Identifier
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00029: Dyck paths —to binary tree: left tree, up step, right tree, down step⟶ Binary trees
Mp00014: Binary trees —to 132-avoiding permutation⟶ Permutations
Images
[1] => [1,0] => [.,.] => [1]
[1,1] => [1,0,1,0] => [[.,.],.] => [1,2]
[2] => [1,1,0,0] => [.,[.,.]] => [2,1]
[1,1,1] => [1,0,1,0,1,0] => [[[.,.],.],.] => [1,2,3]
[1,2] => [1,0,1,1,0,0] => [[.,.],[.,.]] => [3,1,2]
[2,1] => [1,1,0,0,1,0] => [[.,[.,.]],.] => [2,1,3]
[3] => [1,1,1,0,0,0] => [.,[.,[.,.]]] => [3,2,1]
[1,1,1,1] => [1,0,1,0,1,0,1,0] => [[[[.,.],.],.],.] => [1,2,3,4]
[1,1,2] => [1,0,1,0,1,1,0,0] => [[[.,.],.],[.,.]] => [4,1,2,3]
[1,2,1] => [1,0,1,1,0,0,1,0] => [[[.,.],[.,.]],.] => [3,1,2,4]
[1,3] => [1,0,1,1,1,0,0,0] => [[.,.],[.,[.,.]]] => [4,3,1,2]
[2,1,1] => [1,1,0,0,1,0,1,0] => [[[.,[.,.]],.],.] => [2,1,3,4]
[2,2] => [1,1,0,0,1,1,0,0] => [[.,[.,.]],[.,.]] => [4,2,1,3]
[3,1] => [1,1,1,0,0,0,1,0] => [[.,[.,[.,.]]],.] => [3,2,1,4]
[4] => [1,1,1,1,0,0,0,0] => [.,[.,[.,[.,.]]]] => [4,3,2,1]
[1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[[[[.,.],.],.],.],.] => [1,2,3,4,5]
[1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [[[[.,.],.],.],[.,.]] => [5,1,2,3,4]
[1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[[[.,.],.],[.,.]],.] => [4,1,2,3,5]
[1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [[[.,.],.],[.,[.,.]]] => [5,4,1,2,3]
[1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[[[.,.],[.,.]],.],.] => [3,1,2,4,5]
[1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [[[.,.],[.,.]],[.,.]] => [5,3,1,2,4]
[1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [[[.,.],[.,[.,.]]],.] => [4,3,1,2,5]
[1,4] => [1,0,1,1,1,1,0,0,0,0] => [[.,.],[.,[.,[.,.]]]] => [5,4,3,1,2]
[2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[[[.,[.,.]],.],.],.] => [2,1,3,4,5]
[2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [[[.,[.,.]],.],[.,.]] => [5,2,1,3,4]
[2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [[[.,[.,.]],[.,.]],.] => [4,2,1,3,5]
[2,3] => [1,1,0,0,1,1,1,0,0,0] => [[.,[.,.]],[.,[.,.]]] => [5,4,2,1,3]
[3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [[[.,[.,[.,.]]],.],.] => [3,2,1,4,5]
[3,2] => [1,1,1,0,0,0,1,1,0,0] => [[.,[.,[.,.]]],[.,.]] => [5,3,2,1,4]
[4,1] => [1,1,1,1,0,0,0,0,1,0] => [[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5]
[5] => [1,1,1,1,1,0,0,0,0,0] => [.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1]
[1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6]
[1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[.,.],.],.],.],[.,.]] => [6,1,2,3,4,5]
[1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [[[[[.,.],.],.],[.,.]],.] => [5,1,2,3,4,6]
[1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[[[.,.],.],.],[.,[.,.]]] => [6,5,1,2,3,4]
[1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [[[[[.,.],.],[.,.]],.],.] => [4,1,2,3,5,6]
[1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],[.,.]],[.,.]] => [6,4,1,2,3,5]
[1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [[[[.,.],.],[.,[.,.]]],.] => [5,4,1,2,3,6]
[1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [[[.,.],.],[.,[.,[.,.]]]] => [6,5,4,1,2,3]
[1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [[[[[.,.],[.,.]],.],.],.] => [3,1,2,4,5,6]
[1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [[[[.,.],[.,.]],.],[.,.]] => [6,3,1,2,4,5]
[1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [[[[.,.],[.,.]],[.,.]],.] => [5,3,1,2,4,6]
[1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => [[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4]
[1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [[[[.,.],[.,[.,.]]],.],.] => [4,3,1,2,5,6]
[1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => [[[.,.],[.,[.,.]]],[.,.]] => [6,4,3,1,2,5]
[1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [[[.,.],[.,[.,[.,.]]]],.] => [5,4,3,1,2,6]
[1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,.]]]]] => [6,5,4,3,1,2]
[2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6]
[2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [[[[.,[.,.]],.],.],[.,.]] => [6,2,1,3,4,5]
[2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [[[[.,[.,.]],.],[.,.]],.] => [5,2,1,3,4,6]
[2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [[[.,[.,.]],.],[.,[.,.]]] => [6,5,2,1,3,4]
[2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [[[[.,[.,.]],[.,.]],.],.] => [4,2,1,3,5,6]
[2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[.,.]],[.,.]],[.,.]] => [6,4,2,1,3,5]
[2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [[[.,[.,.]],[.,[.,.]]],.] => [5,4,2,1,3,6]
