Identifier
Values
[1] => [1,0,1,0] => [.,[.,.]] => 1
[2] => [1,1,0,0,1,0] => [[.,.],[.,.]] => 2
[1,1] => [1,0,1,1,0,0] => [.,[[.,.],.]] => 1
[3] => [1,1,1,0,0,0,1,0] => [[[.,.],.],[.,.]] => 2
[2,1] => [1,0,1,0,1,0] => [.,[.,[.,.]]] => 1
[1,1,1] => [1,0,1,1,1,0,0,0] => [.,[[[.,.],.],.]] => 1
[4] => [1,1,1,1,0,0,0,0,1,0] => [[[[.,.],.],.],[.,.]] => 2
[3,1] => [1,1,0,1,0,0,1,0] => [[.,[.,.]],[.,.]] => 2
[2,2] => [1,1,0,0,1,1,0,0] => [[.,.],[[.,.],.]] => 2
[2,1,1] => [1,0,1,1,0,1,0,0] => [.,[[.,[.,.]],.]] => 1
[1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [.,[[[[.,.],.],.],.]] => 1
[5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [[[[[.,.],.],.],.],[.,.]] => 2
[4,1] => [1,1,1,0,1,0,0,0,1,0] => [[[.,[.,.]],.],[.,.]] => 2
[3,2] => [1,1,0,0,1,0,1,0] => [[.,.],[.,[.,.]]] => 2
[3,1,1] => [1,0,1,1,0,0,1,0] => [.,[[.,.],[.,.]]] => 2
[2,2,1] => [1,0,1,0,1,1,0,0] => [.,[.,[[.,.],.]]] => 1
[2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [.,[[[.,[.,.]],.],.]] => 1
[1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [.,[[[[[.,.],.],.],.],.]] => 1
[6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[[[[[.,.],.],.],.],.],[.,.]] => 2
[5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [[[[.,[.,.]],.],.],[.,.]] => 2
[4,2] => [1,1,1,0,0,1,0,0,1,0] => [[[.,.],[.,.]],[.,.]] => 3
[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] => [.,[.,[.,[.,.]]]] => 1
[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] => [.,[[.,[[.,.],.]],.]] => 1
[2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [.,[[[[.,[.,.]],.],.],.]] => 1
[1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [.,[[[[[[.,.],.],.],.],.],.]] => 1
[7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => 2
[6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [[[[[.,[.,.]],.],.],.],[.,.]] => 2
[5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [[[[.,.],[.,.]],.],[.,.]] => 3
[5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [[[.,[[.,.],.]],.],[.,.]] => 2
[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] => [.,[[.,[.,[.,.]]],.]] => 1
[3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [.,[[[[.,.],[.,.]],.],.]] => 2
[2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [.,[.,[[[.,.],.],.]]] => 1
[2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [.,[[[.,[[.,.],.]],.],.]] => 1
[2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [.,[[[[[.,[.,.]],.],.],.],.]] => 1
[1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [.,[[[[[[[.,.],.],.],.],.],.],.]] => 1
[8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => 2
[7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => 2
[6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [[[[[.,.],[.,.]],.],.],[.,.]] => 3
[6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[[[.,[[.,.],.]],.],.],[.,.]] => 2
[5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [[[[.,.],.],[.,.]],[.,.]] => 3
[5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [[[.,[.,[.,.]]],.],[.,.]] => 2
[5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [[.,[[[.,.],.],.]],[.,.]] => 2
[4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],.]] => 2
[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] => [[.,.],[[.,.],[.,.]]] => 3
[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] => [.,[[[[.,.],.],[.,.]],.]] => 2
[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] => [.,[.,[[.,[.,.]],.]]] => 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] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [.,[[[[[.,.],[.,.]],.],.],.]] => 2
[2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [[.,.],[[[[.,.],.],.],.]] => 2
[2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [.,[[.,[[[.,.],.],.]],.]] => 1
[2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [.,[[[[.,[[.,.],.]],.],.],.]] => 1
[2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [.,[[[[[[.,[.,.]],.],.],.],.],.]] => 1
[1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => 1
[9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => 2
[8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [[[[[[[.,[.,.]],.],.],.],.],.],[.,.]] => 2
[7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => 3
[7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [[[[[.,[[.,.],.]],.],.],.],[.,.]] => 2
[6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [[[[[.,.],.],[.,.]],.],[.,.]] => 3
[6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [[[[.,[.,[.,.]]],.],.],[.,.]] => 2
[6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[[.,[[[.,.],.],.]],.],[.,.]] => 2
[5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [[[[.,.],.],.],[.,[.,.]]] => 2
[5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [[[.,[.,.]],[.,.]],[.,.]] => 3
[5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [[[.,.],[[.,.],.]],[.,.]] => 3
[5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [[.,[[.,[.,.]],.]],[.,.]] => 2
[5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [.,[[[[.,.],.],.],[.,.]]] => 2
