Identifier
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00034: Dyck paths —to binary tree: up step, left tree, down step, right tree⟶ Binary trees
Mp00018: Binary trees —left border symmetry⟶ Binary trees
Images
[1] => [1,0] => [.,.] => [.,.]
[1,1] => [1,0,1,0] => [.,[.,.]] => [.,[.,.]]
[2] => [1,1,0,0] => [[.,.],.] => [[.,.],.]
[1,1,1] => [1,0,1,0,1,0] => [.,[.,[.,.]]] => [.,[.,[.,.]]]
[1,2] => [1,0,1,1,0,0] => [.,[[.,.],.]] => [.,[[.,.],.]]
[2,1] => [1,1,0,0,1,0] => [[.,.],[.,.]] => [[.,[.,.]],.]
[3] => [1,1,1,0,0,0] => [[[.,.],.],.] => [[[.,.],.],.]
[1,1,1,1] => [1,0,1,0,1,0,1,0] => [.,[.,[.,[.,.]]]] => [.,[.,[.,[.,.]]]]
[1,1,2] => [1,0,1,0,1,1,0,0] => [.,[.,[[.,.],.]]] => [.,[.,[[.,.],.]]]
[1,2,1] => [1,0,1,1,0,0,1,0] => [.,[[.,.],[.,.]]] => [.,[[.,[.,.]],.]]
[1,3] => [1,0,1,1,1,0,0,0] => [.,[[[.,.],.],.]] => [.,[[[.,.],.],.]]
[2,1,1] => [1,1,0,0,1,0,1,0] => [[.,.],[.,[.,.]]] => [[.,[.,[.,.]]],.]
[2,2] => [1,1,0,0,1,1,0,0] => [[.,.],[[.,.],.]] => [[.,[[.,.],.]],.]
[3,1] => [1,1,1,0,0,0,1,0] => [[[.,.],.],[.,.]] => [[[.,[.,.]],.],.]
[4] => [1,1,1,1,0,0,0,0] => [[[[.,.],.],.],.] => [[[[.,.],.],.],.]
[1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,.]]]]] => [.,[.,[.,[.,[.,.]]]]]
[1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[[.,.],.]]]] => [.,[.,[.,[[.,.],.]]]]
[1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [.,[.,[[.,.],[.,.]]]] => [.,[.,[[.,[.,.]],.]]]
[1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [.,[.,[[[.,.],.],.]]] => [.,[.,[[[.,.],.],.]]]
[1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [.,[[.,.],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],.]]
[1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [.,[[.,.],[[.,.],.]]] => [.,[[.,[[.,.],.]],.]]
[1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [.,[[[.,.],.],[.,.]]] => [.,[[[.,[.,.]],.],.]]
[1,4] => [1,0,1,1,1,1,0,0,0,0] => [.,[[[[.,.],.],.],.]] => [.,[[[[.,.],.],.],.]]
[2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],.]
[2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [[.,.],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],.]
[2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [[.,.],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],.]
[2,3] => [1,1,0,0,1,1,1,0,0,0] => [[.,.],[[[.,.],.],.]] => [[.,[[[.,.],.],.]],.]
[3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [[[.,.],.],[.,[.,.]]] => [[[.,[.,[.,.]]],.],.]
[3,2] => [1,1,1,0,0,0,1,1,0,0] => [[[.,.],.],[[.,.],.]] => [[[.,[[.,.],.]],.],.]
[4,1] => [1,1,1,1,0,0,0,0,1,0] => [[[[.,.],.],.],[.,.]] => [[[[.,[.,.]],.],.],.]
[5] => [1,1,1,1,1,0,0,0,0,0] => [[[[[.,.],.],.],.],.] => [[[[[.,.],.],.],.],.]
[1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,.]]]]]] => [.,[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[[.,.],.]]]]] => [.,[.,[.,[.,[[.,.],.]]]]]
[1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [.,[.,[.,[[.,.],[.,.]]]]] => [.,[.,[.,[[.,[.,.]],.]]]]
[1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [.,[.,[.,[[[.,.],.],.]]]] => [.,[.,[.,[[[.,.],.],.]]]]
[1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [.,[.,[[.,.],[.,[.,.]]]]] => [.,[.,[[.,[.,[.,.]]],.]]]
[1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [.,[.,[[.,.],[[.,.],.]]]] => [.,[.,[[.,[[.,.],.]],.]]]
[1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [.,[.,[[[.,.],.],[.,.]]]] => [.,[.,[[[.,[.,.]],.],.]]]
[1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [.,[.,[[[[.,.],.],.],.]]] => [.,[.,[[[[.,.],.],.],.]]]
[1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [.,[[.,.],[.,[.,[.,.]]]]] => [.,[[.,[.,[.,[.,.]]]],.]]
[1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [.,[[.,.],[.,[[.,.],.]]]] => [.,[[.,[.,[[.,.],.]]],.]]
[1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [.,[[.,.],[[.,.],[.,.]]]] => [.,[[.,[[.,[.,.]],.]],.]]
[1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => [.,[[.,.],[[[.,.],.],.]]] => [.,[[.,[[[.,.],.],.]],.]]
[1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [.,[[[.,.],.],[.,[.,.]]]] => [.,[[[.,[.,[.,.]]],.],.]]
[1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => [.,[[[.,.],.],[[.,.],.]]] => [.,[[[.,[[.,.],.]],.],.]]
[1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [.,[[[[.,.],.],.],[.,.]]] => [.,[[[[.,[.,.]],.],.],.]]
[1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [.,[[[[[.,.],.],.],.],.]] => [.,[[[[[.,.],.],.],.],.]]
[2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],.]
[2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[[.,.],.]]]] => [[.,[.,[.,[[.,.],.]]]],.]
[2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],.]
[2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [[.,.],[.,[[[.,.],.],.]]] => [[.,[.,[[[.,.],.],.]]],.]