[2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [[.,[.,.]],[.,[.,[.,.]]]] => [6,5,4,2,1,3]
[3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6]
[3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [[[.,[.,[.,.]]],.],[.,.]] => [6,3,2,1,4,5]
[3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[[.,[.,[.,.]]],[.,.]],.] => [5,3,2,1,4,6]
[3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [[.,[.,[.,.]]],[.,[.,.]]] => [6,5,3,2,1,4]
[4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6]
[4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [[.,[.,[.,[.,.]]]],[.,.]] => [6,4,3,2,1,5]
[5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6]
[6] => [1,1,1,1,1,1,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1]
[1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7]
[1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[.,.],.],.],.],.],[.,.]] => [7,1,2,3,4,5,6]
[1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[[[[[.,.],.],.],.],[.,.]],.] => [6,1,2,3,4,5,7]
[1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[[[[.,.],.],.],.],[.,[.,.]]] => [7,6,1,2,3,4,5]
[1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[[[[[.,.],.],.],[.,.]],.],.] => [5,1,2,3,4,6,7]
[1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[[[[.,.],.],.],[.,.]],[.,.]] => [7,5,1,2,3,4,6]
[1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [[[[[.,.],.],.],[.,[.,.]]],.] => [6,5,1,2,3,4,7]
[1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [7,6,5,1,2,3,4]
[1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[[[[[.,.],.],[.,.]],.],.],.] => [4,1,2,3,5,6,7]
[1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[[[[.,.],.],[.,.]],.],[.,.]] => [7,4,1,2,3,5,6]
[1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[[[[.,.],.],[.,.]],[.,.]],.] => [6,4,1,2,3,5,7]
[1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [7,6,4,1,2,3,5]
[1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[[[[.,.],.],[.,[.,.]]],.],.] => [5,4,1,2,3,6,7]
[1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [7,5,4,1,2,3,6]
[1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [6,5,4,1,2,3,7]
[1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [7,6,5,4,1,2,3]
[1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[[[[.,.],[.,.]],.],.],.],.] => [3,1,2,4,5,6,7]
[1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[[[[.,.],[.,.]],.],.],[.,.]] => [7,3,1,2,4,5,6]
[1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[[[[.,.],[.,.]],.],[.,.]],.] => [6,3,1,2,4,5,7]
[1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [7,6,3,1,2,4,5]
[1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[[[[.,.],[.,.]],[.,.]],.],.] => [5,3,1,2,4,6,7]
[1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [7,5,3,1,2,4,6]
[1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [6,5,3,1,2,4,7]
[1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [7,6,5,3,1,2,4]
[1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[[[[.,.],[.,[.,.]]],.],.],.] => [4,3,1,2,5,6,7]
[1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [7,4,3,1,2,5,6]
[1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [6,4,3,1,2,5,7]
[1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [7,6,4,3,1,2,5]
[1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[[.,.],[.,[.,[.,.]]]],.],.] => [5,4,3,1,2,6,7]
[1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [7,5,4,3,1,2,6]
[1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [6,5,4,3,1,2,7]
[1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [7,6,5,4,3,1,2]
[2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7]
[2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[[[[.,[.,.]],.],.],.],[.,.]] => [7,2,1,3,4,5,6]
[2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[[[[.,[.,.]],.],.],[.,.]],.] => [6,2,1,3,4,5,7]
[2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [7,6,2,1,3,4,5]
[2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[[[[.,[.,.]],.],[.,.]],.],.] => [5,2,1,3,4,6,7]
[2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [7,5,2,1,3,4,6]
>>> Load all 354 entries. <<<
[2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [6,5,2,1,3,4,7]
[2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [7,6,5,2,1,3,4]
[2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[[[[.,[.,.]],[.,.]],.],.],.] => [4,2,1,3,5,6,7]
[2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [7,4,2,1,3,5,6]
[2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [6,4,2,1,3,5,7]
[2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [7,6,4,2,1,3,5]
[2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[[[.,[.,.]],[.,[.,.]]],.],.] => [5,4,2,1,3,6,7]
[2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [7,5,4,2,1,3,6]
