Identifier
Values
[1] => [1,0,1,0] => [.,[.,.]] => 1
[2] => [1,1,0,0,1,0] => [[.,.],[.,.]] => 0
[1,1] => [1,0,1,1,0,0] => [.,[[.,.],.]] => 2
[3] => [1,1,1,0,0,0,1,0] => [[[.,.],.],[.,.]] => 1
[2,1] => [1,0,1,0,1,0] => [.,[.,[.,.]]] => 2
[1,1,1] => [1,0,1,1,1,0,0,0] => [.,[[[.,.],.],.]] => 3
[4] => [1,1,1,1,0,0,0,0,1,0] => [[[[.,.],.],.],[.,.]] => 2
[3,1] => [1,1,0,1,0,0,1,0] => [[.,[.,.]],[.,.]] => 1
[2,2] => [1,1,0,0,1,1,0,0] => [[.,.],[[.,.],.]] => 1
[2,1,1] => [1,0,1,1,0,1,0,0] => [.,[[.,[.,.]],.]] => 3
[1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [.,[[[[.,.],.],.],.]] => 4
[5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [[[[[.,.],.],.],.],[.,.]] => 3
[4,1] => [1,1,1,0,1,0,0,0,1,0] => [[[.,[.,.]],.],[.,.]] => 2
[3,2] => [1,1,0,0,1,0,1,0] => [[.,.],[.,[.,.]]] => 1
[3,1,1] => [1,0,1,1,0,0,1,0] => [.,[[.,.],[.,.]]] => 1
[2,2,1] => [1,0,1,0,1,1,0,0] => [.,[.,[[.,.],.]]] => 3
[2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [.,[[[.,[.,.]],.],.]] => 4
[1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [.,[[[[[.,.],.],.],.],.]] => 5
[6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[[[[[.,.],.],.],.],.],[.,.]] => 4
[5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [[[[.,[.,.]],.],.],[.,.]] => 3
[4,2] => [1,1,1,0,0,1,0,0,1,0] => [[[.,.],[.,.]],[.,.]] => 0
[4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [[.,[[.,.],.]],[.,.]] => 2
[3,3] => [1,1,1,0,0,0,1,1,0,0] => [[[.,.],.],[[.,.],.]] => 2
[3,2,1] => [1,0,1,0,1,0,1,0] => [.,[.,[.,[.,.]]]] => 3
[3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [.,[[[.,.],[.,.]],.]] => 2
[2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [[.,.],[[[.,.],.],.]] => 2
[2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [.,[[.,[[.,.],.]],.]] => 4
[2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [.,[[[[.,[.,.]],.],.],.]] => 5
[1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [.,[[[[[[.,.],.],.],.],.],.]] => 6
[6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [[[[[.,[.,.]],.],.],.],[.,.]] => 4
[5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [[[[.,.],[.,.]],.],[.,.]] => 1
[5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [[[.,[[.,.],.]],.],[.,.]] => 3
[4,3] => [1,1,1,0,0,0,1,0,1,0] => [[[.,.],.],[.,[.,.]]] => 2
[4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [[.,[.,[.,.]]],[.,.]] => 2
[4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [.,[[[.,.],.],[.,.]]] => 2
[3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [[.,[.,.]],[[.,.],.]] => 2
[3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [[.,.],[[.,[.,.]],.]] => 2
[3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [.,[[.,[.,[.,.]]],.]] => 4
[3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [.,[[[[.,.],[.,.]],.],.]] => 3
[2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [.,[.,[[[.,.],.],.]]] => 4
[2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [.,[[[.,[[.,.],.]],.],.]] => 5
[2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [.,[[[[[.,[.,.]],.],.],.],.]] => 6
[1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [.,[[[[[[[.,.],.],.],.],.],.],.]] => 7
[6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [[[[[.,.],[.,.]],.],.],[.,.]] => 2
[6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[[[.,[[.,.],.]],.],.],[.,.]] => 4
[5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [[[[.,.],.],[.,.]],[.,.]] => 1
[5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [[[.,[.,[.,.]]],.],[.,.]] => 3
[5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [[.,[[[.,.],.],.]],[.,.]] => 3
[4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],.]] => 3
[4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [[.,[.,.]],[.,[.,.]]] => 2
[4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [[.,.],[[.,.],[.,.]]] => 0
[4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [.,[[.,[.,.]],[.,.]]] => 2
[4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [.,[[[[.,.],.],[.,.]],.]] => 3
[3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [[.,.],[.,[[.,.],.]]] => 2
[3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [.,[[.,.],[[.,.],.]]] => 2
[3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [.,[.,[[.,[.,.]],.]]] => 4
[3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [.,[[[.,[.,[.,.]]],.],.]] => 5
[3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [.,[[[[[.,.],[.,.]],.],.],.]] => 4
[2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [[.,.],[[[[.,.],.],.],.]] => 3
[2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [.,[[.,[[[.,.],.],.]],.]] => 5
[2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [.,[[[[.,[[.,.],.]],.],.],.]] => 6
[2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [.,[[[[[[.,[.,.]],.],.],.],.],.]] => 7
[6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [[[[[.,.],.],[.,.]],.],[.,.]] => 2
[6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [[[[.,[.,[.,.]]],.],.],[.,.]] => 4
[6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[[.,[[[.,.],.],.]],.],[.,.]] => 4
[5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [[[[.,.],.],.],[.,[.,.]]] => 3
[5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [[[.,[.,.]],[.,.]],[.,.]] => 1
[5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [[[.,.],[[.,.],.]],[.,.]] => 1
[5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [[.,[[.,[.,.]],.]],[.,.]] => 3
[5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [.,[[[[.,.],.],.],[.,.]]] => 3
[4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [[[.,[.,.]],.],[[.,.],.]] => 3
[4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,.]]]] => 2
[4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [.,[[.,.],[.,[.,.]]]] => 2
[4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [.,[.,[[.,.],[.,.]]]] => 2
[4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],[.,.]],.]] => 3
[4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [.,[[[[[.,.],.],[.,.]],.],.]] => 4
[3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [[[.,.],.],[[[.,.],.],.]] => 3
[3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[[.,.],.]]]] => 4
[3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [.,[[[.,.],[[.,.],.]],.]] => 3
[3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [[.,.],[[[.,[.,.]],.],.]] => 3
[3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [.,[[.,[[.,[.,.]],.]],.]] => 5
[3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [.,[[[[.,[.,[.,.]]],.],.],.]] => 6
[3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [.,[[[[[[.,.],[.,.]],.],.],.],.]] => 5
[2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [.,[.,[[[[.,.],.],.],.]]] => 5
[2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [.,[[[.,[[[.,.],.],.]],.],.]] => 6
