Identifier
Values
[.,[.,.]] => [1,0,1,0] => [1] => 1
[.,[.,[.,.]]] => [1,0,1,0,1,0] => [2,1] => 1
[.,[[.,.],.]] => [1,0,1,1,0,0] => [1,1] => 1
[[.,.],[.,.]] => [1,1,0,0,1,0] => [2] => 1
[[.,[.,.]],.] => [1,1,0,1,0,0] => [1] => 1
[.,[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0] => [3,2,1] => 2
[.,[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0] => [2,2,1] => 1
[.,[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0] => [3,1,1] => 1
[.,[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0] => [2,1,1] => 1
[.,[[[.,.],.],.]] => [1,0,1,1,1,0,0,0] => [1,1,1] => 1
[[.,.],[.,[.,.]]] => [1,1,0,0,1,0,1,0] => [3,2] => 1
[[.,.],[[.,.],.]] => [1,1,0,0,1,1,0,0] => [2,2] => 1
[[.,[.,.]],[.,.]] => [1,1,0,1,0,0,1,0] => [3,1] => 1
[[[.,.],.],[.,.]] => [1,1,1,0,0,0,1,0] => [3] => 1
[[.,[.,[.,.]]],.] => [1,1,0,1,0,1,0,0] => [2,1] => 1
[[.,[[.,.],.]],.] => [1,1,0,1,1,0,0,0] => [1,1] => 1
[[[.,.],[.,.]],.] => [1,1,1,0,0,1,0,0] => [2] => 1
[[[.,[.,.]],.],.] => [1,1,1,0,1,0,0,0] => [1] => 1
[.,[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,0,1,0] => [4,3,2,1] => 4
[.,[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => 2
[.,[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,0,1,0] => [4,2,2,1] => 2
[.,[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => 2
[.,[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => 1
[.,[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,0] => [4,3,1,1] => 2
[.,[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,0] => [3,3,1,1] => 3
[.,[[.,[.,.]],[.,.]]] => [1,0,1,1,0,1,0,0,1,0] => [4,2,1,1] => 2
[.,[[[.,.],.],[.,.]]] => [1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => 1
[.,[[.,[.,[.,.]]],.]] => [1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => 2
[.,[[.,[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,0,0] => [2,2,1,1] => 1
[.,[[[.,.],[.,.]],.]] => [1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => 1
[.,[[[.,[.,.]],.],.]] => [1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => 1
[.,[[[[.,.],.],.],.]] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 1
[[.,.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,0] => [4,3,2] => 2
[[.,.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,0] => [3,3,2] => 1
[[.,.],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,0] => [4,2,2] => 3
[[.,.],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,1,0,0] => [3,2,2] => 1
[[.,.],[[[.,.],.],.]] => [1,1,0,0,1,1,1,0,0,0] => [2,2,2] => 1
[[.,[.,.]],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,0] => [4,3,1] => 2
[[.,[.,.]],[[.,.],.]] => [1,1,0,1,0,0,1,1,0,0] => [3,3,1] => 1
[[[.,.],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,0] => [4,3] => 1
[[[.,.],.],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0] => [3,3] => 1
[[.,[.,[.,.]]],[.,.]] => [1,1,0,1,0,1,0,0,1,0] => [4,2,1] => 2
[[.,[[.,.],.]],[.,.]] => [1,1,0,1,1,0,0,0,1,0] => [4,1,1] => 1
[[[.,.],[.,.]],[.,.]] => [1,1,1,0,0,1,0,0,1,0] => [4,2] => 1
[[[.,[.,.]],.],[.,.]] => [1,1,1,0,1,0,0,0,1,0] => [4,1] => 1
[[[[.,.],.],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0] => [4] => 1
[[.,[.,[.,[.,.]]]],.] => [1,1,0,1,0,1,0,1,0,0] => [3,2,1] => 2
[[.,[.,[[.,.],.]]],.] => [1,1,0,1,0,1,1,0,0,0] => [2,2,1] => 1
[[.,[[.,.],[.,.]]],.] => [1,1,0,1,1,0,0,1,0,0] => [3,1,1] => 1
[[.,[[.,[.,.]],.]],.] => [1,1,0,1,1,0,1,0,0,0] => [2,1,1] => 1
[[.,[[[.,.],.],.]],.] => [1,1,0,1,1,1,0,0,0,0] => [1,1,1] => 1
[[[.,.],[.,[.,.]]],.] => [1,1,1,0,0,1,0,1,0,0] => [3,2] => 1
[[[.,.],[[.,.],.]],.] => [1,1,1,0,0,1,1,0,0,0] => [2,2] => 1
[[[.,[.,.]],[.,.]],.] => [1,1,1,0,1,0,0,1,0,0] => [3,1] => 1
[[[[.,.],.],[.,.]],.] => [1,1,1,1,0,0,0,1,0,0] => [3] => 1
[[[.,[.,[.,.]]],.],.] => [1,1,1,0,1,0,1,0,0,0] => [2,1] => 1
[[[.,[[.,.],.]],.],.] => [1,1,1,0,1,1,0,0,0,0] => [1,1] => 1
[[[[.,.],[.,.]],.],.] => [1,1,1,1,0,0,1,0,0,0] => [2] => 1
[[[[.,[.,.]],.],.],.] => [1,1,1,1,0,1,0,0,0,0] => [1] => 1
[.,[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => 9
[.,[.,[.,[.,[[.,.],.]]]]] => [1,0,1,0,1,0,1,0,1,1,0,0] => [4,4,3,2,1] => 5
[.,[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0] => [5,3,3,2,1] => 5
[.,[.,[.,[[.,[.,.]],.]]]] => [1,0,1,0,1,0,1,1,0,1,0,0] => [4,3,3,2,1] => 4
[.,[.,[.,[[[.,.],.],.]]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => [3,3,3,2,1] => 2
[.,[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0] => [5,4,2,2,1] => 5
[.,[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,0,0,1,1,0,0] => [4,4,2,2,1] => 5
[.,[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,0,1,0,0,1,0] => [5,3,2,2,1] => 4
[.,[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,0,0,1,0] => [5,2,2,2,1] => 2
[.,[.,[[.,[.,[.,.]]],.]]] => [1,0,1,0,1,1,0,1,0,1,0,0] => [4,3,2,2,1] => 4
[.,[.,[[.,[[.,.],.]],.]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => [3,3,2,2,1] => 2
[.,[.,[[[.,.],[.,.]],.]]] => [1,0,1,0,1,1,1,0,0,1,0,0] => [4,2,2,2,1] => 2
[.,[.,[[[.,[.,.]],.],.]]] => [1,0,1,0,1,1,1,0,1,0,0,0] => [3,2,2,2,1] => 2
[.,[.,[[[[.,.],.],.],.]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => 1
[.,[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,1] => 5
[.,[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,0,1,1,0,0] => [4,4,3,1,1] => 6
[.,[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,0,0,1,0] => [5,3,3,1,1] => 5
[.,[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,0,1,0,0] => [4,3,3,1,1] => 5
[.,[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => [3,3,3,1,1] => 3
[.,[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,1] => 4
[.,[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,0,0] => [4,4,2,1,1] => 5
[.,[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,0,1,0] => [5,4,1,1,1] => 2
[.,[[[.,.],.],[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,0,0] => [4,4,1,1,1] => 3
[.,[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,1] => 4
[.,[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,0] => [5,2,2,1,1] => 2
[.,[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,0] => [5,3,1,1,1] => 2
[.,[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,0] => [5,2,1,1,1] => 2
[.,[[[[.,.],.],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,0] => [5,1,1,1,1] => 1
[.,[[.,[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,1] => 5
[.,[[.,[.,[[.,.],.]]],.]] => [1,0,1,1,0,1,0,1,1,0,0,0] => [3,3,2,1,1] => 3
