Identifier
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00026: Dyck paths —to ordered tree⟶ Ordered trees
Mp00048: Ordered trees —left-right symmetry⟶ Ordered 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 366 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] => [[],[],[],[],[[]],[],[],[]] => [[],[],[],[[]],[],[],[],[]]
[1,1,1,1,2,3] => [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] => [[],[],[],[],[[[]]],[[]]] => [[[]],[[[]]],[],[],[],[]]
[1,1,1,1,5] => [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] => [[],[],[],[[[]]],[],[],[]] => [[],[],[],[[[]]],[],[],[]]
[1,1,1,6] => [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] => [[],[],[[]],[],[],[],[],[]] => [[],[],[],[],[],[[]],[],[]]
[1,1,2,5] => [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] => [[],[],[[[]]],[[]],[[]]] => [[[]],[[]],[[[]]],[],[]]
[1,1,7] => [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] => [[],[[]],[],[],[],[],[[]]] => [[[]],[],[],[],[],[[]],[]]
[1,2,2,1,1,1,1] => [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] => [[],[[]],[[]],[[[]]],[]] => [[],[[[]]],[[]],[[]],[]]
[1,2,3,1,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[],[[]],[[[]]],[],[],[]] => [[],[],[],[[[]]],[[]],[]]
[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] => [[],[[[]]],[],[],[],[],[]] => [[],[],[],[],[],[[[]]],[]]
[1,4,1,1,1,1] => [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] => [[],[[[[[]]]]],[],[],[]] => [[],[],[],[[[[[]]]]],[]]
[1,6,1,1] => [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] => [[[]],[],[],[],[],[],[[]]] => [[[]],[],[],[],[],[],[[]]]
[2,2,1,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[]],[[]],[],[],[],[],[]] => [[],[],[],[],[],[[]],[[]]]
[2,2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[[]],[[]],[[]],[],[],[]] => [[],[],[],[[]],[[]],[[]]]
[2,2,2,2,1] => [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] => [[[]],[[]],[[[]]],[],[]] => [[],[],[[[]]],[[]],[[]]]
[2,3,1,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[[]],[[[]]],[],[],[],[]] => [[],[],[],[],[[[]]],[[]]]
[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] => [[[[]]],[],[],[],[],[],[]] => [[],[],[],[],[],[],[[[]]]]
[3,2,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[]]],[[]],[[]],[[]]] => [[[]],[[]],[[]],[[[]]]]
[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] => [[[[[]]]],[],[],[],[],[]] => [[],[],[],[],[],[[[[]]]]]
[4,5] => [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] => [[[[[[]]]]],[],[],[],[]] => [[],[],[],[],[[[[[]]]]]]
[5,4] => [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] => [[[[[[[]]]]]],[],[],[]] => [[],[],[],[[[[[[]]]]]]]
[6,3] => [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] => [[],[],[],[],[],[],[[]],[[]]] => [[[]],[[]],[],[],[],[],[],[]]
[1,1,1,1,1,1,4] => [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] => [[],[],[[]],[[]],[[]],[[]]] => [[[]],[[]],[[]],[[]],[],[]]
[1,1,8] => [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] => [[],[[]],[[]],[[]],[[]],[]] => [[],[[]],[[]],[[]],[[]],[]]
[1,8,1] => [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] => [[[]],[],[],[],[],[],[],[[]]] => [[[]],[],[],[],[],[],[],[[]]]
[2,2,1,1,1,1,1,1] => [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] => [[[]],[[]],[[]],[],[],[],[]] => [[],[],[],[],[[]],[[]],[[]]]
[2,2,2,2,1,1] => [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] => [[[]],[[]],[[]],[[]],[[]]] => [[[]],[[]],[[]],[[]],[[]]]
[2,8] => [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] => [[[[]]],[],[],[],[],[],[],[]] => [[],[],[],[],[],[],[],[[[]]]]
[3,7] => [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] => [[[[[]]]],[],[],[],[],[],[]] => [[],[],[],[],[],[],[[[[]]]]]
[4,6] => [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] => [[[[[[]]]]],[],[],[],[],[]] => [[],[],[],[],[],[[[[[]]]]]]
[5,5] => [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] => [[[[[[[]]]]]],[],[],[],[]] => [[],[],[],[],[[[[[[]]]]]]]
[6,4] => [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] => [[[[[[[[]]]]]]],[],[],[]] => [[],[],[],[[[[[[[]]]]]]]]
[7,3] => [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] => [[],[[]],[[]],[[]],[[]],[[]],[]] => [[],[[]],[[]],[[]],[[]],[[]],[]]
[1,1,1,1,1,1,1,1,1,2] => [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 ordered tree
Description
Sends a Dyck path to the ordered tree encoding the heights of the path.
This map is recursively defined as follows: A Dyck path $D$ of semilength $n$ may be decomposed, according to its returns (St000011The number of touch points (or returns) of a Dyck path.), into smaller paths $D_1,\dots,D_k$ of respective semilengths $n_1,\dots,n_k$ (so one has $n = n_1 + \dots n_k$) each of which has no returns.
Denote by $\tilde D_i$ the path of semilength $n_i-1$ obtained from $D_i$ by removing the initial up- and the final down-step.
This map then sends $D$ to the tree $T$ having a root note with ordered children $T_1,\dots,T_k$ which are again ordered trees computed from $D_1,\dots,D_k$ respectively.
The unique path of semilength $1$ is sent to the tree consisting of a single node.
Map
left-right symmetry
Description
Return the left-right symmetrized tree of an ordered tree.