[2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [.,[[[[[.,[[.,.],.]],.],.],.],.]] => 7
[6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [[[[[.,.],.],.],[.,.]],[.,.]] => 2
[6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[[[.,[.,.]],[.,.]],.],[.,.]] => 2
[6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[[[.,.],[[.,.],.]],.],[.,.]] => 2
[6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[[.,[[.,[.,.]],.]],.],[.,.]] => 4
[6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[.,[[[[.,.],.],.],.]],[.,.]] => 4
[5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[[[[.,.],.],.],.],[[.,.],.]] => 4
[5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,.]],.],[.,[.,.]]] => 3
[5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [[[.,.],[.,[.,.]]],[.,.]] => 1
[5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [[.,[[.,.],[.,.]]],[.,.]] => 1
[5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [[.,[.,[[.,.],.]]],[.,.]] => 3
[5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [.,[[[.,[.,.]],.],[.,.]]] => 3
[5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [.,[[[[[.,.],.],.],[.,.]],.]] => 4
[4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [[[.,.],[.,.]],[[.,.],.]] => 1
[4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [[.,[[.,.],.]],[[.,.],.]] => 3
[4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [[[.,.],.],[[.,[.,.]],.]] => 3
>>> Load all 632 entries. <<<
[4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,.]]]]] => 4
[4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [.,[[[.,.],[.,[.,.]]],.]] => 3
[4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [[.,.],[[[.,.],[.,.]],.]] => 1
[4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [.,[[.,[[.,.],[.,.]]],.]] => 3
[4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [.,[[[[.,[.,.]],[.,.]],.],.]] => 4
[4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [.,[[[[[[.,.],.],[.,.]],.],.],.]] => 5
[3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [[.,[.,.]],[[[.,.],.],.]] => 3
[3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [[.,.],[[.,[[.,.],.]],.]] => 3
[3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [.,[[.,[.,[[.,.],.]]],.]] => 5
[3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [.,[[[[.,.],[[.,.],.]],.],.]] => 4
[3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [.,[.,[[[.,[.,.]],.],.]]] => 5
[3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [.,[[[.,[[.,[.,.]],.]],.],.]] => 6
[3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [.,[[[[[.,[.,[.,.]]],.],.],.],.]] => 7
[2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,.],[[[[[.,.],.],.],.],.]] => 4
[2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [.,[[.,[[[[.,.],.],.],.]],.]] => 6
[2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [.,[[[[.,[[[.,.],.],.]],.],.],.]] => 7
[6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[[[[.,.],.],.],.],[.,[.,.]]] => 4
[6,4,1] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [[[[.,[.,.]],.],[.,.]],[.,.]] => 2
[6,3,2] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [[[[.,.],[.,[.,.]]],.],[.,.]] => 2
[6,3,1,1] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [[[.,[[.,.],[.,.]]],.],[.,.]] => 2
[6,2,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [[[.,[.,[[.,.],.]]],.],[.,.]] => 4
[6,2,1,1,1] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [[.,[[[.,[.,.]],.],.]],[.,.]] => 4
[6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [.,[[[[[.,.],.],.],.],[.,.]]] => 4
[5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [[[[.,[.,.]],.],.],[[.,.],.]] => 4
[5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => [[[.,.],[.,.]],[.,[.,.]]] => 1
[5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => [[.,[[.,.],.]],[.,[.,.]]] => 3
[5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[[.,.],.],[[.,.],[.,.]]] => 1
[5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => [[.,[.,[.,[.,.]]]],[.,.]] => 3
[5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => [.,[[[.,.],[.,.]],[.,.]]] => 1
[5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => [[.,.],[[[.,.],.],[.,.]]] => 1
[5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => [.,[[.,[[.,.],.]],[.,.]]] => 3
[5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [.,[[[[.,[.,.]],.],[.,.]],.]] => 4
[5,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [.,[[[[[[.,.],.],.],[.,.]],.],.]] => 5
[4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [[[.,.],.],[.,[[.,.],.]]] => 3
[4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => [[.,[.,[.,.]]],[[.,.],.]] => 3
[4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => [.,[[[.,.],.],[[.,.],.]]] => 3
[4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => [[.,[.,.]],[[.,[.,.]],.]] => 3
[4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => [[.,.],[[.,[.,[.,.]]],.]] => 3
[4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [.,[[.,[.,[.,[.,.]]]],.]] => 5
[4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [.,[[[[.,.],[.,[.,.]]],.],.]] => 4
[4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [.,[.,[[[.,.],[.,.]],.]]] => 3
[4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [.,[[[.,[[.,.],[.,.]]],.],.]] => 4
[4,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [.,[[[[[.,[.,.]],[.,.]],.],.],.]] => 5
[3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => [[.,.],[.,[[[.,.],.],.]]] => 3
[3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => [.,[[.,.],[[[.,.],.],.]]] => 3
[3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => [.,[.,[[.,[[.,.],.]],.]]] => 5
[3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [.,[[[.,[.,[[.,.],.]]],.],.]] => 6
[3,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [.,[[[[[.,.],[[.,.],.]],.],.],.]] => 5
[3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [[.,.],[[[[.,[.,.]],.],.],.]] => 4
[3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [.,[[.,[[[.,[.,.]],.],.]],.]] => 6
[3,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [.,[[[[.,[[.,[.,.]],.]],.],.],.]] => 7
[2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [.,[.,[[[[[.,.],.],.],.],.]]] => 6
[2,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [.,[[[.,[[[[.,.],.],.],.]],.],.]] => 7
[6,5,1] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [[[[.,[.,.]],.],.],[.,[.,.]]] => 4
[6,4,2] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [[[[.,.],[.,.]],[.,.]],[.,.]] => 0
[6,4,1,1] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [[[.,[[.,.],.]],[.,.]],[.,.]] => 2
[6,3,3] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [[[[.,.],.],[[.,.],.]],[.,.]] => 2
[6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => 4
[6,3,1,1,1] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [[.,[[[.,.],[.,.]],.]],[.,.]] => 2
