Identifier
Mp00319: Parking functions —to composition⟶ Integer compositions
Mp00040: Integer compositions —to partition⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Images
[1] => [1] => [1] => [1,0,1,0]
[1,1] => [1,1] => [1,1] => [1,0,1,1,0,0]
[1,2] => [1,2] => [2,1] => [1,0,1,0,1,0]
[2,1] => [2,1] => [2,1] => [1,0,1,0,1,0]
[1,1,1] => [1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0]
[1,1,2] => [1,1,2] => [2,1,1] => [1,0,1,1,0,1,0,0]
[1,2,1] => [1,2,1] => [2,1,1] => [1,0,1,1,0,1,0,0]
[2,1,1] => [2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0]
[1,1,3] => [1,1,3] => [3,1,1] => [1,0,1,1,0,0,1,0]
[1,3,1] => [1,3,1] => [3,1,1] => [1,0,1,1,0,0,1,0]
[3,1,1] => [3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0]
[1,2,2] => [1,2,2] => [2,2,1] => [1,0,1,0,1,1,0,0]
[2,1,2] => [2,1,2] => [2,2,1] => [1,0,1,0,1,1,0,0]
[2,2,1] => [2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0]
[1,2,3] => [1,2,3] => [3,2,1] => [1,0,1,0,1,0,1,0]
[1,3,2] => [1,3,2] => [3,2,1] => [1,0,1,0,1,0,1,0]
[2,1,3] => [2,1,3] => [3,2,1] => [1,0,1,0,1,0,1,0]
[2,3,1] => [2,3,1] => [3,2,1] => [1,0,1,0,1,0,1,0]
[3,1,2] => [3,1,2] => [3,2,1] => [1,0,1,0,1,0,1,0]
[3,2,1] => [3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0]
[1,1,1,1] => [1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0]
[1,1,1,2] => [1,1,1,2] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0]
[1,1,2,1] => [1,1,2,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0]
[1,2,1,1] => [1,2,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0]
[2,1,1,1] => [2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0]
[1,1,1,3] => [1,1,1,3] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0]
[1,1,3,1] => [1,1,3,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0]
[1,3,1,1] => [1,3,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0]
[3,1,1,1] => [3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0]
[1,1,1,4] => [1,1,1,4] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0]
[1,1,4,1] => [1,1,4,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0]
[1,4,1,1] => [1,4,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0]
[4,1,1,1] => [4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0]
[1,1,2,2] => [1,1,2,2] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0]
[1,2,1,2] => [1,2,1,2] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0]
[1,2,2,1] => [1,2,2,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0]
[2,1,1,2] => [2,1,1,2] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0]
[2,1,2,1] => [2,1,2,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0]
[2,2,1,1] => [2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0]
[1,1,2,3] => [1,1,2,3] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0]
[1,1,3,2] => [1,1,3,2] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0]
[1,2,1,3] => [1,2,1,3] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0]
[1,2,3,1] => [1,2,3,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0]
[1,3,1,2] => [1,3,1,2] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0]
[1,3,2,1] => [1,3,2,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0]
[2,1,1,3] => [2,1,1,3] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0]
[2,1,3,1] => [2,1,3,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0]
[2,3,1,1] => [2,3,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0]
[3,1,1,2] => [3,1,1,2] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0]
[3,1,2,1] => [3,1,2,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0]
[3,2,1,1] => [3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0]
[1,1,2,4] => [1,1,2,4] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0]
[1,1,4,2] => [1,1,4,2] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0]
[1,2,1,4] => [1,2,1,4] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0]
[1,2,4,1] => [1,2,4,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0]
[1,4,1,2] => [1,4,1,2] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0]
[1,4,2,1] => [1,4,2,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0]
[2,1,1,4] => [2,1,1,4] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0]
[2,1,4,1] => [2,1,4,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0]
[2,4,1,1] => [2,4,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0]
[4,1,1,2] => [4,1,1,2] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0]
[4,1,2,1] => [4,1,2,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0]
[4,2,1,1] => [4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0]
[1,1,3,3] => [1,1,3,3] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0]
[1,3,1,3] => [1,3,1,3] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0]
[1,3,3,1] => [1,3,3,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0]
[3,1,1,3] => [3,1,1,3] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0]
[3,1,3,1] => [3,1,3,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0]
[3,3,1,1] => [3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0]
[1,1,3,4] => [1,1,3,4] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0]
[1,1,4,3] => [1,1,4,3] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0]
[1,3,1,4] => [1,3,1,4] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0]
[1,3,4,1] => [1,3,4,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0]
[1,4,1,3] => [1,4,1,3] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0]
[1,4,3,1] => [1,4,3,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0]
[3,1,1,4] => [3,1,1,4] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0]
[3,1,4,1] => [3,1,4,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0]
[3,4,1,1] => [3,4,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0]
[4,1,1,3] => [4,1,1,3] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0]
[4,1,3,1] => [4,1,3,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0]
[4,3,1,1] => [4,3,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0]
[1,2,2,2] => [1,2,2,2] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0]
[2,1,2,2] => [2,1,2,2] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0]
[2,2,1,2] => [2,2,1,2] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0]
[2,2,2,1] => [2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0]
[1,2,2,3] => [1,2,2,3] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0]
[1,2,3,2] => [1,2,3,2] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0]
[1,3,2,2] => [1,3,2,2] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0]
[2,1,2,3] => [2,1,2,3] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0]
[2,1,3,2] => [2,1,3,2] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0]
[2,2,1,3] => [2,2,1,3] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0]
[2,2,3,1] => [2,2,3,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0]
[2,3,1,2] => [2,3,1,2] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0]
[2,3,2,1] => [2,3,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0]
[3,1,2,2] => [3,1,2,2] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0]
[3,2,1,2] => [3,2,1,2] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0]
[3,2,2,1] => [3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0]
[1,2,2,4] => [1,2,2,4] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0]
[1,2,4,2] => [1,2,4,2] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0]
[1,4,2,2] => [1,4,2,2] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0]
[2,1,2,4] => [2,1,2,4] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0]
>>> Load all 843 entries. <<<
[2,1,4,2] => [2,1,4,2] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0]
[2,2,1,4] => [2,2,1,4] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0]
[2,2,4,1] => [2,2,4,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0]
[2,4,1,2] => [2,4,1,2] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0]
[2,4,2,1] => [2,4,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0]
[4,1,2,2] => [4,1,2,2] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0]
[4,2,1,2] => [4,2,1,2] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0]
[4,2,2,1] => [4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0]
[1,2,3,3] => [1,2,3,3] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0]
[1,3,2,3] => [1,3,2,3] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0]
[1,3,3,2] => [1,3,3,2] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0]
[2,1,3,3] => [2,1,3,3] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0]
[2,3,1,3] => [2,3,1,3] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0]