[4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [[[.,[.,.]],.],[[.,.],.]] => 2
[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] => [.,[[[.,[.,.]],[.,.]],.]] => 2
[4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [.,[[[[[.,.],.],[.,.]],.],.]] => 2
[3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [[[.,.],.],[[[.,.],.],.]] => 2
[3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[[.,.],.]]]] => 1
[3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [.,[[[.,.],[[.,.],.]],.]] => 2
[3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [[.,.],[[[.,[.,.]],.],.]] => 2
[3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [.,[[.,[[.,[.,.]],.]],.]] => 1
[3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [.,[[[[.,[.,[.,.]]],.],.],.]] => 1
[3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [.,[[[[[[.,.],[.,.]],.],.],.],.]] => 2
[2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [.,[.,[[[[.,.],.],.],.]]] => 1
[2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [.,[[[.,[[[.,.],.],.]],.],.]] => 1
[2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [.,[[[[[.,[[.,.],.]],.],.],.],.]] => 1
[2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [.,[[[[[[[.,[.,.]],.],.],.],.],.],.]] => 1
[1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => 1
[10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => 2
[9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]] => 2
[8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => 3
[8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [[[[[[.,[[.,.],.]],.],.],.],.],[.,.]] => 2
[7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => 3
>>> Load all 508 entries. <<<
[7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]] => 2
[7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [[[[.,[[[.,.],.],.]],.],.],[.,.]] => 2
[6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [[[[[.,.],.],.],[.,.]],[.,.]] => 3
[6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[[[.,[.,.]],[.,.]],.],[.,.]] => 3
[6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[[[.,.],[[.,.],.]],.],[.,.]] => 3
[6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[[.,[[.,[.,.]],.]],.],[.,.]] => 2
[6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[.,[[[[.,.],.],.],.]],[.,.]] => 2
[5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[[[[.,.],.],.],.],[[.,.],.]] => 2
[5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,.]],.],[.,[.,.]]] => 2
[5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [[[.,.],[.,[.,.]]],[.,.]] => 3
[5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [[.,[[.,.],[.,.]]],[.,.]] => 3
[5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [[.,[.,[[.,.],.]]],[.,.]] => 2
[5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [.,[[[.,[.,.]],.],[.,.]]] => 2
[5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [.,[[[[[.,.],.],.],[.,.]],.]] => 2
[4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [[[.,.],[.,.]],[[.,.],.]] => 3
[4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [[.,[[.,.],.]],[[.,.],.]] => 2
[4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [[[.,.],.],[[.,[.,.]],.]] => 2
[4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,.]]]]] => 1
[4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [.,[[[.,.],[.,[.,.]]],.]] => 2
[4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [[.,.],[[[.,.],[.,.]],.]] => 3
[4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [.,[[.,[[.,.],[.,.]]],.]] => 2
[4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [.,[[[[.,[.,.]],[.,.]],.],.]] => 2
[4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [.,[[[[[[.,.],.],[.,.]],.],.],.]] => 2
[3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [[.,[.,.]],[[[.,.],.],.]] => 2
[3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [[.,.],[[.,[[.,.],.]],.]] => 2
[3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [.,[[.,[.,[[.,.],.]]],.]] => 1
[3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [.,[[[[.,.],[[.,.],.]],.],.]] => 2
[3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [.,[.,[[[.,[.,.]],.],.]]] => 1
[3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [.,[[[.,[[.,[.,.]],.]],.],.]] => 1
[3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [.,[[[[[.,[.,[.,.]]],.],.],.],.]] => 1
[3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [.,[[[[[[[.,.],[.,.]],.],.],.],.],.]] => 2
[2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,.],[[[[[.,.],.],.],.],.]] => 2
[2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [.,[[.,[[[[.,.],.],.],.]],.]] => 1
[2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [.,[[[[.,[[[.,.],.],.]],.],.],.]] => 1
[2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [.,[[[[[[.,[[.,.],.]],.],.],.],.],.]] => 1
[2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]] => 1
[1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] => 1
[7,4] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => 3
[6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[[[[.,.],.],.],.],[.,[.,.]]] => 2
