Identifier
-
Mp00012:
Binary trees
—to Dyck path: up step, left tree, down step, right tree⟶
Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00317: Integer partitions —odd parts⟶ Binary words
St000629: Binary words ⟶ ℤ
Values
[.,[.,.]] => [1,0,1,0] => [1] => 1 => 0
[.,[.,[.,.]]] => [1,0,1,0,1,0] => [2,1] => 01 => 0
[.,[[.,.],.]] => [1,0,1,1,0,0] => [1,1] => 11 => 0
[[.,.],[.,.]] => [1,1,0,0,1,0] => [2] => 0 => 0
[[.,[.,.]],.] => [1,1,0,1,0,0] => [1] => 1 => 0
[.,[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0] => [3,2,1] => 101 => 0
[.,[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0] => [2,2,1] => 001 => 0
[.,[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0] => [3,1,1] => 111 => 0
[.,[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0] => [2,1,1] => 011 => 0
[.,[[[.,.],.],.]] => [1,0,1,1,1,0,0,0] => [1,1,1] => 111 => 0
[[.,.],[.,[.,.]]] => [1,1,0,0,1,0,1,0] => [3,2] => 10 => 0
[[.,.],[[.,.],.]] => [1,1,0,0,1,1,0,0] => [2,2] => 00 => 0
[[.,[.,.]],[.,.]] => [1,1,0,1,0,0,1,0] => [3,1] => 11 => 0
[[[.,.],.],[.,.]] => [1,1,1,0,0,0,1,0] => [3] => 1 => 0
[[.,[.,[.,.]]],.] => [1,1,0,1,0,1,0,0] => [2,1] => 01 => 0
[[.,[[.,.],.]],.] => [1,1,0,1,1,0,0,0] => [1,1] => 11 => 0
[[[.,.],[.,.]],.] => [1,1,1,0,0,1,0,0] => [2] => 0 => 0
[[[.,[.,.]],.],.] => [1,1,1,0,1,0,0,0] => [1] => 1 => 0
[.,[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,0,1,0] => [4,3,2,1] => 0101 => 0
[.,[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => 1101 => 0
[.,[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,0,1,0] => [4,2,2,1] => 0001 => 0
[.,[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => 1001 => 0
[.,[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => 0001 => 0
[.,[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,0] => [4,3,1,1] => 0111 => 0
[.,[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,0] => [3,3,1,1] => 1111 => 0
[.,[[.,[.,.]],[.,.]]] => [1,0,1,1,0,1,0,0,1,0] => [4,2,1,1] => 0011 => 0
[.,[[[.,.],.],[.,.]]] => [1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => 0111 => 0
[.,[[.,[.,[.,.]]],.]] => [1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => 1011 => 0
[.,[[.,[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,0,0] => [2,2,1,1] => 0011 => 0
[.,[[[.,.],[.,.]],.]] => [1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => 1111 => 0
[.,[[[.,[.,.]],.],.]] => [1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => 0111 => 0
[.,[[[[.,.],.],.],.]] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 1111 => 0
[[.,.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,0] => [4,3,2] => 010 => 0
[[.,.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,0] => [3,3,2] => 110 => 0
[[.,.],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,0] => [4,2,2] => 000 => 0
[[.,.],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,1,0,0] => [3,2,2] => 100 => 0
[[.,.],[[[.,.],.],.]] => [1,1,0,0,1,1,1,0,0,0] => [2,2,2] => 000 => 0
[[.,[.,.]],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,0] => [4,3,1] => 011 => 0
[[.,[.,.]],[[.,.],.]] => [1,1,0,1,0,0,1,1,0,0] => [3,3,1] => 111 => 0
[[[.,.],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,0] => [4,3] => 01 => 0
[[[.,.],.],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0] => [3,3] => 11 => 0
[[.,[.,[.,.]]],[.,.]] => [1,1,0,1,0,1,0,0,1,0] => [4,2,1] => 001 => 0
[[.,[[.,.],.]],[.,.]] => [1,1,0,1,1,0,0,0,1,0] => [4,1,1] => 011 => 0
[[[.,.],[.,.]],[.,.]] => [1,1,1,0,0,1,0,0,1,0] => [4,2] => 00 => 0
[[[.,[.,.]],.],[.,.]] => [1,1,1,0,1,0,0,0,1,0] => [4,1] => 01 => 0
[[[[.,.],.],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0] => [4] => 0 => 0
[[.,[.,[.,[.,.]]]],.] => [1,1,0,1,0,1,0,1,0,0] => [3,2,1] => 101 => 0
[[.,[.,[[.,.],.]]],.] => [1,1,0,1,0,1,1,0,0,0] => [2,2,1] => 001 => 0
[[.,[[.,.],[.,.]]],.] => [1,1,0,1,1,0,0,1,0,0] => [3,1,1] => 111 => 0
[[.,[[.,[.,.]],.]],.] => [1,1,0,1,1,0,1,0,0,0] => [2,1,1] => 011 => 0
[[.,[[[.,.],.],.]],.] => [1,1,0,1,1,1,0,0,0,0] => [1,1,1] => 111 => 0
[[[.,.],[.,[.,.]]],.] => [1,1,1,0,0,1,0,1,0,0] => [3,2] => 10 => 0
[[[.,.],[[.,.],.]],.] => [1,1,1,0,0,1,1,0,0,0] => [2,2] => 00 => 0
[[[.,[.,.]],[.,.]],.] => [1,1,1,0,1,0,0,1,0,0] => [3,1] => 11 => 0
[[[[.,.],.],[.,.]],.] => [1,1,1,1,0,0,0,1,0,0] => [3] => 1 => 0
[[[.,[.,[.,.]]],.],.] => [1,1,1,0,1,0,1,0,0,0] => [2,1] => 01 => 0
[[[.,[[.,.],.]],.],.] => [1,1,1,0,1,1,0,0,0,0] => [1,1] => 11 => 0
[[[[.,.],[.,.]],.],.] => [1,1,1,1,0,0,1,0,0,0] => [2] => 0 => 0
[[[[.,[.,.]],.],.],.] => [1,1,1,1,0,1,0,0,0,0] => [1] => 1 => 0
[.,[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => 10101 => 0
[.,[.,[.,[.,[[.,.],.]]]]] => [1,0,1,0,1,0,1,0,1,1,0,0] => [4,4,3,2,1] => 00101 => 0
[.,[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0] => [5,3,3,2,1] => 11101 => 0
[.,[.,[.,[[.,[.,.]],.]]]] => [1,0,1,0,1,0,1,1,0,1,0,0] => [4,3,3,2,1] => 01101 => 0
[.,[.,[.,[[[.,.],.],.]]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => [3,3,3,2,1] => 11101 => 0
[.,[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0] => [5,4,2,2,1] => 10001 => 0
[.,[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,0,0,1,1,0,0] => [4,4,2,2,1] => 00001 => 0
[.,[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,0,1,0,0,1,0] => [5,3,2,2,1] => 11001 => 0
[.,[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,0,0,1,0] => [5,2,2,2,1] => 10001 => 0
[.,[.,[[.,[.,[.,.]]],.]]] => [1,0,1,0,1,1,0,1,0,1,0,0] => [4,3,2,2,1] => 01001 => 0
[.,[.,[[.,[[.,.],.]],.]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => [3,3,2,2,1] => 11001 => 0
[.,[.,[[[.,.],[.,.]],.]]] => [1,0,1,0,1,1,1,0,0,1,0,0] => [4,2,2,2,1] => 00001 => 0
[.,[.,[[[.,[.,.]],.],.]]] => [1,0,1,0,1,1,1,0,1,0,0,0] => [3,2,2,2,1] => 10001 => 0
[.,[.,[[[[.,.],.],.],.]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => 00001 => 0
[.,[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,1] => 10111 => 0
[.,[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,0,1,1,0,0] => [4,4,3,1,1] => 00111 => 0
[.,[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,0,0,1,0] => [5,3,3,1,1] => 11111 => 0
[.,[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,0,1,0,0] => [4,3,3,1,1] => 01111 => 0
[.,[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => [3,3,3,1,1] => 11111 => 0
[.,[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,1] => 10011 => 0
[.,[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,0,0] => [4,4,2,1,1] => 00011 => 0
[.,[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,0,1,0] => [5,4,1,1,1] => 10111 => 0
[.,[[[.,.],.],[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,0,0] => [4,4,1,1,1] => 00111 => 0
[.,[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,1] => 11011 => 0
[.,[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,0] => [5,2,2,1,1] => 10011 => 0
[.,[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,0] => [5,3,1,1,1] => 11111 => 0
[.,[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,0] => [5,2,1,1,1] => 10111 => 0
[.,[[[[.,.],.],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,0] => [5,1,1,1,1] => 11111 => 0
[.,[[.,[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,1] => 01011 => 0
[.,[[.,[.,[[.,.],.]]],.]] => [1,0,1,1,0,1,0,1,1,0,0,0] => [3,3,2,1,1] => 11011 => 0
[.,[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,0,1,0,0] => [4,2,2,1,1] => 00011 => 0
[.,[[.,[[.,[.,.]],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,0] => [3,2,2,1,1] => 10011 => 0
[.,[[.,[[[.,.],.],.]],.]] => [1,0,1,1,0,1,1,1,0,0,0,0] => [2,2,2,1,1] => 00011 => 0
[.,[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,1,0,0,1,0,1,0,0] => [4,3,1,1,1] => 01111 => 0
[.,[[[.,.],[[.,.],.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,0] => [3,3,1,1,1] => 11111 => 0
[.,[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,1,0,0,1,0,0] => [4,2,1,1,1] => 00111 => 0
[.,[[[[.,.],.],[.,.]],.]] => [1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => 01111 => 0
[.,[[[.,[.,[.,.]]],.],.]] => [1,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => 10111 => 0
[.,[[[.,[[.,.],.]],.],.]] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 00111 => 0
[.,[[[[.,.],[.,.]],.],.]] => [1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => 11111 => 0
[.,[[[[.,[.,.]],.],.],.]] => [1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => 01111 => 0
[.,[[[[[.,.],.],.],.],.]] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 11111 => 0
>>> Load all 1284 entries. <<<[[.,.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2] => 1010 => 0
[[.,.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,0] => [4,4,3,2] => 0010 => 0
[[.,.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,0,0,1,0] => [5,3,3,2] => 1110 => 0
[[.,.],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,0,1,1,0,1,0,0] => [4,3,3,2] => 0110 => 0
[[.,.],[.,[[[.,.],.],.]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => [3,3,3,2] => 1110 => 0
[[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0] => [5,4,2,2] => 1000 => 0
[[.,.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => 0000 => 0
[[.,.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,0] => [5,3,2,2] => 1100 => 0
[[.,.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,0] => [5,2,2,2] => 1000 => 0
[[.,.],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,0,1,0,0] => [4,3,2,2] => 0100 => 0
[[.,.],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,0] => [3,3,2,2] => 1100 => 0
[[.,.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,0,0] => [4,2,2,2] => 0000 => 0
[[.,.],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,1,0,0,0] => [3,2,2,2] => 1000 => 0
[[.,.],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,2,2] => 0000 => 0
[[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,0,1,0] => [5,4,3,1] => 1011 => 0
[[.,[.,.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => [4,4,3,1] => 0011 => 0
[[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,3,1] => 1111 => 0
[[.,[.,.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,0,1,0,0] => [4,3,3,1] => 0111 => 0
[[.,[.,.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,1,0,0,0] => [3,3,3,1] => 1111 => 0
[[[.,.],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,0,1,0] => [5,4,3] => 101 => 0
[[[.,.],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,0,0] => [4,4,3] => 001 => 0
[[[.,.],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => 111 => 0
[[[.,.],.],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,0,0] => [4,3,3] => 011 => 0
[[[.,.],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => 111 => 0
[[.,[.,[.,.]]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,0,1,0] => [5,4,2,1] => 1001 => 0
[[.,[.,[.,.]]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,0] => [4,4,2,1] => 0001 => 0
[[.,[[.,.],.]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,0,1,0] => [5,4,1,1] => 1011 => 0
[[.,[[.,.],.]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,0] => [4,4,1,1] => 0011 => 0
[[[.,.],[.,.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,0,1,0] => [5,4,2] => 100 => 0
[[[.,.],[.,.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,0] => [4,4,2] => 000 => 0
[[[.,[.,.]],.],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,0,1,0] => [5,4,1] => 101 => 0
[[[.,[.,.]],.],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,0] => [4,4,1] => 001 => 0
[[[[.,.],.],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => 10 => 0
[[[[.,.],.],.],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => 00 => 0
[[.,[.,[.,[.,.]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,0,1,0] => [5,3,2,1] => 1101 => 0
[[.,[.,[[.,.],.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,0] => [5,2,2,1] => 1001 => 0
[[.,[[.,.],[.,.]]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,0] => [5,3,1,1] => 1111 => 0
[[.,[[.,[.,.]],.]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,0] => [5,2,1,1] => 1011 => 0
[[.,[[[.,.],.],.]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,0] => [5,1,1,1] => 1111 => 0
[[[.,.],[.,[.,.]]],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,0] => [5,3,2] => 110 => 0
[[[.,.],[[.,.],.]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,0] => [5,2,2] => 100 => 0
[[[.,[.,.]],[.,.]],[.,.]] => [1,1,1,0,1,0,0,1,0,0,1,0] => [5,3,1] => 111 => 0
[[[[.,.],.],[.,.]],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,0] => [5,3] => 11 => 0
[[[.,[.,[.,.]]],.],[.,.]] => [1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,1] => 101 => 0
[[[.,[[.,.],.]],.],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,0] => [5,1,1] => 111 => 0
[[[[.,.],[.,.]],.],[.,.]] => [1,1,1,1,0,0,1,0,0,0,1,0] => [5,2] => 10 => 0
[[[[.,[.,.]],.],.],[.,.]] => [1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => 11 => 0
[[[[[.,.],.],.],.],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5] => 1 => 0
[[.,[.,[.,[.,[.,.]]]]],.] => [1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => 0101 => 0
[[.,[.,[.,[[.,.],.]]]],.] => [1,1,0,1,0,1,0,1,1,0,0,0] => [3,3,2,1] => 1101 => 0
[[.,[.,[[.,.],[.,.]]]],.] => [1,1,0,1,0,1,1,0,0,1,0,0] => [4,2,2,1] => 0001 => 0
[[.,[.,[[.,[.,.]],.]]],.] => [1,1,0,1,0,1,1,0,1,0,0,0] => [3,2,2,1] => 1001 => 0
[[.,[.,[[[.,.],.],.]]],.] => [1,1,0,1,0,1,1,1,0,0,0,0] => [2,2,2,1] => 0001 => 0
[[.,[[.,.],[.,[.,.]]]],.] => [1,1,0,1,1,0,0,1,0,1,0,0] => [4,3,1,1] => 0111 => 0
[[.,[[.,.],[[.,.],.]]],.] => [1,1,0,1,1,0,0,1,1,0,0,0] => [3,3,1,1] => 1111 => 0
[[.,[[.,[.,.]],[.,.]]],.] => [1,1,0,1,1,0,1,0,0,1,0,0] => [4,2,1,1] => 0011 => 0
[[.,[[[.,.],.],[.,.]]],.] => [1,1,0,1,1,1,0,0,0,1,0,0] => [4,1,1,1] => 0111 => 0
[[.,[[.,[.,[.,.]]],.]],.] => [1,1,0,1,1,0,1,0,1,0,0,0] => [3,2,1,1] => 1011 => 0
[[.,[[.,[[.,.],.]],.]],.] => [1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,1,1] => 0011 => 0
[[.,[[[.,.],[.,.]],.]],.] => [1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,1,1] => 1111 => 0
[[.,[[[.,[.,.]],.],.]],.] => [1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,1] => 0111 => 0
[[.,[[[[.,.],.],.],.]],.] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1] => 1111 => 0
[[[.,.],[.,[.,[.,.]]]],.] => [1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => 010 => 0
[[[.,.],[.,[[.,.],.]]],.] => [1,1,1,0,0,1,0,1,1,0,0,0] => [3,3,2] => 110 => 0
[[[.,.],[[.,.],[.,.]]],.] => [1,1,1,0,0,1,1,0,0,1,0,0] => [4,2,2] => 000 => 0
[[[.,.],[[.,[.,.]],.]],.] => [1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,2] => 100 => 0
[[[.,.],[[[.,.],.],.]],.] => [1,1,1,0,0,1,1,1,0,0,0,0] => [2,2,2] => 000 => 0
[[[.,[.,.]],[.,[.,.]]],.] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => 011 => 0
[[[.,[.,.]],[[.,.],.]],.] => [1,1,1,0,1,0,0,1,1,0,0,0] => [3,3,1] => 111 => 0
[[[[.,.],.],[.,[.,.]]],.] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => 01 => 0
[[[[.,.],.],[[.,.],.]],.] => [1,1,1,1,0,0,0,1,1,0,0,0] => [3,3] => 11 => 0
[[[.,[.,[.,.]]],[.,.]],.] => [1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => 001 => 0
[[[.,[[.,.],.]],[.,.]],.] => [1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,1] => 011 => 0
[[[[.,.],[.,.]],[.,.]],.] => [1,1,1,1,0,0,1,0,0,1,0,0] => [4,2] => 00 => 0
[[[[.,[.,.]],.],[.,.]],.] => [1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => 01 => 0
[[[[[.,.],.],.],[.,.]],.] => [1,1,1,1,1,0,0,0,0,1,0,0] => [4] => 0 => 0
[[[.,[.,[.,[.,.]]]],.],.] => [1,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1] => 101 => 0
[[[.,[.,[[.,.],.]]],.],.] => [1,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1] => 001 => 0
[[[.,[[.,.],[.,.]]],.],.] => [1,1,1,0,1,1,0,0,1,0,0,0] => [3,1,1] => 111 => 0
[[[.,[[.,[.,.]],.]],.],.] => [1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,1] => 011 => 0
[[[.,[[[.,.],.],.]],.],.] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1] => 111 => 0
[[[[.,.],[.,[.,.]]],.],.] => [1,1,1,1,0,0,1,0,1,0,0,0] => [3,2] => 10 => 0