[2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [6,5,4,2,1,3,7]
[2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [7,6,5,4,2,1,3]
[3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7]
[3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[[[.,[.,[.,.]]],.],.],[.,.]] => [7,3,2,1,4,5,6]
[3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[[[.,[.,[.,.]]],.],[.,.]],.] => [6,3,2,1,4,5,7]
[3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [7,6,3,2,1,4,5]
[3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[[[.,[.,[.,.]]],[.,.]],.],.] => [5,3,2,1,4,6,7]
[3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [7,5,3,2,1,4,6]
[3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [6,5,3,2,1,4,7]
[3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [7,6,5,3,2,1,4]
[4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7]
[4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => [7,4,3,2,1,5,6]
[4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => [6,4,3,2,1,5,7]
[4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [7,6,4,3,2,1,5]
[5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7]
[5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [7,5,4,3,2,1,6]
[6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7]
[7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1]
[1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[.,.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8]
[1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [8,1,2,3,4,5,6,7]
[1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[[[[[[.,.],.],.],.],.],[.,.]],.] => [7,1,2,3,4,5,6,8]
[1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [8,7,1,2,3,4,5,6]
[1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[[[[[[.,.],.],.],.],[.,.]],.],.] => [6,1,2,3,4,5,7,8]
[1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => [8,6,1,2,3,4,5,7]
[1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [7,6,1,2,3,4,5,8]
[1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [8,7,6,1,2,3,4,5]
[1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[[[[[[.,.],.],.],[.,.]],.],.],.] => [5,1,2,3,4,6,7,8]
[1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [8,5,1,2,3,4,6,7]
[1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [7,5,1,2,3,4,6,8]
[1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [8,7,5,1,2,3,4,6]
[1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => [6,5,1,2,3,4,7,8]
[1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [8,6,5,1,2,3,4,7]
[1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [7,6,5,1,2,3,4,8]
[1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [8,7,6,5,1,2,3,4]
[1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[[[[[.,.],.],[.,.]],.],.],.],.] => [4,1,2,3,5,6,7,8]
[1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [8,4,1,2,3,5,6,7]
[1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [7,4,1,2,3,5,6,8]
[1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [8,7,4,1,2,3,5,6]
[1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => [6,4,1,2,3,5,7,8]
[1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [8,6,4,1,2,3,5,7]
[1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [7,6,4,1,2,3,5,8]
[1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [8,7,6,4,1,2,3,5]
[1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[[[[[.,.],.],[.,[.,.]]],.],.],.] => [5,4,1,2,3,6,7,8]
[1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [8,5,4,1,2,3,6,7]
[1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [7,5,4,1,2,3,6,8]
[1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [8,7,5,4,1,2,3,6]
[1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [6,5,4,1,2,3,7,8]
[1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [8,6,5,4,1,2,3,7]
[1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [7,6,5,4,1,2,3,8]
[1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [8,7,6,5,4,1,2,3]
[1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[.,.],[.,.]],.],.],.],.],.] => [3,1,2,4,5,6,7,8]
[1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [8,3,1,2,4,5,6,7]
[1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => [7,3,1,2,4,5,6,8]
[1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [8,7,3,1,2,4,5,6]
[1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[[[[[.,.],[.,.]],.],[.,.]],.],.] => [6,3,1,2,4,5,7,8]
[1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [8,6,3,1,2,4,5,7]
[1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [7,6,3,1,2,4,5,8]
[1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [8,7,6,3,1,2,4,5]
[1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[[[[[.,.],[.,.]],[.,.]],.],.],.] => [5,3,1,2,4,6,7,8]
