Identifier
Values
[1] => [1] => [1,0,1,0] => [[.,.],.] => 0
[2] => [1,1] => [1,0,1,1,0,0] => [[.,.],[.,.]] => 1
[1,1] => [2] => [1,1,0,0,1,0] => [[.,[.,.]],.] => 0
[3] => [3] => [1,1,1,0,0,0,1,0] => [[.,[.,[.,.]]],.] => 0
[2,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [[.,.],[.,[.,.]]] => 1
[1,1,1] => [2,1] => [1,0,1,0,1,0] => [[[.,.],.],.] => 0
[4] => [2,2] => [1,1,0,0,1,1,0,0] => [[.,[.,.]],[.,.]] => 1
[3,1] => [3,1] => [1,1,0,1,0,0,1,0] => [[.,[[.,.],.]],.] => 0
[2,2] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [[.,.],[.,[.,[.,.]]]] => 1
[2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [[.,.],[[.,.],.]] => 1
[1,1,1,1] => [4] => [1,1,1,1,0,0,0,0,1,0] => [[.,[.,[.,[.,.]]]],.] => 0
[5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,.]]]]],.] => 0
[4,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => [[[.,.],.],[.,.]] => 1
[3,2] => [3,1,1] => [1,0,1,1,0,0,1,0] => [[[.,.],[.,.]],.] => 1
[3,1,1] => [3,2] => [1,1,0,0,1,0,1,0] => [[[.,[.,.]],.],.] => 0
[2,2,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,.]]]]] => 1
[2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [[.,.],[.,[[.,.],.]]] => 1
[1,1,1,1,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [[.,[.,[[.,.],.]]],.] => 0
[6] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [[.,[.,[.,.]]],[.,.]] => 1
[5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[.,.],.]]]],.] => 0
[4,2] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [[.,.],[[.,.],[.,.]]] => 2
[4,1,1] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [[.,[.,.]],[.,[.,.]]] => 1
[3,3] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => 0
[3,2,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [[.,.],[[.,[.,.]],.]] => 1
[3,1,1,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => [[[[.,.],.],.],.] => 0
[2,2,2] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 1
[2,2,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [[.,.],[.,[.,[[.,.],.]]]] => 1
[2,1,1,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [[.,[[.,.],[.,.]]],.] => 1
[1,1,1,1,1,1] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [[.,[[.,[.,.]],.]],.] => 0
[6,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [[.,[[.,.],.]],[.,.]] => 1
[5,2] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [[.,[.,[[.,.],[.,.]]]],.] => 1
[5,1,1] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [[.,[.,[[.,[.,.]],.]]],.] => 0
[4,3] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [[.,[.,.]],[[.,.],.]] => 1
[4,2,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [[.,.],[.,[[.,.],[.,.]]]] => 2
[4,1,1,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [[[.,.],.],[.,[.,.]]] => 1
[3,3,1] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[[.,.],.]]]]],.] => 0
[3,2,2] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [[.,.],[.,[[.,[.,.]],.]]] => 1
[3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [[.,.],[[[.,.],.],.]] => 1
[3,1,1,1,1] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [[[.,[.,[.,.]]],.],.] => 0
[2,2,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => 1
[2,1,1,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [[[.,.],[.,[.,.]]],.] => 1
[1,1,1,1,1,1,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [[.,[[[.,.],.],.]],.] => 0
[8] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [[.,[.,[.,[.,.]]]],[.,.]] => 1
[6,2] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [[[.,.],[.,.]],[.,.]] => 2
[6,1,1] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [[[.,[.,.]],.],[.,.]] => 1
[5,3] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[.,.]]],.]],.] => 0
[5,2,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [[.,[[.,.],[.,[.,.]]]],.] => 1
[5,1,1,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[.,.],.],.]]],.] => 0
[4,4] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [[.,[.,.]],[.,[.,[.,.]]]] => 1
[4,3,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [[[.,.],.],[[.,.],.]] => 1
[4,2,2] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => 2
[4,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [[.,.],[[.,.],[.,[.,.]]]] => 2
[4,1,1,1,1] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [[[.,[.,.]],[.,.]],.] => 1
[3,3,2] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[.,[.,[.,[[.,.],[.,.]]]]],.] => 1
[3,3,1,1] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[.,[.,.]],.]]]],.] => 0
[3,2,2,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => 1
[3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[.,.],[.,[[[.,.],.],.]]] => 1
[3,1,1,1,1,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [[[.,[[.,.],.]],.],.] => 0