[2,3,3,1] => [2,3,3,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0]
[3,1,2,3] => [3,1,2,3] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0]
[3,1,3,2] => [3,1,3,2] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0]
[3,2,1,3] => [3,2,1,3] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0]
[3,2,3,1] => [3,2,3,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0]
[3,3,1,2] => [3,3,1,2] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0]
[3,3,2,1] => [3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0]
[1,2,3,4] => [1,2,3,4] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0]
[1,2,4,3] => [1,2,4,3] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0]
[1,3,2,4] => [1,3,2,4] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0]
[1,3,4,2] => [1,3,4,2] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0]
[1,4,2,3] => [1,4,2,3] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0]
[1,4,3,2] => [1,4,3,2] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0]
[2,1,3,4] => [2,1,3,4] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0]
[2,1,4,3] => [2,1,4,3] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0]
[2,3,1,4] => [2,3,1,4] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0]
[2,3,4,1] => [2,3,4,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0]
[2,4,1,3] => [2,4,1,3] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0]
[2,4,3,1] => [2,4,3,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0]
[3,1,2,4] => [3,1,2,4] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0]
[3,1,4,2] => [3,1,4,2] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0]
[3,2,1,4] => [3,2,1,4] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0]
[3,2,4,1] => [3,2,4,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0]
[3,4,1,2] => [3,4,1,2] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0]
[3,4,2,1] => [3,4,2,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0]
[4,1,2,3] => [4,1,2,3] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0]
[4,1,3,2] => [4,1,3,2] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0]
[4,2,1,3] => [4,2,1,3] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0]
[4,2,3,1] => [4,2,3,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0]
[4,3,1,2] => [4,3,1,2] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0]
[4,3,2,1] => [4,3,2,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0]
[1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,2] => [1,1,1,1,2] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0]
[1,1,1,2,1] => [1,1,1,2,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0]
[1,1,2,1,1] => [1,1,2,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0]
[1,2,1,1,1] => [1,2,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0]
[2,1,1,1,1] => [2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0]
[1,1,1,1,3] => [1,1,1,1,3] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0]
[1,1,1,3,1] => [1,1,1,3,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0]
[1,1,3,1,1] => [1,1,3,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0]
[1,3,1,1,1] => [1,3,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0]
[3,1,1,1,1] => [3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0]
[1,1,1,1,4] => [1,1,1,1,4] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0]
[1,1,1,4,1] => [1,1,1,4,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0]
[1,1,4,1,1] => [1,1,4,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0]
[1,4,1,1,1] => [1,4,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0]
[4,1,1,1,1] => [4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0]
[1,1,1,1,5] => [1,1,1,1,5] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,5,1] => [1,1,1,5,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,5,1,1] => [1,1,5,1,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0]
[1,5,1,1,1] => [1,5,1,1,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0]
[5,1,1,1,1] => [5,1,1,1,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,2,2] => [1,1,1,2,2] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0]
[1,1,2,1,2] => [1,1,2,1,2] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0]
[1,1,2,2,1] => [1,1,2,2,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0]
[1,2,1,1,2] => [1,2,1,1,2] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0]
[1,2,1,2,1] => [1,2,1,2,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0]
[1,2,2,1,1] => [1,2,2,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0]
[2,1,1,1,2] => [2,1,1,1,2] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0]
[2,1,1,2,1] => [2,1,1,2,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0]
[2,1,2,1,1] => [2,1,2,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0]
[2,2,1,1,1] => [2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0]
[1,1,1,2,3] => [1,1,1,2,3] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0]
[1,1,1,3,2] => [1,1,1,3,2] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0]
[1,1,2,1,3] => [1,1,2,1,3] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0]
[1,1,2,3,1] => [1,1,2,3,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0]
[1,1,3,1,2] => [1,1,3,1,2] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0]
[1,1,3,2,1] => [1,1,3,2,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0]
[1,2,1,1,3] => [1,2,1,1,3] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0]
[1,2,1,3,1] => [1,2,1,3,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0]
[1,2,3,1,1] => [1,2,3,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0]
[1,3,1,1,2] => [1,3,1,1,2] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0]
[1,3,1,2,1] => [1,3,1,2,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0]
[1,3,2,1,1] => [1,3,2,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0]
[2,1,1,1,3] => [2,1,1,1,3] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0]
[2,1,1,3,1] => [2,1,1,3,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0]
[2,1,3,1,1] => [2,1,3,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0]
[2,3,1,1,1] => [2,3,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0]
[3,1,1,1,2] => [3,1,1,1,2] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0]
[3,1,1,2,1] => [3,1,1,2,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0]
[3,1,2,1,1] => [3,1,2,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0]
[3,2,1,1,1] => [3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0]
[1,1,1,2,4] => [1,1,1,2,4] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0]
[1,1,1,4,2] => [1,1,1,4,2] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0]
[1,1,2,1,4] => [1,1,2,1,4] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0]
[1,1,2,4,1] => [1,1,2,4,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0]
[1,1,4,1,2] => [1,1,4,1,2] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0]
[1,1,4,2,1] => [1,1,4,2,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0]
[1,2,1,1,4] => [1,2,1,1,4] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0]
[1,2,1,4,1] => [1,2,1,4,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0]
[1,2,4,1,1] => [1,2,4,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0]
[1,4,1,1,2] => [1,4,1,1,2] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0]
[1,4,1,2,1] => [1,4,1,2,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0]
[1,4,2,1,1] => [1,4,2,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0]
[2,1,1,1,4] => [2,1,1,1,4] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0]
[2,1,1,4,1] => [2,1,1,4,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0]
[2,1,4,1,1] => [2,1,4,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0]
[2,4,1,1,1] => [2,4,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0]
[4,1,1,1,2] => [4,1,1,1,2] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0]
[4,1,1,2,1] => [4,1,1,2,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0]
[4,1,2,1,1] => [4,1,2,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0]
[4,2,1,1,1] => [4,2,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0]
[1,1,1,2,5] => [1,1,1,2,5] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,1,5,2] => [1,1,1,5,2] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,2,1,5] => [1,1,2,1,5] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,2,5,1] => [1,1,2,5,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,5,1,2] => [1,1,5,1,2] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,5,2,1] => [1,1,5,2,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0]