[[[[.,.],[[.,.],.]],.],.] => [1,1,1,1,0,0,1,1,0,0,0,0] => [2,2] => 00 => 0
[[[[.,[.,.]],[.,.]],.],.] => [1,1,1,1,0,1,0,0,1,0,0,0] => [3,1] => 11 => 0
[[[[[.,.],.],[.,.]],.],.] => [1,1,1,1,1,0,0,0,1,0,0,0] => [3] => 1 => 0
[[[[.,[.,[.,.]]],.],.],.] => [1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => 01 => 0
[[[[.,[[.,.],.]],.],.],.] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1] => 11 => 0
[[[[[.,.],[.,.]],.],.],.] => [1,1,1,1,1,0,0,1,0,0,0,0] => [2] => 0 => 0
[[[[[.,[.,.]],.],.],.],.] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1] => 1 => 0
[.,[.,[.,[[.,[[.,.],.]],.]]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => 001101 => 0
[.,[.,[.,[[[.,.],[.,.]],.]]]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2,1] => 111101 => 0
[.,[.,[.,[[[.,[.,.]],.],.]]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2,1] => 011101 => 0
[.,[.,[.,[[[[.,.],.],.],.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2,1] => 111101 => 0
[.,[.,[[.,.],[[[.,.],.],.]]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 000001 => 0
[.,[.,[[[.,.],.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => 110001 => 0
[.,[.,[[.,[[.,.],.]],[.,.]]]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2,1] => 011001 => 0
[.,[.,[[[.,.],[.,.]],[.,.]]]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,2,2,1] => 000001 => 0
[.,[.,[[[.,[.,.]],.],[.,.]]]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,2,2,1] => 010001 => 0
[.,[.,[[[[.,.],.],.],[.,.]]]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2,1] => 000001 => 0
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2,1] => 101001 => 0
[.,[.,[[.,[.,[[.,.],.]]],.]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => 001001 => 0
[.,[.,[[.,[[.,.],[.,.]]],.]]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2,1] => 111001 => 0
[.,[.,[[.,[[.,[.,.]],.]],.]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => 011001 => 0
[.,[.,[[.,[[[.,.],.],.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 111001 => 0
[.,[.,[[[.,.],[.,[.,.]]],.]]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2,1] => 100001 => 0
[.,[.,[[[.,.],[[.,.],.]],.]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => 000001 => 0
[.,[.,[[[.,[.,.]],[.,.]],.]]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2,1] => 110001 => 0
[.,[.,[[[[.,.],.],[.,.]],.]]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2,1] => 100001 => 0
[.,[.,[[[.,[.,[.,.]]],.],.]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2,1] => 010001 => 0
[.,[.,[[[.,[[.,.],.]],.],.]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2,1] => 110001 => 0
[.,[.,[[[[.,.],[.,.]],.],.]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2,1] => 000001 => 0
[.,[.,[[[[.,[.,.]],.],.],.]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2,1] => 100001 => 0
[.,[.,[[[[[.,.],.],.],.],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2,1] => 000001 => 0
[.,[[.,.],[.,[[[.,.],.],.]]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1,1] => 000111 => 0
[.,[[.,.],[[[.,.],.],[.,.]]]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1,1] => 011111 => 0
[.,[[.,.],[[.,[.,[.,.]]],.]]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => 101111 => 0
[.,[[.,.],[[.,[[.,.],.]],.]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => 001111 => 0
[.,[[.,.],[[[.,.],[.,.]],.]]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => 111111 => 0
[.,[[.,.],[[[.,[.,.]],.],.]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => 011111 => 0
[.,[[.,.],[[[[.,.],.],.],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 111111 => 0
[.,[[.,[.,.]],[[.,[.,.]],.]]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => 100011 => 0
[.,[[.,[.,.]],[[[.,.],.],.]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => 000011 => 0
[.,[[[.,.],.],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1,1] => 110111 => 0
[.,[[[.,.],.],[[.,.],[.,.]]]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1,1] => 000111 => 0
[.,[[[.,.],.],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => 100111 => 0
[.,[[[.,.],.],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 000111 => 0
[.,[[.,[.,[.,.]]],[[.,.],.]]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1,1] => 111011 => 0
[.,[[.,[[.,.],.]],[.,[.,.]]]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,2,1,1] => 010011 => 0
[.,[[.,[[.,.],.]],[[.,.],.]]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => 110011 => 0
[.,[[[.,.],[.,.]],[.,[.,.]]]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,1,1] => 011111 => 0
[.,[[[.,.],[.,.]],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1,1] => 111111 => 0
[.,[[[.,[.,.]],.],[.,[.,.]]]] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,1,1] => 010111 => 0
[.,[[[.,[.,.]],.],[[.,.],.]]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1,1] => 110111 => 0
[.,[[[[.,.],.],.],[.,[.,.]]]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1,1,1] => 011111 => 0
[.,[[[[.,.],.],.],[[.,.],.]]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1,1] => 111111 => 0
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,1] => 001011 => 0
[.,[[.,[.,[[.,.],.]]],[.,.]]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2,1,1] => 011011 => 0
[.,[[.,[[.,.],[.,.]]],[.,.]]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,2,1,1] => 000011 => 0
[.,[[.,[[.,[.,.]],.]],[.,.]]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2,1,1] => 010011 => 0
[.,[[.,[[[.,.],.],.]],[.,.]]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2,1,1] => 000011 => 0
[.,[[[.,.],[.,[.,.]]],[.,.]]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,1,1] => 001111 => 0
[.,[[[.,.],[[.,.],.]],[.,.]]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1,1,1] => 011111 => 0
[.,[[[.,[.,.]],[.,.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,1,1] => 000111 => 0
[.,[[[[.,.],.],[.,.]],[.,.]]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1,1,1] => 001111 => 0
[.,[[[.,[.,[.,.]]],.],[.,.]]] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,1,1] => 010111 => 0
[.,[[[.,[[.,.],.]],.],[.,.]]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1,1] => 000111 => 0
[.,[[[[.,.],[.,.]],.],[.,.]]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1,1,1] => 011111 => 0
[.,[[[[.,[.,.]],.],.],[.,.]]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1,1] => 001111 => 0
[.,[[[[[.,.],.],.],.],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1,1] => 011111 => 0
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,1] => 101011 => 0
[.,[[.,[.,[.,[[.,.],.]]]],.]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1,1] => 001011 => 0
[.,[[.,[.,[[.,.],[.,.]]]],.]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1,1] => 111011 => 0
[.,[[.,[.,[[.,[.,.]],.]]],.]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1,1] => 011011 => 0
[.,[[.,[.,[[[.,.],.],.]]],.]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => 111011 => 0
[.,[[.,[[.,.],[.,[.,.]]]],.]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2,1,1] => 100011 => 0
[.,[[.,[[.,.],[[.,.],.]]],.]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => 000011 => 0
[.,[[.,[[.,[.,.]],[.,.]]],.]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1,1] => 110011 => 0
[.,[[.,[[[.,.],.],[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1,1] => 100011 => 0
[.,[[.,[[.,[.,[.,.]]],.]],.]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1,1] => 010011 => 0
[.,[[.,[[.,[[.,.],.]],.]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 110011 => 0
[.,[[.,[[[.,.],[.,.]],.]],.]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1,1] => 000011 => 0
[.,[[.,[[[.,[.,.]],.],.]],.]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1,1] => 100011 => 0
[.,[[.,[[[[.,.],.],.],.]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => 000011 => 0
[.,[[[.,.],[.,[.,[.,.]]]],.]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,1,1] => 101111 => 0
[.,[[[.,.],[.,[[.,.],.]]],.]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1,1] => 001111 => 0
[.,[[[.,.],[[.,.],[.,.]]],.]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1,1] => 111111 => 0
[.,[[[.,.],[[.,[.,.]],.]],.]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1,1] => 011111 => 0
[.,[[[.,.],[[[.,.],.],.]],.]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => 111111 => 0
[.,[[[.,[.,.]],[.,[.,.]]],.]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,1,1] => 100111 => 0
[.,[[[.,[.,.]],[[.,.],.]],.]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1,1] => 000111 => 0
[.,[[[[.,.],.],[.,[.,.]]],.]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1,1] => 101111 => 0
[.,[[[[.,.],.],[[.,.],.]],.]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1,1] => 001111 => 0
[.,[[[.,[.,[.,.]]],[.,.]],.]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1,1] => 110111 => 0
[.,[[[.,[[.,.],.]],[.,.]],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1,1] => 100111 => 0
[.,[[[[.,.],[.,.]],[.,.]],.]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1,1] => 111111 => 0
[.,[[[[.,[.,.]],.],[.,.]],.]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1,1] => 101111 => 0
[.,[[[[[.,.],.],.],[.,.]],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1,1] => 111111 => 0
[.,[[[.,[.,[.,[.,.]]]],.],.]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1,1] => 010111 => 0
[.,[[[.,[.,[[.,.],.]]],.],.]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1,1] => 110111 => 0
[.,[[[.,[[.,.],[.,.]]],.],.]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1,1] => 000111 => 0
[.,[[[.,[[.,[.,.]],.]],.],.]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => 100111 => 0
[.,[[[.,[[[.,.],.],.]],.],.]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => 000111 => 0
[.,[[[[.,.],[.,[.,.]]],.],.]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1,1] => 011111 => 0
[.,[[[[.,.],[[.,.],.]],.],.]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1,1] => 111111 => 0
[.,[[[[.,[.,.]],[.,.]],.],.]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1,1] => 001111 => 0
[.,[[[[[.,.],.],[.,.]],.],.]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1,1] => 011111 => 0
[.,[[[[.,[.,[.,.]]],.],.],.]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1] => 101111 => 0
[.,[[[[.,[[.,.],.]],.],.],.]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1,1] => 001111 => 0
[.,[[[[[.,.],[.,.]],.],.],.]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1,1] => 111111 => 0
[.,[[[[[.,[.,.]],.],.],.],.]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 011111 => 0
[.,[[[[[[.,.],.],.],.],.],.]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 111111 => 0
[[.,.],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2] => 00010 => 0
[[.,.],[.,[[[.,.],.],[.,.]]]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2] => 01110 => 0
[[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2] => 10110 => 0
[[.,.],[.,[[.,[[.,.],.]],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => 00110 => 0
[[.,.],[.,[[[.,.],[.,.]],.]]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2] => 11110 => 0
[[.,.],[.,[[[.,[.,.]],.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2] => 01110 => 0
[[.,.],[.,[[[[.,.],.],.],.]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2] => 11110 => 0
[[.,.],[[.,.],[[.,[.,.]],.]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => 10000 => 0
[[.,.],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 00000 => 0
[[.,.],[[.,[.,.]],[[.,.],.]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2] => 11100 => 0
[[.,.],[[[.,.],.],[.,[.,.]]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => 01000 => 0
[[.,.],[[[.,.],.],[[.,.],.]]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 11000 => 0
[[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,2] => 00100 => 0
[[.,.],[[.,[[.,.],.]],[.,.]]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2] => 01100 => 0
[[.,.],[[[.,.],[.,.]],[.,.]]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,2,2] => 00000 => 0
[[.,.],[[[.,[.,.]],.],[.,.]]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,2,2] => 01000 => 0
[[.,.],[[[[.,.],.],.],[.,.]]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => 00000 => 0
[[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2] => 10100 => 0
[[.,.],[[.,[.,[[.,.],.]]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => 00100 => 0
[[.,.],[[.,[[.,.],[.,.]]],.]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2] => 11100 => 0
[[.,.],[[.,[[.,[.,.]],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => 01100 => 0
[[.,.],[[.,[[[.,.],.],.]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 11100 => 0
[[.,.],[[[.,.],[.,[.,.]]],.]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2] => 10000 => 0
[[.,.],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => 00000 => 0
[[.,.],[[[.,[.,.]],[.,.]],.]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2] => 11000 => 0
[[.,.],[[[[.,.],.],[.,.]],.]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2] => 10000 => 0
[[.,.],[[[.,[.,[.,.]]],.],.]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2] => 01000 => 0
[[.,.],[[[.,[[.,.],.]],.],.]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => 11000 => 0
[[.,.],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2] => 00000 => 0
[[.,.],[[[[.,[.,.]],.],.],.]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2] => 10000 => 0
[[.,.],[[[[[.,.],.],.],.],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => 00000 => 0
[[.,[.,.]],[.,[[.,[.,.]],.]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3,1] => 10011 => 0
[[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1] => 00011 => 0
[[.,[.,.]],[[.,.],[[.,.],.]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1] => 11111 => 0
[[.,[.,.]],[[.,[.,.]],[.,.]]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3,1] => 00111 => 0
[[.,[.,.]],[[[.,.],.],[.,.]]] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1] => 01111 => 0
[[.,[.,.]],[[.,[.,[.,.]]],.]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1] => 10111 => 0
[[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => 00111 => 0
[[.,[.,.]],[[[.,.],[.,.]],.]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1] => 11111 => 0
[[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1] => 01111 => 0
[[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1] => 11111 => 0
[[[.,.],.],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3] => 1101 => 0
[[[.,.],.],[.,[[.,.],[.,.]]]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3] => 0001 => 0
[[[.,.],.],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3] => 1001 => 0
[[[.,.],.],[.,[[[.,.],.],.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3] => 0001 => 0
[[[.,.],.],[[.,.],[.,[.,.]]]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 0111 => 0
[[[.,.],.],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 1111 => 0
[[[.,.],.],[[.,[.,.]],[.,.]]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3] => 0011 => 0
[[[.,.],.],[[[.,.],.],[.,.]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 0111 => 0
[[[.,.],.],[[.,[.,[.,.]]],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3] => 1011 => 0
[[[.,.],.],[[.,[[.,.],.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => 0011 => 0
[[[.,.],.],[[[.,.],[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3] => 1111 => 0
[[[.,.],.],[[[.,[.,.]],.],.]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3] => 0111 => 0
[[[.,.],.],[[[[.,.],.],.],.]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => 1111 => 0
[[.,[.,[.,.]]],[.,[[.,.],.]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [5,5,4,2,1] => 11001 => 0
[[.,[.,[.,.]]],[[.,.],[.,.]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [6,4,4,2,1] => 00001 => 0
[[.,[.,[.,.]]],[[.,[.,.]],.]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1] => 10001 => 0
