Identifier
Values
[.,[.,.]] => [1,0,1,0] => [1] => 10 => 0
[.,[.,[.,.]]] => [1,0,1,0,1,0] => [2,1] => 1010 => 0
[.,[[.,.],.]] => [1,0,1,1,0,0] => [1,1] => 110 => 0
[[.,.],[.,.]] => [1,1,0,0,1,0] => [2] => 100 => 0
[[.,[.,.]],.] => [1,1,0,1,0,0] => [1] => 10 => 0
[.,[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0] => [3,2,1] => 101010 => 0
[.,[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0] => [2,2,1] => 11010 => 0
[.,[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0] => [3,1,1] => 100110 => 0
[.,[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0] => [2,1,1] => 10110 => 0
[.,[[[.,.],.],.]] => [1,0,1,1,1,0,0,0] => [1,1,1] => 1110 => 0
[[.,.],[.,[.,.]]] => [1,1,0,0,1,0,1,0] => [3,2] => 10100 => 0
[[.,.],[[.,.],.]] => [1,1,0,0,1,1,0,0] => [2,2] => 1100 => 0
[[.,[.,.]],[.,.]] => [1,1,0,1,0,0,1,0] => [3,1] => 10010 => 0
[[[.,.],.],[.,.]] => [1,1,1,0,0,0,1,0] => [3] => 1000 => 0
[[.,[.,[.,.]]],.] => [1,1,0,1,0,1,0,0] => [2,1] => 1010 => 0
[[.,[[.,.],.]],.] => [1,1,0,1,1,0,0,0] => [1,1] => 110 => 0
[[[.,.],[.,.]],.] => [1,1,1,0,0,1,0,0] => [2] => 100 => 0
[[[.,[.,.]],.],.] => [1,1,1,0,1,0,0,0] => [1] => 10 => 0
[.,[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,0,1,0] => [4,3,2,1] => 10101010 => 0
[.,[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => 1101010 => 0
[.,[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,0,1,0] => [4,2,2,1] => 10011010 => 0
[.,[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => 1011010 => 0
[.,[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => 111010 => 0
[.,[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,0] => [4,3,1,1] => 10100110 => 0
[.,[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,0] => [3,3,1,1] => 1100110 => 0
[.,[[.,[.,.]],[.,.]]] => [1,0,1,1,0,1,0,0,1,0] => [4,2,1,1] => 10010110 => 0
[.,[[[.,.],.],[.,.]]] => [1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => 10001110 => 0
[.,[[.,[.,[.,.]]],.]] => [1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => 1010110 => 0
[.,[[.,[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,0,0] => [2,2,1,1] => 110110 => 0
[.,[[[.,.],[.,.]],.]] => [1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => 1001110 => 0
[.,[[[.,[.,.]],.],.]] => [1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => 101110 => 0
[.,[[[[.,.],.],.],.]] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 11110 => 0
[[.,.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,0] => [4,3,2] => 1010100 => 0
[[.,.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,0] => [3,3,2] => 110100 => 0
[[.,.],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,0] => [4,2,2] => 1001100 => 0
[[.,.],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,1,0,0] => [3,2,2] => 101100 => 0
[[.,.],[[[.,.],.],.]] => [1,1,0,0,1,1,1,0,0,0] => [2,2,2] => 11100 => 0
[[.,[.,.]],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,0] => [4,3,1] => 1010010 => 0
[[.,[.,.]],[[.,.],.]] => [1,1,0,1,0,0,1,1,0,0] => [3,3,1] => 110010 => 0
[[[.,.],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,0] => [4,3] => 101000 => 0
[[[.,.],.],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0] => [3,3] => 11000 => 0
[[.,[.,[.,.]]],[.,.]] => [1,1,0,1,0,1,0,0,1,0] => [4,2,1] => 1001010 => 0
[[.,[[.,.],.]],[.,.]] => [1,1,0,1,1,0,0,0,1,0] => [4,1,1] => 1000110 => 0
[[[.,.],[.,.]],[.,.]] => [1,1,1,0,0,1,0,0,1,0] => [4,2] => 100100 => 0
[[[.,[.,.]],.],[.,.]] => [1,1,1,0,1,0,0,0,1,0] => [4,1] => 100010 => 0
[[[[.,.],.],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0] => [4] => 10000 => 0
[[.,[.,[.,[.,.]]]],.] => [1,1,0,1,0,1,0,1,0,0] => [3,2,1] => 101010 => 0
[[.,[.,[[.,.],.]]],.] => [1,1,0,1,0,1,1,0,0,0] => [2,2,1] => 11010 => 0
[[.,[[.,.],[.,.]]],.] => [1,1,0,1,1,0,0,1,0,0] => [3,1,1] => 100110 => 0
[[.,[[.,[.,.]],.]],.] => [1,1,0,1,1,0,1,0,0,0] => [2,1,1] => 10110 => 0
[[.,[[[.,.],.],.]],.] => [1,1,0,1,1,1,0,0,0,0] => [1,1,1] => 1110 => 0
[[[.,.],[.,[.,.]]],.] => [1,1,1,0,0,1,0,1,0,0] => [3,2] => 10100 => 0
[[[.,.],[[.,.],.]],.] => [1,1,1,0,0,1,1,0,0,0] => [2,2] => 1100 => 0
[[[.,[.,.]],[.,.]],.] => [1,1,1,0,1,0,0,1,0,0] => [3,1] => 10010 => 0
[[[[.,.],.],[.,.]],.] => [1,1,1,1,0,0,0,1,0,0] => [3] => 1000 => 0
[[[.,[.,[.,.]]],.],.] => [1,1,1,0,1,0,1,0,0,0] => [2,1] => 1010 => 0
[[[.,[[.,.],.]],.],.] => [1,1,1,0,1,1,0,0,0,0] => [1,1] => 110 => 0
[[[[.,.],[.,.]],.],.] => [1,1,1,1,0,0,1,0,0,0] => [2] => 100 => 0
[[[[.,[.,.]],.],.],.] => [1,1,1,1,0,1,0,0,0,0] => [1] => 10 => 0
[.,[.,[.,[.,[[.,.],.]]]]] => [1,0,1,0,1,0,1,0,1,1,0,0] => [4,4,3,2,1] => 110101010 => 0
[.,[.,[.,[[.,[.,.]],.]]]] => [1,0,1,0,1,0,1,1,0,1,0,0] => [4,3,3,2,1] => 101101010 => 0
[.,[.,[.,[[[.,.],.],.]]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => [3,3,3,2,1] => 11101010 => 0
[.,[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,0,0,1,1,0,0] => [4,4,2,2,1] => 110011010 => 0
[.,[.,[[.,[.,[.,.]]],.]]] => [1,0,1,0,1,1,0,1,0,1,0,0] => [4,3,2,2,1] => 101011010 => 0
[.,[.,[[.,[[.,.],.]],.]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => [3,3,2,2,1] => 11011010 => 0
[.,[.,[[[.,.],[.,.]],.]]] => [1,0,1,0,1,1,1,0,0,1,0,0] => [4,2,2,2,1] => 100111010 => 0
[.,[.,[[[.,[.,.]],.],.]]] => [1,0,1,0,1,1,1,0,1,0,0,0] => [3,2,2,2,1] => 10111010 => 0
[.,[.,[[[[.,.],.],.],.]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => 1111010 => 0
[.,[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,0,1,1,0,0] => [4,4,3,1,1] => 110100110 => 0
[.,[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,0,1,0,0] => [4,3,3,1,1] => 101100110 => 0
[.,[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => [3,3,3,1,1] => 11100110 => 0
[.,[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,0,0] => [4,4,2,1,1] => 110010110 => 0
[.,[[[.,.],.],[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,0,0] => [4,4,1,1,1] => 110001110 => 0
[.,[[.,[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,1] => 101010110 => 0
[.,[[.,[.,[[.,.],.]]],.]] => [1,0,1,1,0,1,0,1,1,0,0,0] => [3,3,2,1,1] => 11010110 => 0
[.,[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,0,1,0,0] => [4,2,2,1,1] => 100110110 => 0
[.,[[.,[[.,[.,.]],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,0] => [3,2,2,1,1] => 10110110 => 0
[.,[[.,[[[.,.],.],.]],.]] => [1,0,1,1,0,1,1,1,0,0,0,0] => [2,2,2,1,1] => 1110110 => 0
[.,[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,1,0,0,1,0,1,0,0] => [4,3,1,1,1] => 101001110 => 0
[.,[[[.,.],[[.,.],.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,0] => [3,3,1,1,1] => 11001110 => 0
[.,[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,1,0,0,1,0,0] => [4,2,1,1,1] => 100101110 => 0
[.,[[[[.,.],.],[.,.]],.]] => [1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => 100011110 => 0
[.,[[[.,[.,[.,.]]],.],.]] => [1,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => 10101110 => 0
[.,[[[.,[[.,.],.]],.],.]] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 1101110 => 0
[.,[[[[.,.],[.,.]],.],.]] => [1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => 10011110 => 0
[.,[[[[.,[.,.]],.],.],.]] => [1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => 1011110 => 0
[.,[[[[[.,.],.],.],.],.]] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 111110 => 0
[[.,.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2] => 101010100 => 0
[[.,.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,0] => [4,4,3,2] => 11010100 => 0
[[.,.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,0,0,1,0] => [5,3,3,2] => 100110100 => 0
[[.,.],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,0,1,1,0,1,0,0] => [4,3,3,2] => 10110100 => 0
[[.,.],[.,[[[.,.],.],.]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => [3,3,3,2] => 1110100 => 0
[[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0] => [5,4,2,2] => 101001100 => 0
[[.,.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => 11001100 => 0
[[.,.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,0] => [5,3,2,2] => 100101100 => 0
[[.,.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,0] => [5,2,2,2] => 100011100 => 0
[[.,.],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,0,1,0,0] => [4,3,2,2] => 10101100 => 0
[[.,.],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,0] => [3,3,2,2] => 1101100 => 0
[[.,.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,0,0] => [4,2,2,2] => 10011100 => 0