[6,2,2,2] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [[[.,.],[[[.,.],.],.]],[.,.]] => 2
[6,2,2,1,1] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [[.,[[.,[[.,.],.]],.]],[.,.]] => 4
[6,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [.,[[[[.,[.,.]],.],.],[.,.]]] => 4
[6,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [.,[[[[[[.,.],.],.],.],[.,.]],.]] => 5
[5,5,2] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [[[[.,.],[.,.]],.],[[.,.],.]] => 2
[5,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [[[.,[[.,.],.]],.],[[.,.],.]] => 4
[5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[.,.],.],[.,[.,[.,.]]]] => 3
[5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
[5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [.,[[[.,.],.],[.,[.,.]]]] => 3
[5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => [[.,[.,.]],[[.,.],[.,.]]] => 1
[5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [[.,.],[[.,[.,.]],[.,.]]] => 1
[5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [.,[[.,[.,[.,.]]],[.,.]]] => 3
[5,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [.,[[[[.,.],[.,.]],[.,.]],.]] => 2
[5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [.,[.,[[[.,.],.],[.,.]]]] => 3
[5,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [.,[[[.,[[.,.],.]],[.,.]],.]] => 4
[5,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [.,[[[[[.,[.,.]],.],[.,.]],.],.]] => 5
[4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[[[.,.],.],.],[[[.,.],.],.]] => 4
[4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [[.,[.,.]],[.,[[.,.],.]]] => 3
[4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],.]]] => 1
[4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => [.,[[.,[.,.]],[[.,.],.]]] => 3
[4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [.,[[[[.,.],.],[[.,.],.]],.]] => 4
[4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [[.,.],[.,[[.,[.,.]],.]]] => 3
[4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [.,[[.,.],[[.,[.,.]],.]]] => 3
[4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [.,[.,[[.,[.,[.,.]]],.]]] => 5
[4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [.,[[[.,[.,[.,[.,.]]]],.],.]] => 6
[4,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [.,[[[[[.,.],[.,[.,.]]],.],.],.]] => 5
[4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [[.,.],[[[[.,.],[.,.]],.],.]] => 2
[4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [.,[[.,[[[.,.],[.,.]],.]],.]] => 4
[4,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [.,[[[[.,[[.,.],[.,.]]],.],.],.]] => 5
[3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[[.,.],.],[[[[.,.],.],.],.]] => 4
[3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [.,[.,[.,[[[.,.],.],.]]]] => 5
[3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [.,[[[.,.],[[[.,.],.],.]],.]] => 4
[3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [[.,.],[[[.,[[.,.],.]],.],.]] => 4
[3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [.,[[.,[[.,[[.,.],.]],.]],.]] => 6
[3,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [.,[[[[.,[.,[[.,.],.]]],.],.],.]] => 7
[3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [.,[.,[[[[.,[.,.]],.],.],.]]] => 6
[3,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [.,[[[.,[[[.,[.,.]],.],.]],.],.]] => 7
[2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => 5
[2,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [.,[[.,[[[[[.,.],.],.],.],.]],.]] => 7
[7,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [.,[[[[[[.,.],.],.],.],.],[.,.]]] => 5
[6,5,2] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [[[[.,.],[.,.]],.],[.,[.,.]]] => 2
[6,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [[[.,[[.,.],.]],.],[.,[.,.]]] => 4
[6,4,3] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [[[[.,.],.],[.,[.,.]]],[.,.]] => 2
[6,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => 2
[6,4,1,1,1] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [[.,[[[.,.],.],[.,.]]],[.,.]] => 2
[6,3,3,1] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [[[.,[.,.]],[[.,.],.]],[.,.]] => 2
[6,3,2,2] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [[[.,.],[[.,[.,.]],.]],[.,.]] => 2
[6,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => 4
[6,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [.,[[[[.,.],[.,.]],.],[.,.]]] => 2
[6,2,2,2,1] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [[.,[.,[[[.,.],.],.]]],[.,.]] => 4
[6,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [.,[[[.,[[.,.],.]],.],[.,.]]] => 4
[6,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [.,[[[[[.,[.,.]],.],.],[.,.]],.]] => 5
[5,5,3] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [[[[.,.],.],[.,.]],[[.,.],.]] => 2
[5,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [[[.,[.,[.,.]]],.],[[.,.],.]] => 4
[5,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [[.,[[[.,.],.],.]],[[.,.],.]] => 4
[5,4,4] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [[[[.,.],.],.],[[.,[.,.]],.]] => 4
[5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => [[.,[.,.]],[.,[.,[.,.]]]] => 3
[5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,.]]]] => 1
[5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => [.,[[.,[.,.]],[.,[.,.]]]] => 3
[5,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [.,[[[[.,.],.],[.,[.,.]]],.]] => 4
[5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[[.,.],[.,.]]]] => 1
[5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [.,[[.,.],[[.,.],[.,.]]]] => 1
[5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => [.,[.,[[.,[.,.]],[.,.]]]] => 3
[5,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [.,[[[.,[.,[.,.]]],[.,.]],.]] => 4
[5,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [.,[[[[[.,.],[.,.]],[.,.]],.],.]] => 3
[5,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [[.,.],[[[[.,.],.],[.,.]],.]] => 2
[5,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [.,[[.,[[[.,.],.],[.,.]]],.]] => 4
[5,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [.,[[[[.,[[.,.],.]],[.,.]],.],.]] => 5
[4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [[[.,[.,.]],.],[[[.,.],.],.]] => 4
[4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[[.,.],.]]]] => 3
[4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => [.,[[.,.],[.,[[.,.],.]]]] => 3
[4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => [.,[.,[[.,.],[[.,.],.]]]] => 3
[4,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [.,[[[.,[.,.]],[[.,.],.]],.]] => 4
[4,4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [.,[[[[[.,.],.],[[.,.],.]],.],.]] => 5
[4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [[[.,.],.],[[[.,[.,.]],.],.]] => 4
