.],.]],.],.]] => [1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1,1] => [6,4,3,2,2,1]
[.,[[[[.,[.,.]],[.,[.,.]]],.],.]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2] => [5,5,2,2,2,1]
[.,[[[[.,[.,.]],[[.,.],.]],.],.]] => [1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,2] => [5,5,3,2,2,1]
[.,[[[[[.,.],.],[.,[.,.]]],.],.]] => [1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2,1] => [6,5,2,2,2,1]
[.,[[[[[.,.],.],[[.,.],.]],.],.]] => [1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,2,1] => [6,5,3,2,2,1]
[.,[[[[.,[.,[.,.]]],[.,.]],.],.]] => [1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3] => [4,4,4,2,2,1]
[.,[[[[.,[[.,.],.]],[.,.]],.],.]] => [1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,1] => [5,4,4,2,2,1]
[.,[[[[[.,.],[.,.]],[.,.]],.],.]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,1,1] => [6,4,4,2,2,1]
[.,[[[[[.,[.,.]],.],[.,.]],.],.]] => [1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,2] => [5,5,4,2,2,1]
[.,[[[[[[.,.],.],.],[.,.]],.],.]] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,2,1] => [6,5,4,2,2,1]
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [6,5,4] => [3,3,3,3,2,1]
[.,[[[[.,[.,[[.,.],.]]],.],.],.]] => [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1] => [4,3,3,3,2,1]
[.,[[[[.,[[.,.],[.,.]]],.],.],.]] => [1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,1] => [5,3,3,3,2,1]
[.,[[[[.,[[.,[.,.]],.]],.],.],.]] => [1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2] => [4,4,3,3,2,1]
[.,[[[[.,[[[.,.],.],.]],.],.],.]] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1] => [5,4,3,3,2,1]
[.,[[[[[.,.],[.,[.,.]]],.],.],.]] => [1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,1,1] => [6,3,3,3,2,1]
[.,[[[[[.,.],[[.,.],.]],.],.],.]] => [1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,1] => [6,4,3,3,2,1]
[.,[[[[[.,[.,.]],[.,.]],.],.],.]] => [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2] => [5,5,3,3,2,1]
[.,[[[[[[.,.],.],[.,.]],.],.],.]] => [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2,1] => [6,5,3,3,2,1]
[.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3] => [4,4,4,3,2,1]
[.,[[[[[.,[[.,.],.]],.],.],.],.]] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1] => [5,4,4,3,2,1]
[.,[[[[[[.,.],[.,.]],.],.],.],.]] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,1] => [6,4,4,3,2,1]
[.,[[[[[[.,[.,.]],.],.],.],.],.]] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2] => [5,5,4,3,2,1]
[.,[[[[[[[.,.],.],.],.],.],.],.]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1] => [6,5,4,3,2,1]
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => [7]
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => [7,1]
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => [7,2]
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1,1] => [7,1,1]
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1,1] => [7,2,1]
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => [7,3]
[[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1,1] => [7,3,1]
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1,1] => [7,2,2]
[[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1,1] => [7,3,2]
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1,1] => [7,1,1,1]
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1,1] => [7,2,1,1]
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1,1,1] => [7,3,1,1]
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1,1,1] => [7,2,2,1]
[[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1,1,1] => [7,3,2,1]
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1,1] => [7,4]
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1,1] => [7,4,1]
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1,1] => [7,4,2]
[[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1,1] => [7,4,1,1]
[[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1,1,1] => [7,4,2,1]
[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1,1] => [7,3,3]
[[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1,1] => [7,3,3,1]
[[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1,1] => [7,4,3]
[[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1,1] => [7,4,3,1]
[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1,1] => [7,2,2,2]
[[.,.],[.,[[.,[[.,.],.]],[.,.]]]] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1,1,1] => [7,3,2,2]
[[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1,1] => [7,4,2,2]
[[.,.],[.,[[[.,[.,.]],.],[.,.]]]] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1,1,1] => [7,3,3,2]
[[.,.],[.,[[[[.,.],.],.],[.,.]]]] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1,1,1] => [7,4,3,2]
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1,1] => [7,1,1,1,1]
[[.,.],[.,[[.,[.,[[.,.],.]]],.]]] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1,1,1] => [7,2,1,1,1]
[[.,.],[.,[[.,[[.,.],[.,.]]],.]]] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1,1] => [7,3,1,1,1]
[[.,.],[.,[[.,[[.,[.,.]],.]],.]]] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1,1,1] => [7,2,2,1,1]
[[.,.],[.,[[.,[[[.,.],.],.]],.]]] => [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1,1,1] => [7,3,2,1,1]
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1,1,1] => [7,4,1,1,1]
[[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1,1] => [7,4,2,1,1]
[[.,.],[.,[[[.,[.,.]],[.,.]],.]]] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1,1,1] => [7,3,3,1,1]
[[.,.],[.,[[[[.,.],.],[.,.]],.]]] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1,1,1] => [7,4,3,1,1]
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1,1,1] => [7,2,2,2,1]
[[.,.],[.,[[[.,[[.,.],.]],.],.]]] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1,1,1] => [7,3,2,2,1]
[[.,.],[.,[[[[.,.],[.,.]],.],.]]] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1,1,1] => [7,4,2,2,1]
[[.,.],[.,[[[[.,[.,.]],.],.],.]]] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1,1,1] => [7,3,3,2,1]
[[.,.],[.,[[[[[.,.],.],.],.],.]]] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,1,1] => [7,4,3,2,1]
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => [7,5]
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1,1] => [7,5,1]
[[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1,1] => [7,5,2]
[[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,1,1] => [7,5,1,1]
[[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1,1] => [7,5,2,1]
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => [7,5,3]
[[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => [7,5,3,1]
[[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => [7,5,2,2]
[[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => [7,5,3,2]
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1,1] => [7,5,1,1,1]
[[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1,1] => [7,5,2,1,1]
[[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => [7,5,3,1,1]
