Identifier
Identifier
Images
[1] => [1]
[1,1] => [2]
[2] => [1,1]
[1,1,1] => [3]
[1,2] => [2,1]
[2,1] => [1,2]
[3] => [1,1,1]
[1,1,1,1] => [4]
[1,1,2] => [3,1]
[1,2,1] => [2,2]
[1,3] => [2,1,1]
[2,1,1] => [1,3]
[2,2] => [1,2,1]
[3,1] => [1,1,2]
[4] => [1,1,1,1]
[1,1,1,1,1] => [5]
[1,1,1,2] => [4,1]
[1,1,2,1] => [3,2]
[1,1,3] => [3,1,1]
[1,2,1,1] => [2,3]
[1,2,2] => [2,2,1]
[1,3,1] => [2,1,2]
[1,4] => [2,1,1,1]
[2,1,1,1] => [1,4]
[2,1,2] => [1,3,1]
[2,2,1] => [1,2,2]
[2,3] => [1,2,1,1]
[3,1,1] => [1,1,3]
[3,2] => [1,1,2,1]
[4,1] => [1,1,1,2]
[5] => [1,1,1,1,1]
[1,1,1,1,1,1] => [6]
[1,1,1,1,2] => [5,1]
[1,1,1,2,1] => [4,2]
[1,1,1,3] => [4,1,1]
[1,1,2,1,1] => [3,3]
[1,1,2,2] => [3,2,1]
[1,1,3,1] => [3,1,2]
[1,1,4] => [3,1,1,1]
[1,2,1,1,1] => [2,4]
[1,2,1,2] => [2,3,1]
[1,2,2,1] => [2,2,2]
[1,2,3] => [2,2,1,1]
[1,3,1,1] => [2,1,3]
[1,3,2] => [2,1,2,1]
[1,4,1] => [2,1,1,2]
[1,5] => [2,1,1,1,1]
[2,1,1,1,1] => [1,5]
[2,1,1,2] => [1,4,1]
[2,1,2,1] => [1,3,2]
[2,1,3] => [1,3,1,1]
[2,2,1,1] => [1,2,3]
[2,2,2] => [1,2,2,1]
[2,3,1] => [1,2,1,2]
[2,4] => [1,2,1,1,1]
[3,1,1,1] => [1,1,4]
[3,1,2] => [1,1,3,1]
[3,2,1] => [1,1,2,2]
[3,3] => [1,1,2,1,1]
[4,1,1] => [1,1,1,3]
[4,2] => [1,1,1,2,1]
[5,1] => [1,1,1,1,2]
[6] => [1,1,1,1,1,1]
[1,1,1,1,1,1,1] => [7]
[1,1,1,1,1,2] => [6,1]
[1,1,1,1,2,1] => [5,2]
[1,1,1,1,3] => [5,1,1]
[1,1,1,2,1,1] => [4,3]
[1,1,1,2,2] => [4,2,1]
[1,1,1,3,1] => [4,1,2]
[1,1,1,4] => [4,1,1,1]
[1,1,2,1,1,1] => [3,4]
[1,1,2,1,2] => [3,3,1]
[1,1,2,2,1] => [3,2,2]
[1,1,2,3] => [3,2,1,1]
[1,1,3,1,1] => [3,1,3]
[1,1,3,2] => [3,1,2,1]
[1,1,4,1] => [3,1,1,2]
[1,1,5] => [3,1,1,1,1]
[1,2,1,1,1,1] => [2,5]
[1,2,1,1,2] => [2,4,1]
[1,2,1,2,1] => [2,3,2]
[1,2,1,3] => [2,3,1,1]
[1,2,2,1,1] => [2,2,3]
[1,2,2,2] => [2,2,2,1]
[1,2,3,1] => [2,2,1,2]
[1,2,4] => [2,2,1,1,1]
[1,3,1,1,1] => [2,1,4]
[1,3,1,2] => [2,1,3,1]
[1,3,2,1] => [2,1,2,2]
[1,3,3] => [2,1,2,1,1]
[1,4,1,1] => [2,1,1,3]
[1,4,2] => [2,1,1,2,1]
[1,5,1] => [2,1,1,1,2]
[1,6] => [2,1,1,1,1,1]
[2,1,1,1,1,1] => [1,6]
[2,1,1,1,2] => [1,5,1]
[2,1,1,2,1] => [1,4,2]
[2,1,1,3] => [1,4,1,1]
[2,1,2,1,1] => [1,3,3]
[2,1,2,2] => [1,3,2,1]
[2,1,3,1] => [1,3,1,2]
[2,1,4] => [1,3,1,1,1]
[2,2,1,1,1] => [1,2,4]
[2,2,1,2] => [1,2,3,1]
[2,2,2,1] => [1,2,2,2]
[2,2,3] => [1,2,2,1,1]
[2,3,1,1] => [1,2,1,3]
[2,3,2] => [1,2,1,2,1]
[2,4,1] => [1,2,1,1,2]
[2,5] => [1,2,1,1,1,1]
[3,1,1,1,1] => [1,1,5]
[3,1,1,2] => [1,1,4,1]
[3,1,2,1] => [1,1,3,2]
[3,1,3] => [1,1,3,1,1]
[3,2,1,1] => [1,1,2,3]
[3,2,2] => [1,1,2,2,1]
[3,3,1] => [1,1,2,1,2]
[3,4] => [1,1,2,1,1,1]
[4,1,1,1] => [1,1,1,4]
[4,1,2] => [1,1,1,3,1]
[4,2,1] => [1,1,1,2,2]
[4,3] => [1,1,1,2,1,1]
[5,1,1] => [1,1,1,1,3]
[5,2] => [1,1,1,1,2,1]
[6,1] => [1,1,1,1,1,2]
[7] => [1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1] => [8]
[1,1,1,1,1,1,2] => [7,1]
[1,1,1,1,1,2,1] => [6,2]
[1,1,1,1,1,3] => [6,1,1]
[1,1,1,1,2,1,1] => [5,3]
[1,1,1,1,2,2] => [5,2,1]
[1,1,1,1,3,1] => [5,1,2]
[1,1,1,1,4] => [5,1,1,1]
[1,1,1,2,1,1,1] => [4,4]
[1,1,1,2,1,2] => [4,3,1]
[1,1,1,2,2,1] => [4,2,2]
[1,1,1,2,3] => [4,2,1,1]
[1,1,1,3,1,1] => [4,1,3]
[1,1,1,3,2] => [4,1,2,1]
[1,1,1,4,1] => [4,1,1,2]
[1,1,1,5] => [4,1,1,1,1]
[1,1,2,1,1,1,1] => [3,5]
[1,1,2,1,1,2] => [3,4,1]
[1,1,2,1,2,1] => [3,3,2]
[1,1,2,1,3] => [3,3,1,1]
[1,1,2,2,1,1] => [3,2,3]
[1,1,2,2,2] => [3,2,2,1]
[1,1,2,3,1] => [3,2,1,2]
[1,1,2,4] => [3,2,1,1,1]
[1,1,3,1,1,1] => [3,1,4]
[1,1,3,1,2] => [3,1,3,1]
[1,1,3,2,1] => [3,1,2,2]
[1,1,3,3] => [3,1,2,1,1]
[1,1,4,1,1] => [3,1,1,3]
[1,1,4,2] => [3,1,1,2,1]
[1,1,5,1] => [3,1,1,1,2]
[1,1,6] => [3,1,1,1,1,1]
[1,2,1,1,1,1,1] => [2,6]
[1,2,1,1,1,2] => [2,5,1]
[1,2,1,1,2,1] => [2,4,2]
[1,2,1,1,3] => [2,4,1,1]
[1,2,1,2,1,1] => [2,3,3]
[1,2,1,2,2] => [2,3,2,1]
[1,2,1,3,1] => [2,3,1,2]
[1,2,1,4] => [2,3,1,1,1]
[1,2,2,1,1,1] => [2,2,4]
[1,2,2,1,2] => [2,2,3,1]
[1,2,2,2,1] => [2,2,2,2]
[1,2,2,3] => [2,2,2,1,1]
[1,2,3,1,1] => [2,2,1,3]
[1,2,3,2] => [2,2,1,2,1]
[1,2,4,1] => [2,2,1,1,2]
[1,2,5] => [2,2,1,1,1,1]
[1,3,1,1,1,1] => [2,1,5]
[1,3,1,1,2] => [2,1,4,1]
[1,3,1,2,1] => [2,1,3,2]
[1,3,1,3] => [2,1,3,1,1]
[1,3,2,1,1] => [2,1,2,3]
[1,3,2,2] => [2,1,2,2,1]
[1,3,3,1] => [2,1,2,1,2]
[1,3,4] => [2,1,2,1,1,1]
[1,4,1,1,1] => [2,1,1,4]
[1,4,1,2] => [2,1,1,3,1]
[1,4,2,1] => [2,1,1,2,2]
[1,4,3] => [2,1,1,2,1,1]
[1,5,1,1] => [2,1,1,1,3]
[1,5,2] => [2,1,1,1,2,1]
[1,6,1] => [2,1,1,1,1,2]
[1,7] => [2,1,1,1,1,1,1]
[2,1,1,1,1,1,1] => [1,7]
[2,1,1,1,1,2] => [1,6,1]
[2,1,1,1,2,1] => [1,5,2]