[.,[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,0,1,0,0] => [4,2,2,1,1] => 3
[.,[[.,[[.,[.,.]],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,0] => [3,2,2,1,1] => 2
[.,[[.,[[[.,.],.],.]],.]] => [1,0,1,1,0,1,1,1,0,0,0,0] => [2,2,2,1,1] => 1
[.,[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,1,0,0,1,0,1,0,0] => [4,3,1,1,1] => 3
[.,[[[.,.],[[.,.],.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,0] => [3,3,1,1,1] => 3
[.,[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,1,0,0,1,0,0] => [4,2,1,1,1] => 2
[.,[[[[.,.],.],[.,.]],.]] => [1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => 1
[.,[[[.,[.,[.,.]]],.],.]] => [1,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => 2
[.,[[[.,[[.,.],.]],.],.]] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 1
[.,[[[[.,.],[.,.]],.],.]] => [1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => 1
[.,[[[[.,[.,.]],.],.],.]] => [1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => 1
[.,[[[[[.,.],.],.],.],.]] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
>>> Load all 569 entries. <<<
[[.,.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2] => 5
[[.,.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,0] => [4,4,3,2] => 2
[[.,.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,0,0,1,0] => [5,3,3,2] => 6
[[.,.],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,0,1,1,0,1,0,0] => [4,3,3,2] => 2
[[.,.],[.,[[[.,.],.],.]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => [3,3,3,2] => 1
[[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0] => [5,4,2,2] => 5
[[.,.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => 3
[[.,.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,0] => [5,3,2,2] => 5
[[.,.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,0] => [5,2,2,2] => 3
[[.,.],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,0,1,0,0] => [4,3,2,2] => 2
[[.,.],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,0] => [3,3,2,2] => 1
[[.,.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,0,0] => [4,2,2,2] => 1
[[.,.],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,1,0,0,0] => [3,2,2,2] => 1
[[.,.],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,2,2] => 1
[[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,0,1,0] => [5,4,3,1] => 4
[[.,[.,.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => [4,4,3,1] => 2
[[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,3,1] => 5
[[.,[.,.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,0,1,0,0] => [4,3,3,1] => 3
[[.,[.,.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,1,0,0,0] => [3,3,3,1] => 2
[[[.,.],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,0,1,0] => [5,4,3] => 2
[[[.,.],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,0,0] => [4,4,3] => 1
[[[.,.],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => 3
[[[.,.],.],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,0,0] => [4,3,3] => 2
[[[.,.],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => 1
[[.,[.,[.,.]]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,0,1,0] => [5,4,2,1] => 4
[[.,[.,[.,.]]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,0] => [4,4,2,1] => 2
[[.,[[.,.],.]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,0,1,0] => [5,4,1,1] => 2
[[.,[[.,.],.]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,0] => [4,4,1,1] => 1
[[[.,.],[.,.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,0,1,0] => [5,4,2] => 2
[[[.,.],[.,.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,0] => [4,4,2] => 1
[[[.,[.,.]],.],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,0,1,0] => [5,4,1] => 2
[[[.,[.,.]],.],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,0] => [4,4,1] => 1
[[[[.,.],.],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => 1
[[[[.,.],.],.],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => 1
[[.,[.,[.,[.,.]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,0,1,0] => [5,3,2,1] => 5
[[.,[.,[[.,.],.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,0] => [5,2,2,1] => 3
[[.,[[.,.],[.,.]]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,0] => [5,3,1,1] => 3
[[.,[[.,[.,.]],.]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,0] => [5,2,1,1] => 2
[[.,[[[.,.],.],.]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,0] => [5,1,1,1] => 1
[[[.,.],[.,[.,.]]],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,0] => [5,3,2] => 3
[[[.,.],[[.,.],.]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,0] => [5,2,2] => 3
[[[.,[.,.]],[.,.]],[.,.]] => [1,1,1,0,1,0,0,1,0,0,1,0] => [5,3,1] => 2
[[[[.,.],.],[.,.]],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,0] => [5,3] => 1
[[[.,[.,[.,.]]],.],[.,.]] => [1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,1] => 2
[[[.,[[.,.],.]],.],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,0] => [5,1,1] => 1
[[[[.,.],[.,.]],.],[.,.]] => [1,1,1,1,0,0,1,0,0,0,1,0] => [5,2] => 1
[[[[.,[.,.]],.],.],[.,.]] => [1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => 1
[[[[[.,.],.],.],.],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5] => 1
[[.,[.,[.,[.,[.,.]]]]],.] => [1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => 4
[[.,[.,[.,[[.,.],.]]]],.] => [1,1,0,1,0,1,0,1,1,0,0,0] => [3,3,2,1] => 2
[[.,[.,[[.,.],[.,.]]]],.] => [1,1,0,1,0,1,1,0,0,1,0,0] => [4,2,2,1] => 2
[[.,[.,[[.,[.,.]],.]]],.] => [1,1,0,1,0,1,1,0,1,0,0,0] => [3,2,2,1] => 2
[[.,[.,[[[.,.],.],.]]],.] => [1,1,0,1,0,1,1,1,0,0,0,0] => [2,2,2,1] => 1
[[.,[[.,.],[.,[.,.]]]],.] => [1,1,0,1,1,0,0,1,0,1,0,0] => [4,3,1,1] => 2
[[.,[[.,.],[[.,.],.]]],.] => [1,1,0,1,1,0,0,1,1,0,0,0] => [3,3,1,1] => 3
[[.,[[.,[.,.]],[.,.]]],.] => [1,1,0,1,1,0,1,0,0,1,0,0] => [4,2,1,1] => 2
[[.,[[[.,.],.],[.,.]]],.] => [1,1,0,1,1,1,0,0,0,1,0,0] => [4,1,1,1] => 1
[[.,[[.,[.,[.,.]]],.]],.] => [1,1,0,1,1,0,1,0,1,0,0,0] => [3,2,1,1] => 2
[[.,[[.,[[.,.],.]],.]],.] => [1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,1,1] => 1
[[.,[[[.,.],[.,.]],.]],.] => [1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,1,1] => 1
[[.,[[[.,[.,.]],.],.]],.] => [1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,1] => 1
[[.,[[[[.,.],.],.],.]],.] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1] => 1