[1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [8,5,3,1,2,4,6,7]
[1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [7,5,3,1,2,4,6,8]
[1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [8,7,5,3,1,2,4,6]
[1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[[[[.,.],[.,.]],[.,[.,.]]],.],.] => [6,5,3,1,2,4,7,8]
[1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [8,6,5,3,1,2,4,7]
[1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [7,6,5,3,1,2,4,8]
[1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [8,7,6,5,3,1,2,4]
[1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[[[[[.,.],[.,[.,.]]],.],.],.],.] => [4,3,1,2,5,6,7,8]
[1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [8,4,3,1,2,5,6,7]
[1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [7,4,3,1,2,5,6,8]
[1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [8,7,4,3,1,2,5,6]
[1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [6,4,3,1,2,5,7,8]
[1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [8,6,4,3,1,2,5,7]
[1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [7,6,4,3,1,2,5,8]
[1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [8,7,6,4,3,1,2,5]
[1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [5,4,3,1,2,6,7,8]
[1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [8,5,4,3,1,2,6,7]
[1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [7,5,4,3,1,2,6,8]
[1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [8,7,5,4,3,1,2,6]
[1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [6,5,4,3,1,2,7,8]
[1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [8,6,5,4,3,1,2,7]
[1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [7,6,5,4,3,1,2,8]
[1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,4,3,1,2]
[2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[.,[.,.]],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8]
[2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => [8,2,1,3,4,5,6,7]
[2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[[[[[.,[.,.]],.],.],.],[.,.]],.] => [7,2,1,3,4,5,6,8]
[2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [8,7,2,1,3,4,5,6]
[2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[[[[[.,[.,.]],.],.],[.,.]],.],.] => [6,2,1,3,4,5,7,8]
[2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [8,6,2,1,3,4,5,7]
[2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [[[[[.,[.,.]],.],.],[.,[.,.]]],.] => [7,6,2,1,3,4,5,8]
[2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [8,7,6,2,1,3,4,5]
[2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[[[[[.,[.,.]],.],[.,.]],.],.],.] => [5,2,1,3,4,6,7,8]
[2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [8,5,2,1,3,4,6,7]
[2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [7,5,2,1,3,4,6,8]
[2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [8,7,5,2,1,3,4,6]
[2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[[[[.,[.,.]],.],[.,[.,.]]],.],.] => [6,5,2,1,3,4,7,8]
[2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [8,6,5,2,1,3,4,7]
[2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => [7,6,5,2,1,3,4,8]
[2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [8,7,6,5,2,1,3,4]
[2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[[[[.,[.,.]],[.,.]],.],.],.],.] => [4,2,1,3,5,6,7,8]
[2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [8,4,2,1,3,5,6,7]
[2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[[[[.,[.,.]],[.,.]],.],[.,.]],.] => [7,4,2,1,3,5,6,8]
[2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [8,7,4,2,1,3,5,6]
[2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [6,4,2,1,3,5,7,8]
[2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [8,6,4,2,1,3,5,7]
[2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [7,6,4,2,1,3,5,8]
[2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [8,7,6,4,2,1,3,5]
[2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[[[[.,[.,.]],[.,[.,.]]],.],.],.] => [5,4,2,1,3,6,7,8]
[2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [8,5,4,2,1,3,6,7]
[2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [7,5,4,2,1,3,6,8]
[2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [8,7,5,4,2,1,3,6]
[2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[[.,[.,.]],[.,[.,[.,.]]]],.],.] => [6,5,4,2,1,3,7,8]
[2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [8,6,5,4,2,1,3,7]
[2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [7,6,5,4,2,1,3,8]
[2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [8,7,6,5,4,2,1,3]
[3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,[.,[.,.]]],.],.],.],.],.] => [3,2,1,4,5,6,7,8]
[3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [8,3,2,1,4,5,6,7]
