Identifier
-
Mp00040:
Integer compositions
—to partition⟶
Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000667: Integer partitions ⟶ ℤ
Values
[1,1,1] => [1,1,1] => [1,1] => [1] => 1
[1,1,1,1] => [1,1,1,1] => [1,1,1] => [1,1] => 1
[1,1,2] => [2,1,1] => [1,1] => [1] => 1
[1,2,1] => [2,1,1] => [1,1] => [1] => 1
[2,1,1] => [2,1,1] => [1,1] => [1] => 1
[1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,1,1,2] => [2,1,1,1] => [1,1,1] => [1,1] => 1
[1,1,2,1] => [2,1,1,1] => [1,1,1] => [1,1] => 1
[1,1,3] => [3,1,1] => [1,1] => [1] => 1
[1,2,1,1] => [2,1,1,1] => [1,1,1] => [1,1] => 1
[1,2,2] => [2,2,1] => [2,1] => [1] => 1
[1,3,1] => [3,1,1] => [1,1] => [1] => 1
[2,1,1,1] => [2,1,1,1] => [1,1,1] => [1,1] => 1
[2,1,2] => [2,2,1] => [2,1] => [1] => 1
[2,2,1] => [2,2,1] => [2,1] => [1] => 1
[3,1,1] => [3,1,1] => [1,1] => [1] => 1
[1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,2] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,1,1,2,1] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,1,1,3] => [3,1,1,1] => [1,1,1] => [1,1] => 1
[1,1,2,1,1] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,1,2,2] => [2,2,1,1] => [2,1,1] => [1,1] => 1
[1,1,3,1] => [3,1,1,1] => [1,1,1] => [1,1] => 1
[1,1,4] => [4,1,1] => [1,1] => [1] => 1
[1,2,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,2,1,2] => [2,2,1,1] => [2,1,1] => [1,1] => 1
[1,2,2,1] => [2,2,1,1] => [2,1,1] => [1,1] => 1
[1,2,3] => [3,2,1] => [2,1] => [1] => 1
[1,3,1,1] => [3,1,1,1] => [1,1,1] => [1,1] => 1
[1,3,2] => [3,2,1] => [2,1] => [1] => 1
[1,4,1] => [4,1,1] => [1,1] => [1] => 1
[2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[2,1,1,2] => [2,2,1,1] => [2,1,1] => [1,1] => 1
[2,1,2,1] => [2,2,1,1] => [2,1,1] => [1,1] => 1
[2,1,3] => [3,2,1] => [2,1] => [1] => 1
[2,2,1,1] => [2,2,1,1] => [2,1,1] => [1,1] => 1
[2,2,2] => [2,2,2] => [2,2] => [2] => 2
[2,3,1] => [3,2,1] => [2,1] => [1] => 1
[3,1,1,1] => [3,1,1,1] => [1,1,1] => [1,1] => 1
[3,1,2] => [3,2,1] => [2,1] => [1] => 1
[3,2,1] => [3,2,1] => [2,1] => [1] => 1
[4,1,1] => [4,1,1] => [1,1] => [1] => 1
[1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,2] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,2,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,3] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,1,1,2,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,2,2] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,1,1,3,1] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,1,1,4] => [4,1,1,1] => [1,1,1] => [1,1] => 1
[1,1,2,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,1,2,1,2] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,1,2,2,1] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,1,2,3] => [3,2,1,1] => [2,1,1] => [1,1] => 1
[1,1,3,1,1] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,1,3,2] => [3,2,1,1] => [2,1,1] => [1,1] => 1
[1,1,4,1] => [4,1,1,1] => [1,1,1] => [1,1] => 1
[1,1,5] => [5,1,1] => [1,1] => [1] => 1
[1,2,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,2,1,1,2] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,2,1,2,1] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,2,1,3] => [3,2,1,1] => [2,1,1] => [1,1] => 1
[1,2,2,1,1] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,2,2,2] => [2,2,2,1] => [2,2,1] => [2,1] => 1
[1,2,3,1] => [3,2,1,1] => [2,1,1] => [1,1] => 1
[1,2,4] => [4,2,1] => [2,1] => [1] => 1
[1,3,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,3,1,2] => [3,2,1,1] => [2,1,1] => [1,1] => 1
[1,3,2,1] => [3,2,1,1] => [2,1,1] => [1,1] => 1
[1,3,3] => [3,3,1] => [3,1] => [1] => 1
[1,4,1,1] => [4,1,1,1] => [1,1,1] => [1,1] => 1
[1,4,2] => [4,2,1] => [2,1] => [1] => 1
[1,5,1] => [5,1,1] => [1,1] => [1] => 1
[2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[2,1,1,1,2] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[2,1,1,2,1] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[2,1,1,3] => [3,2,1,1] => [2,1,1] => [1,1] => 1
[2,1,2,1,1] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[2,1,2,2] => [2,2,2,1] => [2,2,1] => [2,1] => 1
[2,1,3,1] => [3,2,1,1] => [2,1,1] => [1,1] => 1
[2,1,4] => [4,2,1] => [2,1] => [1] => 1
[2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[2,2,1,2] => [2,2,2,1] => [2,2,1] => [2,1] => 1
[2,2,2,1] => [2,2,2,1] => [2,2,1] => [2,1] => 1
[2,2,3] => [3,2,2] => [2,2] => [2] => 2
[2,3,1,1] => [3,2,1,1] => [2,1,1] => [1,1] => 1
[2,3,2] => [3,2,2] => [2,2] => [2] => 2
[2,4,1] => [4,2,1] => [2,1] => [1] => 1
[3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[3,1,1,2] => [3,2,1,1] => [2,1,1] => [1,1] => 1
[3,1,2,1] => [3,2,1,1] => [2,1,1] => [1,1] => 1
[3,1,3] => [3,3,1] => [3,1] => [1] => 1
[3,2,1,1] => [3,2,1,1] => [2,1,1] => [1,1] => 1
[3,2,2] => [3,2,2] => [2,2] => [2] => 2
[3,3,1] => [3,3,1] => [3,1] => [1] => 1
[4,1,1,1] => [4,1,1,1] => [1,1,1] => [1,1] => 1
[4,1,2] => [4,2,1] => [2,1] => [1] => 1
[4,2,1] => [4,2,1] => [2,1] => [1] => 1
[5,1,1] => [5,1,1] => [1,1] => [1] => 1
[1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,1,2] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
>>> Load all 2214 entries. <<<[1,1,1,1,1,2,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,3] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,2,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,2,2] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,3,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,4] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,1,1,2,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,2,1,2] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,2,2,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,2,3] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,1,1,3,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,3,2] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,1,1,4,1] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,1,1,5] => [5,1,1,1] => [1,1,1] => [1,1] => 1
[1,1,2,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,2,1,1,2] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,2,1,2,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,2,1,3] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,1,2,2,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,2,2,2] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,1,2,3,1] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,1,2,4] => [4,2,1,1] => [2,1,1] => [1,1] => 1
[1,1,3,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,1,3,1,2] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,1,3,2,1] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,1,3,3] => [3,3,1,1] => [3,1,1] => [1,1] => 1
[1,1,4,1,1] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,1,4,2] => [4,2,1,1] => [2,1,1] => [1,1] => 1
[1,1,5,1] => [5,1,1,1] => [1,1,1] => [1,1] => 1
[1,1,6] => [6,1,1] => [1,1] => [1] => 1
[1,2,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,2,1,1,1,2] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,2,1,1,2,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,2,1,1,3] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,2,1,2,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,2,1,2,2] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,2,1,3,1] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,2,1,4] => [4,2,1,1] => [2,1,1] => [1,1] => 1
[1,2,2,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,2,2,1,2] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,2,2,2,1] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,2,2,3] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[1,2,3,1,1] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,2,3,2] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[1,2,4,1] => [4,2,1,1] => [2,1,1] => [1,1] => 1
[1,2,5] => [5,2,1] => [2,1] => [1] => 1
[1,3,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,3,1,1,2] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,3,1,2,1] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,3,1,3] => [3,3,1,1] => [3,1,1] => [1,1] => 1
[1,3,2,1,1] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,3,2,2] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[1,3,3,1] => [3,3,1,1] => [3,1,1] => [1,1] => 1
[1,3,4] => [4,3,1] => [3,1] => [1] => 1
[1,4,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,4,1,2] => [4,2,1,1] => [2,1,1] => [1,1] => 1
[1,4,2,1] => [4,2,1,1] => [2,1,1] => [1,1] => 1
[1,4,3] => [4,3,1] => [3,1] => [1] => 1
[1,5,1,1] => [5,1,1,1] => [1,1,1] => [1,1] => 1
[1,5,2] => [5,2,1] => [2,1] => [1] => 1
[1,6,1] => [6,1,1] => [1,1] => [1] => 1
[2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[2,1,1,1,1,2] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[2,1,1,1,2,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[2,1,1,1,3] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[2,1,1,2,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[2,1,1,2,2] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[2,1,1,3,1] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[2,1,1,4] => [4,2,1,1] => [2,1,1] => [1,1] => 1
[2,1,2,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[2,1,2,1,2] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[2,1,2,2,1] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[2,1,2,3] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[2,1,3,1,1] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[2,1,3,2] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[2,1,4,1] => [4,2,1,1] => [2,1,1] => [1,1] => 1
[2,1,5] => [5,2,1] => [2,1] => [1] => 1
[2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[2,2,1,1,2] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[2,2,1,2,1] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[2,2,1,3] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[2,2,2,2] => [2,2,2,2] => [2,2,2] => [2,2] => 2
[2,2,3,1] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[2,2,4] => [4,2,2] => [2,2] => [2] => 2
[2,3,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[2,3,1,2] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[2,3,2,1] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[2,3,3] => [3,3,2] => [3,2] => [2] => 2
[2,4,1,1] => [4,2,1,1] => [2,1,1] => [1,1] => 1
[2,4,2] => [4,2,2] => [2,2] => [2] => 2
[2,5,1] => [5,2,1] => [2,1] => [1] => 1
[3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[3,1,1,1,2] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[3,1,1,2,1] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[3,1,1,3] => [3,3,1,1] => [3,1,1] => [1,1] => 1
[3,1,2,1,1] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[3,1,2,2] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[3,1,3,1] => [3,3,1,1] => [3,1,1] => [1,1] => 1
[3,1,4] => [4,3,1] => [3,1] => [1] => 1
[3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[3,2,1,2] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[3,2,2,1] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[3,2,3] => [3,3,2] => [3,2] => [2] => 2
[3,3,1,1] => [3,3,1,1] => [3,1,1] => [1,1] => 1
[3,3,2] => [3,3,2] => [3,2] => [2] => 2
[3,4,1] => [4,3,1] => [3,1] => [1] => 1
[4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[4,1,1,2] => [4,2,1,1] => [2,1,1] => [1,1] => 1
[4,1,2,1] => [4,2,1,1] => [2,1,1] => [1,1] => 1
[4,1,3] => [4,3,1] => [3,1] => [1] => 1
[4,2,1,1] => [4,2,1,1] => [2,1,1] => [1,1] => 1
[4,2,2] => [4,2,2] => [2,2] => [2] => 2
[4,3,1] => [4,3,1] => [3,1] => [1] => 1
[5,1,1,1] => [5,1,1,1] => [1,1,1] => [1,1] => 1
[5,1,2] => [5,2,1] => [2,1] => [1] => 1
[5,2,1] => [5,2,1] => [2,1] => [1] => 1
[6,1,1] => [6,1,1] => [1,1] => [1] => 1
[1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,1,3] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,2,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,2,2] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,3,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,4] => [4,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,2,1,2] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,2,2,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,2,3] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,3,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,3,2] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,4,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,5] => [5,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,1,1,2,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,2,1,1,2] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,2,1,2,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,2,1,3] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,2,2,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,2,2,2] => [2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,2,3,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,2,4] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,1,1,3,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,3,1,2] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,3,2,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,3,3] => [3,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[1,1,1,4,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,4,2] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,1,1,5,1] => [5,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,1,1,6] => [6,1,1,1] => [1,1,1] => [1,1] => 1
[1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,2,1,1,1,2] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,2,1,1,2,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,2,1,1,3] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,2,1,2,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,2,1,2,2] => [2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,1,2,1,3,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,2,1,4] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,1,2,2,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,2,2,1,2] => [2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,1,2,2,2,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,1,2,2,3] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,1,2,3,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,2,3,2] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,1,2,4,1] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,1,2,5] => [5,2,1,1] => [2,1,1] => [1,1] => 1