[[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1,1] => [7,5,2,2,1]
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => [7,4,4]
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => [7,4,4,1]
[[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => [7,4,4,2]
[[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1,1] => [7,4,4,1,1]
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => [7,5,4]
[[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1,1] => [7,5,4,1]
[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => [7,3,3,3]
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1] => [7,3,3,3,1]
[[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1,1] => [7,4,3,3]
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1,1] => [7,2,2,2,2]
[[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1,1,1] => [7,3,2,2,2]
[[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1,1] => [7,4,2,2,2]
[[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1,1] => [7,3,3,2,2]
[[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,2,1,1] => [7,5,4,3,2]
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1,1] => [7,1,1,1,1,1]
[[.,.],[[.,[.,[.,[[.,.],.]]]],.]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1,1,1] => [7,2,1,1,1,1]
[[.,.],[[.,[.,[[.,.],[.,.]]]],.]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1,1,1] => [7,3,1,1,1,1]
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1,1,1] => [7,2,2,1,1,1]
[[.,.],[[.,[.,[[[.,.],.],.]]],.]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,1,1,1] => [7,3,2,1,1,1]
[[.,.],[[.,[[.,.],[.,[.,.]]]],.]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1,1,1] => [7,4,1,1,1,1]
[[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1,1,1] => [7,4,2,1,1,1]
[[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1,1] => [7,3,3,1,1,1]
[[.,.],[[.,[[[.,.],.],[.,.]]],.]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1,1,1] => [7,4,3,1,1,1]
[[.,.],[[.,[[.,[.,[.,.]]],.]],.]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1,1,1,1] => [7,2,2,2,1,1]
[[.,.],[[.,[[.,[[.,.],.]],.]],.]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,1,1,1] => [7,3,2,2,1,1]
[[.,.],[[.,[[[.,.],[.,.]],.]],.]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,1,1,1] => [7,4,2,2,1,1]
[[.,.],[[.,[[[.,[.,.]],.],.]],.]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,1,1,1] => [7,3,3,2,1,1]
[[.,.],[[.,[[[[.,.],.],.],.]],.]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,1,1] => [7,4,3,2,1,1]
[[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1,1] => [7,5,1,1,1,1]
[[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,1,1] => [7,5,2,1,1,1]
[[.,.],[[[[[.,.],.],.],[.,.]],.]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,2,1,1] => [7,5,4,3,1,1]
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1,1,1,1] => [7,2,2,2,2,1]
[[.,.],[[[.,[.,[[.,.],.]]],.],.]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,1,1,1] => [7,3,2,2,2,1]
[[.,.],[[[.,[[.,.],[.,.]]],.],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,1,1,1] => [7,4,2,2,2,1]
[[.,.],[[[.,[[[.,.],.],.]],.],.]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1,1,1] => [7,4,3,2,2,1]
[[.,.],[[[[[.,.],.],[.,.]],.],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,2,1,1] => [7,5,4,2,2,1]
[[.,.],[[[[.,[.,[.,.]]],.],.],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,1,1,1] => [7,3,3,3,2,1]
[[.,.],[[[[.,[[.,.],.]],.],.],.]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,1,1] => [7,4,3,3,2,1]
[[.,.],[[[[[.,.],[.,.]],.],.],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2,1,1] => [7,5,3,3,2,1]
[[.,.],[[[[[.,[.,.]],.],.],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,1,1] => [7,4,4,3,2,1]
[[.,.],[[[[[[.,.],.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,1] => [7,5,4,3,2,1]
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => [6,6]
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2] => [6,6,1]
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2] => [6,6,2]
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,2] => [6,6,1,1]
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,2] => [6,6,2,1]
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => [6,6,3]
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => [6,6,3,1]
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2] => [6,6,2,2]
[[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,2] => [6,6,3,2]
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,2] => [6,6,1,1,1]
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,2] => [6,6,2,1,1]
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,2] => [6,6,3,1,1]
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,2] => [6,6,2,2,1]
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => [6,6,4]
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => [6,6,4,1]
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,2,2] => [6,6,4,3]
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,2] => [6,6,1,1,1,1]
[[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,2] => [6,6,2,1,1,1]
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => [7,6]
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2,1] => [7,6,1]
[[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2,1] => [7,6,2]
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,2,1] => [7,6,1,1]
[[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,2,1] => [7,6,2,1]
[[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2,1] => [7,6,3]
[[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2,1] => [7,6,3,1]
[[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2,1] => [7,6,2,2]
[[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,2,1] => [7,6,3,2]
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,2,1] => [7,6,1,1,1]
[[[.,.],.],[.,[[.,[[.,.],.]],.]]] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,2,1] => [7,6,2,1,1]
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => [7,6,4]
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,2,1] => [7,6,1,1,1,1]
[[[.,.],.],[[.,[.,[[.,.],.]]],.]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,2,1] => [7,6,2,1,1,1]
[[[.,.],.],[[.,[[.,.],[.,.]]],.]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2,2,1] => [7,6,3,1,1,1]
[[[.,.],.],[[.,[[[.,.],.],.]],.]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,2,2,1] => [7,6,3,2,1,1]
[[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2,2,1] => [7,6,2,2,2,1]
[[[.,.],.],[[[.,[[.,.],.]],.],.]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,2,2,1] => [7,6,3,2,2,1]
[[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2,2,1] => [7,6,3,3,2,1]
[[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,2,1] => [7,6,4,3,2,1]
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => [5,5,5]
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3] => [5,5,5,1]
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => [5,5,5,2]