[6,4,1] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [[[[.,[.,.]],.],[.,.]],[.,.]] => 3
[6,3,2] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [[[[.,.],[.,[.,.]]],.],[.,.]] => 3
[6,3,1,1] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [[[.,[[.,.],[.,.]]],.],[.,.]] => 3
[6,2,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [[[.,[.,[[.,.],.]]],.],[.,.]] => 2
[6,2,1,1,1] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [[.,[[[.,[.,.]],.],.]],[.,.]] => 2
[6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [.,[[[[[.,.],.],.],.],[.,.]]] => 2
[5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [[[[.,[.,.]],.],.],[[.,.],.]] => 2
[5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => [[[.,.],[.,.]],[.,[.,.]]] => 3
[5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => [[.,[[.,.],.]],[.,[.,.]]] => 2
[5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[[.,.],.],[[.,.],[.,.]]] => 3
[5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => [[.,[.,[.,[.,.]]]],[.,.]] => 2
[5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => [.,[[[.,.],[.,.]],[.,.]]] => 3
[5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => [[.,.],[[[.,.],.],[.,.]]] => 3
[5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => [.,[[.,[[.,.],.]],[.,.]]] => 2
[5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [.,[[[[.,[.,.]],.],[.,.]],.]] => 2
[4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [[[.,.],.],[.,[[.,.],.]]] => 2
[4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => [[.,[.,[.,.]]],[[.,.],.]] => 2
[4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => [.,[[[.,.],.],[[.,.],.]]] => 2
[4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => [[.,[.,.]],[[.,[.,.]],.]] => 2
[4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => [[.,.],[[.,[.,[.,.]]],.]] => 2
[4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [.,[[.,[.,[.,[.,.]]]],.]] => 1
[4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [.,[[[[.,.],[.,[.,.]]],.],.]] => 2
[4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [.,[.,[[[.,.],[.,.]],.]]] => 2
[4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [.,[[[.,[[.,.],[.,.]]],.],.]] => 2
[3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => [[.,.],[.,[[[.,.],.],.]]] => 2
[3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => [.,[[.,.],[[[.,.],.],.]]] => 2
[3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => [.,[.,[[.,[[.,.],.]],.]]] => 1
[3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [.,[[[.,[.,[[.,.],.]]],.],.]] => 1
[3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [[.,.],[[[[.,[.,.]],.],.],.]] => 2
[3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [.,[[.,[[[.,[.,.]],.],.]],.]] => 1
[2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [.,[.,[[[[[.,.],.],.],.],.]]] => 1
[7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => 3
[6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => 2
[6,5,1] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [[[[.,[.,.]],.],.],[.,[.,.]]] => 2
[6,4,2] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [[[[.,.],[.,.]],[.,.]],[.,.]] => 4
[6,4,1,1] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [[[.,[[.,.],.]],[.,.]],[.,.]] => 3
[6,3,3] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [[[[.,.],.],[[.,.],.]],[.,.]] => 3
[6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => 2
[6,3,1,1,1] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [[.,[[[.,.],[.,.]],.]],[.,.]] => 3
[6,2,2,2] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [[[.,.],[[[.,.],.],.]],[.,.]] => 3
[6,2,2,1,1] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [[.,[[.,[[.,.],.]],.]],[.,.]] => 2
[6,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [.,[[[[.,[.,.]],.],.],[.,.]]] => 2
[5,5,2] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [[[[.,.],[.,.]],.],[[.,.],.]] => 3
[5,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [[[.,[[.,.],.]],.],[[.,.],.]] => 2
[5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[.,.],.],[.,[.,[.,.]]]] => 2
[5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [[.,[.,[.,.]]],[.,[.,.]]] => 2
[5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [.,[[[.,.],.],[.,[.,.]]]] => 2
[5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => [[.,[.,.]],[[.,.],[.,.]]] => 3
[5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [[.,.],[[.,[.,.]],[.,.]]] => 3
[5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [.,[[.,[.,[.,.]]],[.,.]]] => 2
[5,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [.,[[[[.,.],[.,.]],[.,.]],.]] => 3
[5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [.,[.,[[[.,.],.],[.,.]]]] => 2
[5,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [.,[[[.,[[.,.],.]],[.,.]],.]] => 2
[4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[[[.,.],.],.],[[[.,.],.],.]] => 2
[4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [[.,[.,.]],[.,[[.,.],.]]] => 2