[[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1] => 00001 => 0
[[.,[[.,.],.]],[.,[.,[.,.]]]] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,1] => 01011 => 0
[[.,[[.,.],.]],[.,[[.,.],.]]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1] => 11011 => 0
[[.,[[.,.],.]],[[.,.],[.,.]]] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1] => 00011 => 0
[[.,[[.,.],.]],[[.,[.,.]],.]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1] => 10011 => 0
[[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1] => 00011 => 0
[[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2] => 0100 => 0
[[[.,.],[.,.]],[.,[[.,.],.]]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [5,5,4,2] => 1100 => 0
[[[.,.],[.,.]],[[.,.],[.,.]]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [6,4,4,2] => 0000 => 0
[[[.,.],[.,.]],[[.,[.,.]],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2] => 1000 => 0
[[[.,.],[.,.]],[[[.,.],.],.]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2] => 0000 => 0
[[[.,[.,.]],.],[.,[.,[.,.]]]] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1] => 0101 => 0
[[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1] => 1101 => 0
[[[.,[.,.]],.],[[.,.],[.,.]]] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1] => 0001 => 0
[[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1] => 1001 => 0
[[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1] => 0001 => 0
[[[[.,.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [6,5,4] => 010 => 0
[[[[.,.],.],.],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,5,4] => 110 => 0
[[[[.,.],.],.],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 000 => 0
[[[[.,.],.],.],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,4,4] => 100 => 0
[[[[.,.],.],.],[[[.,.],.],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => 000 => 0
[[.,[.,[.,[.,.]]]],[.,[.,.]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1] => 01101 => 0
[[.,[.,[.,[.,.]]]],[[.,.],.]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1] => 11101 => 0
[[.,[.,[[.,.],.]]],[.,[.,.]]] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,2,1] => 01001 => 0
[[.,[.,[[.,.],.]]],[[.,.],.]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1] => 11001 => 0
[[.,[[.,.],[.,.]]],[.,[.,.]]] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,1] => 01111 => 0
[[.,[[.,.],[.,.]]],[[.,.],.]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1] => 11111 => 0
[[.,[[.,[.,.]],.]],[.,[.,.]]] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,1] => 01011 => 0
[[.,[[.,[.,.]],.]],[[.,.],.]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1] => 11011 => 0
[[.,[[[.,.],.],.]],[.,[.,.]]] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1,1] => 01111 => 0
[[.,[[[.,.],.],.]],[[.,.],.]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1] => 11111 => 0
[[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2] => 0110 => 0
[[[.,.],[.,[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2] => 1110 => 0
[[[.,.],[[.,.],.]],[.,[.,.]]] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [6,5,2,2] => 0100 => 0
[[[.,.],[[.,.],.]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2] => 1100 => 0
[[[.,[.,.]],[.,.]],[.,[.,.]]] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1] => 0111 => 0
[[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1] => 1111 => 0
[[[[.,.],.],[.,.]],[.,[.,.]]] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [6,5,3] => 011 => 0
[[[[.,.],.],[.,.]],[[.,.],.]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [5,5,3] => 111 => 0
[[[.,[.,[.,.]]],.],[.,[.,.]]] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1] => 0101 => 0
[[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1] => 1101 => 0
[[[.,[[.,.],.]],.],[.,[.,.]]] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1] => 0111 => 0
[[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1] => 1111 => 0
[[[[.,.],[.,.]],.],[.,[.,.]]] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [6,5,2] => 010 => 0
[[[[.,.],[.,.]],.],[[.,.],.]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,5,2] => 110 => 0
[[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [6,5,1] => 011 => 0
[[[[.,[.,.]],.],.],[[.,.],.]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,5,1] => 111 => 0
[[[[[.,.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => 01 => 0
[[[[[.,.],.],.],.],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 11 => 0
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1] => 00101 => 0
[[.,[.,[.,[[.,.],.]]]],[.,.]] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2,1] => 01101 => 0
[[.,[.,[[.,.],[.,.]]]],[.,.]] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,2,1] => 00001 => 0
[[.,[.,[[.,[.,.]],.]]],[.,.]] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2,1] => 01001 => 0
[[.,[.,[[[.,.],.],.]]],[.,.]] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2,1] => 00001 => 0
[[.,[[.,.],[.,[.,.]]]],[.,.]] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,1] => 00111 => 0
[[.,[[.,.],[[.,.],.]]],[.,.]] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1,1] => 01111 => 0
[[.,[[.,[.,.]],[.,.]]],[.,.]] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,1] => 00011 => 0
[[.,[[[.,.],.],[.,.]]],[.,.]] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1,1] => 00111 => 0
[[.,[[.,[.,[.,.]]],.]],[.,.]] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,1] => 01011 => 0
[[.,[[.,[[.,.],.]],.]],[.,.]] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1] => 00011 => 0
[[.,[[[.,.],[.,.]],.]],[.,.]] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1,1] => 01111 => 0
[[.,[[[.,[.,.]],.],.]],[.,.]] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1] => 00111 => 0
[[.,[[[[.,.],.],.],.]],[.,.]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1] => 01111 => 0
[[[.,.],[.,[.,[.,.]]]],[.,.]] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2] => 0010 => 0
[[[.,.],[.,[[.,.],.]]],[.,.]] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2] => 0110 => 0
[[[.,.],[[.,.],[.,.]]],[.,.]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [6,4,2,2] => 0000 => 0
[[[.,.],[[.,[.,.]],.]],[.,.]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2] => 0100 => 0
[[[.,.],[[[.,.],.],.]],[.,.]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2] => 0000 => 0
[[[.,[.,.]],[.,[.,.]]],[.,.]] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1] => 0011 => 0
[[[.,[.,.]],[[.,.],.]],[.,.]] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1] => 0111 => 0
[[[[.,.],.],[.,[.,.]]],[.,.]] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [6,4,3] => 001 => 0
[[[[.,.],.],[[.,.],.]],[.,.]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [6,3,3] => 011 => 0
[[[.,[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1] => 0001 => 0
[[[.,[[.,.],.]],[.,.]],[.,.]] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1] => 0011 => 0
[[[[.,.],[.,.]],[.,.]],[.,.]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [6,4,2] => 000 => 0
[[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [6,4,1] => 001 => 0
[[[[[.,.],.],.],[.,.]],[.,.]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,4] => 00 => 0
[[[.,[.,[.,[.,.]]]],.],[.,.]] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1] => 0101 => 0
[[[.,[.,[[.,.],.]]],.],[.,.]] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1] => 0001 => 0
[[[.,[[.,.],[.,.]]],.],[.,.]] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1] => 0111 => 0
[[[.,[[.,[.,.]],.]],.],[.,.]] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1] => 0011 => 0
[[[.,[[[.,.],.],.]],.],[.,.]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1] => 0111 => 0
[[[[.,.],[.,[.,.]]],.],[.,.]] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2] => 010 => 0
[[[[.,.],[[.,.],.]],.],[.,.]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,2,2] => 000 => 0
[[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,1] => 011 => 0
[[[[[.,.],.],[.,.]],.],[.,.]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,3] => 01 => 0
[[[[.,[.,[.,.]]],.],.],[.,.]] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,2,1] => 001 => 0
[[[[.,[[.,.],.]],.],.],[.,.]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,1,1] => 011 => 0
[[[[[.,.],[.,.]],.],.],[.,.]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,2] => 00 => 0
[[[[[.,[.,.]],.],.],.],[.,.]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => 01 => 0
[[[[[[.,.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 0 => 0
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1] => 10101 => 0
[[.,[.,[.,[.,[[.,.],.]]]]],.] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1] => 00101 => 0
[[.,[.,[.,[[.,.],[.,.]]]]],.] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1] => 11101 => 0
[[.,[.,[.,[[.,[.,.]],.]]]],.] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1] => 01101 => 0
[[.,[.,[.,[[[.,.],.],.]]]],.] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1] => 11101 => 0
[[.,[.,[[.,.],[.,[.,.]]]]],.] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2,1] => 10001 => 0
[[.,[.,[[.,.],[[.,.],.]]]],.] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1] => 00001 => 0
[[.,[.,[[.,[.,.]],[.,.]]]],.] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1] => 11001 => 0
[[.,[.,[[[.,.],.],[.,.]]]],.] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1] => 10001 => 0
[[.,[.,[[.,[.,[.,.]]],.]]],.] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1] => 01001 => 0
[[.,[.,[[.,[[.,.],.]],.]]],.] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => 11001 => 0
[[.,[.,[[[.,.],[.,.]],.]]],.] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1] => 00001 => 0
[[.,[.,[[[.,[.,.]],.],.]]],.] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1] => 10001 => 0
[[.,[.,[[[[.,.],.],.],.]]],.] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1] => 00001 => 0
[[.,[[.,.],[.,[.,[.,.]]]]],.] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,1] => 10111 => 0
[[.,[[.,.],[.,[[.,.],.]]]],.] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1] => 00111 => 0
[[.,[[.,.],[[.,.],[.,.]]]],.] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1] => 11111 => 0
[[.,[[.,.],[[.,[.,.]],.]]],.] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1] => 01111 => 0
[[.,[[.,.],[[[.,.],.],.]]],.] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => 11111 => 0
[[.,[[.,[.,.]],[.,[.,.]]]],.] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,1] => 10011 => 0
[[.,[[.,[.,.]],[[.,.],.]]],.] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1] => 00011 => 0
[[.,[[[.,.],.],[.,[.,.]]]],.] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1] => 10111 => 0
[[.,[[[.,.],.],[[.,.],.]]],.] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1] => 00111 => 0
[[.,[[.,[.,[.,.]]],[.,.]]],.] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1] => 11011 => 0
[[.,[[.,[[.,.],.]],[.,.]]],.] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1] => 10011 => 0
[[.,[[[.,.],[.,.]],[.,.]]],.] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1] => 11111 => 0
[[.,[[[.,[.,.]],.],[.,.]]],.] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1] => 10111 => 0
[[.,[[[[.,.],.],.],[.,.]]],.] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1] => 11111 => 0
[[.,[[.,[.,[.,[.,.]]]],.]],.] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1] => 01011 => 0
[[.,[[.,[.,[[.,.],.]]],.]],.] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1] => 11011 => 0
[[.,[[.,[[.,.],[.,.]]],.]],.] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1] => 00011 => 0
[[.,[[.,[[.,[.,.]],.]],.]],.] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => 10011 => 0
[[.,[[.,[[[.,.],.],.]],.]],.] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => 00011 => 0
[[.,[[[.,.],[.,[.,.]]],.]],.] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1] => 01111 => 0
[[.,[[[.,.],[[.,.],.]],.]],.] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => 11111 => 0
[[.,[[[.,[.,.]],[.,.]],.]],.] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1] => 00111 => 0
[[.,[[[[.,.],.],[.,.]],.]],.] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1] => 01111 => 0
[[.,[[[.,[.,[.,.]]],.],.]],.] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => 10111 => 0
[[.,[[[.,[[.,.],.]],.],.]],.] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1] => 00111 => 0
[[.,[[[[.,.],[.,.]],.],.]],.] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1] => 11111 => 0
[[.,[[[[.,[.,.]],.],.],.]],.] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1] => 01111 => 0
[[.,[[[[[.,.],.],.],.],.]],.] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => 11111 => 0
[[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2] => 1010 => 0
[[[.,.],[.,[.,[[.,.],.]]]],.] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2] => 0010 => 0
[[[.,.],[.,[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2] => 1110 => 0
[[[.,.],[.,[[.,[.,.]],.]]],.] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2] => 0110 => 0
[[[.,.],[.,[[[.,.],.],.]]],.] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2] => 1110 => 0
[[[.,.],[[.,.],[.,[.,.]]]],.] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2] => 1000 => 0
[[[.,.],[[.,.],[[.,.],.]]],.] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2] => 0000 => 0
[[[.,.],[[.,[.,.]],[.,.]]],.] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2] => 1100 => 0
[[[.,.],[[[.,.],.],[.,.]]],.] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2] => 1000 => 0
[[[.,.],[[.,[.,[.,.]]],.]],.] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2] => 0100 => 0
[[[.,.],[[.,[[.,.],.]],.]],.] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => 1100 => 0
[[[.,.],[[[.,.],[.,.]],.]],.] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2] => 0000 => 0
[[[.,.],[[[.,[.,.]],.],.]],.] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2] => 1000 => 0
[[[.,.],[[[[.,.],.],.],.]],.] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => 0000 => 0
[[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1] => 1011 => 0
[[[.,[.,.]],[.,[[.,.],.]]],.] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1] => 0011 => 0
[[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1] => 1111 => 0
[[[.,[.,.]],[[.,[.,.]],.]],.] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1] => 0111 => 0
[[[.,[.,.]],[[[.,.],.],.]],.] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1] => 1111 => 0
[[[[.,.],.],[.,[.,[.,.]]]],.] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [5,4,3] => 101 => 0
[[[[.,.],.],[.,[[.,.],.]]],.] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,4,3] => 001 => 0
[[[[.,.],.],[[.,.],[.,.]]],.] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [5,3,3] => 111 => 0
[[[[.,.],.],[[.,[.,.]],.]],.] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,3] => 011 => 0
[[[[.,.],.],[[[.,.],.],.]],.] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,3,3] => 111 => 0
[[[.,[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1] => 1001 => 0
[[[.,[.,[.,.]]],[[.,.],.]],.] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1] => 0001 => 0
[[[.,[[.,.],.]],[.,[.,.]]],.] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1] => 1011 => 0
[[[.,[[.,.],.]],[[.,.],.]],.] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1] => 0011 => 0
[[[[.,.],[.,.]],[.,[.,.]]],.] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,4,2] => 100 => 0
[[[[.,.],[.,.]],[[.,.],.]],.] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,4,2] => 000 => 0
[[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,4,1] => 101 => 0
[[[[.,[.,.]],.],[[.,.],.]],.] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,4,1] => 001 => 0
[[[[[.,.],.],.],[.,[.,.]]],.] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4] => 10 => 0
[[[[[.,.],.],.],[[.,.],.]],.] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,4] => 00 => 0