[1,1,3,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,3,1,1,2] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,3,1,2,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,3,1,3] => [3,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[1,1,3,2,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,3,2,2] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,1,3,3,1] => [3,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[1,1,3,4] => [4,3,1,1] => [3,1,1] => [1,1] => 1
[1,1,4,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,1,4,1,2] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,1,4,2,1] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,1,4,3] => [4,3,1,1] => [3,1,1] => [1,1] => 1
[1,1,5,1,1] => [5,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,1,5,2] => [5,2,1,1] => [2,1,1] => [1,1] => 1
[1,1,6,1] => [6,1,1,1] => [1,1,1] => [1,1] => 1
[1,1,7] => [7,1,1] => [1,1] => [1] => 1
[1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,2,1,1,1,1,2] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,2,1,1,1,2,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,2,1,1,1,3] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,2,1,1,2,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,2,1,1,2,2] => [2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,2,1,1,3,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,2,1,1,4] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,2,1,2,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,2,1,2,1,2] => [2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,2,1,2,2,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,2,1,2,3] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,2,1,3,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,2,1,3,2] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,2,1,4,1] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,2,1,5] => [5,2,1,1] => [2,1,1] => [1,1] => 1
[1,2,2,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,2,2,1,1,2] => [2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,2,2,1,2,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,2,2,1,3] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,2,2,2,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,2,2,2,2] => [2,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[1,2,2,3,1] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,2,2,4] => [4,2,2,1] => [2,2,1] => [2,1] => 1
[1,2,3,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,2,3,1,2] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,2,3,2,1] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,2,3,3] => [3,3,2,1] => [3,2,1] => [2,1] => 1
[1,2,4,1,1] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,2,4,2] => [4,2,2,1] => [2,2,1] => [2,1] => 1
[1,2,5,1] => [5,2,1,1] => [2,1,1] => [1,1] => 1
[1,2,6] => [6,2,1] => [2,1] => [1] => 1
[1,3,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,3,1,1,1,2] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,3,1,1,2,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,3,1,1,3] => [3,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[1,3,1,2,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,3,1,2,2] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,3,1,3,1] => [3,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[1,3,1,4] => [4,3,1,1] => [3,1,1] => [1,1] => 1
[1,3,2,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,3,2,1,2] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,3,2,2,1] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,3,2,3] => [3,3,2,1] => [3,2,1] => [2,1] => 1
[1,3,3,1,1] => [3,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[1,3,3,2] => [3,3,2,1] => [3,2,1] => [2,1] => 1
[1,3,4,1] => [4,3,1,1] => [3,1,1] => [1,1] => 1
[1,3,5] => [5,3,1] => [3,1] => [1] => 1
[1,4,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,4,1,1,2] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,4,1,2,1] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,4,1,3] => [4,3,1,1] => [3,1,1] => [1,1] => 1
[1,4,2,1,1] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,4,2,2] => [4,2,2,1] => [2,2,1] => [2,1] => 1
[1,4,3,1] => [4,3,1,1] => [3,1,1] => [1,1] => 1
[1,4,4] => [4,4,1] => [4,1] => [1] => 1
[1,5,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,5,1,2] => [5,2,1,1] => [2,1,1] => [1,1] => 1
[1,5,2,1] => [5,2,1,1] => [2,1,1] => [1,1] => 1
[1,5,3] => [5,3,1] => [3,1] => [1] => 1
[1,6,1,1] => [6,1,1,1] => [1,1,1] => [1,1] => 1
[1,6,2] => [6,2,1] => [2,1] => [1] => 1
[1,7,1] => [7,1,1] => [1,1] => [1] => 1
[2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[2,1,1,1,1,1,2] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[2,1,1,1,1,2,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[2,1,1,1,1,3] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[2,1,1,1,2,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[2,1,1,1,2,2] => [2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[2,1,1,1,3,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[2,1,1,1,4] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[2,1,1,2,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[2,1,1,2,1,2] => [2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[2,1,1,2,2,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[2,1,1,2,3] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[2,1,1,3,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[2,1,1,3,2] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[2,1,1,4,1] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[2,1,1,5] => [5,2,1,1] => [2,1,1] => [1,1] => 1
[2,1,2,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[2,1,2,1,1,2] => [2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[2,1,2,1,2,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[2,1,2,1,3] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[2,1,2,2,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[2,1,2,2,2] => [2,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[2,1,2,3,1] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[2,1,2,4] => [4,2,2,1] => [2,2,1] => [2,1] => 1
[2,1,3,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[2,1,3,1,2] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[2,1,3,2,1] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[2,1,3,3] => [3,3,2,1] => [3,2,1] => [2,1] => 1
[2,1,4,1,1] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[2,1,4,2] => [4,2,2,1] => [2,2,1] => [2,1] => 1
[2,1,5,1] => [5,2,1,1] => [2,1,1] => [1,1] => 1
[2,1,6] => [6,2,1] => [2,1] => [1] => 1
[2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[2,2,1,1,1,2] => [2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[2,2,1,1,2,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[2,2,1,1,3] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[2,2,1,2,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[2,2,1,2,2] => [2,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[2,2,1,3,1] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[2,2,1,4] => [4,2,2,1] => [2,2,1] => [2,1] => 1
[2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[2,2,2,1,2] => [2,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[2,2,2,3] => [3,2,2,2] => [2,2,2] => [2,2] => 2
[2,2,3,1,1] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[2,2,3,2] => [3,2,2,2] => [2,2,2] => [2,2] => 2
[2,2,4,1] => [4,2,2,1] => [2,2,1] => [2,1] => 1
[2,2,5] => [5,2,2] => [2,2] => [2] => 2
[2,3,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[2,3,1,1,2] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[2,3,1,2,1] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[2,3,1,3] => [3,3,2,1] => [3,2,1] => [2,1] => 1
[2,3,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[2,3,2,2] => [3,2,2,2] => [2,2,2] => [2,2] => 2
[2,3,3,1] => [3,3,2,1] => [3,2,1] => [2,1] => 1
[2,3,4] => [4,3,2] => [3,2] => [2] => 2
[2,4,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[2,4,1,2] => [4,2,2,1] => [2,2,1] => [2,1] => 1
[2,4,2,1] => [4,2,2,1] => [2,2,1] => [2,1] => 1
[2,4,3] => [4,3,2] => [3,2] => [2] => 2
[2,5,1,1] => [5,2,1,1] => [2,1,1] => [1,1] => 1
[2,5,2] => [5,2,2] => [2,2] => [2] => 2
[2,6,1] => [6,2,1] => [2,1] => [1] => 1
[3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[3,1,1,1,1,2] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[3,1,1,1,2,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[3,1,1,1,3] => [3,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[3,1,1,2,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[3,1,1,2,2] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[3,1,1,3,1] => [3,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[3,1,1,4] => [4,3,1,1] => [3,1,1] => [1,1] => 1
[3,1,2,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[3,1,2,1,2] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[3,1,2,2,1] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[3,1,2,3] => [3,3,2,1] => [3,2,1] => [2,1] => 1
[3,1,3,1,1] => [3,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[3,1,3,2] => [3,3,2,1] => [3,2,1] => [2,1] => 1
[3,1,4,1] => [4,3,1,1] => [3,1,1] => [1,1] => 1
[3,1,5] => [5,3,1] => [3,1] => [1] => 1
[3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[3,2,1,1,2] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[3,2,1,2,1] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[3,2,1,3] => [3,3,2,1] => [3,2,1] => [2,1] => 1
[3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[3,2,2,2] => [3,2,2,2] => [2,2,2] => [2,2] => 2
[3,2,3,1] => [3,3,2,1] => [3,2,1] => [2,1] => 1
[3,2,4] => [4,3,2] => [3,2] => [2] => 2
[3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[3,3,1,2] => [3,3,2,1] => [3,2,1] => [2,1] => 1
[3,3,2,1] => [3,3,2,1] => [3,2,1] => [2,1] => 1
[3,3,3] => [3,3,3] => [3,3] => [3] => 3
[3,4,1,1] => [4,3,1,1] => [3,1,1] => [1,1] => 1
[3,4,2] => [4,3,2] => [3,2] => [2] => 2
[3,5,1] => [5,3,1] => [3,1] => [1] => 1
[4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[4,1,1,1,2] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[4,1,1,2,1] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[4,1,1,3] => [4,3,1,1] => [3,1,1] => [1,1] => 1
[4,1,2,1,1] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[4,1,2,2] => [4,2,2,1] => [2,2,1] => [2,1] => 1
[4,1,3,1] => [4,3,1,1] => [3,1,1] => [1,1] => 1
[4,1,4] => [4,4,1] => [4,1] => [1] => 1
[4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[4,2,1,2] => [4,2,2,1] => [2,2,1] => [2,1] => 1
[4,2,2,1] => [4,2,2,1] => [2,2,1] => [2,1] => 1
[4,2,3] => [4,3,2] => [3,2] => [2] => 2
[4,3,1,1] => [4,3,1,1] => [3,1,1] => [1,1] => 1
[4,3,2] => [4,3,2] => [3,2] => [2] => 2
[4,4,1] => [4,4,1] => [4,1] => [1] => 1
[5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[5,1,1,2] => [5,2,1,1] => [2,1,1] => [1,1] => 1
[5,1,2,1] => [5,2,1,1] => [2,1,1] => [1,1] => 1
[5,1,3] => [5,3,1] => [3,1] => [1] => 1
[5,2,1,1] => [5,2,1,1] => [2,1,1] => [1,1] => 1
[5,2,2] => [5,2,2] => [2,2] => [2] => 2
[5,3,1] => [5,3,1] => [3,1] => [1] => 1
[6,1,1,1] => [6,1,1,1] => [1,1,1] => [1,1] => 1
[6,1,2] => [6,2,1] => [2,1] => [1] => 1
[6,2,1] => [6,2,1] => [2,1] => [1] => 1
[7,1,1] => [7,1,1] => [1,1] => [1] => 1
[1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,3] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,1,2,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,2,2] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,1,3,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,1,4] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,2,1,2] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,2,2,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,2,3] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,3,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,3,2] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,4,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,5] => [5,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,2,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,2,1,1,2] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,2,1,2,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,2,1,3] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,2,2,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,2,2,2] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,1,2,3,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,2,4] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,3,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,3,1,2] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,3,2,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,3,3] => [3,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,4,1,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,4,2] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,5,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,6] => [6,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,2,1,1,1,2] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,2,1,1,2,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,2,1,1,3] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,2,1,2,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,2,1,2,2] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,2,1,3,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,2,1,4] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,2,2,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,2,2,1,2] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,2,2,2,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,2,2,3] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,2,3,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,2,3,2] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,2,4,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,2,5] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,1,1,3,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,3,1,1,2] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,3,1,2,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,3,1,3] => [3,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,3,2,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,3,2,2] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,3,3,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,3,4] => [4,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[1,1,1,4,1,1,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,4,1,2] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,4,2,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,4,3] => [4,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[1,1,1,5,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,5,2] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,1,1,6,1] => [6,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,1,1,7] => [7,1,1,1] => [1,1,1] => [1,1] => 1