[2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],.]
[2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],.]]] => [[.,[[.,[[.,.],.]],.]],.]
[2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [[.,.],[[[.,.],.],[.,.]]] => [[.,[[[.,[.,.]],.],.]],.]
[2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [[.,.],[[[[.,.],.],.],.]] => [[.,[[[[.,.],.],.],.]],.]
[3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[.,.],.],[.,[.,[.,.]]]] => [[[.,[.,[.,[.,.]]]],.],.]
[3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [[[.,.],.],[.,[[.,.],.]]] => [[[.,[.,[[.,.],.]]],.],.]
[3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[[.,.],.],[[.,.],[.,.]]] => [[[.,[[.,[.,.]],.]],.],.]
[3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [[[.,.],.],[[[.,.],.],.]] => [[[.,[[[.,.],.],.]],.],.]
[4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [[[[.,.],.],.],[.,[.,.]]] => [[[[.,[.,[.,.]]],.],.],.]
[4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],.]] => [[[[.,[[.,.],.]],.],.],.]
[5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [[[[[.,.],.],.],.],[.,.]] => [[[[[.,[.,.]],.],.],.],.]
[6] => [1,1,1,1,1,1,0,0,0,0,0,0] => [[[[[[.,.],.],.],.],.],.] => [[[[[[.,.],.],.],.],.],.]
[1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => [.,[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => [.,[.,[.,[.,[[.,[.,.]],.]]]]]
[1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [.,[.,[.,[.,[[[.,.],.],.]]]]] => [.,[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => [.,[.,[.,[[.,[.,[.,.]]],.]]]]
[1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => [.,[.,[.,[[.,[[.,.],.]],.]]]]
[1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [.,[.,[.,[[[.,.],.],[.,.]]]]] => [.,[.,[.,[[[.,[.,.]],.],.]]]]
[1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [.,[.,[.,[[[[.,.],.],.],.]]]] => [.,[.,[.,[[[[.,.],.],.],.]]]]
[1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [.,[.,[[.,[.,[.,[.,.]]]],.]]]
[1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => [.,[.,[[.,[.,[[.,.],.]]],.]]]
[1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [.,[.,[[.,[[.,[.,.]],.]],.]]]
[1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [.,[.,[[.,.],[[[.,.],.],.]]]] => [.,[.,[[.,[[[.,.],.],.]],.]]]
[1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => [.,[.,[[[.,[.,[.,.]]],.],.]]]
[1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [.,[.,[[[.,.],.],[[.,.],.]]]] => [.,[.,[[[.,[[.,.],.]],.],.]]]
[1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [.,[.,[[[[.,.],.],.],[.,.]]]] => [.,[.,[[[[.,[.,.]],.],.],.]]]
[1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [.,[.,[[[[[.,.],.],.],.],.]]] => [.,[.,[[[[[.,.],.],.],.],.]]]
[1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [.,[[.,[.,[.,[.,[.,.]]]]],.]]
[1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [.,[[.,[.,[.,[[.,.],.]]]],.]]
[1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [.,[[.,[.,[[.,[.,.]],.]]],.]]
[1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [.,[[.,.],[.,[[[.,.],.],.]]]] => [.,[[.,[.,[[[.,.],.],.]]],.]]
[1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [.,[[.,[[.,[.,[.,.]]],.]],.]]
[1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [.,[[.,[[.,[[.,.],.]],.]],.]]
[1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [.,[[.,[[[.,[.,.]],.],.]],.]]
[1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [.,[[.,.],[[[[.,.],.],.],.]]] => [.,[[.,[[[[.,.],.],.],.]],.]]
[1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [.,[[[.,[.,[.,[.,.]]]],.],.]]
[1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [.,[[[.,[.,[[.,.],.]]],.],.]]
[1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [.,[[[.,[[.,[.,.]],.]],.],.]]
[1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [.,[[[.,.],.],[[[.,.],.],.]]] => [.,[[[.,[[[.,.],.],.]],.],.]]
[1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [.,[[[[.,[.,[.,.]]],.],.],.]]
[1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [.,[[[[.,.],.],.],[[.,.],.]]] => [.,[[[[.,[[.,.],.]],.],.],.]]
[1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [.,[[[[[.,.],.],.],.],[.,.]]] => [.,[[[[[.,[.,.]],.],.],.],.]]
[1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [.,[[[[[[.,.],.],.],.],.],.]] => [.,[[[[[[.,.],.],.],.],.],.]]
[2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [[.,[.,[.,[.,[.,[.,.]]]]]],.]
[2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [[.,[.,[.,[.,[[.,.],.]]]]],.]
[2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [[.,[.,[.,[[.,[.,.]],.]]]],.]
[2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[.,.],[.,[.,[[[.,.],.],.]]]] => [[.,[.,[.,[[[.,.],.],.]]]],.]
[2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [[.,[.,[[.,[.,[.,.]]],.]]],.]
[2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [[.,[.,[[.,[[.,.],.]],.]]],.]
>>> Load all 465 entries. <<<
[2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [[.,[.,[[[.,[.,.]],.],.]]],.]
[2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[.,.],[.,[[[[.,.],.],.],.]]] => [[.,[.,[[[[.,.],.],.],.]]],.]
[2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [[.,[[.,[.,[.,[.,.]]]],.]],.]
[2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [[.,[[.,[.,[[.,.],.]]],.]],.]
[2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],.]
[2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[.,.],[[.,.],[[[.,.],.],.]]] => [[.,[[.,[[[.,.],.],.]],.]],.]
[2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [[.,[[[.,[.,[.,.]]],.],.]],.]
[2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[.,.],[[[.,.],.],[[.,.],.]]] => [[.,[[[.,[[.,.],.]],.],.]],.]
[2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[.,.],[[[[.,.],.],.],[.,.]]] => [[.,[[[[.,[.,.]],.],.],.]],.]
