Identifier
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00066: Permutations —inverse⟶ Permutations
Images
[1] => [1,0] => [1] => [1]
[1,1] => [1,0,1,0] => [2,1] => [2,1]
[2] => [1,1,0,0] => [1,2] => [1,2]
[1,1,1] => [1,0,1,0,1,0] => [3,2,1] => [3,2,1]
[1,2] => [1,0,1,1,0,0] => [2,3,1] => [3,1,2]
[2,1] => [1,1,0,0,1,0] => [3,1,2] => [2,3,1]
[3] => [1,1,1,0,0,0] => [1,2,3] => [1,2,3]
[1,1,1,1] => [1,0,1,0,1,0,1,0] => [4,3,2,1] => [4,3,2,1]
[1,1,2] => [1,0,1,0,1,1,0,0] => [3,4,2,1] => [4,3,1,2]
[1,2,1] => [1,0,1,1,0,0,1,0] => [4,2,3,1] => [4,2,3,1]
[1,3] => [1,0,1,1,1,0,0,0] => [2,3,4,1] => [4,1,2,3]
[2,1,1] => [1,1,0,0,1,0,1,0] => [4,3,1,2] => [3,4,2,1]
[2,2] => [1,1,0,0,1,1,0,0] => [3,4,1,2] => [3,4,1,2]
[3,1] => [1,1,1,0,0,0,1,0] => [4,1,2,3] => [2,3,4,1]
[4] => [1,1,1,1,0,0,0,0] => [1,2,3,4] => [1,2,3,4]
[1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => [5,4,3,2,1]
[1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => [5,4,3,1,2]
[1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => [5,4,2,3,1]
[1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => [5,4,1,2,3]
[1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => [5,3,4,2,1]
[1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => [5,3,4,1,2]
[1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => [5,2,3,4,1]
[1,4] => [1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [5,1,2,3,4]
[2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => [4,5,3,2,1]
[2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => [4,5,3,1,2]
[2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => [4,5,2,3,1]
[2,3] => [1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => [4,5,1,2,3]
[3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => [3,4,5,2,1]
[3,2] => [1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => [3,4,5,1,2]
[4,1] => [1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => [2,3,4,5,1]
[5] => [1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [1,2,3,4,5]
[1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => [6,5,4,3,2,1]
[1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [5,6,4,3,2,1] => [6,5,4,3,1,2]
[1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,5,3,2,1] => [6,5,4,2,3,1]
[1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => [6,5,4,1,2,3]
[1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,4,2,1] => [6,5,3,4,2,1]
[1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [5,6,3,4,2,1] => [6,5,3,4,1,2]
[1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,4,5,2,1] => [6,5,2,3,4,1]
[1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => [6,5,1,2,3,4]
[1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,3,1] => [6,4,5,3,2,1]
[1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [5,6,4,2,3,1] => [6,4,5,3,1,2]
[1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,5,2,3,1] => [6,4,5,2,3,1]
[1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => [6,4,5,1,2,3]
[1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,3,4,1] => [6,3,4,5,2,1]
[1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => [5,6,2,3,4,1] => [6,3,4,5,1,2]
[1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => [6,2,3,4,5,1]
[1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [6,1,2,3,4,5]
[2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,2] => [5,6,4,3,2,1]
[2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [5,6,4,3,1,2] => [5,6,4,3,1,2]
[2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,5,3,1,2] => [5,6,4,2,3,1]
[2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [4,5,6,3,1,2] => [5,6,4,1,2,3]
[2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,4,1,2] => [5,6,3,4,2,1]
[2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [5,6,3,4,1,2] => [5,6,3,4,1,2]
[2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,4,5,1,2] => [5,6,2,3,4,1]
[2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => [5,6,1,2,3,4]
[3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,2,3] => [4,5,6,3,2,1]
[3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [5,6,4,1,2,3] => [4,5,6,3,1,2]
[3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,5,1,2,3] => [4,5,6,2,3,1]
[3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => [4,5,6,1,2,3]
[4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => [3,4,5,6,2,1]
[4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => [3,4,5,6,1,2]
[5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [2,3,4,5,6,1]
[6] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [1,2,3,4,5,6]
[1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1]
[1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,2,1] => [7,6,5,4,3,1,2]
[1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,2,1] => [7,6,5,4,2,3,1]
[1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,2,1] => [7,6,5,4,1,2,3]
[1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,2,1] => [7,6,5,3,4,2,1]