[[[.,.],[.,[.,[.,.]]]],.] => [1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => 2
[[[.,.],[.,[[.,.],.]]],.] => [1,1,1,0,0,1,0,1,1,0,0,0] => [3,3,2] => 1
[[[.,.],[[.,.],[.,.]]],.] => [1,1,1,0,0,1,1,0,0,1,0,0] => [4,2,2] => 3
[[[.,.],[[.,[.,.]],.]],.] => [1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,2] => 1
[[[.,.],[[[.,.],.],.]],.] => [1,1,1,0,0,1,1,1,0,0,0,0] => [2,2,2] => 1
[[[.,[.,.]],[.,[.,.]]],.] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => 2
[[[.,[.,.]],[[.,.],.]],.] => [1,1,1,0,1,0,0,1,1,0,0,0] => [3,3,1] => 1
[[[[.,.],.],[.,[.,.]]],.] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => 1
[[[[.,.],.],[[.,.],.]],.] => [1,1,1,1,0,0,0,1,1,0,0,0] => [3,3] => 1
[[[.,[.,[.,.]]],[.,.]],.] => [1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => 2
[[[.,[[.,.],.]],[.,.]],.] => [1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,1] => 1
[[[[.,.],[.,.]],[.,.]],.] => [1,1,1,1,0,0,1,0,0,1,0,0] => [4,2] => 1
[[[[.,[.,.]],.],[.,.]],.] => [1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => 1
[[[[[.,.],.],.],[.,.]],.] => [1,1,1,1,1,0,0,0,0,1,0,0] => [4] => 1
[[[.,[.,[.,[.,.]]]],.],.] => [1,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1] => 2
[[[.,[.,[[.,.],.]]],.],.] => [1,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1] => 1
[[[.,[[.,.],[.,.]]],.],.] => [1,1,1,0,1,1,0,0,1,0,0,0] => [3,1,1] => 1
[[[.,[[.,[.,.]],.]],.],.] => [1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,1] => 1
[[[.,[[[.,.],.],.]],.],.] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1] => 1
[[[[.,.],[.,[.,.]]],.],.] => [1,1,1,1,0,0,1,0,1,0,0,0] => [3,2] => 1
[[[[.,.],[[.,.],.]],.],.] => [1,1,1,1,0,0,1,1,0,0,0,0] => [2,2] => 1
[[[[.,[.,.]],[.,.]],.],.] => [1,1,1,1,0,1,0,0,1,0,0,0] => [3,1] => 1
[[[[[.,.],.],[.,.]],.],.] => [1,1,1,1,1,0,0,0,1,0,0,0] => [3] => 1
[[[[.,[.,[.,.]]],.],.],.] => [1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => 1
[[[[.,[[.,.],.]],.],.],.] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1] => 1
[[[[[.,.],[.,.]],.],.],.] => [1,1,1,1,1,0,0,1,0,0,0,0] => [2] => 1
[[[[[.,[.,.]],.],.],.],.] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1] => 1
[.,[[.,[[.,[[.,.],.]],.]],.]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 3
[.,[[.,[[[[.,.],.],.],.]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => 1
[.,[[[[[.,.],.],.],[.,.]],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1,1] => 1
[.,[[[.,[[.,[.,.]],.]],.],.]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => 2
[.,[[[.,[[[.,.],.],.]],.],.]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => 1
[.,[[[[.,.],[[.,.],.]],.],.]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1,1] => 3
[.,[[[[.,[.,.]],[.,.]],.],.]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1,1] => 2
[.,[[[[[.,.],.],[.,.]],.],.]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1,1] => 1
[.,[[[[.,[.,[.,.]]],.],.],.]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1] => 2
[.,[[[[.,[[.,.],.]],.],.],.]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1,1] => 1
[.,[[[[[.,.],[.,.]],.],.],.]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1,1] => 1
[.,[[[[[.,[.,.]],.],.],.],.]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[.,[[[[[[.,.],.],.],.],.],.]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[[.,.],[[[[[.,.],.],.],.],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => 1
[[[[[.,.],.],.],.],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 1
[[.,[[[[.,.],.],.],.]],[.,.]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1] => 1
[[[[.,.],[.,.]],[.,.]],[.,.]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [6,4,2] => 3
[[[[[.,.],.],.],[.,.]],[.,.]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,4] => 1
[[[.,[[.,[.,.]],.]],.],[.,.]] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1] => 2
[[[.,[[[.,.],.],.]],.],[.,.]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1] => 1
[[[[.,.],[[.,.],.]],.],[.,.]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,2,2] => 3
[[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,1] => 2
[[[[[.,.],.],[.,.]],.],[.,.]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,3] => 1
[[[[.,[.,[.,.]]],.],.],[.,.]] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,2,1] => 2
[[[[.,[[.,.],.]],.],.],[.,.]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,1,1] => 1
[[[[[.,.],[.,.]],.],.],[.,.]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,2] => 1
[[[[[.,[.,.]],.],.],.],[.,.]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => 1
[[[[[[.,.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1] => 9
[[.,[.,[.,[.,[[.,.],.]]]]],.] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1] => 5
[[.,[.,[.,[[.,.],[.,.]]]]],.] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1] => 5
[[.,[.,[.,[[.,[.,.]],.]]]],.] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1] => 4
[[.,[.,[.,[[[.,.],.],.]]]],.] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1] => 2
[[.,[.,[[.,.],[.,[.,.]]]]],.] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2,1] => 5
[[.,[.,[[.,.],[[.,.],.]]]],.] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1] => 5
[[.,[.,[[.,[.,.]],[.,.]]]],.] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1] => 4
[[.,[.,[[[.,.],.],[.,.]]]],.] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1] => 2
[[.,[.,[[.,[.,[.,.]]],.]]],.] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1] => 4
[[.,[.,[[.,[[.,.],.]],.]]],.] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => 2
[[.,[.,[[[.,.],[.,.]],.]]],.] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1] => 2
[[.,[.,[[[.,[.,.]],.],.]]],.] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1] => 2
[[.,[.,[[[[.,.],.],.],.]]],.] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1] => 1
[[.,[[.,.],[.,[.,[.,.]]]]],.] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,1] => 5
[[.,[[.,.],[.,[[.,.],.]]]],.] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1] => 6
[[.,[[.,.],[[.,.],[.,.]]]],.] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1] => 5
[[.,[[.,.],[[.,[.,.]],.]]],.] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1] => 5
[[.,[[.,.],[[[.,.],.],.]]],.] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => 3
[[.,[[.,[.,.]],[.,[.,.]]]],.] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,1] => 4
[[.,[[.,[.,.]],[[.,.],.]]],.] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1] => 5