[2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,.],[[[[[.,.],.],.],.],.]] => [[.,[[[[[.,.],.],.],.],.]],.]
[3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [[[.,[.,[.,[.,[.,.]]]]],.],.]
[3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [[[.,[.,[.,[[.,.],.]]]],.],.]
[3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [[[.,[.,[[.,[.,.]],.]]],.],.]
[3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[[.,.],.],[.,[[[.,.],.],.]]] => [[[.,[.,[[[.,.],.],.]]],.],.]
[3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [[[.,[[.,[.,[.,.]]],.]],.],.]
[3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[.,.],.],[[.,.],[[.,.],.]]] => [[[.,[[.,[[.,.],.]],.]],.],.]
[3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[[.,.],.],[[[.,.],.],[.,.]]] => [[[.,[[[.,[.,.]],.],.]],.],.]
[3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[[.,.],.],[[[[.,.],.],.],.]] => [[[.,[[[[.,.],.],.],.]],.],.]
[4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [[[[.,[.,[.,[.,.]]]],.],.],.]
[4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[[[.,.],.],.],[.,[[.,.],.]]] => [[[[.,[.,[[.,.],.]]],.],.],.]
[4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[[[.,.],.],.],[[.,.],[.,.]]] => [[[[.,[[.,[.,.]],.]],.],.],.]
[4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[[[.,.],.],.],[[[.,.],.],.]] => [[[[.,[[[.,.],.],.]],.],.],.]
[5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[[[[.,.],.],.],.],[.,[.,.]]] => [[[[[.,[.,[.,.]]],.],.],.],.]
[5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[[[[.,.],.],.],.],[[.,.],.]] => [[[[[.,[[.,.],.]],.],.],.],.]
[6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[[[[[.,.],.],.],.],.],[.,.]] => [[[[[[.,[.,.]],.],.],.],.],.]
[7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[[[[.,.],.],.],.],.],.],.] => [[[[[[[.,.],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] => [.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]
[1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => [.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]
[1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]
[1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] => [.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]
[1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => [.,[.,[.,[.,[[[[.,.],.],.],.]]]]]
[1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]
[1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]
[1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]
[1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [.,[.,[.,[[.,.],[[[.,.],.],.]]]]] => [.,[.,[.,[[.,[[[.,.],.],.]],.]]]]
[1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => [.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]
[1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [.,[.,[.,[[[.,.],.],[[.,.],.]]]]] => [.,[.,[.,[[[.,[[.,.],.]],.],.]]]]
[1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => [.,[.,[.,[[[[.,[.,.]],.],.],.]]]]
[1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [.,[.,[.,[[[[[.,.],.],.],.],.]]]] => [.,[.,[.,[[[[[.,.],.],.],.],.]]]]
[1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]
[1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]
[1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [.,[.,[[.,[.,[[.,[.,.]],.]]],.]]]
[1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [.,[.,[[.,.],[.,[[[.,.],.],.]]]]] => [.,[.,[[.,[.,[[[.,.],.],.]]],.]]]
[1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]
[1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [.,[.,[[.,[[.,[[.,.],.]],.]],.]]]
[1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [.,[.,[[.,.],[[[.,.],.],[.,.]]]]] => [.,[.,[[.,[[[.,[.,.]],.],.]],.]]]
[1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [.,[.,[[.,.],[[[[.,.],.],.],.]]]] => [.,[.,[[.,[[[[.,.],.],.],.]],.]]]
[1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => [.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]
[1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [.,[.,[[[.,.],.],[.,[[.,.],.]]]]] => [.,[.,[[[.,[.,[[.,.],.]]],.],.]]]
[1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [.,[.,[[[.,.],.],[[.,.],[.,.]]]]] => [.,[.,[[[.,[[.,[.,.]],.]],.],.]]]
[1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [.,[.,[[[.,.],.],[[[.,.],.],.]]]] => [.,[.,[[[.,[[[.,.],.],.]],.],.]]]
[1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => [.,[.,[[[[.,[.,[.,.]]],.],.],.]]]
[1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [.,[.,[[[[.,.],.],.],[[.,.],.]]]] => [.,[.,[[[[.,[[.,.],.]],.],.],.]]]
[1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [.,[.,[[[[[.,.],.],.],.],[.,.]]]] => [.,[.,[[[[[.,[.,.]],.],.],.],.]]]
[1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [.,[.,[[[[[[.,.],.],.],.],.],.]]] => [.,[.,[[[[[[.,.],.],.],.],.],.]]]
[1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]
[1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]
[1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [.,[[.,.],[.,[.,[[[.,.],.],.]]]]] => [.,[[.,[.,[.,[[[.,.],.],.]]]],.]]
[1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [.,[[.,[.,[[.,[.,[.,.]]],.]]],.]]
[1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]] => [.,[[.,[.,[[.,[[.,.],.]],.]]],.]]
[1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]] => [.,[[.,[.,[[[.,[.,.]],.],.]]],.]]
[1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [.,[[.,.],[.,[[[[.,.],.],.],.]]]] => [.,[[.,[.,[[[[.,.],.],.],.]]],.]]
[1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]
[1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => [.,[[.,[[.,[.,[[.,.],.]]],.]],.]]
[1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]]
[1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]] => [.,[[.,[[.,[[[.,.],.],.]],.]],.]]
[1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [.,[[.,[[[.,[.,[.,.]]],.],.]],.]]
[1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [.,[[.,[[[.,[[.,.],.]],.],.]],.]]
[1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [.,[[.,.],[[[[.,.],.],.],[.,.]]]] => [.,[[.,[[[[.,[.,.]],.],.],.]],.]]
[1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [.,[[.,.],[[[[[.,.],.],.],.],.]]] => [.,[[.,[[[[[.,.],.],.],.],.]],.]]