[2,2,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [[.,.],[[.,[.,[.,.]]],.]] => 1
[2,1,1,1,1,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [[[.,.],[[.,.],.]],.] => 1
[8,1] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [[.,[.,[[.,.],.]]],[.,.]] => 1
[6,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [[.,[.,[.,.]]],[.,[.,.]]] => 1
[6,2,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [[.,.],[[.,[.,.]],[.,.]]] => 2
[6,1,1,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [[[[.,.],.],.],[.,.]] => 1
[5,4] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [[.,[[.,[.,.]],[.,.]]],.] => 1
[5,3,1] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[.,.],.]],.]],.] => 0
[5,2,2] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [[[.,.],[.,[.,[.,.]]]],.] => 1
[5,2,1,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [[.,[[.,.],[[.,.],.]]],.] => 1
[5,1,1,1,1] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,.]]]],.],.] => 0
[4,4,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [[[.,.],.],[.,[.,[.,.]]]] => 1
[4,3,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[.,.],[[.,.],[[.,.],.]]] => 2
[4,3,1,1] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [[.,[.,.]],[.,[[.,.],.]]] => 1
[4,2,1,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 2
[4,1,1,1,1,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[[[.,.],.],[.,.]],.] => 1
[3,3,3] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => 0
[3,3,2,1] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => 1
[3,3,1,1,1] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[[.,.],.],.]]]],.] => 0
[3,2,2,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[.,.],[.,[.,[[[.,.],.],.]]]] => 1
[3,2,1,1,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[[[.,.],[.,.]],.],.] => 1
[3,1,1,1,1,1,1] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [[[[.,[.,.]],.],.],.] => 0
[2,2,1,1,1,1,1] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => 1
[2,1,1,1,1,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,.],.]],.]] => 1
[10] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 1
[8,2] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [[.,[[.,.],[.,.]]],[.,.]] => 2
[8,1,1] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[.,.]],.]],[.,.]] => 1
[6,4] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[6,3,1] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [[.,[[.,.],.]],[.,[.,.]]] => 1
[6,2,2] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => 2
[6,2,1,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[.,.],[[[.,.],.],[.,.]]] => 2
[6,1,1,1,1] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [[.,[.,[.,.]]],[[.,.],.]] => 1
[5,4,1] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [[.,[[[.,.],.],[.,.]]],.] => 1
[5,3,2] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [[.,[[[.,.],[.,.]],.]],.] => 1
[5,3,1,1] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [[.,[[[.,[.,.]],.],.]],.] => 0
[5,2,2,1] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => 1
[5,2,1,1,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[[.,.],[.,[[.,.],.]]],.] => 1
[5,1,1,1,1,1] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[.,.],.]]],.],.] => 0
[4,4,2] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 2
[4,4,1,1] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 1
[4,3,3] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => 1
[4,3,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[.,.],[.,[[.,.],[[.,.],.]]]] => 2
[4,3,1,1,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[[.,.],.],[.,[[.,.],.]]] => 1
>>> Load all 381 entries. <<<
[4,2,1,1,1,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[.,.],[[[.,.],[.,.]],.]] => 2
[4,1,1,1,1,1,1] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [[.,[.,.]],[[.,[.,.]],.]] => 1
[3,3,3,1] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[.,[.,[[.,[[.,.],.]],.]]],.] => 0
[3,3,2,2] => [6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => 1
[3,3,2,1,1] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[.,[.,[[.,.],[[.,.],.]]]],.] => 1
[3,3,1,1,1,1] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => 0
[3,2,1,1,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[.,.],[[[.,[.,.]],.],.]] => 1
[3,1,1,1,1,1,1,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[[[[.,.],.],.],.],.] => 0
[2,2,1,1,1,1,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[.,.],[.,[[.,[[.,.],.]],.]]] => 1
[10,1] => [5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => 1
[8,3] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [[[.,[.,[.,.]]],.],[.,.]] => 1