[[.,[[[.,.],.],[.,[.,.]]]],.] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1] => 2
[[.,[[[.,.],.],[[.,.],.]]],.] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1] => 3
[[.,[[.,[.,[.,.]]],[.,.]]],.] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1] => 4
[[.,[[.,[[.,.],.]],[.,.]]],.] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1] => 2
[[.,[[[.,.],[.,.]],[.,.]]],.] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1] => 2
[[.,[[[.,[.,.]],.],[.,.]]],.] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1] => 2
[[.,[[[[.,.],.],.],[.,.]]],.] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1] => 1
[[.,[[.,[.,[.,[.,.]]]],.]],.] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1] => 5
[[.,[[.,[.,[[.,.],.]]],.]],.] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1] => 3
[[.,[[.,[[.,.],[.,.]]],.]],.] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1] => 3
[[.,[[.,[[.,[.,.]],.]],.]],.] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => 2
[[.,[[.,[[[.,.],.],.]],.]],.] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => 1
[[.,[[[.,.],[.,[.,.]]],.]],.] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1] => 3
[[.,[[[.,.],[[.,.],.]],.]],.] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => 3
[[.,[[[.,[.,.]],[.,.]],.]],.] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1] => 2
[[.,[[[[.,.],.],[.,.]],.]],.] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1] => 1
[[.,[[[.,[.,[.,.]]],.],.]],.] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => 2
[[.,[[[.,[[.,.],.]],.],.]],.] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1] => 1
[[.,[[[[.,.],[.,.]],.],.]],.] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1] => 1
[[.,[[[[.,[.,.]],.],.],.]],.] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1] => 1
[[.,[[[[[.,.],.],.],.],.]],.] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => 1
[[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2] => 5
[[[.,.],[.,[.,[[.,.],.]]]],.] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2] => 2
[[[.,.],[.,[[.,.],[.,.]]]],.] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2] => 6
[[[.,.],[.,[[.,[.,.]],.]]],.] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2] => 2
[[[.,.],[.,[[[.,.],.],.]]],.] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2] => 1
[[[.,.],[[.,.],[.,[.,.]]]],.] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2] => 5
[[[.,.],[[.,.],[[.,.],.]]],.] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2] => 3
[[[.,.],[[.,[.,.]],[.,.]]],.] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2] => 5
[[[.,.],[[[.,.],.],[.,.]]],.] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2] => 3
[[[.,.],[[.,[.,[.,.]]],.]],.] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2] => 2
[[[.,.],[[.,[[.,.],.]],.]],.] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => 1
[[[.,.],[[[.,.],[.,.]],.]],.] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2] => 1
[[[.,.],[[[.,[.,.]],.],.]],.] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2] => 1
[[[.,.],[[[[.,.],.],.],.]],.] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => 1
[[[.,[.,.]],[.,[.,[.,.]]]],.] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1] => 4
[[[.,[.,.]],[.,[[.,.],.]]],.] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1] => 2
[[[.,[.,.]],[[.,.],[.,.]]],.] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1] => 5
[[[.,[.,.]],[[.,[.,.]],.]],.] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1] => 3
[[[.,[.,.]],[[[.,.],.],.]],.] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1] => 2
[[[[.,.],.],[.,[.,[.,.]]]],.] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [5,4,3] => 2
[[[[.,.],.],[.,[[.,.],.]]],.] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,4,3] => 1
[[[[.,.],.],[[.,.],[.,.]]],.] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [5,3,3] => 3
[[[[.,.],.],[[.,[.,.]],.]],.] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,3] => 2
[[[[.,.],.],[[[.,.],.],.]],.] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,3,3] => 1
[[[.,[.,[.,.]]],[.,[.,.]]],.] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1] => 4
[[[.,[.,[.,.]]],[[.,.],.]],.] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1] => 2
[[[.,[[.,.],.]],[.,[.,.]]],.] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1] => 2
[[[.,[[.,.],.]],[[.,.],.]],.] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1] => 1
[[[[.,.],[.,.]],[.,[.,.]]],.] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,4,2] => 2
[[[[.,.],[.,.]],[[.,.],.]],.] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,4,2] => 1
[[[[.,[.,.]],.],[.,[.,.]]],.] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,4,1] => 2
[[[[.,[.,.]],.],[[.,.],.]],.] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,4,1] => 1
[[[[[.,.],.],.],[.,[.,.]]],.] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4] => 1
[[[[[.,.],.],.],[[.,.],.]],.] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,4] => 1
[[[.,[.,[.,[.,.]]]],[.,.]],.] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1] => 5
[[[.,[.,[[.,.],.]]],[.,.]],.] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1] => 3
[[[.,[[.,.],[.,.]]],[.,.]],.] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1] => 3
[[[.,[[.,[.,.]],.]],[.,.]],.] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1] => 2
[[[.,[[[.,.],.],.]],[.,.]],.] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1] => 1
[[[[.,.],[.,[.,.]]],[.,.]],.] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [5,3,2] => 3
[[[[.,.],[[.,.],.]],[.,.]],.] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [5,2,2] => 3
[[[[.,[.,.]],[.,.]],[.,.]],.] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,3,1] => 2
[[[[[.,.],.],[.,.]],[.,.]],.] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,3] => 1
[[[[.,[.,[.,.]]],.],[.,.]],.] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => 2
[[[[.,[[.,.],.]],.],[.,.]],.] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,1] => 1
[[[[[.,.],[.,.]],.],[.,.]],.] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => 1
[[[[[.,[.,.]],.],.],[.,.]],.] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1] => 1
[[[[[[.,.],.],.],.],[.,.]],.] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => 1
[[[.,[.,[.,[.,[.,.]]]]],.],.] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1] => 4