[2,1,1,1,3] => [1,5,1,1]
[2,1,1,2,1,1] => [1,4,3]
[2,1,1,2,2] => [1,4,2,1]
[2,1,1,3,1] => [1,4,1,2]
[2,1,1,4] => [1,4,1,1,1]
[2,1,2,1,1,1] => [1,3,4]
[2,1,2,1,2] => [1,3,3,1]
[2,1,2,2,1] => [1,3,2,2]
[2,1,2,3] => [1,3,2,1,1]
[2,1,3,1,1] => [1,3,1,3]
[2,1,3,2] => [1,3,1,2,1]
[2,1,4,1] => [1,3,1,1,2]
[2,1,5] => [1,3,1,1,1,1]
[2,2,1,1,1,1] => [1,2,5]
[2,2,1,1,2] => [1,2,4,1]
[2,2,1,2,1] => [1,2,3,2]
[2,2,1,3] => [1,2,3,1,1]
[2,2,2,1,1] => [1,2,2,3]
[2,2,2,2] => [1,2,2,2,1]
[2,2,3,1] => [1,2,2,1,2]
[2,2,4] => [1,2,2,1,1,1]
[2,3,1,1,1] => [1,2,1,4]
[2,3,1,2] => [1,2,1,3,1]
[2,3,2,1] => [1,2,1,2,2]
[2,3,3] => [1,2,1,2,1,1]
[2,4,1,1] => [1,2,1,1,3]
[2,4,2] => [1,2,1,1,2,1]
[2,5,1] => [1,2,1,1,1,2]
[2,6] => [1,2,1,1,1,1,1]
[3,1,1,1,1,1] => [1,1,6]
[3,1,1,1,2] => [1,1,5,1]
[3,1,1,2,1] => [1,1,4,2]
[3,1,1,3] => [1,1,4,1,1]
[3,1,2,1,1] => [1,1,3,3]
[3,1,2,2] => [1,1,3,2,1]
[3,1,3,1] => [1,1,3,1,2]
[3,1,4] => [1,1,3,1,1,1]
[3,2,1,1,1] => [1,1,2,4]
[3,2,1,2] => [1,1,2,3,1]
[3,2,2,1] => [1,1,2,2,2]
[3,2,3] => [1,1,2,2,1,1]
[3,3,1,1] => [1,1,2,1,3]
[3,3,2] => [1,1,2,1,2,1]
[3,4,1] => [1,1,2,1,1,2]
[3,5] => [1,1,2,1,1,1,1]
[4,1,1,1,1] => [1,1,1,5]
[4,1,1,2] => [1,1,1,4,1]
[4,1,2,1] => [1,1,1,3,2]
[4,1,3] => [1,1,1,3,1,1]
[4,2,1,1] => [1,1,1,2,3]
[4,2,2] => [1,1,1,2,2,1]
[4,3,1] => [1,1,1,2,1,2]
[4,4] => [1,1,1,2,1,1,1]
[5,1,1,1] => [1,1,1,1,4]
[5,1,2] => [1,1,1,1,3,1]
[5,2,1] => [1,1,1,1,2,2]
[5,3] => [1,1,1,1,2,1,1]
[6,1,1] => [1,1,1,1,1,3]
[6,2] => [1,1,1,1,1,2,1]
[7,1] => [1,1,1,1,1,1,2]
[8] => [1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1] => [9]
[1,1,1,1,1,1,1,2] => [8,1]
[1,1,1,1,1,1,2,1] => [7,2]
[1,1,1,1,1,1,3] => [7,1,1]
[1,1,1,1,1,2,1,1] => [6,3]
[1,1,1,1,1,2,2] => [6,2,1]
[1,1,1,1,1,3,1] => [6,1,2]
[1,1,1,1,1,4] => [6,1,1,1]
[1,1,1,1,2,1,1,1] => [5,4]
[1,1,1,1,2,1,2] => [5,3,1]
[1,1,1,1,2,2,1] => [5,2,2]
[1,1,1,1,2,3] => [5,2,1,1]
[1,1,1,1,3,1,1] => [5,1,3]
[1,1,1,1,3,2] => [5,1,2,1]
[1,1,1,1,4,1] => [5,1,1,2]
[1,1,1,1,5] => [5,1,1,1,1]
[1,1,1,2,1,1,1,1] => [4,5]
[1,1,1,2,1,1,2] => [4,4,1]
[1,1,1,2,1,2,1] => [4,3,2]
[1,1,1,2,1,3] => [4,3,1,1]
[1,1,1,2,2,1,1] => [4,2,3]
[1,1,1,2,2,2] => [4,2,2,1]
[1,1,1,2,3,1] => [4,2,1,2]
[1,1,1,2,4] => [4,2,1,1,1]
[1,1,1,3,1,1,1] => [4,1,4]
[1,1,1,3,1,2] => [4,1,3,1]
[1,1,1,3,2,1] => [4,1,2,2]
[1,1,1,3,3] => [4,1,2,1,1]
[1,1,1,4,1,1] => [4,1,1,3]
[1,1,1,4,2] => [4,1,1,2,1]
[1,1,1,5,1] => [4,1,1,1,2]
[1,1,1,6] => [4,1,1,1,1,1]
[1,1,2,1,1,1,1,1] => [3,6]
[1,1,2,1,1,1,2] => [3,5,1]
[1,1,2,1,1,2,1] => [3,4,2]
[1,1,2,1,1,3] => [3,4,1,1]
[1,1,2,1,2,1,1] => [3,3,3]
[1,1,2,1,2,2] => [3,3,2,1]
[1,1,2,1,3,1] => [3,3,1,2]
[1,1,2,1,4] => [3,3,1,1,1]
[1,1,2,2,1,1,1] => [3,2,4]
[1,1,2,2,1,2] => [3,2,3,1]
[1,1,2,2,2,1] => [3,2,2,2]
[1,1,2,2,3] => [3,2,2,1,1]
[1,1,2,3,1,1] => [3,2,1,3]
[1,1,2,3,2] => [3,2,1,2,1]
[1,1,2,4,1] => [3,2,1,1,2]
[1,1,2,5] => [3,2,1,1,1,1]
[1,1,3,1,1,1,1] => [3,1,5]
[1,1,3,1,1,2] => [3,1,4,1]
[1,1,3,1,2,1] => [3,1,3,2]
[1,1,3,1,3] => [3,1,3,1,1]
[1,1,3,2,1,1] => [3,1,2,3]
[1,1,3,2,2] => [3,1,2,2,1]
[1,1,3,3,1] => [3,1,2,1,2]
[1,1,3,4] => [3,1,2,1,1,1]
[1,1,4,1,1,1] => [3,1,1,4]
[1,1,4,1,2] => [3,1,1,3,1]
[1,1,4,2,1] => [3,1,1,2,2]
[1,1,4,3] => [3,1,1,2,1,1]
[1,1,5,1,1] => [3,1,1,1,3]
[1,1,5,2] => [3,1,1,1,2,1]
[1,1,6,1] => [3,1,1,1,1,2]
[1,1,7] => [3,1,1,1,1,1,1]
[1,2,1,1,1,1,1,1] => [2,7]
[1,2,1,1,1,1,2] => [2,6,1]
[1,2,1,1,1,2,1] => [2,5,2]
[1,2,1,1,1,3] => [2,5,1,1]
[1,2,1,1,2,1,1] => [2,4,3]
[1,2,1,1,2,2] => [2,4,2,1]
[1,2,1,1,3,1] => [2,4,1,2]
[1,2,1,1,4] => [2,4,1,1,1]
[1,2,1,2,1,1,1] => [2,3,4]
[1,2,1,2,1,2] => [2,3,3,1]
[1,2,1,2,2,1] => [2,3,2,2]
[1,2,1,2,3] => [2,3,2,1,1]
[1,2,1,3,1,1] => [2,3,1,3]
[1,2,1,3,2] => [2,3,1,2,1]
[1,2,1,4,1] => [2,3,1,1,2]
[1,2,1,5] => [2,3,1,1,1,1]
[1,2,2,1,1,1,1] => [2,2,5]
[1,2,2,1,1,2] => [2,2,4,1]
[1,2,2,1,2,1] => [2,2,3,2]
[1,2,2,1,3] => [2,2,3,1,1]
[1,2,2,2,1,1] => [2,2,2,3]
[1,2,2,2,2] => [2,2,2,2,1]
[1,2,2,3,1] => [2,2,2,1,2]
[1,2,2,4] => [2,2,2,1,1,1]
[1,2,3,1,1,1] => [2,2,1,4]
[1,2,3,1,2] => [2,2,1,3,1]
[1,2,3,2,1] => [2,2,1,2,2]
[1,2,3,3] => [2,2,1,2,1,1]
[1,2,4,1,1] => [2,2,1,1,3]
[1,2,4,2] => [2,2,1,1,2,1]
[1,2,5,1] => [2,2,1,1,1,2]
[1,2,6] => [2,2,1,1,1,1,1]
[1,3,1,1,1,1,1] => [2,1,6]
[1,3,1,1,1,2] => [2,1,5,1]
[1,3,1,1,2,1] => [2,1,4,2]
[1,3,1,1,3] => [2,1,4,1,1]
[1,3,1,2,1,1] => [2,1,3,3]
[1,3,1,2,2] => [2,1,3,2,1]
[1,3,1,3,1] => [2,1,3,1,2]
[1,3,1,4] => [2,1,3,1,1,1]
[1,3,2,1,1,1] => [2,1,2,4]
[1,3,2,1,2] => [2,1,2,3,1]
