Identifier
Values
[1,0,1,0] => [1] => [1,0,1,0] => [[.,.],.] => 2
[1,0,1,0,1,0] => [2,1] => [1,0,1,0,1,0] => [[[.,.],.],.] => 3
[1,0,1,1,0,0] => [1,1] => [1,0,1,1,0,0] => [[.,.],[.,.]] => 2
[1,1,0,0,1,0] => [2] => [1,1,0,0,1,0] => [[.,[.,.]],.] => 2
[1,1,0,1,0,0] => [1] => [1,0,1,0] => [[.,.],.] => 2
[1,0,1,0,1,0,1,0] => [3,2,1] => [1,0,1,0,1,0,1,0] => [[[[.,.],.],.],.] => 4
[1,0,1,0,1,1,0,0] => [2,2,1] => [1,0,1,0,1,1,0,0] => [[[.,.],.],[.,.]] => 3
[1,0,1,1,0,0,1,0] => [3,1,1] => [1,0,1,1,0,0,1,0] => [[[.,.],[.,.]],.] => 3
[1,0,1,1,0,1,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => [[.,.],[[.,.],.]] => 2
[1,0,1,1,1,0,0,0] => [1,1,1] => [1,0,1,1,1,0,0,0] => [[.,.],[.,[.,.]]] => 2
[1,1,0,0,1,0,1,0] => [3,2] => [1,1,0,0,1,0,1,0] => [[[.,[.,.]],.],.] => 3
[1,1,0,0,1,1,0,0] => [2,2] => [1,1,0,0,1,1,0,0] => [[.,[.,.]],[.,.]] => 2
[1,1,0,1,0,0,1,0] => [3,1] => [1,1,0,1,0,0,1,0] => [[.,[[.,.],.]],.] => 2
[1,1,0,1,0,1,0,0] => [2,1] => [1,0,1,0,1,0] => [[[.,.],.],.] => 3
[1,1,0,1,1,0,0,0] => [1,1] => [1,0,1,1,0,0] => [[.,.],[.,.]] => 2
[1,1,1,0,0,0,1,0] => [3] => [1,1,1,0,0,0,1,0] => [[.,[.,[.,.]]],.] => 2
[1,1,1,0,0,1,0,0] => [2] => [1,1,0,0,1,0] => [[.,[.,.]],.] => 2
[1,1,1,0,1,0,0,0] => [1] => [1,0,1,0] => [[.,.],.] => 2
[1,0,1,0,1,0,1,0,1,0] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[[[[.,.],.],.],.],.] => 5
[1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [[[[.,.],.],.],[.,.]] => 4
[1,0,1,0,1,1,0,0,1,0] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[[[.,.],.],[.,.]],.] => 4
[1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [[[.,.],.],[[.,.],.]] => 3
[1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [[[.,.],.],[.,[.,.]]] => 3
[1,0,1,1,0,0,1,0,1,0] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[[[.,.],[.,.]],.],.] => 4
[1,0,1,1,0,0,1,1,0,0] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [[[.,.],[.,.]],[.,.]] => 3
[1,0,1,1,0,1,0,0,1,0] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [[[.,.],[[.,.],.]],.] => 3
[1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [[.,.],[[[.,.],.],.]] => 2
[1,0,1,1,0,1,1,0,0,0] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [[.,.],[[.,.],[.,.]]] => 2
[1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [[[.,.],[.,[.,.]]],.] => 3
[1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [[.,.],[[.,[.,.]],.]] => 2
[1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [[.,.],[.,[[.,.],.]]] => 2
[1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [[.,.],[.,[.,[.,.]]]] => 2
[1,1,0,0,1,0,1,0,1,0] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [[[[.,[.,.]],.],.],.] => 4
[1,1,0,0,1,0,1,1,0,0] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [[[.,[.,.]],.],[.,.]] => 3
[1,1,0,0,1,1,0,0,1,0] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [[[.,[.,.]],[.,.]],.] => 3
[1,1,0,0,1,1,0,1,0,0] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [[.,[.,.]],[[.,.],.]] => 2
[1,1,0,0,1,1,1,0,0,0] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [[.,[.,.]],[.,[.,.]]] => 2
[1,1,0,1,0,0,1,0,1,0] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [[[.,[[.,.],.]],.],.] => 3
[1,1,0,1,0,0,1,1,0,0] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [[.,[[.,.],.]],[.,.]] => 2
[1,1,0,1,0,1,0,0,1,0] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [[.,[[[.,.],.],.]],.] => 2
[1,1,0,1,0,1,0,1,0,0] => [3,2,1] => [1,0,1,0,1,0,1,0] => [[[[.,.],.],.],.] => 4
[1,1,0,1,0,1,1,0,0,0] => [2,2,1] => [1,0,1,0,1,1,0,0] => [[[.,.],.],[.,.]] => 3
[1,1,0,1,1,0,0,0,1,0] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [[.,[[.,.],[.,.]]],.] => 2
[1,1,0,1,1,0,0,1,0,0] => [3,1,1] => [1,0,1,1,0,0,1,0] => [[[.,.],[.,.]],.] => 3
[1,1,0,1,1,0,1,0,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => [[.,.],[[.,.],.]] => 2
[1,1,0,1,1,1,0,0,0,0] => [1,1,1] => [1,0,1,1,1,0,0,0] => [[.,.],[.,[.,.]]] => 2
[1,1,1,0,0,0,1,0,1,0] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [[[.,[.,[.,.]]],.],.] => 3
[1,1,1,0,0,0,1,1,0,0] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [[.,[.,[.,.]]],[.,.]] => 2
[1,1,1,0,0,1,0,0,1,0] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [[.,[[.,[.,.]],.]],.] => 2
[1,1,1,0,0,1,0,1,0,0] => [3,2] => [1,1,0,0,1,0,1,0] => [[[.,[.,.]],.],.] => 3
[1,1,1,0,0,1,1,0,0,0] => [2,2] => [1,1,0,0,1,1,0,0] => [[.,[.,.]],[.,.]] => 2
[1,1,1,0,1,0,0,0,1,0] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [[.,[.,[[.,.],.]]],.] => 2
[1,1,1,0,1,0,0,1,0,0] => [3,1] => [1,1,0,1,0,0,1,0] => [[.,[[.,.],.]],.] => 2
[1,1,1,0,1,0,1,0,0,0] => [2,1] => [1,0,1,0,1,0] => [[[.,.],.],.] => 3
[1,1,1,0,1,1,0,0,0,0] => [1,1] => [1,0,1,1,0,0] => [[.,.],[.,.]] => 2
[1,1,1,1,0,0,0,0,1,0] => [4] => [1,1,1,1,0,0,0,0,1,0] => [[.,[.,[.,[.,.]]]],.] => 2
[1,1,1,1,0,0,0,1,0,0] => [3] => [1,1,1,0,0,0,1,0] => [[.,[.,[.,.]]],.] => 2
[1,1,1,1,0,0,1,0,0,0] => [2] => [1,1,0,0,1,0] => [[.,[.,.]],.] => 2
[1,1,1,1,0,1,0,0,0,0] => [1] => [1,0,1,0] => [[.,.],.] => 2
[1,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,.],.],.],.],.],.] => 6
[1,0,1,0,1,0,1,0,1,1,0,0] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[.,.],.],.],.],[.,.]] => 5
[1,0,1,0,1,0,1,1,0,0,1,0] => [5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [[[[[.,.],.],.],[.,.]],.] => 5
[1,0,1,0,1,0,1,1,0,1,0,0] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [[[[.,.],.],.],[[.,.],.]] => 4
[1,0,1,0,1,0,1,1,1,0,0,0] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[[[.,.],.],.],[.,[.,.]]] => 4
[1,0,1,0,1,1,0,0,1,0,1,0] => [5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [[[[[.,.],.],[.,.]],.],.] => 5
[1,0,1,0,1,1,0,0,1,1,0,0] => [4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],[.,.]],[.,.]] => 4
[1,0,1,0,1,1,0,1,0,0,1,0] => [5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => [[[[.,.],.],[[.,.],.]],.] => 4
[1,0,1,0,1,1,0,1,0,1,0,0] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[[.,.],.],[[[.,.],.],.]] => 3
[1,0,1,0,1,1,0,1,1,0,0,0] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => [[[.,.],.],[[.,.],[.,.]]] => 3
[1,0,1,0,1,1,1,0,0,0,1,0] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [[[[.,.],.],[.,[.,.]]],.] => 4
[1,0,1,0,1,1,1,0,0,1,0,0] => [4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [[[.,.],.],[[.,[.,.]],.]] => 3
[1,0,1,0,1,1,1,0,1,0,0,0] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[[.,.],.],[.,[[.,.],.]]] => 3
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [[[.,.],.],[.,[.,[.,.]]]] => 3
[1,0,1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [[[[[.,.],[.,.]],.],.],.] => 5
[1,0,1,1,0,0,1,0,1,1,0,0] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => [[[[.,.],[.,.]],.],[.,.]] => 4