[1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]
[1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [.,[[[.,.],.],[.,[.,[[.,.],.]]]]] => [.,[[[.,[.,[.,[[.,.],.]]]],.],.]]
[1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => [.,[[[.,[.,[[.,[.,.]],.]]],.],.]]
[1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [.,[[[.,[.,[[[.,.],.],.]]],.],.]]
[1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [.,[[[.,[[.,[.,[.,.]]],.]],.],.]]
[1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [.,[[[.,[[.,[[.,.],.]],.]],.],.]]
[1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [.,[[[.,[[[.,[.,.]],.],.]],.],.]]
[1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [.,[[[.,.],.],[[[[.,.],.],.],.]]] => [.,[[[.,[[[[.,.],.],.],.]],.],.]]
[1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [.,[[[[.,[.,[.,[.,.]]]],.],.],.]]
[1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [.,[[[[.,.],.],.],[.,[[.,.],.]]]] => [.,[[[[.,[.,[[.,.],.]]],.],.],.]]
[1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [.,[[[[.,[[.,[.,.]],.]],.],.],.]]
[1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [.,[[[[.,.],.],.],[[[.,.],.],.]]] => [.,[[[[.,[[[.,.],.],.]],.],.],.]]
[1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [.,[[[[[.,[.,[.,.]]],.],.],.],.]]
[1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [.,[[[[[.,.],.],.],.],[[.,.],.]]] => [.,[[[[[.,[[.,.],.]],.],.],.],.]]
[1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [.,[[[[[[.,.],.],.],.],.],[.,.]]] => [.,[[[[[[.,[.,.]],.],.],.],.],.]]
[1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [.,[[[[[[[.,.],.],.],.],.],.],.]] => [.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]
[2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]
[2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [[.,[.,[.,[.,[[[.,.],.],.]]]]],.]
[2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]
[2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [[.,[.,[.,[[.,[[.,.],.]],.]]]],.]
[2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [[.,[.,[.,[[[.,[.,.]],.],.]]]],.]
[2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [[.,[.,[.,[[[[.,.],.],.],.]]]],.]
[2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]
[2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [[.,[.,[[.,[.,[[.,.],.]]],.]]],.]
[2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [[.,[.,[[.,[[.,[.,.]],.]],.]]],.]
[2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [[.,[.,[[.,[[[.,.],.],.]],.]]],.]
[2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [[.,[.,[[[.,[.,[.,.]]],.],.]]],.]
[2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [[.,[.,[[[.,[[.,.],.]],.],.]]],.]
[2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => [[.,[.,[[[[.,[.,.]],.],.],.]]],.]
[2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[.,.],[.,[[[[[.,.],.],.],.],.]]] => [[.,[.,[[[[[.,.],.],.],.],.]]],.]
[2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]
[2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [[.,[[.,[.,[.,[[.,.],.]]]],.]],.]
[2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [[.,[[.,[.,[[.,[.,.]],.]]],.]],.]
[2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [[.,[[.,[.,[[[.,.],.],.]]],.]],.]
[2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [[.,[[.,[[.,[.,[.,.]]],.]],.]],.]
[2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.]
[2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [[.,[[.,[[[.,[.,.]],.],.]],.]],.]
[2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => [[.,[[.,[[[[.,.],.],.],.]],.]],.]
[2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [[.,[[[.,[.,[.,[.,.]]]],.],.]],.]
[2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [[.,[[[.,[.,[[.,.],.]]],.],.]],.]
[2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [[.,[[[.,[[.,[.,.]],.]],.],.]],.]
[2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [[.,[[[.,[[[.,.],.],.]],.],.]],.]
[2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [[.,[[[[.,[.,[.,.]]],.],.],.]],.]
[2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [[.,[[[[.,[[.,.],.]],.],.],.]],.]
[2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [[.,[[[[[.,[.,.]],.],.],.],.]],.]
[2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => [[.,[[[[[[.,.],.],.],.],.],.]],.]
[3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]
[3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [[[.,[.,[.,[.,[[.,.],.]]]]],.],.]
[3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [[[.,[.,[.,[[.,[.,.]],.]]]],.],.]
[3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [[[.,[.,[.,[[[.,.],.],.]]]],.],.]
[3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [[[.,[.,[[.,[.,[.,.]]],.]]],.],.]
[3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [[[.,[.,[[.,[[.,.],.]],.]]],.],.]
[3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [[[.,[.,[[[.,[.,.]],.],.]]],.],.]
[3,1,4] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [[[.,.],.],[.,[[[[.,.],.],.],.]]] => [[[.,[.,[[[[.,.],.],.],.]]],.],.]
[3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [[[.,[[.,[.,[.,[.,.]]]],.]],.],.]
[3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [[[.,[[.,[.,[[.,.],.]]],.]],.],.]
[3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [[[.,[[.,[[.,[.,.]],.]],.]],.],.]
[3,2,3] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [[[.,[[.,[[[.,.],.],.]],.]],.],.]
[3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [[[.,[[[.,[.,[.,.]]],.],.]],.],.]
[3,3,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [[[.,[[[.,[[.,.],.]],.],.]],.],.]
[3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [[[.,[[[[.,[.,.]],.],.],.]],.],.]
[3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [[[.,[[[[[.,.],.],.],.],.]],.],.]
[4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [[[[.,[.,[.,[.,[.,.]]]]],.],.],.]
[4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [[[[.,[.,[.,[[.,.],.]]]],.],.],.]
[4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [[[[.,[.,[[.,[.,.]],.]]],.],.],.]
[4,1,3] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => [[[[.,[.,[[[.,.],.],.]]],.],.],.]
[4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [[[[.,[[.,[.,[.,.]]],.]],.],.],.]
[4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [[[[.,[[.,[[.,.],.]],.]],.],.],.]