[1,3,2,2,1] => [2,1,2,2,2]
[1,3,2,3] => [2,1,2,2,1,1]
[1,3,3,1,1] => [2,1,2,1,3]
[1,3,3,2] => [2,1,2,1,2,1]
[1,3,4,1] => [2,1,2,1,1,2]
[1,3,5] => [2,1,2,1,1,1,1]
[1,4,1,1,1,1] => [2,1,1,5]
[1,4,1,1,2] => [2,1,1,4,1]
[1,4,1,2,1] => [2,1,1,3,2]
[1,4,1,3] => [2,1,1,3,1,1]
[1,4,2,1,1] => [2,1,1,2,3]
[1,4,2,2] => [2,1,1,2,2,1]
[1,4,3,1] => [2,1,1,2,1,2]
[1,4,4] => [2,1,1,2,1,1,1]
[1,5,1,1,1] => [2,1,1,1,4]
[1,5,1,2] => [2,1,1,1,3,1]
[1,5,2,1] => [2,1,1,1,2,2]
[1,5,3] => [2,1,1,1,2,1,1]
[1,6,1,1] => [2,1,1,1,1,3]
[1,6,2] => [2,1,1,1,1,2,1]
[1,7,1] => [2,1,1,1,1,1,2]
[1,8] => [2,1,1,1,1,1,1,1]
[2,1,1,1,1,1,1,1] => [1,8]
[2,1,1,1,1,1,2] => [1,7,1]
[2,1,1,1,1,2,1] => [1,6,2]
[2,1,1,1,1,3] => [1,6,1,1]
[2,1,1,1,2,1,1] => [1,5,3]
[2,1,1,1,2,2] => [1,5,2,1]
[2,1,1,1,3,1] => [1,5,1,2]
[2,1,1,1,4] => [1,5,1,1,1]
[2,1,1,2,1,1,1] => [1,4,4]
[2,1,1,2,1,2] => [1,4,3,1]
[2,1,1,2,2,1] => [1,4,2,2]
[2,1,1,2,3] => [1,4,2,1,1]
[2,1,1,3,1,1] => [1,4,1,3]
[2,1,1,3,2] => [1,4,1,2,1]
[2,1,1,4,1] => [1,4,1,1,2]
[2,1,1,5] => [1,4,1,1,1,1]
[2,1,2,1,1,1,1] => [1,3,5]
[2,1,2,1,1,2] => [1,3,4,1]
[2,1,2,1,2,1] => [1,3,3,2]
[2,1,2,1,3] => [1,3,3,1,1]
[2,1,2,2,1,1] => [1,3,2,3]
[2,1,2,2,2] => [1,3,2,2,1]
[2,1,2,3,1] => [1,3,2,1,2]
[2,1,2,4] => [1,3,2,1,1,1]
[2,1,3,1,1,1] => [1,3,1,4]
[2,1,3,1,2] => [1,3,1,3,1]
[2,1,3,2,1] => [1,3,1,2,2]
[2,1,3,3] => [1,3,1,2,1,1]
[2,1,4,1,1] => [1,3,1,1,3]
[2,1,4,2] => [1,3,1,1,2,1]
[2,1,5,1] => [1,3,1,1,1,2]
[2,1,6] => [1,3,1,1,1,1,1]
[2,2,1,1,1,1,1] => [1,2,6]
[2,2,1,1,1,2] => [1,2,5,1]
[2,2,1,1,2,1] => [1,2,4,2]
[2,2,1,1,3] => [1,2,4,1,1]
[2,2,1,2,1,1] => [1,2,3,3]
[2,2,1,2,2] => [1,2,3,2,1]
[2,2,1,3,1] => [1,2,3,1,2]
[2,2,1,4] => [1,2,3,1,1,1]
[2,2,2,1,1,1] => [1,2,2,4]
[2,2,2,1,2] => [1,2,2,3,1]
[2,2,2,2,1] => [1,2,2,2,2]
[2,2,2,3] => [1,2,2,2,1,1]
[2,2,3,1,1] => [1,2,2,1,3]
[2,2,3,2] => [1,2,2,1,2,1]
[2,2,4,1] => [1,2,2,1,1,2]
[2,2,5] => [1,2,2,1,1,1,1]
[2,3,1,1,1,1] => [1,2,1,5]
[2,3,1,1,2] => [1,2,1,4,1]
[2,3,1,2,1] => [1,2,1,3,2]
[2,3,1,3] => [1,2,1,3,1,1]
[2,3,2,1,1] => [1,2,1,2,3]
[2,3,2,2] => [1,2,1,2,2,1]
[2,3,3,1] => [1,2,1,2,1,2]
[2,3,4] => [1,2,1,2,1,1,1]
[2,4,1,1,1] => [1,2,1,1,4]
[2,4,1,2] => [1,2,1,1,3,1]
[2,4,2,1] => [1,2,1,1,2,2]
[2,4,3] => [1,2,1,1,2,1,1]
[2,5,1,1] => [1,2,1,1,1,3]
[2,5,2] => [1,2,1,1,1,2,1]
[2,6,1] => [1,2,1,1,1,1,2]
[2,7] => [1,2,1,1,1,1,1,1]
[3,1,1,1,1,1,1] => [1,1,7]
[3,1,1,1,1,2] => [1,1,6,1]
[3,1,1,1,2,1] => [1,1,5,2]
[3,1,1,1,3] => [1,1,5,1,1]
[3,1,1,2,1,1] => [1,1,4,3]
[3,1,1,2,2] => [1,1,4,2,1]
[3,1,1,3,1] => [1,1,4,1,2]
[3,1,1,4] => [1,1,4,1,1,1]
[3,1,2,1,1,1] => [1,1,3,4]
[3,1,2,1,2] => [1,1,3,3,1]
[3,1,2,2,1] => [1,1,3,2,2]
[3,1,2,3] => [1,1,3,2,1,1]
[3,1,3,1,1] => [1,1,3,1,3]
[3,1,3,2] => [1,1,3,1,2,1]
[3,1,4,1] => [1,1,3,1,1,2]
[3,1,5] => [1,1,3,1,1,1,1]
[3,2,1,1,1,1] => [1,1,2,5]
[3,2,1,1,2] => [1,1,2,4,1]
[3,2,1,2,1] => [1,1,2,3,2]
[3,2,1,3] => [1,1,2,3,1,1]
[3,2,2,1,1] => [1,1,2,2,3]
[3,2,2,2] => [1,1,2,2,2,1]
[3,2,3,1] => [1,1,2,2,1,2]
[3,2,4] => [1,1,2,2,1,1,1]
[3,3,1,1,1] => [1,1,2,1,4]
[3,3,1,2] => [1,1,2,1,3,1]
[3,3,2,1] => [1,1,2,1,2,2]
[3,3,3] => [1,1,2,1,2,1,1]
[3,4,1,1] => [1,1,2,1,1,3]
[3,4,2] => [1,1,2,1,1,2,1]
[3,5,1] => [1,1,2,1,1,1,2]
[3,6] => [1,1,2,1,1,1,1,1]
[4,1,1,1,1,1] => [1,1,1,6]
[4,1,1,1,2] => [1,1,1,5,1]
[4,1,1,2,1] => [1,1,1,4,2]
[4,1,1,3] => [1,1,1,4,1,1]
[4,1,2,1,1] => [1,1,1,3,3]
[4,1,2,2] => [1,1,1,3,2,1]
[4,1,3,1] => [1,1,1,3,1,2]
[4,1,4] => [1,1,1,3,1,1,1]
[4,2,1,1,1] => [1,1,1,2,4]
[4,2,1,2] => [1,1,1,2,3,1]
[4,2,2,1] => [1,1,1,2,2,2]
[4,2,3] => [1,1,1,2,2,1,1]
[4,3,1,1] => [1,1,1,2,1,3]
[4,3,2] => [1,1,1,2,1,2,1]
[4,4,1] => [1,1,1,2,1,1,2]
[4,5] => [1,1,1,2,1,1,1,1]
[5,1,1,1,1] => [1,1,1,1,5]
[5,1,1,2] => [1,1,1,1,4,1]
[5,1,2,1] => [1,1,1,1,3,2]
[5,1,3] => [1,1,1,1,3,1,1]
[5,2,1,1] => [1,1,1,1,2,3]
[5,2,2] => [1,1,1,1,2,2,1]
[5,3,1] => [1,1,1,1,2,1,2]
[5,4] => [1,1,1,1,2,1,1,1]
[6,1,1,1] => [1,1,1,1,1,4]
[6,1,2] => [1,1,1,1,1,3,1]
[6,2,1] => [1,1,1,1,1,2,2]
[6,3] => [1,1,1,1,1,2,1,1]
[7,1,1] => [1,1,1,1,1,1,3]
[7,2] => [1,1,1,1,1,1,2,1]
[8,1] => [1,1,1,1,1,1,1,2]
[9] => [1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,1] => [10]
[1,1,1,1,1,1,1,1,2] => [9,1]
[1,1,1,1,1,1,1,2,1] => [8,2]
[1,1,1,1,1,1,1,3] => [8,1,1]
[1,1,1,1,1,1,2,1,1] => [7,3]
[1,1,1,1,1,1,2,2] => [7,2,1]
[1,1,1,1,1,1,3,1] => [7,1,2]
[1,1,1,1,1,1,4] => [7,1,1,1]
[1,1,1,1,1,2,1,1,1] => [6,4]
[1,1,1,1,1,2,1,2] => [6,3,1]
[1,1,1,1,1,2,2,1] => [6,2,2]
[1,1,1,1,1,2,3] => [6,2,1,1]