[1,0,1,1,0,0,1,1,0,0,1,0] => [5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [[[[.,.],[.,.]],[.,.]],.] => 4
[1,0,1,1,0,0,1,1,0,1,0,0] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [[[.,.],[.,.]],[[.,.],.]] => 3
[1,0,1,1,0,0,1,1,1,0,0,0] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => [[[.,.],[.,.]],[.,[.,.]]] => 3
[1,0,1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => [[[[.,.],[[.,.],.]],.],.] => 4
[1,0,1,1,0,1,0,0,1,1,0,0] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => [[[.,.],[[.,.],.]],[.,.]] => 3
[1,0,1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [[[.,.],[[[.,.],.],.]],.] => 3
[1,0,1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [[.,.],[[[[.,.],.],.],.]] => 2
[1,0,1,1,0,1,0,1,1,0,0,0] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[.,.],[[[.,.],.],[.,.]]] => 2
[1,0,1,1,0,1,1,0,0,0,1,0] => [5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => [[[.,.],[[.,.],[.,.]]],.] => 3
[1,0,1,1,0,1,1,0,0,1,0,0] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[.,.],[[[.,.],[.,.]],.]] => 2
[1,0,1,1,0,1,1,0,1,0,0,0] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[.,.],[[.,.],[[.,.],.]]] => 2
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [[.,.],[[.,.],[.,[.,.]]]] => 2
[1,0,1,1,1,0,0,0,1,0,1,0] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [[[[.,.],[.,[.,.]]],.],.] => 4
[1,0,1,1,1,0,0,0,1,1,0,0] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => [[[.,.],[.,[.,.]]],[.,.]] => 3
[1,0,1,1,1,0,0,1,0,0,1,0] => [5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => [[[.,.],[[.,[.,.]],.]],.] => 3
[1,0,1,1,1,0,0,1,0,1,0,0] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[.,.],[[[.,[.,.]],.],.]] => 2
[1,0,1,1,1,0,0,1,1,0,0,0] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [[.,.],[[.,[.,.]],[.,.]]] => 2
[1,0,1,1,1,0,1,0,0,0,1,0] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[[.,.],[.,[[.,.],.]]],.] => 3
[1,0,1,1,1,0,1,0,0,1,0,0] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,.],.]],.]] => 2
[1,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[.,.],[.,[[[.,.],.],.]]] => 2
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [[.,.],[.,[[.,.],[.,.]]]] => 2
[1,0,1,1,1,1,0,0,0,0,1,0] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [[[.,.],[.,[.,[.,.]]]],.] => 3
[1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [[.,.],[[.,[.,[.,.]]],.]] => 2
[1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [[.,.],[.,[[.,[.,.]],.]]] => 2
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [[.,.],[.,[.,[[.,.],.]]]] => 2
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,.]]]]] => 2
>>> Load all 604 entries. <<<
[1,1,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,.]],.],.],.],.] => 5
[1,1,0,0,1,0,1,0,1,1,0,0] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [[[[.,[.,.]],.],.],[.,.]] => 4
[1,1,0,0,1,0,1,1,0,0,1,0] => [5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => [[[[.,[.,.]],.],[.,.]],.] => 4
[1,1,0,0,1,0,1,1,0,1,0,0] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [[[.,[.,.]],.],[[.,.],.]] => 3
[1,1,0,0,1,0,1,1,1,0,0,0] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => [[[.,[.,.]],.],[.,[.,.]]] => 3
[1,1,0,0,1,1,0,0,1,0,1,0] => [5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => [[[[.,[.,.]],[.,.]],.],.] => 4
[1,1,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[.,.]],[.,.]],[.,.]] => 3
[1,1,0,0,1,1,0,1,0,0,1,0] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [[[.,[.,.]],[[.,.],.]],.] => 3
[1,1,0,0,1,1,0,1,0,1,0,0] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => [[.,[.,.]],[[[.,.],.],.]] => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[1,1,0,0,1,1,1,0,0,0,1,0] => [5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => [[[.,[.,.]],[.,[.,.]]],.] => 3
[1,1,0,0,1,1,1,0,0,1,0,0] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [[.,[.,.]],[[.,[.,.]],.]] => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [[.,[.,.]],[.,[[.,.],.]]] => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [[.,[.,.]],[.,[.,[.,.]]]] => 2
[1,1,0,1,0,0,1,0,1,0,1,0] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[.,.],.]],.],.],.] => 4
[1,1,0,1,0,0,1,0,1,1,0,0] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [[[.,[[.,.],.]],.],[.,.]] => 3
[1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => [[[.,[[.,.],.]],[.,.]],.] => 3
[1,1,0,1,0,0,1,1,0,1,0,0] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,.],.]],[[.,.],.]] => 2
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [[.,[[.,.],.]],[.,[.,.]]] => 2
[1,1,0,1,0,1,0,0,1,0,1,0] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[.,.],.],.]],.],.] => 3
[1,1,0,1,0,1,0,0,1,1,0,0] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => [[.,[[[.,.],.],.]],[.,.]] => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[.,.],.],.],.]],.] => 2
[1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[[[[.,.],.],.],.],.] => 5
[1,1,0,1,0,1,0,1,1,0,0,0] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [[[[.,.],.],.],[.,.]] => 4
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [[.,[[[.,.],.],[.,.]]],.] => 2
[1,1,0,1,0,1,1,0,0,1,0,0] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[[[.,.],.],[.,.]],.] => 4
[1,1,0,1,0,1,1,0,1,0,0,0] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [[[.,.],.],[[.,.],.]] => 3
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [[[.,.],.],[.,[.,.]]] => 3
[1,1,0,1,1,0,0,0,1,0,1,0] => [5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => [[[.,[[.,.],[.,.]]],.],.] => 3
[1,1,0,1,1,0,0,0,1,1,0,0] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [[.,[[.,.],[.,.]]],[.,.]] => 2
[1,1,0,1,1,0,0,1,0,0,1,0] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [[.,[[[.,.],[.,.]],.]],.] => 2
[1,1,0,1,1,0,0,1,0,1,0,0] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[[[.,.],[.,.]],.],.] => 4
[1,1,0,1,1,0,0,1,1,0,0,0] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [[[.,.],[.,.]],[.,.]] => 3
[1,1,0,1,1,0,1,0,0,0,1,0] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [[.,[[.,.],[[.,.],.]]],.] => 2
[1,1,0,1,1,0,1,0,0,1,0,0] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [[[.,.],[[.,.],.]],.] => 3
[1,1,0,1,1,0,1,0,1,0,0,0] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [[.,.],[[[.,.],.],.]] => 2
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [[.,.],[[.,.],[.,.]]] => 2
[1,1,0,1,1,1,0,0,0,0,1,0] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [[.,[[.,.],[.,[.,.]]]],.] => 2
[1,1,0,1,1,1,0,0,0,1,0,0] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [[[.,.],[.,[.,.]]],.] => 3
[1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [[.,.],[[.,[.,.]],.]] => 2
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [[.,.],[.,[[.,.],.]]] => 2