[[.,.],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,1,0,0,0] => [3,2,2,2] => 1011100 => 0
[[.,.],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,2,2] => 111100 => 0
>>> Load all 664 entries. <<<
[[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,0,1,0] => [5,4,3,1] => 101010010 => 0
[[.,[.,.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => [4,4,3,1] => 11010010 => 0
[[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,3,1] => 100110010 => 0
[[.,[.,.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,0,1,0,0] => [4,3,3,1] => 10110010 => 0
[[.,[.,.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,1,0,0,0] => [3,3,3,1] => 1110010 => 0
[[[.,.],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,0,1,0] => [5,4,3] => 10101000 => 0
[[[.,.],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,0,0] => [4,4,3] => 1101000 => 0
[[[.,.],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => 10011000 => 0
[[[.,.],.],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,0,0] => [4,3,3] => 1011000 => 0
[[[.,.],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => 111000 => 0
[[.,[.,[.,.]]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,0,1,0] => [5,4,2,1] => 101001010 => 0
[[.,[.,[.,.]]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,0] => [4,4,2,1] => 11001010 => 0
[[.,[[.,.],.]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,0,1,0] => [5,4,1,1] => 101000110 => 0
[[.,[[.,.],.]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,0] => [4,4,1,1] => 11000110 => 0
[[[.,.],[.,.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,0,1,0] => [5,4,2] => 10100100 => 0
[[[.,.],[.,.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,0] => [4,4,2] => 1100100 => 0
[[[.,[.,.]],.],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,0,1,0] => [5,4,1] => 10100010 => 0
[[[.,[.,.]],.],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,0] => [4,4,1] => 1100010 => 0
[[[[.,.],.],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => 1010000 => 0
[[[[.,.],.],.],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => 110000 => 0
[[.,[.,[.,[.,.]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,0,1,0] => [5,3,2,1] => 100101010 => 0
[[.,[.,[[.,.],.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,0] => [5,2,2,1] => 100011010 => 0
[[.,[[.,.],[.,.]]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,0] => [5,3,1,1] => 100100110 => 0
[[.,[[.,[.,.]],.]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,0] => [5,2,1,1] => 100010110 => 0
[[.,[[[.,.],.],.]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,0] => [5,1,1,1] => 100001110 => 0
[[[.,.],[.,[.,.]]],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,0] => [5,3,2] => 10010100 => 0
[[[.,.],[[.,.],.]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,0] => [5,2,2] => 10001100 => 0
[[[.,[.,.]],[.,.]],[.,.]] => [1,1,1,0,1,0,0,1,0,0,1,0] => [5,3,1] => 10010010 => 0
[[[[.,.],.],[.,.]],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,0] => [5,3] => 1001000 => 0
[[[.,[.,[.,.]]],.],[.,.]] => [1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,1] => 10001010 => 0
[[[.,[[.,.],.]],.],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,0] => [5,1,1] => 10000110 => 0
[[[[.,.],[.,.]],.],[.,.]] => [1,1,1,1,0,0,1,0,0,0,1,0] => [5,2] => 1000100 => 0
[[[[.,[.,.]],.],.],[.,.]] => [1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => 1000010 => 0
[[[[[.,.],.],.],.],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5] => 100000 => 0
[[.,[.,[.,[.,[.,.]]]]],.] => [1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => 10101010 => 0
[[.,[.,[.,[[.,.],.]]]],.] => [1,1,0,1,0,1,0,1,1,0,0,0] => [3,3,2,1] => 1101010 => 0
[[.,[.,[[.,.],[.,.]]]],.] => [1,1,0,1,0,1,1,0,0,1,0,0] => [4,2,2,1] => 10011010 => 0
[[.,[.,[[.,[.,.]],.]]],.] => [1,1,0,1,0,1,1,0,1,0,0,0] => [3,2,2,1] => 1011010 => 0
[[.,[.,[[[.,.],.],.]]],.] => [1,1,0,1,0,1,1,1,0,0,0,0] => [2,2,2,1] => 111010 => 0
[[.,[[.,.],[.,[.,.]]]],.] => [1,1,0,1,1,0,0,1,0,1,0,0] => [4,3,1,1] => 10100110 => 0
[[.,[[.,.],[[.,.],.]]],.] => [1,1,0,1,1,0,0,1,1,0,0,0] => [3,3,1,1] => 1100110 => 0
[[.,[[.,[.,.]],[.,.]]],.] => [1,1,0,1,1,0,1,0,0,1,0,0] => [4,2,1,1] => 10010110 => 0
[[.,[[[.,.],.],[.,.]]],.] => [1,1,0,1,1,1,0,0,0,1,0,0] => [4,1,1,1] => 10001110 => 0
[[.,[[.,[.,[.,.]]],.]],.] => [1,1,0,1,1,0,1,0,1,0,0,0] => [3,2,1,1] => 1010110 => 0
[[.,[[.,[[.,.],.]],.]],.] => [1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,1,1] => 110110 => 0
[[.,[[[.,.],[.,.]],.]],.] => [1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,1,1] => 1001110 => 0
[[.,[[[.,[.,.]],.],.]],.] => [1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,1] => 101110 => 0
[[.,[[[[.,.],.],.],.]],.] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1] => 11110 => 0
[[[.,.],[.,[.,[.,.]]]],.] => [1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => 1010100 => 0
[[[.,.],[.,[[.,.],.]]],.] => [1,1,1,0,0,1,0,1,1,0,0,0] => [3,3,2] => 110100 => 0
[[[.,.],[[.,.],[.,.]]],.] => [1,1,1,0,0,1,1,0,0,1,0,0] => [4,2,2] => 1001100 => 0
[[[.,.],[[.,[.,.]],.]],.] => [1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,2] => 101100 => 0
[[[.,.],[[[.,.],.],.]],.] => [1,1,1,0,0,1,1,1,0,0,0,0] => [2,2,2] => 11100 => 0
[[[.,[.,.]],[.,[.,.]]],.] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => 1010010 => 0
[[[.,[.,.]],[[.,.],.]],.] => [1,1,1,0,1,0,0,1,1,0,0,0] => [3,3,1] => 110010 => 0
[[[[.,.],.],[.,[.,.]]],.] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => 101000 => 0
[[[[.,.],.],[[.,.],.]],.] => [1,1,1,1,0,0,0,1,1,0,0,0] => [3,3] => 11000 => 0
[[[.,[.,[.,.]]],[.,.]],.] => [1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => 1001010 => 0
[[[.,[[.,.],.]],[.,.]],.] => [1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,1] => 1000110 => 0
[[[[.,.],[.,.]],[.,.]],.] => [1,1,1,1,0,0,1,0,0,1,0,0] => [4,2] => 100100 => 0
[[[[.,[.,.]],.],[.,.]],.] => [1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => 100010 => 0
[[[[[.,.],.],.],[.,.]],.] => [1,1,1,1,1,0,0,0,0,1,0,0] => [4] => 10000 => 0
[[[.,[.,[.,[.,.]]]],.],.] => [1,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1] => 101010 => 0
[[[.,[.,[[.,.],.]]],.],.] => [1,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1] => 11010 => 0
[[[.,[[.,.],[.,.]]],.],.] => [1,1,1,0,1,1,0,0,1,0,0,0] => [3,1,1] => 100110 => 0
[[[.,[[.,[.,.]],.]],.],.] => [1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,1] => 10110 => 0
[[[.,[[[.,.],.],.]],.],.] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1] => 1110 => 0
[[[[.,.],[.,[.,.]]],.],.] => [1,1,1,1,0,0,1,0,1,0,0,0] => [3,2] => 10100 => 0
[[[[.,.],[[.,.],.]],.],.] => [1,1,1,1,0,0,1,1,0,0,0,0] => [2,2] => 1100 => 0
[[[[.,[.,.]],[.,.]],.],.] => [1,1,1,1,0,1,0,0,1,0,0,0] => [3,1] => 10010 => 0
[[[[[.,.],.],[.,.]],.],.] => [1,1,1,1,1,0,0,0,1,0,0,0] => [3] => 1000 => 0
[[[[.,[.,[.,.]]],.],.],.] => [1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => 1010 => 0
[[[[.,[[.,.],.]],.],.],.] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1] => 110 => 0
[[[[[.,.],[.,.]],.],.],.] => [1,1,1,1,1,0,0,1,0,0,0,0] => [2] => 100 => 0
[[[[[.,[.,.]],.],.],.],.] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1] => 10 => 0
[.,[.,[.,[[[[.,.],.],.],.]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2,1] => 111101010 => 0
[.,[.,[[.,[[[.,.],.],.]],.]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 111011010 => 0
[.,[.,[[[.,[[.,.],.]],.],.]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2,1] => 110111010 => 0
[.,[.,[[[[.,[.,.]],.],.],.]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2,1] => 101111010 => 0
[.,[.,[[[[[.,.],.],.],.],.]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2,1] => 11111010 => 0
[.,[[.,.],[[[[.,.],.],.],.]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 111100110 => 0
[.,[[.,[.,[[[.,.],.],.]]],.]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => 111010110 => 0
[.,[[.,[[.,[[.,.],.]],.]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 110110110 => 0
[.,[[.,[[[.,[.,.]],.],.]],.]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1,1] => 101110110 => 0
[.,[[.,[[[[.,.],.],.],.]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => 11110110 => 0
[.,[[[.,.],[[[.,.],.],.]],.]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => 111001110 => 0
[.,[[[.,[.,[[.,.],.]]],.],.]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1,1] => 110101110 => 0