[[[.,[.,[.,[.,.]]]],[.,.]],.] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1] => 1101 => 0
[[[.,[.,[[.,.],.]]],[.,.]],.] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1] => 1001 => 0
[[[.,[[.,.],[.,.]]],[.,.]],.] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1] => 1111 => 0
[[[.,[[.,[.,.]],.]],[.,.]],.] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1] => 1011 => 0
[[[.,[[[.,.],.],.]],[.,.]],.] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1] => 1111 => 0
[[[[.,.],[.,[.,.]]],[.,.]],.] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [5,3,2] => 110 => 0
[[[[.,.],[[.,.],.]],[.,.]],.] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [5,2,2] => 100 => 0
[[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,3,1] => 111 => 0
[[[[[.,.],.],[.,.]],[.,.]],.] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,3] => 11 => 0
[[[[.,[.,[.,.]]],.],[.,.]],.] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => 101 => 0
[[[[.,[[.,.],.]],.],[.,.]],.] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,1] => 111 => 0
[[[[[.,.],[.,.]],.],[.,.]],.] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => 10 => 0
[[[[[.,[.,.]],.],.],[.,.]],.] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1] => 11 => 0
[[[[[[.,.],.],.],.],[.,.]],.] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => 1 => 0
[[[.,[.,[.,[.,[.,.]]]]],.],.] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1] => 0101 => 0
[[[.,[.,[.,[[.,.],.]]]],.],.] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1] => 1101 => 0
[[[.,[.,[[.,.],[.,.]]]],.],.] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1] => 0001 => 0
[[[.,[.,[[.,[.,.]],.]]],.],.] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => 1001 => 0
[[[.,[.,[[[.,.],.],.]]],.],.] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1] => 0001 => 0
[[[.,[[.,.],[.,[.,.]]]],.],.] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1] => 0111 => 0
[[[.,[[.,.],[[.,.],.]]],.],.] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1] => 1111 => 0
[[[.,[[.,[.,.]],[.,.]]],.],.] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1] => 0011 => 0
[[[.,[[[.,.],.],[.,.]]],.],.] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1] => 0111 => 0
[[[.,[[.,[.,[.,.]]],.]],.],.] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => 1011 => 0
[[[.,[[.,[[.,.],.]],.]],.],.] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1] => 0011 => 0
[[[.,[[[.,.],[.,.]],.]],.],.] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1] => 1111 => 0
[[[.,[[[.,[.,.]],.],.]],.],.] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1] => 0111 => 0
[[[.,[[[[.,.],.],.],.]],.],.] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1] => 1111 => 0
[[[[.,.],[.,[.,[.,.]]]],.],.] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,2] => 010 => 0
[[[[.,.],[.,[[.,.],.]]],.],.] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,3,2] => 110 => 0
[[[[.,.],[[.,.],[.,.]]],.],.] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,2] => 000 => 0
[[[[.,.],[[.,[.,.]],.]],.],.] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2] => 100 => 0
[[[[.,.],[[[.,.],.],.]],.],.] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,2,2] => 000 => 0
[[[[.,[.,.]],[.,[.,.]]],.],.] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,3,1] => 011 => 0
[[[[.,[.,.]],[[.,.],.]],.],.] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [3,3,1] => 111 => 0
[[[[[.,.],.],[.,[.,.]]],.],.] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [4,3] => 01 => 0
[[[[[.,.],.],[[.,.],.]],.],.] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,3] => 11 => 0
[[[[.,[.,[.,.]]],[.,.]],.],.] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,2,1] => 001 => 0
[[[[.,[[.,.],.]],[.,.]],.],.] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,1,1] => 011 => 0
[[[[[.,.],[.,.]],[.,.]],.],.] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [4,2] => 00 => 0
[[[[[.,[.,.]],.],[.,.]],.],.] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [4,1] => 01 => 0
[[[[[[.,.],.],.],[.,.]],.],.] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [4] => 0 => 0
[[[[.,[.,[.,[.,.]]]],.],.],.] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => 101 => 0
[[[[.,[.,[[.,.],.]]],.],.],.] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,2,1] => 001 => 0
[[[[.,[[.,.],[.,.]]],.],.],.] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [3,1,1] => 111 => 0
[[[[.,[[.,[.,.]],.]],.],.],.] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,1,1] => 011 => 0
[[[[.,[[[.,.],.],.]],.],.],.] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1] => 111 => 0
[[[[[.,.],[.,[.,.]]],.],.],.] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,2] => 10 => 0
[[[[[.,.],[[.,.],.]],.],.],.] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,2] => 00 => 0
[[[[[.,[.,.]],[.,.]],.],.],.] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,1] => 11 => 0
[[[[[[.,.],.],[.,.]],.],.],.] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => 1 => 0
[[[[[.,[.,[.,.]]],.],.],.],.] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => 01 => 0
[[[[[.,[[.,.],.]],.],.],.],.] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1] => 11 => 0
[[[[[[.,.],[.,.]],.],.],.],.] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => 0 => 0
[[[[[[.,[.,.]],.],.],.],.],.] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1] => 1 => 0
[.,[.,[[.,[[[[.,.],.],.],.]],.]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => 1111001 => 0
[.,[.,[[[[[.,.],.],.],[.,.]],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,2,1] => 0000001 => 0
[.,[.,[[[.,[[.,[.,.]],.]],.],.]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2,1] => 0110001 => 0
[.,[.,[[[.,[[[.,.],.],.]],.],.]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2,1] => 1110001 => 0
[.,[.,[[[[.,.],[[.,.],.]],.],.]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2,1] => 0000001 => 0
[.,[.,[[[[.,[.,.]],[.,.]],.],.]]] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,2,1] => 1100001 => 0
[.,[.,[[[[[.,.],.],[.,.]],.],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,2,1] => 1000001 => 0
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,2,1] => 0100001 => 0
[.,[.,[[[[.,[[.,.],.]],.],.],.]]] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2,1] => 1100001 => 0
[.,[.,[[[[[.,.],[.,.]],.],.],.]]] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,2,1] => 0000001 => 0
[.,[.,[[[[[.,[.,.]],.],.],.],.]]] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2,1] => 1000001 => 0
[.,[.,[[[[[[.,.],.],.],.],.],.]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => 0000001 => 0
[.,[[.,.],[[[[[.,.],.],.],.],.]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => 1111111 => 0
[.,[[[[[.,.],.],.],.],[[.,.],.]]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1,1] => 0011111 => 0
[.,[[.,[[[[.,.],.],.],.]],[.,.]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,1,1] => 1000011 => 0
[.,[[[[[.,.],.],.],[.,.]],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,1,1,1,1] => 1111111 => 0
[.,[[[.,[[.,[.,.]],.]],.],[.,.]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,1,1,1] => 1100111 => 0
[.,[[[.,[[[.,.],.],.]],.],[.,.]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,1,1,1] => 1000111 => 0
[.,[[[[.,.],[[.,.],.]],.],[.,.]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1,1,1,1] => 1111111 => 0
[.,[[[[.,[.,.]],[.,.]],.],[.,.]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,1,1,1] => 1001111 => 0
[.,[[[[[.,.],.],[.,.]],.],[.,.]]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,1,1,1,1] => 1011111 => 0
[.,[[[[.,[.,[.,.]]],.],.],[.,.]]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,1,1,1] => 1101111 => 0
[.,[[[[.,[[.,.],.]],.],.],[.,.]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1,1,1,1] => 1001111 => 0
[.,[[[[[.,.],[.,.]],.],.],[.,.]]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,1,1,1,1] => 1111111 => 0
[.,[[[[[.,[.,.]],.],.],.],[.,.]]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1,1,1,1] => 1011111 => 0
[.,[[[[[[.,.],.],.],.],.],[.,.]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1,1,1] => 1111111 => 0
[.,[[.,[.,[[[.,[.,.]],.],.]]],.]] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1,1] => 0111011 => 0
[.,[[.,[.,[[[[.,.],.],.],.]]],.]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => 1111011 => 0
[.,[[.,[[[.,[.,.]],.],[.,.]]],.]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,1,1] => 0100011 => 0
[.,[[.,[[[[.,.],.],.],[.,.]]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1,1] => 0000011 => 0
[.,[[.,[[.,[.,[[.,.],.]]],.]],.]] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => 0010011 => 0
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => 1110011 => 0
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => 0110011 => 0
[.,[[.,[[.,[[[.,.],.],.]],.]],.]] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => 1110011 => 0
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1,1] => 1000011 => 0
[.,[[.,[[[.,.],[[.,.],.]],.]],.]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => 0000011 => 0
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1,1] => 1100011 => 0
[.,[[.,[[[[.,.],.],[.,.]],.]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1,1] => 1000011 => 0
[.,[[.,[[[.,[.,[.,.]]],.],.]],.]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1,1] => 0100011 => 0
[.,[[.,[[[.,[[.,.],.]],.],.]],.]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1,1] => 1100011 => 0
[.,[[.,[[[[.,.],[.,.]],.],.]],.]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,1,1] => 0000011 => 0
[.,[[.,[[[[.,[.,.]],.],.],.]],.]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1,1] => 1000011 => 0
[.,[[.,[[[[[.,.],.],.],.],.]],.]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => 0000011 => 0
[.,[[[.,.],[[.,[[.,.],.]],.]],.]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => 0011111 => 0
[.,[[[.,.],[[[.,.],[.,.]],.]],.]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1,1] => 1111111 => 0
[.,[[[.,.],[[[.,[.,.]],.],.]],.]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => 0111111 => 0
[.,[[[.,.],[[[[.,.],.],.],.]],.]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => 1111111 => 0
[.,[[[.,[.,.]],[[[.,.],.],.]],.]] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1,1] => 0000111 => 0
[.,[[[[.,.],.],[[.,[.,.]],.]],.]] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1] => 1001111 => 0
[.,[[[[.,.],.],[[[.,.],.],.]],.]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => 0001111 => 0
[.,[[[.,[[.,.],.]],[[.,.],.]],.]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1,1] => 1100111 => 0
[.,[[[[.,.],[.,.]],[[.,.],.]],.]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1,1] => 1111111 => 0
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,1,1,1] => 0101111 => 0
[.,[[[[.,[.,.]],.],[[.,.],.]],.]] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1,1,1] => 1101111 => 0
[.,[[[[[.,.],.],.],[.,[.,.]]],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1,1,1,1] => 0111111 => 0
[.,[[[[[.,.],.],.],[[.,.],.]],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1,1] => 1111111 => 0
[.,[[[.,[.,[[.,.],.]]],[.,.]],.]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1,1,1] => 0110111 => 0
[.,[[[.,[[.,.],[.,.]]],[.,.]],.]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,1,1,1] => 0000111 => 0
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1,1,1] => 0100111 => 0
[.,[[[.,[[[.,.],.],.]],[.,.]],.]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1,1,1] => 0000111 => 0
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,1,1,1] => 0011111 => 0
[.,[[[[.,.],[[.,.],.]],[.,.]],.]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1,1] => 0111111 => 0
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,1,1,1] => 0001111 => 0
[.,[[[[[.,.],.],[.,.]],[.,.]],.]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1,1,1,1] => 0011111 => 0
[.,[[[[.,[.,[.,.]]],.],[.,.]],.]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,1,1,1] => 0101111 => 0
[.,[[[[.,[[.,.],.]],.],[.,.]],.]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1,1,1] => 0001111 => 0
[.,[[[[[.,.],[.,.]],.],[.,.]],.]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1,1,1] => 0111111 => 0
[.,[[[[[.,[.,.]],.],.],[.,.]],.]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1,1,1] => 0011111 => 0
[.,[[[[[[.,.],.],.],.],[.,.]],.]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1,1] => 0111111 => 0
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,1,1] => 1010111 => 0
[.,[[[.,[.,[.,[[.,.],.]]]],.],.]] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1,1,1] => 0010111 => 0
[.,[[[.,[.,[[.,.],[.,.]]]],.],.]] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1,1,1] => 1110111 => 0
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1,1] => 0110111 => 0
[.,[[[.,[.,[[[.,.],.],.]]],.],.]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1,1] => 1110111 => 0
[.,[[[.,[[.,.],[.,[.,.]]]],.],.]] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1,1,1] => 1000111 => 0
[.,[[[.,[[.,.],[[.,.],.]]],.],.]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1,1] => 0000111 => 0
[.,[[[.,[[.,[.,.]],[.,.]]],.],.]] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1,1] => 1100111 => 0
[.,[[[.,[[[.,.],.],[.,.]]],.],.]] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1,1,1] => 1000111 => 0
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1,1,1] => 0100111 => 0
[.,[[[.,[[.,[[.,.],.]],.]],.],.]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1,1] => 1100111 => 0
[.,[[[.,[[[.,.],[.,.]],.]],.],.]] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1,1] => 0000111 => 0
[.,[[[.,[[[.,[.,.]],.],.]],.],.]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1,1] => 1000111 => 0
[.,[[[.,[[[[.,.],.],.],.]],.],.]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1,1] => 0000111 => 0
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1,1,1] => 1011111 => 0
[.,[[[[.,.],[.,[[.,.],.]]],.],.]] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1,1,1] => 0011111 => 0
[.,[[[[.,.],[[.,.],[.,.]]],.],.]] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1,1,1] => 1111111 => 0
[.,[[[[.,.],[[.,[.,.]],.]],.],.]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1,1] => 0111111 => 0
[.,[[[[.,.],[[[.,.],.],.]],.],.]] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1,1] => 1111111 => 0
[.,[[[[.,[.,.]],[.,[.,.]]],.],.]] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1,1,1] => 1001111 => 0
[.,[[[[.,[.,.]],[[.,.],.]],.],.]] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1,1,1] => 0001111 => 0
[.,[[[[[.,.],.],[.,[.,.]]],.],.]] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1,1,1] => 1011111 => 0
[.,[[[[[.,.],.],[[.,.],.]],.],.]] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1,1] => 0011111 => 0
[.,[[[[.,[.,[.,.]]],[.,.]],.],.]] => [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1,1,1] => 1101111 => 0
[.,[[[[.,[[.,.],.]],[.,.]],.],.]] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1,1] => 1001111 => 0
[.,[[[[[.,.],[.,.]],[.,.]],.],.]] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1,1,1] => 1111111 => 0
[.,[[[[[.,[.,.]],.],[.,.]],.],.]] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1,1,1] => 1011111 => 0
[.,[[[[[[.,.],.],.],[.,.]],.],.]] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1,1] => 1111111 => 0
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1,1,1] => 0101111 => 0
[.,[[[[.,[.,[[.,.],.]]],.],.],.]] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1,1] => 1101111 => 0
[.,[[[[.,[[.,.],[.,.]]],.],.],.]] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1,1,1] => 0001111 => 0
[.,[[[[.,[[.,[.,.]],.]],.],.],.]] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1,1] => 1001111 => 0
[.,[[[[.,[[[.,.],.],.]],.],.],.]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => 0001111 => 0