[4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],.]]] => 3
[4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => [.,[[.,[.,.]],[[.,.],.]]] => 2
[4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [.,[[[[.,.],.],[[.,.],.]],.]] => 2
[4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [[.,.],[.,[[.,[.,.]],.]]] => 2
[4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [.,[[.,.],[[.,[.,.]],.]]] => 2
[4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [.,[.,[[.,[.,[.,.]]],.]]] => 1
[4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [.,[[[.,[.,[.,[.,.]]]],.],.]] => 1
[4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [[.,.],[[[[.,.],[.,.]],.],.]] => 3
[4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [.,[[.,[[[.,.],[.,.]],.]],.]] => 2
[3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[[.,.],.],[[[[.,.],.],.],.]] => 2
[3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [.,[.,[.,[[[.,.],.],.]]]] => 1
[3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [.,[[[.,.],[[[.,.],.],.]],.]] => 2
[3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [[.,.],[[[.,[[.,.],.]],.],.]] => 2
[3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [.,[[.,[[.,[[.,.],.]],.]],.]] => 1
[3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [.,[.,[[[[.,[.,.]],.],.],.]]] => 1
[2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => 2
[6,5,2] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [[[[.,.],[.,.]],.],[.,[.,.]]] => 3
[6,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [[[.,[[.,.],.]],.],[.,[.,.]]] => 2
[6,4,3] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [[[[.,.],.],[.,[.,.]]],[.,.]] => 3
[6,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => 3
[6,4,1,1,1] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [[.,[[[.,.],.],[.,.]]],[.,.]] => 3
[6,3,3,1] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [[[.,[.,.]],[[.,.],.]],[.,.]] => 3
[6,3,2,2] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [[[.,.],[[.,[.,.]],.]],[.,.]] => 3
[6,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => 2
[6,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [.,[[[[.,.],[.,.]],.],[.,.]]] => 3
[6,2,2,2,1] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [[.,[.,[[[.,.],.],.]]],[.,.]] => 2
[6,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [.,[[[.,[[.,.],.]],.],[.,.]]] => 2
[5,5,3] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [[[[.,.],.],[.,.]],[[.,.],.]] => 3
[5,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [[[.,[.,[.,.]]],.],[[.,.],.]] => 2
[5,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [[.,[[[.,.],.],.]],[[.,.],.]] => 2
[5,4,4] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [[[[.,.],.],.],[[.,[.,.]],.]] => 2
[5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => [[.,[.,.]],[.,[.,[.,.]]]] => 2
[5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,.]]]] => 3
[5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => [.,[[.,[.,.]],[.,[.,.]]]] => 2
[5,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [.,[[[[.,.],.],[.,[.,.]]],.]] => 2
[5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[[.,.],[.,.]]]] => 3
[5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [.,[[.,.],[[.,.],[.,.]]]] => 3
[5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => [.,[.,[[.,[.,.]],[.,.]]]] => 2
[5,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [.,[[[.,[.,[.,.]]],[.,.]],.]] => 2
[5,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [[.,.],[[[[.,.],.],[.,.]],.]] => 3
[5,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [.,[[.,[[[.,.],.],[.,.]]],.]] => 2
[4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [[[.,[.,.]],.],[[[.,.],.],.]] => 2
[4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[[.,.],.]]]] => 2
[4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => [.,[[.,.],[.,[[.,.],.]]]] => 2
[4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => [.,[.,[[.,.],[[.,.],.]]]] => 2
[4,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [.,[[[.,[.,.]],[[.,.],.]],.]] => 2
[4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [[[.,.],.],[[[.,[.,.]],.],.]] => 2
[4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [.,[.,[.,[[.,[.,.]],.]]]] => 1
[4,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [.,[[[.,.],[[.,[.,.]],.]],.]] => 2
[4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [[.,.],[[[.,[.,[.,.]]],.],.]] => 2
[4,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [.,[[.,[[.,[.,[.,.]]],.]],.]] => 1
[4,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [.,[.,[[[[.,.],[.,.]],.],.]]] => 2
[3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [[.,[.,.]],[[[[.,.],.],.],.]] => 2
[3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [[.,.],[[.,[[[.,.],.],.]],.]] => 2
[3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [.,[[.,[.,[[[.,.],.],.]]],.]] => 1
[3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [.,[.,[[[.,[[.,.],.]],.],.]]] => 1
[6,6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [[[[.,[[.,.],.]],.],.],[[.,.],.]] => 2