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,3,3,3] => [5,5,5,1,1]
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,3,3] => [5,5,5,2,1]
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1] => [6,5,5]
[[.,[[.,.],.]],[.,[.,[[.,.],.]]]] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3,1] => [6,5,5,1]
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]] => [1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3,1] => [6,5,5,2]
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [5,5,3,3,3,1] => [6,5,5,2,2]
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => [7,5,5]
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2] => [6,6,5]
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2,1] => [7,6,5]
[[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3,2,1] => [7,6,5,1]
[[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,3,3,3,2,1] => [7,6,5,1,1,1]
[[[[.,.],.],.],[[.,[[.,.],.]],.]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,3,3,2,1] => [7,6,5,2,1,1]
[[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,3,3,2,1] => [7,6,5,2,2,1]
[[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,3,2,1] => [7,6,5,3,2,1]
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => [4,4,4,4]
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4] => [4,4,4,4,1]
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => [4,4,4,4,2]
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [6,4,4,4] => [4,4,4,4,1,1]
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [6,5,4,4] => [4,4,4,4,2,1]
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,1] => [5,4,4,4]
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4,1] => [5,4,4,4,1]
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,1,1] => [6,4,4,4]
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [6,4,4,4,1,1] => [6,4,4,4,1,1]
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,2] => [5,5,4,4]
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4,2] => [5,5,4,4,2]
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]] => [1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,2,1] => [6,5,4,4]
[[.,[[[.,.],.],.]],[[[.,.],.],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,4,2,1] => [6,5,4,4,2,1]
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,1,1,1] => [7,4,4,4]
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,2,1,1] => [7,5,4,4]
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,2,2] => [6,6,4,4]
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4,2,2] => [6,6,4,4,1]
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,2,2,1] => [7,6,4,4]
[[[[.,.],.],[.,.]],[[[.,.],.],.]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,4,2,2,1] => [7,6,4,4,2,1]
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3] => [5,5,5,4]
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,1] => [6,5,5,4]
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,1,1] => [7,5,5,4]
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,2] => [6,6,5,4]
[[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,4,3,2] => [6,6,5,4,2,1]
[[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,2,1] => [7,6,5,4]
[[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,4,4,3,2,1] => [7,6,5,4,1]
[[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [5,5,4,4,3,2,1] => [7,6,5,4,2]
[[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,4,4,3,2,1] => [7,6,5,4,1,1]
[[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,4,3,2,1] => [7,6,5,4,2,1]
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => [3,3,3,3,3]
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [6,5,5] => [3,3,3,3,3,1]
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]] => [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1] => [4,3,3,3,3]
[[.,[.,[.,[[.,.],.]]]],[[.,.],.]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [6,5,5,1] => [4,3,3,3,3,1]
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1,1] => [5,3,3,3,3]
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,5,5,2] => [4,4,3,3,3]
[[.,[[[.,.],[.,.]],.]],[.,[.,.]]] => [1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [5,5,5,3,1,1] => [6,4,4,3,3]
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1,1,1,1] => [7,3,3,3,3]
[[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [5,5,5,2,1,1,1] => [7,4,3,3,3]
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [5,5,5,2,2,2,1] => [7,6,3,3,3]
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [5,5,5,3,3,1,1] => [7,5,5,3,3]
[[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [5,5,5,3,3,2,1] => [7,6,5,3,3]
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [5,5,5,4] => [4,4,4,4,3]
[[[.,[.,[[.,.],.]]],.],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [6,5,5,4,1] => [5,4,4,4,3,1]
[[[.,[[[.,.],.],.]],.],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [6,5,5,4,2,1] => [6,5,4,4,3,1]
[[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [6,5,5,4,1,1,1] => [7,4,4,4,3,1]
[[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [6,5,5,4,2,1,1] => [7,5,4,4,3,1]
[[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [6,5,5,4,2,2,1] => [7,6,4,4,3,1]
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [5,5,5,4,3] => [5,5,5,4,3]
[[[[.,[.,[.,.]]],.],.],[[.,.],.]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3] => [5,5,5,4,3,1]
[[[[.,[[.,.],.]],.],.],[[.,.],.]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3,1] => [6,5,5,4,3,1]
[[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3,1,1] => [7,5,5,4,3,1]
[[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,5,5,4,3,2] => [6,6,5,4,3]
[[[[[.,[.,.]],.],.],.],[[.,.],.]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3,2] => [6,6,5,4,3,1]
[[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,5,5,4,3,2,1] => [7,6,5,4,3]
[[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3,2,1] => [7,6,5,4,3,1]
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => [2,2,2,2,2,2]
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,6,1] => [3,2,2,2,2,2]
[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1] => [4,2,2,2,2,2]
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,6,2] => [3,3,2,2,2,2]
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1] => [4,3,2,2,2,2]
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1] => [5,2,2,2,2,2]
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]] => [1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1,1] => [5,3,2,2,2,2]
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2] => [4,4,2,2,2,2]
[[.,[.,[[[.,.],.],[.,.]]]],[.,.]] => [1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,1] => [5,4,2,2,2,2]
[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,6,3] => [3,3,3,2,2,2]
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]] => [1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [6,6,3,1] => [4,3,3,2,2,2]