[.,[[[[[.,.],[.,[.,.]]],.],.],.]] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1,1,1] => 0111111 => 0
[.,[[[[[.,.],[[.,.],.]],.],.],.]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1,1] => 1111111 => 0
[.,[[[[[.,[.,.]],[.,.]],.],.],.]] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1,1] => 0011111 => 0
[.,[[[[[[.,.],.],[.,.]],.],.],.]] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1,1] => 0111111 => 0
[.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1,1] => 1011111 => 0
[.,[[[[[.,[[.,.],.]],.],.],.],.]] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => 0011111 => 0
[.,[[[[[[.,.],[.,.]],.],.],.],.]] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1,1] => 1111111 => 0
[.,[[[[[[.,[.,.]],.],.],.],.],.]] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => 0111111 => 0
[.,[[[[[[[.,.],.],.],.],.],.],.]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1111111 => 0
[[.,.],[.,[[[[[.,.],.],.],.],.]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2] => 111110 => 0
[[.,.],[[[[[.,.],.],.],.],[.,.]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,2] => 100000 => 0
[[.,.],[[.,[[[.,[.,.]],.],.]],.]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => 011100 => 0
[[.,.],[[.,[[[[.,.],.],.],.]],.]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 111100 => 0
[[.,.],[[[[.,[.,.]],.],[.,.]],.]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,2] => 010000 => 0
[[.,.],[[[[[.,.],.],.],[.,.]],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,2] => 000000 => 0
[[.,.],[[[.,[.,[[.,.],.]]],.],.]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,2] => 001000 => 0
[[.,.],[[[.,[[.,.],[.,.]]],.],.]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,2] => 111000 => 0
[[.,.],[[[.,[[.,[.,.]],.]],.],.]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => 011000 => 0
[[.,.],[[[.,[[[.,.],.],.]],.],.]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 111000 => 0
[[.,.],[[[[.,.],[.,[.,.]]],.],.]] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,2] => 100000 => 0
[[.,.],[[[[.,.],[[.,.],.]],.],.]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2] => 000000 => 0
[[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,2] => 110000 => 0
[[.,.],[[[[[.,.],.],[.,.]],.],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,2] => 100000 => 0
[[.,.],[[[[.,[.,[.,.]]],.],.],.]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,2] => 010000 => 0
[[.,.],[[[[.,[[.,.],.]],.],.],.]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2] => 110000 => 0
[[.,.],[[[[[.,.],[.,.]],.],.],.]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,2] => 000000 => 0
[[.,.],[[[[[.,[.,.]],.],.],.],.]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2] => 100000 => 0
[[.,.],[[[[[[.,.],.],.],.],.],.]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => 000000 => 0
[[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3,1] => 011111 => 0
[[.,[.,.]],[[[[[.,.],.],.],.],.]] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1] => 111111 => 0
[[[.,.],.],[[[.,[[.,.],.]],.],.]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 00111 => 0
[[[.,.],.],[[[[.,.],[.,.]],.],.]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,3,3,3] => 11111 => 0
[[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3] => 01111 => 0
[[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 11111 => 0
[[[.,[.,.]],.],[[[[.,.],.],.],.]] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,1] => 00001 => 0
[[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4] => 1000 => 0
[[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 0000 => 0
[[[.,[[.,.],.]],.],[[[.,.],.],.]] => [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1,1] => 11111 => 0
[[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,5,5,2] => 1110 => 0
[[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [6,5,5,1] => 0111 => 0
[[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1] => 1111 => 0
[[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [6,6,5] => 001 => 0
[[[[[.,.],.],.],.],[[.,.],[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [7,5,5] => 111 => 0
[[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [6,5,5] => 011 => 0
[[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 111 => 0
[[.,[[[.,[.,.]],.],.]],[[.,.],.]] => [1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1,1,1] => 000111 => 0
[[.,[[[[.,.],.],.],.]],[.,[.,.]]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,1,1,1] => 101111 => 0
[[.,[[[[.,.],.],.],.]],[[.,.],.]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1] => 001111 => 0
[[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [6,6,4,1] => 0001 => 0
[[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [7,6,4] => 100 => 0
[[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [6,6,4] => 000 => 0
[[[.,[.,[[.,.],.]]],.],[[.,.],.]] => [1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,1] => 00001 => 0
[[[.,[[.,.],[.,.]]],.],[[.,.],.]] => [1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [6,6,3,1,1] => 00111 => 0
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [7,6,2,1,1] => 10011 => 0
[[[.,[[.,[.,.]],.]],.],[[.,.],.]] => [1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1,1] => 00011 => 0
[[[.,[[[.,.],.],.]],.],[.,[.,.]]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,1,1] => 10111 => 0
[[[.,[[[.,.],.],.]],.],[[.,.],.]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1] => 00111 => 0
[[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [6,6,3,2] => 0010 => 0
[[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [7,6,2,2] => 1000 => 0
[[[[.,.],[[.,.],.]],.],[[.,.],.]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2] => 0000 => 0
[[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [7,6,3,1] => 1011 => 0
[[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [6,6,3,1] => 0011 => 0
[[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [7,6,3] => 101 => 0
[[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,6,3] => 001 => 0
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [7,6,2,1] => 1001 => 0
[[[[.,[.,[.,.]]],.],.],[[.,.],.]] => [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1] => 0001 => 0
[[[[.,[[.,.],.]],.],.],[.,[.,.]]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,1] => 1011 => 0
[[[[.,[[.,.],.]],.],.],[[.,.],.]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1] => 0011 => 0
[[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [7,6,2] => 100 => 0
[[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,6,2] => 000 => 0
[[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [7,6,1] => 101 => 0
[[[[[.,[.,.]],.],.],.],[[.,.],.]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,6,1] => 001 => 0
[[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [7,6] => 10 => 0
[[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => 00 => 0
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,2,1] => 110001 => 0
[[.,[.,[[[[.,.],.],.],.]]],[.,.]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,1] => 100001 => 0
[[.,[[[.,[.,.]],.],[.,.]]],[.,.]] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,1,1] => 110111 => 0
[[.,[[[[.,.],.],.],[.,.]]],[.,.]] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,1,1,1] => 111111 => 0
[[.,[[.,[.,[[.,.],.]]],.]],[.,.]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,1,1] => 111011 => 0
[[.,[[.,[[.,.],[.,.]]],.]],[.,.]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,2,1,1] => 100011 => 0
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,1,1] => 110011 => 0
[[.,[[.,[[[.,.],.],.]],.]],[.,.]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,1,1] => 100011 => 0
[[.,[[[.,.],[.,[.,.]]],.]],[.,.]] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,1,1] => 101111 => 0
[[.,[[[.,.],[[.,.],.]],.]],[.,.]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1,1,1] => 111111 => 0
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,1,1] => 100111 => 0
[[.,[[[[.,.],.],[.,.]],.]],[.,.]] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,1,1,1] => 101111 => 0
[[.,[[[.,[.,[.,.]]],.],.]],[.,.]] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,1,1] => 110111 => 0
[[.,[[[.,[[.,.],.]],.],.]],[.,.]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1,1,1] => 100111 => 0
[[.,[[[[.,.],[.,.]],.],.]],[.,.]] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,1,1,1] => 111111 => 0
[[.,[[[[.,[.,.]],.],.],.]],[.,.]] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1,1,1] => 101111 => 0
[[.,[[[[[.,.],.],.],.],.]],[.,.]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1,1] => 111111 => 0
[[[.,.],[[.,[[.,.],.]],.]],[.,.]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,2] => 11100 => 0
[[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,2,2] => 10000 => 0
[[[.,.],[[[.,[.,.]],.],.]],[.,.]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,2] => 11000 => 0
[[[.,.],[[[[.,.],.],.],.]],[.,.]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2] => 10000 => 0
[[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [7,3,3,3,1] => 11111 => 0
[[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [7,4,3,3] => 1011 => 0
[[[[.,.],.],[[[.,.],.],.]],[.,.]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [7,3,3,3] => 1111 => 0
[[[.,[[.,.],.]],[[.,.],.]],[.,.]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [7,4,4,1,1] => 10011 => 0
[[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [7,4,4,2] => 1000 => 0
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [7,5,4,1] => 1101 => 0
[[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [7,4,4,1] => 1001 => 0
[[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [7,5,4] => 110 => 0
[[[[[.,.],.],.],[[.,.],.]],[.,.]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [7,4,4] => 100 => 0
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,2,1] => 11001 => 0
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1,1] => 11111 => 0
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,1] => 11011 => 0
[[[.,[[[.,.],.],.]],[.,.]],[.,.]] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,1,1] => 11111 => 0
[[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2] => 1110 => 0
[[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,2] => 1100 => 0
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1] => 1111 => 0
[[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [7,5,3] => 111 => 0
[[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1] => 1101 => 0
[[[[.,[[.,.],.]],.],[.,.]],[.,.]] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,1] => 1111 => 0
[[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [7,5,2] => 110 => 0
[[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [7,5,1] => 111 => 0
[[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [7,5] => 11 => 0
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,1] => 10101 => 0
[[[.,[.,[.,[[.,.],.]]]],.],[.,.]] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,1] => 11101 => 0
[[[.,[.,[[.,.],[.,.]]]],.],[.,.]] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,2,1] => 10001 => 0
[[[.,[.,[[.,[.,.]],.]]],.],[.,.]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,1] => 11001 => 0
[[[.,[.,[[[.,.],.],.]]],.],[.,.]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,1] => 10001 => 0
[[[.,[[.,.],[.,[.,.]]]],.],[.,.]] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,1] => 10111 => 0
[[[.,[[.,.],[[.,.],.]]],.],[.,.]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1,1] => 11111 => 0
[[[.,[[.,[.,.]],[.,.]]],.],[.,.]] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,1] => 10011 => 0
[[[.,[[[.,.],.],[.,.]]],.],[.,.]] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,1,1] => 10111 => 0
[[[.,[[.,[.,[.,.]]],.]],.],[.,.]] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,1] => 11011 => 0
[[[.,[[.,[[.,.],.]],.]],.],[.,.]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1,1] => 10011 => 0
[[[.,[[[.,.],[.,.]],.]],.],[.,.]] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,1,1] => 11111 => 0
[[[.,[[[.,[.,.]],.],.]],.],[.,.]] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1,1] => 10111 => 0
[[[.,[[[[.,.],.],.],.]],.],[.,.]] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1] => 11111 => 0
[[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2] => 1010 => 0
[[[[.,.],[.,[[.,.],.]]],.],[.,.]] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2] => 1110 => 0
[[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,2] => 1000 => 0
[[[[.,.],[[.,[.,.]],.]],.],[.,.]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2] => 1100 => 0
[[[[.,.],[[[.,.],.],.]],.],[.,.]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2] => 1000 => 0
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1] => 1011 => 0
[[[[.,[.,.]],[[.,.],.]],.],[.,.]] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1] => 1111 => 0
[[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [7,4,3] => 101 => 0
[[[[[.,.],.],[[.,.],.]],.],[.,.]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [7,3,3] => 111 => 0
[[[[.,[.,[.,.]]],[.,.]],.],[.,.]] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1] => 1001 => 0
[[[[.,[[.,.],.]],[.,.]],.],[.,.]] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,1] => 1011 => 0
[[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [7,4,2] => 100 => 0
[[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [7,4,1] => 101 => 0
[[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,4] => 10 => 0
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1] => 1101 => 0
[[[[.,[.,[[.,.],.]]],.],.],[.,.]] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1] => 1001 => 0
[[[[.,[[.,.],[.,.]]],.],.],[.,.]] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,1] => 1111 => 0
[[[[.,[[.,[.,.]],.]],.],.],[.,.]] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1] => 1011 => 0
[[[[.,[[[.,.],.],.]],.],.],[.,.]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1] => 1111 => 0
[[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [7,3,2] => 110 => 0
[[[[[.,.],[[.,.],.]],.],.],[.,.]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [7,2,2] => 100 => 0
[[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [7,3,1] => 111 => 0
[[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,3] => 11 => 0
[[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,2,1] => 101 => 0
[[[[[.,[[.,.],.]],.],.],.],[.,.]] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,1,1] => 111 => 0
[[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,2] => 10 => 0
[[[[[[.,[.,.]],.],.],.],.],[.,.]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => 11 => 0
[[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1 => 0
[[.,[.,[.,[[.,[[.,.],.]],.]]]],.] => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2,1] => 001101 => 0
[[.,[.,[.,[[[.,.],[.,.]],.]]]],.] => [1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2,1] => 111101 => 0
[[.,[.,[.,[[[.,[.,.]],.],.]]]],.] => [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1] => 011101 => 0
[[.,[.,[.,[[[[.,.],.],.],.]]]],.] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1] => 111101 => 0
[[.,[.,[[.,.],[[[.,.],.],.]]]],.] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,1] => 000001 => 0
[[.,[.,[[[.,.],.],[[.,.],.]]]],.] => [1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2,1] => 110001 => 0
[[.,[.,[[.,[[.,.],.]],[.,.]]]],.] => [1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2,1] => 011001 => 0
[[.,[.,[[[.,.],[.,.]],[.,.]]]],.] => [1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,2,1] => 000001 => 0
[[.,[.,[[[.,[.,.]],.],[.,.]]]],.] => [1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,1] => 010001 => 0
[[.,[.,[[[[.,.],.],.],[.,.]]]],.] => [1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1] => 000001 => 0