[[[.,[.,[.,[[.,.],.]]]],.],.] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1] => 2
[[[.,[.,[[.,.],[.,.]]]],.],.] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1] => 2
[[[.,[.,[[.,[.,.]],.]]],.],.] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => 2
[[[.,[.,[[[.,.],.],.]]],.],.] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1] => 1
[[[.,[[.,.],[.,[.,.]]]],.],.] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1] => 2
[[[.,[[.,.],[[.,.],.]]],.],.] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1] => 3
[[[.,[[.,[.,.]],[.,.]]],.],.] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1] => 2
[[[.,[[[.,.],.],[.,.]]],.],.] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1] => 1
[[[.,[[.,[.,[.,.]]],.]],.],.] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => 2
[[[.,[[.,[[.,.],.]],.]],.],.] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1] => 1
[[[.,[[[.,.],[.,.]],.]],.],.] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1] => 1
[[[.,[[[.,[.,.]],.],.]],.],.] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1] => 1
[[[.,[[[[.,.],.],.],.]],.],.] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1] => 1
[[[[.,.],[.,[.,[.,.]]]],.],.] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,2] => 2
[[[[.,.],[.,[[.,.],.]]],.],.] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,3,2] => 1
[[[[.,.],[[.,.],[.,.]]],.],.] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,2] => 3
[[[[.,.],[[.,[.,.]],.]],.],.] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2] => 1
[[[[.,.],[[[.,.],.],.]],.],.] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,2,2] => 1
[[[[.,[.,.]],[.,[.,.]]],.],.] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,3,1] => 2
[[[[.,[.,.]],[[.,.],.]],.],.] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [3,3,1] => 1
[[[[[.,.],.],[.,[.,.]]],.],.] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [4,3] => 1
[[[[[.,.],.],[[.,.],.]],.],.] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,3] => 1
[[[[.,[.,[.,.]]],[.,.]],.],.] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,2,1] => 2
[[[[.,[[.,.],.]],[.,.]],.],.] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,1,1] => 1
[[[[[.,.],[.,.]],[.,.]],.],.] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [4,2] => 1
[[[[[.,[.,.]],.],[.,.]],.],.] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [4,1] => 1
[[[[[[.,.],.],.],[.,.]],.],.] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [4] => 1
[[[[.,[.,[.,[.,.]]]],.],.],.] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => 2
[[[[.,[.,[[.,.],.]]],.],.],.] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,2,1] => 1
[[[[.,[[.,.],[.,.]]],.],.],.] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [3,1,1] => 1
[[[[.,[[.,[.,.]],.]],.],.],.] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,1,1] => 1
[[[[.,[[[.,.],.],.]],.],.],.] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1] => 1
[[[[[.,.],[.,[.,.]]],.],.],.] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,2] => 1
[[[[[.,.],[[.,.],.]],.],.],.] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,2] => 1
[[[[[.,[.,.]],[.,.]],.],.],.] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,1] => 1
[[[[[[.,.],.],[.,.]],.],.],.] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => 1
[[[[[.,[.,[.,.]]],.],.],.],.] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => 1
[[[[[.,[[.,.],.]],.],.],.],.] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1] => 1
[[[[[[.,.],[.,.]],.],.],.],.] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => 1
[[[[[[.,[.,.]],.],.],.],.],.] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1] => 1
[.,[[[[.,[[[.,.],.],.]],.],.],.]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => 1
[.,[[[[[[.,.],.],[.,.]],.],.],.]] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1,1] => 1
[.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1,1] => 2
[.,[[[[[.,[[.,.],.]],.],.],.],.]] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => 1
[.,[[[[[[.,.],[.,.]],.],.],.],.]] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1,1] => 1
[.,[[[[[[.,[.,.]],.],.],.],.],.]] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => 1
[.,[[[[[[[.,.],.],.],.],.],.],.]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[[[[.,[[[.,.],.],.]],.],.],[.,.]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1] => 1
[[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,3] => 1
[[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,2,1] => 2
[[[[[.,[[.,.],.]],.],.],.],[.,.]] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,1,1] => 1
[[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,2] => 1
[[[[[[.,[.,.]],.],.],.],.],[.,.]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => 1
[[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[[.,[[.,[[.,[[.,.],.]],.]],.]],.] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => 3
[[.,[[.,[[[[.,.],.],.],.]],.]],.] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1] => 1
[[.,[[[[[.,.],.],.],[.,.]],.]],.] => [1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1] => 1
[[.,[[[.,[[.,[.,.]],.]],.],.]],.] => [1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1] => 2
[[.,[[[.,[[[.,.],.],.]],.],.]],.] => [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1] => 1
[[.,[[[[.,.],[[.,.],.]],.],.]],.] => [1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1] => 3
[[.,[[[[.,[.,.]],[.,.]],.],.]],.] => [1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1] => 2
[[.,[[[[[.,.],.],[.,.]],.],.]],.] => [1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1] => 1
[[.,[[[[.,[.,[.,.]]],.],.],.]],.] => [1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1] => 2
[[.,[[[[.,[[.,.],.]],.],.],.]],.] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1] => 1
[[.,[[[[[.,.],[.,.]],.],.],.]],.] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1] => 1
[[.,[[[[[.,[.,.]],.],.],.],.]],.] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1] => 1
[[.,[[[[[[.,.],.],.],.],.],.]],.] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[[[.,.],[[[[[.,.],.],.],.],.]],.] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2] => 1
[[[[[[.,.],.],.],.],[[.,.],.]],.] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [5,5] => 1