[3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [[[[[.,[.,[.,.]]],.],.],[.,.]],.] => [7,3,2,1,4,5,6,8]
[3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [8,7,3,2,1,4,5,6]
[3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [[[[[.,[.,[.,.]]],.],[.,.]],.],.] => [6,3,2,1,4,5,7,8]
[3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [8,6,3,2,1,4,5,7]
[3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [7,6,3,2,1,4,5,8]
[3,1,4] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [8,7,6,3,2,1,4,5]
[3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [[[[[.,[.,[.,.]]],[.,.]],.],.],.] => [5,3,2,1,4,6,7,8]
[3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [[[[.,[.,[.,.]]],[.,.]],.],[.,.]] => [8,5,3,2,1,4,6,7]
[3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [7,5,3,2,1,4,6,8]
[3,2,3] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [8,7,5,3,2,1,4,6]
[3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [[[[.,[.,[.,.]]],[.,[.,.]]],.],.] => [6,5,3,2,1,4,7,8]
[3,3,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [8,6,5,3,2,1,4,7]
[3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [7,6,5,3,2,1,4,8]
[3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [8,7,6,5,3,2,1,4]
[4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [4,3,2,1,5,6,7,8]
[4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [8,4,3,2,1,5,6,7]
[4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => [7,4,3,2,1,5,6,8]
[4,1,3] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [8,7,4,3,2,1,5,6]
[4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [[[[.,[.,[.,[.,.]]]],[.,.]],.],.] => [6,4,3,2,1,5,7,8]
[4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [8,6,4,3,2,1,5,7]
[4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [7,6,4,3,2,1,5,8]
[4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [8,7,6,4,3,2,1,5]
[5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [5,4,3,2,1,6,7,8]
[5,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => [8,5,4,3,2,1,6,7]
[5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] => [7,5,4,3,2,1,6,8]
[5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [8,7,5,4,3,2,1,6]
[6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [6,5,4,3,2,1,7,8]
[6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [8,6,5,4,3,2,1,7]
[7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [7,6,5,4,3,2,1,8]
[8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [8,7,6,5,4,3,2,1]
[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] => [[[[[[[[[.,.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9]
[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] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [9,1,2,3,4,5,6,7,8]
[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] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],.] => [8,1,2,3,4,5,6,7,9]
[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] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [9,8,1,2,3,4,5,6,7]
[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] => [[[[[[[[.,.],.],.],.],.],[.,.]],.],.] => [7,1,2,3,4,5,6,8,9]
[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] => [[[[[[[.,.],.],.],.],.],[.,.]],[.,.]] => [9,7,1,2,3,4,5,6,8]
[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] => [[[[[[[.,.],.],.],.],.],[.,[.,.]]],.] => [8,7,1,2,3,4,5,6,9]
[1,1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => [9,8,7,1,2,3,4,5,6]
[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] => [[[[[[[[.,.],.],.],.],[.,.]],.],.],.] => [6,1,2,3,4,5,7,8,9]
[1,1,1,1,2,3] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]] => [9,8,6,1,2,3,4,5,7]
[1,1,1,1,4,1] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[[[[.,.],.],.],.],[.,[.,[.,.]]]],.] => [8,7,6,1,2,3,4,5,9]
[1,1,1,1,5] => [1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => [9,8,7,6,1,2,3,4,5]
[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] => [[[[[[[[.,.],.],.],[.,.]],.],.],.],.] => [5,1,2,3,4,6,7,8,9]
[1,1,1,2,4] => [1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]] => [9,8,7,5,1,2,3,4,6]
[1,1,1,5,1] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[[[.,.],.],.],[.,[.,[.,[.,.]]]]],.] => [8,7,6,5,1,2,3,4,9]
[1,1,1,6] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [9,8,7,6,5,1,2,3,4]
[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] => [[[[[[[[.,.],.],[.,.]],.],.],.],.],.] => [4,1,2,3,5,6,7,8,9]
[1,1,2,5] => [1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]] => [9,8,7,6,4,1,2,3,5]
[1,1,6,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.] => [8,7,6,5,4,1,2,3,9]
[1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [9,8,7,6,5,4,1,2,3]