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2,1] => 101001 => 0
[[.,[.,[[.,[.,[[.,.],.]]],.]]],.] => [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1] => 001001 => 0
[[.,[.,[[.,[[.,.],[.,.]]],.]]],.] => [1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1] => 111001 => 0
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1] => 011001 => 0
[[.,[.,[[.,[[[.,.],.],.]],.]]],.] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1] => 111001 => 0
[[.,[.,[[[.,.],[.,[.,.]]],.]]],.] => [1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1] => 100001 => 0
[[.,[.,[[[.,.],[[.,.],.]],.]]],.] => [1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1] => 000001 => 0
[[.,[.,[[[.,[.,.]],[.,.]],.]]],.] => [1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1] => 110001 => 0
[[.,[.,[[[[.,.],.],[.,.]],.]]],.] => [1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1] => 100001 => 0
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.] => [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1] => 010001 => 0
[[.,[.,[[[.,[[.,.],.]],.],.]]],.] => [1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1] => 110001 => 0
[[.,[.,[[[[.,.],[.,.]],.],.]]],.] => [1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,1] => 000001 => 0
[[.,[.,[[[[.,[.,.]],.],.],.]]],.] => [1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1] => 100001 => 0
[[.,[.,[[[[[.,.],.],.],.],.]]],.] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1] => 000001 => 0
[[.,[[.,.],[.,[[[.,.],.],.]]]],.] => [1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1,1] => 000111 => 0
[[.,[[.,.],[[[.,.],.],[.,.]]]],.] => [1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,1,1] => 011111 => 0
[[.,[[.,.],[[.,[.,[.,.]]],.]]],.] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1,1] => 101111 => 0
[[.,[[.,.],[[.,[[.,.],.]],.]]],.] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => 001111 => 0
[[.,[[.,.],[[[.,.],[.,.]],.]]],.] => [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1] => 111111 => 0
[[.,[[.,.],[[[.,[.,.]],.],.]]],.] => [1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1] => 011111 => 0
[[.,[[.,.],[[[[.,.],.],.],.]]],.] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1] => 111111 => 0
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1,1] => 100011 => 0
[[.,[[.,[.,.]],[[[.,.],.],.]]],.] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1] => 000011 => 0
[[.,[[[.,.],.],[.,[[.,.],.]]]],.] => [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1,1] => 110111 => 0
[[.,[[[.,.],.],[[.,.],[.,.]]]],.] => [1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1,1,1] => 000111 => 0
[[.,[[[.,.],.],[[.,[.,.]],.]]],.] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1] => 100111 => 0
[[.,[[[.,.],.],[[[.,.],.],.]]],.] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1] => 000111 => 0
[[.,[[.,[.,[.,.]]],[[.,.],.]]],.] => [1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,1,1] => 111011 => 0
[[.,[[.,[[.,.],.]],[.,[.,.]]]],.] => [1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,1,1] => 010011 => 0
[[.,[[.,[[.,.],.]],[[.,.],.]]],.] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1] => 110011 => 0
[[.,[[[.,.],[.,.]],[.,[.,.]]]],.] => [1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,1,1] => 011111 => 0
[[.,[[[.,.],[.,.]],[[.,.],.]]],.] => [1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1] => 111111 => 0
[[.,[[[.,[.,.]],.],[.,[.,.]]]],.] => [1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,1,1] => 010111 => 0
[[.,[[[.,[.,.]],.],[[.,.],.]]],.] => [1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1,1] => 110111 => 0
[[.,[[[[.,.],.],.],[.,[.,.]]]],.] => [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1,1,1] => 011111 => 0
[[.,[[[[.,.],.],.],[[.,.],.]]],.] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1] => 111111 => 0
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.] => [1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,1] => 001011 => 0
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.] => [1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1,1] => 011011 => 0
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.] => [1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,1,1] => 000011 => 0
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.] => [1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1,1] => 010011 => 0
[[.,[[.,[[[.,.],.],.]],[.,.]]],.] => [1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1,1] => 000011 => 0
[[.,[[[.,.],[.,[.,.]]],[.,.]]],.] => [1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,1,1] => 001111 => 0
[[.,[[[.,.],[[.,.],.]],[.,.]]],.] => [1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1] => 011111 => 0
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => [1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,1,1] => 000111 => 0
[[.,[[[[.,.],.],[.,.]],[.,.]]],.] => [1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1,1,1] => 001111 => 0
[[.,[[[.,[.,[.,.]]],.],[.,.]]],.] => [1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,1,1] => 010111 => 0
[[.,[[[.,[[.,.],.]],.],[.,.]]],.] => [1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1,1] => 000111 => 0
[[.,[[[[.,.],[.,.]],.],[.,.]]],.] => [1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1,1] => 011111 => 0
[[.,[[[[.,[.,.]],.],.],[.,.]]],.] => [1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1,1] => 001111 => 0
[[.,[[[[[.,.],.],.],.],[.,.]]],.] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1] => 011111 => 0
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,1] => 101011 => 0
[[.,[[.,[.,[.,[[.,.],.]]]],.]],.] => [1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1,1] => 001011 => 0
[[.,[[.,[.,[[.,.],[.,.]]]],.]],.] => [1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1,1] => 111011 => 0
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.] => [1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1] => 011011 => 0
[[.,[[.,[.,[[[.,.],.],.]]],.]],.] => [1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1] => 111011 => 0
[[.,[[.,[[.,.],[.,[.,.]]]],.]],.] => [1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1,1] => 100011 => 0
[[.,[[.,[[.,.],[[.,.],.]]],.]],.] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1] => 000011 => 0
[[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => [1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1] => 110011 => 0
[[.,[[.,[[[.,.],.],[.,.]]],.]],.] => [1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1,1] => 100011 => 0
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.] => [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1,1] => 010011 => 0
[[.,[[.,[[.,[[.,.],.]],.]],.]],.] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => 110011 => 0
[[.,[[.,[[[.,.],[.,.]],.]],.]],.] => [1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1] => 000011 => 0
[[.,[[.,[[[.,[.,.]],.],.]],.]],.] => [1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1] => 100011 => 0
[[.,[[.,[[[[.,.],.],.],.]],.]],.] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1] => 000011 => 0
[[.,[[[.,.],[.,[.,[.,.]]]],.]],.] => [1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1,1] => 101111 => 0
[[.,[[[.,.],[.,[[.,.],.]]],.]],.] => [1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1,1] => 001111 => 0
[[.,[[[.,.],[[.,.],[.,.]]],.]],.] => [1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1,1] => 111111 => 0
[[.,[[[.,.],[[.,[.,.]],.]],.]],.] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1] => 011111 => 0
[[.,[[[.,.],[[[.,.],.],.]],.]],.] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1] => 111111 => 0
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.] => [1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1,1] => 100111 => 0
[[.,[[[.,[.,.]],[[.,.],.]],.]],.] => [1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1,1] => 000111 => 0
[[.,[[[[.,.],.],[.,[.,.]]],.]],.] => [1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1,1] => 101111 => 0
[[.,[[[[.,.],.],[[.,.],.]],.]],.] => [1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1] => 001111 => 0
[[.,[[[.,[.,[.,.]]],[.,.]],.]],.] => [1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1,1] => 110111 => 0
[[.,[[[.,[[.,.],.]],[.,.]],.]],.] => [1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1] => 100111 => 0
[[.,[[[[.,.],[.,.]],[.,.]],.]],.] => [1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1,1] => 111111 => 0
[[.,[[[[.,[.,.]],.],[.,.]],.]],.] => [1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1,1] => 101111 => 0
[[.,[[[[[.,.],.],.],[.,.]],.]],.] => [1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1] => 111111 => 0
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.] => [1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1,1] => 010111 => 0
[[.,[[[.,[.,[[.,.],.]]],.],.]],.] => [1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1] => 110111 => 0
[[.,[[[.,[[.,.],[.,.]]],.],.]],.] => [1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1,1] => 000111 => 0
[[.,[[[.,[[.,[.,.]],.]],.],.]],.] => [1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1] => 100111 => 0
[[.,[[[.,[[[.,.],.],.]],.],.]],.] => [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1] => 000111 => 0
[[.,[[[[.,.],[.,[.,.]]],.],.]],.] => [1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1,1] => 011111 => 0
[[.,[[[[.,.],[[.,.],.]],.],.]],.] => [1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1] => 111111 => 0
[[.,[[[[.,[.,.]],[.,.]],.],.]],.] => [1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1] => 001111 => 0
[[.,[[[[[.,.],.],[.,.]],.],.]],.] => [1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1] => 011111 => 0
[[.,[[[[.,[.,[.,.]]],.],.],.]],.] => [1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1] => 101111 => 0
[[.,[[[[.,[[.,.],.]],.],.],.]],.] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1] => 001111 => 0
[[.,[[[[[.,.],[.,.]],.],.],.]],.] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1] => 111111 => 0
[[.,[[[[[.,[.,.]],.],.],.],.]],.] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1] => 011111 => 0
[[.,[[[[[[.,.],.],.],.],.],.]],.] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 111111 => 0
[[[.,.],[.,[.,[[[.,.],.],.]]]],.] => [1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,2] => 00010 => 0
[[[.,.],[.,[[[.,.],.],[.,.]]]],.] => [1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,2] => 01110 => 0
[[[.,.],[.,[[.,[.,[.,.]]],.]]],.] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2] => 10110 => 0
[[[.,.],[.,[[.,[[.,.],.]],.]]],.] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2] => 00110 => 0
[[[.,.],[.,[[[.,.],[.,.]],.]]],.] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2] => 11110 => 0
[[[.,.],[.,[[[.,[.,.]],.],.]]],.] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2] => 01110 => 0
[[[.,.],[.,[[[[.,.],.],.],.]]],.] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2] => 11110 => 0
[[[.,.],[[.,.],[[.,[.,.]],.]]],.] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2] => 10000 => 0
[[[.,.],[[.,.],[[[.,.],.],.]]],.] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2] => 00000 => 0
[[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,2] => 11100 => 0
[[[.,.],[[[.,.],.],[.,[.,.]]]],.] => [1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2] => 01000 => 0
[[[.,.],[[[.,.],.],[[.,.],.]]],.] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2] => 11000 => 0
[[[.,.],[[.,[.,[.,.]]],[.,.]]],.] => [1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,2] => 00100 => 0
[[[.,.],[[.,[[.,.],.]],[.,.]]],.] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2] => 01100 => 0
[[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,2] => 00000 => 0
[[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2] => 01000 => 0
[[[.,.],[[[[.,.],.],.],[.,.]]],.] => [1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2] => 00000 => 0
[[[.,.],[[.,[.,[.,[.,.]]]],.]],.] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2] => 10100 => 0
[[[.,.],[[.,[.,[[.,.],.]]],.]],.] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2] => 00100 => 0
[[[.,.],[[.,[[.,.],[.,.]]],.]],.] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2] => 11100 => 0
[[[.,.],[[.,[[.,[.,.]],.]],.]],.] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2] => 01100 => 0
[[[.,.],[[.,[[[.,.],.],.]],.]],.] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2] => 11100 => 0
[[[.,.],[[[.,.],[.,[.,.]]],.]],.] => [1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2] => 10000 => 0
[[[.,.],[[[.,.],[[.,.],.]],.]],.] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => 00000 => 0
[[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2] => 11000 => 0
[[[.,.],[[[[.,.],.],[.,.]],.]],.] => [1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2] => 10000 => 0
[[[.,.],[[[.,[.,[.,.]]],.],.]],.] => [1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2] => 01000 => 0
[[[.,.],[[[.,[[.,.],.]],.],.]],.] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2] => 11000 => 0
[[[.,.],[[[[.,.],[.,.]],.],.]],.] => [1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2] => 00000 => 0
[[[.,.],[[[[.,[.,.]],.],.],.]],.] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2] => 10000 => 0
[[[.,.],[[[[[.,.],.],.],.],.]],.] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2] => 00000 => 0
[[[.,[.,.]],[.,[[.,[.,.]],.]]],.] => [1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,1] => 10011 => 0
[[[.,[.,.]],[.,[[[.,.],.],.]]],.] => [1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1] => 00011 => 0
[[[.,[.,.]],[[.,.],[[.,.],.]]],.] => [1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1] => 11111 => 0
[[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3,1] => 00111 => 0
[[[.,[.,.]],[[[.,.],.],[.,.]]],.] => [1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,1] => 01111 => 0
[[[.,[.,.]],[[.,[.,[.,.]]],.]],.] => [1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1] => 10111 => 0
[[[.,[.,.]],[[.,[[.,.],.]],.]],.] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1] => 00111 => 0
[[[.,[.,.]],[[[.,.],[.,.]],.]],.] => [1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1] => 11111 => 0
[[[.,[.,.]],[[[.,[.,.]],.],.]],.] => [1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1] => 01111 => 0
[[[.,[.,.]],[[[[.,.],.],.],.]],.] => [1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1] => 11111 => 0
[[[[.,.],.],[.,[.,[[.,.],.]]]],.] => [1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3] => 1101 => 0
[[[[.,.],.],[.,[[.,.],[.,.]]]],.] => [1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3] => 0001 => 0
[[[[.,.],.],[.,[[.,[.,.]],.]]],.] => [1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3] => 1001 => 0
[[[[.,.],.],[.,[[[.,.],.],.]]],.] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3] => 0001 => 0
[[[[.,.],.],[[.,.],[.,[.,.]]]],.] => [1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3] => 0111 => 0
[[[[.,.],.],[[.,.],[[.,.],.]]],.] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3] => 1111 => 0
[[[[.,.],.],[[.,[.,.]],[.,.]]],.] => [1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3] => 0011 => 0
[[[[.,.],.],[[[.,.],.],[.,.]]],.] => [1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3] => 0111 => 0
[[[[.,.],.],[[.,[.,[.,.]]],.]],.] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3] => 1011 => 0
[[[[.,.],.],[[.,[[.,.],.]],.]],.] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3] => 0011 => 0
[[[[.,.],.],[[[.,.],[.,.]],.]],.] => [1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3] => 1111 => 0
[[[[.,.],.],[[[.,[.,.]],.],.]],.] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3] => 0111 => 0
[[[[.,.],.],[[[[.,.],.],.],.]],.] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3] => 1111 => 0