[[[.,[[[[.,.],.],.],.]],[.,.]],.] => [1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1] => 1
[[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [6,4,2] => 3
[[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,4] => 1
[[[[.,[[.,[.,.]],.]],.],[.,.]],.] => [1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1] => 2
[[[[.,[[[.,.],.],.]],.],[.,.]],.] => [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1] => 1
[[[[[.,.],[[.,.],.]],.],[.,.]],.] => [1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [6,2,2] => 3
[[[[[.,[.,.]],[.,.]],.],[.,.]],.] => [1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [6,3,1] => 2
[[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,3] => 1
[[[[[.,[.,[.,.]]],.],.],[.,.]],.] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [6,2,1] => 2
[[[[[.,[[.,.],.]],.],.],[.,.]],.] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [6,1,1] => 1
[[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,2] => 1
[[[[[[.,[.,.]],.],.],.],[.,.]],.] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1] => 1
[[[[[[[.,.],.],.],.],.],[.,.]],.] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 1
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1] => 9
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1] => 5
[[[.,[.,[.,[[.,.],[.,.]]]]],.],.] => [1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1] => 5
[[[.,[.,[.,[[.,[.,.]],.]]]],.],.] => [1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1] => 4
[[[.,[.,[.,[[[.,.],.],.]]]],.],.] => [1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1] => 2
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.] => [1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1] => 5
[[[.,[.,[[.,.],[[.,.],.]]]],.],.] => [1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1] => 5
[[[.,[.,[[.,[.,.]],[.,.]]]],.],.] => [1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1] => 4
[[[.,[.,[[[.,.],.],[.,.]]]],.],.] => [1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1] => 2
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.] => [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1] => 4
[[[.,[.,[[.,[[.,.],.]],.]]],.],.] => [1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1] => 2
[[[.,[.,[[[.,.],[.,.]],.]]],.],.] => [1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1] => 2
[[[.,[.,[[[.,[.,.]],.],.]]],.],.] => [1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1] => 2
[[[.,[.,[[[[.,.],.],.],.]]],.],.] => [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1] => 1
[[[.,[[.,.],[.,[.,[.,.]]]]],.],.] => [1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1] => 5
[[[.,[[.,.],[.,[[.,.],.]]]],.],.] => [1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1] => 6
[[[.,[[.,.],[[.,.],[.,.]]]],.],.] => [1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1] => 5
[[[.,[[.,.],[[.,[.,.]],.]]],.],.] => [1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1] => 5
[[[.,[[.,.],[[[.,.],.],.]]],.],.] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1] => 3
[[[.,[[.,[.,.]],[.,[.,.]]]],.],.] => [1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1] => 4
[[[.,[[.,[.,.]],[[.,.],.]]],.],.] => [1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1] => 5
[[[.,[[[.,.],.],[.,[.,.]]]],.],.] => [1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1] => 2
[[[.,[[[.,.],.],[[.,.],.]]],.],.] => [1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1] => 3
[[[.,[[.,[.,[.,.]]],[.,.]]],.],.] => [1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1] => 4
[[[.,[[.,[[.,.],.]],[.,.]]],.],.] => [1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1] => 2
[[[.,[[[.,.],[.,.]],[.,.]]],.],.] => [1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1] => 2
[[[.,[[[.,[.,.]],.],[.,.]]],.],.] => [1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1] => 2
[[[.,[[[[.,.],.],.],[.,.]]],.],.] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1] => 1
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.] => [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1] => 5
[[[.,[[.,[.,[[.,.],.]]],.]],.],.] => [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1] => 3
[[[.,[[.,[[.,.],[.,.]]],.]],.],.] => [1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1] => 3
[[[.,[[.,[[.,[.,.]],.]],.]],.],.] => [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => 2
[[[.,[[.,[[[.,.],.],.]],.]],.],.] => [1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1] => 1
[[[.,[[[.,.],[.,[.,.]]],.]],.],.] => [1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1] => 3
[[[.,[[[.,.],[[.,.],.]],.]],.],.] => [1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1] => 3
[[[.,[[[.,[.,.]],[.,.]],.]],.],.] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1] => 2
[[[.,[[[[.,.],.],[.,.]],.]],.],.] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1] => 1
[[[.,[[[.,[.,[.,.]]],.],.]],.],.] => [1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1] => 2
[[[.,[[[.,[[.,.],.]],.],.]],.],.] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => 1
[[[.,[[[[.,.],[.,.]],.],.]],.],.] => [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1] => 1
[[[.,[[[[.,[.,.]],.],.],.]],.],.] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1] => 1
[[[.,[[[[[.,.],.],.],.],.]],.],.] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1] => 1
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2] => 5
[[[[.,.],[.,[.,[[.,.],.]]]],.],.] => [1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2] => 2
[[[[.,.],[.,[[.,.],[.,.]]]],.],.] => [1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2] => 6
[[[[.,.],[.,[[.,[.,.]],.]]],.],.] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2] => 2
[[[[.,.],[.,[[[.,.],.],.]]],.],.] => [1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2] => 1
[[[[.,.],[[.,.],[.,[.,.]]]],.],.] => [1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2] => 5
[[[[.,.],[[.,.],[[.,.],.]]],.],.] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2] => 3
[[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2] => 5
[[[[.,.],[[[.,.],.],[.,.]]],.],.] => [1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2] => 3
[[[[.,.],[[.,[.,[.,.]]],.]],.],.] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2] => 2
[[[[.,.],[[.,[[.,.],.]],.]],.],.] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => 1