[1,1,1,1,1,3,1,1] => [6,1,3]
[1,1,1,1,1,3,2] => [6,1,2,1]
[1,1,1,1,1,4,1] => [6,1,1,2]
[1,1,1,1,1,5] => [6,1,1,1,1]
[1,1,1,1,2,1,1,1,1] => [5,5]
[1,1,1,1,2,1,1,2] => [5,4,1]
[1,1,1,1,2,1,2,1] => [5,3,2]
[1,1,1,1,2,1,3] => [5,3,1,1]
[1,1,1,1,2,2,1,1] => [5,2,3]
[1,1,1,1,2,2,2] => [5,2,2,1]
[1,1,1,1,2,3,1] => [5,2,1,2]
[1,1,1,1,2,4] => [5,2,1,1,1]
[1,1,1,1,3,1,1,1] => [5,1,4]
[1,1,1,1,3,1,2] => [5,1,3,1]
[1,1,1,1,3,2,1] => [5,1,2,2]
[1,1,1,1,3,3] => [5,1,2,1,1]
[1,1,1,1,4,1,1] => [5,1,1,3]
[1,1,1,1,4,2] => [5,1,1,2,1]
[1,1,1,1,5,1] => [5,1,1,1,2]
[1,1,1,1,6] => [5,1,1,1,1,1]
[1,1,1,2,1,1,1,1,1] => [4,6]
[1,1,1,2,1,1,1,2] => [4,5,1]
[1,1,1,2,1,1,2,1] => [4,4,2]
[1,1,1,2,1,1,3] => [4,4,1,1]
[1,1,1,2,1,2,1,1] => [4,3,3]
[1,1,1,2,1,2,2] => [4,3,2,1]
[1,1,1,2,1,3,1] => [4,3,1,2]
[1,1,1,2,1,4] => [4,3,1,1,1]
[1,1,1,2,2,1,1,1] => [4,2,4]
[1,1,1,2,2,1,2] => [4,2,3,1]
[1,1,1,2,2,2,1] => [4,2,2,2]
[1,1,1,2,2,3] => [4,2,2,1,1]
[1,1,1,2,3,1,1] => [4,2,1,3]
[1,1,1,2,3,2] => [4,2,1,2,1]
[1,1,1,2,4,1] => [4,2,1,1,2]
[1,1,1,2,5] => [4,2,1,1,1,1]
[1,1,1,3,1,1,1,1] => [4,1,5]
[1,1,1,3,1,1,2] => [4,1,4,1]
[1,1,1,3,1,2,1] => [4,1,3,2]
[1,1,1,3,1,3] => [4,1,3,1,1]
[1,1,1,3,2,1,1] => [4,1,2,3]
[1,1,1,3,2,2] => [4,1,2,2,1]
[1,1,1,3,3,1] => [4,1,2,1,2]
[1,1,1,3,4] => [4,1,2,1,1,1]
[1,1,1,4,1,1,1] => [4,1,1,4]
[1,1,1,4,1,2] => [4,1,1,3,1]
[1,1,1,4,2,1] => [4,1,1,2,2]
[1,1,1,4,3] => [4,1,1,2,1,1]
[1,1,1,5,1,1] => [4,1,1,1,3]
[1,1,1,5,2] => [4,1,1,1,2,1]
[1,1,1,6,1] => [4,1,1,1,1,2]
[1,1,1,7] => [4,1,1,1,1,1,1]
[1,1,2,1,1,1,1,1,1] => [3,7]
[1,1,2,1,1,1,1,2] => [3,6,1]
[1,1,2,1,1,1,2,1] => [3,5,2]
[1,1,2,1,1,1,3] => [3,5,1,1]
[1,1,2,1,1,2,1,1] => [3,4,3]
[1,1,2,1,1,2,2] => [3,4,2,1]
[1,1,2,1,1,3,1] => [3,4,1,2]
[1,1,2,1,1,4] => [3,4,1,1,1]
[1,1,2,1,2,1,1,1] => [3,3,4]
[1,1,2,1,2,1,2] => [3,3,3,1]
[1,1,2,1,2,2,1] => [3,3,2,2]
[1,1,2,1,2,3] => [3,3,2,1,1]
[1,1,2,1,3,1,1] => [3,3,1,3]
[1,1,2,1,3,2] => [3,3,1,2,1]
[1,1,2,1,4,1] => [3,3,1,1,2]
[1,1,2,1,5] => [3,3,1,1,1,1]
[1,1,2,2,1,1,1,1] => [3,2,5]
[1,1,2,2,1,1,2] => [3,2,4,1]
[1,1,2,2,1,2,1] => [3,2,3,2]
[1,1,2,2,1,3] => [3,2,3,1,1]
[1,1,2,2,2,1,1] => [3,2,2,3]
[1,1,2,2,2,2] => [3,2,2,2,1]
[1,1,2,2,3,1] => [3,2,2,1,2]
[1,1,2,2,4] => [3,2,2,1,1,1]
[1,1,2,3,1,1,1] => [3,2,1,4]
[1,1,2,3,1,2] => [3,2,1,3,1]
[1,1,2,3,2,1] => [3,2,1,2,2]
[1,1,2,3,3] => [3,2,1,2,1,1]
[1,1,2,4,1,1] => [3,2,1,1,3]
[1,1,2,4,2] => [3,2,1,1,2,1]
[1,1,2,5,1] => [3,2,1,1,1,2]
[1,1,2,6] => [3,2,1,1,1,1,1]
[1,1,3,1,1,1,1,1] => [3,1,6]
[1,1,3,1,1,1,2] => [3,1,5,1]
[1,1,3,1,1,2,1] => [3,1,4,2]
[1,1,3,1,1,3] => [3,1,4,1,1]
[1,1,3,1,2,1,1] => [3,1,3,3]
[1,1,3,1,2,2] => [3,1,3,2,1]
[1,1,3,1,3,1] => [3,1,3,1,2]
[1,1,3,1,4] => [3,1,3,1,1,1]
[1,1,3,2,1,1,1] => [3,1,2,4]
[1,1,3,2,1,2] => [3,1,2,3,1]
[1,1,3,2,2,1] => [3,1,2,2,2]
[1,1,3,2,3] => [3,1,2,2,1,1]
[1,1,3,3,1,1] => [3,1,2,1,3]
[1,1,3,3,2] => [3,1,2,1,2,1]
[1,1,3,4,1] => [3,1,2,1,1,2]
[1,1,3,5] => [3,1,2,1,1,1,1]
[1,1,4,1,1,1,1] => [3,1,1,5]
[1,1,4,1,1,2] => [3,1,1,4,1]
[1,1,4,1,2,1] => [3,1,1,3,2]
[1,1,4,1,3] => [3,1,1,3,1,1]
[1,1,4,2,1,1] => [3,1,1,2,3]
[1,1,4,2,2] => [3,1,1,2,2,1]
[1,1,4,3,1] => [3,1,1,2,1,2]
[1,1,4,4] => [3,1,1,2,1,1,1]
[1,1,5,1,1,1] => [3,1,1,1,4]
[1,1,5,1,2] => [3,1,1,1,3,1]
[1,1,5,2,1] => [3,1,1,1,2,2]
[1,1,5,3] => [3,1,1,1,2,1,1]
[1,1,6,1,1] => [3,1,1,1,1,3]
[1,1,6,2] => [3,1,1,1,1,2,1]
[1,1,7,1] => [3,1,1,1,1,1,2]
[1,1,8] => [3,1,1,1,1,1,1,1]
[1,2,1,1,1,1,1,1,1] => [2,8]
[1,2,1,1,1,1,1,2] => [2,7,1]
[1,2,1,1,1,1,2,1] => [2,6,2]
[1,2,1,1,1,1,3] => [2,6,1,1]
[1,2,1,1,1,2,1,1] => [2,5,3]
[1,2,1,1,1,2,2] => [2,5,2,1]
[1,2,1,1,1,3,1] => [2,5,1,2]
[1,2,1,1,1,4] => [2,5,1,1,1]
[1,2,1,1,2,1,1,1] => [2,4,4]
[1,2,1,1,2,1,2] => [2,4,3,1]
[1,2,1,1,2,2,1] => [2,4,2,2]
[1,2,1,1,2,3] => [2,4,2,1,1]
[1,2,1,1,3,1,1] => [2,4,1,3]
[1,2,1,1,3,2] => [2,4,1,2,1]
[1,2,1,1,4,1] => [2,4,1,1,2]
[1,2,1,1,5] => [2,4,1,1,1,1]
[1,2,1,2,1,1,1,1] => [2,3,5]
[1,2,1,2,1,1,2] => [2,3,4,1]
[1,2,1,2,1,2,1] => [2,3,3,2]
[1,2,1,2,1,3] => [2,3,3,1,1]
[1,2,1,2,2,1,1] => [2,3,2,3]
[1,2,1,2,2,2] => [2,3,2,2,1]
[1,2,1,2,3,1] => [2,3,2,1,2]
[1,2,1,2,4] => [2,3,2,1,1,1]
[1,2,1,3,1,1,1] => [2,3,1,4]
[1,2,1,3,1,2] => [2,3,1,3,1]
[1,2,1,3,2,1] => [2,3,1,2,2]
[1,2,1,3,3] => [2,3,1,2,1,1]
[1,2,1,4,1,1] => [2,3,1,1,3]
[1,2,1,4,2] => [2,3,1,1,2,1]
[1,2,1,5,1] => [2,3,1,1,1,2]
[1,2,1,6] => [2,3,1,1,1,1,1]
[1,2,2,1,1,1,1,1] => [2,2,6]
[1,2,2,1,1,1,2] => [2,2,5,1]
[1,2,2,1,1,2,1] => [2,2,4,2]
[1,2,2,1,1,3] => [2,2,4,1,1]
