Processing math: 100%

Identifier
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00034: Dyck paths —to binary tree: up step, left tree, down step, right tree⟶ 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 549 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] => [.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[1,1,1,2,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [.,[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]]
[1,1,1,2,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [.,[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]]
[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] => [.,[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]]
[1,1,1,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [.,[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]]
[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] => [.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,2,1,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]]
[1,1,2,1,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [.,[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]]
[1,1,2,1,1,3] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [.,[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]]
[1,1,2,1,2,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [.,[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]]
[1,1,2,2,1,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [.,[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]]
[1,1,2,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [.,[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,2,2,3] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [.,[.,[[.,.],[[.,.],[[[.,.],.],.]]]]]
[1,1,2,3,2] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [.,[.,[[.,.],[[[.,.],.],[[.,.],.]]]]]
[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] => [.,[.,[[[.,.],.],[[.,.],[[.,.],.]]]]]
[1,1,4,1,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [.,[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]]
[1,1,4,3] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [.,[.,[[[[.,.],.],.],[[[.,.],.],.]]]]
[1,1,5,1,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [.,[.,[[[[[.,.],.],.],.],[.,[.,.]]]]]
[1,1,5,2] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [.,[.,[[[[[.,.],.],.],.],[[.,.],.]]]]
[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] => [.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,2,1,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [.,[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,2,1,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [.,[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]]
[1,2,1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [.,[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]]
[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] => [.,[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,2,2,1,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [.,[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]]
[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] => [.,[[.,.],[[[.,.],.],[[[.,.],.],.]]]]
[1,2,5,1] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [.,[[.,.],[[[[[.,.],.],.],.],[.,.]]]]
[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] => [.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]
[1,3,2,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [.,[[[.,.],.],[[.,.],[[.,.],[.,.]]]]]
[1,3,3,1,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [.,[[[.,.],.],[[[.,.],.],[.,[.,.]]]]]
[1,3,3,2] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [.,[[[.,.],.],[[[.,.],.],[[.,.],.]]]]
[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] => [.,[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]]
[1,4,1,3] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [.,[[[[.,.],.],.],[.,[[[.,.],.],.]]]]
[1,4,2,1,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [.,[[[[.,.],.],.],[[.,.],[.,[.,.]]]]]
[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] => [[.,.],[.,[.,[[.,.],[[[.,.],.],.]]]]]
[2,1,1,4,1] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[.,.],[.,[.,[[[[.,.],.],.],[.,.]]]]]
[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] => [[.,.],[.,[[.,.],[[.,.],[[.,.],.]]]]]
[2,1,3,3] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[.,.],[.,[[[.,.],.],[[[.,.],.],.]]]]
[2,1,5,1] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[.,.],[.,[[[[[.,.],.],.],.],[.,.]]]]
[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] => [[.,.],[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[2,2,1,4] => [1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[.,.],[[.,.],[.,[[[[.,.],.],.],.]]]]
[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] => [[.,.],[[.,.],[[[.,.],.],[.,[.,.]]]]]
[2,2,3,2] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[.,.],[[.,.],[[[.,.],.],[[.,.],.]]]]
[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] => [[.,.],[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[2,3,3,1] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[.,.],[[[.,.],.],[[[.,.],.],[.,.]]]]
[2,3,4] => [1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[.,.],[[[.,.],.],[[[[.,.],.],.],.]]]
[2,4,1,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[.,.],[[[[.,.],.],.],[.,[.,[.,.]]]]]
[2,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[.,.],[[[[.,.],.],.],[[[.,.],.],.]]]
[2,5,1,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[.,.],[[[[[.,.],.],.],.],[.,[.,.]]]]
[2,5,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[.,.],[[[[[.,.],.],.],.],[[.,.],.]]]
[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] => [[[.,.],.],[.,[.,[.,[[.,.],[.,.]]]]]]
[3,1,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[[.,.],.],[.,[.,[.,[[[.,.],.],.]]]]]
[3,1,2,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[[.,.],.],[.,[[.,.],[.,[[.,.],.]]]]]
[3,1,2,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[[.,.],.],[.,[[.,.],[[.,.],[.,.]]]]]
[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] => [[[.,.],.],[[[.,.],.],[[[.,.],.],.]]]
[3,4,2] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[.,.],.],[[[[.,.],.],.],[[.,.],.]]]
[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] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[4,1,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,1,0,0] => [[[[.,.],.],.],[.,[.,[.,[[.,.],.]]]]]
[4,1,1,3] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,0,0,0] => [[[[.,.],.],.],[.,[.,[[[.,.],.],.]]]]
[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] => [[[[.,.],.],.],[[.,.],[[.,.],[.,.]]]]
[4,2,3] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0] => [[[[.,.],.],.],[[.,.],[[[.,.],.],.]]]