[1,1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,2,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,2,1,1,1,2,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,2,1,1,1,3] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,2,1,1,2,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,2,1,1,2,2] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,2,1,1,3,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,2,1,1,4] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,2,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,2,1,2,1,2] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,2,1,2,2,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,2,1,2,3] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,1,2,1,3,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,2,1,3,2] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,1,2,1,4,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,2,1,5] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,1,2,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,2,2,1,1,2] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,2,2,1,2,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,2,2,1,3] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,1,2,2,2,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,2,2,2,2] => [2,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[1,1,2,2,3,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,1,2,2,4] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,1,2,3,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,2,3,1,2] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,1,2,3,2,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,1,2,3,3] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[1,1,2,4,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,2,4,2] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,1,2,5,1] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,1,2,6] => [6,2,1,1] => [2,1,1] => [1,1] => 1
[1,1,3,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,3,1,1,1,2] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,3,1,1,2,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,3,1,1,3] => [3,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,3,1,2,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,3,1,2,2] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,1,3,1,3,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,3,1,4] => [4,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[1,1,3,2,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,3,2,1,2] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,1,3,2,2,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,1,3,2,3] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[1,1,3,3,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,3,3,2] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[1,1,3,4,1] => [4,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[1,1,3,5] => [5,3,1,1] => [3,1,1] => [1,1] => 1
[1,1,4,1,1,1,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,4,1,1,2] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,4,1,2,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,4,1,3] => [4,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[1,1,4,2,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,4,2,2] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,1,4,3,1] => [4,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[1,1,4,4] => [4,4,1,1] => [4,1,1] => [1,1] => 1
[1,1,5,1,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,1,5,1,2] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,1,5,2,1] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,1,5,3] => [5,3,1,1] => [3,1,1] => [1,1] => 1
[1,1,6,1,1] => [6,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,1,6,2] => [6,2,1,1] => [2,1,1] => [1,1] => 1
[1,1,7,1] => [7,1,1,1] => [1,1,1] => [1,1] => 1
[1,1,8] => [8,1,1] => [1,1] => [1] => 1
[1,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,2,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,2,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,2,1,1,1,1,3] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,2,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,2,1,1,1,2,2] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,2,1,1,1,3,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,2,1,1,1,4] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,2,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,2,1,1,2,1,2] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,2,1,1,2,2,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,2,1,1,2,3] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,2,1,1,3,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,2,1,1,3,2] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,2,1,1,4,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,2,1,1,5] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,2,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,2,1,2,1,1,2] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,2,1,2,1,2,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,2,1,2,1,3] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,2,1,2,2,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,2,1,2,2,2] => [2,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[1,2,1,2,3,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,2,1,2,4] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,2,1,3,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,2,1,3,1,2] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,2,1,3,2,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,2,1,3,3] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[1,2,1,4,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,2,1,4,2] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,2,1,5,1] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,2,1,6] => [6,2,1,1] => [2,1,1] => [1,1] => 1
[1,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,2,2,1,1,1,2] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,2,2,1,1,2,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,2,2,1,1,3] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,2,2,1,2,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,2,2,1,2,2] => [2,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[1,2,2,1,3,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,2,2,1,4] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,2,2,2,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,2,2,2,1,2] => [2,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[1,2,2,2,2,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[1,2,2,2,3] => [3,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[1,2,2,3,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,2,2,3,2] => [3,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[1,2,2,4,1] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,2,2,5] => [5,2,2,1] => [2,2,1] => [2,1] => 1
[1,2,3,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,2,3,1,1,2] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,2,3,1,2,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,2,3,1,3] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[1,2,3,2,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,2,3,2,2] => [3,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[1,2,3,3,1] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[1,2,3,4] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[1,2,4,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,2,4,1,2] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,2,4,2,1] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,2,4,3] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[1,2,5,1,1] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,2,5,2] => [5,2,2,1] => [2,2,1] => [2,1] => 1
[1,2,6,1] => [6,2,1,1] => [2,1,1] => [1,1] => 1
[1,2,7] => [7,2,1] => [2,1] => [1] => 1
[1,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,3,1,1,1,1,2] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,3,1,1,1,2,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,3,1,1,1,3] => [3,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,3,1,1,2,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,3,1,1,2,2] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,3,1,1,3,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,3,1,1,4] => [4,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[1,3,1,2,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,3,1,2,1,2] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,3,1,2,2,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,3,1,2,3] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[1,3,1,3,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,3,1,3,2] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[1,3,1,4,1] => [4,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[1,3,1,5] => [5,3,1,1] => [3,1,1] => [1,1] => 1
[1,3,2,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,3,2,1,1,2] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,3,2,1,2,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,3,2,1,3] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[1,3,2,2,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,3,2,2,2] => [3,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[1,3,2,3,1] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[1,3,2,4] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[1,3,3,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,3,3,1,2] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[1,3,3,2,1] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[1,3,3,3] => [3,3,3,1] => [3,3,1] => [3,1] => 1
[1,3,4,1,1] => [4,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[1,3,4,2] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[1,3,5,1] => [5,3,1,1] => [3,1,1] => [1,1] => 1
[1,3,6] => [6,3,1] => [3,1] => [1] => 1
[1,4,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,4,1,1,1,2] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,4,1,1,2,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,4,1,1,3] => [4,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[1,4,1,2,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,4,1,2,2] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,4,1,3,1] => [4,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[1,4,1,4] => [4,4,1,1] => [4,1,1] => [1,1] => 1
[1,4,2,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,4,2,1,2] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,4,2,2,1] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,4,2,3] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[1,4,3,1,1] => [4,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[1,4,3,2] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[1,4,4,1] => [4,4,1,1] => [4,1,1] => [1,1] => 1
[1,4,5] => [5,4,1] => [4,1] => [1] => 1
[1,5,1,1,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,5,1,1,2] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,5,1,2,1] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,5,1,3] => [5,3,1,1] => [3,1,1] => [1,1] => 1
[1,5,2,1,1] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,5,2,2] => [5,2,2,1] => [2,2,1] => [2,1] => 1
[1,5,3,1] => [5,3,1,1] => [3,1,1] => [1,1] => 1
[1,5,4] => [5,4,1] => [4,1] => [1] => 1
[1,6,1,1,1] => [6,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,6,1,2] => [6,2,1,1] => [2,1,1] => [1,1] => 1
[1,6,2,1] => [6,2,1,1] => [2,1,1] => [1,1] => 1
[1,6,3] => [6,3,1] => [3,1] => [1] => 1
[1,7,1,1] => [7,1,1,1] => [1,1,1] => [1,1] => 1
[1,7,2] => [7,2,1] => [2,1] => [1] => 1
[1,8,1] => [8,1,1] => [1,1] => [1] => 1
[2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[2,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[2,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[2,1,1,1,1,1,3] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[2,1,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[2,1,1,1,1,2,2] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[2,1,1,1,1,3,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[2,1,1,1,1,4] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[2,1,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[2,1,1,1,2,1,2] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[2,1,1,1,2,2,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[2,1,1,1,2,3] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[2,1,1,1,3,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[2,1,1,1,3,2] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[2,1,1,1,4,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[2,1,1,1,5] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[2,1,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[2,1,1,2,1,1,2] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[2,1,1,2,1,2,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[2,1,1,2,1,3] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[2,1,1,2,2,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[2,1,1,2,2,2] => [2,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[2,1,1,2,3,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[2,1,1,2,4] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[2,1,1,3,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[2,1,1,3,1,2] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[2,1,1,3,2,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[2,1,1,3,3] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[2,1,1,4,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[2,1,1,4,2] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[2,1,1,5,1] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[2,1,1,6] => [6,2,1,1] => [2,1,1] => [1,1] => 1