[.,[[[.,[[.,[.,.]],.]],.],.]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => 101101110 => 0
[.,[[[.,[[[.,.],.],.]],.],.]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => 11101110 => 0
[.,[[[[.,.],[[.,.],.]],.],.]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1,1] => 110011110 => 0
[.,[[[[.,[.,[.,.]]],.],.],.]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1] => 101011110 => 0
[.,[[[[.,[[.,.],.]],.],.],.]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1,1] => 11011110 => 0
[.,[[[[[.,.],[.,.]],.],.],.]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1,1] => 100111110 => 0
[.,[[[[[.,[.,.]],.],.],.],.]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 10111110 => 0
[.,[[[[[[.,.],.],.],.],.],.]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1111110 => 0
[[.,.],[.,[.,[[[.,.],.],.]]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2] => 111010100 => 0
[[.,.],[.,[[.,[[.,.],.]],.]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => 110110100 => 0
[[.,.],[.,[[[.,[.,.]],.],.]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2] => 101110100 => 0
[[.,.],[.,[[[[.,.],.],.],.]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2] => 11110100 => 0
[[.,.],[[.,.],[[[.,.],.],.]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 111001100 => 0
[[.,.],[[.,[.,[[.,.],.]]],.]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => 110101100 => 0
[[.,.],[[.,[[.,[.,.]],.]],.]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => 101101100 => 0
[[.,.],[[.,[[[.,.],.],.]],.]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 11101100 => 0
[[.,.],[[[.,.],[[.,.],.]],.]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => 110011100 => 0
[[.,.],[[[.,[.,[.,.]]],.],.]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2] => 101011100 => 0
[[.,.],[[[.,[[.,.],.]],.],.]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => 11011100 => 0
[[.,.],[[[[.,.],[.,.]],.],.]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2] => 100111100 => 0
[[.,.],[[[[.,[.,.]],.],.],.]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2] => 10111100 => 0
[[.,.],[[[[[.,.],.],.],.],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => 1111100 => 0
[[.,[.,.]],[.,[[[.,.],.],.]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1] => 111010010 => 0
[[.,[.,.]],[[.,[[.,.],.]],.]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => 110110010 => 0
[[.,[.,.]],[[[.,[.,.]],.],.]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1] => 101110010 => 0
[[.,[.,.]],[[[[.,.],.],.],.]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1] => 11110010 => 0
[[[.,.],.],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3] => 110101000 => 0
[[[.,.],.],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3] => 101101000 => 0
[[[.,.],.],[.,[[[.,.],.],.]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3] => 11101000 => 0
[[[.,.],.],[[.,.],[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 110011000 => 0
[[[.,.],.],[[.,[.,[.,.]]],.]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3] => 101011000 => 0
[[[.,.],.],[[.,[[.,.],.]],.]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => 11011000 => 0
[[[.,.],.],[[[.,.],[.,.]],.]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3] => 100111000 => 0
[[[.,.],.],[[[.,[.,.]],.],.]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3] => 10111000 => 0
[[[.,.],.],[[[[.,.],.],.],.]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => 1111000 => 0
[[.,[.,[.,.]]],[[[.,.],.],.]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1] => 111001010 => 0
[[.,[[.,.],.]],[[[.,.],.],.]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1] => 111000110 => 0
[[[.,.],[.,.]],[.,[[.,.],.]]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [5,5,4,2] => 110100100 => 0
[[[.,.],[.,.]],[[.,[.,.]],.]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2] => 101100100 => 0
[[[.,.],[.,.]],[[[.,.],.],.]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2] => 11100100 => 0
[[[.,[.,.]],.],[.,[[.,.],.]]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1] => 110100010 => 0
[[[.,[.,.]],.],[[.,[.,.]],.]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1] => 101100010 => 0
[[[.,[.,.]],.],[[[.,.],.],.]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1] => 11100010 => 0
[[[[.,.],.],.],[.,[.,[.,.]]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [6,5,4] => 101010000 => 0
[[[[.,.],.],.],[.,[[.,.],.]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,5,4] => 11010000 => 0
[[[[.,.],.],.],[[.,.],[.,.]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 100110000 => 0
[[[[.,.],.],.],[[.,[.,.]],.]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,4,4] => 10110000 => 0
[[[[.,.],.],.],[[[.,.],.],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => 1110000 => 0
[[[.,.],[.,[.,.]]],[[.,.],.]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2] => 110010100 => 0
[[[.,.],[[.,.],.]],[[.,.],.]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2] => 110001100 => 0
[[[.,[.,.]],[.,.]],[[.,.],.]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1] => 110010010 => 0
[[[[.,.],.],[.,.]],[.,[.,.]]] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [6,5,3] => 101001000 => 0
[[[[.,.],.],[.,.]],[[.,.],.]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [5,5,3] => 11001000 => 0
[[[.,[.,[.,.]]],.],[[.,.],.]] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1] => 110001010 => 0
[[[.,[[.,.],.]],.],[[.,.],.]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1] => 110000110 => 0
[[[[.,.],[.,.]],.],[.,[.,.]]] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [6,5,2] => 101000100 => 0
[[[[.,.],[.,.]],.],[[.,.],.]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,5,2] => 11000100 => 0
[[[[.,[.,.]],.],.],[.,[.,.]]] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [6,5,1] => 101000010 => 0
[[[[.,[.,.]],.],.],[[.,.],.]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,5,1] => 11000010 => 0
[[[[[.,.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => 10100000 => 0
[[[[[.,.],.],.],.],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 1100000 => 0
[[[[.,.],.],[.,[.,.]]],[.,.]] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [6,4,3] => 100101000 => 0
[[[[.,.],.],[[.,.],.]],[.,.]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [6,3,3] => 100011000 => 0
[[[[.,.],[.,.]],[.,.]],[.,.]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [6,4,2] => 100100100 => 0
[[[[.,[.,.]],.],[.,.]],[.,.]] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [6,4,1] => 100100010 => 0
[[[[[.,.],.],.],[.,.]],[.,.]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,4] => 10010000 => 0
[[[[.,.],[.,[.,.]]],.],[.,.]] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2] => 100010100 => 0
[[[[.,.],[[.,.],.]],.],[.,.]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,2,2] => 100001100 => 0
[[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,1] => 100010010 => 0
[[[[[.,.],.],[.,.]],.],[.,.]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,3] => 10001000 => 0
[[[[.,[.,[.,.]]],.],.],[.,.]] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,2,1] => 100001010 => 0
[[[[.,[[.,.],.]],.],.],[.,.]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,1,1] => 100000110 => 0
[[[[[.,.],[.,.]],.],.],[.,.]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,2] => 10000100 => 0
[[[[[.,[.,.]],.],.],.],[.,.]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => 10000010 => 0
[[[[[[.,.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1000000 => 0
[[.,[.,[.,[.,[[.,.],.]]]]],.] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1] => 110101010 => 0
[[.,[.,[.,[[.,[.,.]],.]]]],.] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1] => 101101010 => 0
[[.,[.,[.,[[[.,.],.],.]]]],.] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1] => 11101010 => 0
[[.,[.,[[.,.],[[.,.],.]]]],.] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1] => 110011010 => 0
[[.,[.,[[.,[.,[.,.]]],.]]],.] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1] => 101011010 => 0
[[.,[.,[[.,[[.,.],.]],.]]],.] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => 11011010 => 0
[[.,[.,[[[.,.],[.,.]],.]]],.] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1] => 100111010 => 0
[[.,[.,[[[.,[.,.]],.],.]]],.] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1] => 10111010 => 0