[8,2,1] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => [[[.,.],[.,[.,.]]],[.,.]] => 2
[8,1,1,1] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => [[.,[[[.,.],.],.]],[.,.]] => 1
[6,5] => [5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[[.,[.,[.,.]]],[.,.]],.] => 1
[6,4,1] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => [[[.,.],.],[[.,.],[.,.]]] => 2
[6,3,2] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => [[[.,.],[.,.]],[.,[.,.]]] => 2
[6,3,1,1] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => [[[.,[.,.]],.],[.,[.,.]]] => 1
[6,2,1,1,1] => [3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [[.,.],[.,[[[.,.],.],[.,.]]]] => 2
[6,1,1,1,1,1] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,.],.]],[[.,.],.]] => 1
[5,4,2] => [5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => [[[.,.],[[.,.],[.,.]]],.] => 2
[5,4,1,1] => [5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => [[[.,[.,.]],[.,[.,.]]],.] => 1
[5,3,3] => [6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,[.,.]]]]],.],.] => 0
[5,3,2,1] => [5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => [[[.,.],[[.,[.,.]],.]],.] => 1
[5,3,1,1,1] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[.,.],.],.],.]],.] => 0
[5,2,2,1,1] => [5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[.,.],[[.,[.,[[.,.],.]]],.]] => 1
[5,2,1,1,1,1] => [5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => [[[.,[[.,.],[.,.]]],.],.] => 1
[5,1,1,1,1,1,1] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[.,.]],.]],.],.] => 0
[4,4,3] => [3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => 1
[4,4,1,1,1] => [2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 1
[4,3,3,1] => [6,2,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [[.,[.,[[[.,.],.],[.,.]]]],.] => 1
[4,3,2,1,1] => [3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [[.,.],[[.,.],[.,[[.,.],.]]]] => 2
[4,3,1,1,1,1] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => [[.,[.,.]],[[[.,.],.],.]] => 1
[4,2,1,1,1,1,1] => [4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [[.,.],[.,[[[.,.],[.,.]],.]]] => 2
[4,1,1,1,1,1,1,1] => [4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [[[.,.],.],[[.,[.,.]],.]] => 1
[3,3,3,2] => [6,3,1,1] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [[.,[.,[[[.,.],[.,.]],.]]],.] => 1
[3,3,3,1,1] => [6,3,2] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[.,[.,.]],.],.]]],.] => 0
[3,3,2,2,1] => [6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => 1
[3,3,2,1,1,1] => [6,2,1,1,1] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [[.,[[.,.],[.,[[.,.],.]]]],.] => 1
[3,3,1,1,1,1,1] => [6,4,1] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[[.,.],.]]],.]],.] => 0
[3,2,2,1,1,1,1] => [4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [[.,.],[.,[[[.,[.,.]],.],.]]] => 1
[3,2,1,1,1,1,1,1] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [[.,.],[[[[.,.],.],.],.]] => 1
[10,2] => [5,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => 2
[10,1,1] => [5,5,2] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => 1
[8,4] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[.,.]],[.,.]],[.,.]] => 2
[8,3,1] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [[[.,[[.,.],.]],.],[.,.]] => 1
[8,2,2] => [4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => 2
[8,2,1,1] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => [[[.,.],[[.,.],.]],[.,.]] => 2
[8,1,1,1,1] => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 1
[6,6] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 1
[6,5,1] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => [[[.,[[.,.],.]],[.,.]],.] => 1
[6,4,2] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [[.,.],[[.,.],[[.,.],[.,.]]]] => 3
[6,4,1,1] => [3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => 2
[6,3,3] => [6,3,3] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => 1
[6,3,2,1] => [3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => 2
[6,3,1,1,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[[[.,.],.],.],[.,[.,.]]] => 1
[6,2,1,1,1,1] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [[[.,.],[.,.]],[[.,.],.]] => 2
[6,1,1,1,1,1,1] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [[[.,[.,.]],.],[[.,.],.]] => 1
[5,4,3] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [[[.,[.,.]],[[.,.],.]],.] => 1
[5,4,2,1] => [5,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [[.,.],[[.,[[.,.],[.,.]]],.]] => 2
[5,4,1,1,1] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [[[[.,.],.],[.,[.,.]]],.] => 1
[5,3,3,1] => [6,5,1] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[[.,.],.]]]],.],.] => 0