[1,2,2,1,2,1,1] => [2,2,3,3]
[1,2,2,1,2,2] => [2,2,3,2,1]
[1,2,2,1,3,1] => [2,2,3,1,2]
[1,2,2,1,4] => [2,2,3,1,1,1]
[1,2,2,2,1,1,1] => [2,2,2,4]
[1,2,2,2,1,2] => [2,2,2,3,1]
[1,2,2,2,2,1] => [2,2,2,2,2]
[1,2,2,2,3] => [2,2,2,2,1,1]
[1,2,2,3,1,1] => [2,2,2,1,3]
[1,2,2,3,2] => [2,2,2,1,2,1]
[1,2,2,4,1] => [2,2,2,1,1,2]
[1,2,2,5] => [2,2,2,1,1,1,1]
[1,2,3,1,1,1,1] => [2,2,1,5]
[1,2,3,1,1,2] => [2,2,1,4,1]
[1,2,3,1,2,1] => [2,2,1,3,2]
[1,2,3,1,3] => [2,2,1,3,1,1]
[1,2,3,2,1,1] => [2,2,1,2,3]
[1,2,3,2,2] => [2,2,1,2,2,1]
[1,2,3,3,1] => [2,2,1,2,1,2]
[1,2,3,4] => [2,2,1,2,1,1,1]
[1,2,4,1,1,1] => [2,2,1,1,4]
[1,2,4,1,2] => [2,2,1,1,3,1]
[1,2,4,2,1] => [2,2,1,1,2,2]
[1,2,4,3] => [2,2,1,1,2,1,1]
[1,2,5,1,1] => [2,2,1,1,1,3]
[1,2,5,2] => [2,2,1,1,1,2,1]
[1,2,6,1] => [2,2,1,1,1,1,2]
[1,2,7] => [2,2,1,1,1,1,1,1]
[1,3,1,1,1,1,1,1] => [2,1,7]
[1,3,1,1,1,1,2] => [2,1,6,1]
[1,3,1,1,1,2,1] => [2,1,5,2]
[1,3,1,1,1,3] => [2,1,5,1,1]
[1,3,1,1,2,1,1] => [2,1,4,3]
[1,3,1,1,2,2] => [2,1,4,2,1]
[1,3,1,1,3,1] => [2,1,4,1,2]
[1,3,1,1,4] => [2,1,4,1,1,1]
[1,3,1,2,1,1,1] => [2,1,3,4]
[1,3,1,2,1,2] => [2,1,3,3,1]
[1,3,1,2,2,1] => [2,1,3,2,2]
[1,3,1,2,3] => [2,1,3,2,1,1]
[1,3,1,3,1,1] => [2,1,3,1,3]
[1,3,1,3,2] => [2,1,3,1,2,1]
[1,3,1,4,1] => [2,1,3,1,1,2]
[1,3,1,5] => [2,1,3,1,1,1,1]
[1,3,2,1,1,1,1] => [2,1,2,5]
[1,3,2,1,1,2] => [2,1,2,4,1]
[1,3,2,1,2,1] => [2,1,2,3,2]
[1,3,2,1,3] => [2,1,2,3,1,1]
[1,3,2,2,1,1] => [2,1,2,2,3]
[1,3,2,2,2] => [2,1,2,2,2,1]
[1,3,2,3,1] => [2,1,2,2,1,2]
[1,3,2,4] => [2,1,2,2,1,1,1]
[1,3,3,1,1,1] => [2,1,2,1,4]
[1,3,3,1,2] => [2,1,2,1,3,1]
[1,3,3,2,1] => [2,1,2,1,2,2]
[1,3,3,3] => [2,1,2,1,2,1,1]
[1,3,4,1,1] => [2,1,2,1,1,3]
[1,3,4,2] => [2,1,2,1,1,2,1]
[1,3,5,1] => [2,1,2,1,1,1,2]
[1,3,6] => [2,1,2,1,1,1,1,1]
[1,4,1,1,1,1,1] => [2,1,1,6]
[1,4,1,1,1,2] => [2,1,1,5,1]
[1,4,1,1,2,1] => [2,1,1,4,2]
[1,4,1,1,3] => [2,1,1,4,1,1]
[1,4,1,2,1,1] => [2,1,1,3,3]
[1,4,1,2,2] => [2,1,1,3,2,1]
[1,4,1,3,1] => [2,1,1,3,1,2]
[1,4,1,4] => [2,1,1,3,1,1,1]
[1,4,2,1,1,1] => [2,1,1,2,4]
[1,4,2,1,2] => [2,1,1,2,3,1]
[1,4,2,2,1] => [2,1,1,2,2,2]
[1,4,2,3] => [2,1,1,2,2,1,1]
[1,4,3,1,1] => [2,1,1,2,1,3]
[1,4,3,2] => [2,1,1,2,1,2,1]
[1,4,4,1] => [2,1,1,2,1,1,2]
[1,4,5] => [2,1,1,2,1,1,1,1]
[1,5,1,1,1,1] => [2,1,1,1,5]
[1,5,1,1,2] => [2,1,1,1,4,1]
[1,5,1,2,1] => [2,1,1,1,3,2]
[1,5,1,3] => [2,1,1,1,3,1,1]
[1,5,2,1,1] => [2,1,1,1,2,3]
[1,5,2,2] => [2,1,1,1,2,2,1]
[1,5,3,1] => [2,1,1,1,2,1,2]
[1,5,4] => [2,1,1,1,2,1,1,1]
[1,6,1,1,1] => [2,1,1,1,1,4]
[1,6,1,2] => [2,1,1,1,1,3,1]
[1,6,2,1] => [2,1,1,1,1,2,2]
[1,6,3] => [2,1,1,1,1,2,1,1]
[1,7,1,1] => [2,1,1,1,1,1,3]
[1,7,2] => [2,1,1,1,1,1,2,1]
[1,8,1] => [2,1,1,1,1,1,1,2]
[1,9] => [2,1,1,1,1,1,1,1,1]
[2,1,1,1,1,1,1,1,1] => [1,9]
[2,1,1,1,1,1,1,2] => [1,8,1]
[2,1,1,1,1,1,2,1] => [1,7,2]
[2,1,1,1,1,1,3] => [1,7,1,1]
[2,1,1,1,1,2,1,1] => [1,6,3]
[2,1,1,1,1,2,2] => [1,6,2,1]
[2,1,1,1,1,3,1] => [1,6,1,2]
[2,1,1,1,1,4] => [1,6,1,1,1]
[2,1,1,1,2,1,1,1] => [1,5,4]
[2,1,1,1,2,1,2] => [1,5,3,1]
[2,1,1,1,2,2,1] => [1,5,2,2]
[2,1,1,1,2,3] => [1,5,2,1,1]
[2,1,1,1,3,1,1] => [1,5,1,3]
[2,1,1,1,3,2] => [1,5,1,2,1]
[2,1,1,1,4,1] => [1,5,1,1,2]
[2,1,1,1,5] => [1,5,1,1,1,1]
[2,1,1,2,1,1,1,1] => [1,4,5]
[2,1,1,2,1,1,2] => [1,4,4,1]
[2,1,1,2,1,2,1] => [1,4,3,2]
[2,1,1,2,1,3] => [1,4,3,1,1]
[2,1,1,2,2,1,1] => [1,4,2,3]
[2,1,1,2,2,2] => [1,4,2,2,1]
[2,1,1,2,3,1] => [1,4,2,1,2]
[2,1,1,2,4] => [1,4,2,1,1,1]
[2,1,1,3,1,1,1] => [1,4,1,4]
[2,1,1,3,1,2] => [1,4,1,3,1]
[2,1,1,3,2,1] => [1,4,1,2,2]
[2,1,1,3,3] => [1,4,1,2,1,1]
[2,1,1,4,1,1] => [1,4,1,1,3]
[2,1,1,4,2] => [1,4,1,1,2,1]
[2,1,1,5,1] => [1,4,1,1,1,2]
[2,1,1,6] => [1,4,1,1,1,1,1]
[2,1,2,1,1,1,1,1] => [1,3,6]
[2,1,2,1,1,1,2] => [1,3,5,1]
[2,1,2,1,1,2,1] => [1,3,4,2]
[2,1,2,1,1,3] => [1,3,4,1,1]
[2,1,2,1,2,1,1] => [1,3,3,3]
[2,1,2,1,2,2] => [1,3,3,2,1]
[2,1,2,1,3,1] => [1,3,3,1,2]
[2,1,2,1,4] => [1,3,3,1,1,1]
[2,1,2,2,1,1,1] => [1,3,2,4]
[2,1,2,2,1,2] => [1,3,2,3,1]
[2,1,2,2,2,1] => [1,3,2,2,2]
[2,1,2,2,3] => [1,3,2,2,1,1]
[2,1,2,3,1,1] => [1,3,2,1,3]
[2,1,2,3,2] => [1,3,2,1,2,1]
[2,1,2,4,1] => [1,3,2,1,1,2]
[2,1,2,5] => [1,3,2,1,1,1,1]
[2,1,3,1,1,1,1] => [1,3,1,5]
[2,1,3,1,1,2] => [1,3,1,4,1]
[2,1,3,1,2,1] => [1,3,1,3,2]
[2,1,3,1,3] => [1,3,1,3,1,1]
[2,1,3,2,1,1] => [1,3,1,2,3]
[2,1,3,2,2] => [1,3,1,2,2,1]
[2,1,3,3,1] => [1,3,1,2,1,2]
[2,1,3,4] => [1,3,1,2,1,1,1]
[2,1,4,1,1,1] => [1,3,1,1,4]
[2,1,4,1,2] => [1,3,1,1,3,1]
[2,1,4,2,1] => [1,3,1,1,2,2]
[2,1,4,3] => [1,3,1,1,2,1,1]
[2,1,5,1,1] => [1,3,1,1,1,3]