[2,1,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[2,1,2,1,1,1,2] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[2,1,2,1,1,2,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[2,1,2,1,1,3] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[2,1,2,1,2,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[2,1,2,1,2,2] => [2,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[2,1,2,1,3,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[2,1,2,1,4] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[2,1,2,2,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[2,1,2,2,1,2] => [2,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[2,1,2,2,2,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[2,1,2,2,3] => [3,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[2,1,2,3,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[2,1,2,3,2] => [3,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[2,1,2,4,1] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[2,1,2,5] => [5,2,2,1] => [2,2,1] => [2,1] => 1
[2,1,3,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[2,1,3,1,1,2] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[2,1,3,1,2,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[2,1,3,1,3] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[2,1,3,2,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[2,1,3,2,2] => [3,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[2,1,3,3,1] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[2,1,3,4] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[2,1,4,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[2,1,4,1,2] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[2,1,4,2,1] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[2,1,4,3] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[2,1,5,1,1] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[2,1,5,2] => [5,2,2,1] => [2,2,1] => [2,1] => 1
[2,1,6,1] => [6,2,1,1] => [2,1,1] => [1,1] => 1
[2,1,7] => [7,2,1] => [2,1] => [1] => 1
[2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[2,2,1,1,1,1,2] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[2,2,1,1,1,2,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[2,2,1,1,1,3] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[2,2,1,1,2,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[2,2,1,1,2,2] => [2,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[2,2,1,1,3,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[2,2,1,1,4] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[2,2,1,2,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[2,2,1,2,1,2] => [2,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[2,2,1,2,2,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[2,2,1,2,3] => [3,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[2,2,1,3,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[2,2,1,3,2] => [3,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[2,2,1,4,1] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[2,2,1,5] => [5,2,2,1] => [2,2,1] => [2,1] => 1
[2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[2,2,2,1,1,2] => [2,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[2,2,2,1,2,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[2,2,2,1,3] => [3,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => [2,2,2] => 2
[2,2,2,3,1] => [3,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[2,2,2,4] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[2,2,3,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[2,2,3,1,2] => [3,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[2,2,3,2,1] => [3,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[2,2,3,3] => [3,3,2,2] => [3,2,2] => [2,2] => 2
[2,2,4,1,1] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[2,2,4,2] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[2,2,5,1] => [5,2,2,1] => [2,2,1] => [2,1] => 1
[2,2,6] => [6,2,2] => [2,2] => [2] => 2
[2,3,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[2,3,1,1,1,2] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[2,3,1,1,2,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[2,3,1,1,3] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[2,3,1,2,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[2,3,1,2,2] => [3,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[2,3,1,3,1] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[2,3,1,4] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[2,3,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[2,3,2,1,2] => [3,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[2,3,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[2,3,2,3] => [3,3,2,2] => [3,2,2] => [2,2] => 2
[2,3,3,1,1] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[2,3,3,2] => [3,3,2,2] => [3,2,2] => [2,2] => 2
[2,3,4,1] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[2,3,5] => [5,3,2] => [3,2] => [2] => 2
[2,4,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[2,4,1,1,2] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[2,4,1,2,1] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[2,4,1,3] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[2,4,2,1,1] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[2,4,2,2] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[2,4,3,1] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[2,4,4] => [4,4,2] => [4,2] => [2] => 2
[2,5,1,1,1] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[2,5,1,2] => [5,2,2,1] => [2,2,1] => [2,1] => 1
[2,5,2,1] => [5,2,2,1] => [2,2,1] => [2,1] => 1
[2,5,3] => [5,3,2] => [3,2] => [2] => 2
[2,6,1,1] => [6,2,1,1] => [2,1,1] => [1,1] => 1
[2,6,2] => [6,2,2] => [2,2] => [2] => 2
[2,7,1] => [7,2,1] => [2,1] => [1] => 1
[3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[3,1,1,1,1,1,2] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[3,1,1,1,1,2,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[3,1,1,1,1,3] => [3,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[3,1,1,1,2,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[3,1,1,1,2,2] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[3,1,1,1,3,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[3,1,1,1,4] => [4,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[3,1,1,2,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[3,1,1,2,1,2] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[3,1,1,2,2,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[3,1,1,2,3] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[3,1,1,3,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[3,1,1,3,2] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[3,1,1,4,1] => [4,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[3,1,1,5] => [5,3,1,1] => [3,1,1] => [1,1] => 1
[3,1,2,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[3,1,2,1,1,2] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[3,1,2,1,2,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[3,1,2,1,3] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[3,1,2,2,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[3,1,2,2,2] => [3,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[3,1,2,3,1] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[3,1,2,4] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[3,1,3,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[3,1,3,1,2] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[3,1,3,2,1] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[3,1,3,3] => [3,3,3,1] => [3,3,1] => [3,1] => 1
[3,1,4,1,1] => [4,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[3,1,4,2] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[3,1,5,1] => [5,3,1,1] => [3,1,1] => [1,1] => 1
[3,1,6] => [6,3,1] => [3,1] => [1] => 1
[3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[3,2,1,1,1,2] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[3,2,1,1,2,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[3,2,1,1,3] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[3,2,1,2,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[3,2,1,2,2] => [3,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[3,2,1,3,1] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[3,2,1,4] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[3,2,2,1,2] => [3,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[3,2,2,3] => [3,3,2,2] => [3,2,2] => [2,2] => 2
[3,2,3,1,1] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[3,2,3,2] => [3,3,2,2] => [3,2,2] => [2,2] => 2
[3,2,4,1] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[3,2,5] => [5,3,2] => [3,2] => [2] => 2
[3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[3,3,1,1,2] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[3,3,1,2,1] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[3,3,1,3] => [3,3,3,1] => [3,3,1] => [3,1] => 1
[3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[3,3,2,2] => [3,3,2,2] => [3,2,2] => [2,2] => 2
[3,3,3,1] => [3,3,3,1] => [3,3,1] => [3,1] => 1
[3,3,4] => [4,3,3] => [3,3] => [3] => 3
[3,4,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[3,4,1,2] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[3,4,2,1] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[3,4,3] => [4,3,3] => [3,3] => [3] => 3
[3,5,1,1] => [5,3,1,1] => [3,1,1] => [1,1] => 1
[3,5,2] => [5,3,2] => [3,2] => [2] => 2
[3,6,1] => [6,3,1] => [3,1] => [1] => 1
[4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[4,1,1,1,1,2] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[4,1,1,1,2,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[4,1,1,1,3] => [4,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[4,1,1,2,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[4,1,1,2,2] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[4,1,1,3,1] => [4,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[4,1,1,4] => [4,4,1,1] => [4,1,1] => [1,1] => 1
[4,1,2,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[4,1,2,1,2] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[4,1,2,2,1] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[4,1,2,3] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[4,1,3,1,1] => [4,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[4,1,3,2] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[4,1,4,1] => [4,4,1,1] => [4,1,1] => [1,1] => 1
[4,1,5] => [5,4,1] => [4,1] => [1] => 1
[4,2,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[4,2,1,1,2] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[4,2,1,2,1] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[4,2,1,3] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[4,2,2,1,1] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[4,2,2,2] => [4,2,2,2] => [2,2,2] => [2,2] => 2
[4,2,3,1] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[4,2,4] => [4,4,2] => [4,2] => [2] => 2
[4,3,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[4,3,1,2] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[4,3,2,1] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[4,3,3] => [4,3,3] => [3,3] => [3] => 3
[4,4,1,1] => [4,4,1,1] => [4,1,1] => [1,1] => 1
[4,4,2] => [4,4,2] => [4,2] => [2] => 2
[4,5,1] => [5,4,1] => [4,1] => [1] => 1
[5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[5,1,1,1,2] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[5,1,1,2,1] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[5,1,1,3] => [5,3,1,1] => [3,1,1] => [1,1] => 1
[5,1,2,1,1] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[5,1,2,2] => [5,2,2,1] => [2,2,1] => [2,1] => 1
[5,1,3,1] => [5,3,1,1] => [3,1,1] => [1,1] => 1
[5,1,4] => [5,4,1] => [4,1] => [1] => 1
[5,2,1,1,1] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[5,2,1,2] => [5,2,2,1] => [2,2,1] => [2,1] => 1
[5,2,2,1] => [5,2,2,1] => [2,2,1] => [2,1] => 1
[5,2,3] => [5,3,2] => [3,2] => [2] => 2
[5,3,1,1] => [5,3,1,1] => [3,1,1] => [1,1] => 1
[5,3,2] => [5,3,2] => [3,2] => [2] => 2
[5,4,1] => [5,4,1] => [4,1] => [1] => 1
[6,1,1,1,1] => [6,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[6,1,1,2] => [6,2,1,1] => [2,1,1] => [1,1] => 1
[6,1,2,1] => [6,2,1,1] => [2,1,1] => [1,1] => 1
[6,1,3] => [6,3,1] => [3,1] => [1] => 1
[6,2,1,1] => [6,2,1,1] => [2,1,1] => [1,1] => 1
[6,2,2] => [6,2,2] => [2,2] => [2] => 2
[6,3,1] => [6,3,1] => [3,1] => [1] => 1
[7,1,1,1] => [7,1,1,1] => [1,1,1] => [1,1] => 1
[7,1,2] => [7,2,1] => [2,1] => [1] => 1
[7,2,1] => [7,2,1] => [2,1] => [1] => 1
[8,1,1] => [8,1,1] => [1,1] => [1] => 1
[1,8,1,1] => [8,1,1,1] => [1,1,1] => [1,1] => 1
[1,7,2,1] => [7,2,1,1] => [2,1,1] => [1,1] => 1
[1,6,3,1] => [6,3,1,1] => [3,1,1] => [1,1] => 1
[1,5,4,1] => [5,4,1,1] => [4,1,1] => [1,1] => 1
[1,4,5,1] => [5,4,1,1] => [4,1,1] => [1,1] => 1
[1,3,6,1] => [6,3,1,1] => [3,1,1] => [1,1] => 1
[1,2,7,1] => [7,2,1,1] => [2,1,1] => [1,1] => 1
[1,1,8,1] => [8,1,1,1] => [1,1,1] => [1,1] => 1