[1,2,1,1,5] => [1,2,1,1,5] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0]
[1,2,1,5,1] => [1,2,1,5,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0]
[1,2,5,1,1] => [1,2,5,1,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0]
[1,5,1,1,2] => [1,5,1,1,2] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0]
[1,5,1,2,1] => [1,5,1,2,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0]
[1,5,2,1,1] => [1,5,2,1,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0]
[2,1,1,1,5] => [2,1,1,1,5] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0]
[2,1,1,5,1] => [2,1,1,5,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0]
[2,1,5,1,1] => [2,1,5,1,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0]
[2,5,1,1,1] => [2,5,1,1,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0]
[5,1,1,1,2] => [5,1,1,1,2] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0]
[5,1,1,2,1] => [5,1,1,2,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0]
[5,1,2,1,1] => [5,1,2,1,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0]
[5,2,1,1,1] => [5,2,1,1,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,1,3,3] => [1,1,1,3,3] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0]
[1,1,3,1,3] => [1,1,3,1,3] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0]
[1,1,3,3,1] => [1,1,3,3,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0]
[1,3,1,1,3] => [1,3,1,1,3] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0]
[1,3,1,3,1] => [1,3,1,3,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0]
[1,3,3,1,1] => [1,3,3,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0]
[3,1,1,1,3] => [3,1,1,1,3] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0]
[3,1,1,3,1] => [3,1,1,3,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0]
[3,1,3,1,1] => [3,1,3,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0]
[3,3,1,1,1] => [3,3,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0]
[1,1,1,3,4] => [1,1,1,3,4] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0]
[1,1,1,4,3] => [1,1,1,4,3] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0]
[1,1,3,1,4] => [1,1,3,1,4] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0]
[1,1,3,4,1] => [1,1,3,4,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0]
[1,1,4,1,3] => [1,1,4,1,3] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0]
[1,1,4,3,1] => [1,1,4,3,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0]
[1,3,1,1,4] => [1,3,1,1,4] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0]
[1,3,1,4,1] => [1,3,1,4,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0]
[1,3,4,1,1] => [1,3,4,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0]
[1,4,1,1,3] => [1,4,1,1,3] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0]
[1,4,1,3,1] => [1,4,1,3,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0]
[1,4,3,1,1] => [1,4,3,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0]
[3,1,1,1,4] => [3,1,1,1,4] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0]
[3,1,1,4,1] => [3,1,1,4,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0]
[3,1,4,1,1] => [3,1,4,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0]
[3,4,1,1,1] => [3,4,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0]
[4,1,1,1,3] => [4,1,1,1,3] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0]
[4,1,1,3,1] => [4,1,1,3,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0]
[4,1,3,1,1] => [4,1,3,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0]
[4,3,1,1,1] => [4,3,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0]
[1,3,1,5,1] => [1,3,1,5,1] => [5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0]
[1,5,1,3,1] => [1,5,1,3,1] => [5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0]
[1,4,1,4,1] => [1,4,1,4,1] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,4,1,5] => [1,1,4,1,5] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,4,5,1] => [1,1,4,5,1] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0]
[1,5,4,1,1] => [1,5,4,1,1] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0]
[5,1,4,1,1] => [5,1,4,1,1] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,2,2,2] => [1,1,2,2,2] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0]
[1,2,1,2,2] => [1,2,1,2,2] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0]
[1,2,2,1,2] => [1,2,2,1,2] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0]
[1,2,2,2,1] => [1,2,2,2,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0]
[2,1,1,2,2] => [2,1,1,2,2] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0]
[2,1,2,1,2] => [2,1,2,1,2] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0]
[2,1,2,2,1] => [2,1,2,2,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0]
[2,2,1,1,2] => [2,2,1,1,2] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0]
[2,2,1,2,1] => [2,2,1,2,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0]
[2,2,2,1,1] => [2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0]
[1,1,2,2,3] => [1,1,2,2,3] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0]
[1,1,2,3,2] => [1,1,2,3,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0]
[1,1,3,2,2] => [1,1,3,2,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0]
[1,2,1,2,3] => [1,2,1,2,3] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0]
[1,2,1,3,2] => [1,2,1,3,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0]
[1,2,2,1,3] => [1,2,2,1,3] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0]
[1,2,2,3,1] => [1,2,2,3,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0]
[1,2,3,1,2] => [1,2,3,1,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0]
[1,2,3,2,1] => [1,2,3,2,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0]
[1,3,1,2,2] => [1,3,1,2,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0]
[1,3,2,1,2] => [1,3,2,1,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0]
[1,3,2,2,1] => [1,3,2,2,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0]
[2,1,1,2,3] => [2,1,1,2,3] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0]
[2,1,1,3,2] => [2,1,1,3,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0]
[2,1,2,1,3] => [2,1,2,1,3] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0]
[2,1,2,3,1] => [2,1,2,3,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0]
[2,1,3,1,2] => [2,1,3,1,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0]
[2,1,3,2,1] => [2,1,3,2,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0]
[2,2,1,1,3] => [2,2,1,1,3] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0]
[2,2,1,3,1] => [2,2,1,3,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0]
[2,2,3,1,1] => [2,2,3,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0]
[2,3,1,1,2] => [2,3,1,1,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0]
[2,3,1,2,1] => [2,3,1,2,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0]
[2,3,2,1,1] => [2,3,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0]
[3,1,1,2,2] => [3,1,1,2,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0]
[3,1,2,1,2] => [3,1,2,1,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0]
[3,1,2,2,1] => [3,1,2,2,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0]
[3,2,1,1,2] => [3,2,1,1,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0]
[3,2,1,2,1] => [3,2,1,2,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0]
[3,2,2,1,1] => [3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0]
[1,1,2,2,4] => [1,1,2,2,4] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0]
[1,1,2,4,2] => [1,1,2,4,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0]
[1,1,4,2,2] => [1,1,4,2,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0]
[1,2,1,2,4] => [1,2,1,2,4] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0]
[1,2,1,4,2] => [1,2,1,4,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0]
[1,2,2,1,4] => [1,2,2,1,4] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0]
[1,2,2,4,1] => [1,2,2,4,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0]
[1,2,4,1,2] => [1,2,4,1,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0]
[1,2,4,2,1] => [1,2,4,2,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0]
[1,4,1,2,2] => [1,4,1,2,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0]
[1,4,2,1,2] => [1,4,2,1,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0]
[1,4,2,2,1] => [1,4,2,2,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0]
[2,1,1,2,4] => [2,1,1,2,4] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0]
[2,1,1,4,2] => [2,1,1,4,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0]
[2,1,2,1,4] => [2,1,2,1,4] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0]