[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] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[5,1,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,1,0,0] => [[[[[.,.],.],.],.],[.,[.,[[.,.],.]]]]
[5,1,2,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,1,0] => [[[[[.,.],.],.],.],[.,[[.,.],[.,.]]]]
[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] => [.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,2,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [.,[.,[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]]]
[1,1,1,1,1,4,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [.,[.,[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]]]
[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] => [.,[.,[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]]]
[1,1,1,1,3,1,1,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [.,[.,[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]]]
[1,1,1,1,5,1] => [1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [.,[.,[.,[.,[[[[[.,.],.],.],.],[.,.]]]]]]
[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] => [.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,2,1,1,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,2,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [.,[.,[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]]]
[1,1,1,2,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [.,[.,[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]]]
[1,1,1,3,1,1,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]]]
[1,1,1,4,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [.,[.,[.,[[[[.,.],.],.],[[.,.],[.,.]]]]]]
[1,1,1,6,1] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [.,[.,[.,[[[[[[.,.],.],.],.],.],[.,.]]]]]
[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] => [.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,2,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [.,[.,[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]]]
[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] => [.,[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,3,1,1,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,4,1,1,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [.,[.,[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]]]
[1,1,4,4] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [.,[.,[[[[.,.],.],.],[[[[.,.],.],.],.]]]]
[1,1,5,1,1,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [.,[.,[[[[[.,.],.],.],.],[.,[.,[.,.]]]]]]
[1,1,6,2] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [.,[.,[[[[[[.,.],.],.],.],.],[[.,.],.]]]]
[1,1,7,1] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [.,[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]]
[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] => [.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,2,1,1,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [.,[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,2,1,1,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [.,[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,2,1,3,1,2] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [.,[[.,.],[.,[[[.,.],.],[.,[[.,.],.]]]]]]
[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] => [.,[[.,.],[[.,.],[[.,.],[[[.,.],.],.]]]]]
[1,2,3,2,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [.,[[.,.],[[[.,.],.],[[.,.],[[.,.],.]]]]]
[1,2,3,4] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [.,[[.,.],[[[.,.],.],[[[[.,.],.],.],.]]]]
[1,2,4,1,1,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [.,[[.,.],[[[[.,.],.],.],[.,[.,[.,.]]]]]]
[1,2,7] => [1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [.,[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]]
[1,3,1,1,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[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] => [.,[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]]
[1,4,1,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [.,[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]]
[1,4,5] => [1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [.,[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]]
[1,5,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [.,[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]]
[1,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [.,[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]]
[1,6,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [.,[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]]
[1,7,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [.,[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]]
[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] => [[.,.],[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[2,1,4,1,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[.,.],[.,[[[[.,.],.],.],[.,[[.,.],.]]]]]
[2,1,6,1] => [1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[.,.],[.,[[[[[[.,.],.],.],.],.],[.,.]]]]
[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] => [[.,.],[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[2,2,1,1,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]]
[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] => [[.,.],[[.,.],[[.,.],[[[[.,.],.],.],.]]]]
[2,2,3,1,1,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[.,.],[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]]
[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] => [[.,.],[[[[.,.],.],.],[[[[.,.],.],.],.]]]
[2,6,1,1] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [[.,.],[[[[[[.,.],.],.],.],.],[.,[.,.]]]]
[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] => [[[.,.],.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[3,1,5,1] => [1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[.,.],.],[.,[[[[[.,.],.],.],.],[.,.]]]]
[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] => [[[.,.],.],[[[.,.],.],[[[[.,.],.],.],.]]]
[3,4,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[[.,.],.],[[[[.,.],.],.],[[[.,.],.],.]]]
[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] => [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[4,1,1,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[.,.],.],.],[.,[.,[.,[.,[[.,.],.]]]]]]
[4,1,1,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[.,[.,[[[[.,.],.],.],.]]]]
[4,1,4,1] => [1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[[.,.],.],.],[.,[[[[.,.],.],.],[.,.]]]]
[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] => [[[[.,.],.],.],[[[[.,.],.],.],[[.,.],.]]]
[4,5,1] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[[.,.],.],.],[[[[[.,.],.],.],.],[.,.]]]
[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] => [[[[[.,.],.],.],.],[.,[.,[.,[[.,.],.]]]]]
[5,1,3,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0,1,0] => [[[[[.,.],.],.],.],[.,[[[.,.],.],[.,.]]]]
[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] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[6,1,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,1,0,0] => [[[[[[.,.],.],.],.],.],[.,[.,[[.,.],.]]]]
[6,1,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0,1,0] => [[[[[[.,.],.],.],.],.],[.,[[.,.],[.,.]]]]
[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] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]
[1,2,2,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
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 n1,n2 with n1+n2=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.