[1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,2,2] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,2,2,1,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,2,1,1,2] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,3,3] => [3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,2,2,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,2,2,2,2] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[1,1,1,1,2,1,1,2,1,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,2,1,1,1,1,2] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,2,1,2,3] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,1,1,1,3,3,1,1] => [3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,3,2,1,2] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,1,1,1,3,1,1,3] => [3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,4,4] => [4,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,2,2,1,1,2,2] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[1,1,2,2,2,2,1,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[1,1,2,2,2,1,1,2] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[1,1,2,2,3,3] => [3,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 1
[1,1,2,1,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,2,1,1,2,2,2] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[1,1,2,1,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,2,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,2,1,1,1,2,3] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,1,2,1,2,3,1,1] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,1,2,1,2,2,1,2] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[1,1,2,1,2,1,1,3] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,1,2,1,3,4] => [4,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,1,3,3,1,1,1,1] => [3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,3,3,2,2] => [3,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 1
[1,1,3,2,1,2,1,1] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,1,3,2,1,1,1,2] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,1,3,2,2,3] => [3,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 1
[1,1,3,1,1,3,1,1] => [3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,3,1,1,2,1,2] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,1,3,1,1,1,1,3] => [3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,3,1,2,4] => [4,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,1,4,4,1,1] => [4,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,4,3,1,2] => [4,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,1,4,2,1,3] => [4,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,1,4,1,1,4] => [4,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,5,5] => [5,5,1,1] => [5,1,1] => [1,1] => 1
[2,2,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[2,2,1,1,1,1,2,2] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[2,2,1,1,2,2,1,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[2,2,1,1,2,1,1,2] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[2,2,1,1,3,3] => [3,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 1
[2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 2
[2,2,2,1,1,2,1,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[2,2,2,1,1,1,1,2] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[2,2,2,1,2,3] => [3,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 1
[2,2,3,3,1,1] => [3,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 1
[2,2,3,2,1,2] => [3,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 1
[2,2,3,1,1,3] => [3,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 1
[2,2,4,4] => [4,4,2,2] => [4,2,2] => [2,2] => 2
[2,1,1,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[2,1,1,2,1,1,2,2] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[2,1,1,2,2,2,1,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[2,1,1,2,2,1,1,2] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[2,1,1,2,3,3] => [3,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 1
[2,1,1,1,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[2,1,1,1,1,2,2,2] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[2,1,1,1,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[2,1,1,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[2,1,1,1,1,1,2,3] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[2,1,1,1,2,3,1,1] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[2,1,1,1,2,2,1,2] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[2,1,1,1,2,1,1,3] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[2,1,1,1,3,4] => [4,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[2,1,2,3,1,1,1,1] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[2,1,2,3,2,2] => [3,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 1
[2,1,2,2,1,2,1,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[2,1,2,2,1,1,1,2] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[2,1,2,2,2,3] => [3,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 1
[2,1,2,1,1,3,1,1] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[2,1,2,1,1,2,1,2] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[2,1,2,1,1,1,1,3] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[2,1,2,1,2,4] => [4,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[2,1,3,4,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[2,1,3,3,1,2] => [3,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 1
[2,1,3,2,1,3] => [3,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 1
[2,1,3,1,1,4] => [4,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[2,1,4,5] => [5,4,2,1] => [4,2,1] => [2,1] => 1
[3,3,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[3,3,1,1,2,2] => [3,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 1
[3,3,2,2,1,1] => [3,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 1
[3,3,2,1,1,2] => [3,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 1
[3,3,3,3] => [3,3,3,3] => [3,3,3] => [3,3] => 3
[3,2,1,2,1,1,1,1] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[3,2,1,2,2,2] => [3,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 1
[3,2,1,1,1,2,1,1] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[3,2,1,1,1,1,1,2] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[3,2,1,1,2,3] => [3,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 1
[3,2,2,3,1,1] => [3,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 1
[3,2,2,2,1,2] => [3,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 1
[3,2,2,1,1,3] => [3,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 1
[3,2,3,4] => [4,3,3,2] => [3,3,2] => [3,2] => 1
[3,1,1,3,1,1,1,1] => [3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[3,1,1,3,2,2] => [3,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 1
[3,1,1,2,1,2,1,1] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[3,1,1,2,1,1,1,2] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[3,1,1,2,2,3] => [3,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 1
[3,1,1,1,1,3,1,1] => [3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[3,1,1,1,1,2,1,2] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[3,1,1,1,1,1,1,3] => [3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[3,1,1,1,2,4] => [4,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[3,1,2,4,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[3,1,2,3,1,2] => [3,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 1
[3,1,2,2,1,3] => [3,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 1
[3,1,2,1,1,4] => [4,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[3,1,3,5] => [5,3,3,1] => [3,3,1] => [3,1] => 1
[4,4,1,1,1,1] => [4,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[4,4,2,2] => [4,4,2,2] => [4,2,2] => [2,2] => 2
[4,3,1,2,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[4,3,1,1,1,2] => [4,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[4,3,2,3] => [4,3,3,2] => [3,3,2] => [3,2] => 1
[4,2,1,3,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[4,2,1,2,1,2] => [4,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[4,2,1,1,1,3] => [4,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[4,2,2,4] => [4,4,2,2] => [4,2,2] => [2,2] => 2
[4,1,1,4,1,1] => [4,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[4,1,1,3,1,2] => [4,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[4,1,1,2,1,3] => [4,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[4,1,1,1,1,4] => [4,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[4,1,2,5] => [5,4,2,1] => [4,2,1] => [2,1] => 1
[5,5,1,1] => [5,5,1,1] => [5,1,1] => [1,1] => 1
[5,4,1,2] => [5,4,2,1] => [4,2,1] => [2,1] => 1
[5,3,1,3] => [5,3,3,1] => [3,3,1] => [3,1] => 1
[5,2,1,4] => [5,4,2,1] => [4,2,1] => [2,1] => 1
[5,1,1,5] => [5,5,1,1] => [5,1,1] => [1,1] => 1
[1,2,2,2,2,2,1] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[1,2,2,2,3,2] => [3,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 1
[1,2,2,3,3,1] => [3,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 1
[1,2,2,3,2,2] => [3,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 1
[1,2,2,4,3] => [4,3,2,2,1] => [3,2,2,1] => [2,2,1] => 1
[1,2,3,3,2,1] => [3,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 1
[1,2,3,4,2] => [4,3,2,2,1] => [3,2,2,1] => [2,2,1] => 1
[1,2,3,2,3,1] => [3,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 1
[1,2,3,2,2,2] => [3,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 1
[1,2,3,3,3] => [3,3,3,2,1] => [3,3,2,1] => [3,2,1] => 1
[1,2,4,4,1] => [4,4,2,1,1] => [4,2,1,1] => [2,1,1] => 1
[1,2,4,3,2] => [4,3,2,2,1] => [3,2,2,1] => [2,2,1] => 1
[1,2,4,2,3] => [4,3,2,2,1] => [3,2,2,1] => [2,2,1] => 1
[1,2,5,4] => [5,4,2,1] => [4,2,1] => [2,1] => 1
[1,3,3,2,2,1] => [3,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 1
[1,3,3,3,2] => [3,3,3,2,1] => [3,3,2,1] => [3,2,1] => 1
[1,3,4,3,1] => [4,3,3,1,1] => [3,3,1,1] => [3,1,1] => 1
[1,3,4,2,2] => [4,3,2,2,1] => [3,2,2,1] => [2,2,1] => 1
[1,3,5,3] => [5,3,3,1] => [3,3,1] => [3,1] => 1
[1,3,2,3,2,1] => [3,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 1
[1,3,2,4,2] => [4,3,2,2,1] => [3,2,2,1] => [2,2,1] => 1
[1,3,2,2,3,1] => [3,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 1
[1,3,2,2,2,2] => [3,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 1
[1,3,2,3,3] => [3,3,3,2,1] => [3,3,2,1] => [3,2,1] => 1
[1,3,3,4,1] => [4,3,3,1,1] => [3,3,1,1] => [3,1,1] => 1
[1,3,3,2,3] => [3,3,3,2,1] => [3,3,2,1] => [3,2,1] => 1
[1,3,4,4] => [4,4,3,1] => [4,3,1] => [3,1] => 1
[1,4,4,2,1] => [4,4,2,1,1] => [4,2,1,1] => [2,1,1] => 1
[1,4,5,2] => [5,4,2,1] => [4,2,1] => [2,1] => 1
[1,4,3,3,1] => [4,3,3,1,1] => [3,3,1,1] => [3,1,1] => 1
[1,4,3,2,2] => [4,3,2,2,1] => [3,2,2,1] => [2,2,1] => 1
[1,4,4,3] => [4,4,3,1] => [4,3,1] => [3,1] => 1
[1,4,2,4,1] => [4,4,2,1,1] => [4,2,1,1] => [2,1,1] => 1
[1,4,2,3,2] => [4,3,2,2,1] => [3,2,2,1] => [2,2,1] => 1
[1,4,2,2,3] => [4,3,2,2,1] => [3,2,2,1] => [2,2,1] => 1
[1,4,3,4] => [4,4,3,1] => [4,3,1] => [3,1] => 1
[1,5,5,1] => [5,5,1,1] => [5,1,1] => [1,1] => 1
[1,5,4,2] => [5,4,2,1] => [4,2,1] => [2,1] => 1
[1,5,3,3] => [5,3,3,1] => [3,3,1] => [3,1] => 1
[1,5,2,4] => [5,4,2,1] => [4,2,1] => [2,1] => 1
[1,6,5] => [6,5,1] => [5,1] => [1] => 1
[2,3,2,2,2,1] => [3,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 1
[2,3,2,3,2] => [3,3,2,2,2] => [3,2,2,2] => [2,2,2] => 2
[2,3,3,3,1] => [3,3,3,2,1] => [3,3,2,1] => [3,2,1] => 1
[2,3,3,2,2] => [3,3,2,2,2] => [3,2,2,2] => [2,2,2] => 2
[2,3,4,3] => [4,3,3,2] => [3,3,2] => [3,2] => 1
[2,4,3,2,1] => [4,3,2,2,1] => [3,2,2,1] => [2,2,1] => 1
[2,4,4,2] => [4,4,2,2] => [4,2,2] => [2,2] => 2
[2,4,2,3,1] => [4,3,2,2,1] => [3,2,2,1] => [2,2,1] => 1
[2,4,2,2,2] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 2
[2,4,3,3] => [4,3,3,2] => [3,3,2] => [3,2] => 1
[2,5,4,1] => [5,4,2,1] => [4,2,1] => [2,1] => 1
[2,5,3,2] => [5,3,2,2] => [3,2,2] => [2,2] => 2
[2,5,2,3] => [5,3,2,2] => [3,2,2] => [2,2] => 2
[2,6,4] => [6,4,2] => [4,2] => [2] => 2
[2,2,3,2,2,1] => [3,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 1
[2,2,3,3,2] => [3,3,2,2,2] => [3,2,2,2] => [2,2,2] => 2
[2,2,4,3,1] => [4,3,2,2,1] => [3,2,2,1] => [2,2,1] => 1
[2,2,4,2,2] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 2
[2,2,5,3] => [5,3,2,2] => [3,2,2] => [2,2] => 2
[2,2,2,3,2,1] => [3,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 1
[2,2,2,4,2] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 2
[2,2,2,2,3,1] => [3,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 1
[2,2,2,3,3] => [3,3,2,2,2] => [3,2,2,2] => [2,2,2] => 2
[2,2,3,4,1] => [4,3,2,2,1] => [3,2,2,1] => [2,2,1] => 1
[2,2,3,2,3] => [3,3,2,2,2] => [3,2,2,2] => [2,2,2] => 2
[2,3,4,2,1] => [4,3,2,2,1] => [3,2,2,1] => [2,2,1] => 1
[2,3,5,2] => [5,3,2,2] => [3,2,2] => [2,2] => 2
[2,3,2,4,1] => [4,3,2,2,1] => [3,2,2,1] => [2,2,1] => 1
[2,3,2,2,3] => [3,3,2,2,2] => [3,2,2,2] => [2,2,2] => 2
[2,3,3,4] => [4,3,3,2] => [3,3,2] => [3,2] => 1
[2,4,5,1] => [5,4,2,1] => [4,2,1] => [2,1] => 1
[2,4,2,4] => [4,4,2,2] => [4,2,2] => [2,2] => 2
[2,5,5] => [5,5,2] => [5,2] => [2] => 2
[3,4,2,2,1] => [4,3,2,2,1] => [3,2,2,1] => [2,2,1] => 1
[3,4,3,2] => [4,3,3,2] => [3,3,2] => [3,2] => 1
[3,5,3,1] => [5,3,3,1] => [3,3,1] => [3,1] => 1
[3,5,2,2] => [5,3,2,2] => [3,2,2] => [2,2] => 2
[3,6,3] => [6,3,3] => [3,3] => [3] => 3
[3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => [3,2,1] => 1
[3,3,4,2] => [4,3,3,2] => [3,3,2] => [3,2] => 1
[3,3,2,3,1] => [3,3,3,2,1] => [3,3,2,1] => [3,2,1] => 1
[3,3,2,2,2] => [3,3,2,2,2] => [3,2,2,2] => [2,2,2] => 2
[3,4,4,1] => [4,4,3,1] => [4,3,1] => [3,1] => 1
[3,4,2,3] => [4,3,3,2] => [3,3,2] => [3,2] => 1
[3,5,4] => [5,4,3] => [4,3] => [3] => 3
[3,2,4,2,1] => [4,3,2,2,1] => [3,2,2,1] => [2,2,1] => 1
[3,2,5,2] => [5,3,2,2] => [3,2,2] => [2,2] => 2
[3,2,3,3,1] => [3,3,3,2,1] => [3,3,2,1] => [3,2,1] => 1
[3,2,3,2,2] => [3,3,2,2,2] => [3,2,2,2] => [2,2,2] => 2
[3,2,4,3] => [4,3,3,2] => [3,3,2] => [3,2] => 1
[3,2,2,4,1] => [4,3,2,2,1] => [3,2,2,1] => [2,2,1] => 1
[3,2,2,3,2] => [3,3,2,2,2] => [3,2,2,2] => [2,2,2] => 2
[3,2,2,2,3] => [3,3,2,2,2] => [3,2,2,2] => [2,2,2] => 2
[3,3,5,1] => [5,3,3,1] => [3,3,1] => [3,1] => 1
[3,3,2,4] => [4,3,3,2] => [3,3,2] => [3,2] => 1
[3,4,5] => [5,4,3] => [4,3] => [3] => 3
[4,5,2,1] => [5,4,2,1] => [4,2,1] => [2,1] => 1
[4,6,2] => [6,4,2] => [4,2] => [2] => 2
[4,4,3,1] => [4,4,3,1] => [4,3,1] => [3,1] => 1
[4,5,3] => [5,4,3] => [4,3] => [3] => 3
[4,3,4,1] => [4,4,3,1] => [4,3,1] => [3,1] => 1
[4,3,3,2] => [4,3,3,2] => [3,3,2] => [3,2] => 1
[4,4,4] => [4,4,4] => [4,4] => [4] => 4
[4,2,5,1] => [5,4,2,1] => [4,2,1] => [2,1] => 1