[4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [.,[.,[.,[[.,[.,.]],.]]]] => 5
[4,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [.,[[[.,.],[[.,[.,.]],.]],.]] => 4
[4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [[.,.],[[[.,[.,[.,.]]],.],.]] => 4
[4,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [.,[[.,[[.,[.,[.,.]]],.]],.]] => 6
[4,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [.,[[[[.,[.,[.,[.,.]]]],.],.],.]] => 7
[4,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [.,[.,[[[[.,.],[.,.]],.],.]]] => 4
[4,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [.,[[[.,[[[.,.],[.,.]],.]],.],.]] => 5
[3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [[.,[.,.]],[[[[.,.],.],.],.]] => 4
[3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [[.,.],[[.,[[[.,.],.],.]],.]] => 4
[3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [.,[[.,[.,[[[.,.],.],.]]],.]] => 6
[3,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [.,[[[[.,.],[[[.,.],.],.]],.],.]] => 5
[3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [.,[.,[[[.,[[.,.],.]],.],.]]] => 6
[3,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [.,[[[.,[[.,[[.,.],.]],.]],.],.]] => 7
[3,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[.,.],[[[[[.,[.,.]],.],.],.],.]] => 5
[3,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [.,[[.,[[[[.,[.,.]],.],.],.]],.]] => 7
[2,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [.,[.,[[[[[[.,.],.],.],.],.],.]]] => 7
[7,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [.,[[[[[.,[.,.]],.],.],.],[.,.]]] => 5
[6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [[[[.,.],.],[.,.]],[.,[.,.]]] => 2
[6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => 4
[6,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [[.,[[[.,.],.],.]],[.,[.,.]]] => 4
[6,4,4] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[[[.,.],.],.],[[.,.],[.,.]]] => 2
[6,4,3,1] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => 2
[6,4,2,2] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [[[.,.],[[.,.],[.,.]]],[.,.]] => 0
[6,4,2,1,1] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => 2
[6,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [.,[[[[.,.],.],[.,.]],[.,.]]] => 2
[6,3,3,2] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [[[.,.],[.,[[.,.],.]]],[.,.]] => 2
[6,3,3,1,1] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [[.,[[.,.],[[.,.],.]]],[.,.]] => 2
[6,3,2,2,1] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => 4
[6,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [.,[[[.,[.,[.,.]]],.],[.,.]]] => 4
[6,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [.,[[[[[.,.],[.,.]],.],[.,.]],.]] => 3
[6,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[.,.],[[[[.,.],.],.],[.,.]]] => 2
[6,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [.,[[.,[[[.,.],.],.]],[.,.]]] => 4
[6,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [.,[[[[.,[[.,.],.]],.],[.,.]],.]] => 5
[5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[[[.,.],.],.],[.,[[.,.],.]]] => 4
[5,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[.,.]],[[.,.],.]] => 2
[5,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [[[.,.],[[.,.],.]],[[.,.],.]] => 2
[5,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [[.,[[.,[.,.]],.]],[[.,.],.]] => 4
[5,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [.,[[[[.,.],.],.],[[.,.],.]]] => 4
[5,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[[.,[.,.]],.],[[.,[.,.]],.]] => 4
[5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,.]]]]] => 3
[5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [.,[[.,.],[.,[.,[.,.]]]]] => 3
[5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [.,[.,[[.,.],[.,[.,.]]]]] => 3
[5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [.,[[[.,[.,.]],[.,[.,.]]],.]] => 4
[5,4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [.,[[[[[.,.],.],[.,[.,.]]],.],.]] => 5
[5,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [[[.,.],.],[[[.,.],[.,.]],.]] => 2
[5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [.,[.,[.,[[.,.],[.,.]]]]] => 3
[5,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,.],[[.,.],[.,.]]],.]] => 2
[5,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,.],[[[.,[.,.]],[.,.]],.]] => 2
[5,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [.,[[.,[[.,[.,.]],[.,.]]],.]] => 4
[5,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [.,[[[[.,[.,[.,.]]],[.,.]],.],.]] => 5
[5,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [.,[.,[[[[.,.],.],[.,.]],.]]] => 4
[5,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [.,[[[.,[[[.,.],.],[.,.]]],.],.]] => 5
[4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [[[.,.],[.,.]],[[[.,.],.],.]] => 2
[4,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [[.,[[.,.],.]],[[[.,.],.],.]] => 4
[4,4,3,3] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [[[.,.],.],[[.,[[.,.],.]],.]] => 4
[4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[[.,.],.]]]]] => 5
[4,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [.,[[[.,.],[.,[[.,.],.]]],.]] => 4
[4,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [[.,.],[[[.,.],[[.,.],.]],.]] => 2
[4,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [.,[[.,[[.,.],[[.,.],.]]],.]] => 4
[4,4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [.,[[[[.,[.,.]],[[.,.],.]],.],.]] => 5
[4,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [[.,[.,.]],[[[.,[.,.]],.],.]] => 4
[4,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,.],[[.,[[.,[.,.]],.]],.]] => 4
[4,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [.,[[.,[.,[[.,[.,.]],.]]],.]] => 6
[4,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [.,[[[[.,.],[[.,[.,.]],.]],.],.]] => 5
[4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [.,[.,[[[.,[.,[.,.]]],.],.]]] => 6
[4,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [.,[[[.,[[.,[.,[.,.]]],.]],.],.]] => 7
[4,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[.,.],[[[[[.,.],[.,.]],.],.],.]] => 3
[4,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [.,[[.,[[[[.,.],[.,.]],.],.]],.]] => 5
[3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[.,.],[.,[[[[.,.],.],.],.]]] => 4
[3,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [.,[[.,.],[[[[.,.],.],.],.]]] => 4
[3,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [.,[.,[[.,[[[.,.],.],.]],.]]] => 6
[3,3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [.,[[[.,[.,[[[.,.],.],.]]],.],.]] => 7
[3,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[.,.],[[[[.,[[.,.],.]],.],.],.]] => 5
[3,3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [.,[[.,[[[.,[[.,.],.]],.],.]],.]] => 7