[1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,2,1] => [7,6,5,3,4,1,2]
[1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,2,1] => [7,6,5,2,3,4,1]
[1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,2,1] => [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] => [7,6,5,3,4,2,1] => [7,6,4,5,3,2,1]
[1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,2,1] => [7,6,4,5,3,1,2]
[1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,2,1] => [7,6,4,5,2,3,1]
[1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,2,1] => [7,6,4,5,1,2,3]
[1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,2,1] => [7,6,3,4,5,2,1]
[1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,2,1] => [7,6,3,4,5,1,2]
[1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1] => [7,6,2,3,4,5,1]
[1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,2,1] => [7,6,1,2,3,4,5]
[1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,3,1] => [7,5,6,4,3,2,1]
[1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,3,1] => [7,5,6,4,3,1,2]
[1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,3,1] => [7,5,6,4,2,3,1]
[1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,3,1] => [7,5,6,4,1,2,3]
[1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,3,1] => [7,5,6,3,4,2,1]
[1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,3,1] => [7,5,6,3,4,1,2]
[1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,3,1] => [7,5,6,2,3,4,1]
[1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,3,1] => [7,5,6,1,2,3,4]
[1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,4,1] => [7,4,5,6,3,2,1]
[1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,4,1] => [7,4,5,6,3,1,2]
[1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,4,1] => [7,4,5,6,2,3,1]
[1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,4,1] => [7,4,5,6,1,2,3]
[1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,5,1] => [7,3,4,5,6,2,1]
[1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,5,1] => [7,3,4,5,6,1,2]
[1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,6,1] => [7,2,3,4,5,6,1]
[1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,1,2,3,4,5,6]
[2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,1,2] => [6,7,5,4,3,2,1]
[2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,1,2] => [6,7,5,4,3,1,2]
[2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,1,2] => [6,7,5,4,2,3,1]
[2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,1,2] => [6,7,5,4,1,2,3]
[2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,1,2] => [6,7,5,3,4,2,1]
[2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,1,2] => [6,7,5,3,4,1,2]
>>> Load all 432 entries. <<<
[2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,1,2] => [6,7,5,2,3,4,1]
[2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,1,2] => [6,7,5,1,2,3,4]
[2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,1,2] => [6,7,4,5,3,2,1]
[2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,1,2] => [6,7,4,5,3,1,2]
[2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,1,2] => [6,7,4,5,2,3,1]
[2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,1,2] => [6,7,4,5,1,2,3]
[2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,1,2] => [6,7,3,4,5,2,1]
[2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,1,2] => [6,7,3,4,5,1,2]
[2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,1,2] => [6,7,2,3,4,5,1]
[2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2] => [6,7,1,2,3,4,5]
[3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1,2,3] => [5,6,7,4,3,2,1]
[3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,1,2,3] => [5,6,7,4,3,1,2]
[3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,1,2,3] => [5,6,7,4,2,3,1]
[3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,1,2,3] => [5,6,7,4,1,2,3]
[3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,1,2,3] => [5,6,7,3,4,2,1]
[3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,1,2,3] => [5,6,7,3,4,1,2]
[3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,1,2,3] => [5,6,7,2,3,4,1]
[3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,1,2,3] => [5,6,7,1,2,3,4]
[4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [7,6,5,1,2,3,4] => [4,5,6,7,3,2,1]
[4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [6,7,5,1,2,3,4] => [4,5,6,7,3,1,2]
[4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [7,5,6,1,2,3,4] => [4,5,6,7,2,3,1]
[4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4] => [4,5,6,7,1,2,3]
[5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,2,3,4,5] => [3,4,5,6,7,2,1]
[5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5] => [3,4,5,6,7,1,2]
[6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6] => [2,3,4,5,6,7,1]
[7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7]
[1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1]