[4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [[[[.,[[[.,[.,.]],.],.]],.],.],.]
[4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [[[[.,[[[[.,.],.],.],.]],.],.],.]
[5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [[[[[.,[.,[.,[.,.]]]],.],.],.],.]
[5,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [[[[[.,[.,[[.,.],.]]],.],.],.],.]
[5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => [[[[[.,[[.,[.,.]],.]],.],.],.],.]
[5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [[[[[.,[[[.,.],.],.]],.],.],.],.]
[6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [[[[[[.,[.,[.,.]]],.],.],.],.],.]
[6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [[[[[[.,[[.,.],.]],.],.],.],.],.]
[7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [[[[[[[.,[.,.]],.],.],.],.],.],.]
[8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[[[[[[[.,.],.],.],.],.],.],.],.] => [[[[[[[[.,.],.],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]] => [.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]
[1,1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]] => [.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]
[1,1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]] => [.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]
[1,1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]] => [.,[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]]
[1,1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]] => [.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]]
[1,1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]] => [.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]
[1,1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]] => [.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]
[1,1,1,1,2,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [.,[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]] => [.,[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]]
[1,1,1,1,2,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [.,[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]] => [.,[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]]
[1,1,1,1,2,3] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [.,[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]] => [.,[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]]
[1,1,1,1,3,1,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [.,[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]] => [.,[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]]
[1,1,1,1,3,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [.,[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]] => [.,[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]]
[1,1,1,1,4,1] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [.,[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]] => [.,[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]]
[1,1,1,1,5] => [1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]] => [.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]
[1,1,1,2,1,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]] => [.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]
[1,1,1,2,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [.,[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]] => [.,[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]]
[1,1,1,2,4] => [1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [.,[.,[.,[[.,.],[[[[.,.],.],.],.]]]]] => [.,[.,[.,[[.,[[[[.,.],.],.],.]],.]]]]
[1,1,1,3,1,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [.,[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]] => [.,[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]]
[1,1,1,3,3] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [.,[.,[.,[[[.,.],.],[[[.,.],.],.]]]]] => [.,[.,[.,[[[.,[[[.,.],.],.]],.],.]]]]
[1,1,1,5,1] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [.,[.,[.,[[[[[.,.],.],.],.],[.,.]]]]] => [.,[.,[.,[[[[[.,[.,.]],.],.],.],.]]]]
[1,1,1,6] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]] => [.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]
[1,1,2,1,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]] => [.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]
[1,1,2,1,1,3] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [.,[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]] => [.,[.,[[.,[.,[.,[[[.,.],.],.]]]],.]]]
[1,1,2,2,3] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [.,[.,[[.,.],[[.,.],[[[.,.],.],.]]]]] => [.,[.,[[.,[[.,[[[.,.],.],.]],.]],.]]]
[1,1,2,5] => [1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]] => [.,[.,[[.,[[[[[.,.],.],.],.],.]],.]]]
[1,1,3,1,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [.,[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]] => [.,[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]]
[1,1,3,2,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [.,[.,[[[.,.],.],[[.,.],[[.,.],.]]]]] => [.,[.,[[[.,[[.,[[.,.],.]],.]],.],.]]]
[1,1,6,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [.,[.,[[[[[[.,.],.],.],.],.],[.,.]]]] => [.,[.,[[[[[[.,[.,.]],.],.],.],.],.]]]
[1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [.,[.,[[[[[[[.,.],.],.],.],.],.],.]]] => [.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]
[1,2,1,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,2,1,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]] => [.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]]
[1,2,1,5] => [1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [.,[[.,.],[.,[[[[[.,.],.],.],.],.]]]] => [.,[[.,[.,[[[[[.,.],.],.],.],.]]],.]]
[1,2,2,1,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [.,[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]] => [.,[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]]
[1,2,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [.,[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]] => [.,[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]]
[1,2,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]
[1,2,2,3,1] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [.,[[.,.],[[.,.],[[[.,.],.],[.,.]]]]] => [.,[[.,[[.,[[[.,[.,.]],.],.]],.]],.]]
[1,2,2,4] => [1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [.,[[.,.],[[.,.],[[[[.,.],.],.],.]]]] => [.,[[.,[[.,[[[[.,.],.],.],.]],.]],.]]
[1,2,3,1,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [.,[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]] => [.,[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]]
[1,2,3,3] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [.,[[.,.],[[[.,.],.],[[[.,.],.],.]]]] => [.,[[.,[[[.,[[[.,.],.],.]],.],.]],.]]
[1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [.,[[.,.],[[[[[[.,.],.],.],.],.],.]]] => [.,[[.,[[[[[[.,.],.],.],.],.],.]],.]]
[1,3,1,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]] => [.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]]
[1,3,5] => [1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [.,[[[.,.],.],[[[[[.,.],.],.],.],.]]] => [.,[[[.,[[[[[.,.],.],.],.],.]],.],.]]
[1,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [.,[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]] => [.,[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]]
[1,4,4] => [1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [.,[[[[.,.],.],.],[[[[.,.],.],.],.]]] => [.,[[[[.,[[[[.,.],.],.],.]],.],.],.]]
[1,5,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [.,[[[[[.,.],.],.],.],[.,[.,[.,.]]]]] => [.,[[[[[.,[.,[.,[.,.]]]],.],.],.],.]]
[1,5,3] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [.,[[[[[.,.],.],.],.],[[[.,.],.],.]]] => [.,[[[[[.,[[[.,.],.],.]],.],.],.],.]]
[1,6,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [.,[[[[[[.,.],.],.],.],.],[.,[.,.]]]] => [.,[[[[[[.,[.,[.,.]]],.],.],.],.],.]]
[1,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [.,[[[[[[.,.],.],.],.],.],[[.,.],.]]] => [.,[[[[[[.,[[.,.],.]],.],.],.],.],.]]