[2,1,2,4,1] => [2,1,2,4,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0]
[2,1,4,1,2] => [2,1,4,1,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0]
[2,1,4,2,1] => [2,1,4,2,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0]
[2,2,1,1,4] => [2,2,1,1,4] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0]
[2,2,1,4,1] => [2,2,1,4,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0]
[2,2,4,1,1] => [2,2,4,1,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0]
[2,4,1,1,2] => [2,4,1,1,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0]
[2,4,1,2,1] => [2,4,1,2,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0]
[2,4,2,1,1] => [2,4,2,1,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0]
[4,1,1,2,2] => [4,1,1,2,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0]
[4,1,2,1,2] => [4,1,2,1,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0]
[4,1,2,2,1] => [4,1,2,2,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0]
[4,2,1,1,2] => [4,2,1,1,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0]
[4,2,1,2,1] => [4,2,1,2,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0]
[4,2,2,1,1] => [4,2,2,1,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0]
[1,2,5,2,1] => [1,2,5,2,1] => [5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0]
[1,5,2,1,2] => [1,5,2,1,2] => [5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0]
[2,1,2,5,1] => [2,1,2,5,1] => [5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0]
[1,1,2,3,3] => [1,1,2,3,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0]
[1,1,3,2,3] => [1,1,3,2,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0]
[1,1,3,3,2] => [1,1,3,3,2] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0]
[1,2,1,3,3] => [1,2,1,3,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0]
[1,2,3,1,3] => [1,2,3,1,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0]
[1,2,3,3,1] => [1,2,3,3,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0]
[1,3,1,2,3] => [1,3,1,2,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0]
[1,3,1,3,2] => [1,3,1,3,2] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0]
[1,3,2,1,3] => [1,3,2,1,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0]
[1,3,2,3,1] => [1,3,2,3,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0]
[1,3,3,1,2] => [1,3,3,1,2] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0]
[1,3,3,2,1] => [1,3,3,2,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0]
[2,1,1,3,3] => [2,1,1,3,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0]
[2,1,3,1,3] => [2,1,3,1,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0]
[2,1,3,3,1] => [2,1,3,3,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0]
[2,3,1,1,3] => [2,3,1,1,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0]
[2,3,1,3,1] => [2,3,1,3,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0]
[2,3,3,1,1] => [2,3,3,1,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0]
[3,1,1,2,3] => [3,1,1,2,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0]
[3,1,1,3,2] => [3,1,1,3,2] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0]
[3,1,2,1,3] => [3,1,2,1,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0]
[3,1,2,3,1] => [3,1,2,3,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0]
[3,1,3,1,2] => [3,1,3,1,2] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0]
[3,1,3,2,1] => [3,1,3,2,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0]
[3,2,1,1,3] => [3,2,1,1,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0]
[3,2,1,3,1] => [3,2,1,3,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0]
[3,2,3,1,1] => [3,2,3,1,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0]
[3,3,1,1,2] => [3,3,1,1,2] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0]
[3,3,1,2,1] => [3,3,1,2,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0]
[3,3,2,1,1] => [3,3,2,1,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0]
[1,2,3,4,1] => [1,2,3,4,1] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0]
[1,4,3,2,1] => [1,4,3,2,1] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0]
[1,1,2,3,5] => [1,1,2,3,5] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0]
[1,1,2,5,3] => [1,1,2,5,3] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0]
[1,3,2,1,5] => [1,3,2,1,5] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0]
[1,3,2,5,1] => [1,3,2,5,1] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0]
[1,3,5,2,1] => [1,3,5,2,1] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0]
[1,5,2,1,3] => [1,5,2,1,3] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0]
[1,5,2,3,1] => [1,5,2,3,1] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0]
[1,5,3,2,1] => [1,5,3,2,1] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0]
[3,1,2,1,5] => [3,1,2,1,5] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0]
[3,1,2,5,1] => [3,1,2,5,1] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0]
[3,5,2,1,1] => [3,5,2,1,1] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0]
[5,1,2,1,3] => [5,1,2,1,3] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0]
[5,1,2,3,1] => [5,1,2,3,1] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0]
[5,3,2,1,1] => [5,3,2,1,1] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0]
[1,2,4,4,1] => [1,2,4,4,1] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0]
[1,4,2,4,1] => [1,4,2,4,1] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0]
[1,4,4,2,1] => [1,4,4,2,1] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0]
[1,2,5,4,1] => [1,2,5,4,1] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0]
[1,4,5,2,1] => [1,4,5,2,1] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,4,3,3] => [1,1,4,3,3] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0]
[1,3,3,4,1] => [1,3,3,4,1] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0]
[1,3,4,1,3] => [1,3,4,1,3] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0]
[1,3,4,3,1] => [1,3,4,3,1] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0]
[1,4,3,3,1] => [1,4,3,3,1] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0]
[3,1,4,1,3] => [3,1,4,1,3] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0]
[3,1,4,3,1] => [3,1,4,3,1] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0]
[3,3,4,1,1] => [3,3,4,1,1] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0]
[1,4,3,4,1] => [1,4,3,4,1] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0]
[1,2,2,2,2] => [1,2,2,2,2] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0]
[2,1,2,2,2] => [2,1,2,2,2] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0]
[2,2,1,2,2] => [2,2,1,2,2] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0]
[2,2,2,1,2] => [2,2,2,1,2] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0]
[2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0]
[1,2,2,2,3] => [1,2,2,2,3] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0]
[1,2,2,3,2] => [1,2,2,3,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0]
[1,2,3,2,2] => [1,2,3,2,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0]
[1,3,2,2,2] => [1,3,2,2,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0]
[2,1,2,2,3] => [2,1,2,2,3] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0]
[2,1,2,3,2] => [2,1,2,3,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0]
[2,1,3,2,2] => [2,1,3,2,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0]
[2,2,1,2,3] => [2,2,1,2,3] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0]
[2,2,1,3,2] => [2,2,1,3,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0]
[2,2,2,1,3] => [2,2,2,1,3] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0]
[2,2,2,3,1] => [2,2,2,3,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0]
[2,2,3,1,2] => [2,2,3,1,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0]
[2,2,3,2,1] => [2,2,3,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0]
[2,3,1,2,2] => [2,3,1,2,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0]
[2,3,2,1,2] => [2,3,2,1,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0]
[2,3,2,2,1] => [2,3,2,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0]
[3,1,2,2,2] => [3,1,2,2,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0]
[3,2,1,2,2] => [3,2,1,2,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0]
[3,2,2,1,2] => [3,2,2,1,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0]
[3,2,2,2,1] => [3,2,2,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0]
[1,2,2,2,5] => [1,2,2,2,5] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0]