[[.,[.,[[[.,.],[.,.]],.]]],[.,.]] => [1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [6,6,3,1,1] => [5,3,3,2,2,2]
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]] => [1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [6,6,3,2] => [4,4,3,2,2,2]
[[.,[.,[[[[.,.],.],.],.]]],[.,.]] => [1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [6,6,3,2,1] => [5,4,3,2,2,2]
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1] => [6,2,2,2,2,2]
[[.,[[.,.],[.,[[.,.],.]]]],[.,.]] => [1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1,1,1] => [6,3,2,2,2,2]
[[.,[[.,.],[[.,[.,.]],.]]],[.,.]] => [1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [6,6,3,1,1,1] => [6,3,3,2,2,2]
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]] => [1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [6,6,3,3,1,1] => [6,4,4,2,2,2]
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [6,6,4] => [3,3,3,3,2,2]
[[.,[[.,[.,[[.,.],.]]],.]],[.,.]] => [1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [6,6,4,1] => [4,3,3,3,2,2]
[[.,[[[[[.,.],.],.],.],.]],[.,.]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [6,6,4,3,2,1] => [6,5,4,3,2,2]
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1,1] => [7,2,2,2,2,2]
[[[.,.],[.,[.,[[.,.],.]]]],[.,.]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1,1,1,1] => [7,3,2,2,2,2]
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => [6,6,2,2,2,2]
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [6,6,3,2,2,2] => [6,6,3,2,2,2]
[[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2,1] => [7,6,2,2,2,2]
[[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [6,6,3,3,3,2,1] => [7,6,5,2,2,2]
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [6,6,4,4] => [4,4,4,4,2,2]
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]] => [1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [6,6,4,4,1] => [5,4,4,4,2,2]
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]] => [1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [6,6,4,4,1,1] => [6,4,4,4,2,2]
[[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [6,6,4,4,1,1,1] => [7,4,4,4,2,2]
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [6,6,4,4,2,2] => [6,6,4,4,2,2]
[[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [6,6,4,4,2,2,1] => [7,6,4,4,2,2]
[[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [6,6,4,4,3,2,1] => [7,6,5,4,2,2]
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [6,6,5] => [3,3,3,3,3,2]
[[[.,[[[.,.],[.,.]],.]],.],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [6,6,5,3,1,1] => [6,4,4,3,3,2]
[[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [6,6,5,3,3,2,1] => [7,6,5,3,3,2]
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [6,6,5,4] => [4,4,4,4,3,2]
[[[[[.,.],[[.,.],.]],.],.],[.,.]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [6,6,5,4,2,1,1] => [7,5,4,4,3,2]
[[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [6,6,5,4,2,2,1] => [7,6,4,4,3,2]
[[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [6,6,5,4,3] => [5,5,5,4,3,2]
[[[[[.,[[.,.],.]],.],.],.],[.,.]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [6,6,5,4,3,1] => [6,5,5,4,3,2]
[[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [6,6,5,4,3,1,1] => [7,5,5,4,3,2]
[[[[[[.,[.,.]],.],.],.],.],[.,.]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,6,5,4,3,2] => [6,6,5,4,3,2]
[[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,6,5,4,3,2,1] => [7,6,5,4,3,2]
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => [1,1,1,1,1,1,1]
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1]
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,1,1] => [3,1,1,1,1,1,1]
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,2] => [2,2,1,1,1,1,1]
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,2,1] => [3,2,1,1,1,1,1]
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1] => [4,1,1,1,1,1,1]
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1] => [4,2,1,1,1,1,1]
[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [7,2,2] => [3,3,1,1,1,1,1]
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1] => [4,3,1,1,1,1,1]
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,3] => [2,2,2,1,1,1,1]
[[.,[.,[.,[[.,[[.,.],.]],.]]]],.] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [7,3,1] => [3,2,2,1,1,1,1]
[[.,[.,[.,[[[.,.],[.,.]],.]]]],.] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,1] => [4,2,2,1,1,1,1]
[[.,[.,[.,[[[.,[.,.]],.],.]]]],.] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [7,3,2] => [3,3,2,1,1,1,1]
[[.,[.,[.,[[[[.,.],.],.],.]]]],.] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1] => [4,3,2,1,1,1,1]
[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1] => [5,1,1,1,1,1,1]
[[.,[.,[[.,.],[.,[[.,.],.]]]]],.] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1,1] => [5,2,1,1,1,1,1]
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1,1] => [5,3,1,1,1,1,1]
[[.,[.,[[.,.],[[.,[.,.]],.]]]],.] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,1,1] => [5,2,2,1,1,1,1]
[[.,[.,[[.,.],[[[.,.],.],.]]]],.] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,1] => [5,3,2,1,1,1,1]
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2] => [4,4,1,1,1,1,1]
[[.,[.,[[.,[.,.]],[[.,.],.]]]],.] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2] => [4,4,2,1,1,1,1]
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,1] => [5,4,1,1,1,1,1]
[[.,[.,[[[.,.],.],[[.,.],.]]]],.] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,1] => [5,4,2,1,1,1,1]
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [7,3,3] => [3,3,3,1,1,1,1]
[[.,[.,[[.,[[.,.],.]],[.,.]]]],.] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1] => [4,3,3,1,1,1,1]
[[.,[.,[[[.,.],[.,.]],[.,.]]]],.] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1,1] => [5,3,3,1,1,1,1]
[[.,[.,[[[.,[.,.]],.],[.,.]]]],.] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2] => [4,4,3,1,1,1,1]
[[.,[.,[[[[.,.],.],.],[.,.]]]],.] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,1] => [5,4,3,1,1,1,1]
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,4] => [2,2,2,2,1,1,1]
[[.,[.,[[.,[.,[[.,.],.]]],.]]],.] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [7,4,1] => [3,2,2,2,1,1,1]
[[.,[.,[[.,[[.,.],[.,.]]],.]]],.] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,1] => [4,2,2,2,1,1,1]
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [7,4,2] => [3,3,2,2,1,1,1]
[[.,[.,[[.,[[[.,.],.],.]],.]]],.] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1] => [4,3,2,2,1,1,1]
[[.,[.,[[[.,.],[.,[.,.]]],.]]],.] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,1,1] => [5,2,2,2,1,1,1]
[[.,[.,[[[.,.],[[.,.],.]],.]]],.] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,1] => [5,3,2,2,1,1,1]
[[.,[.,[[[.,[.,.]],[.,.]],.]]],.] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,2] => [4,4,2,2,1,1,1]
[[.,[.,[[[[.,.],.],[.,.]],.]]],.] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,2,1] => [5,4,2,2,1,1,1]