[6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [[[[.,.],.],[.,.]],[.,[.,.]]] => 3
[6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => 2
[6,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [[.,[[[.,.],.],.]],[.,[.,.]]] => 2
[6,4,4] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[[[.,.],.],.],[[.,.],[.,.]]] => 3
[6,4,3,1] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => 3
[6,4,2,2] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [[[.,.],[[.,.],[.,.]]],[.,.]] => 4
[6,4,2,1,1] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => 3
[6,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [.,[[[[.,.],.],[.,.]],[.,.]]] => 3
[6,3,3,2] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [[[.,.],[.,[[.,.],.]]],[.,.]] => 3
[6,3,3,1,1] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [[.,[[.,.],[[.,.],.]]],[.,.]] => 3
[6,3,2,2,1] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => 2
[6,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [.,[[[.,[.,[.,.]]],.],[.,.]]] => 2
[6,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[.,.],[[[[.,.],.],.],[.,.]]] => 3
[6,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [.,[[.,[[[.,.],.],.]],[.,.]]] => 2
[5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[[[.,.],.],.],[.,[[.,.],.]]] => 2
[5,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[.,.]],[[.,.],.]] => 3
[5,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [[[.,.],[[.,.],.]],[[.,.],.]] => 3
[5,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [[.,[[.,[.,.]],.]],[[.,.],.]] => 2
[5,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [.,[[[[.,.],.],.],[[.,.],.]]] => 2
[5,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[[.,[.,.]],.],[[.,[.,.]],.]] => 2
[5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,.]]]]] => 2
[5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [.,[[.,.],[.,[.,[.,.]]]]] => 2
[5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [.,[.,[[.,.],[.,[.,.]]]]] => 2
[5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [.,[[[.,[.,.]],[.,[.,.]]],.]] => 2
[5,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [[[.,.],.],[[[.,.],[.,.]],.]] => 3
[5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [.,[.,[.,[[.,.],[.,.]]]]] => 2
[5,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,.],[[.,.],[.,.]]],.]] => 3
[5,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,.],[[[.,[.,.]],[.,.]],.]] => 3
[5,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [.,[[.,[[.,[.,.]],[.,.]]],.]] => 2
[5,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [.,[.,[[[[.,.],.],[.,.]],.]]] => 2
[4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [[[.,.],[.,.]],[[[.,.],.],.]] => 3
[4,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [[.,[[.,.],.]],[[[.,.],.],.]] => 2
[4,4,3,3] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [[[.,.],.],[[.,[[.,.],.]],.]] => 2
[4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[[.,.],.]]]]] => 1
[4,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [.,[[[.,.],[.,[[.,.],.]]],.]] => 2
[4,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [[.,.],[[[.,.],[[.,.],.]],.]] => 3
[4,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [.,[[.,[[.,.],[[.,.],.]]],.]] => 2
[4,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [[.,[.,.]],[[[.,[.,.]],.],.]] => 2
[4,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,.],[[.,[[.,[.,.]],.]],.]] => 2
[4,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [.,[[.,[.,[[.,[.,.]],.]]],.]] => 1
[4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [.,[.,[[[.,[.,[.,.]]],.],.]]] => 1
[3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[.,.],[.,[[[[.,.],.],.],.]]] => 2
[3,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [.,[[.,.],[[[[.,.],.],.],.]]] => 2
[3,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [.,[.,[[.,[[[.,.],.],.]],.]]] => 1
[7,4,2,1,1] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [[[.,[[.,[.,.]],[.,.]]],.],[.,.]] => 3
[6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[[[.,.],.],.],[.,[.,[.,.]]]] => 2
[6,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => 3
[6,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [[[.,.],[[.,.],.]],[.,[.,.]]] => 3
[6,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => 2
[6,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [.,[[[[.,.],.],.],[.,[.,.]]]] => 2
[6,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [[[.,[.,.]],.],[[.,.],[.,.]]] => 3
[6,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => 3
[6,4,3,1,1] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => 3
[6,4,2,2,1] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => 3
[6,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => 3
[6,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[[.,.],.],[[[.,.],.],[.,.]]] => 3
[6,3,3,2,1] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => 2
[6,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [.,[[[.,.],[[.,.],.]],[.,.]]] => 3