[1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [.,[[[[[[[.,.],.],.],.],.],.],[.,.]]] => [.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]
[1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => [.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[2,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]
[2,1,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.]
[2,1,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[.,.],[.,[.,[.,[.,[[[.,.],.],.]]]]]] => [[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.]
[2,1,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => [[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]],.]
[2,1,1,1,2,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[.,.],[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]],.]
[2,1,1,1,3,1] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [[.,.],[.,[.,[.,[[[.,.],.],[.,.]]]]]] => [[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]],.]
[2,1,1,1,4] => [1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[.,.],[.,[.,[.,[[[[.,.],.],.],.]]]]] => [[.,[.,[.,[.,[[[[.,.],.],.],.]]]]],.]
[2,1,1,2,1,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[.,.],[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]],.]
[2,1,1,2,3] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[.,.],[.,[.,[[.,.],[[[.,.],.],.]]]]] => [[.,[.,[.,[[.,[[[.,.],.],.]],.]]]],.]
[2,1,1,5] => [1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[.,.],[.,[.,[[[[[.,.],.],.],.],.]]]] => [[.,[.,[.,[[[[[.,.],.],.],.],.]]]],.]
[2,1,2,1,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]],.]
[2,1,2,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[.,[[.,.],[[.,.],[[.,.],.]]]]] => [[.,[.,[[.,[[.,[[.,.],.]],.]],.]]],.]
[2,1,6] => [1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[.,.],[.,[[[[[[.,.],.],.],.],.],.]]] => [[.,[.,[[[[[[.,.],.],.],.],.],.]]],.]
[2,2,1,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.]
[2,2,1,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[.,.],[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]],.]
[2,2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[.,.],[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]],.]
[2,2,2,1,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[.,[[.,.],.]]]]] => [[.,[[.,[[.,[.,[[.,.],.]]],.]],.]],.]
[2,2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]] => [[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]
[2,2,2,3] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[.,.],[[.,.],[[.,.],[[[.,.],.],.]]]] => [[.,[[.,[[.,[[[.,.],.],.]],.]],.]],.]
[2,2,3,1,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[.,.],[[.,.],[[[.,.],.],[.,[.,.]]]]] => [[.,[[.,[[[.,[.,[.,.]]],.],.]],.]],.]
[2,2,5] => [1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,.],[[.,.],[[[[[.,.],.],.],.],.]]] => [[.,[[.,[[[[[.,.],.],.],.],.]],.]],.]
[2,3,1,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[.,.],[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]],.]
[2,3,4] => [1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[.,.],[[[.,.],.],[[[[.,.],.],.],.]]] => [[.,[[[.,[[[[.,.],.],.],.]],.],.]],.]
[2,6,1] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[.,.],[[[[[[.,.],.],.],.],.],[.,.]]] => [[.,[[[[[[.,[.,.]],.],.],.],.],.]],.]
[2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[.,.],[[[[[[[.,.],.],.],.],.],.],.]] => [[.,[[[[[[[.,.],.],.],.],.],.],.]],.]
[3,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]
[3,1,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[.,.],.],[.,[.,[.,[.,[[.,.],.]]]]]] => [[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.]
[3,1,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[[.,.],.],[.,[.,[.,[[.,.],[.,.]]]]]] => [[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.],.]
[3,1,4,1] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[.,.],.],[.,[[[[.,.],.],.],[.,.]]]] => [[[.,[.,[[[[.,[.,.]],.],.],.]]],.],.]
[3,1,5] => [1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[[.,.],.],[.,[[[[[.,.],.],.],.],.]]] => [[[.,[.,[[[[[.,.],.],.],.],.]]],.],.]
[3,2,1,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[.,.],.],[[.,.],[.,[.,[.,[.,.]]]]]] => [[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.],.]
[3,2,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[.,.],.],[[.,.],[[.,.],[[.,.],.]]]] => [[[.,[[.,[[.,[[.,.],.]],.]],.]],.],.]
[3,3,1,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[[.,.],.],[[[.,.],.],[.,[.,[.,.]]]]] => [[[.,[[[.,[.,[.,[.,.]]]],.],.]],.],.]
[3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[.,.],.],[[[.,.],.],[[[.,.],.],.]]] => [[[.,[[[.,[[[.,.],.],.]],.],.]],.],.]
[3,5,1] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[.,.],.],[[[[[.,.],.],.],.],[.,.]]] => [[[.,[[[[[.,[.,.]],.],.],.],.]],.],.]
[3,6] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[[.,.],.],[[[[[[.,.],.],.],.],.],.]] => [[[.,[[[[[[.,.],.],.],.],.],.]],.],.]
[4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]
[4,1,3,1] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,0] => [[[[.,.],.],.],[.,[[[.,.],.],[.,.]]]] => [[[[.,[.,[[[.,[.,.]],.],.]]],.],.],.]
[4,1,4] => [1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[.,[[[[.,.],.],.],.]]] => [[[[.,[.,[[[[.,.],.],.],.]]],.],.],.]
[4,2,1,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0] => [[[[.,.],.],.],[[.,.],[.,[.,[.,.]]]]] => [[[[.,[[.,[.,[.,[.,.]]]],.]],.],.],.]
[4,2,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [[[[.,.],.],.],[[.,.],[[.,.],[.,.]]]] => [[[[.,[[.,[[.,[.,.]],.]],.]],.],.],.]
[4,3,1,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0] => [[[[.,.],.],.],[[[.,.],.],[.,[.,.]]]] => [[[[.,[[[.,[.,[.,.]]],.],.]],.],.],.]
[4,3,2] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0] => [[[[.,.],.],.],[[[.,.],.],[[.,.],.]]] => [[[[.,[[[.,[[.,.],.]],.],.]],.],.],.]
[4,4,1] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [[[[.,.],.],.],[[[[.,.],.],.],[.,.]]] => [[[[.,[[[[.,[.,.]],.],.],.]],.],.],.]