[1,2,5,2,2] => [1,2,5,2,2] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0]
[1,5,2,2,2] => [1,5,2,2,2] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0]
[2,2,5,2,1] => [2,2,5,2,1] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0]
[2,5,2,2,1] => [2,5,2,2,1] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0]
[5,2,2,2,1] => [5,2,2,2,1] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0]
[1,2,2,4,3] => [1,2,2,4,3] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0]
[1,2,3,4,2] => [1,2,3,4,2] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0]
[1,2,4,2,3] => [1,2,4,2,3] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0]
[1,2,4,3,2] => [1,2,4,3,2] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0]
[1,3,2,4,2] => [1,3,2,4,2] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0]
[1,3,4,2,2] => [1,3,4,2,2] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0]
[1,4,2,2,3] => [1,4,2,2,3] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0]
[1,4,2,3,2] => [1,4,2,3,2] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0]
[1,4,3,2,2] => [1,4,3,2,2] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0]
[2,2,3,4,1] => [2,2,3,4,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0]
[2,2,4,3,1] => [2,2,4,3,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0]
[2,3,2,4,1] => [2,3,2,4,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0]
[2,3,4,2,1] => [2,3,4,2,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0]
[2,4,2,3,1] => [2,4,2,3,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0]
[2,4,3,2,1] => [2,4,3,2,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0]
[3,2,2,4,1] => [3,2,2,4,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0]
[3,2,4,2,1] => [3,2,4,2,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0]
[3,4,2,2,1] => [3,4,2,2,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0]
[4,2,2,3,1] => [4,2,2,3,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0]
[4,2,3,2,1] => [4,2,3,2,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0]
[4,3,2,2,1] => [4,3,2,2,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0]
[1,2,3,3,3] => [1,2,3,3,3] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0]
[1,3,2,3,3] => [1,3,2,3,3] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0]
[1,3,3,2,3] => [1,3,3,2,3] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0]
[1,3,3,3,2] => [1,3,3,3,2] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0]
[2,3,3,3,1] => [2,3,3,3,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0]
[3,1,2,3,3] => [3,1,2,3,3] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0]
[3,2,3,3,1] => [3,2,3,3,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0]
[3,3,2,1,3] => [3,3,2,1,3] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0]
[3,3,2,3,1] => [3,3,2,3,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0]
[3,3,3,2,1] => [3,3,3,2,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,2] => [1,1,1,1,1,2] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,1,1,1,2,1] => [1,1,1,1,2,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,1,1,2,1,1] => [1,1,1,2,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,1,2,1,1,1] => [1,1,2,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,2,1,1,1,1] => [1,2,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[2,1,1,1,1,1] => [2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,1,1,1,1,3] => [1,1,1,1,1,3] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,1,1,1,3,1] => [1,1,1,1,3,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,1,1,3,1,1] => [1,1,1,3,1,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,1,3,1,1,1] => [1,1,3,1,1,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,3,1,1,1,1] => [1,3,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[3,1,1,1,1,1] => [3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,1,1,1,1,4] => [1,1,1,1,1,4] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,1,1,1,4,1] => [1,1,1,1,4,1] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,1,1,4,1,1] => [1,1,1,4,1,1] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,1,4,1,1,1] => [1,1,4,1,1,1] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,4,1,1,1,1] => [1,4,1,1,1,1] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[4,1,1,1,1,1] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,1,1,1,1,5] => [1,1,1,1,1,5] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,1,1,1,5,1] => [1,1,1,1,5,1] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,1,1,5,1,1] => [1,1,1,5,1,1] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,1,5,1,1,1] => [1,1,5,1,1,1] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,5,1,1,1,1] => [1,5,1,1,1,1] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[5,1,1,1,1,1] => [5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,1,1,1,1,6] => [1,1,1,1,1,6] => [6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[6,1,1,1,1,1] => [6,1,1,1,1,1] => [6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,1,2,2] => [1,1,1,1,2,2] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,1,1,2,1,2] => [1,1,1,2,1,2] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,1,1,2,2,1] => [1,1,1,2,2,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,1,2,1,1,2] => [1,1,2,1,1,2] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,1,2,1,2,1] => [1,1,2,1,2,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,1,2,2,1,1] => [1,1,2,2,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,2,1,1,1,2] => [1,2,1,1,1,2] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,2,1,1,2,1] => [1,2,1,1,2,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,2,1,2,1,1] => [1,2,1,2,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,2,2,1,1,1] => [1,2,2,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[2,1,1,1,1,2] => [2,1,1,1,1,2] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[2,1,1,1,2,1] => [2,1,1,1,2,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[2,1,1,2,1,1] => [2,1,1,2,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[2,1,2,1,1,1] => [2,1,2,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,1,1,1,2,3] => [1,1,1,1,2,3] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,1,1,1,3,2] => [1,1,1,1,3,2] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,1,1,2,1,3] => [1,1,1,2,1,3] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,1,1,2,3,1] => [1,1,1,2,3,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,1,1,3,1,2] => [1,1,1,3,1,2] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,1,1,3,2,1] => [1,1,1,3,2,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,1,2,1,1,3] => [1,1,2,1,1,3] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,1,2,1,3,1] => [1,1,2,1,3,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,1,2,3,1,1] => [1,1,2,3,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,1,3,1,1,2] => [1,1,3,1,1,2] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,1,3,1,2,1] => [1,1,3,1,2,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,1,3,2,1,1] => [1,1,3,2,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,2,1,1,1,3] => [1,2,1,1,1,3] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,2,1,1,3,1] => [1,2,1,1,3,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,2,1,3,1,1] => [1,2,1,3,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,2,3,1,1,1] => [1,2,3,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,3,1,1,1,2] => [1,3,1,1,1,2] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,3,1,1,2,1] => [1,3,1,1,2,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,3,1,2,1,1] => [1,3,1,2,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,3,2,1,1,1] => [1,3,2,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[2,1,1,1,1,3] => [2,1,1,1,1,3] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[2,1,1,1,3,1] => [2,1,1,1,3,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[2,1,1,3,1,1] => [2,1,1,3,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[2,1,3,1,1,1] => [2,1,3,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[2,3,1,1,1,1] => [2,3,1,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[3,1,1,1,1,2] => [3,1,1,1,1,2] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[3,1,1,1,2,1] => [3,1,1,1,2,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[3,1,1,2,1,1] => [3,1,1,2,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[3,1,2,1,1,1] => [3,1,2,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[3,2,1,1,1,1] => [3,2,1,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,1,1,1,2,4] => [1,1,1,1,2,4] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