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [[.,.],[.,[.,[.,.]]]] => 2
[1,1,1,0,0,0,1,0,1,0,1,0] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[.,.]]],.],.],.] => 4
[1,1,1,0,0,0,1,0,1,1,0,0] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [[[.,[.,[.,.]]],.],[.,.]] => 3
[1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[[.,[.,[.,.]]],[.,.]],.] => 3
[1,1,1,0,0,0,1,1,0,1,0,0] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [[.,[.,[.,.]]],[[.,.],.]] => 2
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [[.,[.,[.,.]]],[.,[.,.]]] => 2
[1,1,1,0,0,1,0,0,1,0,1,0] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[.,.]],.]],.],.] => 3
[1,1,1,0,0,1,0,0,1,1,0,0] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[.,.]],.]],[.,.]] => 2
[1,1,1,0,0,1,0,1,0,0,1,0] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [[.,[[[.,[.,.]],.],.]],.] => 2
[1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [[[[.,[.,.]],.],.],.] => 4
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [[[.,[.,.]],.],[.,.]] => 3
[1,1,1,0,0,1,1,0,0,0,1,0] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [[.,[[.,[.,.]],[.,.]]],.] => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [[[.,[.,.]],[.,.]],.] => 3
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [[.,[.,.]],[[.,.],.]] => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [[.,[.,.]],[.,[.,.]]] => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[.,.],.]]],.],.] => 3
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [[.,[.,[[.,.],.]]],[.,.]] => 2
[1,1,1,0,1,0,0,1,0,0,1,0] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[.,.],.]],.]],.] => 2
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [[[.,[[.,.],.]],.],.] => 3
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [[.,[[.,.],.]],[.,.]] => 2
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[.,.],.],.]]],.] => 2
[1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [[.,[[[.,.],.],.]],.] => 2
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1] => [1,0,1,0,1,0,1,0] => [[[[.,.],.],.],.] => 4
[1,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1] => [1,0,1,0,1,1,0,0] => [[[.,.],.],[.,.]] => 3
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [[.,[.,[[.,.],[.,.]]]],.] => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [[.,[[.,.],[.,.]]],.] => 2
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,1,1] => [1,0,1,1,0,0,1,0] => [[[.,.],[.,.]],.] => 3
[1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => [[.,.],[[.,.],.]] => 2
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1] => [1,0,1,1,1,0,0,0] => [[.,.],[.,[.,.]]] => 2
[1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,.]]]],.],.] => 3
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [[.,[.,[.,[.,.]]]],[.,.]] => 2
[1,1,1,1,0,0,0,1,0,0,1,0] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[.,.]]],.]],.] => 2
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [[[.,[.,[.,.]]],.],.] => 3
[1,1,1,1,0,0,0,1,1,0,0,0] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [[.,[.,[.,.]]],[.,.]] => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [[.,[.,[[.,[.,.]],.]]],.] => 2
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [[.,[[.,[.,.]],.]],.] => 2
[1,1,1,1,0,0,1,0,1,0,0,0] => [3,2] => [1,1,0,0,1,0,1,0] => [[[.,[.,.]],.],.] => 3
[1,1,1,1,0,0,1,1,0,0,0,0] => [2,2] => [1,1,0,0,1,1,0,0] => [[.,[.,.]],[.,.]] => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[.,.],.]]]],.] => 2
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [[.,[.,[[.,.],.]]],.] => 2
[1,1,1,1,0,1,0,0,1,0,0,0] => [3,1] => [1,1,0,1,0,0,1,0] => [[.,[[.,.],.]],.] => 2
[1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => [1,0,1,0,1,0] => [[[.,.],.],.] => 3
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,1] => [1,0,1,1,0,0] => [[.,.],[.,.]] => 2
[1,1,1,1,1,0,0,0,0,0,1,0] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,.]]]]],.] => 2
[1,1,1,1,1,0,0,0,0,1,0,0] => [4] => [1,1,1,1,0,0,0,0,1,0] => [[.,[.,[.,[.,.]]]],.] => 2
[1,1,1,1,1,0,0,0,1,0,0,0] => [3] => [1,1,1,0,0,0,1,0] => [[.,[.,[.,.]]],.] => 2
[1,1,1,1,1,0,0,1,0,0,0,0] => [2] => [1,1,0,0,1,0] => [[.,[.,.]],.] => 2
[1,1,1,1,1,0,1,0,0,0,0,0] => [1] => [1,0,1,0] => [[.,.],.] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,.],.],.],.],.],.] => 6
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[.,.],.],.],.],[.,.]] => 5
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [[[[[.,.],.],.],[.,.]],.] => 5
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [[[[.,.],.],.],[[.,.],.]] => 4
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[[[.,.],.],.],[.,[.,.]]] => 4
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [[[[[.,.],.],[.,.]],.],.] => 5
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],[.,.]],[.,.]] => 4
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => [[[[.,.],.],[[.,.],.]],.] => 4
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[[.,.],.],[[[.,.],.],.]] => 3
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => [[[.,.],.],[[.,.],[.,.]]] => 3
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [[[[.,.],.],[.,[.,.]]],.] => 4
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [[[.,.],.],[[.,[.,.]],.]] => 3
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[[.,.],.],[.,[[.,.],.]]] => 3
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [[[.,.],.],[.,[.,[.,.]]]] => 3
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [[[[[.,.],[.,.]],.],.],.] => 5
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => [[[[.,.],[.,.]],.],[.,.]] => 4
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [[[[.,.],[.,.]],[.,.]],.] => 4
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [[[.,.],[.,.]],[[.,.],.]] => 3
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => [[[.,.],[.,.]],[.,[.,.]]] => 3
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => [[[[.,.],[[.,.],.]],.],.] => 4
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => [[[.,.],[[.,.],.]],[.,.]] => 3
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [[[.,.],[[[.,.],.],.]],.] => 3
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [[.,.],[[[[.,.],.],.],.]] => 2
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[.,.],[[[.,.],.],[.,.]]] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => [[[.,.],[[.,.],[.,.]]],.] => 3
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[.,.],[[[.,.],[.,.]],.]] => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[.,.],[[.,.],[[.,.],.]]] => 2
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [[.,.],[[.,.],[.,[.,.]]]] => 2
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [[[[.,.],[.,[.,.]]],.],.] => 4