[4,2,4,2] => [4,4,2,2] => [4,2,2] => [2,2] => 2
[4,2,3,3] => [4,3,3,2] => [3,3,2] => [3,2] => 1
[4,3,5] => [5,4,3] => [4,3] => [3] => 3
[5,6,1] => [6,5,1] => [5,1] => [1] => 1
[5,5,2] => [5,5,2] => [5,2] => [2] => 2
[5,4,3] => [5,4,3] => [4,3] => [3] => 3
[5,3,4] => [5,4,3] => [4,3] => [3] => 3
[5,2,5] => [5,5,2] => [5,2] => [2] => 2
[1,8,2] => [8,2,1] => [2,1] => [1] => 1
[1,7,1,2] => [7,2,1,1] => [2,1,1] => [1,1] => 1
[1,6,1,1,2] => [6,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,5,1,1,1,2] => [5,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,4,1,1,1,1,2] => [4,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,3,1,1,1,1,1,2] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,2,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,9,2] => [9,2,1] => [2,1] => [1] => 1
[1,7,3] => [7,3,1] => [3,1] => [1] => 1
[1,8,1,2] => [8,2,1,1] => [2,1,1] => [1,1] => 1
[1,6,2,2] => [6,2,2,1] => [2,2,1] => [2,1] => 1
[1,7,1,1,2] => [7,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,5,2,1,2] => [5,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,6,1,1,1,2] => [6,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,4,2,1,1,2] => [4,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,5,1,1,1,1,2] => [5,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,3,2,1,1,1,2] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,4,1,1,1,1,1,2] => [4,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,2,2,1,1,1,1,2] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,3,1,1,1,1,1,1,2] => [3,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,2,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,2,1,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[1,2,2,2,2,2] => [2,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 1
[1,2,2,2,1,3] => [3,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[1,2,2,1,3,2] => [3,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[1,2,2,1,2,3] => [3,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[1,2,2,1,1,4] => [4,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,2,1,3,2,2] => [3,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[1,2,1,3,1,3] => [3,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,2,1,2,3,2] => [3,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[1,2,1,2,2,3] => [3,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[1,2,1,2,1,4] => [4,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,2,1,1,4,2] => [4,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,2,1,1,3,3] => [3,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,2,1,1,2,4] => [4,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,2,1,1,1,5] => [5,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,3,2,2,2] => [3,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[1,1,3,2,1,3] => [3,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,1,3,1,3,2] => [3,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,1,3,1,2,3] => [3,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,1,3,1,1,4] => [4,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,2,3,2,2] => [3,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[1,1,2,3,1,3] => [3,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,1,2,2,3,2] => [3,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[1,1,2,2,2,3] => [3,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[1,1,2,2,1,4] => [4,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,1,2,1,4,2] => [4,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,1,2,1,3,3] => [3,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,1,2,1,2,4] => [4,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,1,2,1,1,5] => [5,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,4,2,2] => [4,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,4,1,3] => [4,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,3,3,2] => [3,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,3,2,3] => [3,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,3,1,4] => [4,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,2,4,2] => [4,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,2,3,3] => [3,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,2,2,4] => [4,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,2,1,5] => [5,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,5,2] => [5,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,4,3] => [4,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,3,4] => [4,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,2,5] => [5,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,6] => [6,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,2,2,2,2,2,2] => [2,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => 1
[1,2,2,2,2,1,3] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[1,2,2,2,1,3,2] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[1,2,2,2,1,2,3] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[1,2,2,2,1,1,4] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,2,2,1,3,2,2] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[1,2,2,1,3,1,3] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,2,2,1,2,3,2] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[1,2,2,1,2,2,3] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[1,2,2,1,2,1,4] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,2,2,1,1,4,2] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,2,2,1,1,3,3] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,2,2,1,1,2,4] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,2,2,1,1,1,5] => [5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,2,1,3,2,2,2] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[1,2,1,3,2,1,3] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,2,1,3,1,3,2] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,2,1,3,1,2,3] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,2,1,3,1,1,4] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,2,1,2,3,2,2] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[1,2,1,2,3,1,3] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,2,1,2,2,3,2] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[1,2,1,2,2,2,3] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[1,2,1,2,2,1,4] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,2,1,2,1,4,2] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,2,1,2,1,3,3] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,2,1,2,1,2,4] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,2,1,2,1,1,5] => [5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,2,1,1,4,2,2] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,2,1,1,4,1,3] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,2,1,1,3,3,2] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,2,1,1,3,2,3] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,2,1,1,3,1,4] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,2,1,1,2,4,2] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,2,1,1,2,3,3] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,2,1,1,2,2,4] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,2,1,1,2,1,5] => [5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,2,1,1,1,5,2] => [5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,2,1,1,1,4,3] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,2,1,1,1,3,4] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,2,1,1,1,2,5] => [5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,2,1,1,1,1,6] => [6,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,3,2,2,2,2] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[1,1,3,2,2,1,3] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,1,3,2,1,3,2] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,1,3,2,1,2,3] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,1,3,2,1,1,4] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,3,1,3,2,2] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,1,3,1,3,1,3] => [3,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 1
[1,1,3,1,2,3,2] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,1,3,1,2,2,3] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,1,3,1,2,1,4] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,3,1,1,4,2] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,3,1,1,3,3] => [3,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 1
[1,1,3,1,1,2,4] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,3,1,1,1,5] => [5,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,2,3,2,2,2] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[1,1,2,3,2,1,3] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,1,2,3,1,3,2] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,1,2,3,1,2,3] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,1,2,3,1,1,4] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,2,2,3,2,2] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[1,1,2,2,3,1,3] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,1,2,2,2,3,2] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[1,1,2,2,2,2,3] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[1,1,2,2,2,1,4] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,1,2,2,1,4,2] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,1,2,2,1,3,3] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,1,2,2,1,2,4] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,1,2,2,1,1,5] => [5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,2,1,4,2,2] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,1,2,1,4,1,3] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,2,1,3,3,2] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,1,2,1,3,2,3] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,1,2,1,3,1,4] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,2,1,2,4,2] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,1,2,1,2,3,3] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,1,2,1,2,2,4] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,1,2,1,2,1,5] => [5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,2,1,1,5,2] => [5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,2,1,1,4,3] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,2,1,1,3,4] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,2,1,1,2,5] => [5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,2,1,1,1,6] => [6,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,4,2,2,2] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,1,1,4,2,1,3] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,4,1,3,2] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,4,1,2,3] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,4,1,1,4] => [4,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,3,3,2,2] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,1,1,3,3,1,3] => [3,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 1
[1,1,1,3,2,3,2] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,1,1,3,2,2,3] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,1,1,3,2,1,4] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,3,1,4,2] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,3,1,3,3] => [3,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 1
[1,1,1,3,1,2,4] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,3,1,1,5] => [5,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,2,4,2,2] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,1,1,2,4,1,3] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,2,3,3,2] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,1,1,2,3,2,3] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,1,1,2,3,1,4] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,2,2,4,2] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,1,1,2,2,3,3] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,1,1,2,2,2,4] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,1,1,2,2,1,5] => [5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,2,1,5,2] => [5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,2,1,4,3] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,2,1,3,4] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,2,1,2,5] => [5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,2,1,1,6] => [6,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,5,2,2] => [5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,1,5,1,3] => [5,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,4,3,2] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,1,4,2,3] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,1,4,1,4] => [4,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,3,4,2] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,1,3,3,3] => [3,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 1
[1,1,1,1,3,2,4] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,1,3,1,5] => [5,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,2,5,2] => [5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,1,2,4,3] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,1,2,3,4] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,1,2,2,5] => [5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,1,2,1,6] => [6,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,6,2] => [6,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,5,3] => [5,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,4,4] => [4,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,3,5] => [5,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,2,6] => [6,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,1,7] => [7,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,2,9] => [9,2,1] => [2,1] => [1] => 1
[3,2,7] => [7,3,2] => [3,2] => [2] => 2
[1,4,7] => [7,4,1] => [4,1] => [1] => 1
[1,1,2,1,7] => [7,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,2,2,2,5] => [5,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[1,1,2,3,5] => [5,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[3,1,2,1,5] => [5,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[1,3,2,1,5] => [5,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[1,1,4,1,5] => [5,4,1,1,1] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,2,1,1,5] => [5,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[7,2,3] => [7,3,2] => [3,2] => [2] => 2