[2,1,5,2] => [1,3,1,1,1,2,1]
[2,1,6,1] => [1,3,1,1,1,1,2]
[2,1,7] => [1,3,1,1,1,1,1,1]
[2,2,1,1,1,1,1,1] => [1,2,7]
[2,2,1,1,1,1,2] => [1,2,6,1]
[2,2,1,1,1,2,1] => [1,2,5,2]
[2,2,1,1,1,3] => [1,2,5,1,1]
[2,2,1,1,2,1,1] => [1,2,4,3]
[2,2,1,1,2,2] => [1,2,4,2,1]
[2,2,1,1,3,1] => [1,2,4,1,2]
[2,2,1,1,4] => [1,2,4,1,1,1]
[2,2,1,2,1,1,1] => [1,2,3,4]
[2,2,1,2,1,2] => [1,2,3,3,1]
[2,2,1,2,2,1] => [1,2,3,2,2]
[2,2,1,2,3] => [1,2,3,2,1,1]
[2,2,1,3,1,1] => [1,2,3,1,3]
[2,2,1,3,2] => [1,2,3,1,2,1]
[2,2,1,4,1] => [1,2,3,1,1,2]
[2,2,1,5] => [1,2,3,1,1,1,1]
[2,2,2,1,1,1,1] => [1,2,2,5]
[2,2,2,1,1,2] => [1,2,2,4,1]
[2,2,2,1,2,1] => [1,2,2,3,2]
[2,2,2,1,3] => [1,2,2,3,1,1]
[2,2,2,2,1,1] => [1,2,2,2,3]
[2,2,2,2,2] => [1,2,2,2,2,1]
[2,2,2,3,1] => [1,2,2,2,1,2]
[2,2,2,4] => [1,2,2,2,1,1,1]
[2,2,3,1,1,1] => [1,2,2,1,4]
[2,2,3,1,2] => [1,2,2,1,3,1]
[2,2,3,2,1] => [1,2,2,1,2,2]
[2,2,3,3] => [1,2,2,1,2,1,1]
[2,2,4,1,1] => [1,2,2,1,1,3]
[2,2,4,2] => [1,2,2,1,1,2,1]
[2,2,5,1] => [1,2,2,1,1,1,2]
[2,2,6] => [1,2,2,1,1,1,1,1]
[2,3,1,1,1,1,1] => [1,2,1,6]
[2,3,1,1,1,2] => [1,2,1,5,1]
[2,3,1,1,2,1] => [1,2,1,4,2]
[2,3,1,1,3] => [1,2,1,4,1,1]
[2,3,1,2,1,1] => [1,2,1,3,3]
[2,3,1,2,2] => [1,2,1,3,2,1]
[2,3,1,3,1] => [1,2,1,3,1,2]
[2,3,1,4] => [1,2,1,3,1,1,1]
[2,3,2,1,1,1] => [1,2,1,2,4]
[2,3,2,1,2] => [1,2,1,2,3,1]
[2,3,2,2,1] => [1,2,1,2,2,2]
[2,3,2,3] => [1,2,1,2,2,1,1]
[2,3,3,1,1] => [1,2,1,2,1,3]
[2,3,3,2] => [1,2,1,2,1,2,1]
[2,3,4,1] => [1,2,1,2,1,1,2]
[2,3,5] => [1,2,1,2,1,1,1,1]
[2,4,1,1,1,1] => [1,2,1,1,5]
[2,4,1,1,2] => [1,2,1,1,4,1]
[2,4,1,2,1] => [1,2,1,1,3,2]
[2,4,1,3] => [1,2,1,1,3,1,1]
[2,4,2,1,1] => [1,2,1,1,2,3]
[2,4,2,2] => [1,2,1,1,2,2,1]
[2,4,3,1] => [1,2,1,1,2,1,2]
[2,4,4] => [1,2,1,1,2,1,1,1]
[2,5,1,1,1] => [1,2,1,1,1,4]
[2,5,1,2] => [1,2,1,1,1,3,1]
[2,5,2,1] => [1,2,1,1,1,2,2]
[2,5,3] => [1,2,1,1,1,2,1,1]
[2,6,1,1] => [1,2,1,1,1,1,3]
[2,6,2] => [1,2,1,1,1,1,2,1]
[2,7,1] => [1,2,1,1,1,1,1,2]
[2,8] => [1,2,1,1,1,1,1,1,1]
[3,1,1,1,1,1,1,1] => [1,1,8]
[3,1,1,1,1,1,2] => [1,1,7,1]
[3,1,1,1,1,2,1] => [1,1,6,2]
[3,1,1,1,1,3] => [1,1,6,1,1]
[3,1,1,1,2,1,1] => [1,1,5,3]
[3,1,1,1,2,2] => [1,1,5,2,1]
[3,1,1,1,3,1] => [1,1,5,1,2]
[3,1,1,1,4] => [1,1,5,1,1,1]
[3,1,1,2,1,1,1] => [1,1,4,4]
[3,1,1,2,1,2] => [1,1,4,3,1]
[3,1,1,2,2,1] => [1,1,4,2,2]
[3,1,1,2,3] => [1,1,4,2,1,1]
[3,1,1,3,1,1] => [1,1,4,1,3]
[3,1,1,3,2] => [1,1,4,1,2,1]
[3,1,1,4,1] => [1,1,4,1,1,2]
[3,1,1,5] => [1,1,4,1,1,1,1]
[3,1,2,1,1,1,1] => [1,1,3,5]
[3,1,2,1,1,2] => [1,1,3,4,1]
[3,1,2,1,2,1] => [1,1,3,3,2]
[3,1,2,1,3] => [1,1,3,3,1,1]
[3,1,2,2,1,1] => [1,1,3,2,3]
[3,1,2,2,2] => [1,1,3,2,2,1]
[3,1,2,3,1] => [1,1,3,2,1,2]
[3,1,2,4] => [1,1,3,2,1,1,1]
[3,1,3,1,1,1] => [1,1,3,1,4]
[3,1,3,1,2] => [1,1,3,1,3,1]
[3,1,3,2,1] => [1,1,3,1,2,2]
[3,1,3,3] => [1,1,3,1,2,1,1]
[3,1,4,1,1] => [1,1,3,1,1,3]
[3,1,4,2] => [1,1,3,1,1,2,1]
[3,1,5,1] => [1,1,3,1,1,1,2]
[3,1,6] => [1,1,3,1,1,1,1,1]
[3,2,1,1,1,1,1] => [1,1,2,6]
[3,2,1,1,1,2] => [1,1,2,5,1]
[3,2,1,1,2,1] => [1,1,2,4,2]
[3,2,1,1,3] => [1,1,2,4,1,1]
[3,2,1,2,1,1] => [1,1,2,3,3]
[3,2,1,2,2] => [1,1,2,3,2,1]
[3,2,1,3,1] => [1,1,2,3,1,2]
[3,2,1,4] => [1,1,2,3,1,1,1]
[3,2,2,1,1,1] => [1,1,2,2,4]
[3,2,2,1,2] => [1,1,2,2,3,1]
[3,2,2,2,1] => [1,1,2,2,2,2]
[3,2,2,3] => [1,1,2,2,2,1,1]
[3,2,3,1,1] => [1,1,2,2,1,3]
[3,2,3,2] => [1,1,2,2,1,2,1]
[3,2,4,1] => [1,1,2,2,1,1,2]
[3,2,5] => [1,1,2,2,1,1,1,1]
[3,3,1,1,1,1] => [1,1,2,1,5]
[3,3,1,1,2] => [1,1,2,1,4,1]
[3,3,1,2,1] => [1,1,2,1,3,2]
[3,3,1,3] => [1,1,2,1,3,1,1]
[3,3,2,1,1] => [1,1,2,1,2,3]
[3,3,2,2] => [1,1,2,1,2,2,1]
[3,3,3,1] => [1,1,2,1,2,1,2]
[3,3,4] => [1,1,2,1,2,1,1,1]
[3,4,1,1,1] => [1,1,2,1,1,4]
[3,4,1,2] => [1,1,2,1,1,3,1]
[3,4,2,1] => [1,1,2,1,1,2,2]
[3,4,3] => [1,1,2,1,1,2,1,1]
[3,5,1,1] => [1,1,2,1,1,1,3]
[3,5,2] => [1,1,2,1,1,1,2,1]
[3,6,1] => [1,1,2,1,1,1,1,2]
[3,7] => [1,1,2,1,1,1,1,1,1]
[4,1,1,1,1,1,1] => [1,1,1,7]
[4,1,1,1,1,2] => [1,1,1,6,1]
[4,1,1,1,2,1] => [1,1,1,5,2]
[4,1,1,1,3] => [1,1,1,5,1,1]
[4,1,1,2,1,1] => [1,1,1,4,3]
[4,1,1,2,2] => [1,1,1,4,2,1]
[4,1,1,3,1] => [1,1,1,4,1,2]
[4,1,1,4] => [1,1,1,4,1,1,1]
[4,1,2,1,1,1] => [1,1,1,3,4]
[4,1,2,1,2] => [1,1,1,3,3,1]
[4,1,2,2,1] => [1,1,1,3,2,2]
[4,1,2,3] => [1,1,1,3,2,1,1]
[4,1,3,1,1] => [1,1,1,3,1,3]
[4,1,3,2] => [1,1,1,3,1,2,1]
[4,1,4,1] => [1,1,1,3,1,1,2]
[4,1,5] => [1,1,1,3,1,1,1,1]
[4,2,1,1,1,1] => [1,1,1,2,5]
[4,2,1,1,2] => [1,1,1,2,4,1]
[4,2,1,2,1] => [1,1,1,2,3,2]
[4,2,1,3] => [1,1,1,2,3,1,1]
[4,2,2,1,1] => [1,1,1,2,2,3]