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => [[[.,.],[.,[.,.]]],[.,.]] => 3
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => [[[.,.],[[.,[.,.]],.]],.] => 3
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[.,.],[[[.,[.,.]],.],.]] => 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [[.,.],[[.,[.,.]],[.,.]]] => 2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[[.,.],[.,[[.,.],.]]],.] => 3
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,.],.]],.]] => 2
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[.,.],[.,[[[.,.],.],.]]] => 2
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [[.,.],[.,[[.,.],[.,.]]]] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [[[.,.],[.,[.,[.,.]]]],.] => 3
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [[.,.],[[.,[.,[.,.]]],.]] => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [[.,.],[.,[[.,[.,.]],.]]] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [[.,.],[.,[.,[[.,.],.]]]] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,.]]]]] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,.]],.],.],.],.] => 5
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [[[[.,[.,.]],.],.],[.,.]] => 4
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => [[[[.,[.,.]],.],[.,.]],.] => 4
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [[[.,[.,.]],.],[[.,.],.]] => 3
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => [[[.,[.,.]],.],[.,[.,.]]] => 3
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => [[[[.,[.,.]],[.,.]],.],.] => 4
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[.,.]],[.,.]],[.,.]] => 3
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [[[.,[.,.]],[[.,.],.]],.] => 3
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => [[.,[.,.]],[[[.,.],.],.]] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => [[[.,[.,.]],[.,[.,.]]],.] => 3
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [[.,[.,.]],[[.,[.,.]],.]] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [[.,[.,.]],[.,[[.,.],.]]] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [[.,[.,.]],[.,[.,[.,.]]]] => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[.,.],.]],.],.],.] => 4
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [[[.,[[.,.],.]],.],[.,.]] => 3
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => [[[.,[[.,.],.]],[.,.]],.] => 3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,.],.]],[[.,.],.]] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [[.,[[.,.],.]],[.,[.,.]]] => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[.,.],.],.]],.],.] => 3
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => [[.,[[[.,.],.],.]],[.,.]] => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[.,.],.],.],.]],.] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[[[[.,.],.],.],.],.] => 5
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [[[[.,.],.],.],[.,.]] => 4
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [[.,[[[.,.],.],[.,.]]],.] => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[[[.,.],.],[.,.]],.] => 4
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [[[.,.],.],[[.,.],.]] => 3
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [[[.,.],.],[.,[.,.]]] => 3
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => [[[.,[[.,.],[.,.]]],.],.] => 3
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [[.,[[.,.],[.,.]]],[.,.]] => 2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [[.,[[[.,.],[.,.]],.]],.] => 2
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[[[.,.],[.,.]],.],.] => 4
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [[[.,.],[.,.]],[.,.]] => 3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [[.,[[.,.],[[.,.],.]]],.] => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [[[.,.],[[.,.],.]],.] => 3
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [[.,.],[[[.,.],.],.]] => 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [[.,.],[[.,.],[.,.]]] => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [[.,[[.,.],[.,[.,.]]]],.] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [[[.,.],[.,[.,.]]],.] => 3
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [[.,.],[[.,[.,.]],.]] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [[.,.],[.,[[.,.],.]]] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [[.,.],[.,[.,[.,.]]]] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[.,.]]],.],.],.] => 4
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [[[.,[.,[.,.]]],.],[.,.]] => 3
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[[.,[.,[.,.]]],[.,.]],.] => 3
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [[.,[.,[.,.]]],[[.,.],.]] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [[.,[.,[.,.]]],[.,[.,.]]] => 2
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[.,.]],.]],.],.] => 3
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[.,.]],.]],[.,.]] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [[.,[[[.,[.,.]],.],.]],.] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [[[[.,[.,.]],.],.],.] => 4
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [[[.,[.,.]],.],[.,.]] => 3
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [[.,[[.,[.,.]],[.,.]]],.] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [[[.,[.,.]],[.,.]],.] => 3
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [[.,[.,.]],[[.,.],.]] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [[.,[.,.]],[.,[.,.]]] => 2
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[.,.],.]]],.],.] => 3
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [[.,[.,[[.,.],.]]],[.,.]] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[.,.],.]],.]],.] => 2
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [[[.,[[.,.],.]],.],.] => 3
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [[.,[[.,.],.]],[.,.]] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[.,.],.],.]]],.] => 2
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [[.,[[[.,.],.],.]],.] => 2
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => [1,0,1,0,1,0,1,0] => [[[[.,.],.],.],.] => 4
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,2,1] => [1,0,1,0,1,1,0,0] => [[[.,.],.],[.,.]] => 3
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [[.,[.,[[.,.],[.,.]]]],.] => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [[.,[[.,.],[.,.]]],.] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [3,1,1] => [1,0,1,1,0,0,1,0] => [[[.,.],[.,.]],.] => 3
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => [[.,.],[[.,.],.]] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1] => [1,0,1,1,1,0,0,0] => [[.,.],[.,[.,.]]] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,.]]]],.],.] => 3