[1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,2,1] => [8,7,6,5,4,3,1,2]
[1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,3,2,1] => [8,7,6,5,4,2,3,1]
[1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,3,2,1] => [8,7,6,5,4,1,2,3]
[1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,3,2,1] => [8,7,6,5,3,4,2,1]
[1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,3,2,1] => [8,7,6,5,3,4,1,2]
[1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,3,2,1] => [8,7,6,5,2,3,4,1]
[1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,2,1] => [8,7,6,5,1,2,3,4]
[1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,3,2,1] => [8,7,6,4,5,3,2,1]
[1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,2,1] => [8,7,6,4,5,3,1,2]
[1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,3,2,1] => [8,7,6,4,5,2,3,1]
[1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,3,2,1] => [8,7,6,4,5,1,2,3]
[1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,3,2,1] => [8,7,6,3,4,5,2,1]
[1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,3,2,1] => [8,7,6,3,4,5,1,2]
[1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,3,2,1] => [8,7,6,2,3,4,5,1]
[1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,2,1] => [8,7,6,1,2,3,4,5]
[1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,4,2,1] => [8,7,5,6,4,3,2,1]
[1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,4,2,1] => [8,7,5,6,4,3,1,2]
[1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,4,2,1] => [8,7,5,6,4,2,3,1]
[1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,4,2,1] => [8,7,5,6,4,1,2,3]
[1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,2,1] => [8,7,5,6,3,4,2,1]
[1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,4,2,1] => [8,7,5,6,3,4,1,2]
[1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,4,2,1] => [8,7,5,6,2,3,4,1]
[1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,2,1] => [8,7,5,6,1,2,3,4]
[1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,5,2,1] => [8,7,4,5,6,3,2,1]
[1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,5,2,1] => [8,7,4,5,6,3,1,2]
[1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,5,2,1] => [8,7,4,5,6,2,3,1]
[1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,5,2,1] => [8,7,4,5,6,1,2,3]
[1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,6,2,1] => [8,7,3,4,5,6,2,1]
[1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,6,2,1] => [8,7,3,4,5,6,1,2]
[1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,7,2,1] => [8,7,2,3,4,5,6,1]
[1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,2,1] => [8,7,1,2,3,4,5,6]
[1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2,3,1] => [8,6,7,5,4,3,2,1]
[1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,2,3,1] => [8,6,7,5,4,3,1,2]
[1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,3,1] => [8,6,7,5,4,2,3,1]
[1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,2,3,1] => [8,6,7,5,4,1,2,3]
[1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,2,3,1] => [8,6,7,5,3,4,2,1]
[1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,2,3,1] => [8,6,7,5,3,4,1,2]
[1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,2,3,1] => [8,6,7,5,2,3,4,1]
[1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,3,1] => [8,6,7,5,1,2,3,4]
[1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,2,3,1] => [8,6,7,4,5,3,2,1]
[1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,2,3,1] => [8,6,7,4,5,3,1,2]
[1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,2,3,1] => [8,6,7,4,5,2,3,1]
[1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,2,3,1] => [8,6,7,4,5,1,2,3]
[1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,2,3,1] => [8,6,7,3,4,5,2,1]
[1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,2,3,1] => [8,6,7,3,4,5,1,2]
[1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,2,3,1] => [8,6,7,2,3,4,5,1]
[1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,2,3,1] => [8,6,7,1,2,3,4,5]
[1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,3,4,1] => [8,5,6,7,4,3,2,1]
[1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,2,3,4,1] => [8,5,6,7,4,3,1,2]
[1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,2,3,4,1] => [8,5,6,7,4,2,3,1]
[1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,3,4,1] => [8,5,6,7,4,1,2,3]
[1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,3,4,1] => [8,5,6,7,3,4,2,1]
[1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,3,4,1] => [8,5,6,7,3,4,1,2]
[1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,3,4,1] => [8,5,6,7,2,3,4,1]
[1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,4,1] => [8,5,6,7,1,2,3,4]
[1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,4,5,1] => [8,4,5,6,7,3,2,1]
[1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,3,4,5,1] => [8,4,5,6,7,3,1,2]
[1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,3,4,5,1] => [8,4,5,6,7,2,3,1]