[[[.,[.,[.,.]]],[.,[[.,.],.]]],.] => [1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,1] => 11001 => 0
[[[.,[.,[.,.]]],[[.,.],[.,.]]],.] => [1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,1] => 00001 => 0
[[[.,[.,[.,.]]],[[.,[.,.]],.]],.] => [1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1] => 10001 => 0
[[[.,[.,[.,.]]],[[[.,.],.],.]],.] => [1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1] => 00001 => 0
[[[.,[[.,.],.]],[.,[.,[.,.]]]],.] => [1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,1] => 01011 => 0
[[[.,[[.,.],.]],[.,[[.,.],.]]],.] => [1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1] => 11011 => 0
[[[.,[[.,.],.]],[[.,.],[.,.]]],.] => [1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1,1] => 00011 => 0
[[[.,[[.,.],.]],[[.,[.,.]],.]],.] => [1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1] => 10011 => 0
[[[.,[[.,.],.]],[[[.,.],.],.]],.] => [1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1] => 00011 => 0
[[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2] => 0100 => 0
[[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2] => 1100 => 0
[[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2] => 0000 => 0
[[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2] => 1000 => 0
[[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2] => 0000 => 0
[[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1] => 0101 => 0
[[[[.,[.,.]],.],[.,[[.,.],.]]],.] => [1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1] => 1101 => 0
[[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1] => 0001 => 0
[[[[.,[.,.]],.],[[.,[.,.]],.]],.] => [1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1] => 1001 => 0
[[[[.,[.,.]],.],[[[.,.],.],.]],.] => [1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1] => 0001 => 0
[[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [6,5,4] => 010 => 0
[[[[[.,.],.],.],[.,[[.,.],.]]],.] => [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,5,4] => 110 => 0
[[[[[.,.],.],.],[[.,.],[.,.]]],.] => [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [6,4,4] => 000 => 0
[[[[[.,.],.],.],[[.,[.,.]],.]],.] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,4] => 100 => 0
[[[[[.,.],.],.],[[[.,.],.],.]],.] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [4,4,4] => 000 => 0
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1] => 01101 => 0
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.] => [1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,1] => 11101 => 0
[[[.,[.,[[.,.],.]]],[.,[.,.]]],.] => [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,1] => 01001 => 0
[[[.,[.,[[.,.],.]]],[[.,.],.]],.] => [1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1] => 11001 => 0
[[[.,[[.,.],[.,.]]],[.,[.,.]]],.] => [1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,1] => 01111 => 0
[[[.,[[.,.],[.,.]]],[[.,.],.]],.] => [1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1] => 11111 => 0
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.] => [1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,1] => 01011 => 0
[[[.,[[.,[.,.]],.]],[[.,.],.]],.] => [1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1] => 11011 => 0
[[[.,[[[.,.],.],.]],[.,[.,.]]],.] => [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1,1] => 01111 => 0
[[[.,[[[.,.],.],.]],[[.,.],.]],.] => [1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1] => 11111 => 0
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2] => 0110 => 0
[[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2] => 1110 => 0
[[[[.,.],[[.,.],.]],[.,[.,.]]],.] => [1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2] => 0100 => 0
[[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2] => 1100 => 0
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1] => 0111 => 0
[[[[.,[.,.]],[.,.]],[[.,.],.]],.] => [1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1] => 1111 => 0
[[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [6,5,3] => 011 => 0
[[[[[.,.],.],[.,.]],[[.,.],.]],.] => [1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,5,3] => 111 => 0
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1] => 0101 => 0
[[[[.,[.,[.,.]]],.],[[.,.],.]],.] => [1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1] => 1101 => 0
[[[[.,[[.,.],.]],.],[.,[.,.]]],.] => [1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1] => 0111 => 0
[[[[.,[[.,.],.]],.],[[.,.],.]],.] => [1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1] => 1111 => 0
[[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [6,5,2] => 010 => 0
[[[[[.,.],[.,.]],.],[[.,.],.]],.] => [1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,5,2] => 110 => 0
[[[[[.,[.,.]],.],.],[.,[.,.]]],.] => [1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [6,5,1] => 011 => 0
[[[[[.,[.,.]],.],.],[[.,.],.]],.] => [1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [5,5,1] => 111 => 0
[[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5] => 01 => 0
[[[[[[.,.],.],.],.],[[.,.],.]],.] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [5,5] => 11 => 0
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1] => 00101 => 0
[[[.,[.,[.,[[.,.],.]]]],[.,.]],.] => [1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1] => 01101 => 0
[[[.,[.,[[.,.],[.,.]]]],[.,.]],.] => [1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,1] => 00001 => 0
[[[.,[.,[[.,[.,.]],.]]],[.,.]],.] => [1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1] => 01001 => 0
[[[.,[.,[[[.,.],.],.]]],[.,.]],.] => [1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1] => 00001 => 0
[[[.,[[.,.],[.,[.,.]]]],[.,.]],.] => [1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,1] => 00111 => 0
[[[.,[[.,.],[[.,.],.]]],[.,.]],.] => [1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1] => 01111 => 0
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.] => [1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,1] => 00011 => 0
[[[.,[[[.,.],.],[.,.]]],[.,.]],.] => [1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1,1] => 00111 => 0
[[[.,[[.,[.,[.,.]]],.]],[.,.]],.] => [1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,1] => 01011 => 0
[[[.,[[.,[[.,.],.]],.]],[.,.]],.] => [1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1] => 00011 => 0
[[[.,[[[.,.],[.,.]],.]],[.,.]],.] => [1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1] => 01111 => 0
[[[.,[[[.,[.,.]],.],.]],[.,.]],.] => [1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1] => 00111 => 0
[[[.,[[[[.,.],.],.],.]],[.,.]],.] => [1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1] => 01111 => 0
[[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2] => 0010 => 0
[[[[.,.],[.,[[.,.],.]]],[.,.]],.] => [1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2] => 0110 => 0
[[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2] => 0000 => 0
[[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2] => 0100 => 0
[[[[.,.],[[[.,.],.],.]],[.,.]],.] => [1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2] => 0000 => 0
[[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1] => 0011 => 0
[[[[.,[.,.]],[[.,.],.]],[.,.]],.] => [1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1] => 0111 => 0
[[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [6,4,3] => 001 => 0
[[[[[.,.],.],[[.,.],.]],[.,.]],.] => [1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [6,3,3] => 011 => 0
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1] => 0001 => 0
[[[[.,[[.,.],.]],[.,.]],[.,.]],.] => [1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1] => 0011 => 0
[[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [6,4,2] => 000 => 0
[[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [6,4,1] => 001 => 0
[[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,4] => 00 => 0
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1] => 0101 => 0
[[[[.,[.,[[.,.],.]]],.],[.,.]],.] => [1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1] => 0001 => 0
[[[[.,[[.,.],[.,.]]],.],[.,.]],.] => [1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1] => 0111 => 0
[[[[.,[[.,[.,.]],.]],.],[.,.]],.] => [1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1] => 0011 => 0
[[[[.,[[[.,.],.],.]],.],[.,.]],.] => [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1] => 0111 => 0
[[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [6,3,2] => 010 => 0
[[[[[.,.],[[.,.],.]],.],[.,.]],.] => [1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [6,2,2] => 000 => 0
[[[[[.,[.,.]],[.,.]],.],[.,.]],.] => [1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [6,3,1] => 011 => 0
[[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,3] => 01 => 0
[[[[[.,[.,[.,.]]],.],.],[.,.]],.] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [6,2,1] => 001 => 0
[[[[[.,[[.,.],.]],.],.],[.,.]],.] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [6,1,1] => 011 => 0
[[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,2] => 00 => 0
[[[[[[.,[.,.]],.],.],.],[.,.]],.] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1] => 01 => 0
[[[[[[[.,.],.],.],.],.],[.,.]],.] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 0 => 0
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1] => 10101 => 0
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1] => 00101 => 0
[[[.,[.,[.,[[.,.],[.,.]]]]],.],.] => [1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1] => 11101 => 0
[[[.,[.,[.,[[.,[.,.]],.]]]],.],.] => [1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1] => 01101 => 0
[[[.,[.,[.,[[[.,.],.],.]]]],.],.] => [1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1] => 11101 => 0
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.] => [1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1] => 10001 => 0
[[[.,[.,[[.,.],[[.,.],.]]]],.],.] => [1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1] => 00001 => 0
[[[.,[.,[[.,[.,.]],[.,.]]]],.],.] => [1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1] => 11001 => 0
[[[.,[.,[[[.,.],.],[.,.]]]],.],.] => [1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1] => 10001 => 0
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.] => [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1] => 01001 => 0
[[[.,[.,[[.,[[.,.],.]],.]]],.],.] => [1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1] => 11001 => 0
[[[.,[.,[[[.,.],[.,.]],.]]],.],.] => [1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1] => 00001 => 0
[[[.,[.,[[[.,[.,.]],.],.]]],.],.] => [1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1] => 10001 => 0
[[[.,[.,[[[[.,.],.],.],.]]],.],.] => [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1] => 00001 => 0
[[[.,[[.,.],[.,[.,[.,.]]]]],.],.] => [1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1] => 10111 => 0
[[[.,[[.,.],[.,[[.,.],.]]]],.],.] => [1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1] => 00111 => 0
[[[.,[[.,.],[[.,.],[.,.]]]],.],.] => [1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1] => 11111 => 0
[[[.,[[.,.],[[.,[.,.]],.]]],.],.] => [1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1] => 01111 => 0
[[[.,[[.,.],[[[.,.],.],.]]],.],.] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1] => 11111 => 0
[[[.,[[.,[.,.]],[.,[.,.]]]],.],.] => [1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1] => 10011 => 0
[[[.,[[.,[.,.]],[[.,.],.]]],.],.] => [1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1] => 00011 => 0
[[[.,[[[.,.],.],[.,[.,.]]]],.],.] => [1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1] => 10111 => 0
[[[.,[[[.,.],.],[[.,.],.]]],.],.] => [1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1] => 00111 => 0
[[[.,[[.,[.,[.,.]]],[.,.]]],.],.] => [1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1] => 11011 => 0
[[[.,[[.,[[.,.],.]],[.,.]]],.],.] => [1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1] => 10011 => 0
[[[.,[[[.,.],[.,.]],[.,.]]],.],.] => [1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1] => 11111 => 0
[[[.,[[[.,[.,.]],.],[.,.]]],.],.] => [1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1] => 10111 => 0
[[[.,[[[[.,.],.],.],[.,.]]],.],.] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1] => 11111 => 0
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.] => [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1] => 01011 => 0
[[[.,[[.,[.,[[.,.],.]]],.]],.],.] => [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1] => 11011 => 0
[[[.,[[.,[[.,.],[.,.]]],.]],.],.] => [1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1] => 00011 => 0
[[[.,[[.,[[.,[.,.]],.]],.]],.],.] => [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => 10011 => 0
[[[.,[[.,[[[.,.],.],.]],.]],.],.] => [1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1] => 00011 => 0
[[[.,[[[.,.],[.,[.,.]]],.]],.],.] => [1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1] => 01111 => 0
[[[.,[[[.,.],[[.,.],.]],.]],.],.] => [1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1] => 11111 => 0
[[[.,[[[.,[.,.]],[.,.]],.]],.],.] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1] => 00111 => 0
[[[.,[[[[.,.],.],[.,.]],.]],.],.] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1] => 01111 => 0
[[[.,[[[.,[.,[.,.]]],.],.]],.],.] => [1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1] => 10111 => 0
[[[.,[[[.,[[.,.],.]],.],.]],.],.] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => 00111 => 0
[[[.,[[[[.,.],[.,.]],.],.]],.],.] => [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1] => 11111 => 0
[[[.,[[[[.,[.,.]],.],.],.]],.],.] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1] => 01111 => 0
[[[.,[[[[[.,.],.],.],.],.]],.],.] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1] => 11111 => 0
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2] => 1010 => 0
[[[[.,.],[.,[.,[[.,.],.]]]],.],.] => [1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2] => 0010 => 0
[[[[.,.],[.,[[.,.],[.,.]]]],.],.] => [1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2] => 1110 => 0
[[[[.,.],[.,[[.,[.,.]],.]]],.],.] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2] => 0110 => 0
[[[[.,.],[.,[[[.,.],.],.]]],.],.] => [1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2] => 1110 => 0
[[[[.,.],[[.,.],[.,[.,.]]]],.],.] => [1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2] => 1000 => 0
[[[[.,.],[[.,.],[[.,.],.]]],.],.] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2] => 0000 => 0
[[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2] => 1100 => 0
[[[[.,.],[[[.,.],.],[.,.]]],.],.] => [1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2] => 1000 => 0
[[[[.,.],[[.,[.,[.,.]]],.]],.],.] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2] => 0100 => 0
[[[[.,.],[[.,[[.,.],.]],.]],.],.] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => 1100 => 0
[[[[.,.],[[[.,.],[.,.]],.]],.],.] => [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2] => 0000 => 0
[[[[.,.],[[[.,[.,.]],.],.]],.],.] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2] => 1000 => 0
[[[[.,.],[[[[.,.],.],.],.]],.],.] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2] => 0000 => 0
[[[[.,[.,.]],[.,[.,[.,.]]]],.],.] => [1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1] => 1011 => 0
[[[[.,[.,.]],[.,[[.,.],.]]],.],.] => [1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1] => 0011 => 0
[[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1] => 1111 => 0
[[[[.,[.,.]],[[.,[.,.]],.]],.],.] => [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1] => 0111 => 0
[[[[.,[.,.]],[[[.,.],.],.]],.],.] => [1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1] => 1111 => 0
[[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3] => 101 => 0
[[[[[.,.],.],[.,[[.,.],.]]],.],.] => [1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [4,4,3] => 001 => 0