[5,3,2,2] => [5,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,[.,.]],.]],.]] => 1
[5,3,2,1,1] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [[[.,.],[[[.,.],.],.]],.] => 1
[5,3,1,1,1,1] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[.,.]]],.],.],.] => 0
[5,2,1,1,1,1,1] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [[[[.,.],[.,[.,.]]],.],.] => 1
[5,1,1,1,1,1,1,1] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[.,.],.],.]],.],.] => 0
[4,4,3,1] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[[.,.],.],[.,[.,[[.,.],.]]]] => 1
[4,4,1,1,1,1] => [4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => 1
[4,3,3,2] => [6,2,2,1,1] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [[.,[[.,.],[[.,.],[.,.]]]],.] => 2
[4,3,3,1,1] => [6,2,2,2] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => 1
[4,3,1,1,1,1,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[[.,.],.],[[[.,.],.],.]] => 1
[4,2,1,1,1,1,1,1] => [4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [[.,.],[[.,.],[[.,[.,.]],.]]] => 2
[3,3,3,2,1] => [6,3,1,1,1] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [[.,[[.,.],[[.,[.,.]],.]]],.] => 1
[3,3,3,1,1,1] => [6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[[.,.],.],.],.]]],.] => 0
[3,3,2,2,1,1] => [6,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [[[.,.],[.,[.,[[.,.],.]]]],.] => 1
[3,3,2,1,1,1,1] => [6,4,1,1] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [[.,[[.,[[.,.],[.,.]]],.]],.] => 1
[3,3,1,1,1,1,1,1] => [6,4,2] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[.,[.,.]],.]],.]],.] => 0
[3,2,1,1,1,1,1,1,1] => [4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [[.,.],[.,[[[[.,.],.],.],.]]] => 1
[10,3] => [5,5,3] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => 1
[10,2,1] => [5,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => 2
[10,1,1,1] => [5,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [[.,[.,[[[.,.],.],.]]],[.,.]] => 1
[8,5] => [5,4,4] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => 1
[8,4,1] => [4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],[.,.]],[.,.]] => 2
[8,3,2] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => [[[[.,.],[.,.]],.],[.,.]] => 2
[8,3,1,1] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [[[[.,[.,.]],.],.],[.,.]] => 1
[8,2,1,1,1] => [4,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [[.,.],[[.,[[.,.],.]],[.,.]]] => 2
[8,1,1,1,1,1] => [4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => 1
[6,6,1] => [3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => 1
[6,5,2] => [5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [[[[.,.],[.,.]],[.,.]],.] => 2
[6,5,1,1] => [5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => [[[[.,[.,.]],.],[.,.]],.] => 1
[6,4,3] => [3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2
[6,4,1,1,1] => [3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [[[.,.],.],[.,[[.,.],[.,.]]]] => 2
[6,3,3,1] => [6,3,3,1] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [[.,[[.,[[.,.],.]],[.,.]]],.] => 1
[6,3,2,1,1] => [3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [[.,.],[[[.,.],.],[.,[.,.]]]] => 2
[6,3,1,1,1,1] => [4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => 1
[6,2,1,1,1,1,1] => [4,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [[.,.],[[.,[.,.]],[[.,.],.]]] => 2
[6,1,1,1,1,1,1,1] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [[[[.,.],.],.],[[.,.],.]] => 1
[5,4,4] => [5,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => 1
[5,4,3,1] => [5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => [[[[.,.],.],[[.,.],.]],.] => 1
[5,4,2,1,1] => [5,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [[.,.],[[[.,.],[.,[.,.]]],.]] => 2
[5,4,1,1,1,1] => [5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => [[[[.,[.,.]],[.,.]],.],.] => 1
[5,3,3,2] => [6,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [[[.,[.,[[.,.],[.,.]]]],.],.] => 1
[5,3,3,1,1] => [6,5,2] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[.,[.,.]],.]]],.],.] => 0
[5,3,2,1,1,1] => [5,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [[.,.],[[.,[[[.,.],.],.]],.]] => 1
[5,3,1,1,1,1,1] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[.,.],.]],.],.],.] => 0
[5,2,2,1,1,1,1] => [5,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [[.,.],[[[.,[.,[.,.]]],.],.]] => 1
[5,2,1,1,1,1,1,1] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => [[[[.,.],[[.,.],.]],.],.] => 1
[4,4,1,1,1,1,1] => [4,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [[[.,.],.],[.,[[.,[.,.]],.]]] => 1