[1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,4,5,1] => [8,4,5,6,7,1,2,3]
[1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,5,6,1] => [8,3,4,5,6,7,2,1]
[1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,5,6,1] => [8,3,4,5,6,7,1,2]
[1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,6,7,1] => [8,2,3,4,5,6,7,1]
[1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => [8,1,2,3,4,5,6,7]
[2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,1,2] => [7,8,6,5,4,3,2,1]
[2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,1,2] => [7,8,6,5,4,3,1,2]
[2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,3,1,2] => [7,8,6,5,4,2,3,1]
[2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,3,1,2] => [7,8,6,5,4,1,2,3]
[2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,3,1,2] => [7,8,6,5,3,4,2,1]
[2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,3,1,2] => [7,8,6,5,3,4,1,2]
[2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,3,1,2] => [7,8,6,5,2,3,4,1]
[2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,1,2] => [7,8,6,5,1,2,3,4]
[2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,3,1,2] => [7,8,6,4,5,3,2,1]
[2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,1,2] => [7,8,6,4,5,3,1,2]
[2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,3,1,2] => [7,8,6,4,5,2,3,1]
[2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,3,1,2] => [7,8,6,4,5,1,2,3]
[2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,3,1,2] => [7,8,6,3,4,5,2,1]
[2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,3,1,2] => [7,8,6,3,4,5,1,2]
[2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,3,1,2] => [7,8,6,2,3,4,5,1]
[2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,1,2] => [7,8,6,1,2,3,4,5]
[2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,4,1,2] => [7,8,5,6,4,3,2,1]
[2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,4,1,2] => [7,8,5,6,4,3,1,2]
[2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,4,1,2] => [7,8,5,6,4,2,3,1]
[2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,4,1,2] => [7,8,5,6,4,1,2,3]
[2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,1,2] => [7,8,5,6,3,4,2,1]
[2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,4,1,2] => [7,8,5,6,3,4,1,2]
[2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,4,1,2] => [7,8,5,6,2,3,4,1]
[2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,1,2] => [7,8,5,6,1,2,3,4]
[2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,5,1,2] => [7,8,4,5,6,3,2,1]
[2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,5,1,2] => [7,8,4,5,6,3,1,2]
[2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,5,1,2] => [7,8,4,5,6,2,3,1]
[2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,5,1,2] => [7,8,4,5,6,1,2,3]
[2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,6,1,2] => [7,8,3,4,5,6,2,1]
[2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,6,1,2] => [7,8,3,4,5,6,1,2]
[2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,7,1,2] => [7,8,2,3,4,5,6,1]
[2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2] => [7,8,1,2,3,4,5,6]
[3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,1,2,3] => [6,7,8,5,4,3,2,1]
[3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,1,2,3] => [6,7,8,5,4,3,1,2]
[3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,1,2,3] => [6,7,8,5,4,2,3,1]
[3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,1,2,3] => [6,7,8,5,4,1,2,3]
[3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,1,2,3] => [6,7,8,5,3,4,2,1]
[3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,1,2,3] => [6,7,8,5,3,4,1,2]
[3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,1,2,3] => [6,7,8,5,2,3,4,1]
[3,1,4] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,1,2,3] => [6,7,8,5,1,2,3,4]
[3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,1,2,3] => [6,7,8,4,5,3,2,1]
[3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,1,2,3] => [6,7,8,4,5,3,1,2]
[3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,1,2,3] => [6,7,8,4,5,2,3,1]
[3,2,3] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,1,2,3] => [6,7,8,4,5,1,2,3]
[3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,1,2,3] => [6,7,8,3,4,5,2,1]
[3,3,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,1,2,3] => [6,7,8,3,4,5,1,2]
[3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,1,2,3] => [6,7,8,2,3,4,5,1]
[3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,1,2,3] => [6,7,8,1,2,3,4,5]
[4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,1,2,3,4] => [5,6,7,8,4,3,2,1]
[4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,1,2,3,4] => [5,6,7,8,4,3,1,2]
[4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,1,2,3,4] => [5,6,7,8,4,2,3,1]
[4,1,3] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,1,2,3,4] => [5,6,7,8,4,1,2,3]
[4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,1,2,3,4] => [5,6,7,8,3,4,2,1]