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [7,4,3] => [3,3,3,2,1,1,1]
[[.,[.,[[[.,[[.,.],.]],.],.]]],.] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1] => [4,3,3,2,1,1,1]
[[.,[.,[[[[.,.],[.,.]],.],.]]],.] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,1] => [5,3,3,2,1,1,1]
[[.,[.,[[[[.,[.,.]],.],.],.]]],.] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2] => [4,4,3,2,1,1,1]
[[.,[.,[[[[[.,.],.],.],.],.]]],.] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,1] => [5,4,3,2,1,1,1]
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1,1] => [6,1,1,1,1,1,1]
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1,1,1] => [6,2,1,1,1,1,1]
[[.,[[.,.],[.,[[.,.],[.,.]]]]],.] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1,1,1] => [6,3,1,1,1,1,1]
[[.,[[.,.],[.,[[.,[.,.]],.]]]],.] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,1,1,1] => [6,2,2,1,1,1,1]
[[.,[[.,.],[.,[[[.,.],.],.]]]],.] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,1,1] => [6,3,2,1,1,1,1]
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,1,1] => [6,4,1,1,1,1,1]
[[.,[[.,.],[[.,.],[[.,.],.]]]],.] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,1,1] => [6,4,2,1,1,1,1]
[[.,[[.,.],[[.,[.,.]],[.,.]]]],.] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1,1,1] => [6,3,3,1,1,1,1]
[[.,[[.,.],[[[.,.],.],[.,.]]]],.] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,1,1] => [6,4,3,1,1,1,1]
[[.,[[.,.],[[.,[.,[.,.]]],.]]],.] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,1,1,1] => [6,2,2,2,1,1,1]
[[.,[[.,.],[[.,[[.,.],.]],.]]],.] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,1,1] => [6,3,2,2,1,1,1]
[[.,[[.,.],[[[.,.],[.,.]],.]]],.] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,2,1,1] => [6,4,2,2,1,1,1]
[[.,[[.,.],[[[.,[.,.]],.],.]]],.] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,1,1] => [6,3,3,2,1,1,1]
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2] => [5,5,1,1,1,1,1]
[[.,[[.,[.,.]],[.,[[.,.],.]]]],.] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,2] => [5,5,2,1,1,1,1]
[[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,2] => [5,5,3,1,1,1,1]
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,2,2] => [5,5,2,2,1,1,1]
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,1] => [6,5,1,1,1,1,1]
[[.,[[[.,.],.],[.,[[.,.],.]]]],.] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,2,1] => [6,5,2,1,1,1,1]
[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [7,3,3,3] => [4,4,4,1,1,1,1]
[[.,[[.,[.,[.,.]]],[[.,.],.]]],.] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [7,4,3,3] => [4,4,4,2,1,1,1]
[[.,[[.,[[.,.],.]],[.,[.,.]]]],.] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [7,3,3,3,1] => [5,4,4,1,1,1,1]
[[.,[[[[.,.],.],.],[.,[.,.]]]],.] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [7,3,3,3,2,1] => [6,5,4,1,1,1,1]
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [7,4,4] => [3,3,3,3,1,1,1]
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [7,4,4,1] => [4,3,3,3,1,1,1]
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [7,4,4,1,1] => [5,3,3,3,1,1,1]
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [7,4,4,2] => [4,4,3,3,1,1,1]
[[.,[[[[[.,.],.],.],.],[.,.]]],.] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [7,4,4,3,2,1] => [6,5,4,3,1,1,1]
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [7,5] => [2,2,2,2,2,1,1]
[[.,[[.,[.,[.,[[.,.],.]]]],.]],.] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [7,5,1] => [3,2,2,2,2,1,1]
[[.,[[.,[.,[[.,.],[.,.]]]],.]],.] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,1] => [4,2,2,2,2,1,1]
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [7,5,2] => [3,3,2,2,2,1,1]
[[.,[[.,[.,[[[.,.],.],.]]],.]],.] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1] => [4,3,2,2,2,1,1]
[[.,[[.,[[.,.],[.,[.,.]]]],.]],.] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,1,1] => [5,2,2,2,2,1,1]
[[.,[[.,[[.,.],[[.,.],.]]],.]],.] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,1] => [5,3,2,2,2,1,1]
[[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,2] => [4,4,2,2,2,1,1]
[[.,[[.,[[[.,.],.],[.,.]]],.]],.] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,2,1] => [5,4,2,2,2,1,1]
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [7,5,3] => [3,3,3,2,2,1,1]
[[.,[[.,[[.,[[.,.],.]],.]],.]],.] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1] => [4,3,3,2,2,1,1]
[[.,[[.,[[[.,.],[.,.]],.]],.]],.] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1,1] => [5,3,3,2,2,1,1]
[[.,[[.,[[[.,[.,.]],.],.]],.]],.] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2] => [4,4,3,2,2,1,1]
[[.,[[[.,.],[.,[.,[.,.]]]],.]],.] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,1,1,1] => [6,2,2,2,2,1,1]
[[.,[[[.,.],[.,[[.,.],.]]],.]],.] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,1,1] => [6,3,2,2,2,1,1]
[[.,[[[[.,.],[.,.]],[.,.]],.]],.] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [7,5,3,3,1,1] => [6,4,4,2,2,1,1]
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [7,5,4] => [3,3,3,3,2,1,1]
[[.,[[[.,[.,[[.,.],.]]],.],.]],.] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [7,5,4,1] => [4,3,3,3,2,1,1]
[[.,[[[[.,[.,[.,.]]],.],.],.]],.] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3] => [4,4,4,3,2,1,1]
[[.,[[[[.,[[.,.],.]],.],.],.]],.] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,1] => [5,4,4,3,2,1,1]
[[.,[[[[[.,[.,.]],.],.],.],.]],.] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2] => [5,5,4,3,2,1,1]
[[.,[[[[[[.,.],.],.],.],.],.]],.] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,1] => [6,5,4,3,2,1,1]
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1,1,1] => [7,1,1,1,1,1,1]
[[[.,.],[.,[.,[.,[[.,.],.]]]]],.] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1,1,1,1] => [7,2,1,1,1,1,1]
[[[.,.],[.,[.,[[.,.],[.,.]]]]],.] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1,1,1,1] => [7,3,1,1,1,1,1]
[[[.,.],[.,[.,[[.,[.,.]],.]]]],.] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,1,1,1,1] => [7,2,2,1,1,1,1]
[[[.,.],[.,[.,[[[.,.],.],.]]]],.] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,1,1,1] => [7,3,2,1,1,1,1]
[[[.,.],[.,[[.,.],[.,[.,.]]]]],.] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,1,1,1] => [7,4,1,1,1,1,1]
[[[.,.],[.,[[.,.],[[.,.],.]]]],.] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,1,1,1] => [7,4,2,1,1,1,1]
[[[.,.],[.,[[.,[.,.]],[.,.]]]],.] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1,1,1,1] => [7,3,3,1,1,1,1]
[[[.,.],[.,[[.,[.,[.,.]]],.]]],.] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,1,1,1,1] => [7,2,2,2,1,1,1]
[[[.,.],[.,[[.,[[.,.],.]],.]]],.] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,1,1,1] => [7,3,2,2,1,1,1]
[[[.,.],[.,[[[[.,.],.],.],.]]],.] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,1,1,1] => [7,4,3,2,1,1,1]