[6,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [[.,.],[[[.,[.,.]],.],[.,.]]] => 3
[6,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => 2
[6,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [.,[.,[[[[.,.],.],.],[.,.]]]] => 2
[5,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [[[.,[.,.]],.],[.,[[.,.],.]]] => 2
[5,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [[[.,.],[.,[.,.]]],[[.,.],.]] => 3
[5,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,.],[.,.]]],[[.,.],.]] => 3
[5,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [[.,[.,[[.,.],.]]],[[.,.],.]] => 2
[5,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [.,[[[.,[.,.]],.],[[.,.],.]]] => 2
[5,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [[[.,.],[.,.]],[[.,[.,.]],.]] => 3
[5,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],.]],[[.,[.,.]],.]] => 2
[5,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [[[.,.],.],[[.,[.,[.,.]]],.]] => 2
[5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,.]]]]]] => 1
[5,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [.,[[[.,.],[.,[.,[.,.]]]],.]] => 2
[5,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [[.,.],[[[.,.],[.,[.,.]]],.]] => 3
[5,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [.,[[.,[[.,.],[.,[.,.]]]],.]] => 2
[5,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[.,.]],[[[.,.],[.,.]],.]] => 3
[5,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [[.,.],[[.,[[.,.],[.,.]]],.]] => 3
[5,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [.,[[.,[.,[[.,.],[.,.]]]],.]] => 2
[5,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [.,[.,[[[.,[.,.]],[.,.]],.]]] => 2
[4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[[.,.],.],[.,[[[.,.],.],.]]] => 2
[4,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [[.,[.,[.,.]]],[[[.,.],.],.]] => 2
[4,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [.,[[[.,.],.],[[[.,.],.],.]]] => 2
[4,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [[.,[.,.]],[[.,[[.,.],.]],.]] => 2
[4,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [[.,.],[[.,[.,[[.,.],.]]],.]] => 2
[4,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [.,[[.,[.,[.,[[.,.],.]]]],.]] => 1
[4,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [.,[.,[[[.,.],[[.,.],.]],.]]] => 2
[4,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [[.,.],[.,[[[.,[.,.]],.],.]]] => 2
[4,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [.,[[.,.],[[[.,[.,.]],.],.]]] => 2
[4,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [.,[.,[[.,[[.,[.,.]],.]],.]]] => 1
[3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [.,[.,[.,[[[[.,.],.],.],.]]]] => 1
[7,6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => 2
[7,5,3,1] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => 4
[7,5,2,2] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => 4
[7,5,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => 3
[7,4,4,1] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => 3
[7,4,2,1,1,1] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => 3
[7,3,3,3] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => 3
[7,3,2,2,1,1] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => 2
[6,6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => 3
[6,6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => 3
[6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => 2
[6,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => 3
[6,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => 3
[6,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => 2
[6,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => 2
[6,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [[[.,.],[.,.]],[[.,.],[.,.]]] => 4
[6,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [[.,[[.,.],.]],[[.,.],[.,.]]] => 3
[6,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [[[.,.],.],[[.,[.,.]],[.,.]]] => 3
[6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 2
[6,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => 3
[6,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [[.,.],[[[.,.],[.,.]],[.,.]]] => 4
[6,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => 3
[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] => [[.,[.,.]],[[[.,.],.],[.,.]]] => 3
[6,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [[.,.],[[.,[[.,.],.]],[.,.]]] => 3
[6,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [.,[[.,[.,[[.,.],.]]],[.,.]]] => 2
[6,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [.,[.,[[[.,[.,.]],.],[.,.]]]] => 2
[6,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => 2
[5,5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => 2
[5,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [[[.,.],[.,.]],[.,[[.,.],.]]] => 3
[5,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [[.,[[.,.],.]],[.,[[.,.],.]]] => 2
[5,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[.,.],.],[[.,.],[[.,.],.]]] => 3