[1,1,1,1,4,2] => [1,1,1,1,4,2] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[1,1,1,2,1,4] => [1,1,1,2,1,4] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[1,1,1,2,4,1] => [1,1,1,2,4,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[1,1,1,4,1,2] => [1,1,1,4,1,2] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[1,1,1,4,2,1] => [1,1,1,4,2,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[1,1,2,1,1,4] => [1,1,2,1,1,4] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[1,1,2,1,4,1] => [1,1,2,1,4,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[1,1,2,4,1,1] => [1,1,2,4,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[1,1,4,1,1,2] => [1,1,4,1,1,2] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[1,1,4,1,2,1] => [1,1,4,1,2,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[1,1,4,2,1,1] => [1,1,4,2,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[1,2,1,1,1,4] => [1,2,1,1,1,4] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[1,2,1,1,4,1] => [1,2,1,1,4,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[1,2,1,4,1,1] => [1,2,1,4,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[1,2,4,1,1,1] => [1,2,4,1,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[1,4,1,1,1,2] => [1,4,1,1,1,2] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[1,4,1,1,2,1] => [1,4,1,1,2,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[1,4,1,2,1,1] => [1,4,1,2,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[1,4,2,1,1,1] => [1,4,2,1,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[2,1,1,1,1,4] => [2,1,1,1,1,4] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[2,1,1,1,4,1] => [2,1,1,1,4,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[2,1,1,4,1,1] => [2,1,1,4,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[2,1,4,1,1,1] => [2,1,4,1,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[2,4,1,1,1,1] => [2,4,1,1,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[4,1,1,1,1,2] => [4,1,1,1,1,2] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[4,1,1,1,2,1] => [4,1,1,1,2,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[4,1,1,2,1,1] => [4,1,1,2,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[4,1,2,1,1,1] => [4,1,2,1,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[4,2,1,1,1,1] => [4,2,1,1,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[1,1,1,1,2,5] => [1,1,1,1,2,5] => [5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[1,1,1,1,5,2] => [1,1,1,1,5,2] => [5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[1,1,1,2,1,5] => [1,1,1,2,1,5] => [5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[1,1,2,1,1,5] => [1,1,2,1,1,5] => [5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[1,1,2,5,1,1] => [1,1,2,5,1,1] => [5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[1,1,5,2,1,1] => [1,1,5,2,1,1] => [5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[1,2,1,1,1,5] => [1,2,1,1,1,5] => [5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[1,5,1,1,1,2] => [1,5,1,1,1,2] => [5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[2,1,1,1,5,1] => [2,1,1,1,5,1] => [5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[2,5,1,1,1,1] => [2,5,1,1,1,1] => [5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[5,1,1,1,1,2] => [5,1,1,1,1,2] => [5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[5,1,1,1,2,1] => [5,1,1,1,2,1] => [5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[5,1,1,2,1,1] => [5,1,1,2,1,1] => [5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[5,1,2,1,1,1] => [5,1,2,1,1,1] => [5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[5,2,1,1,1,1] => [5,2,1,1,1,1] => [5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[1,6,1,1,1,2] => [1,6,1,1,1,2] => [6,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[2,1,1,1,6,1] => [2,1,1,1,6,1] => [6,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[1,1,1,1,3,3] => [1,1,1,1,3,3] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,1,1,3,1,3] => [1,1,1,3,1,3] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,1,1,3,3,1] => [1,1,1,3,3,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,1,3,1,1,3] => [1,1,3,1,1,3] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,1,3,1,3,1] => [1,1,3,1,3,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,1,3,3,1,1] => [1,1,3,3,1,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,3,1,1,1,3] => [1,3,1,1,1,3] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,3,1,1,3,1] => [1,3,1,1,3,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,3,1,3,1,1] => [1,3,1,3,1,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,3,3,1,1,1] => [1,3,3,1,1,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[3,1,1,1,1,3] => [3,1,1,1,1,3] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[3,1,1,1,3,1] => [3,1,1,1,3,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[3,1,1,3,1,1] => [3,1,1,3,1,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[3,1,3,1,1,1] => [3,1,3,1,1,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,1,1,1,3,4] => [1,1,1,1,3,4] => [4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[1,1,1,1,4,3] => [1,1,1,1,4,3] => [4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[1,1,1,3,1,4] => [1,1,1,3,1,4] => [4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[1,1,1,4,1,3] => [1,1,1,4,1,3] => [4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[1,1,3,1,1,4] => [1,1,3,1,1,4] => [4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[3,1,4,1,1,1] => [3,1,4,1,1,1] => [4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[3,4,1,1,1,1] => [3,4,1,1,1,1] => [4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[4,1,1,3,1,1] => [4,1,1,3,1,1] => [4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[4,1,3,1,1,1] => [4,1,3,1,1,1] => [4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[4,3,1,1,1,1] => [4,3,1,1,1,1] => [4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[1,1,1,1,4,4] => [1,1,1,1,4,4] => [4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[1,1,4,1,1,4] => [1,1,4,1,1,4] => [4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[1,1,4,4,1,1] => [1,1,4,4,1,1] => [4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[4,1,1,1,1,4] => [4,1,1,1,1,4] => [4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[4,1,1,4,1,1] => [4,1,1,4,1,1] => [4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[4,4,1,1,1,1] => [4,4,1,1,1,1] => [4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[1,1,1,2,2,2] => [1,1,1,2,2,2] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,1,2,1,2,2] => [1,1,2,1,2,2] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,1,2,2,1,2] => [1,1,2,2,1,2] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,1,2,2,2,1] => [1,1,2,2,2,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,2,1,1,2,2] => [1,2,1,1,2,2] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,2,1,2,1,2] => [1,2,1,2,1,2] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,2,1,2,2,1] => [1,2,1,2,2,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,2,2,1,1,2] => [1,2,2,1,1,2] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,2,2,1,2,1] => [1,2,2,1,2,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,2,2,2,1,1] => [1,2,2,2,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[2,1,1,1,2,2] => [2,1,1,1,2,2] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[2,1,1,2,1,2] => [2,1,1,2,1,2] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[2,1,1,2,2,1] => [2,1,1,2,2,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[2,1,2,1,1,2] => [2,1,2,1,1,2] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[2,1,2,1,2,1] => [2,1,2,1,2,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[2,1,2,2,1,1] => [2,1,2,2,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[2,2,1,1,1,2] => [2,2,1,1,1,2] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[2,2,1,1,2,1] => [2,2,1,1,2,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[2,2,1,2,1,1] => [2,2,1,2,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,1,1,2,2,3] => [1,1,1,2,2,3] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,1,1,2,3,2] => [1,1,1,2,3,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,1,1,3,2,2] => [1,1,1,3,2,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,1,2,1,2,3] => [1,1,2,1,2,3] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,1,2,1,3,2] => [1,1,2,1,3,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,1,2,2,1,3] => [1,1,2,2,1,3] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,1,2,2,3,1] => [1,1,2,2,3,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,1,2,3,1,2] => [1,1,2,3,1,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,1,2,3,2,1] => [1,1,2,3,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,1,3,1,2,2] => [1,1,3,1,2,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,1,3,2,1,2] => [1,1,3,2,1,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,1,3,2,2,1] => [1,1,3,2,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,2,1,1,2,3] => [1,2,1,1,2,3] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,2,1,1,3,2] => [1,2,1,1,3,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,2,1,2,1,3] => [1,2,1,2,1,3] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,2,1,2,3,1] => [1,2,1,2,3,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,2,1,3,1,2] => [1,2,1,3,1,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,2,1,3,2,1] => [1,2,1,3,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,2,2,1,1,3] => [1,2,2,1,1,3] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,2,2,1,3,1] => [1,2,2,1,3,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,2,2,3,1,1] => [1,2,2,3,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,2,3,1,1,2] => [1,2,3,1,1,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,2,3,1,2,1] => [1,2,3,1,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,2,3,2,1,1] => [1,2,3,2,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,3,1,1,2,2] => [1,3,1,1,2,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,3,1,2,1,2] => [1,3,1,2,1,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,3,1,2,2,1] => [1,3,1,2,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,3,2,1,1,2] => [1,3,2,1,1,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,3,2,1,2,1] => [1,3,2,1,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,3,2,2,1,1] => [1,3,2,2,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[2,1,1,1,2,3] => [2,1,1,1,2,3] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[2,1,1,1,3,2] => [2,1,1,1,3,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[2,1,1,2,1,3] => [2,1,1,2,1,3] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[2,1,1,2,3,1] => [2,1,1,2,3,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[2,1,1,3,1,2] => [2,1,1,3,1,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[2,1,1,3,2,1] => [2,1,1,3,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[2,1,2,1,1,3] => [2,1,2,1,1,3] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[2,1,2,1,3,1] => [2,1,2,1,3,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[2,1,2,3,1,1] => [2,1,2,3,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[2,1,3,1,1,2] => [2,1,3,1,1,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[2,1,3,1,2,1] => [2,1,3,1,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[2,1,3,2,1,1] => [2,1,3,2,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[2,2,1,1,1,3] => [2,2,1,1,1,3] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[2,2,1,1,3,1] => [2,2,1,1,3,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[2,2,1,3,1,1] => [2,2,1,3,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[2,2,3,1,1,1] => [2,2,3,1,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[2,3,1,1,1,2] => [2,3,1,1,1,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[2,3,1,1,2,1] => [2,3,1,1,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[2,3,1,2,1,1] => [2,3,1,2,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[2,3,2,1,1,1] => [2,3,2,1,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[3,1,1,1,2,2] => [3,1,1,1,2,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[3,1,1,2,1,2] => [3,1,1,2,1,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[3,1,1,2,2,1] => [3,1,1,2,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[3,1,2,1,1,2] => [3,1,2,1,1,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[3,1,2,1,2,1] => [3,1,2,1,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[3,1,2,2,1,1] => [3,1,2,2,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[3,2,1,1,1,2] => [3,2,1,1,1,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[3,2,1,1,2,1] => [3,2,1,1,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[3,2,1,2,1,1] => [3,2,1,2,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[3,2,2,1,1,1] => [3,2,2,1,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,1,1,2,2,4] => [1,1,1,2,2,4] => [4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[1,1,1,2,4,2] => [1,1,1,2,4,2] => [4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[1,1,1,4,2,2] => [1,1,1,4,2,2] => [4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[1,1,2,1,2,4] => [1,1,2,1,2,4] => [4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[1,1,2,1,4,2] => [1,1,2,1,4,2] => [4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[1,1,2,2,1,4] => [1,1,2,2,1,4] => [4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[1,1,2,2,4,1] => [1,1,2,2,4,1] => [4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[1,2,1,1,2,4] => [1,2,1,1,2,4] => [4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[1,2,1,1,4,2] => [1,2,1,1,4,2] => [4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[1,2,1,2,1,4] => [1,2,1,2,1,4] => [4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[1,2,2,1,1,4] => [1,2,2,1,1,4] => [4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[1,4,2,1,1,2] => [1,4,2,1,1,2] => [4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[1,4,2,2,1,1] => [1,4,2,2,1,1] => [4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[2,1,1,2,4,1] => [2,1,1,2,4,1] => [4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[2,2,4,1,1,1] => [2,2,4,1,1,1] => [4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[2,4,1,1,2,1] => [2,4,1,1,2,1] => [4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[2,4,1,2,1,1] => [2,4,1,2,1,1] => [4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[2,4,2,1,1,1] => [2,4,2,1,1,1] => [4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[4,1,1,2,2,1] => [4,1,1,2,2,1] => [4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[4,1,2,1,2,1] => [4,1,2,1,2,1] => [4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[4,1,2,2,1,1] => [4,1,2,2,1,1] => [4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[4,2,1,1,2,1] => [4,2,1,1,2,1] => [4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[4,2,1,2,1,1] => [4,2,1,2,1,1] => [4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[4,2,2,1,1,1] => [4,2,2,1,1,1] => [4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[1,1,1,2,3,3] => [1,1,1,2,3,3] => [3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[1,1,1,3,2,3] => [1,1,1,3,2,3] => [3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[1,1,1,3,3,2] => [1,1,1,3,3,2] => [3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[1,1,2,1,3,3] => [1,1,2,1,3,3] => [3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[1,1,2,3,1,3] => [1,1,2,3,1,3] => [3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[1,1,3,1,2,3] => [1,1,3,1,2,3] => [3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[1,1,3,1,3,2] => [1,1,3,1,3,2] => [3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[1,1,3,2,1,3] => [1,1,3,2,1,3] => [3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[1,2,1,1,3,3] => [1,2,1,1,3,3] => [3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[1,2,1,3,1,3] => [1,2,1,3,1,3] => [3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[2,3,1,3,1,1] => [2,3,1,3,1,1] => [3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[2,3,3,1,1,1] => [2,3,3,1,1,1] => [3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[3,1,2,3,1,1] => [3,1,2,3,1,1] => [3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[3,1,3,1,2,1] => [3,1,3,1,2,1] => [3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[3,1,3,2,1,1] => [3,1,3,2,1,1] => [3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[3,2,1,3,1,1] => [3,2,1,3,1,1] => [3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[3,2,3,1,1,1] => [3,2,3,1,1,1] => [3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[3,3,1,1,2,1] => [3,3,1,1,2,1] => [3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[3,3,1,2,1,1] => [3,3,1,2,1,1] => [3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[3,3,2,1,1,1] => [3,3,2,1,1,1] => [3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[1,1,2,1,3,4] => [1,1,2,1,3,4] => [4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[1,1,3,1,2,4] => [1,1,3,1,2,4] => [4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[1,1,4,2,1,3] => [1,1,4,2,1,3] => [4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