[[[.,.],[[.,.],[.,[.,[.,.]]]]],.] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,1,1] => [7,5,1,1,1,1,1]
[[[.,.],[[[[.,.],.],.],[.,.]]],.] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [7,4,4,3,2,1,1] => [7,5,4,3,1,1,1]
[[[.,.],[[.,[.,[.,[.,.]]]],.]],.] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,1,1,1,1] => [7,2,2,2,2,1,1]
[[[.,.],[[.,[[.,.],[.,.]]],.]],.] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,2,1,1,1] => [7,4,2,2,2,1,1]
[[[.,.],[[[.,.],[[.,.],.]],.]],.] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,2,1,1] => [7,5,3,2,2,1,1]
[[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [7,5,3,3,1,1,1] => [7,4,4,2,2,1,1]
[[[.,.],[[[[[.,.],.],.],.],.]],.] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,1,1] => [7,5,4,3,2,1,1]
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,2] => [6,6,1,1,1,1,1]
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,2,1] => [7,6,1,1,1,1,1]
[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [7,3,3,3,3] => [5,5,5,1,1,1,1]
[[[.,[[.,.],.]],[[.,[.,.]],.]],.] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,3,3,1] => [6,5,5,2,2,1,1]
[[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [7,3,3,3,3,1,1] => [7,5,5,1,1,1,1]
[[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [7,3,3,3,3,2,1] => [7,6,5,1,1,1,1]
[[[[[.,.],.],.],[[.,.],[.,.]]],.] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [7,4,4,3,3,2,1] => [7,6,5,3,1,1,1]
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [7,4,4,4,1,1,1] => [7,4,4,4,1,1,1]
[[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,4,2,1,1] => [7,5,4,4,2,1,1]
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [7,4,4,4,2,2] => [6,6,4,4,1,1,1]
[[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [7,4,4,4,3,2,1] => [7,6,5,4,1,1,1]
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [7,5,5] => [3,3,3,3,3,1,1]
[[[.,[[.,[[.,.],.]],.]],[.,.]],.] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [7,5,5,3,1] => [5,4,4,3,3,1,1]
[[[.,[[[.,.],[.,.]],.]],[.,.]],.] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [7,5,5,3,1,1] => [6,4,4,3,3,1,1]
[[[.,[[[[.,.],.],.],.]],[.,.]],.] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [7,5,5,3,2,1] => [6,5,4,3,3,1,1]
[[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [7,5,5,3,1,1,1] => [7,4,4,3,3,1,1]
[[[[.,[[.,.],.]],[.,.]],[.,.]],.] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [7,5,5,3,3,1] => [6,5,5,3,3,1,1]
[[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [7,5,5,3,3,1,1] => [7,5,5,3,3,1,1]
[[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [7,5,5,4,3,1,1] => [7,5,5,4,3,1,1]
[[[[[[.,[.,.]],.],.],.],[.,.]],.] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,5,5,4,3,2] => [6,6,5,4,3,1,1]
[[[[[[[.,.],.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,5,5,4,3,2,1] => [7,6,5,4,3,1,1]
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [7,6] => [2,2,2,2,2,2,1]
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [7,6,1] => [3,2,2,2,2,2,1]
[[[.,[.,[.,[[.,.],[.,.]]]]],.],.] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,1] => [4,2,2,2,2,2,1]
[[[.,[.,[.,[[.,[.,.]],.]]]],.],.] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [7,6,2] => [3,3,2,2,2,2,1]
[[[.,[.,[.,[[[.,.],.],.]]]],.],.] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [7,6,2,1] => [4,3,2,2,2,2,1]
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,1,1] => [5,2,2,2,2,2,1]
[[[.,[.,[[.,.],[[.,.],.]]]],.],.] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [7,6,2,1,1] => [5,3,2,2,2,2,1]
[[[.,[.,[[.,[.,.]],[.,.]]]],.],.] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [7,6,2,2] => [4,4,2,2,2,2,1]
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [7,6,3] => [3,3,3,2,2,2,1]
[[[.,[.,[[.,[[.,.],.]],.]]],.],.] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [7,6,3,1] => [4,3,3,2,2,2,1]
[[[.,[.,[[[[.,.],.],.],.]]],.],.] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,1] => [5,4,3,2,2,2,1]
[[[.,[[.,.],[.,[.,[.,.]]]]],.],.] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,1,1,1] => [6,2,2,2,2,2,1]
[[[.,[[[.,.],.],[.,[.,.]]]],.],.] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,2,2,1] => [6,5,2,2,2,2,1]
[[[.,[[[[.,.],.],.],[.,.]]],.],.] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,3,2,1] => [6,5,4,2,2,2,1]
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [7,6,4] => [3,3,3,3,2,2,1]
[[[.,[[[[[.,.],.],.],.],.]],.],.] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,1] => [6,5,4,3,2,2,1]
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,1,1,1,1] => [7,2,2,2,2,2,1]
[[[[.,.],[.,[[[.,.],.],.]]],.],.] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,1,1,1] => [7,4,3,2,2,2,1]
[[[[.,.],[[[.,.],.],[.,.]]],.],.] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,3,2,1,1] => [7,5,4,2,2,2,1]
[[[[.,[.,.]],[.,[.,[.,.]]]],.],.] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,2,2,2] => [6,6,2,2,2,2,1]
[[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,2,2,2,1] => [7,6,2,2,2,2,1]
[[[[[.,.],.],[.,[[.,.],.]]],.],.] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,2,2,1] => [7,6,3,2,2,2,1]
[[[[[.,.],.],[[.,.],[.,.]]],.],.] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,3,2,2,1] => [7,6,4,2,2,2,1]
[[[[[.,.],.],[[[.,.],.],.]],.],.] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,2,1] => [7,6,4,3,2,2,1]
[[[[[.,.],[.,.]],[.,[.,.]]],.],.] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,3,3,1,1] => [7,5,5,2,2,2,1]
[[[[[[.,.],.],.],[.,[.,.]]],.],.] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,3,3,2,1] => [7,6,5,2,2,2,1]
[[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,4,2,2] => [6,6,4,4,2,2,1]
[[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,4,2,2,1] => [7,6,4,4,2,2,1]
[[[[[[.,[.,.]],.],.],[.,.]],.],.] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,4,3,2] => [6,6,5,4,2,2,1]
[[[[[[[.,.],.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,4,3,2,1] => [7,6,5,4,2,2,1]
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [7,6,5] => [3,3,3,3,3,2,1]
[[[[.,[.,[[[.,.],.],.]]],.],.],.] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,1] => [5,4,3,3,3,2,1]
[[[[.,[[.,.],[.,[.,.]]]],.],.],.] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [7,6,5,1,1,1] => [6,3,3,3,3,2,1]
[[[[.,[[[.,.],.],[.,.]]],.],.],.] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,2,1] => [6,5,3,3,3,2,1]
[[[[.,[[[.,.],[.,.]],.]],.],.],.] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,1,1] => [6,4,4,3,3,2,1]
[[[[.,[[[[.,.],.],.],.]],.],.],.] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,1] => [6,5,4,3,3,2,1]
[[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [7,6,5,1,1,1,1] => [7,3,3,3,3,2,1]
[[[[[.,.],[.,[[.,.],.]]],.],.],.] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,1,1,1] => [7,4,3,3,3,2,1]
[[[[[.,.],[[.,.],[.,.]]],.],.],.] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,2,1,1] => [7,5,3,3,3,2,1]