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [[.,[.,[.,[.,.]]]],[.,.]] => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[.,.]]],.]],.] => 2
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [[[.,[.,[.,.]]],.],.] => 3
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [[.,[.,[.,.]]],[.,.]] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [[.,[.,[[.,[.,.]],.]]],.] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [[.,[[.,[.,.]],.]],.] => 2
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,2] => [1,1,0,0,1,0,1,0] => [[[.,[.,.]],.],.] => 3
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,2] => [1,1,0,0,1,1,0,0] => [[.,[.,.]],[.,.]] => 2
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[.,.],.]]]],.] => 2
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [[.,[.,[[.,.],.]]],.] => 2
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,1] => [1,1,0,1,0,0,1,0] => [[.,[[.,.],.]],.] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => [1,0,1,0,1,0] => [[[.,.],.],.] => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1] => [1,0,1,1,0,0] => [[.,.],[.,.]] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,.]]]]],.] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [4] => [1,1,1,1,0,0,0,0,1,0] => [[.,[.,[.,[.,.]]]],.] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => [1,1,1,0,0,0,1,0] => [[.,[.,[.,.]]],.] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => [1,1,0,0,1,0] => [[.,[.,.]],.] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1] => [1,0,1,0] => [[.,.],.] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,.],.],.],.],.],.] => 6
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[.,.],.],.],.],[.,.]] => 5
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [[[[[.,.],.],.],[.,.]],.] => 5
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [[[[.,.],.],.],[[.,.],.]] => 4
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[[[.,.],.],.],[.,[.,.]]] => 4
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [[[[[.,.],.],[.,.]],.],.] => 5
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],[.,.]],[.,.]] => 4
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => [[[[.,.],.],[[.,.],.]],.] => 4
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[[.,.],.],[[[.,.],.],.]] => 3
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => [[[.,.],.],[[.,.],[.,.]]] => 3
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [[[[.,.],.],[.,[.,.]]],.] => 4
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [[[.,.],.],[[.,[.,.]],.]] => 3
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[[.,.],.],[.,[[.,.],.]]] => 3
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [[[.,.],.],[.,[.,[.,.]]]] => 3
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [[[[[.,.],[.,.]],.],.],.] => 5
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => [[[[.,.],[.,.]],.],[.,.]] => 4
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [[[[.,.],[.,.]],[.,.]],.] => 4
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [[[.,.],[.,.]],[[.,.],.]] => 3
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => [[[.,.],[.,.]],[.,[.,.]]] => 3
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => [[[[.,.],[[.,.],.]],.],.] => 4
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => [[[.,.],[[.,.],.]],[.,.]] => 3
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [[[.,.],[[[.,.],.],.]],.] => 3
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [[.,.],[[[[.,.],.],.],.]] => 2
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[.,.],[[[.,.],.],[.,.]]] => 2
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => [[[.,.],[[.,.],[.,.]]],.] => 3
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[.,.],[[[.,.],[.,.]],.]] => 2
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[.,.],[[.,.],[[.,.],.]]] => 2
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [[.,.],[[.,.],[.,[.,.]]]] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [[[[.,.],[.,[.,.]]],.],.] => 4
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => [[[.,.],[.,[.,.]]],[.,.]] => 3
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => [[[.,.],[[.,[.,.]],.]],.] => 3
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[.,.],[[[.,[.,.]],.],.]] => 2
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [[.,.],[[.,[.,.]],[.,.]]] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[[.,.],[.,[[.,.],.]]],.] => 3
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,.],.]],.]] => 2
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[.,.],[.,[[[.,.],.],.]]] => 2
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [[.,.],[.,[[.,.],[.,.]]]] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [[[.,.],[.,[.,[.,.]]]],.] => 3
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [[.,.],[[.,[.,[.,.]]],.]] => 2
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [[.,.],[.,[[.,[.,.]],.]]] => 2
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [[.,.],[.,[.,[[.,.],.]]]] => 2
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,.]]]]] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,.]],.],.],.],.] => 5
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [[[[.,[.,.]],.],.],[.,.]] => 4
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => [[[[.,[.,.]],.],[.,.]],.] => 4
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [[[.,[.,.]],.],[[.,.],.]] => 3
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => [[[.,[.,.]],.],[.,[.,.]]] => 3
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => [[[[.,[.,.]],[.,.]],.],.] => 4
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[.,.]],[.,.]],[.,.]] => 3
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [[[.,[.,.]],[[.,.],.]],.] => 3
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => [[.,[.,.]],[[[.,.],.],.]] => 2
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => [[[.,[.,.]],[.,[.,.]]],.] => 3
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [[.,[.,.]],[[.,[.,.]],.]] => 2
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [[.,[.,.]],[.,[[.,.],.]]] => 2
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [[.,[.,.]],[.,[.,[.,.]]]] => 2
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[.,.],.]],.],.],.] => 4
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [[[.,[[.,.],.]],.],[.,.]] => 3
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => [[[.,[[.,.],.]],[.,.]],.] => 3
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,.],.]],[[.,.],.]] => 2
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [[.,[[.,.],.]],[.,[.,.]]] => 2
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[.,.],.],.]],.],.] => 3