[3,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [.,[.,[[[[[.,[.,.]],.],.],.],.]]] => 7
[7,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [.,[[[[[.,.],[.,.]],.],.],[.,.]]] => 3
[7,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [.,[[[[.,[[.,.],.]],.],.],[.,.]]] => 5
[6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 4
[6,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => 2
[6,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [[[.,.],[[.,.],.]],[.,[.,.]]] => 2
[6,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => 4
[6,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [.,[[[[.,.],.],.],[.,[.,.]]]] => 4
[6,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [[[.,[.,.]],.],[[.,.],[.,.]]] => 2
[6,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => 2
[6,4,3,1,1] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => 2
[6,4,2,2,1] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => 2
[6,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => 2
[6,4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [.,[[[[[.,.],.],[.,.]],[.,.]],.]] => 3
[6,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[[.,.],.],[[[.,.],.],[.,.]]] => 2
[6,3,3,2,1] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => 4
[6,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [.,[[[.,.],[[.,.],.]],[.,.]]] => 2
[6,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [[.,.],[[[.,[.,.]],.],[.,.]]] => 2
[6,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => 4
[6,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [.,[[[[.,[.,[.,.]]],.],[.,.]],.]] => 5
[6,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [.,[.,[[[[.,.],.],.],[.,.]]]] => 4
[6,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [.,[[[.,[[[.,.],.],.]],[.,.]],.]] => 5
[5,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [[[.,[.,.]],.],[.,[[.,.],.]]] => 4
[5,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [[[.,.],[.,[.,.]]],[[.,.],.]] => 2
[5,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,.],[.,.]]],[[.,.],.]] => 2
[5,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [[.,[.,[[.,.],.]]],[[.,.],.]] => 4
[5,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [.,[[[.,[.,.]],.],[[.,.],.]]] => 4
[5,5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [.,[[[[[.,.],.],.],[[.,.],.]],.]] => 5
[5,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [[[.,.],[.,.]],[[.,[.,.]],.]] => 2
[5,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],.]],[[.,[.,.]],.]] => 4
[5,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [[[.,.],.],[[.,[.,[.,.]]],.]] => 4
[5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,.]]]]]] => 5
[5,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [.,[[[.,.],[.,[.,[.,.]]]],.]] => 4
[5,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [[.,.],[[[.,.],[.,[.,.]]],.]] => 2
[5,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [.,[[.,[[.,.],[.,[.,.]]]],.]] => 4
[5,4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [.,[[[[.,[.,.]],[.,[.,.]]],.],.]] => 5
[5,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[.,.]],[[[.,.],[.,.]],.]] => 2
[5,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [[.,.],[[.,[[.,.],[.,.]]],.]] => 2
[5,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [.,[[.,[.,[[.,.],[.,.]]]],.]] => 4
[5,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [.,[[[[.,.],[[.,.],[.,.]]],.],.]] => 3
[5,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [.,[.,[[[.,[.,.]],[.,.]],.]]] => 4
[5,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [.,[[[.,[[.,[.,.]],[.,.]]],.],.]] => 5
[5,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[.,.],[[[[[.,.],.],[.,.]],.],.]] => 3
[5,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [.,[[.,[[[[.,.],.],[.,.]],.]],.]] => 5
[4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[[.,.],.],[.,[[[.,.],.],.]]] => 4
[4,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [[.,[.,[.,.]]],[[[.,.],.],.]] => 4
[4,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [.,[[[.,.],.],[[[.,.],.],.]]] => 4
[4,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [[.,[.,.]],[[.,[[.,.],.]],.]] => 4
[4,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [[.,.],[[.,[.,[[.,.],.]]],.]] => 4
[4,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [.,[[.,[.,[.,[[.,.],.]]]],.]] => 6
[4,4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [.,[[[[.,.],[.,[[.,.],.]]],.],.]] => 5
[4,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [.,[.,[[[.,.],[[.,.],.]],.]]] => 4
[4,4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [.,[[[.,[[.,.],[[.,.],.]]],.],.]] => 5
[4,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [[.,.],[.,[[[.,[.,.]],.],.]]] => 4
[4,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [.,[[.,.],[[[.,[.,.]],.],.]]] => 4
[4,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [.,[.,[[.,[[.,[.,.]],.]],.]]] => 6
[4,3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [.,[[[.,[.,[[.,[.,.]],.]]],.],.]] => 7
[4,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[.,.],[[[[.,[.,[.,.]]],.],.],.]] => 5
[4,3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [.,[[.,[[[.,[.,[.,.]]],.],.]],.]] => 7
[4,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [.,[.,[[[[[.,.],[.,.]],.],.],.]]] => 5
[3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [.,[.,[.,[[[[.,.],.],.],.]]]] => 6
[3,3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [.,[[[.,.],[[[[.,.],.],.],.]],.]] => 5
[3,3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[.,.],[[[.,[[[.,.],.],.]],.],.]] => 5
[3,3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [.,[[.,[[.,[[[.,.],.],.]],.]],.]] => 7
[3,3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [.,[.,[[[[.,[[.,.],.]],.],.],.]]] => 7
[7,4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [.,[[[[[.,.],.],[.,.]],.],[.,.]]] => 3
[7,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [.,[[[[.,[.,[.,.]]],.],.],[.,.]]] => 5
[7,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [.,[[[.,[[[.,.],.],.]],.],[.,.]]] => 5
[6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => 4
[6,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => 2
[6,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => 2
[6,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => 4
[6,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => 4
[6,5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [.,[[[[[.,.],.],.],[.,[.,.]]],.]] => 5
[6,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [[[.,.],[.,.]],[[.,.],[.,.]]] => 0
[6,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [[.,[[.,.],.]],[[.,.],[.,.]]] => 2
[6,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [[[.,.],.],[[.,[.,.]],[.,.]]] => 2