[1,1,4,3,1,2] => [1,1,4,3,1,2] => [4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[2,1,1,1,3,4] => [2,1,1,1,3,4] => [4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[2,1,3,1,1,4] => [2,1,3,1,1,4] => [4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[2,1,3,4,1,1] => [2,1,3,4,1,1] => [4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[3,1,1,1,2,4] => [3,1,1,1,2,4] => [4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[3,1,2,1,1,4] => [3,1,2,1,1,4] => [4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[3,1,2,4,1,1] => [3,1,2,4,1,1] => [4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[4,1,1,2,1,3] => [4,1,1,2,1,3] => [4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[4,1,1,3,1,2] => [4,1,1,3,1,2] => [4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[4,2,1,1,1,3] => [4,2,1,1,1,3] => [4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[4,2,1,3,1,1] => [4,2,1,3,1,1] => [4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[4,3,1,1,1,2] => [4,3,1,1,1,2] => [4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[4,3,1,2,1,1] => [4,3,1,2,1,1] => [4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[1,1,2,2,2,2] => [1,1,2,2,2,2] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,2,1,2,2,2] => [1,2,1,2,2,2] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,2,2,1,2,2] => [1,2,2,1,2,2] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,2,2,2,1,2] => [1,2,2,2,1,2] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,2,2,2,2,1] => [1,2,2,2,2,1] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[2,1,1,2,2,2] => [2,1,1,2,2,2] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[2,1,2,1,2,2] => [2,1,2,1,2,2] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[2,1,2,2,1,2] => [2,1,2,2,1,2] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[2,1,2,2,2,1] => [2,1,2,2,2,1] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[2,2,1,1,2,2] => [2,2,1,1,2,2] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[2,2,1,2,1,2] => [2,2,1,2,1,2] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[2,2,1,2,2,1] => [2,2,1,2,2,1] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[2,2,2,1,1,2] => [2,2,2,1,1,2] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[2,2,2,1,2,1] => [2,2,2,1,2,1] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,1,2,2,2,3] => [1,1,2,2,2,3] => [3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[1,1,2,2,3,2] => [1,1,2,2,3,2] => [3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[1,1,2,3,2,2] => [1,1,2,3,2,2] => [3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[1,1,3,2,2,2] => [1,1,3,2,2,2] => [3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[1,2,1,2,2,3] => [1,2,1,2,2,3] => [3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[1,2,1,2,3,2] => [1,2,1,2,3,2] => [3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[1,2,1,3,2,2] => [1,2,1,3,2,2] => [3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[1,2,2,1,2,3] => [1,2,2,1,2,3] => [3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[1,2,2,1,3,2] => [1,2,2,1,3,2] => [3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[1,2,2,2,1,3] => [1,2,2,2,1,3] => [3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[2,2,2,3,1,1] => [2,2,2,3,1,1] => [3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[2,2,3,1,2,1] => [2,2,3,1,2,1] => [3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[2,2,3,2,1,1] => [2,2,3,2,1,1] => [3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[2,3,1,2,2,1] => [2,3,1,2,2,1] => [3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[2,3,2,1,2,1] => [2,3,2,1,2,1] => [3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[2,3,2,2,1,1] => [2,3,2,2,1,1] => [3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[3,1,2,2,2,1] => [3,1,2,2,2,1] => [3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[3,2,1,2,2,1] => [3,2,1,2,2,1] => [3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[3,2,2,1,2,1] => [3,2,2,1,2,1] => [3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[3,2,2,2,1,1] => [3,2,2,2,1,1] => [3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[1,1,2,2,2,4] => [1,1,2,2,2,4] => [4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[1,2,2,4,2,1] => [1,2,2,4,2,1] => [4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[1,2,4,2,2,1] => [1,2,4,2,2,1] => [4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[1,4,2,2,2,1] => [1,4,2,2,2,1] => [4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[2,1,2,1,2,4] => [2,1,2,1,2,4] => [4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[4,2,1,2,1,2] => [4,2,1,2,1,2] => [4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[1,1,2,2,3,3] => [1,1,2,2,3,3] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[1,1,2,3,2,3] => [1,1,2,3,2,3] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[1,1,3,2,2,3] => [1,1,3,2,2,3] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[1,1,3,3,2,2] => [1,1,3,3,2,2] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[1,2,2,3,3,1] => [1,2,2,3,3,1] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[1,2,3,2,3,1] => [1,2,3,2,3,1] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[1,2,3,3,2,1] => [1,2,3,3,2,1] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[1,3,2,2,3,1] => [1,3,2,2,3,1] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[1,3,2,3,2,1] => [1,3,2,3,2,1] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[1,3,3,2,2,1] => [1,3,3,2,2,1] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[2,1,1,2,3,3] => [2,1,1,2,3,3] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[2,1,3,2,1,3] => [2,1,3,2,1,3] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[2,1,3,3,1,2] => [2,1,3,3,1,2] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[2,2,1,1,3,3] => [2,2,1,1,3,3] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[2,2,3,1,1,3] => [2,2,3,1,1,3] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[2,2,3,3,1,1] => [2,2,3,3,1,1] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[3,1,1,2,2,3] => [3,1,1,2,2,3] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[3,1,1,3,2,2] => [3,1,1,3,2,2] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[3,1,2,2,1,3] => [3,1,2,2,1,3] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[3,1,2,3,1,2] => [3,1,2,3,1,2] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[3,2,1,1,2,3] => [3,2,1,1,2,3] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[3,2,2,1,1,3] => [3,2,2,1,1,3] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[3,2,2,3,1,1] => [3,2,2,3,1,1] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[3,3,1,1,2,2] => [3,3,1,1,2,2] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[3,3,2,1,1,2] => [3,3,2,1,1,2] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[3,3,2,2,1,1] => [3,3,2,2,1,1] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[1,2,2,2,2,2] => [1,2,2,2,2,2] => [2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,2,2,2,3] => [1,2,2,2,2,3] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[1,2,2,2,3,2] => [1,2,2,2,3,2] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[1,2,2,3,2,2] => [1,2,2,3,2,2] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[1,2,3,2,2,2] => [1,2,3,2,2,2] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[1,3,2,2,2,2] => [1,3,2,2,2,2] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[2,1,2,2,2,3] => [2,1,2,2,2,3] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[2,1,2,3,2,2] => [2,1,2,3,2,2] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[2,2,2,1,2,3] => [2,2,2,1,2,3] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[2,2,2,2,3,1] => [2,2,2,2,3,1] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[2,2,2,3,2,1] => [2,2,2,3,2,1] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[2,2,3,2,1,2] => [2,2,3,2,1,2] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[2,2,3,2,2,1] => [2,2,3,2,2,1] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[2,3,2,2,2,1] => [2,3,2,2,2,1] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[3,2,1,2,2,2] => [3,2,1,2,2,2] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[3,2,2,2,1,2] => [3,2,2,2,1,2] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[3,2,2,2,2,1] => [3,2,2,2,2,1] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0]
Map
to composition
Description
Return the parking function interpreted as an integer composition.
Map
to partition
Description
Sends a composition to the partition obtained by sorting the entries.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.