[1,1,2,1,2,2,3] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,8,3] => [8,3,1] => [3,1] => [1] => 1
[1,1,2,5,3] => [5,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[3,1,2,3,3] => [3,3,3,2,1] => [3,3,2,1] => [3,2,1] => 1
[1,1,4,3,3] => [4,3,3,1,1] => [3,3,1,1] => [3,1,1] => 1
[1,1,1,2,1,3,3] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[5,1,2,1,3] => [5,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[1,2,2,1,2,1,3] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[3,3,2,1,3] => [3,3,3,2,1] => [3,3,2,1] => [3,2,1] => 1
[1,5,2,1,3] => [5,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[1,1,2,2,2,1,3] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[3,1,4,1,3] => [4,3,3,1,1] => [3,3,1,1] => [3,1,1] => 1
[1,3,4,1,3] => [4,3,3,1,1] => [3,3,1,1] => [3,1,1] => 1
[1,1,6,1,3] => [6,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[1,1,1,2,3,1,3] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[3,1,1,2,1,1,3] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,3,1,2,1,1,3] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,3,2,1,1,3] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,4,1,1,3] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,2,1,1,1,3] => [3,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[9,2,1] => [9,2,1] => [2,1] => [1] => 1
[1,2,6,2,1] => [6,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,1,2,1,4,2,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[5,2,2,2,1] => [5,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[1,6,2,2,1] => [6,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,1,2,3,2,2,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[3,1,2,1,2,2,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,3,2,1,2,2,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,1,4,1,2,2,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,2,1,1,2,2,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[7,4,1] => [7,4,1] => [4,1] => [1] => 1
[1,1,2,1,2,4,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,2,2,6,1] => [6,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[3,8,1] => [8,3,1] => [3,1] => [1] => 1
[1,10,1] => [10,1,1] => [1,1] => [1] => 1
[1,1,2,7,1] => [7,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[3,1,2,5,1] => [5,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[1,3,2,5,1] => [5,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[1,1,4,5,1] => [5,4,1,1,1] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,2,1,5,1] => [5,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[5,1,2,3,1] => [5,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[1,2,2,1,2,3,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,5,2,3,1] => [5,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[1,1,2,2,2,3,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[3,1,4,3,1] => [4,3,3,1,1] => [3,3,1,1] => [3,1,1] => 1
[1,1,6,3,1] => [6,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[1,1,1,2,3,3,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[3,1,1,2,1,3,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,3,1,2,1,3,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,3,2,1,3,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,4,1,3,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,2,1,1,3,1] => [3,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[7,1,2,1,1] => [7,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,2,4,1,2,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[3,2,2,1,2,1,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,4,2,1,2,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,2,1,2,1,2,1,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[5,3,2,1,1] => [5,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[1,2,2,3,2,1,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[3,5,2,1,1] => [5,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[1,7,2,1,1] => [7,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,1,2,4,2,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[3,1,2,2,2,1,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,3,2,2,2,1,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,1,4,2,2,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,2,1,2,2,1,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[5,1,4,1,1] => [5,4,1,1,1] => [4,1,1,1] => [1,1,1] => 1
[1,2,2,1,4,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[3,3,4,1,1] => [4,3,3,1,1] => [3,3,1,1] => [3,1,1] => 1
[1,5,4,1,1] => [5,4,1,1,1] => [4,1,1,1] => [1,1,1] => 1
[1,1,2,2,4,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[3,1,6,1,1] => [6,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[1,3,6,1,1] => [6,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[1,1,8,1,1] => [8,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,1,1,2,5,1,1] => [5,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[3,1,1,2,3,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,3,1,2,3,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,3,2,3,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,4,3,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,2,1,3,1,1] => [3,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[5,1,1,2,1,1,1] => [5,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,2,2,1,1,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[3,3,1,2,1,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,5,1,2,1,1,1] => [5,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,2,2,1,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[3,1,3,2,1,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,3,3,2,1,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,5,2,1,1,1] => [5,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,2,2,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[3,1,1,4,1,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,3,1,4,1,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,3,4,1,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,6,1,1,1] => [6,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,2,3,1,1,1] => [3,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[3,1,1,1,2,1,1,1,1] => [3,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,3,1,1,2,1,1,1,1] => [3,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,3,1,2,1,1,1,1] => [3,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,3,2,1,1,1,1] => [3,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,4,1,1,1,1] => [4,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[2,2,2,2,1,2,1] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[2,2,2,1,2,1,2] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[2,2,2,1,2,2,1] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[2,2,2,1,1,2,2] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[2,2,1,2,1,2,2] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[2,2,1,2,1,1,2,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[2,2,1,2,2,1,2] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[2,2,1,2,2,2,1] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[2,2,1,1,2,2,2] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[2,2,1,1,2,1,2,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[2,2,1,1,1,2,2,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[2,1,2,1,2,2,2] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[2,1,2,1,2,1,2,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[2,1,2,1,1,2,2,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[2,1,2,1,1,1,2,2] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[2,1,2,2,1,2,2] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[2,1,2,2,1,1,2,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[2,1,2,2,2,1,2] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[2,1,2,2,2,2,1] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[2,1,1,2,2,2,2] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[2,1,1,2,2,1,2,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[2,1,1,2,1,2,1,2] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[2,1,1,2,1,2,2,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[2,1,1,1,2,2,2,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[2,1,1,1,2,1,2,2] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[1,2,1,2,2,2,2] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[1,2,1,2,2,1,2,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[1,2,1,2,1,2,1,2] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[1,2,1,2,1,2,2,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[1,2,1,2,1,1,2,2] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[1,2,1,1,2,1,2,2] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[1,2,1,1,2,1,1,2,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,2,1,1,2,2,1,2] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[1,2,1,1,2,2,2,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[1,2,1,1,1,2,2,2] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[1,2,1,1,1,2,1,2,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,2,1,1,1,1,2,2,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,2,2,1,2,2,2] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[1,2,2,1,2,1,2,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[1,2,2,1,1,2,1,2] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[1,2,2,1,1,2,2,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[1,2,2,1,1,1,2,2] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[1,2,2,2,1,2,2] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[1,2,2,2,1,1,2,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[1,2,2,2,2,1,2] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[1,1,2,2,2,2,2] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[1,1,2,2,2,1,2,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[1,1,2,2,1,2,1,2] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[1,1,2,2,1,2,2,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[1,1,2,1,2,1,2,2] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[1,1,2,1,2,1,1,2,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,1,2,1,2,2,2,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[1,1,2,1,1,2,1,2,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,1,2,1,1,1,2,2,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,1,1,2,2,1,2,2] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[1,1,1,2,2,1,1,2,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,1,1,2,2,2,1,2] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[1,1,1,2,2,2,2,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[1,1,1,2,1,2,2,2] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[1,1,1,2,1,2,1,2,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,2,2,1,2,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,2,1,2,2,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,1,2,2,2,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[3,2,2,2,2,1] => [3,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 1
[4,3,2,2,1] => [4,3,2,2,1] => [3,2,2,1] => [2,2,1] => 1
[4,2,3,2,1] => [4,3,2,2,1] => [3,2,2,1] => [2,2,1] => 1
[4,2,2,3,1] => [4,3,2,2,1] => [3,2,2,1] => [2,2,1] => 1
[4,2,2,2,2] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 2
[5,4,2,1] => [5,4,2,1] => [4,2,1] => [2,1] => 1
[5,3,3,1] => [5,3,3,1] => [3,3,1] => [3,1] => 1
[5,3,2,2] => [5,3,2,2] => [3,2,2] => [2,2] => 2
[5,2,4,1] => [5,4,2,1] => [4,2,1] => [2,1] => 1
[5,2,3,2] => [5,3,2,2] => [3,2,2] => [2,2] => 2
[5,2,2,3] => [5,3,2,2] => [3,2,2] => [2,2] => 2
[6,5,1] => [6,5,1] => [5,1] => [1] => 1
[6,4,2] => [6,4,2] => [4,2] => [2] => 2
[6,3,3] => [6,3,3] => [3,3] => [3] => 3
[6,2,4] => [6,4,2] => [4,2] => [2] => 2
[2,8,1] => [8,2,1] => [2,1] => [1] => 1
[2,1,7,1] => [7,2,1,1] => [2,1,1] => [1,1] => 1
[2,1,1,6,1] => [6,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[2,1,1,1,5,1] => [5,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[2,1,1,1,1,4,1] => [4,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[2,1,1,1,1,1,3,1] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[2,1,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[2,9,1] => [9,2,1] => [2,1] => [1] => 1
[3,7,1] => [7,3,1] => [3,1] => [1] => 1
[2,1,8,1] => [8,2,1,1] => [2,1,1] => [1,1] => 1
[2,2,6,1] => [6,2,2,1] => [2,2,1] => [2,1] => 1
[2,1,1,7,1] => [7,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[2,1,2,5,1] => [5,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[2,1,1,1,6,1] => [6,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[2,1,1,2,4,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[2,1,1,1,1,5,1] => [5,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[2,1,1,1,2,3,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[2,1,1,1,1,1,4,1] => [4,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[2,1,1,1,1,2,2,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[2,1,1,1,1,1,1,3,1] => [3,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[2,1,1,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[2,1,1,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[2,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 1