[4,2,2,2] => [1,1,1,2,2,2,1]
[4,2,3,1] => [1,1,1,2,2,1,2]
[4,2,4] => [1,1,1,2,2,1,1,1]
[4,3,1,1,1] => [1,1,1,2,1,4]
[4,3,1,2] => [1,1,1,2,1,3,1]
[4,3,2,1] => [1,1,1,2,1,2,2]
[4,3,3] => [1,1,1,2,1,2,1,1]
[4,4,1,1] => [1,1,1,2,1,1,3]
[4,4,2] => [1,1,1,2,1,1,2,1]
[4,5,1] => [1,1,1,2,1,1,1,2]
[4,6] => [1,1,1,2,1,1,1,1,1]
[5,1,1,1,1,1] => [1,1,1,1,6]
[5,1,1,1,2] => [1,1,1,1,5,1]
[5,1,1,2,1] => [1,1,1,1,4,2]
[5,1,1,3] => [1,1,1,1,4,1,1]
[5,1,2,1,1] => [1,1,1,1,3,3]
[5,1,2,2] => [1,1,1,1,3,2,1]
[5,1,3,1] => [1,1,1,1,3,1,2]
[5,1,4] => [1,1,1,1,3,1,1,1]
[5,2,1,1,1] => [1,1,1,1,2,4]
[5,2,1,2] => [1,1,1,1,2,3,1]
[5,2,2,1] => [1,1,1,1,2,2,2]
[5,2,3] => [1,1,1,1,2,2,1,1]
[5,3,1,1] => [1,1,1,1,2,1,3]
[5,3,2] => [1,1,1,1,2,1,2,1]
[5,4,1] => [1,1,1,1,2,1,1,2]
[5,5] => [1,1,1,1,2,1,1,1,1]
[6,1,1,1,1] => [1,1,1,1,1,5]
[6,1,1,2] => [1,1,1,1,1,4,1]
[6,1,2,1] => [1,1,1,1,1,3,2]
[6,1,3] => [1,1,1,1,1,3,1,1]
[6,2,1,1] => [1,1,1,1,1,2,3]
[6,2,2] => [1,1,1,1,1,2,2,1]
[6,3,1] => [1,1,1,1,1,2,1,2]
[6,4] => [1,1,1,1,1,2,1,1,1]
[7,1,1,1] => [1,1,1,1,1,1,4]
[7,1,2] => [1,1,1,1,1,1,3,1]
[7,2,1] => [1,1,1,1,1,1,2,2]
[7,3] => [1,1,1,1,1,1,2,1,1]
[8,1,1] => [1,1,1,1,1,1,1,3]
[8,2] => [1,1,1,1,1,1,1,2,1]
[9,1] => [1,1,1,1,1,1,1,1,2]
[10] => [1,1,1,1,1,1,1,1,1,1]
[5,5,1,1] => [1,1,1,1,2,1,1,1,3]
[1,1,5,5] => [3,1,1,1,2,1,1,1,1]
[] => []
[10,1] => [1,1,1,1,1,1,1,1,1,2]
[1,10] => [2,1,1,1,1,1,1,1,1,1]
[1,8,1,1] => [2,1,1,1,1,1,1,3]
[1,7,2,1] => [2,1,1,1,1,1,2,2]
[1,6,3,1] => [2,1,1,1,1,2,1,2]
[1,5,4,1] => [2,1,1,1,2,1,1,2]
[1,4,5,1] => [2,1,1,2,1,1,1,2]
[1,3,6,1] => [2,1,2,1,1,1,1,2]
[1,2,7,1] => [2,2,1,1,1,1,1,2]
[1,1,8,1] => [3,1,1,1,1,1,1,2]
[2,1,1,1,1,1,1,1,1,1] => [1,10]
[1,1,1,1,1,1,1,1,1,2] => [10,1]
[2,9] => [1,2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,3] => [9,1,1]
[1,1,1,1,1,1,1,1,2,1] => [9,2]
[11] => [1,1,1,1,1,1,1,1,1,1,1]
[3,1,1,1,1,1,1,1,1] => [1,1,9]
[9,2] => [1,1,1,1,1,1,1,1,2,1]
[1,1,6,6] => [3,1,1,1,1,2,1,1,1,1,1]
[1,1,4,1,1,4] => [3,1,1,4,1,1,1]
[4,1,1,4,1,1] => [1,1,1,4,1,1,3]
[6,6,1,1] => [1,1,1,1,1,2,1,1,1,1,3]
[1,1,7,7] => [3,1,1,1,1,1,2,1,1,1,1,1,1]
[1,1,5,1,1,5] => [3,1,1,1,4,1,1,1,1]
[1,1,3,1,2,4] => [3,1,3,2,1,1,1]
[1,1,4,2,1,3] => [3,1,1,2,3,1,1]
[3,1,2,4,1,1] => [1,1,3,2,1,1,3]
[4,2,1,3,1,1] => [1,1,1,2,3,1,3]
[5,1,1,5,1,1] => [1,1,1,1,4,1,1,1,3]
[7,7,1,1] => [1,1,1,1,1,1,2,1,1,1,1,1,3]
[1,1,8,8] => [3,1,1,1,1,1,1,2,1,1,1,1,1,1,1]
[1,1,6,1,1,6] => [3,1,1,1,1,4,1,1,1,1,1]
[1,1,4,1,2,5] => [3,1,1,3,2,1,1,1,1]
[1,1,5,2,1,4] => [3,1,1,1,2,3,1,1,1]
[1,1,2,1,3,4] => [3,3,1,2,1,1,1]
[1,1,3,1,1,1,1,3] => [3,1,6,1,1]
[1,1,4,3,1,2] => [3,1,1,2,1,3,1]
[2,2,4,4] => [1,2,2,1,1,2,1,1,1]
[2,1,3,4,1,1] => [1,3,1,2,1,1,3]
[3,1,1,1,1,3,1,1] => [1,1,6,1,3]
[4,1,2,5,1,1] => [1,1,1,3,2,1,1,1,3]
[4,4,2,2] => [1,1,1,2,1,1,2,2,1]
[4,3,1,2,1,1] => [1,1,1,2,1,3,3]
[5,2,1,4,1,1] => [1,1,1,1,2,3,1,1,3]
[6,1,1,6,1,1] => [1,1,1,1,1,4,1,1,1,1,3]
[8,8,1,1] => [1,1,1,1,1,1,1,2,1,1,1,1,1,1,3]
[1,1,9,9] => [3,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1]
[1,1,7,1,1,7] => [3,1,1,1,1,1,4,1,1,1,1,1,1]
[1,1,5,1,2,6] => [3,1,1,1,3,2,1,1,1,1,1]
[1,1,6,2,1,5] => [3,1,1,1,1,2,3,1,1,1,1]
[1,1,3,1,3,5] => [3,1,3,1,2,1,1,1,1]
[1,1,4,1,1,1,1,4] => [3,1,1,6,1,1,1]
[1,1,5,3,1,3] => [3,1,1,1,2,1,3,1,1]
[1,1,1,1,4,4] => [5,1,1,2,1,1,1]
[1,1,2,1,2,1,1,3] => [3,3,4,1,1]
[1,1,3,2,2,3] => [3,1,2,2,2,1,1]
[1,1,3,1,1,2,1,2] => [3,1,4,3,1]
[1,1,4,4,1,1] => [3,1,1,2,1,1,3]
[2,2,3,1,1,3] => [1,2,2,1,4,1,1]
[2,1,2,1,1,3,1,1] => [1,3,4,1,3]
[3,1,3,5,1,1] => [1,1,3,1,2,1,1,1,3]
[3,3,3,3] => [1,1,2,1,2,1,2,1,1]
[3,2,2,3,1,1] => [1,1,2,2,2,1,3]
[3,1,1,3,2,2] => [1,1,4,1,2,2,1]
[3,1,1,2,1,2,1,1] => [1,1,4,3,3]
[4,1,1,1,1,4,1,1] => [1,1,1,6,1,1,3]
[5,1,2,6,1,1] => [1,1,1,1,3,2,1,1,1,1,3]
[4,4,1,1,1,1] => [1,1,1,2,1,1,5]
[5,3,1,3,1,1] => [1,1,1,1,2,1,3,1,3]
[6,2,1,5,1,1] => [1,1,1,1,1,2,3,1,1,1,3]
[7,1,1,7,1,1] => [1,1,1,1,1,1,4,1,1,1,1,1,3]
[9,9,1,1] => [1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,3]
[1,1,10,10] => [3,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1]
[1,1,8,1,1,8] => [3,1,1,1,1,1,1,4,1,1,1,1,1,1,1]
[1,1,6,1,2,7] => [3,1,1,1,1,3,2,1,1,1,1,1,1]
[1,1,7,2,1,6] => [3,1,1,1,1,1,2,3,1,1,1,1,1]
[1,1,4,1,3,6] => [3,1,1,3,1,2,1,1,1,1,1]
[1,1,5,1,1,1,1,5] => [3,1,1,1,6,1,1,1,1]
[1,1,6,3,1,4] => [3,1,1,1,1,2,1,3,1,1,1]
[1,1,2,1,4,5] => [3,3,1,1,2,1,1,1,1]
[1,1,3,1,2,1,1,4] => [3,1,3,4,1,1,1]
[1,1,4,2,2,4] => [3,1,1,2,2,2,1,1,1]
[1,1,4,1,1,2,1,3] => [3,1,1,4,3,1,1]