[[[[.,.],[[[.,.],[.,.]],.]],.],.] => [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2] => 1
[[[[.,.],[[[.,[.,.]],.],.]],.],.] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2] => 1
[[[[.,.],[[[[.,.],.],.],.]],.],.] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2] => 1
[[[[.,[.,.]],[.,[.,[.,.]]]],.],.] => [1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1] => 4
[[[[.,[.,.]],[.,[[.,.],.]]],.],.] => [1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1] => 2
[[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1] => 5
[[[[.,[.,.]],[[.,[.,.]],.]],.],.] => [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1] => 3
[[[[.,[.,.]],[[[.,.],.],.]],.],.] => [1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1] => 2
[[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3] => 2
[[[[[.,.],.],[.,[[.,.],.]]],.],.] => [1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [4,4,3] => 1
[[[[[.,.],.],[[.,.],[.,.]]],.],.] => [1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,3,3] => 3
[[[[[.,.],.],[[.,[.,.]],.]],.],.] => [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [4,3,3] => 2
[[[[[.,.],.],[[[.,.],.],.]],.],.] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => 1
[[[[.,[.,[.,.]]],[.,[.,.]]],.],.] => [1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1] => 4
[[[[.,[.,[.,.]]],[[.,.],.]],.],.] => [1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1] => 2
[[[[.,[[.,.],.]],[.,[.,.]]],.],.] => [1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1] => 2
[[[[.,[[.,.],.]],[[.,.],.]],.],.] => [1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1] => 1
[[[[[.,.],[.,.]],[.,[.,.]]],.],.] => [1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [5,4,2] => 2
[[[[[.,.],[.,.]],[[.,.],.]],.],.] => [1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [4,4,2] => 1
[[[[[.,[.,.]],.],[.,[.,.]]],.],.] => [1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,4,1] => 2
[[[[[.,[.,.]],.],[[.,.],.]],.],.] => [1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [4,4,1] => 1
[[[[[[.,.],.],.],[.,[.,.]]],.],.] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [5,4] => 1
[[[[[[.,.],.],.],[[.,.],.]],.],.] => [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [4,4] => 1
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.] => [1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1] => 5
[[[[.,[.,[[.,.],.]]],[.,.]],.],.] => [1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1] => 3
[[[[.,[[.,.],[.,.]]],[.,.]],.],.] => [1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1] => 3
[[[[.,[[.,[.,.]],.]],[.,.]],.],.] => [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1] => 2
[[[[.,[[[.,.],.],.]],[.,.]],.],.] => [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1] => 1
[[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,3,2] => 3
[[[[[.,.],[[.,.],.]],[.,.]],.],.] => [1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,2,2] => 3
[[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,3,1] => 2
[[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [5,3] => 1
[[[[[.,[.,[.,.]]],.],[.,.]],.],.] => [1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,2,1] => 2
[[[[[.,[[.,.],.]],.],[.,.]],.],.] => [1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,1,1] => 1
[[[[[[.,.],[.,.]],.],[.,.]],.],.] => [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [5,2] => 1
[[[[[[.,[.,.]],.],.],[.,.]],.],.] => [1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [5,1] => 1
[[[[[[[.,.],.],.],.],[.,.]],.],.] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => 1
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1] => 4
[[[[.,[.,[.,[[.,.],.]]]],.],.],.] => [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1] => 2
[[[[.,[.,[[.,.],[.,.]]]],.],.],.] => [1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1] => 2
[[[[.,[.,[[.,[.,.]],.]]],.],.],.] => [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => 2
[[[[.,[.,[[[.,.],.],.]]],.],.],.] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1] => 1
[[[[.,[[.,.],[.,[.,.]]]],.],.],.] => [1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1] => 2
[[[[.,[[.,.],[[.,.],.]]],.],.],.] => [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1] => 3
[[[[.,[[.,[.,.]],[.,.]]],.],.],.] => [1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1] => 2
[[[[.,[[[.,.],.],[.,.]]],.],.],.] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1] => 1
[[[[.,[[.,[.,[.,.]]],.]],.],.],.] => [1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1] => 2
[[[[.,[[.,[[.,.],.]],.]],.],.],.] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1] => 1
[[[[.,[[[.,.],[.,.]],.]],.],.],.] => [1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1] => 1
[[[[.,[[[.,[.,.]],.],.]],.],.],.] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1] => 1
[[[[.,[[[[.,.],.],.],.]],.],.],.] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1] => 1
[[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [4,3,2] => 2
[[[[[.,.],[.,[[.,.],.]]],.],.],.] => [1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [3,3,2] => 1
[[[[[.,.],[[.,.],[.,.]]],.],.],.] => [1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [4,2,2] => 3
[[[[[.,.],[[.,[.,.]],.]],.],.],.] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [3,2,2] => 1
[[[[[.,.],[[[.,.],.],.]],.],.],.] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [2,2,2] => 1
[[[[[.,[.,.]],[.,[.,.]]],.],.],.] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [4,3,1] => 2
[[[[[.,[.,.]],[[.,.],.]],.],.],.] => [1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [3,3,1] => 1
[[[[[[.,.],.],[.,[.,.]]],.],.],.] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [4,3] => 1
[[[[[[.,.],.],[[.,.],.]],.],.],.] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [3,3] => 1
[[[[[.,[.,[.,.]]],[.,.]],.],.],.] => [1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [4,2,1] => 2
[[[[[.,[[.,.],.]],[.,.]],.],.],.] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [4,1,1] => 1
[[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [4,2] => 1
[[[[[[.,[.,.]],.],[.,.]],.],.],.] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,1] => 1
[[[[[[[.,.],.],.],[.,.]],.],.],.] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => 1
[[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => 2