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => [[.,[[[.,.],.],.]],[.,.]] => 2
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[.,.],.],.],.]],.] => 2
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[[[[.,.],.],.],.],.] => 5
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [[[[.,.],.],.],[.,.]] => 4
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [[.,[[[.,.],.],[.,.]]],.] => 2
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[[[.,.],.],[.,.]],.] => 4
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [[[.,.],.],[[.,.],.]] => 3
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [[[.,.],.],[.,[.,.]]] => 3
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => [[[.,[[.,.],[.,.]]],.],.] => 3
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [[.,[[.,.],[.,.]]],[.,.]] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [[.,[[[.,.],[.,.]],.]],.] => 2
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[[[.,.],[.,.]],.],.] => 4
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [[[.,.],[.,.]],[.,.]] => 3
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [[.,[[.,.],[[.,.],.]]],.] => 2
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [[[.,.],[[.,.],.]],.] => 3
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [[.,.],[[[.,.],.],.]] => 2
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [[.,.],[[.,.],[.,.]]] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [[.,[[.,.],[.,[.,.]]]],.] => 2
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [[[.,.],[.,[.,.]]],.] => 3
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [[.,.],[[.,[.,.]],.]] => 2
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [[.,.],[.,[[.,.],.]]] => 2
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [[.,.],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[.,.]]],.],.],.] => 4
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [[[.,[.,[.,.]]],.],[.,.]] => 3
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[[.,[.,[.,.]]],[.,.]],.] => 3
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [[.,[.,[.,.]]],[[.,.],.]] => 2
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [[.,[.,[.,.]]],[.,[.,.]]] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[.,.]],.]],.],.] => 3
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[.,.]],.]],[.,.]] => 2
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [[.,[[[.,[.,.]],.],.]],.] => 2
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [[[[.,[.,.]],.],.],.] => 4
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [[[.,[.,.]],.],[.,.]] => 3
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [[.,[[.,[.,.]],[.,.]]],.] => 2
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [[[.,[.,.]],[.,.]],.] => 3
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [[.,[.,.]],[[.,.],.]] => 2
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [[.,[.,.]],[.,[.,.]]] => 2
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[.,.],.]]],.],.] => 3
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [[.,[.,[[.,.],.]]],[.,.]] => 2
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[.,.],.]],.]],.] => 2
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [[[.,[[.,.],.]],.],.] => 3
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [[.,[[.,.],.]],[.,.]] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[.,.],.],.]]],.] => 2
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [[.,[[[.,.],.],.]],.] => 2
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => [1,0,1,0,1,0,1,0] => [[[[.,.],.],.],.] => 4
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [2,2,1] => [1,0,1,0,1,1,0,0] => [[[.,.],.],[.,.]] => 3
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [[.,[.,[[.,.],[.,.]]]],.] => 2
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [[.,[[.,.],[.,.]]],.] => 2
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [3,1,1] => [1,0,1,1,0,0,1,0] => [[[.,.],[.,.]],.] => 3
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => [[.,.],[[.,.],.]] => 2
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1] => [1,0,1,1,1,0,0,0] => [[.,.],[.,[.,.]]] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,.]]]],.],.] => 3
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [[.,[.,[.,[.,.]]]],[.,.]] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[.,.]]],.]],.] => 2
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [[[.,[.,[.,.]]],.],.] => 3
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [[.,[.,[.,.]]],[.,.]] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [[.,[.,[[.,[.,.]],.]]],.] => 2
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [[.,[[.,[.,.]],.]],.] => 2
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => [1,1,0,0,1,0,1,0] => [[[.,[.,.]],.],.] => 3
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,2] => [1,1,0,0,1,1,0,0] => [[.,[.,.]],[.,.]] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[.,.],.]]]],.] => 2
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [[.,[.,[[.,.],.]]],.] => 2
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => [1,1,0,1,0,0,1,0] => [[.,[[.,.],.]],.] => 2
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => [1,0,1,0,1,0] => [[[.,.],.],.] => 3
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1] => [1,0,1,1,0,0] => [[.,.],[.,.]] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,.]]]]],.] => 2
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => [1,1,1,1,0,0,0,0,1,0] => [[.,[.,[.,[.,.]]]],.] => 2
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => [1,1,1,0,0,0,1,0] => [[.,[.,[.,.]]],.] => 2
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => [1,1,0,0,1,0] => [[.,[.,.]],.] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1] => [1,0,1,0] => [[.,.],.] => 2
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,.],.],.],.],.],.] => 6
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[.,.],.],.],.],[.,.]] => 5
[1,1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0,0] => [5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [[[[[.,.],.],.],[.,.]],.] => 5
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [[[[.,.],.],.],[[.,.],.]] => 4
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[[[.,.],.],.],[.,[.,.]]] => 4
[1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [[[[[.,.],.],[.,.]],.],.] => 5
[1,1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => [[[[.,.],.],[[.,.],.]],.] => 4
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[[.,.],.],[[[.,.],.],.]] => 3
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[[.,.],.],[.,[[.,.],.]]] => 3
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [[[.,.],.],[.,[.,[.,.]]]] => 3
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => [[[[.,.],[.,.]],.],[.,.]] => 4