[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] => [[[[[[[[.,.],[.,.]],.],.],.],.],.],.] => [3,1,2,4,5,6,7,8,9]
[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] => [[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => [9,3,1,2,4,5,6,7,8]
[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] => [[[[[[[.,.],[.,.]],[.,.]],.],.],.],.] => [5,3,1,2,4,6,7,8,9]
[1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [9,8,7,6,5,3,1,2,4]
[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] => [[[[[[[.,.],[.,[.,.]]],.],.],.],.],.] => [4,3,1,2,5,6,7,8,9]
[1,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[[[.,.],[.,[.,[.,.]]]],.],.],.],.] => [5,4,3,1,2,6,7,8,9]
[1,5,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [[[[[.,.],[.,[.,[.,[.,.]]]]],.],.],.] => [6,5,4,3,1,2,7,8,9]
[1,6,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.] => [7,6,5,4,3,1,2,8,9]
[1,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [9,7,6,5,4,3,1,2,8]
[1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [8,7,6,5,4,3,1,2,9]
[1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,5,4,3,1,2]
[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] => [[[[[[[[.,[.,.]],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9]
[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] => [[[[[[[.,[.,.]],.],.],.],.],.],[.,.]] => [9,2,1,3,4,5,6,7,8]
[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] => [[[[[[[.,[.,.]],.],.],.],.],[.,.]],.] => [8,2,1,3,4,5,6,7,9]
[2,1,1,1,2,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[[[[[.,[.,.]],.],.],.],[.,.]],[.,.]] => [9,7,2,1,3,4,5,6,8]
[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] => [[[[[[[.,[.,.]],[.,.]],.],.],.],.],.] => [4,2,1,3,5,6,7,8,9]
[2,6,1] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.] => [8,7,6,5,4,2,1,3,9]
[2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [9,8,7,6,5,4,2,1,3]
[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] => [[[[[[[.,[.,[.,.]]],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9]
[3,2,1,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[[[[.,[.,[.,.]]],[.,.]],.],.],.],.] => [5,3,2,1,4,6,7,8,9]
[3,6] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [9,8,7,6,5,3,2,1,4]
[4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9]
[4,1,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,1,0,0] => [[[[[.,[.,[.,[.,.]]]],.],.],.],[.,.]] => [9,4,3,2,1,5,6,7,8]
[4,2,1,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0] => [[[[[.,[.,[.,[.,.]]]],[.,.]],.],.],.] => [6,4,3,2,1,5,7,8,9]
[4,5] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [9,8,7,6,4,3,2,1,5]
[5,1,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.] => [5,4,3,2,1,6,7,8,9]
[5,2,1,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.],.] => [7,5,4,3,2,1,6,8,9]
[5,3,1] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]],.] => [8,7,5,4,3,2,1,6,9]
[5,4] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [9,8,7,5,4,3,2,1,6]
[6,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.] => [6,5,4,3,2,1,7,8,9]
[6,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.] => [8,6,5,4,3,2,1,7,9]
[6,3] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [9,8,6,5,4,3,2,1,7]
[7,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.] => [7,6,5,4,3,2,1,8,9]
[7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [9,7,6,5,4,3,2,1,8]
[8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [8,7,6,5,4,3,2,1,9]
[9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [9,8,7,6,5,4,3,2,1]
[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] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10]
[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] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [10,1,2,3,4,5,6,7,8,9]
[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] => [[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.] => [9,1,2,3,4,5,6,7,8,10]
[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] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [10,9,1,2,3,4,5,6,7,8]
[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] => [[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.] => [8,1,2,3,4,5,6,7,9,10]
[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] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]] => [10,8,1,2,3,4,5,6,7,9]
[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] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => [10,9,8,1,2,3,4,5,6,7]
[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] => [[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.] => [7,1,2,3,4,5,6,8,9,10]