[6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 4
[6,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => 2
[6,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [[.,.],[[[.,.],[.,.]],[.,.]]] => 0
[6,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => 2
[6,4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => 3
[6,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [[.,[.,.]],[[[.,.],.],[.,.]]] => 2
[6,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [[.,.],[[.,[[.,.],.]],[.,.]]] => 2
[6,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [.,[[.,[.,[[.,.],.]]],[.,.]]] => 4
[6,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [.,[[[[.,.],[[.,.],.]],[.,.]],.]] => 3
[6,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [.,[.,[[[.,[.,.]],.],[.,.]]]] => 4
[6,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => 5
[6,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[.,.],[[[[[.,.],.],.],[.,.]],.]] => 3
[6,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [.,[[.,[[[[.,.],.],.],[.,.]]],.]] => 5
[5,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [[[.,.],[.,.]],[.,[[.,.],.]]] => 2
[5,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [[.,[[.,.],.]],[.,[[.,.],.]]] => 4
[5,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[.,.],.],[[.,.],[[.,.],.]]] => 2
[5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => 4
[5,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [.,[[[.,.],[.,.]],[[.,.],.]]] => 2
[5,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[.,.],[[[.,.],.],[[.,.],.]]] => 2
[5,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [.,[[.,[[.,.],.]],[[.,.],.]]] => 4
[5,5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [.,[[[[.,[.,.]],.],[[.,.],.]],.]] => 5
[5,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [[[.,.],.],[.,[[.,[.,.]],.]]] => 4
[5,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => 4
[5,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [.,[[[.,.],.],[[.,[.,.]],.]]] => 4
[5,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => 4
[5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => 4
[5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [.,[[.,[.,[.,[.,[.,.]]]]],.]] => 6
[5,4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [.,[[[[.,.],[.,[.,[.,.]]]],.],.]] => 5
[5,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [.,[.,[[[.,.],[.,[.,.]]],.]]] => 4
[5,4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [.,[[[.,[[.,.],[.,[.,.]]]],.],.]] => 5
[5,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [[.,.],[.,[[[.,.],[.,.]],.]]] => 2
[5,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [.,[[.,.],[[[.,.],[.,.]],.]]] => 2
[5,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [.,[.,[[.,[[.,.],[.,.]]],.]]] => 4
[5,3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [.,[[[.,[.,[[.,.],[.,.]]]],.],.]] => 5
[5,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[.,.],[[[[.,[.,.]],[.,.]],.],.]] => 3
[5,3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => 5
[5,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [.,[.,[[[[[.,.],.],[.,.]],.],.]]] => 5
[4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [[.,[.,.]],[.,[[[.,.],.],.]]] => 4
[4,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[.,.],[[.,.],[[[.,.],.],.]]] => 2
[4,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [.,[[.,[.,.]],[[[.,.],.],.]]] => 4
[4,4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [.,[[[[.,.],.],[[[.,.],.],.]],.]] => 5
[4,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [[.,.],[.,[[.,[[.,.],.]],.]]] => 4
[4,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [.,[[.,.],[[.,[[.,.],.]],.]]] => 4
[4,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [.,[.,[[.,[.,[[.,.],.]]],.]]] => 6
[4,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [.,[[[.,[.,[.,[[.,.],.]]]],.],.]] => 7
[4,4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[.,.],[[[[.,.],[[.,.],.]],.],.]] => 3
[4,4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [.,[[.,[[[.,.],[[.,.],.]],.]],.]] => 5
[4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [.,[.,[.,[[[.,[.,.]],.],.]]]] => 6
[4,3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [.,[[[.,.],[[[.,[.,.]],.],.]],.]] => 5
[4,3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[.,.],[[[.,[[.,[.,.]],.]],.],.]] => 5
[4,3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => 7
[4,3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [.,[.,[[[[.,[.,[.,.]]],.],.],.]]] => 7
[3,3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[.,.],[[.,[[[[.,.],.],.],.]],.]] => 5
[3,3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [.,[[.,[.,[[[[.,.],.],.],.]]],.]] => 7
[3,3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [.,[.,[[[.,[[[.,.],.],.]],.],.]]] => 7
[7,5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [.,[[[[[.,.],.],.],[.,.]],[.,.]]] => 3
[7,4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [.,[[[[.,[.,.]],[.,.]],.],[.,.]]] => 3
[7,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [.,[[[[.,.],[[.,.],.]],.],[.,.]]] => 3
[7,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [.,[[[.,[[.,[.,.]],.]],.],[.,.]]] => 5
[7,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => 3
[7,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [.,[[.,[[[[.,.],.],.],.]],[.,.]]] => 5
[6,6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [.,[[[[[.,.],.],.],.],[[.,.],.]]] => 5
[6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => 2
[6,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => 4
[6,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[[.,.],.],[[.,.],[.,[.,.]]]] => 2
[6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 4
[6,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => 2
[6,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[.,.],[[[.,.],.],[.,[.,.]]]] => 2
[6,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => 4
[6,5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [.,[[[[.,[.,.]],.],[.,[.,.]]],.]] => 5
[6,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[[.,.],.],[.,[[.,.],[.,.]]]] => 2
[6,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => 2
[6,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [.,[[[.,.],.],[[.,.],[.,.]]]] => 2
[6,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => 2
[6,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => 2
[6,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 4
[6,4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [.,[[[[.,.],[.,[.,.]]],[.,.]],.]] => 3
[6,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => 2
[6,4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [.,[[[.,[[.,.],[.,.]]],[.,.]],.]] => 3
[6,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[.,.],[.,[[[.,.],.],[.,.]]]] => 2