[[[[[.,[.,.]],[.,[.,.]]],.],.],.] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,2,2] => [6,6,3,3,3,2,1]
[[[[[[.,.],.],[.,[.,.]]],.],.],.] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,2,2,1] => [7,6,3,3,3,2,1]
[[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,3,1,1] => [7,5,5,3,3,2,1]
[[[[[[[.,.],.],.],[.,.]],.],.],.] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,3,2,1] => [7,6,5,3,3,2,1]
[[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4] => [4,4,4,4,3,2,1]
[[[[[.,[.,[[.,.],.]]],.],.],.],.] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1] => [5,4,4,4,3,2,1]
[[[[[.,[[.,.],[.,.]]],.],.],.],.] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1,1] => [6,4,4,4,3,2,1]
[[[[[.,[[[.,.],.],.]],.],.],.],.] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,1] => [6,5,4,4,3,2,1]
[[[[[[.,.],[.,[.,.]]],.],.],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1,1,1] => [7,4,4,4,3,2,1]
[[[[[[.,[.,.]],[.,.]],.],.],.],.] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,2] => [6,6,4,4,3,2,1]
[[[[[[[.,.],.],[.,.]],.],.],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,2,1] => [7,6,4,4,3,2,1]
[[[[[[.,[.,[.,.]]],.],.],.],.],.] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3] => [5,5,5,4,3,2,1]
[[[[[[.,[[.,.],.]],.],.],.],.],.] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,1] => [6,5,5,4,3,2,1]
[[[[[[[.,.],[.,.]],.],.],.],.],.] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,1,1] => [7,5,5,4,3,2,1]
[[[[[[[.,[.,.]],.],.],.],.],.],.] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2] => [6,6,5,4,3,2,1]
[[[[[[[[.,.],.],.],.],.],.],.],.] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1]
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [] => []
[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1] => [1]
[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => [2,1]
[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]] => [1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1] => [3,2,1]
[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]] => [1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1] => [4,3,2,1]
[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1] => [5,4,3,2,1]
[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,1] => [6,5,4,3,2,1]
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,1] => [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] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1]
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [] => []
[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1] => [1]
[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1] => [2]
[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]] => [1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [2,1] => [2,1]
[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]] => [1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1] => [3,1]
[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]] => [1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1] => [3,2,1]
[.,[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]] => [1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1] => [4,2,1]
[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]] => [1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1] => [4,3,2,1]
[.,[.,[.,[[.,.],[[[[.,.],.],.],.]]]]] => [1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,1] => [5,3,2,1]
[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]] => [1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,1] => [5,4,3,2,1]
[.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]] => [1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1,1] => [6,4,3,2,1]
[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,1] => [6,5,4,3,2,1]
[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,1,1] => [7,5,4,3,2,1]
[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1]
[[.,.],[[[[[[[.,.],.],.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,1,1] => [8,6,5,4,3,2,1]
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,2,1] => [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] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1]
[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [5] => [1,1,1,1,1]
[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [6] => [1,1,1,1,1,1]
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => [1,1,1,1,1,1,1,1]
[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]] => [1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [4] => [1,1,1,1]
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1,1,1,1,1,1] => [8,1,1,1,1,1,1,1]
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => [1,1,1,1,1,1,1,1,1]
[.,[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]] => [1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0] => [8,5,5,3,3,1,1] => [7,5,5,3,3,1,1,1]
[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [7,7,5,5,3,3,1,1] => [8,6,6,4,4,2,2]
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [8,8,6,6,4,4,2,2] => [8,8,6,6,4,4,2,2]
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2]
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2]
[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,7,6,5,4,3,1,1] => [8,6,6,5,4,3,2]
[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,7,6,5,4,3,1] => [7,6,6,5,4,3,2]
[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,1,1] => [7,5,5,4,3,2,1]
[[.,.],[[[[[[.,[.,.]],.],.],.],.],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,1,1,1] => [8,5,5,4,3,2,1]
[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,2,1,1] => [9,7,6,5,4,3,2,1]
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => [8]
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1] => [2,1,1,1,1,1,1,1]
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1] => [9]
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10] => [1,1,1,1,1,1,1,1,1,1]
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => [2,1,1,1,1,1,1,1,1]
[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [8,2] => [2,2,1,1,1,1,1,1]
[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [8,6,4,2] => [4,4,3,3,2,2,1,1]
[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [8,6,6,4,4,2,2] => [7,7,5,5,3,3,1,1]
[.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]] => [1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [10,8,6,4,2] => [5,5,4,4,3,3,2,2,1,1]
[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2] => [7,7]
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,3] => [6,6,6]
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,4,4,4,4] => [5,5,5,5]
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,5,5,5] => [4,4,4,4,4]
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,6,6] => [3,3,3,3,3,3]
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,7] => [2,2,2,2,2,2,2]
[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2,1] => [8,7]