[[.,[.,[[[[.,.],.],.],.]]],.] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1] => 1111010 => 0
[[.,[[.,.],[.,[[.,.],.]]]],.] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1] => 110100110 => 0
[[.,[[.,.],[[.,[.,.]],.]]],.] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1] => 101100110 => 0
[[.,[[.,.],[[[.,.],.],.]]],.] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => 11100110 => 0
[[.,[[.,[.,.]],[[.,.],.]]],.] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1] => 110010110 => 0
[[.,[[[.,.],.],[[.,.],.]]],.] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1] => 110001110 => 0
[[.,[[.,[.,[.,[.,.]]]],.]],.] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1] => 101010110 => 0
[[.,[[.,[.,[[.,.],.]]],.]],.] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1] => 11010110 => 0
[[.,[[.,[[.,.],[.,.]]],.]],.] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1] => 100110110 => 0
[[.,[[.,[[.,[.,.]],.]],.]],.] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => 10110110 => 0
[[.,[[.,[[[.,.],.],.]],.]],.] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => 1110110 => 0
[[.,[[[.,.],[.,[.,.]]],.]],.] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1] => 101001110 => 0
[[.,[[[.,.],[[.,.],.]],.]],.] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => 11001110 => 0
[[.,[[[.,[.,.]],[.,.]],.]],.] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1] => 100101110 => 0
[[.,[[[[.,.],.],[.,.]],.]],.] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1] => 100011110 => 0
[[.,[[[.,[.,[.,.]]],.],.]],.] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => 10101110 => 0
[[.,[[[.,[[.,.],.]],.],.]],.] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1] => 1101110 => 0
[[.,[[[[.,.],[.,.]],.],.]],.] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1] => 10011110 => 0
[[.,[[[[.,[.,.]],.],.],.]],.] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1] => 1011110 => 0
[[.,[[[[[.,.],.],.],.],.]],.] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => 111110 => 0
[[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2] => 101010100 => 0
[[[.,.],[.,[.,[[.,.],.]]]],.] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2] => 11010100 => 0
[[[.,.],[.,[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2] => 100110100 => 0
[[[.,.],[.,[[.,[.,.]],.]]],.] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2] => 10110100 => 0
[[[.,.],[.,[[[.,.],.],.]]],.] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2] => 1110100 => 0
[[[.,.],[[.,.],[.,[.,.]]]],.] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2] => 101001100 => 0
[[[.,.],[[.,.],[[.,.],.]]],.] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2] => 11001100 => 0
[[[.,.],[[.,[.,.]],[.,.]]],.] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2] => 100101100 => 0
[[[.,.],[[[.,.],.],[.,.]]],.] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2] => 100011100 => 0
[[[.,.],[[.,[.,[.,.]]],.]],.] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2] => 10101100 => 0
[[[.,.],[[.,[[.,.],.]],.]],.] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => 1101100 => 0
[[[.,.],[[[.,.],[.,.]],.]],.] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2] => 10011100 => 0
[[[.,.],[[[.,[.,.]],.],.]],.] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2] => 1011100 => 0
[[[.,.],[[[[.,.],.],.],.]],.] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => 111100 => 0
[[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1] => 101010010 => 0
[[[.,[.,.]],[.,[[.,.],.]]],.] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1] => 11010010 => 0
[[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1] => 100110010 => 0
[[[.,[.,.]],[[.,[.,.]],.]],.] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1] => 10110010 => 0
[[[.,[.,.]],[[[.,.],.],.]],.] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1] => 1110010 => 0
[[[[.,.],.],[.,[.,[.,.]]]],.] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [5,4,3] => 10101000 => 0
[[[[.,.],.],[.,[[.,.],.]]],.] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,4,3] => 1101000 => 0
[[[[.,.],.],[[.,.],[.,.]]],.] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [5,3,3] => 10011000 => 0
[[[[.,.],.],[[.,[.,.]],.]],.] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,3] => 1011000 => 0
[[[[.,.],.],[[[.,.],.],.]],.] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,3,3] => 111000 => 0
[[[.,[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1] => 101001010 => 0
[[[.,[.,[.,.]]],[[.,.],.]],.] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1] => 11001010 => 0
[[[.,[[.,.],.]],[.,[.,.]]],.] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1] => 101000110 => 0
[[[.,[[.,.],.]],[[.,.],.]],.] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1] => 11000110 => 0
[[[[.,.],[.,.]],[.,[.,.]]],.] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,4,2] => 10100100 => 0
[[[[.,.],[.,.]],[[.,.],.]],.] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,4,2] => 1100100 => 0
[[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,4,1] => 10100010 => 0
[[[[.,[.,.]],.],[[.,.],.]],.] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,4,1] => 1100010 => 0
[[[[[.,.],.],.],[.,[.,.]]],.] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4] => 1010000 => 0
[[[[[.,.],.],.],[[.,.],.]],.] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,4] => 110000 => 0
[[[.,[.,[.,[.,.]]]],[.,.]],.] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1] => 100101010 => 0
[[[.,[.,[[.,.],.]]],[.,.]],.] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1] => 100011010 => 0
[[[.,[[.,.],[.,.]]],[.,.]],.] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1] => 100100110 => 0
[[[.,[[.,[.,.]],.]],[.,.]],.] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1] => 100010110 => 0
[[[.,[[[.,.],.],.]],[.,.]],.] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1] => 100001110 => 0
[[[[.,.],[.,[.,.]]],[.,.]],.] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [5,3,2] => 10010100 => 0
[[[[.,.],[[.,.],.]],[.,.]],.] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [5,2,2] => 10001100 => 0
[[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,3,1] => 10010010 => 0
[[[[[.,.],.],[.,.]],[.,.]],.] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,3] => 1001000 => 0
[[[[.,[.,[.,.]]],.],[.,.]],.] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => 10001010 => 0
[[[[.,[[.,.],.]],.],[.,.]],.] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,1] => 10000110 => 0
[[[[[.,.],[.,.]],.],[.,.]],.] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => 1000100 => 0
[[[[[.,[.,.]],.],.],[.,.]],.] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1] => 1000010 => 0
[[[[[[.,.],.],.],.],[.,.]],.] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => 100000 => 0
[[[.,[.,[.,[.,[.,.]]]]],.],.] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1] => 10101010 => 0
[[[.,[.,[.,[[.,.],.]]]],.],.] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1] => 1101010 => 0
[[[.,[.,[[.,.],[.,.]]]],.],.] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1] => 10011010 => 0
[[[.,[.,[[.,[.,.]],.]]],.],.] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => 1011010 => 0
[[[.,[.,[[[.,.],.],.]]],.],.] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1] => 111010 => 0
[[[.,[[.,.],[.,[.,.]]]],.],.] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1] => 10100110 => 0
[[[.,[[.,.],[[.,.],.]]],.],.] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1] => 1100110 => 0
[[[.,[[.,[.,.]],[.,.]]],.],.] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1] => 10010110 => 0
[[[.,[[[.,.],.],[.,.]]],.],.] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1] => 10001110 => 0
[[[.,[[.,[.,[.,.]]],.]],.],.] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => 1010110 => 0
[[[.,[[.,[[.,.],.]],.]],.],.] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1] => 110110 => 0
[[[.,[[[.,.],[.,.]],.]],.],.] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1] => 1001110 => 0
[[[.,[[[.,[.,.]],.],.]],.],.] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1] => 101110 => 0
[[[.,[[[[.,.],.],.],.]],.],.] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1] => 11110 => 0
[[[[.,.],[.,[.,[.,.]]]],.],.] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,2] => 1010100 => 0
[[[[.,.],[.,[[.,.],.]]],.],.] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,3,2] => 110100 => 0