[4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,1,2,3,4] => [5,6,7,8,3,4,1,2]
[4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,1,2,3,4] => [5,6,7,8,2,3,4,1]
[4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => [5,6,7,8,1,2,3,4]
[5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [8,7,6,1,2,3,4,5] => [4,5,6,7,8,3,2,1]
[5,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [7,8,6,1,2,3,4,5] => [4,5,6,7,8,3,1,2]
[5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [8,6,7,1,2,3,4,5] => [4,5,6,7,8,2,3,1]
[5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,7,8,1,2,3,4,5] => [4,5,6,7,8,1,2,3]
[6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [8,7,1,2,3,4,5,6] => [3,4,5,6,7,8,2,1]
[6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,8,1,2,3,4,5,6] => [3,4,5,6,7,8,1,2]
[7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7] => [2,3,4,5,6,7,8,1]
[8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8]
[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] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1]
[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] => [8,9,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,1,2]
[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] => [9,7,8,6,5,4,3,2,1] => [9,8,7,6,5,4,2,3,1]
[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] => [7,8,9,6,5,4,3,2,1] => [9,8,7,6,5,4,1,2,3]
[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] => [9,8,6,7,5,4,3,2,1] => [9,8,7,6,5,3,4,2,1]
[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] => [8,9,6,7,5,4,3,2,1] => [9,8,7,6,5,3,4,1,2]
[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] => [9,6,7,8,5,4,3,2,1] => [9,8,7,6,5,2,3,4,1]
[1,1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [6,7,8,9,5,4,3,2,1] => [9,8,7,6,5,1,2,3,4]
[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] => [9,8,7,5,6,4,3,2,1] => [9,8,7,6,4,5,3,2,1]
[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] => [8,9,7,5,6,4,3,2,1] => [9,8,7,6,4,5,3,1,2]
[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] => [9,7,8,5,6,4,3,2,1] => [9,8,7,6,4,5,2,3,1]
[1,1,1,1,2,3] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [7,8,9,5,6,4,3,2,1] => [9,8,7,6,4,5,1,2,3]
[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] => [9,8,5,6,7,4,3,2,1] => [9,8,7,6,3,4,5,2,1]
[1,1,1,1,5] => [1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,4,3,2,1] => [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] => [9,8,7,6,4,5,3,2,1] => [9,8,7,5,6,4,3,2,1]
[1,1,1,2,4] => [1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,4,5,3,2,1] => [9,8,7,5,6,1,2,3,4]
[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] => [9,8,7,4,5,6,3,2,1] => [9,8,7,4,5,6,3,2,1]
[1,1,1,6] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,3,2,1] => [9,8,7,1,2,3,4,5,6]
[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] => [9,8,7,6,5,3,4,2,1] => [9,8,6,7,5,4,3,2,1]
[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] => [8,9,7,6,5,3,4,2,1] => [9,8,6,7,5,4,3,1,2]
[1,1,2,1,1,3] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [7,8,9,6,5,3,4,2,1] => [9,8,6,7,5,4,1,2,3]
[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] => [9,8,7,5,6,3,4,2,1] => [9,8,6,7,4,5,3,2,1]
[1,1,2,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [9,7,8,5,6,3,4,2,1] => [9,8,6,7,4,5,2,3,1]
[1,1,2,5] => [1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,3,4,2,1] => [9,8,6,7,1,2,3,4,5]
[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] => [9,8,7,6,3,4,5,2,1] => [9,8,5,6,7,4,3,2,1]
[1,1,4,1,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [9,8,7,3,4,5,6,2,1] => [9,8,4,5,6,7,3,2,1]
[1,1,4,3] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [7,8,9,3,4,5,6,2,1] => [9,8,4,5,6,7,1,2,3]
[1,1,5,1,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [9,8,3,4,5,6,7,2,1] => [9,8,3,4,5,6,7,2,1]
[1,1,6,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [9,3,4,5,6,7,8,2,1] => [9,8,2,3,4,5,6,7,1]
[1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,2,1] => [9,8,1,2,3,4,5,6,7]
[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] => [9,8,7,6,5,4,2,3,1] => [9,7,8,6,5,4,3,2,1]
[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] => [8,9,7,6,5,4,2,3,1] => [9,7,8,6,5,4,3,1,2]
[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] => [9,7,8,6,5,4,2,3,1] => [9,7,8,6,5,4,2,3,1]
[1,2,1,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [7,8,9,6,5,4,2,3,1] => [9,7,8,6,5,4,1,2,3]
[1,2,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [9,8,6,7,4,5,2,3,1] => [9,7,8,5,6,3,4,2,1]
[1,2,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [8,9,6,7,4,5,2,3,1] => [9,7,8,5,6,3,4,1,2]
[1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,2,3,1] => [9,7,8,1,2,3,4,5,6]
[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] => [9,8,7,6,5,2,3,4,1] => [9,6,7,8,5,4,3,2,1]
[1,3,5] => [1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,2,3,4,1] => [9,6,7,8,1,2,3,4,5]