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [8,7] => [2,2,2,2,2,2,2,1]
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3] => [6,6,6,5,4,3,2,1]
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,2] => [7,7,6,5,4,3,2,1]
[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [9,8] => [2,2,2,2,2,2,2,2,1]
[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,1,1,1] => [8,5,5,5,4,3,2,1]
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,3] => [7,7,7,6,5,4,3,2,1]
[[[[[[[[.,.],[.,.]],.],.],.],.],.],.] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,1,1] => [8,6,6,5,4,3,2,1]
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,3,2] => [8,8,7,6,5,4,3,2,1]
[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => [7]
[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,6,5,4,3,2,1] => [7,6,5,4,3,2]
[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2]
[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2,2] => [7,7,5,5,4,3,2,1]
[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [8,6,6] => [3,3,3,3,3,3,1,1]
[.,[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]] => [1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [3,1] => [2,1,1]
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,2,1] => [7,6,5,4,3,2,1,1]
[[[[[[[.,[[.,.],.]],.],.],.],.],.],.] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,1] => [7,6,6,5,4,3,2,1]
[[[[[[.,[[.,.],[.,.]]],.],.],.],.],.] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,1,1] => [7,5,5,5,4,3,2,1]
[[[[[.,[[[.,.],.],[.,.]]],.],.],.],.] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,2,1] => [7,6,4,4,4,3,2,1]
[[[[.,[[[[.,.],.],.],[.,.]]],.],.],.] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,3,2,1] => [7,6,5,3,3,3,2,1]
[[[.,[[[[[.,.],.],.],.],[.,.]]],.],.] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,4,3,2,1] => [7,6,5,4,2,2,2,1]
[[.,[[[[[[.,.],.],.],.],.],[.,.]]],.] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [8,5,5,4,3,2,1] => [7,6,5,4,3,1,1,1]
[[[[[[[[.,.],.],[.,.]],.],.],.],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2,2,1] => [8,7,5,5,4,3,2,1]
[[[[[[[[.,.],.],.],[.,.]],.],.],.],.] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,3,2,1] => [8,7,6,4,4,3,2,1]
[[[[[[[[.,.],.],.],.],[.,.]],.],.],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,4,3,2,1] => [8,7,6,5,3,3,2,1]
[[[[[[[[.,.],.],.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,5,4,3,2,1] => [8,7,6,5,4,2,2,1]
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,6,5,4,3,2,1] => [8,7,6,5,4,3,1,1]
[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,3,1,1] => [9,7,7,6,5,4,3,2,1]
[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,2,2,1] => [9,8,6,6,5,4,3,2,1]
[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,3,3,2,1] => [9,8,7,5,5,4,3,2,1]
[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,4,3,2,1] => [9,8,7,6,4,4,3,2,1]
[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [9,8,7,5,5,4,3,2,1] => [9,8,7,6,5,3,3,2,1]
[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [9,8,6,6,5,4,3,2,1] => [9,8,7,6,5,4,2,2,1]
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [9,7,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,1,1]
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [6,6] => [2,2,2,2,2,2]
[.,[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0] => [7,6,5] => [3,3,3,3,3,2,1]
[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [7,6,6] => [3,3,3,3,3,3,1]
[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2,2,1] => [9,8]
[.,[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]] => [1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,1,1] => [7,5,5]
[.,[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]] => [1,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [4,4,3,3,1,1] => [6,4,4,2]
[.,[[[[[[.,.],.],.],.],[.,.]],[.,.]]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [6,6,4,4,3,2,1] => [7,6,5,4,2,2]
[.,[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0] => [6,6,5] => [3,3,3,3,3,2]
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [7,7] => [2,2,2,2,2,2,2]
[.,[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0] => [6,5,5] => [3,3,3,3,3,1]
[.,[.,[[.,[.,[[[[.,.],.],.],.]]],.]]] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0] => [6,3,2,1] => [4,3,2,1,1,1]
[.,[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1] => [3,2,1,1,1,1,1]
[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1] => [3,2,1,1,1,1,1,1]
[[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0] => [9,2,1] => [3,2,1,1,1,1,1,1,1]
[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,7,5,5,4,3,2,1] => [8,7,6,5,4,2,2]
[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [8,8,6,6,5,4,3,2,1] => [9,8,7,6,5,4,2,2]
[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]] => [1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [1] => [1]
[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [7,1] => [2,1,1,1,1,1,1]
[.,[.,[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]]] => [1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2] => [3,3,2,1]
[.,[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [7,5] => [2,2,2,2,2,1,1]
[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1,1,1,1,1] => [8,1,1,1,1,1,1]
[.,[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]] => [1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1] => [2,1]
[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [8,7,1] => [3,2,2,2,2,2,2,1]
[[.,[.,[.,[.,[.,.]]]]],[.,[[.,.],.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [6,5,5,5] => [4,4,4,4,4,1]
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 $r$.
Map
to partition
Description
The cut-out partition of a Dyck path.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ is the number of down-steps before the $(n+1-i)$-th up-step of $D$.
This map is a bijection between Dyck paths of size $n$ and partitions inside the staircase partition $(n-1,\ldots,2,1)$.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ is the number of down-steps before the $(n+1-i)$-th up-step of $D$.
This map is a bijection between Dyck paths of size $n$ and partitions inside the staircase partition $(n-1,\ldots,2,1)$.
Map
conjugate
Description
Return the conjugate partition of the partition.
The conjugate partition of the partition $\lambda$ of $n$ is the partition $\lambda^*$ whose Ferrers diagram is obtained from the diagram of $\lambda$ by interchanging rows with columns.
This is also called the associated partition or the transpose in the literature.
The conjugate partition of the partition $\lambda$ of $n$ is the partition $\lambda^*$ whose Ferrers diagram is obtained from the diagram of $\lambda$ by interchanging rows with columns.
This is also called the associated partition or the transpose in the literature.
searching the database
Sorry, this map was not found in the database.