[4,5] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[[[.,.],.],.],[[[[[.,.],.],.],.],.]] => [[[[.,[[[[[.,.],.],.],.],.]],.],.],.]
[5,1,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => [[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]
[5,1,3] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0] => [[[[[.,.],.],.],.],[.,[[[.,.],.],.]]] => [[[[[.,[.,[[[.,.],.],.]]],.],.],.],.]
[5,2,1,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [[[[[.,.],.],.],.],[[.,.],[.,[.,.]]]] => [[[[[.,[[.,[.,[.,.]]],.]],.],.],.],.]
[5,3,1] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [[[[[.,.],.],.],.],[[[.,.],.],[.,.]]] => [[[[[.,[[[.,[.,.]],.],.]],.],.],.],.]
[5,4] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[[.,.],.],.],.],[[[[.,.],.],.],.]] => [[[[[.,[[[[.,.],.],.],.]],.],.],.],.]
[6,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => [[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]
[6,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0] => [[[[[[.,.],.],.],.],.],[.,[[.,.],.]]] => [[[[[[.,[.,[[.,.],.]]],.],.],.],.],.]
[6,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [[[[[[.,.],.],.],.],.],[[.,.],[.,.]]] => [[[[[[.,[[.,[.,.]],.]],.],.],.],.],.]
[6,3] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [[[[[[.,.],.],.],.],.],[[[.,.],.],.]] => [[[[[[.,[[[.,.],.],.]],.],.],.],.],.]
[7,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]
[7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [[[[[[[.,.],.],.],.],.],.],[[.,.],.]] => [[[[[[[.,[[.,.],.]],.],.],.],.],.],.]
[8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [[[[[[[[.,[.,.]],.],.],.],.],.],.],.]
[9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [[[[[[[[[.,.],.],.],.],.],.],.],.],.] => [[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[1,1,1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]] => [.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]
[1,1,1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]] => [.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]
[1,1,1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]] => [.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]]
[1,1,1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [.,[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]] => [.,[.,[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]]]
[1,1,1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [.,[.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]]] => [.,[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]]]
[1,1,1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]] => [.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]]
[1,1,1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]] => [.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]]
[1,1,1,1,1,5] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]] => [.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]
[1,1,1,1,2,1,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]] => [.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]]
[1,1,1,1,2,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [.,[.,[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]]] => [.,[.,[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]]]
[1,1,1,1,6] => [1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]] => [.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]
[1,1,1,2,1,1,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]] => [.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]]
[1,1,1,7] => [1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]] => [.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]]
[1,1,2,1,1,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]
[1,1,2,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [.,[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => [.,[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]]
[1,1,4,4] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [.,[.,[[[[.,.],.],.],[[[[.,.],.],.],.]]]] => [.,[.,[[[[.,[[[[.,.],.],.],.]],.],.],.]]]
[1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]] => [.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]]
[1,2,1,1,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]
[1,2,2,1,1,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [.,[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]] => [.,[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.]]
[1,2,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [.,[[.,.],[[.,.],[[.,.],[.,[.,[.,.]]]]]]] => [.,[[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]],.]]
[1,2,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]] => [.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]
[1,2,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [.,[[.,.],[[.,.],[[.,.],[[[.,.],.],.]]]]] => [.,[[.,[[.,[[.,[[[.,.],.],.]],.]],.]],.]]
[1,2,3,4] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [.,[[.,.],[[[.,.],.],[[[[.,.],.],.],.]]]] => [.,[[.,[[[.,[[[[.,.],.],.],.]],.],.]],.]]
[1,2,7] => [1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [.,[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]] => [.,[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]]
[1,3,2,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [.,[[[.,.],.],[[.,.],[[.,.],[[.,.],.]]]]] => [.,[[[.,[[.,[[.,[[.,.],.]],.]],.]],.],.]]
[1,3,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [.,[[[.,.],.],[[[.,.],.],[[[.,.],.],.]]]] => [.,[[[.,[[[.,[[[.,.],.],.]],.],.]],.],.]]
[1,3,6] => [1,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [.,[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]] => [.,[[[.,[[[[[[.,.],.],.],.],.],.]],.],.]]
[1,4,5] => [1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [.,[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]] => [.,[[[[.,[[[[[.,.],.],.],.],.]],.],.],.]]
[1,7,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [.,[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]] => [.,[[[[[[[.,[[.,.],.]],.],.],.],.],.],.]]
[1,8,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]] => [.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]]
[1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => [.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[2,1,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[2,1,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]
[2,1,1,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]] => [[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]],.]
[2,1,1,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]] => [[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.]
[2,1,1,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]] => [[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]],.]
[2,1,1,1,1,3,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [[.,.],[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]] => [[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]],.]
[2,1,1,1,1,4] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[.,.],[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]] => [[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]],.]
[2,1,1,1,5] => [1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[.,.],[.,[.,[.,[[[[[.,.],.],.],.],.]]]]] => [[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]],.]
[2,1,2,1,1,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]] => [[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]],.]
[2,1,7] => [1,1,0,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[.,.],[.,[[[[[[[.,.],.],.],.],.],.],.]]] => [[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]],.]
[2,2,1,1,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]],.]
[2,2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[.,.],[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]] => [[.,[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]],.]
[2,2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[.,.],[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]] => [[.,[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]],.]
[2,2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[.,.],[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]] => [[.,[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]],.]
[2,2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]
[2,2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[.,.],[[.,.],[[.,.],[[[.,.],.],[.,.]]]]] => [[.,[[.,[[.,[[[.,[.,.]],.],.]],.]],.]],.]
[2,2,2,4] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[.,.],[[.,.],[[.,.],[[[[.,.],.],.],.]]]] => [[.,[[.,[[.,[[[[.,.],.],.],.]],.]],.]],.]