[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] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => [10,9,8,7,1,2,3,4,5,6]
[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] => [[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.] => [6,1,2,3,4,5,7,8,9,10]
[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] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [10,9,8,7,6,1,2,3,4,5]
[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] => [[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.] => [5,1,2,3,4,6,7,8,9,10]
[1,1,1,7] => [1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [10,9,8,7,6,5,1,2,3,4]
[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] => [[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.] => [4,1,2,3,5,6,7,8,9,10]
[1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [10,9,8,7,6,5,4,1,2,3]
[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] => [[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.] => [3,1,2,4,5,6,7,8,9,10]
[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] => [[[[[[[[.,.],[.,.]],.],.],.],.],.],[.,.]] => [10,3,1,2,4,5,6,7,8,9]
[1,7,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [10,8,7,6,5,4,3,1,2,9]
[1,8,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [9,8,7,6,5,4,3,1,2,10]
[1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [10,9,8,7,6,5,4,3,1,2]
[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] => [[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10]
[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] => [[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]] => [10,2,1,3,4,5,6,7,8,9]
[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] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [10,8,6,4,2,1,3,5,7,9]
[2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [10,9,8,7,6,5,4,2,1,3]
[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] => [[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9,10]
[3,7] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [10,9,8,7,6,5,3,2,1,4]
[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] => [[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9,10]
[4,6] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]] => [10,9,8,7,6,4,3,2,1,5]
[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] => [[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.] => [5,4,3,2,1,6,7,8,9,10]
[5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]] => [10,9,8,7,5,4,3,2,1,6]
[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] => [[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.] => [6,5,4,3,2,1,7,8,9,10]
[6,4] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]] => [10,9,8,6,5,4,3,2,1,7]
[7,1,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.] => [7,6,5,4,3,2,1,8,9,10]
[7,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.] => [9,7,6,5,4,3,2,1,8,10]
[7,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]] => [10,9,7,6,5,4,3,2,1,8]
[8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.] => [8,7,6,5,4,3,2,1,9,10]
[8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]] => [10,8,7,6,5,4,3,2,1,9]
[9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [9,8,7,6,5,4,3,2,1,10]
[10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [10,9,8,7,6,5,4,3,2,1]
[1,10] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [11,10,9,8,7,6,5,4,3,1,2]
[10,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => [10,9,8,7,6,5,4,3,2,1,11]
[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] => [[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [12,10,8,6,4,2,1,3,5,7,9,11]
[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] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => [11,1,2,3,4,5,6,7,8,9,10]
Map
bounce path
Description
The bounce path determined by an integer composition.
Map
to binary tree: left tree, up step, right tree, down step
Description
Return the binary tree corresponding to the Dyck path under the transformation left tree - up step - right tree - down step.
A Dyck path $D$ of semilength $n$ with $n > 1$ may be uniquely decomposed into $L 1 R 0$ for Dyck paths $L,R$ of respective semilengths $n_1,n_2$ with $n_1+n_2 = n-1$.
This map sends $D$ to the binary tree $T$ consisting of a root node with a left child according to $L$ and a right child according to $R$ and then recursively proceeds.
The base case of the unique Dyck path of semilength $1$ is sent to a single node.
This map may also be described as the unique map sending the Tamari orders on Dyck paths to the Tamari order on binary trees.
Map
to 132-avoiding permutation
Description
Return a 132-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.