[1,4,4] => [1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,2,3,4,5,1] => [9,5,6,7,8,1,2,3,4]
[1,5,3] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [7,8,9,2,3,4,5,6,1] => [9,4,5,6,7,8,1,2,3]
[1,6,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [9,8,2,3,4,5,6,7,1] => [9,3,4,5,6,7,8,2,1]
[1,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [8,9,2,3,4,5,6,7,1] => [9,3,4,5,6,7,8,1,2]
[1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,4,5,6,7,8,1] => [9,2,3,4,5,6,7,8,1]
[1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => [9,1,2,3,4,5,6,7,8]
[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] => [9,8,7,6,5,4,3,1,2] => [8,9,7,6,5,4,3,2,1]
[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] => [8,9,7,6,5,4,3,1,2] => [8,9,7,6,5,4,3,1,2]
[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] => [9,7,8,6,5,4,3,1,2] => [8,9,7,6,5,4,2,3,1]
[2,1,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [7,8,9,6,5,4,3,1,2] => [8,9,7,6,5,4,1,2,3]
[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] => [9,8,6,7,5,4,3,1,2] => [8,9,7,6,5,3,4,2,1]
[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] => [9,8,7,5,6,4,3,1,2] => [8,9,7,6,4,5,3,2,1]
[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] => [9,8,7,6,4,5,3,1,2] => [8,9,7,5,6,4,3,2,1]
[2,1,3,3] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [7,8,9,4,5,6,3,1,2] => [8,9,7,4,5,6,1,2,3]
[2,1,6] => [1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,3,1,2] => [8,9,7,1,2,3,4,5,6]
[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] => [9,8,7,6,5,3,4,1,2] => [8,9,6,7,5,4,3,2,1]
[2,2,1,4] => [1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [6,7,8,9,5,3,4,1,2] => [8,9,6,7,5,1,2,3,4]
[2,2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [9,8,7,5,6,3,4,1,2] => [8,9,6,7,4,5,3,2,1]
[2,2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [9,7,8,5,6,3,4,1,2] => [8,9,6,7,4,5,2,3,1]
[2,2,5] => [1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,3,4,1,2] => [8,9,6,7,1,2,3,4,5]
[2,4,1,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [9,8,7,3,4,5,6,1,2] => [8,9,4,5,6,7,3,2,1]
[2,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [7,8,9,3,4,5,6,1,2] => [8,9,4,5,6,7,1,2,3]
[2,5,1,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [9,8,3,4,5,6,7,1,2] => [8,9,3,4,5,6,7,2,1]
[2,5,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [8,9,3,4,5,6,7,1,2] => [8,9,3,4,5,6,7,1,2]
[2,6,1] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [9,3,4,5,6,7,8,1,2] => [8,9,2,3,4,5,6,7,1]
[2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,1,2] => [8,9,1,2,3,4,5,6,7]
[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] => [9,8,7,6,5,4,1,2,3] => [7,8,9,6,5,4,3,2,1]
[3,1,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,9,7,6,5,4,1,2,3] => [7,8,9,6,5,4,3,1,2]
[3,2,1,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,5,1,2,3] => [7,8,9,5,6,4,3,2,1]
[3,2,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [8,9,6,7,4,5,1,2,3] => [7,8,9,5,6,3,4,1,2]
[3,3,1,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [9,8,7,4,5,6,1,2,3] => [7,8,9,4,5,6,3,2,1]
[3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [7,8,9,4,5,6,1,2,3] => [7,8,9,4,5,6,1,2,3]
[3,4,2] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [8,9,4,5,6,7,1,2,3] => [7,8,9,3,4,5,6,1,2]
[3,6] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,1,2,3] => [7,8,9,1,2,3,4,5,6]
[4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,1,2,3,4] => [6,7,8,9,5,4,3,2,1]
[4,1,4] => [1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0] => [6,7,8,9,5,1,2,3,4] => [6,7,8,9,5,1,2,3,4]
[4,2,1,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0] => [9,8,7,5,6,1,2,3,4] => [6,7,8,9,4,5,3,2,1]
[4,2,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [9,7,8,5,6,1,2,3,4] => [6,7,8,9,4,5,2,3,1]
[4,3,1,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0] => [9,8,5,6,7,1,2,3,4] => [6,7,8,9,3,4,5,2,1]
[4,3,2] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0] => [8,9,5,6,7,1,2,3,4] => [6,7,8,9,3,4,5,1,2]
[4,4,1] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [9,5,6,7,8,1,2,3,4] => [6,7,8,9,2,3,4,5,1]
[4,5] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,1,2,3,4] => [6,7,8,9,1,2,3,4,5]
[5,1,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,1,2,3,4,5] => [5,6,7,8,9,4,3,2,1]
[5,1,3] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0] => [7,8,9,6,1,2,3,4,5] => [5,6,7,8,9,4,1,2,3]
[5,2,1,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [9,8,6,7,1,2,3,4,5] => [5,6,7,8,9,3,4,2,1]
[5,3,1] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [9,6,7,8,1,2,3,4,5] => [5,6,7,8,9,2,3,4,1]
[5,4] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,1,2,3,4,5] => [5,6,7,8,9,1,2,3,4]
[6,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [9,8,7,1,2,3,4,5,6] => [4,5,6,7,8,9,3,2,1]