[1,1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => [[[[.,.],[[.,.],.]],.],.] => 4
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [[.,.],[[[[.,.],.],.],.]] => 2
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[.,.],[[.,.],[[.,.],.]]] => 2
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [[.,.],[[.,.],[.,[.,.]]]] => 2
[1,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [[[[.,.],[.,[.,.]]],.],.] => 4
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => [[[.,.],[.,[.,.]]],[.,.]] => 3
[1,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[.,.],[[[.,[.,.]],.],.]] => 2
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [[.,.],[[.,[.,.]],[.,.]]] => 2
[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[[.,.],[.,[[.,.],.]]],.] => 3
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[.,.],[.,[[[.,.],.],.]]] => 2
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [[.,.],[.,[[.,.],[.,.]]]] => 2
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [[[.,.],[.,[.,[.,.]]]],.] => 3
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [[.,.],[.,[.,[[.,.],.]]]] => 2
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,.]]]]] => 2
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,.]],.],.],.],.] => 5
[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [[[[.,[.,.]],.],.],[.,.]] => 4
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[.,.]],[.,.]],[.,.]] => 3
[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0] => [5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => [[[.,[.,.]],[.,[.,.]]],.] => 3
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[.,.],.]],.],.],.] => 4
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,.],.]],[[.,.],.]] => 2
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [[.,[[.,.],.]],[.,[.,.]]] => 2
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[.,.],.],.]],.],.] => 3
[1,1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => [[.,[[[.,.],.],.]],[.,.]] => 2
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[.,.],.],.],.]],.] => 2
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[[[[.,.],.],.],.],.] => 5
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [[[[.,.],.],.],[.,.]] => 4
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[[[.,.],.],[.,.]],.] => 4
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [[[.,.],.],[[.,.],.]] => 3
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [[[.,.],.],[.,[.,.]]] => 3
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[[[.,.],[.,.]],.],.] => 4
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [[[.,.],[.,.]],[.,.]] => 3
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [[[.,.],[[.,.],.]],.] => 3
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [[.,.],[[[.,.],.],.]] => 2
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [[.,.],[[.,.],[.,.]]] => 2
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [[.,[[.,.],[.,[.,.]]]],.] => 2
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [[[.,.],[.,[.,.]]],.] => 3
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [[.,.],[[.,[.,.]],.]] => 2
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [[.,.],[.,[[.,.],.]]] => 2
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [[.,.],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[.,.]]],.],.],.] => 4
[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [[[.,[.,[.,.]]],.],[.,.]] => 3
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [[.,[.,[.,.]]],[[.,.],.]] => 2
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [[.,[.,[.,.]]],[.,[.,.]]] => 2
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[.,.]],.]],.],.] => 3
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[.,.]],.]],[.,.]] => 2
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [[.,[[[.,[.,.]],.],.]],.] => 2
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [[[[.,[.,.]],.],.],.] => 4
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [[[.,[.,.]],.],[.,.]] => 3
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [[[.,[.,.]],[.,.]],.] => 3
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [[.,[.,.]],[[.,.],.]] => 2
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [[.,[.,.]],[.,[.,.]]] => 2
[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[.,.],.]]],.],.] => 3
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [[.,[.,[[.,.],.]]],[.,.]] => 2
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[.,.],.]],.]],.] => 2
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [[[.,[[.,.],.]],.],.] => 3
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [[.,[[.,.],.]],[.,.]] => 2
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[.,.],.],.]]],.] => 2
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [[.,[[[.,.],.],.]],.] => 2
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1] => [1,0,1,0,1,0,1,0] => [[[[.,.],.],.],.] => 4
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1] => [1,0,1,0,1,1,0,0] => [[[.,.],.],[.,.]] => 3
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [[.,[[.,.],[.,.]]],.] => 2
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1] => [1,0,1,1,0,0,1,0] => [[[.,.],[.,.]],.] => 3
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => [[.,.],[[.,.],.]] => 2
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1] => [1,0,1,1,1,0,0,0] => [[.,.],[.,[.,.]]] => 2
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [[.,[.,[.,[.,.]]]],[.,.]] => 2
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [[[.,[.,[.,.]]],.],.] => 3
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [[.,[.,[.,.]]],[.,.]] => 2
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [[.,[[.,[.,.]],.]],.] => 2
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [3,2] => [1,1,0,0,1,0,1,0] => [[[.,[.,.]],.],.] => 3
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [2,2] => [1,1,0,0,1,1,0,0] => [[.,[.,.]],[.,.]] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[.,.],.]]]],.] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [[.,[.,[[.,.],.]]],.] => 2
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [3,1] => [1,1,0,1,0,0,1,0] => [[.,[[.,.],.]],.] => 2
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => [1,0,1,0,1,0] => [[[.,.],.],.] => 3
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1] => [1,0,1,1,0,0] => [[.,.],[.,.]] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,.]]]]],.] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [4] => [1,1,1,1,0,0,0,0,1,0] => [[.,[.,[.,[.,.]]]],.] => 2
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [3] => [1,1,1,0,0,0,1,0] => [[.,[.,[.,.]]],.] => 2
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2] => [1,1,0,0,1,0] => [[.,[.,.]],.] => 2