[[[[[.,[.,[[.,.],.]]],.],.],.],.] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [2,2,1] => 1
[[[[[.,[[.,.],[.,.]]],.],.],.],.] => [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [3,1,1] => 1
[[[[[.,[[.,[.,.]],.]],.],.],.],.] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,1,1] => 1
[[[[[.,[[[.,.],.],.]],.],.],.],.] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1] => 1
[[[[[[.,.],[.,[.,.]]],.],.],.],.] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => 1
[[[[[[.,.],[[.,.],.]],.],.],.],.] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,2] => 1
[[[[[[.,[.,.]],[.,.]],.],.],.],.] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => 1
[[[[[[[.,.],.],[.,.]],.],.],.],.] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => 1
[[[[[[.,[.,[.,.]]],.],.],.],.],.] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 1
[[[[[[.,[[.,.],.]],.],.],.],.],.] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1] => 1
[[[[[[[.,.],[.,.]],.],.],.],.],.] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 1
[[[[[[[.,[.,.]],.],.],.],.],.],.] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1] => 1
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => 1
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1] => 1
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 1
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => 1
[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [8,2] => 1
[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1] => 1
[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]] => [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] => 1
[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1] => 9
[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.] => [1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1] => 4
[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.] => [1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1] => 2
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => 1
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1] => 1
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.] => [1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,1] => 9
[[[[[.,.],[.,[.,[.,[.,.]]]]],.],.],.] => [1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2] => 5
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.] => [1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1] => 4
[[[[[[.,.],[.,[.,[.,.]]]],.],.],.],.] => [1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2] => 2
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.] => [1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1] => 2
[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.] => [1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [3,2] => 1
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.] => [1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [2,1] => 1
[[[[[[[[.,.],[.,.]],.],.],.],.],.],.] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2] => 1
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1] => 1
[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.] => [1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [3,1] => 1
[[[[[[.,[.,[.,.]]],[.,.]],.],.],.],.] => [1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1] => 2
[[[[[.,[.,[.,[.,.]]]],[.,.]],.],.],.] => [1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1] => 5
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.] => [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] => 1
[[[[[[[.,[[.,.],.]],.],.],.],.],.],.] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1] => 1
[[[[[[.,[[.,.],[.,.]]],.],.],.],.],.] => [1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1] => 1
[[[[[.,[[[.,.],.],[.,.]]],.],.],.],.] => [1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1] => 1
[[[[.,[[[[.,.],.],.],[.,.]]],.],.],.] => [1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1] => 1
[[[[[[[[.,.],.],[.,.]],.],.],.],.],.] => [1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [3] => 1
[[[[[[[[.,.],.],.],[.,.]],.],.],.],.] => [1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [4] => 1
[[[[[[[[.,.],.],.],.],[.,.]],.],.],.] => [1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [5] => 1
[[[[[[[[.,.],.],.],.],.],[.,.]],.],.] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [6] => 1
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => 1
[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.] => [1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [2] => 1
[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.] => [1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [3] => 1
[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.] => [1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [4] => 1
[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [5] => 1
[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [6] => 1
[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [7] => 1
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [8] => 1
[[[[[[.,.],[[[.,.],.],.]],.],.],.],.] => [1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2] => 1
[[[[[[[.,.],.],[[.,.],.]],.],.],.],.] => [1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [3,3] => 1
[[[[[[.,[.,.]],[[.,.],.]],.],.],.],.] => [1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1] => 1
[[[[[[.,[[.,.],.]],[.,.]],.],.],.],.] => [1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1] => 1
[[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.] => [1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2,1] => 2
[[[[[[[.,.],[[.,.],.]],.],.],.],.],.] => [1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [2,2] => 1
search for individual values
searching the database for the individual values of this statistic
Description
The number of proper colouring schemes of a Ferrers diagram.
A colouring of a Ferrers diagram is proper if no two cells in a row or in a column have the same colour. The minimal number of colours needed is the maximum of the length and the first part of the partition, because we can restrict a latin square to the shape. We can associate to each colouring the integer partition recording how often each colour is used, see [1].
This statistic is the number of distinct such integer partitions that occur.
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 $(n-1,\ldots,2,1)$.