[4,3,3,3] => [6,3,2,2] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [[.,[[.,[.,.]],[[.,.],.]]],.] => 1
[4,3,3,2,1] => [6,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [[[.,.],[.,[[.,.],[.,.]]]],.] => 2
[4,3,3,1,1,1] => [6,2,2,2,1] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [[.,[[[.,.],.],[.,[.,.]]]],.] => 1
[4,3,2,1,1,1,1] => [4,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [[.,.],[[.,.],[[[.,.],.],.]]] => 2
[4,3,1,1,1,1,1,1] => [4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [[.,[.,.]],[.,[[[.,.],.],.]]] => 1
[3,3,3,2,2] => [6,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [[[.,.],[.,[[.,[.,.]],.]]],.] => 1
[3,3,3,2,1,1] => [6,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [[.,[[.,.],[[[.,.],.],.]]],.] => 1
[3,3,3,1,1,1,1] => [6,4,3] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [[.,[[[.,[.,[.,.]]],.],.]],.] => 0
[3,3,2,1,1,1,1,1] => [6,4,1,1,1] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [[.,[[[.,.],[.,[.,.]]],.]],.] => 1
[3,3,1,1,1,1,1,1,1] => [6,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[[.,.],.],.]],.]],.] => 0
[10,4] => [5,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => 2
[10,3,1] => [5,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[[.,.],.]],.]],[.,.]] => 1
[10,2,2] => [5,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => 2
[10,2,1,1] => [5,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [[.,[[.,.],[[.,.],.]]],[.,.]] => 2
[10,1,1,1,1] => [5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => 1
[8,6] => [4,4,3,3] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => 2
[8,5,1] => [5,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[.,[.,[[.,.],.]]],[[.,.],.]] => 1
[8,4,2] => [4,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [[.,.],[[[.,.],[.,.]],[.,.]]] => 3
[8,4,1,1] => [4,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => 2
[8,3,3] => [6,4,4] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => 1
[8,3,2,1] => [4,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [[.,.],[[[.,[.,.]],.],[.,.]]] => 2
[8,3,1,1,1] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[.,.],.],.],.],[.,.]] => 1
[8,2,1,1,1,1] => [4,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => 2
[8,1,1,1,1,1,1] => [4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => 1
[6,6,2] => [3,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => 2
[6,6,1,1] => [3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => 1
[6,5,3] => [5,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => 1
[6,5,2,1] => [5,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[.,.],[[[.,[.,.]],[.,.]],.]] => 2
[6,5,1,1,1] => [5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [[[[[.,.],.],.],[.,.]],.] => 1
[6,4,3,1] => [3,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [[[.,.],.],[[.,.],[.,[.,.]]]] => 2
[6,4,1,1,1,1] => [4,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[.,.]],[[.,.],[[.,.],.]]] => 2
[6,3,3,2] => [6,3,3,1,1] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [[.,[[[.,.],[.,.]],[.,.]]],.] => 2
[6,3,3,1,1] => [6,3,3,2] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [[.,[[[.,[.,.]],.],[.,.]]],.] => 1
[6,3,1,1,1,1,1] => [4,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [[.,[[.,.],.]],[.,[[.,.],.]]] => 1
[6,2,1,1,1,1,1,1] => [4,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [[.,.],[[[.,.],.],[[.,.],.]]] => 2
[5,4,4,1] => [5,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [[[.,.],.],[[.,[.,[.,.]]],.]] => 1
[5,4,3,2] => [5,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [[.,.],[[[.,.],[[.,.],.]],.]] => 2
[5,4,3,1,1] => [5,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[.,.]],[[.,[[.,.],.]],.]] => 1
[5,4,1,1,1,1,1] => [5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [[[[[.,.],.],[.,.]],.],.] => 1
[5,3,3,3] => [6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[.,[.,.]]],.]],.],.] => 0
[5,3,3,2,1] => [6,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [[[.,[[.,.],[.,[.,.]]]],.],.] => 1
[5,3,3,1,1,1] => [6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[[.,.],.],.]]],.],.] => 0
[5,3,2,1,1,1,1] => [5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [[[[[.,.],[.,.]],.],.],.] => 1
[5,3,1,1,1,1,1,1] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,.]],.],.],.],.] => 0
[5,2,1,1,1,1,1,1,1] => [5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [[.,.],[[[.,[[.,.],.]],.],.]] => 1
[4,4,3,3] => [6,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => 1
[4,3,3,3,1] => [6,3,2,2,1] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [[.,[[[.,.],.],[[.,.],.]]],.] => 1