[6,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [9,7,8,1,2,3,4,5,6] => [4,5,6,7,8,9,2,3,1]
[6,3] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [7,8,9,1,2,3,4,5,6] => [4,5,6,7,8,9,1,2,3]
[7,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [9,8,1,2,3,4,5,6,7] => [3,4,5,6,7,8,9,2,1]
[7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [8,9,1,2,3,4,5,6,7] => [3,4,5,6,7,8,9,1,2]
[8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,8] => [2,3,4,5,6,7,8,9,1]
[9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9]
[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] => [10,9,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,2,1]
[1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [9,10,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,1,2]
[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] => [10,8,9,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,2,3,1]
[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] => [8,9,10,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,1,2,3]
[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] => [10,9,7,8,6,5,4,3,2,1] => [10,9,8,7,6,5,3,4,2,1]
[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] => [9,10,7,8,6,5,4,3,2,1] => [10,9,8,7,6,5,3,4,1,2]
[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] => [7,8,9,10,6,5,4,3,2,1] => [10,9,8,7,6,5,1,2,3,4]
[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] => [10,9,8,6,7,5,4,3,2,1] => [10,9,8,7,6,4,5,3,2,1]
[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] => [10,8,9,6,7,5,4,3,2,1] => [10,9,8,7,6,4,5,2,3,1]
[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] => [6,7,8,9,10,5,4,3,2,1] => [10,9,8,7,6,1,2,3,4,5]
[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] => [10,9,8,7,5,6,4,3,2,1] => [10,9,8,7,5,6,4,3,2,1]
[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] => [5,6,7,8,9,10,4,3,2,1] => [10,9,8,7,1,2,3,4,5,6]
[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] => [10,9,8,7,6,4,5,3,2,1] => [10,9,8,6,7,5,4,3,2,1]
[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] => [9,10,8,7,6,4,5,3,2,1] => [10,9,8,6,7,5,4,3,1,2]
[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] => [10,9,8,6,7,4,5,3,2,1] => [10,9,8,6,7,4,5,3,2,1]
[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] => [10,8,9,6,7,4,5,3,2,1] => [10,9,8,6,7,4,5,2,3,1]
[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] => [10,9,8,7,4,5,6,3,2,1] => [10,9,8,5,6,7,4,3,2,1]
[1,1,1,7] => [1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,6,7,8,9,10,3,2,1] => [10,9,8,1,2,3,4,5,6,7]
[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] => [10,9,8,7,6,5,3,4,2,1] => [10,9,7,8,6,5,4,3,2,1]
[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] => [9,10,7,8,5,6,3,4,2,1] => [10,9,7,8,5,6,3,4,1,2]
[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] => [10,9,8,3,4,5,6,7,2,1] => [10,9,4,5,6,7,8,3,2,1]
[1,1,7,1] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [10,3,4,5,6,7,8,9,2,1] => [10,9,2,3,4,5,6,7,8,1]
[1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,2,1] => [10,9,1,2,3,4,5,6,7,8]
[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] => [10,9,8,7,6,5,4,2,3,1] => [10,8,9,7,6,5,4,3,2,1]
[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] => [9,10,8,7,6,5,4,2,3,1] => [10,8,9,7,6,5,4,3,1,2]
[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] => [10,8,9,7,6,5,4,2,3,1] => [10,8,9,7,6,5,4,2,3,1]
[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] => [10,9,8,7,6,4,5,2,3,1] => [10,8,9,6,7,5,4,3,2,1]
[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] => [10,9,8,6,7,4,5,2,3,1] => [10,8,9,6,7,4,5,3,2,1]
[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] => [10,8,9,6,7,4,5,2,3,1] => [10,8,9,6,7,4,5,2,3,1]
[1,2,3,4] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,4,5,6,2,3,1] => [10,8,9,5,6,7,1,2,3,4]
[1,2,7] => [1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,6,7,8,9,10,2,3,1] => [10,8,9,1,2,3,4,5,6,7]
[1,3,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [8,9,10,5,6,7,2,3,4,1] => [10,7,8,9,4,5,6,1,2,3]
[1,3,6] => [1,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,9,10,2,3,4,1] => [10,7,8,9,1,2,3,4,5,6]
[1,4,5] => [1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [6,7,8,9,10,2,3,4,5,1] => [10,6,7,8,9,1,2,3,4,5]
[1,7,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [10,9,2,3,4,5,6,7,8,1] => [10,3,4,5,6,7,8,9,2,1]
[1,7,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [9,10,2,3,4,5,6,7,8,1] => [10,3,4,5,6,7,8,9,1,2]
[1,8,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,4,5,6,7,8,9,1] => [10,2,3,4,5,6,7,8,9,1]
[1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1] => [10,1,2,3,4,5,6,7,8,9]
[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] => [10,9,8,7,6,5,4,3,1,2] => [9,10,8,7,6,5,4,3,2,1]
[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] => [9,10,8,7,6,5,4,3,1,2] => [9,10,8,7,6,5,4,3,1,2]