[2,2,3,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[.,.],[[.,.],[[[.,.],.],[[[.,.],.],.]]]] => [[.,[[.,[[[.,[[[.,.],.],.]],.],.]],.]],.]
[2,3,1,1,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]] => [[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]],.]
[2,3,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [[.,.],[[[.,.],.],[[[.,.],.],[[.,.],.]]]] => [[.,[[[.,[[[.,[[.,.],.]],.],.]],.],.]],.]
[2,4,3,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [[.,.],[[[[.,.],.],.],[[[.,.],.],[.,.]]]] => [[.,[[[[.,[[[.,[.,.]],.],.]],.],.],.]],.]
[2,4,4] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[.,.],[[[[.,.],.],.],[[[[.,.],.],.],.]]] => [[.,[[[[.,[[[[.,.],.],.],.]],.],.],.]],.]
[2,6,2] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [[.,.],[[[[[[.,.],.],.],.],.],[[.,.],.]]] => [[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]],.]
[2,7,1] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[.,.],[[[[[[[.,.],.],.],.],.],.],[.,.]]] => [[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]],.]
[2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]] => [[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]
[3,1,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]
[3,1,1,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[.,.],.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.],.]
[3,1,1,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[[.,.],.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.],.]
[3,2,1,1,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[.,.],.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.],.]
[3,2,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[.,.],.],[[.,.],[[.,.],[[.,.],[.,.]]]]] => [[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.],.]
[3,2,2,3] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[[.,.],.],[[.,.],[[.,.],[[[.,.],.],.]]]] => [[[.,[[.,[[.,[[[.,.],.],.]],.]],.]],.],.]
[3,3,2,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[.,.],.],[[[.,.],.],[[.,.],[[.,.],.]]]] => [[[.,[[[.,[[.,[[.,.],.]],.]],.],.]],.],.]
[3,3,4] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[[.,.],.],[[[.,.],.],[[[[.,.],.],.],.]]] => [[[.,[[[.,[[[[.,.],.],.],.]],.],.]],.],.]
[3,6,1] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[[.,.],.],[[[[[[.,.],.],.],.],.],[.,.]]] => [[[.,[[[[[[.,[.,.]],.],.],.],.],.]],.],.]
[3,7] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]] => [[[.,[[[[[[[.,.],.],.],.],.],.],.]],.],.]
[4,1,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]
[4,2,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],[[.,.],.]]]] => [[[[.,[[.,[[.,[[.,.],.]],.]],.]],.],.],.]
[4,2,4] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[[.,.],[[[[.,.],.],.],.]]] => [[[[.,[[.,[[[[.,.],.],.],.]],.]],.],.],.]
[4,3,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[[.,.],.],.],[[[.,.],.],[[[.,.],.],.]]] => [[[[.,[[[.,[[[.,.],.],.]],.],.]],.],.],.]
[4,4,1,1] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[[.,.],.],.],[[[[.,.],.],.],[.,[.,.]]]] => [[[[.,[[[[.,[.,[.,.]]],.],.],.]],.],.],.]
[4,4,2] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[[.,.],.],.],[[[[.,.],.],.],[[.,.],.]]] => [[[[.,[[[[.,[[.,.],.]],.],.],.]],.],.],.]
[4,6] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]] => [[[[.,[[[[[[.,.],.],.],.],.],.]],.],.],.]
[5,1,1,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]
[5,1,1,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,1,0,0] => [[[[[.,.],.],.],.],[.,[.,[.,[[.,.],.]]]]] => [[[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.],.]
[5,1,4] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,1,0,0,0,0] => [[[[[.,.],.],.],.],[.,[[[[.,.],.],.],.]]] => [[[[[.,[.,[[[[.,.],.],.],.]]],.],.],.],.]
[5,2,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [[[[[.,.],.],.],.],[[.,.],[[.,.],[.,.]]]] => [[[[[.,[[.,[[.,[.,.]],.]],.]],.],.],.],.]
[5,4,1] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [[[[[.,.],.],.],.],[[[[.,.],.],.],[.,.]]] => [[[[[.,[[[[.,[.,.]],.],.],.]],.],.],.],.]
[5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]] => [[[[[.,[[[[[.,.],.],.],.],.]],.],.],.],.]
[6,1,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => [[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]
[6,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,1,0,0,0] => [[[[[[.,.],.],.],.],.],[.,[[[.,.],.],.]]] => [[[[[[.,[.,[[[.,.],.],.]]],.],.],.],.],.]
[6,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0] => [[[[[[.,.],.],.],.],.],[[[.,.],.],[.,.]]] => [[[[[[.,[[[.,[.,.]],.],.]],.],.],.],.],.]
[6,4] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]] => [[[[[[.,[[[[.,.],.],.],.]],.],.],.],.],.]
[7,1,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => [[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]
[7,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,1,0,0] => [[[[[[[.,.],.],.],.],.],.],[.,[[.,.],.]]] => [[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.],.]
[7,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [[[[[[[.,.],.],.],.],.],.],[[.,.],[.,.]]] => [[[[[[[.,[[.,[.,.]],.]],.],.],.],.],.],.]
[7,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]] => [[[[[[[.,[[[.,.],.],.]],.],.],.],.],.],.]
[8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]
[8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]] => [[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.]
[9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]
[10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[1,10] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] => [.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[10,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => [[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]
[2,2,2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => [[.,[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]],.]
[1,2,2,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]] => [.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]]
[1,8,2] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [.,[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]] => [.,[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.]]
[1,1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]
Map
bounce path
Description
The bounce path determined by an integer composition.
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
left border symmetry
Description
Return the tree where a symmetry has been applied recursively on all left borders. If a tree is made of three trees $T_1, T_2, T_3$ on its left border, it becomes $T_3, T_2, T_1$ where same symmetry has been applied to $T_1, T_2, T_3$.