[4,3,3,2,1,1] => [6,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [[[.,.],[[.,.],[.,[.,.]]]],.] => 2
[4,3,3,1,1,1,1] => [6,4,2,2] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [[.,[[[.,[.,.]],[.,.]],.]],.] => 1
[4,3,1,1,1,1,1,1,1] => [4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [[[.,.],.],[.,[[[.,.],.],.]]] => 1
[3,3,3,2,1,1,1] => [6,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [[[.,.],[.,[[[.,.],.],.]]],.] => 1
[3,3,3,1,1,1,1,1] => [6,4,3,1] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [[.,[[[.,[[.,.],.]],.],.]],.] => 0
[3,3,2,2,1,1,1,1] => [6,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [[[.,.],[[.,[.,[.,.]]],.]],.] => 1
[3,3,2,1,1,1,1,1,1] => [6,4,2,1,1] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [[.,[[[.,.],[[.,.],.]],.]],.] => 1
[10,4,1] => [5,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [[.,[[[.,.],.],[.,.]]],[.,.]] => 2
[10,3,2] => [5,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[[.,.],[.,.]],.]],[.,.]] => 2
[10,3,1,1] => [5,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [[.,[[[.,[.,.]],.],.]],[.,.]] => 1
[10,2,1,1,1] => [5,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [[[.,.],[.,[[.,.],.]]],[.,.]] => 2
[10,1,1,1,1,1] => [5,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [[[.,[.,[[.,.],.]]],.],[.,.]] => 1
[8,6,1] => [4,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [[.,[[.,.],.]],[[.,.],[.,.]]] => 2
[8,5,2] => [5,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],[.,.]]],[[.,.],.]] => 2
[8,5,1,1] => [5,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,[.,.]],.]],[[.,.],.]] => 1
[8,4,3] => [4,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [[.,[.,.]],[[[.,.],.],[.,.]]] => 2
[8,4,1,1,1] => [4,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [[[.,.],.],[[.,[.,.]],[.,.]]] => 2
[8,3,3,1] => [6,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [[[.,[.,[[.,.],.]]],[.,.]],.] => 1
[8,3,2,1,1] => [4,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [[.,.],[[[[.,.],.],.],[.,.]]] => 2
[8,3,1,1,1,1] => [4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => 1
[8,2,1,1,1,1,1] => [4,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => 2
[8,1,1,1,1,1,1,1] => [4,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [[.,[[[.,.],.],.]],[.,[.,.]]] => 1
[6,6,1,1,1] => [3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 1
[6,5,4] => [5,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [[.,[.,.]],[[[.,.],[.,.]],.]] => 2
[6,5,3,1] => [5,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[[.,.],.]],[[.,[.,.]],.]] => 1
[6,5,2,1,1] => [5,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [[.,.],[[[[.,.],.],[.,.]],.]] => 2
[6,5,1,1,1,1] => [5,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [[.,[.,[.,.]]],[[[.,.],.],.]] => 1
[6,4,1,1,1,1,1] => [4,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [[[.,.],.],[[.,.],[[.,.],.]]] => 2
[6,3,3,3] => [6,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => 1
[6,3,3,2,1] => [6,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [[[.,.],[[.,[.,.]],[.,.]]],.] => 2
[6,3,3,1,1,1] => [6,3,3,2,1] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[.,[[[[.,.],.],.],[.,.]]],.] => 1
[6,3,2,1,1,1,1] => [4,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [[[.,.],[.,.]],[.,[[.,.],.]]] => 2
[6,3,1,1,1,1,1,1] => [4,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [[[.,[.,.]],.],[.,[[.,.],.]]] => 1
[5,4,3,3] => [6,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [[[.,[[.,[.,.]],[.,.]]],.],.] => 1
[5,4,3,1,1,1] => [5,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [[[.,.],.],[[.,[[.,.],.]],.]] => 1
[5,4,2,1,1,1,1] => [5,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [[.,.],[[[[.,.],[.,.]],.],.]] => 2
[5,4,1,1,1,1,1,1] => [5,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [[.,[.,.]],[[[.,[.,.]],.],.]] => 1
[5,3,3,3,1] => [6,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[[.,.],.]],.]],.],.] => 0
[5,3,3,2,2] => [6,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[[.,.],[.,[.,[.,.]]]],.],.] => 1
[5,3,3,2,1,1] => [6,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [[[.,[[.,.],[[.,.],.]]],.],.] => 1
[5,3,3,1,1,1,1] => [6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[.,[.,.]]]],.],.],.] => 0
[5,3,2,1,1,1,1,1] => [5,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[.,.],[[[[.,[.,.]],.],.],.]] => 1
[5,3,1,1,1,1,1,1,1] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,.],.],.],.],.],.] => 0
[4,4,3,3,1] => [6,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[[.,.],.],[.,[.,[.,.]]]],.] => 1