[[[[.,.],[[.,.],[.,.]]],.],.] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,2] => 1001100 => 0
[[[[.,.],[[.,[.,.]],.]],.],.] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2] => 101100 => 0
[[[[.,.],[[[.,.],.],.]],.],.] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,2,2] => 11100 => 0
[[[[.,[.,.]],[.,[.,.]]],.],.] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,3,1] => 1010010 => 0
[[[[.,[.,.]],[[.,.],.]],.],.] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [3,3,1] => 110010 => 0
[[[[[.,.],.],[.,[.,.]]],.],.] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [4,3] => 101000 => 0
[[[[[.,.],.],[[.,.],.]],.],.] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,3] => 11000 => 0
[[[[.,[.,[.,.]]],[.,.]],.],.] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,2,1] => 1001010 => 0
[[[[.,[[.,.],.]],[.,.]],.],.] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,1,1] => 1000110 => 0
[[[[[.,.],[.,.]],[.,.]],.],.] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [4,2] => 100100 => 0
[[[[[.,[.,.]],.],[.,.]],.],.] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [4,1] => 100010 => 0
[[[[[[.,.],.],.],[.,.]],.],.] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [4] => 10000 => 0
[[[[.,[.,[.,[.,.]]]],.],.],.] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => 101010 => 0
[[[[.,[.,[[.,.],.]]],.],.],.] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,2,1] => 11010 => 0
[[[[.,[[.,.],[.,.]]],.],.],.] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [3,1,1] => 100110 => 0
[[[[.,[[.,[.,.]],.]],.],.],.] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,1,1] => 10110 => 0
[[[[.,[[[.,.],.],.]],.],.],.] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1] => 1110 => 0
[[[[[.,.],[.,[.,.]]],.],.],.] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,2] => 10100 => 0
[[[[[.,.],[[.,.],.]],.],.],.] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,2] => 1100 => 0
[[[[[.,[.,.]],[.,.]],.],.],.] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,1] => 10010 => 0
[[[[[[.,.],.],[.,.]],.],.],.] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => 1000 => 0
[[[[[.,[.,[.,.]]],.],.],.],.] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => 1010 => 0
[[[[[.,[[.,.],.]],.],.],.],.] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1] => 110 => 0
[[[[[[.,.],[.,.]],.],.],.],.] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => 100 => 0
[[[[[[.,[.,.]],.],.],.],.],.] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1] => 10 => 0
[.,[.,[[[[[[.,.],.],.],.],.],.]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => 111111010 => 0
[.,[[.,[[[[[.,.],.],.],.],.]],.]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => 111110110 => 0
[.,[[[.,[[[[.,.],.],.],.]],.],.]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1,1] => 111101110 => 0
[.,[[[[.,[[[.,.],.],.]],.],.],.]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => 111011110 => 0
[.,[[[[[.,[[.,.],.]],.],.],.],.]] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => 110111110 => 0
[.,[[[[[[.,[.,.]],.],.],.],.],.]] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => 101111110 => 0
[.,[[[[[[[.,.],.],.],.],.],.],.]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 11111110 => 0
[[.,.],[.,[[[[[.,.],.],.],.],.]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2] => 111110100 => 0
[[.,.],[[.,[[[[.,.],.],.],.]],.]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 111101100 => 0
[[.,.],[[[.,[[[.,.],.],.]],.],.]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 111011100 => 0
[[.,.],[[[[.,[[.,.],.]],.],.],.]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2] => 110111100 => 0
[[.,.],[[[[[.,[.,.]],.],.],.],.]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2] => 101111100 => 0
[[.,.],[[[[[[.,.],.],.],.],.],.]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => 11111100 => 0
[[.,[.,.]],[[[[[.,.],.],.],.],.]] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1] => 111110010 => 0
[[[.,.],.],[[[.,[[.,.],.]],.],.]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 110111000 => 0
[[[.,.],.],[[[[.,[.,.]],.],.],.]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3] => 101111000 => 0
[[[.,.],.],[[[[[.,.],.],.],.],.]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 11111000 => 0
[[[.,.],[.,.]],[[[[.,.],.],.],.]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,2] => 111100100 => 0
[[[.,[.,.]],.],[[[[.,.],.],.],.]] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,1] => 111100010 => 0
[[[[.,.],.],.],[[[.,[.,.]],.],.]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4] => 101110000 => 0
[[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 11110000 => 0
[[[[.,.],[.,.]],.],[[[.,.],.],.]] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,5,5,2] => 111000100 => 0
[[[[.,[.,.]],.],.],[[[.,.],.],.]] => [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1] => 111000010 => 0
[[[[[.,.],.],.],.],[.,[[.,.],.]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [6,6,5] => 110100000 => 0
[[[[[.,.],.],.],.],[[.,[.,.]],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [6,5,5] => 101100000 => 0
[[[[[.,.],.],.],.],[[[.,.],.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 11100000 => 0
[[[[[.,.],.],.],[.,.]],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [6,6,4] => 110010000 => 0
[[[[[.,.],.],[.,.]],.],[[.,.],.]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,6,3] => 110001000 => 0
[[[[[.,.],[.,.]],.],.],[[.,.],.]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,6,2] => 110000100 => 0
[[[[[.,[.,.]],.],.],.],[[.,.],.]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,6,1] => 110000010 => 0
[[[[[[.,.],.],.],.],.],[.,[.,.]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [7,6] => 101000000 => 0
[[[[[[.,.],.],.],.],.],[[.,.],.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => 11000000 => 0
[[[[[[.,.],.],.],.],[.,.]],[.,.]] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [7,5] => 100100000 => 0
[[[[[[.,.],.],.],[.,.]],.],[.,.]] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,4] => 100010000 => 0
[[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,3] => 100001000 => 0
[[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,2] => 100000100 => 0
[[[[[[.,[.,.]],.],.],.],.],[.,.]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => 100000010 => 0
[[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 10000000 => 0
[[.,[.,[.,[[[[.,.],.],.],.]]]],.] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1] => 111101010 => 0
[[.,[.,[[.,[[[.,.],.],.]],.]]],.] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1] => 111011010 => 0
[[.,[.,[[[.,[[.,.],.]],.],.]]],.] => [1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1] => 110111010 => 0
[[.,[.,[[[[.,[.,.]],.],.],.]]],.] => [1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1] => 101111010 => 0
[[.,[.,[[[[[.,.],.],.],.],.]]],.] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1] => 11111010 => 0
[[.,[[.,.],[[[[.,.],.],.],.]]],.] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1] => 111100110 => 0
[[.,[[.,[.,[[[.,.],.],.]]],.]],.] => [1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1] => 111010110 => 0
[[.,[[.,[[.,[[.,.],.]],.]],.]],.] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => 110110110 => 0
[[.,[[.,[[[.,[.,.]],.],.]],.]],.] => [1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1] => 101110110 => 0
[[.,[[.,[[[[.,.],.],.],.]],.]],.] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1] => 11110110 => 0
[[.,[[[.,.],[[[.,.],.],.]],.]],.] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1] => 111001110 => 0
[[.,[[[.,[.,[[.,.],.]]],.],.]],.] => [1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1] => 110101110 => 0
[[.,[[[.,[[.,[.,.]],.]],.],.]],.] => [1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1] => 101101110 => 0
[[.,[[[.,[[[.,.],.],.]],.],.]],.] => [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1] => 11101110 => 0
[[.,[[[[.,.],[[.,.],.]],.],.]],.] => [1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1] => 110011110 => 0
[[.,[[[[.,[.,[.,.]]],.],.],.]],.] => [1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1] => 101011110 => 0
[[.,[[[[.,[[.,.],.]],.],.],.]],.] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1] => 11011110 => 0
[[.,[[[[[.,.],[.,.]],.],.],.]],.] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1] => 100111110 => 0