[[[[[.,.],.],[[.,.],[.,.]]],.],.] => [1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,3,3] => 111 => 0
[[[[[.,.],.],[[.,[.,.]],.]],.],.] => [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [4,3,3] => 011 => 0
[[[[[.,.],.],[[[.,.],.],.]],.],.] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => 111 => 0
[[[[.,[.,[.,.]]],[.,[.,.]]],.],.] => [1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1] => 1001 => 0
[[[[.,[.,[.,.]]],[[.,.],.]],.],.] => [1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1] => 0001 => 0
[[[[.,[[.,.],.]],[.,[.,.]]],.],.] => [1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1] => 1011 => 0
[[[[.,[[.,.],.]],[[.,.],.]],.],.] => [1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1] => 0011 => 0
[[[[[.,.],[.,.]],[.,[.,.]]],.],.] => [1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [5,4,2] => 100 => 0
[[[[[.,.],[.,.]],[[.,.],.]],.],.] => [1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [4,4,2] => 000 => 0
[[[[[.,[.,.]],.],[.,[.,.]]],.],.] => [1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,4,1] => 101 => 0
[[[[[.,[.,.]],.],[[.,.],.]],.],.] => [1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [4,4,1] => 001 => 0
[[[[[[.,.],.],.],[.,[.,.]]],.],.] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [5,4] => 10 => 0
[[[[[[.,.],.],.],[[.,.],.]],.],.] => [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [4,4] => 00 => 0
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.] => [1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1] => 1101 => 0
[[[[.,[.,[[.,.],.]]],[.,.]],.],.] => [1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1] => 1001 => 0
[[[[.,[[.,.],[.,.]]],[.,.]],.],.] => [1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1] => 1111 => 0
[[[[.,[[.,[.,.]],.]],[.,.]],.],.] => [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1] => 1011 => 0
[[[[.,[[[.,.],.],.]],[.,.]],.],.] => [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1] => 1111 => 0
[[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,3,2] => 110 => 0
[[[[[.,.],[[.,.],.]],[.,.]],.],.] => [1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,2,2] => 100 => 0
[[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,3,1] => 111 => 0
[[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [5,3] => 11 => 0
[[[[[.,[.,[.,.]]],.],[.,.]],.],.] => [1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,2,1] => 101 => 0
[[[[[.,[[.,.],.]],.],[.,.]],.],.] => [1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,1,1] => 111 => 0
[[[[[[.,.],[.,.]],.],[.,.]],.],.] => [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [5,2] => 10 => 0
[[[[[[.,[.,.]],.],.],[.,.]],.],.] => [1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [5,1] => 11 => 0
[[[[[[[.,.],.],.],.],[.,.]],.],.] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => 1 => 0
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1] => 0101 => 0
[[[[.,[.,[.,[[.,.],.]]]],.],.],.] => [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1] => 1101 => 0
[[[[.,[.,[[.,.],[.,.]]]],.],.],.] => [1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1] => 0001 => 0
[[[[.,[.,[[.,[.,.]],.]]],.],.],.] => [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => 1001 => 0
[[[[.,[.,[[[.,.],.],.]]],.],.],.] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1] => 0001 => 0
[[[[.,[[.,.],[.,[.,.]]]],.],.],.] => [1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1] => 0111 => 0
[[[[.,[[.,.],[[.,.],.]]],.],.],.] => [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1] => 1111 => 0
[[[[.,[[.,[.,.]],[.,.]]],.],.],.] => [1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1] => 0011 => 0
[[[[.,[[[.,.],.],[.,.]]],.],.],.] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1] => 0111 => 0
[[[[.,[[.,[.,[.,.]]],.]],.],.],.] => [1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1] => 1011 => 0
[[[[.,[[.,[[.,.],.]],.]],.],.],.] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1] => 0011 => 0
[[[[.,[[[.,.],[.,.]],.]],.],.],.] => [1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1] => 1111 => 0
[[[[.,[[[.,[.,.]],.],.]],.],.],.] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1] => 0111 => 0
[[[[.,[[[[.,.],.],.],.]],.],.],.] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1] => 1111 => 0
[[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [4,3,2] => 010 => 0
[[[[[.,.],[.,[[.,.],.]]],.],.],.] => [1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [3,3,2] => 110 => 0
[[[[[.,.],[[.,.],[.,.]]],.],.],.] => [1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [4,2,2] => 000 => 0
[[[[[.,.],[[.,[.,.]],.]],.],.],.] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [3,2,2] => 100 => 0
[[[[[.,.],[[[.,.],.],.]],.],.],.] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [2,2,2] => 000 => 0
[[[[[.,[.,.]],[.,[.,.]]],.],.],.] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [4,3,1] => 011 => 0
[[[[[.,[.,.]],[[.,.],.]],.],.],.] => [1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [3,3,1] => 111 => 0
[[[[[[.,.],.],[.,[.,.]]],.],.],.] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [4,3] => 01 => 0
[[[[[[.,.],.],[[.,.],.]],.],.],.] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [3,3] => 11 => 0
[[[[[.,[.,[.,.]]],[.,.]],.],.],.] => [1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [4,2,1] => 001 => 0
[[[[[.,[[.,.],.]],[.,.]],.],.],.] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [4,1,1] => 011 => 0
[[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [4,2] => 00 => 0
[[[[[[.,[.,.]],.],[.,.]],.],.],.] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,1] => 01 => 0
[[[[[[[.,.],.],.],[.,.]],.],.],.] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => 0 => 0
[[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => 101 => 0
[[[[[.,[.,[[.,.],.]]],.],.],.],.] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [2,2,1] => 001 => 0
[[[[[.,[[.,.],[.,.]]],.],.],.],.] => [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [3,1,1] => 111 => 0
[[[[[.,[[.,[.,.]],.]],.],.],.],.] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,1,1] => 011 => 0
[[[[[.,[[[.,.],.],.]],.],.],.],.] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1] => 111 => 0
[[[[[[.,.],[.,[.,.]]],.],.],.],.] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => 10 => 0
[[[[[[.,.],[[.,.],.]],.],.],.],.] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,2] => 00 => 0
[[[[[[.,[.,.]],[.,.]],.],.],.],.] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => 11 => 0
[[[[[[[.,.],.],[.,.]],.],.],.],.] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => 1 => 0
[[[[[[.,[.,[.,.]]],.],.],.],.],.] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 01 => 0
[[[[[[.,[[.,.],.]],.],.],.],.],.] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1] => 11 => 0
[[[[[[[.,.],[.,.]],.],.],.],.],.] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 0 => 0
[[[[[[[.,[.,.]],.],.],.],.],.],.] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1] => 1 => 0
[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]] => [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] => 00000001 => 0
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => [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] => 11111111 => 0
[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]] => [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] => 000000001 => 0
[[.,.],[[[[[[[.,.],.],.],.],.],.],.]] => [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] => 0000000 => 0
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => [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] => 111111111 => 0
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 0 => 0
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => 1 => 0
[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [8,2] => 00 => 0
[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1] => 011 => 0
[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1,1,1,1,1] => 11111111 => 0
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [8,7] => 01 => 0
[[.,.],[[[[[[.,[.,.]],.],.],.],.],.]] => [1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,2,2,2] => 1000000 => 0
[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2,2] => 00000000 => 0
[[[[.,[[.,[.,[.,.]]],.]],[.,.]],.],.] => [1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0] => [6,3,2,1,1] => 01011 => 0
[.,[[[[.,[[.,[.,.]],.]],[.,.]],.],.]] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [6,3,2,2,1,1,1,1] => 01001111 => 0
[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1] => 10101 => 0
[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.] => [1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1] => 0101 => 0
[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.] => [1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1] => 101 => 0
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => 01 => 0
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1] => 1 => 0
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.] => [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] => 10101 => 0
[[[[[.,.],[.,[.,[.,[.,.]]]]],.],.],.] => [1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2] => 1010 => 0
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.] => [1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1] => 0101 => 0
[[[[[[.,.],[.,[.,[.,.]]]],.],.],.],.] => [1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2] => 010 => 0
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.] => [1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1] => 101 => 0
[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.] => [1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [3,2] => 10 => 0
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.] => [1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [2,1] => 01 => 0
[[[[[[[[.,.],[.,.]],.],.],.],.],.],.] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2] => 0 => 0
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1] => 1 => 0
[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]] => [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] => 01111111 => 0
[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,1,1,1,1,1,1,1] => 111111111 => 0
[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.] => [1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [3,1] => 11 => 0
[[[[[[.,[.,[.,.]]],[.,.]],.],.],.],.] => [1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1] => 001 => 0
[[[[[.,[.,[.,[.,.]]]],[.,.]],.],.],.] => [1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1] => 1101 => 0
[[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.],.] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,1] => 00101 => 0
[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]] => [1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,1,1] => 00000011 => 0
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.] => [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] => 1111111 => 0
[[[[[[[.,[[.,.],.]],.],.],.],.],.],.] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1] => 11 => 0
[[[[[[.,[[.,.],[.,.]]],.],.],.],.],.] => [1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1] => 111 => 0
[[[[[.,[[[.,.],.],[.,.]]],.],.],.],.] => [1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1] => 0111 => 0
[[[[.,[[[[.,.],.],.],[.,.]]],.],.],.] => [1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1] => 11111 => 0
[[[.,[[[[[.,.],.],.],.],[.,.]]],.],.] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1,1,1] => 011111 => 0
[[.,[[[[[[.,.],.],.],.],.],[.,.]]],.] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1,1,1,1] => 1111111 => 0
[[[[[[[[.,.],.],[.,.]],.],.],.],.],.] => [1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [3] => 1 => 0
[[[[[[[[.,.],.],.],[.,.]],.],.],.],.] => [1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [4] => 0 => 0
[[[[[[[[.,.],.],.],.],[.,.]],.],.],.] => [1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [5] => 1 => 0
[[[[[[[[.,.],.],.],.],.],[.,.]],.],.] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [6] => 0 => 0
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => 1 => 0
[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.] => [1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [2] => 0 => 0
[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.] => [1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [3] => 1 => 0
[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.] => [1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [4] => 0 => 0
[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [5] => 1 => 0
[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [6] => 0 => 0
[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [7] => 1 => 0
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [8] => 0 => 0
[[[[[[.,.],[[[.,.],.],.]],.],.],.],.] => [1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2] => 000 => 0
[[[[[[[.,.],.],[[.,.],.]],.],.],.],.] => [1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [3,3] => 11 => 0
[[[[[[.,[.,.]],[[.,.],.]],.],.],.],.] => [1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1] => 111 => 0
[[[.,.],[[[[[[.,.],.],.],.],.],.]],.] => [1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2] => 000000 => 0
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [9,8] => 10 => 0
[[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]],.] => [1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1,1,1] => 1010111 => 0
[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [8,6] => 00 => 0
[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => [9,7] => 11 => 0
[[[[[[.,[[.,.],.]],[.,.]],.],.],.],.] => [1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1] => 011 => 0
[[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.] => [1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2,1] => 1101 => 0
[[[[[.,[.,[.,[.,.]]]],.],.],.],[.,.]] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2,1] => 0101 => 0
[[[[[[[.,.],.],.],.],.],[.,[.,.]]],.] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [7,6] => 10 => 0
[[[[[[[.,.],[[.,.],.]],.],.],.],.],.] => [1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [2,2] => 00 => 0
[[[[[[[[.,.],[.,.]],.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0] => [9,2] => 10 => 0
[[[[[[.,[.,.]],.],.],.],[.,.]],[.,.]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0] => [8,6,1] => 001 => 0
[[[.,[[[[[.,.],.],.],.],.]],.],[.,.]] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1,1,1,1] => 011111 => 0
search for individual values
searching the database for the individual values of this statistic
Description
The defect of a binary word.
The defect of a finite word $w$ is given by the difference between the maximum possible number and the actual number of palindromic factors contained in $w$. The maximum possible number of palindromic factors in a word $w$ is $|w|+1$.
The defect of a finite word $w$ is given by the difference between the maximum possible number and the actual number of palindromic factors contained in $w$. The maximum possible number of palindromic factors in a word $w$ is $|w|+1$.
Map
odd parts
Description
Return the binary word indicating which parts of the partition are odd.
Map
to Dyck path: up step, left tree, down step, right tree
Description
Return the associated Dyck path, using the bijection 1L0R.
This is given recursively as follows:
This is given recursively as follows:
- a leaf is associated to the empty Dyck Word
- a tree with children $l,r$ is associated with the Dyck path described by 1L0R where $L$ and $R$ are respectively the Dyck words associated with the trees $l$ and $r$.
Map
to 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 $(n-1,\ldots,2,1)$.
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