[4,3,3,3,2] => [6,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [[[.,.],[[.,.],[[.,.],.]]],.] => 2
[4,3,3,3,1,1] => [6,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [[[.,[.,.]],[.,[[.,.],.]]],.] => 1
[4,3,3,1,1,1,1,1] => [6,4,2,2,1] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [[.,[[[[.,.],.],[.,.]],.]],.] => 1
[3,3,3,2,1,1,1,1] => [6,4,3,1,1] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [[.,[[[[.,.],[.,.]],.],.]],.] => 1
[3,3,3,1,1,1,1,1,1] => [6,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[.,[.,.]],.],.],.]],.] => 0
[3,3,2,1,1,1,1,1,1,1] => [6,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [[[.,.],[[.,[[.,.],.]],.]],.] => 1
[10,6] => [5,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => 2
[10,4,2] => [5,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [[[.,.],[[.,.],[.,.]]],[.,.]] => 3
[10,4,1,1] => [5,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => 2
[10,3,2,1] => [5,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[.,.],[[.,[.,.]],.]],[.,.]] => 2
[10,3,1,1,1] => [5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[.,[[[[.,.],.],.],.]],[.,.]] => 1
[10,2,1,1,1,1] => [5,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [[[.,[[.,.],[.,.]]],.],[.,.]] => 2
[10,1,1,1,1,1,1] => [5,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [[[.,[[.,[.,.]],.]],.],[.,.]] => 1
[8,6,2] => [4,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [[[.,.],[.,.]],[[.,.],[.,.]]] => 3
[8,6,1,1] => [4,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [[[.,[.,.]],.],[[.,.],[.,.]]] => 2
[8,5,3] => [5,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [[[.,[.,[.,.]]],.],[[.,.],.]] => 1
[8,5,2,1] => [5,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [[[.,.],[.,[.,.]]],[[.,.],.]] => 2
[8,5,1,1,1] => [5,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[.,[[[.,.],.],.]],[[.,.],.]] => 1
[8,4,3,1] => [4,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [[[.,.],.],[[[.,.],.],[.,.]]] => 2
[8,4,1,1,1,1] => [4,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => 2
[8,3,3,2] => [6,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [[[.,[[.,.],[.,.]]],[.,.]],.] => 2
[8,3,3,1,1] => [6,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [[[.,[[.,[.,.]],.]],[.,.]],.] => 1
[8,3,1,1,1,1,1] => [4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [[[.,[[.,.],.]],.],[.,[.,.]]] => 1
[8,2,1,1,1,1,1,1] => [4,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [[[.,.],[[.,.],.]],[.,[.,.]]] => 2
[6,5,4,1] => [5,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [[[.,.],.],[[[.,.],[.,.]],.]] => 2
[6,5,3,2] => [5,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[[.,.],[.,.]],[[.,[.,.]],.]] => 2
[6,5,3,1,1] => [5,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [[[.,[.,.]],.],[[.,[.,.]],.]] => 1
[6,5,1,1,1,1,1] => [5,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[.,[[.,.],.]],[[[.,.],.],.]] => 1
[6,4,3,3] => [6,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [[[.,[.,.]],[[.,.],[.,.]]],.] => 2
[6,3,3,3,1] => [6,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [[[.,[[.,.],.]],[.,[.,.]]],.] => 1
[6,3,3,2,1,1] => [6,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [[[.,.],[[[.,.],.],[.,.]]],.] => 2
[6,3,3,1,1,1,1] => [6,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [[[.,[.,[.,.]]],[[.,.],.]],.] => 1
[6,3,1,1,1,1,1,1,1] => [4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [[[[.,.],.],.],[.,[[.,.],.]]] => 1
[5,4,3,3,1] => [6,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [[[.,[[[.,.],.],[.,.]]],.],.] => 1
[5,4,3,1,1,1,1] => [5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[.,[.,.]],[[[[.,.],.],.],.]] => 1
[5,4,1,1,1,1,1,1,1] => [5,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[[.,.],.],[[[.,[.,.]],.],.]] => 1
[5,3,3,3,2] => [6,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [[[.,[[[.,.],[.,.]],.]],.],.] => 1
[5,3,3,3,1,1] => [6,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[.,[.,.]],.],.]],.],.] => 0
[5,3,3,2,1,1,1] => [6,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [[[[.,.],[.,[[.,.],.]]],.],.] => 1
[5,3,3,1,1,1,1,1] => [6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[[.,.],.]]],.],.],.] => 0
[5,3,2,1,1,1,1,1,1] => [5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[.,.],[[[[[.,.],.],.],.],.]] => 1
[4,3,3,3,1,1,1] => [6,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [[[[.,.],.],[.,[[.,.],.]]],.] => 1
[4,3,3,2,1,1,1,1] => [6,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [[[.,.],[[[.,.],[.,.]],.]],.] => 2
[4,3,3,1,1,1,1,1,1] => [6,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [[[.,[.,.]],[[.,[.,.]],.]],.] => 1