[5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => 2
[5,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [.,[[[.,.],[.,.]],[[.,.],.]]] => 3
[5,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[.,.],[[[.,.],.],[[.,.],.]]] => 3
[5,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [.,[[.,[[.,.],.]],[[.,.],.]]] => 2
[5,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [[[.,.],.],[.,[[.,[.,.]],.]]] => 2
[5,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => 2
[5,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [.,[[[.,.],.],[[.,[.,.]],.]]] => 2
[5,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => 2
[5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => 2
[5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [.,[[.,[.,[.,[.,[.,.]]]]],.]] => 1
[5,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [.,[.,[[[.,.],[.,[.,.]]],.]]] => 2
[5,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [[.,.],[.,[[[.,.],[.,.]],.]]] => 3
[5,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [.,[[.,.],[[[.,.],[.,.]],.]]] => 3
[5,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [.,[.,[[.,[[.,.],[.,.]]],.]]] => 2
[5,3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => 2
[4,4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => 2
[4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [[.,[.,.]],[.,[[[.,.],.],.]]] => 2
[4,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[.,.],[[.,.],[[[.,.],.],.]]] => 3
[4,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [.,[[.,[.,.]],[[[.,.],.],.]]] => 2
[4,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [[.,.],[.,[[.,[[.,.],.]],.]]] => 2
[4,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [.,[[.,.],[[.,[[.,.],.]],.]]] => 2
[4,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [.,[.,[[.,[.,[[.,.],.]]],.]]] => 1
[4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [.,[.,[.,[[[.,[.,.]],.],.]]]] => 1
[4,3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => 1
[3,3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,[.,.]],[[[[[.,.],.],.],.],.]] => 2
[7,6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => 3
[7,5,3,2] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => 4
[7,4,4,2] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => 4
[7,4,3,3] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => 3
[6,6,4,1] => [1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => 3
[6,6,3,2] => [1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => 3
[6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => 3
[6,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => 2
[6,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[[.,.],.],[[.,.],[.,[.,.]]]] => 3
[6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 2
[6,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => 3
[6,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[.,.],[[[.,.],.],[.,[.,.]]]] => 3
[6,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => 2
[6,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[[.,.],.],[.,[[.,.],[.,.]]]] => 3
[6,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => 3
[6,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [.,[[[.,.],.],[[.,.],[.,.]]]] => 3
[6,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => 3
[6,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => 3
[6,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 2
[6,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => 3
[6,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[.,.],[.,[[[.,.],.],[.,.]]]] => 3
[6,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [.,[[.,.],[[[.,.],.],[.,.]]]] => 3
[6,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [.,[.,[[.,[[.,.],.]],[.,.]]]] => 2
[5,5,5,2] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => 3
[5,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[[.,.],.],[.,[.,[[.,.],.]]]] => 2
[5,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => 2
[5,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [.,[[[.,.],.],[.,[[.,.],.]]]] => 2
[5,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[.,[.,.]],[[.,.],[[.,.],.]]] => 3
[5,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[.,.],[[.,[.,.]],[[.,.],.]]] => 3
[5,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => 2
[5,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [.,[.,[[[.,.],.],[[.,.],.]]]] => 2
[5,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => 2
[5,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[.,.],[[.,.],[[.,[.,.]],.]]] => 3
[5,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => 2
[5,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => 2
[5,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => 2
[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] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [.,[.,[.,[[[.,.],[.,.]],.]]]] => 2
[5,3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => 2
[4,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[.,.],[.,[.,[[[.,.],.],.]]]] => 2