[6,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [.,[[.,.],[[[.,.],.],[.,.]]]] => 2
[6,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [.,[.,[[.,[[.,.],.]],[.,.]]]] => 4
[6,3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [.,[[[.,[.,[[.,.],.]]],[.,.]],.]] => 5
[6,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[.,.],[[[[.,[.,.]],.],[.,.]],.]] => 3
[6,3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [.,[[.,[[[.,[.,.]],.],[.,.]]],.]] => 5
[6,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [.,[.,[[[[[.,.],.],.],[.,.]],.]]] => 5
[5,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[[.,.],.],[.,[.,[[.,.],.]]]] => 4
[5,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => 4
[5,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [.,[[[.,.],.],[.,[[.,.],.]]]] => 4
[5,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[.,[.,.]],[[.,.],[[.,.],.]]] => 2
[5,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[.,.],[[.,[.,.]],[[.,.],.]]] => 2
[5,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => 4
[5,5,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [.,[[[[.,.],[.,.]],[[.,.],.]],.]] => 3
[5,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [.,[.,[[[.,.],.],[[.,.],.]]]] => 4
[5,5,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [.,[[[.,[[.,.],.]],[[.,.],.]],.]] => 5
[5,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => 4
[5,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[.,.],[[.,.],[[.,[.,.]],.]]] => 2
[5,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => 4
[5,4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [.,[[[[.,.],.],[[.,[.,.]],.]],.]] => 5
[5,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => 4
[5,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => 4
[5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [.,[.,[[.,[.,[.,[.,.]]]],.]]] => 6
[5,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[[[.,[.,[.,[.,[.,.]]]]],.],.]] => 7
[5,4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [[.,.],[[[[.,.],[.,[.,.]]],.],.]] => 3
[5,4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [.,[[.,[[[.,.],[.,[.,.]]],.]],.]] => 5
[5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [.,[.,[.,[[[.,.],[.,.]],.]]]] => 4
[5,3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [.,[[[.,.],[[[.,.],[.,.]],.]],.]] => 3
[5,3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [[.,.],[[[.,[[.,.],[.,.]]],.],.]] => 3
[5,3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => 5
[5,3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [.,[.,[[[[.,[.,.]],[.,.]],.],.]]] => 5
[4,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[.,.],[.,[.,[[[.,.],.],.]]]] => 4
[4,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [.,[[.,.],[.,[[[.,.],.],.]]]] => 4
[4,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [.,[.,[[.,.],[[[.,.],.],.]]]] => 4
[4,4,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [.,[[[.,[.,.]],[[[.,.],.],.]],.]] => 5
[4,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [.,[.,[.,[[.,[[.,.],.]],.]]]] => 6
[4,4,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [.,[[[.,.],[[.,[[.,.],.]],.]],.]] => 5
[4,4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [[.,.],[[[.,[.,[[.,.],.]]],.],.]] => 5
[4,4,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [.,[[.,[[.,[.,[[.,.],.]]],.]],.]] => 7
[4,4,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [.,[.,[[[[.,.],[[.,.],.]],.],.]]] => 5
[4,3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [[.,.],[[.,[[[.,[.,.]],.],.]],.]] => 5
[4,3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [.,[[.,[.,[[[.,[.,.]],.],.]]],.]] => 7
[4,3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [.,[.,[[[.,[[.,[.,.]],.]],.],.]]] => 7
[3,3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[.,.],[.,[[[[[.,.],.],.],.],.]]] => 5
[3,3,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [.,[[.,.],[[[[[.,.],.],.],.],.]]] => 5
[3,3,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [.,[.,[[.,[[[[.,.],.],.],.]],.]]] => 7
[6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 6
[5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 6
[6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 4
[5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => 6
[4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [.,[.,[.,[.,[[[.,.],.],.]]]]] => 6
[6,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 4
[5,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => 4
[6,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 4
[5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => 6
[6,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [.,[.,[.,[[[.,.],.],[.,.]]]]] => 4
[6,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 4
[5,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => 4
[6,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => 2
[5,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => 4
[6,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 4
[5,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => 4
[6,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 4
[6,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => 4
[6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 4
[5,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => 4
[6,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => 2
[5,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => 4
[6,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 2
[5,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [.,[[.,.],[[.,.],[[.,.],.]]]] => 2
[6,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => 2
[6,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 4
[5,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => 4
[6,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => 2
[6,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 4
[6,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => 4
[6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 4
[5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => 4
[6,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => 2
[5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => 4
[6,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 2
[5,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[.,.],[.,[[.,.],[[.,.],.]]]] => 2
[6,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => 2
[6,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 2
[5,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[.,.],[[.,.],[.,[[.,.],.]]]] => 2
[6,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[.,.],[[.,.],[[.,.],[.,.]]]] => 0
[6,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => 2