[3,3,3,2,1,1,1,1,1] => [6,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [[[.,.],[[[.,[.,.]],.],.]],.] => 1
[3,3,3,1,1,1,1,1,1,1] => [6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[[.,.],.],.],.],.]],.] => 0
[10,6,1] => [5,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[[.,.],.]],[.,.]],[.,.]] => 2
[10,4,3] => [5,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[[.,.],.]],[.,.]] => 2
[10,4,1,1,1] => [5,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[[.,.],.],[.,[.,.]]],[.,.]] => 2
[10,3,2,1,1] => [5,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [[[.,.],[[[.,.],.],.]],[.,.]] => 2
[10,3,1,1,1,1] => [5,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[[[.,[.,[.,.]]],.],.],[.,.]] => 1
[10,2,1,1,1,1,1] => [5,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[[.,.],[.,[.,.]]],.],[.,.]] => 2
[10,1,1,1,1,1,1,1] => [5,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[[.,[[[.,.],.],.]],.],[.,.]] => 1
[8,6,1,1,1] => [4,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [[[[.,.],.],.],[[.,.],[.,.]]] => 2
[8,5,4] => [5,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[[.,[.,.]],[.,.]],[[.,.],.]] => 2
[8,5,3,1] => [5,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[[.,[[.,.],.]],.],[[.,.],.]] => 1
[8,5,2,1,1] => [5,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [[[.,.],[[.,.],.]],[[.,.],.]] => 2
[8,4,1,1,1,1,1] => [4,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[[[.,.],.],[.,.]],[.,[.,.]]] => 2
[8,3,3,3] => [6,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[[[.,[.,[.,.]]],.],[.,.]],.] => 1
[8,3,3,2,1] => [6,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[[.,.],[.,[.,.]]],[.,.]],.] => 2
[8,3,3,1,1,1] => [6,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[[.,[[[.,.],.],.]],[.,.]],.] => 1
[8,3,2,1,1,1,1] => [4,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[[.,.],[.,.]],.],[.,[.,.]]] => 2
[8,3,1,1,1,1,1,1] => [4,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[[[.,[.,.]],.],.],[.,[.,.]]] => 1
[6,5,3,3] => [6,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[[[.,[.,[.,.]]],[.,.]],.],.] => 1
[6,5,3,1,1,1] => [5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [[[[.,.],.],.],[[.,[.,.]],.]] => 1
[6,5,2,1,1,1,1] => [5,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [[[.,.],[.,.]],[[[.,.],.],.]] => 2
[6,5,1,1,1,1,1,1] => [5,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[[.,[.,.]],.],[[[.,.],.],.]] => 1
[6,4,3,3,1] => [6,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [[[[.,.],.],[[.,.],[.,.]]],.] => 2
[6,3,3,3,2] => [6,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[[.,.],[.,.]],[.,[.,.]]],.] => 2
[6,3,3,3,1,1] => [6,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[[[.,[.,.]],.],[.,[.,.]]],.] => 1
[6,3,3,1,1,1,1,1] => [6,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[[.,[[.,.],.]],[[.,.],.]],.] => 1
[5,4,3,3,2] => [6,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [[[[.,.],[[.,.],[.,.]]],.],.] => 2
[5,4,3,3,1,1] => [6,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[[[.,[.,.]],[.,[.,.]]],.],.] => 1
[5,4,3,1,1,1,1,1] => [5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[[.,.],.],[[[[.,.],.],.],.]] => 1
[5,3,3,3,2,1] => [6,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [[[[.,.],[[.,[.,.]],.]],.],.] => 1
[5,3,3,3,1,1,1] => [6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[[.,.],.],.],.]],.],.] => 0
[5,3,3,2,1,1,1,1] => [6,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[[[.,[[.,.],[.,.]]],.],.],.] => 1
[5,3,3,1,1,1,1,1,1] => [6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[.,[.,.]],.]],.],.],.] => 0
[4,3,3,3,1,1,1,1] => [6,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[[.,[.,.]],[[[.,.],.],.]],.] => 1
[4,3,3,1,1,1,1,1,1,1] => [6,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [[[[.,.],.],[[.,[.,.]],.]],.] => 1
[3,3,3,2,1,1,1,1,1,1] => [6,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [[[.,.],[[[[.,.],.],.],.]],.] => 1
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Description
The number of occurrences of the contiguous pattern [[.,.],[.,.]] in a binary tree.
Equivalently, this is the number of branches in the tree, i.e. the number of nodes with two children. Binary trees avoiding this pattern are counted by $2^{n-2}$.
Map
Glaisher-Franklin
Description
The Glaisher-Franklin bijection on integer partitions.
This map sends the set of even part sizes, each divided by two, to the set of repeated part sizes, see [1, 3.3.1].
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 Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.