[4,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [.,[[.,.],[.,[[[.,.],.],.]]]] => 2
[4,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [.,[.,[[.,.],[[[.,.],.],.]]]] => 2
[4,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [.,[.,[.,[[.,[[.,.],.]],.]]]] => 1
[6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 1
[6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => 1
[4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [.,[.,[.,[.,[[[.,.],.],.]]]]] => 1
[6,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[5,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => 2
[6,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 2
[5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => 1
[6,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [.,[.,[.,[[[.,.],.],[.,.]]]]] => 2
[6,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[5,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => 2
[6,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => 3
[5,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => 2
[6,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[5,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => 2
[6,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 2
[6,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => 2
[6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[5,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => 2
[6,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => 3
[5,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => 2
[6,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 3
[5,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [.,[[.,.],[[.,.],[[.,.],.]]]] => 3
[6,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => 3
[6,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[5,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => 2
[6,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => 3
[6,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[6,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => 2
[6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 2
[5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => 2
[6,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => 3
[5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => 2
[6,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => 3
[5,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[.,.],[.,[[.,.],[[.,.],.]]]] => 3
[6,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => 3
[6,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => 3
[5,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[.,.],[[.,.],[.,[[.,.],.]]]] => 3
[6,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[.,.],[[.,.],[[.,.],[.,.]]]] => 4
[6,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => 3
[6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 2
[5,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => 2
[6,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => 3
[6,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => 3
[6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => 2
[7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => 2
[6,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => 2
[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] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => 2
[5,5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => 2
[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] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => 2
[6,6,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => 3
[4,4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => 2
[5,5,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => 2
[7,6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => 2
[7,6,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => 3
[7,6,4,3] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => 3
[9,7,5,3,1] => [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => 5
[8,7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => 2
[9,8,7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => 2
[7,7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => 2
[7,6,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => 2
[8,8,7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => 2
[10,9,8,7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => 2
[8,6,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => 3
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searching the database for the individual values of this statistic
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Description
The number of leaf nodes in a binary tree.
Equivalently, the number of cherries [1] in the complete binary tree.
The number of binary trees of size $n$, at least $1$, with exactly one leaf node for is $2^{n-1}$, see [2].
The number of binary tree of size $n$, at least $3$, with exactly two leaf nodes is $n(n+1)2^{n-2}$, see [3].
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.