[1,1,5,4,1,2] => [3,1,1,1,2,1,1,3,1]
[2,2,5,5] => [1,2,2,1,1,1,2,1,1,1,1]
[1,1,1,1,3,1,1,3] => [5,1,4,1,1]
[1,1,2,1,1,1,2,3] => [3,5,2,1,1]
[1,1,2,1,2,2,1,2] => [3,3,2,3,1]
[1,1,3,2,1,1,1,2] => [3,1,2,5,1]
[1,1,3,1,1,3,1,1] => [3,1,4,1,3]
[2,1,4,5,1,1] => [1,3,1,1,2,1,1,1,3]
[2,2,2,1,2,3] => [1,2,2,3,2,1,1]
[2,2,3,2,1,2] => [1,2,2,1,2,3,1]
[2,1,1,2,3,3] => [1,4,2,1,2,1,1]
[2,1,1,1,2,3,1,1] => [1,5,2,1,3]
[2,1,2,3,2,2] => [1,3,2,1,2,2,1]
[2,1,2,2,1,2,1,1] => [1,3,2,3,3]
[3,1,2,1,1,4,1,1] => [1,1,3,4,1,1,3]
[4,1,3,6,1,1] => [1,1,1,3,1,2,1,1,1,1,3]
[3,3,2,1,1,2] => [1,1,2,1,2,4,1]
[3,2,1,2,2,2] => [1,1,2,3,2,2,1]
[3,2,1,1,1,2,1,1] => [1,1,2,5,3]
[4,2,2,4,1,1] => [1,1,1,2,2,2,1,1,3]
[3,1,1,3,1,1,1,1] => [1,1,4,1,5]
[4,1,1,2,1,3,1,1] => [1,1,1,4,3,1,3]
[5,1,1,1,1,5,1,1] => [1,1,1,1,6,1,1,1,3]
[6,1,2,7,1,1] => [1,1,1,1,1,3,2,1,1,1,1,1,3]
[5,5,2,2] => [1,1,1,1,2,1,1,1,2,2,1]
[5,4,1,2,1,1] => [1,1,1,1,2,1,1,3,3]
[6,3,1,4,1,1] => [1,1,1,1,1,2,1,3,1,1,3]
[7,2,1,6,1,1] => [1,1,1,1,1,1,2,3,1,1,1,1,3]
[8,1,1,8,1,1] => [1,1,1,1,1,1,1,4,1,1,1,1,1,1,3]
[10,10,1,1] => [1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,3]
[3,1,1,1,1,1,1,2] => [1,1,8,1]
[2,2,1,1,1,1,1,2] => [1,2,7,1]
[2,1,2,1,1,1,1,2] => [1,3,6,1]
[2,1,1,2,1,1,1,2] => [1,4,5,1]
[2,1,1,1,2,1,1,2] => [1,5,4,1]
[2,1,1,1,1,2,1,2] => [1,6,3,1]
[2,1,1,1,1,1,2,2] => [1,7,2,1]
[2,1,1,1,1,1,1,3] => [1,8,1,1]
[2,1,7,1] => [1,3,1,1,1,1,1,2]
[1,1,1,1,6,1] => [5,1,1,1,1,2]
[1,2,1,1,5,1] => [2,4,1,1,1,2]
[1,3,1,1,4,1] => [2,1,4,1,1,2]
[1,4,1,1,3,1] => [2,1,1,4,1,2]
[1,5,1,1,2,1] => [2,1,1,1,4,2]
[1,6,1,1,1,1] => [2,1,1,1,1,5]
[1,7,1,2] => [2,1,1,1,1,1,3,1]
[9,1,1] => [1,1,1,1,1,1,1,1,3]
[2,7,1,1] => [1,2,1,1,1,1,1,3]
[3,6,1,1] => [1,1,2,1,1,1,1,3]
[4,5,1,1] => [1,1,1,2,1,1,1,3]
[5,4,1,1] => [1,1,1,1,2,1,1,3]
[6,3,1,1] => [1,1,1,1,1,2,1,3]
[7,2,1,1] => [1,1,1,1,1,1,2,3]
[8,1,1,1] => [1,1,1,1,1,1,1,4]
[1,1,1,8] => [4,1,1,1,1,1,1,1]
[1,1,2,7] => [3,2,1,1,1,1,1,1]
[1,1,3,6] => [3,1,2,1,1,1,1,1]
[1,1,4,5] => [3,1,1,2,1,1,1,1]
[1,1,5,4] => [3,1,1,1,2,1,1,1]
[1,1,6,3] => [3,1,1,1,1,2,1,1]
[1,1,7,2] => [3,1,1,1,1,1,2,1]
[1,1,9] => [3,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,1,1] => [11]
[1,2,1,1,1,1,1,1,1,1] => [2,9]
[2,1,1,1,1,1,1,1,2] => [1,9,1]
[1,1,1,1,1,2,1,1,1,1] => [6,5]
[1,1,1,1,2,1,1,1,1,1] => [5,6]
[1,1,1,1,1,1,1,2,1,1] => [8,3]
[2,1,1,1,2,1,1,1,1] => [1,5,5]
[1,1,1,1,1,1,2,1,1,1] => [7,4]
[1,1,1,1,1,1,2,1,1,2] => [7,4,1]
[1,1,1,1,1,1,1,1,2,2] => [9,2,1]
[2,2,1,1,2,1,1,2] => [1,2,4,4,1]
[2,2,1,1,1,1,2,2] => [1,2,6,2,1]
[2,1,1,2,2,1,1,2] => [1,4,2,4,1]
[1,1,2,2,2,1,1,2] => [3,2,2,4,1]
[2,1,1,2,1,1,2,2] => [1,4,4,2,1]
[1,1,2,2,1,1,2,2] => [3,2,4,2,1]
[1,1,1,1,3,2,1,2] => [5,1,2,3,1]
[1,1,2,1,1,1,1,1,1,2] => [3,8,1]
[1,1,2,1,1,2,2,2] => [3,4,2,2,1]
[3,3,1,1,2,2] => [1,1,2,1,4,2,1]
[1,1,1,1,2,1,1,1,1,2] => [5,6,1]
[1,1,1,1,2,2,2,2] => [5,2,2,2,1]
[3,2,2,2,1,2] => [1,1,2,2,2,3,1]
[2,1,1,1,2,2,1,2] => [1,5,2,3,1]
[1,1,1,1,2,1,2,3] => [5,3,2,1,1]
[3,2,1,1,1,1,1,2] => [1,1,2,7,1]
[2,1,1,1,1,1,1,1,1,2] => [1,10,1]
[2,1,1,1,1,2,2,2] => [1,6,2,2,1]
[2,2,2,1,1,1,1,2] => [1,2,2,6,1]
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Description
The complement of a composition.
The complement of a composition $I$ is defined as follows:
If $I$ is the empty composition, then the complement is also the empty composition. Otherwise, let $S$ be the descent set corresponding to $I=(i_1,\dots,i_k)$, that is, the subset
$$\{ i_1, i_1 + i_2, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$$
of $\{ 1, 2, \ldots, |I|-1 \}$. Then, the complement of $I$ is the composition of the same size as $I$, whose descent set is $\{ 1, 2, \ldots, |I|-1 \} \setminus S$.
The complement of a composition $I$ coincides with the reversal ( Mp00038reverse) of the composition conjugate ( Mp00041conjugate) to $I$.
Properties
bijectiveA map $\phi: A \rightarrow B$ is bijective if it is both injective and surjective. This is if (1) $\phi(a) = \phi(b)$ implies $a=b$, and (2) for any $b \in B$, there is an $a \in A$ such that $\phi(a) = b$., gradedA map $\phi: A \rightarrow B$ is graded for graded sets $A$ and $B$ if $\operatorname{deg}(a) = \operatorname{deg}(a')$ implies $\operatorname{deg}(\phi(a)) = \operatorname{deg}(\phi(a'))$ for all $a, a' \in A$., involutiveA map $\phi: A \rightarrow A$ is involutive if $\phi\circ\phi(a) = a$ for any $a \in A$.
Code
def complement(elt):
    return elt.conjugate().reversed()