[[.,[[[[[.,[.,.]],.],.],.],.]],.] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1] => 10111110 => 0
[[.,[[[[[[.,.],.],.],.],.],.]],.] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1111110 => 0
[[[.,.],[.,[.,[[[.,.],.],.]]]],.] => [1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,2] => 111010100 => 0
[[[.,.],[.,[[.,[[.,.],.]],.]]],.] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2] => 110110100 => 0
[[[.,.],[.,[[[.,[.,.]],.],.]]],.] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2] => 101110100 => 0
[[[.,.],[.,[[[[.,.],.],.],.]]],.] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2] => 11110100 => 0
[[[.,.],[[.,.],[[[.,.],.],.]]],.] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2] => 111001100 => 0
[[[.,.],[[.,[.,[[.,.],.]]],.]],.] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2] => 110101100 => 0
[[[.,.],[[.,[[.,[.,.]],.]],.]],.] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2] => 101101100 => 0
[[[.,.],[[.,[[[.,.],.],.]],.]],.] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2] => 11101100 => 0
[[[.,.],[[[.,.],[[.,.],.]],.]],.] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => 110011100 => 0
[[[.,.],[[[.,[.,[.,.]]],.],.]],.] => [1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2] => 101011100 => 0
[[[.,.],[[[.,[[.,.],.]],.],.]],.] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2] => 11011100 => 0
[[[.,.],[[[[.,.],[.,.]],.],.]],.] => [1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2] => 100111100 => 0
[[[.,.],[[[[.,[.,.]],.],.],.]],.] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2] => 10111100 => 0
[[[.,.],[[[[[.,.],.],.],.],.]],.] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2] => 1111100 => 0
[[[.,[.,.]],[.,[[[.,.],.],.]]],.] => [1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1] => 111010010 => 0
[[[.,[.,.]],[[.,[[.,.],.]],.]],.] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1] => 110110010 => 0
[[[.,[.,.]],[[[.,[.,.]],.],.]],.] => [1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1] => 101110010 => 0
[[[.,[.,.]],[[[[.,.],.],.],.]],.] => [1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1] => 11110010 => 0
[[[[.,.],.],[.,[.,[[.,.],.]]]],.] => [1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3] => 110101000 => 0
[[[[.,.],.],[.,[[.,[.,.]],.]]],.] => [1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3] => 101101000 => 0
[[[[.,.],.],[.,[[[.,.],.],.]]],.] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3] => 11101000 => 0
[[[[.,.],.],[[.,.],[[.,.],.]]],.] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3] => 110011000 => 0
[[[[.,.],.],[[.,[.,[.,.]]],.]],.] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3] => 101011000 => 0
[[[[.,.],.],[[.,[[.,.],.]],.]],.] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3] => 11011000 => 0
[[[[.,.],.],[[[.,.],[.,.]],.]],.] => [1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3] => 100111000 => 0
[[[[.,.],.],[[[.,[.,.]],.],.]],.] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3] => 10111000 => 0
[[[[.,.],.],[[[[.,.],.],.],.]],.] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3] => 1111000 => 0
[[[.,[.,[.,.]]],[[[.,.],.],.]],.] => [1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1] => 111001010 => 0
[[[.,[[.,.],.]],[[[.,.],.],.]],.] => [1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1] => 111000110 => 0
[[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2] => 110100100 => 0
[[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2] => 101100100 => 0
[[[[.,.],[.,.]],[[[.,.],.],.]],.] => [1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2] => 11100100 => 0
[[[[.,[.,.]],.],[.,[[.,.],.]]],.] => [1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1] => 110100010 => 0
[[[[.,[.,.]],.],[[.,[.,.]],.]],.] => [1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1] => 101100010 => 0
[[[[.,[.,.]],.],[[[.,.],.],.]],.] => [1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1] => 11100010 => 0
[[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [6,5,4] => 101010000 => 0
[[[[[.,.],.],.],[.,[[.,.],.]]],.] => [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,5,4] => 11010000 => 0
[[[[[.,.],.],.],[[.,.],[.,.]]],.] => [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [6,4,4] => 100110000 => 0
[[[[[.,.],.],.],[[.,[.,.]],.]],.] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,4] => 10110000 => 0
[[[[[.,.],.],.],[[[.,.],.],.]],.] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [4,4,4] => 1110000 => 0
[[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2] => 110010100 => 0
[[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2] => 110001100 => 0
[[[[.,[.,.]],[.,.]],[[.,.],.]],.] => [1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1] => 110010010 => 0
[[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [6,5,3] => 101001000 => 0
[[[[[.,.],.],[.,.]],[[.,.],.]],.] => [1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,5,3] => 11001000 => 0
[[[[.,[.,[.,.]]],.],[[.,.],.]],.] => [1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1] => 110001010 => 0
[[[[.,[[.,.],.]],.],[[.,.],.]],.] => [1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1] => 110000110 => 0
[[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [6,5,2] => 101000100 => 0
[[[[[.,.],[.,.]],.],[[.,.],.]],.] => [1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,5,2] => 11000100 => 0
[[[[[.,[.,.]],.],.],[.,[.,.]]],.] => [1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [6,5,1] => 101000010 => 0
[[[[[.,[.,.]],.],.],[[.,.],.]],.] => [1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [5,5,1] => 11000010 => 0
[[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5] => 10100000 => 0
[[[[[[.,.],.],.],.],[[.,.],.]],.] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [5,5] => 1100000 => 0
[[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [6,4,3] => 100101000 => 0
[[[[[.,.],.],[[.,.],.]],[.,.]],.] => [1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [6,3,3] => 100011000 => 0
[[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [6,4,2] => 100100100 => 0
[[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [6,4,1] => 100100010 => 0
[[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,4] => 10010000 => 0
[[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [6,3,2] => 100010100 => 0
[[[[[.,.],[[.,.],.]],.],[.,.]],.] => [1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [6,2,2] => 100001100 => 0
[[[[[.,[.,.]],[.,.]],.],[.,.]],.] => [1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [6,3,1] => 100010010 => 0
[[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,3] => 10001000 => 0
[[[[[.,[.,[.,.]]],.],.],[.,.]],.] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [6,2,1] => 100001010 => 0
[[[[[.,[[.,.],.]],.],.],[.,.]],.] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [6,1,1] => 100000110 => 0
[[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,2] => 10000100 => 0
[[[[[[.,[.,.]],.],.],.],[.,.]],.] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1] => 10000010 => 0
[[[[[[[.,.],.],.],.],.],[.,.]],.] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 1000000 => 0
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1] => 110101010 => 0
[[[.,[.,[.,[[.,[.,.]],.]]]],.],.] => [1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1] => 101101010 => 0
[[[.,[.,[.,[[[.,.],.],.]]]],.],.] => [1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1] => 11101010 => 0
[[[.,[.,[[.,.],[[.,.],.]]]],.],.] => [1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1] => 110011010 => 0
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.] => [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1] => 101011010 => 0
[[[.,[.,[[.,[[.,.],.]],.]]],.],.] => [1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1] => 11011010 => 0
[[[.,[.,[[[.,.],[.,.]],.]]],.],.] => [1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1] => 100111010 => 0
[[[.,[.,[[[.,[.,.]],.],.]]],.],.] => [1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1] => 10111010 => 0
[[[.,[.,[[[[.,.],.],.],.]]],.],.] => [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1] => 1111010 => 0
[[[.,[[.,.],[.,[[.,.],.]]]],.],.] => [1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1] => 110100110 => 0