[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] => [10,8,9,7,6,5,4,3,1,2] => [9,10,8,7,6,5,4,2,3,1]
[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] => [10,9,7,8,6,5,4,3,1,2] => [9,10,8,7,6,5,3,4,2,1]
[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] => [10,9,8,7,6,4,5,3,1,2] => [9,10,8,6,7,5,4,3,2,1]
[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] => [10,9,8,7,6,5,3,4,1,2] => [9,10,7,8,6,5,4,3,2,1]
[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] => [10,9,8,7,5,6,3,4,1,2] => [9,10,7,8,5,6,4,3,2,1]
[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] => [10,9,7,8,5,6,3,4,1,2] => [9,10,7,8,5,6,3,4,2,1]
[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] => [9,10,7,8,5,6,3,4,1,2] => [9,10,7,8,5,6,3,4,1,2]
[2,6,1,1] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [10,9,3,4,5,6,7,8,1,2] => [9,10,3,4,5,6,7,8,2,1]
[2,6,2] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [9,10,3,4,5,6,7,8,1,2] => [9,10,3,4,5,6,7,8,1,2]
[2,7,1] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [10,3,4,5,6,7,8,9,1,2] => [9,10,2,3,4,5,6,7,8,1]
[2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,1,2] => [9,10,1,2,3,4,5,6,7,8]
[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] => [10,9,8,7,6,5,4,1,2,3] => [8,9,10,7,6,5,4,3,2,1]
[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] => [10,9,8,7,6,4,5,1,2,3] => [8,9,10,6,7,5,4,3,2,1]
[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] => [10,8,9,6,7,4,5,1,2,3] => [8,9,10,6,7,4,5,2,3,1]
[3,3,2,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,4,5,6,1,2,3] => [8,9,10,5,6,7,3,4,1,2]
[3,7] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,6,7,8,9,10,1,2,3] => [8,9,10,1,2,3,4,5,6,7]
[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] => [10,9,8,7,6,5,1,2,3,4] => [7,8,9,10,6,5,4,3,2,1]
[4,2,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,5,6,1,2,3,4] => [7,8,9,10,5,6,3,4,1,2]
[4,3,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [8,9,10,5,6,7,1,2,3,4] => [7,8,9,10,4,5,6,1,2,3]
[4,4,1,1] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [10,9,5,6,7,8,1,2,3,4] => [7,8,9,10,3,4,5,6,2,1]
[4,4,2] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [9,10,5,6,7,8,1,2,3,4] => [7,8,9,10,3,4,5,6,1,2]
[4,6] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,9,10,1,2,3,4] => [7,8,9,10,1,2,3,4,5,6]
[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] => [10,9,8,7,6,1,2,3,4,5] => [6,7,8,9,10,5,4,3,2,1]
[5,1,4] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,1,0,0,0,0] => [7,8,9,10,6,1,2,3,4,5] => [6,7,8,9,10,5,1,2,3,4]
[5,2,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [10,8,9,6,7,1,2,3,4,5] => [6,7,8,9,10,4,5,2,3,1]
[5,4,1] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [10,6,7,8,9,1,2,3,4,5] => [6,7,8,9,10,2,3,4,5,1]
[5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [6,7,8,9,10,1,2,3,4,5] => [6,7,8,9,10,1,2,3,4,5]
[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] => [10,9,8,7,1,2,3,4,5,6] => [5,6,7,8,9,10,4,3,2,1]
[6,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0] => [10,7,8,9,1,2,3,4,5,6] => [5,6,7,8,9,10,2,3,4,1]
[6,4] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,1,2,3,4,5,6] => [5,6,7,8,9,10,1,2,3,4]
[7,1,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [10,9,8,1,2,3,4,5,6,7] => [4,5,6,7,8,9,10,3,2,1]
[7,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [10,8,9,1,2,3,4,5,6,7] => [4,5,6,7,8,9,10,2,3,1]
[7,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [8,9,10,1,2,3,4,5,6,7] => [4,5,6,7,8,9,10,1,2,3]
[8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [10,9,1,2,3,4,5,6,7,8] => [3,4,5,6,7,8,9,10,2,1]
[8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [9,10,1,2,3,4,5,6,7,8] => [3,4,5,6,7,8,9,10,1,2]
[9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1,2,3,4,5,6,7,8,9] => [2,3,4,5,6,7,8,9,10,1]
[10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10]
[1,10] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => [11,1,2,3,4,5,6,7,8,9,10]
[10,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [11,1,2,3,4,5,6,7,8,9,10] => [2,3,4,5,6,7,8,9,10,11,1]
[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] => [11,12,9,10,7,8,5,6,3,4,1,2] => [11,12,9,10,7,8,5,6,3,4,1,2]
[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] => [12,10,11,8,9,6,7,4,5,2,3,1] => [12,10,11,8,9,6,7,4,5,2,3,1]
[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] => [10,11,2,3,4,5,6,7,8,9,1] => [11,3,4,5,6,7,8,9,10,1,2]
[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] => [10,11,9,8,7,6,5,4,3,2,1] => [11,10,9,8,7,6,5,4,3,1,2]
[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] => [10,11,8,9,6,7,4,5,2,3,1] => [11,9,10,7,8,5,6,3,4,1,2]
Map
bounce path
Description
The bounce path determined by an integer composition.
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
Map
inverse
Description
Sends a permutation to its inverse.