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1] => [1,0,1,0] => [[.,.],.] => 2
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[.,.],.],.],.],[.,.]] => 5
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,.]],.],.],.],.] => 5
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [1,1] => [1,0,1,1,0,0] => [[.,.],[.,.]] => 2
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [2] => [1,1,0,0,1,0] => [[.,[.,.]],.] => 2
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1] => [1,0,1,1,0,0] => [[.,.],[.,.]] => 2
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1] => [1,0,1,0,1,1,0,0] => [[[.,.],.],[.,.]] => 3
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [3,2] => [1,1,0,0,1,0,1,0] => [[[.,[.,.]],.],.] => 3
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [2] => [1,1,0,0,1,0] => [[.,[.,.]],.] => 2
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1] => [1,0,1,0] => [[.,.],.] => 2
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1] => [1,0,1,1,1,0,0,0] => [[.,.],[.,[.,.]]] => 2
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [[.,.],[.,[.,[.,.]]]] => 2
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,.]]]]] => 2
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [1] => [1,0,1,0] => [[.,.],.] => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,.]]]]],.] => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [4] => [1,1,1,1,0,0,0,0,1,0] => [[.,[.,[.,[.,.]]]],.] => 2
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [3] => [1,1,1,0,0,0,1,0] => [[.,[.,[.,.]]],.] => 2
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [2,2] => [1,1,0,0,1,1,0,0] => [[.,[.,.]],[.,.]] => 2
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [[.,[.,[.,.]]],[.,.]] => 2
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [[.,[.,[.,.]]],[.,[.,.]]] => 2
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => [[.,.],[[.,.],.]] => 2
[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] => [1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,.],.],.],.],.],.] => 6
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [[[[.,[.,.]],.],.],.] => 4
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [3,1] => [1,1,0,1,0,0,1,0] => [[.,[[.,.],.]],.] => 2
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [2,1] => [1,0,1,0,1,0] => [[[.,.],.],.] => 3
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1] => [1,0,1,0,1,0] => [[[.,.],.],.] => 3
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[[[[.,.],.],.],.],.] => 5
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1] => [1,0,1,0,1,0,1,0] => [[[[.,.],.],.],.] => 4
[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0] => [3] => [1,1,1,0,0,0,1,0] => [[.,[.,[.,.]]],.] => 2
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[.,.],.],.],.]],.] => 2
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[.,.],.],.]],.],.] => 3
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[.,.],.]],.],.],.] => 4
[1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0] => [3,1] => [1,1,0,1,0,0,1,0] => [[.,[[.,.],.]],.] => 2
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [[.,[[.,[.,.]],.]],.] => 2
[1,1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [[[[.,.],.],.],[[.,.],.]] => 4
[1,1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[[.,.],.],[[[.,.],.],.]] => 3
[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [[.,.],[[[[.,.],.],.],.]] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[.,.],.]]],.],.] => 3
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [[[.,[[.,.],.]],.],.] => 3
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [[.,[.,.]],[.,[.,.]]] => 2
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[.,.],.]]]],.] => 2
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [[.,[.,[[.,.],.]]],.] => 2
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [[.,.],[.,[[.,.],.]]] => 2
[1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [[.,.],[.,[.,[[.,.],.]]]] => 2
[1,1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => [[.,.],[[.,.],.]] => 2
[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [[[.,.],.],[[.,.],.]] => 3
[1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1] => [1,0,1,1,1,0,0,0] => [[.,.],[.,[.,.]]] => 2
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1] => [1,0,1,1,0,0,1,0] => [[[.,.],[.,.]],.] => 3
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [[.,.],[[.,.],[.,.]]] => 2
[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [[.,.],[[[.,.],.],.]] => 2
[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0] => [2,2] => [1,1,0,0,1,1,0,0] => [[.,[.,.]],[.,.]] => 2
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,.],.],.],.],.],.] => 6
[1,1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [[.,[.,[.,.]]],[.,.]] => 2
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0] => [3] => [1,1,1,0,0,0,1,0] => [[.,[.,[.,.]]],.] => 2
[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,1] => [1,0,1,1,0,0] => [[.,.],[.,.]] => 2
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0,0] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[.,.],.]]]],.] => 2
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [[.,[.,[[.,.],.]]],.] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [[.,[.,[.,[.,.]]]],[.,.]] => 2
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[.,.],.]],.]],.] => 2
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [[[.,.],.],[.,[.,.]]] => 3
[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [[[.,[.,.]],.],[.,.]] => 3
search for individual values
searching the database for the individual values of this statistic
Description
The number of nodes on the left branch of a binary tree.
Also corresponds to ST000011 after applying the Tamari bijection between binary trees and Dyck path.
Map
to binary tree: left tree, up step, right tree, down step
Description
Return the binary tree corresponding to the Dyck path under the transformation left tree - up step - right tree - down step.
A Dyck path $D$ of semilength $n$ with $n > 1$ may be uniquely decomposed into $L 1 R 0$ for Dyck paths $L,R$ of respective semilengths $n_1,n_2$ with $n_1+n_2 = n-1$.
This map sends $D$ to the binary tree $T$ consisting of a root node with a left child according to $L$ and a right child according to $R$ and then recursively proceeds.
The base case of the unique Dyck path of semilength $1$ is sent to a single node.
This map may also be described as the unique map sending the Tamari orders on Dyck paths to the Tamari order on binary trees.
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 Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.