[[[.,[[.,.],[[.,[.,.]],.]]],.],.] => [1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1] => 101100110 => 0
[[[.,[[.,.],[[[.,.],.],.]]],.],.] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1] => 11100110 => 0
[[[.,[[.,[.,.]],[[.,.],.]]],.],.] => [1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1] => 110010110 => 0
[[[.,[[[.,.],.],[[.,.],.]]],.],.] => [1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1] => 110001110 => 0
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.] => [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1] => 101010110 => 0
[[[.,[[.,[.,[[.,.],.]]],.]],.],.] => [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1] => 11010110 => 0
[[[.,[[.,[[.,.],[.,.]]],.]],.],.] => [1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1] => 100110110 => 0
[[[.,[[.,[[.,[.,.]],.]],.]],.],.] => [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => 10110110 => 0
[[[.,[[.,[[[.,.],.],.]],.]],.],.] => [1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1] => 1110110 => 0
[[[.,[[[.,.],[.,[.,.]]],.]],.],.] => [1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1] => 101001110 => 0
[[[.,[[[.,.],[[.,.],.]],.]],.],.] => [1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1] => 11001110 => 0
[[[.,[[[.,[.,.]],[.,.]],.]],.],.] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1] => 100101110 => 0
[[[.,[[[[.,.],.],[.,.]],.]],.],.] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1] => 100011110 => 0
[[[.,[[[.,[.,[.,.]]],.],.]],.],.] => [1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1] => 10101110 => 0
[[[.,[[[.,[[.,.],.]],.],.]],.],.] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => 1101110 => 0
[[[.,[[[[.,.],[.,.]],.],.]],.],.] => [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1] => 10011110 => 0
[[[.,[[[[.,[.,.]],.],.],.]],.],.] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1] => 1011110 => 0
[[[.,[[[[[.,.],.],.],.],.]],.],.] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1] => 111110 => 0
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2] => 101010100 => 0
[[[[.,.],[.,[.,[[.,.],.]]]],.],.] => [1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2] => 11010100 => 0
[[[[.,.],[.,[[.,.],[.,.]]]],.],.] => [1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2] => 100110100 => 0
[[[[.,.],[.,[[.,[.,.]],.]]],.],.] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2] => 10110100 => 0
[[[[.,.],[.,[[[.,.],.],.]]],.],.] => [1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2] => 1110100 => 0
[[[[.,.],[[.,.],[.,[.,.]]]],.],.] => [1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2] => 101001100 => 0
[[[[.,.],[[.,.],[[.,.],.]]],.],.] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2] => 11001100 => 0
[[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2] => 100101100 => 0
[[[[.,.],[[[.,.],.],[.,.]]],.],.] => [1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2] => 100011100 => 0
[[[[.,.],[[.,[.,[.,.]]],.]],.],.] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2] => 10101100 => 0
[[[[.,.],[[.,[[.,.],.]],.]],.],.] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => 1101100 => 0
[[[[.,.],[[[.,.],[.,.]],.]],.],.] => [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2] => 10011100 => 0
[[[[.,.],[[[.,[.,.]],.],.]],.],.] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2] => 1011100 => 0
[[[[.,.],[[[[.,.],.],.],.]],.],.] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2] => 111100 => 0
[[[[.,[.,.]],[.,[.,[.,.]]]],.],.] => [1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1] => 101010010 => 0
[[[[.,[.,.]],[.,[[.,.],.]]],.],.] => [1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1] => 11010010 => 0
[[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1] => 100110010 => 0
[[[[.,[.,.]],[[.,[.,.]],.]],.],.] => [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1] => 10110010 => 0
[[[[.,[.,.]],[[[.,.],.],.]],.],.] => [1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1] => 1110010 => 0
[[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3] => 10101000 => 0
[[[[[.,.],.],[.,[[.,.],.]]],.],.] => [1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [4,4,3] => 1101000 => 0
[[[[[.,.],.],[[.,.],[.,.]]],.],.] => [1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,3,3] => 10011000 => 0
[[[[[.,.],.],[[.,[.,.]],.]],.],.] => [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [4,3,3] => 1011000 => 0
[[[[[.,.],.],[[[.,.],.],.]],.],.] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => 111000 => 0
[[[[.,[.,[.,.]]],[.,[.,.]]],.],.] => [1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1] => 101001010 => 0
[[[[.,[.,[.,.]]],[[.,.],.]],.],.] => [1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1] => 11001010 => 0
[[[[.,[[.,.],.]],[.,[.,.]]],.],.] => [1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1] => 101000110 => 0
[[[[.,[[.,.],.]],[[.,.],.]],.],.] => [1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1] => 11000110 => 0
[[[[[.,.],[.,.]],[.,[.,.]]],.],.] => [1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [5,4,2] => 10100100 => 0
[[[[[.,.],[.,.]],[[.,.],.]],.],.] => [1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [4,4,2] => 1100100 => 0
[[[[[.,[.,.]],.],[.,[.,.]]],.],.] => [1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,4,1] => 10100010 => 0
[[[[[.,[.,.]],.],[[.,.],.]],.],.] => [1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [4,4,1] => 1100010 => 0
[[[[[[.,.],.],.],[.,[.,.]]],.],.] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [5,4] => 1010000 => 0
[[[[[[.,.],.],.],[[.,.],.]],.],.] => [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [4,4] => 110000 => 0
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.] => [1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1] => 100101010 => 0
[[[[.,[.,[[.,.],.]]],[.,.]],.],.] => [1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1] => 100011010 => 0
[[[[.,[[.,.],[.,.]]],[.,.]],.],.] => [1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1] => 100100110 => 0
[[[[.,[[.,[.,.]],.]],[.,.]],.],.] => [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1] => 100010110 => 0
[[[[.,[[[.,.],.],.]],[.,.]],.],.] => [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1] => 100001110 => 0
[[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,3,2] => 10010100 => 0
[[[[[.,.],[[.,.],.]],[.,.]],.],.] => [1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,2,2] => 10001100 => 0
[[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,3,1] => 10010010 => 0
[[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [5,3] => 1001000 => 0
[[[[[.,[.,[.,.]]],.],[.,.]],.],.] => [1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,2,1] => 10001010 => 0
[[[[[.,[[.,.],.]],.],[.,.]],.],.] => [1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,1,1] => 10000110 => 0
[[[[[[.,.],[.,.]],.],[.,.]],.],.] => [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [5,2] => 1000100 => 0
[[[[[[.,[.,.]],.],.],[.,.]],.],.] => [1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [5,1] => 1000010 => 0
[[[[[[[.,.],.],.],.],[.,.]],.],.] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => 100000 => 0
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1] => 10101010 => 0
[[[[.,[.,[.,[[.,.],.]]]],.],.],.] => [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1] => 1101010 => 0
[[[[.,[.,[[.,.],[.,.]]]],.],.],.] => [1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1] => 10011010 => 0
[[[[.,[.,[[.,[.,.]],.]]],.],.],.] => [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => 1011010 => 0
[[[[.,[.,[[[.,.],.],.]]],.],.],.] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1] => 111010 => 0
[[[[.,[[.,.],[.,[.,.]]]],.],.],.] => [1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1] => 10100110 => 0
[[[[.,[[.,.],[[.,.],.]]],.],.],.] => [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1] => 1100110 => 0
[[[[.,[[.,[.,.]],[.,.]]],.],.],.] => [1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1] => 10010110 => 0
[[[[.,[[[.,.],.],[.,.]]],.],.],.] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1] => 10001110 => 0
[[[[.,[[.,[.,[.,.]]],.]],.],.],.] => [1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1] => 1010110 => 0
[[[[.,[[.,[[.,.],.]],.]],.],.],.] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1] => 110110 => 0
[[[[.,[[[.,.],[.,.]],.]],.],.],.] => [1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1] => 1001110 => 0