[6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 4
[5,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => 4
[6,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => 2
[6,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => 2
[6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 4
[6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 4
[7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 7
[6,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => 7
[7,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => 5
[6,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => 7
[5,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] => 7
[7,6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => 5
[6,6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => 5
[7,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => 5
[6,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => 7
[5,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [.,[.,[.,[.,[[.,[[.,.],.]],.]]]]] => 7
[7,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] => 5
[6,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [.,[.,[.,[.,[[[.,.],[.,.]],.]]]]] => 5
[5,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [.,[.,[.,[.,[[[.,[.,.]],.],.]]]]] => 7
[4,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => 7
[6,6,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => 5
[6,5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => 7
[6,5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [.,[.,[.,[[[.,.],[.,[.,.]]],.]]]] => 5
[6,4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [.,[.,[.,[[[.,[.,.]],[.,.]],.]]]] => 5
[5,4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [.,[.,[.,[[[.,[.,[.,.]]],.],.]]]] => 7
[6,3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [.,[.,[.,[[[[.,.],.],[.,.]],.]]]] => 5
[3,3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [.,[.,[.,[[[[[.,.],.],.],.],.]]]] => 7
[6,6,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => 5
[6,5,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [.,[.,[[.,.],[.,[[.,[.,.]],.]]]]] => 5
[6,5,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [.,[.,[[.,.],[[.,[.,[.,.]]],.]]]] => 5
[6,5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => 7
[5,5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [.,[.,[[.,[.,[.,[[.,.],.]]]],.]]] => 7
[7,6,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => 5
[6,5,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [.,[.,[[[.,.],[.,[.,[.,.]]]],.]]] => 5
[6,5,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [.,[.,[[[.,[.,.]],[.,[.,.]]],.]]] => 5
[6,4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [.,[.,[[[.,[.,[.,.]]],[.,.]],.]]] => 5
[5,4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [.,[.,[[[.,[.,[.,[.,.]]]],.],.]]] => 7
[6,5,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [.,[.,[[[[.,.],.],[.,[.,.]]],.]]] => 5
[7,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [.,[.,[[[[[.,.],.],.],.],[.,.]]]] => 5
[7,6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => 5
[6,6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => 5
[6,5,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] => 5
[6,6,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => 5
[6,5,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => 5
[4,4,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [.,[[.,[.,.]],[[[[.,.],.],.],.]]] => 5
[6,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => 7
[5,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [.,[[.,[.,[.,[.,[[.,.],.]]]]],.]] => 7
[7,6,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => 5
[6,5,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [.,[[[.,.],.],[.,[[.,[.,.]],.]]]] => 5
[6,5,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => 5
[7,6,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => 5
[5,5,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [.,[[[.,[.,.]],.],[[[.,.],.],.]]] => 5
[7,5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => 3
[6,5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => 5
[7,6,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => 5
[7,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [.,[[[.,[.,[.,[.,.]]]],.],[.,.]]] => 5
[6,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [.,[[[.,[.,[.,[.,.]]]],[.,.]],.]] => 5
[6,5,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => 5
[6,6,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [.,[[[[.,[.,.]],.],.],[[.,.],.]]] => 5
[7,6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]] => 5
[7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => 5
[6,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => 5
[7,5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => 3
[6,5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => 5
[5,5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => 5
[7,6,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => 3
[6,5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => 5
[6,5,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => 5
[5,4,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [[.,.],[.,[[[.,[.,[.,.]]],.],.]]] => 5
[4,3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[.,.],[.,[[[[.,[.,.]],.],.],.]]] => 5
[6,5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => 5
[4,4,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [[.,.],[[.,[.,[[[.,.],.],.]]],.]] => 5
[7,6,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => 3
[6,5,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => 3
[5,4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => 5
[6,6,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => 3
[7,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => 5
[6,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => 5
[6,5,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => 5
[4,4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => 5
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Description
The number of vertices with out-degree 1 in a binary tree.
See the references for several connections of this statistic.
In particular, the number $T(n,k)$ of binary trees with $n$ vertices and $k$ out-degree $1$ vertices is given by $T(n,k) = 0$ for $n-k$ odd and
$$T(n,k)=\frac{2^k}{n+1}\binom{n+1}{k}\binom{n+1-k}{(n-k)/2}$$
for $n-k$ is even.
Map
to binary tree: up step, left tree, down step, right tree
Description
Return the binary tree corresponding to the Dyck path under the transformation up step - left tree - down step - right tree.
A Dyck path $D$ of semilength $n$ with $ n > 1$ may be uniquely decomposed into $1L0R$ 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.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.