[[[[.,[[[.,[.,.]],.],.]],.],.],.] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1] => 101110 => 0
[[[[.,[[[[.,.],.],.],.]],.],.],.] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1] => 11110 => 0
[[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [4,3,2] => 1010100 => 0
[[[[[.,.],[.,[[.,.],.]]],.],.],.] => [1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [3,3,2] => 110100 => 0
[[[[[.,.],[[.,.],[.,.]]],.],.],.] => [1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [4,2,2] => 1001100 => 0
[[[[[.,.],[[.,[.,.]],.]],.],.],.] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [3,2,2] => 101100 => 0
[[[[[.,.],[[[.,.],.],.]],.],.],.] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [2,2,2] => 11100 => 0
[[[[[.,[.,.]],[.,[.,.]]],.],.],.] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [4,3,1] => 1010010 => 0
[[[[[.,[.,.]],[[.,.],.]],.],.],.] => [1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [3,3,1] => 110010 => 0
[[[[[[.,.],.],[.,[.,.]]],.],.],.] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [4,3] => 101000 => 0
[[[[[[.,.],.],[[.,.],.]],.],.],.] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [3,3] => 11000 => 0
[[[[[.,[.,[.,.]]],[.,.]],.],.],.] => [1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [4,2,1] => 1001010 => 0
[[[[[.,[[.,.],.]],[.,.]],.],.],.] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [4,1,1] => 1000110 => 0
[[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [4,2] => 100100 => 0
[[[[[[.,[.,.]],.],[.,.]],.],.],.] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,1] => 100010 => 0
[[[[[[[.,.],.],.],[.,.]],.],.],.] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => 10000 => 0
[[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => 101010 => 0
[[[[[.,[.,[[.,.],.]]],.],.],.],.] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [2,2,1] => 11010 => 0
[[[[[.,[[.,.],[.,.]]],.],.],.],.] => [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [3,1,1] => 100110 => 0
[[[[[.,[[.,[.,.]],.]],.],.],.],.] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,1,1] => 10110 => 0
[[[[[.,[[[.,.],.],.]],.],.],.],.] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1] => 1110 => 0
[[[[[[.,.],[.,[.,.]]],.],.],.],.] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => 10100 => 0
[[[[[[.,.],[[.,.],.]],.],.],.],.] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,2] => 1100 => 0
[[[[[[.,[.,.]],[.,.]],.],.],.],.] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => 10010 => 0
[[[[[[[.,.],.],[.,.]],.],.],.],.] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => 1000 => 0
[[[[[[.,[.,[.,.]]],.],.],.],.],.] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 1010 => 0
[[[[[[.,[[.,.],.]],.],.],.],.],.] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1] => 110 => 0
[[[[[[[.,.],[.,.]],.],.],.],.],.] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 100 => 0
[[[[[[[.,[.,.]],.],.],.],.],.],.] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1] => 10 => 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] => 111111110 => 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] => 111111100 => 0
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 100000000 => 0
[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.] => [1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1] => 10101010 => 0
[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.] => [1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1] => 101010 => 0
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => 1010 => 0
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1] => 10 => 0
[[[[[.,.],[.,[.,[.,[.,.]]]]],.],.],.] => [1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2] => 101010100 => 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] => 10101010 => 0
[[[[[[.,.],[.,[.,[.,.]]]],.],.],.],.] => [1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2] => 1010100 => 0
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.] => [1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1] => 101010 => 0
[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.] => [1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [3,2] => 10100 => 0
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.] => [1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [2,1] => 1010 => 0
[[[[[[[[.,.],[.,.]],.],.],.],.],.],.] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2] => 100 => 0
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1] => 10 => 0
[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.] => [1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [3,1] => 10010 => 0
[[[[[[.,[.,[.,.]]],[.,.]],.],.],.],.] => [1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1] => 1001010 => 0
[[[[[.,[.,[.,[.,.]]]],[.,.]],.],.],.] => [1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1] => 100101010 => 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] => 11111110 => 0
[[[[[[[.,[[.,.],.]],.],.],.],.],.],.] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1] => 110 => 0
[[[[[[.,[[.,.],[.,.]]],.],.],.],.],.] => [1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1] => 100110 => 0
[[[[[.,[[[.,.],.],[.,.]]],.],.],.],.] => [1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1] => 10001110 => 0
[[[[[[[[.,.],.],[.,.]],.],.],.],.],.] => [1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [3] => 1000 => 0
[[[[[[[[.,.],.],.],[.,.]],.],.],.],.] => [1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [4] => 10000 => 0
[[[[[[[[.,.],.],.],.],[.,.]],.],.],.] => [1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [5] => 100000 => 0
[[[[[[[[.,.],.],.],.],.],[.,.]],.],.] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [6] => 1000000 => 0
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => 10000000 => 0
[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.] => [1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [2] => 100 => 0
[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.] => [1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [3] => 1000 => 0
[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.] => [1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [4] => 10000 => 0
[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [5] => 100000 => 0
[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [6] => 1000000 => 0
[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [7] => 10000000 => 0
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [8] => 100000000 => 0
[[[[[[.,.],[[[.,.],.],.]],.],.],.],.] => [1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2] => 11100 => 0
[[[[[[[.,.],.],[[.,.],.]],.],.],.],.] => [1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [3,3] => 11000 => 0
[[[[[[.,[.,.]],[[.,.],.]],.],.],.],.] => [1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1] => 110010 => 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] => 11111100 => 0
[[[[[[.,[[.,.],.]],[.,.]],.],.],.],.] => [1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1] => 1000110 => 0
[[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.] => [1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2,1] => 1101010 => 0
[[[[[[[.,.],.],.],.],.],[.,[.,.]]],.] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [7,6] => 101000000 => 0
[[[[[[[.,.],[[.,.],.]],.],.],.],.],.] => [1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [2,2] => 1100 => 0
search for individual values
searching the database for the individual values of this statistic
Description
The length of the longest Yamanouchi prefix of a binary word.
This is the largest index $i$ such that in each of the prefixes $w_1$, $w_1w_2$, $w_1w_2\dots w_i$ the number of zeros is greater than or equal to the number of ones.
Map
to Dyck path: up step, left tree, down step, right tree
Description
Return the associated Dyck path, using the bijection 1L0R.
This is given recursively as follows:
  • a leaf is associated to the empty Dyck Word
  • a tree with children $l,r$ is associated with the Dyck path described by 1L0R where $L$ and $R$ are respectively the Dyck words associated with the trees $l$ and $r$.
Map
to 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 $(n-1,\ldots,2,1)$.
Map
to binary word
Description
Return the partition as binary word, by traversing its shape from the first row to the last row, down steps as 1 and left steps as 0.