[3,1,2,2,2,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[2,3,1,2,2,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[3,2,1,2,2,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[4,1,1,2,2,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[2,2,3,1,2,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[3,1,3,1,2,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[2,3,2,1,2,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[3,2,2,1,2,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[4,1,2,1,2,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[2,4,1,1,2,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[3,3,1,1,2,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[4,2,1,1,2,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[5,1,1,1,2,1] => [5,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[2,2,2,3,1,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[3,1,2,3,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[2,3,1,3,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[3,2,1,3,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[4,1,1,3,1,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[2,2,3,2,1,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[3,1,3,2,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[2,3,2,2,1,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[3,2,2,2,1,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[4,1,2,2,1,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[2,4,1,2,1,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[3,3,1,2,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[4,2,1,2,1,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[5,1,1,2,1,1] => [5,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[2,2,4,1,1,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[3,1,4,1,1,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[2,3,3,1,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[3,2,3,1,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[4,1,3,1,1,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[2,4,2,1,1,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[3,3,2,1,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[4,2,2,1,1,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[5,1,2,1,1,1] => [5,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[2,5,1,1,1,1] => [5,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[3,4,1,1,1,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[4,3,1,1,1,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[5,2,1,1,1,1] => [5,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[6,1,1,1,1,1] => [6,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => 1
[3,1,2,2,2,2,1] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[2,3,1,2,2,2,1] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[3,2,1,2,2,2,1] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[4,1,1,2,2,2,1] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[2,2,3,1,2,2,1] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[3,1,3,1,2,2,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[2,3,2,1,2,2,1] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[3,2,2,1,2,2,1] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[4,1,2,1,2,2,1] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[2,4,1,1,2,2,1] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[3,3,1,1,2,2,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[4,2,1,1,2,2,1] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[5,1,1,1,2,2,1] => [5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[2,2,2,3,1,2,1] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[3,1,2,3,1,2,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[2,3,1,3,1,2,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[3,2,1,3,1,2,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[4,1,1,3,1,2,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[2,2,3,2,1,2,1] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[3,1,3,2,1,2,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[2,3,2,2,1,2,1] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[3,2,2,2,1,2,1] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[4,1,2,2,1,2,1] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[2,4,1,2,1,2,1] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[3,3,1,2,1,2,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[4,2,1,2,1,2,1] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[5,1,1,2,1,2,1] => [5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[2,2,4,1,1,2,1] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[3,1,4,1,1,2,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[2,3,3,1,1,2,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[3,2,3,1,1,2,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[4,1,3,1,1,2,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[2,4,2,1,1,2,1] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[3,3,2,1,1,2,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[4,2,2,1,1,2,1] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[5,1,2,1,1,2,1] => [5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[2,5,1,1,1,2,1] => [5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[3,4,1,1,1,2,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[4,3,1,1,1,2,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[5,2,1,1,1,2,1] => [5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[6,1,1,1,1,2,1] => [6,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[2,2,2,2,3,1,1] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[3,1,2,2,3,1,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[2,3,1,2,3,1,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[3,2,1,2,3,1,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[4,1,1,2,3,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[2,2,3,1,3,1,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[3,1,3,1,3,1,1] => [3,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 1
[2,3,2,1,3,1,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[3,2,2,1,3,1,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[4,1,2,1,3,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[2,4,1,1,3,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[3,3,1,1,3,1,1] => [3,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 1
[4,2,1,1,3,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[5,1,1,1,3,1,1] => [5,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[2,2,2,3,2,1,1] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[3,1,2,3,2,1,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[2,3,1,3,2,1,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[3,2,1,3,2,1,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[4,1,1,3,2,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[2,2,3,2,2,1,1] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[3,1,3,2,2,1,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[2,3,2,2,2,1,1] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[3,2,2,2,2,1,1] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[4,1,2,2,2,1,1] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[2,4,1,2,2,1,1] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[3,3,1,2,2,1,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[4,2,1,2,2,1,1] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[5,1,1,2,2,1,1] => [5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[2,2,4,1,2,1,1] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[3,1,4,1,2,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[2,3,3,1,2,1,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[3,2,3,1,2,1,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[4,1,3,1,2,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[2,4,2,1,2,1,1] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[3,3,2,1,2,1,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[4,2,2,1,2,1,1] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[5,1,2,1,2,1,1] => [5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[2,5,1,1,2,1,1] => [5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[3,4,1,1,2,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[4,3,1,1,2,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[5,2,1,1,2,1,1] => [5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[6,1,1,1,2,1,1] => [6,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[2,2,2,4,1,1,1] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[3,1,2,4,1,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[2,3,1,4,1,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[3,2,1,4,1,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[4,1,1,4,1,1,1] => [4,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[2,2,3,3,1,1,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[3,1,3,3,1,1,1] => [3,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 1
[2,3,2,3,1,1,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[3,2,2,3,1,1,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[4,1,2,3,1,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[2,4,1,3,1,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[3,3,1,3,1,1,1] => [3,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 1
[4,2,1,3,1,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[5,1,1,3,1,1,1] => [5,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[2,2,4,2,1,1,1] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[3,1,4,2,1,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[2,3,3,2,1,1,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[3,2,3,2,1,1,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[4,1,3,2,1,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[2,4,2,2,1,1,1] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[3,3,2,2,1,1,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[4,2,2,2,1,1,1] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[5,1,2,2,1,1,1] => [5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[2,5,1,2,1,1,1] => [5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[3,4,1,2,1,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[4,3,1,2,1,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[5,2,1,2,1,1,1] => [5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[6,1,1,2,1,1,1] => [6,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[2,2,5,1,1,1,1] => [5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[3,1,5,1,1,1,1] => [5,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[2,3,4,1,1,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[3,2,4,1,1,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[4,1,4,1,1,1,1] => [4,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[2,4,3,1,1,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[3,3,3,1,1,1,1] => [3,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 1
[4,2,3,1,1,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[5,1,3,1,1,1,1] => [5,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[2,5,2,1,1,1,1] => [5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[3,4,2,1,1,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[4,3,2,1,1,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[5,2,2,1,1,1,1] => [5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[6,1,2,1,1,1,1] => [6,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[2,6,1,1,1,1,1] => [6,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[3,5,1,1,1,1,1] => [5,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[4,4,1,1,1,1,1] => [4,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[5,3,1,1,1,1,1] => [5,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[6,2,1,1,1,1,1] => [6,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[7,1,1,1,1,1,1] => [7,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[2,2,1,2,1,2,1,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[2,2,1,1,1,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[2,1,2,1,1,1,2,1,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[2,1,2,1,2,1,1,2] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[2,1,2,1,2,2,1,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[2,1,2,1,1,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[2,1,1,2,1,1,1,2,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[2,1,1,2,1,1,2,1,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[2,1,1,2,1,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[2,1,1,1,2,1,1,1,2] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[2,1,1,1,2,1,1,2,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[2,1,1,1,2,1,2,1,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[2,1,1,1,2,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,2,1,2,1,1,2,1,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,2,1,1,2,1,2,1,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,2,1,1,1,2,1,1,2] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,2,1,1,1,2,2,1,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,2,1,1,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,2,2,1,1,1,2,1,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,2,2,2,1,2,1,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[1,2,2,1,2,1,1,2] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[1,2,2,1,2,2,1,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[1,2,1,2,1,1,1,2,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,2,1,2,2,1,1,2] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[1,2,1,2,2,2,1,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[1,2,1,2,1,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,2,1,1,2,1,1,1,2] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,2,1,1,2,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,2,1,1,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,2,1,1,1,2,1,2] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,1,2,1,1,2,1,1,2] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,1,2,1,1,2,2,1,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,1,2,1,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,2,2,1,1,1,2,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,1,2,2,1,1,2,1,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,1,2,1,2,1,1,1,2] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,1,2,1,2,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,1,1,2,1,1,1,2,2] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,1,1,2,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,2,1,1,2,1,2] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,1,1,2,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,2,1,2,1,1,2] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,1,1,2,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,2,2,1,1,1,2] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,1,1,2,2,1,2,1,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,1,1,2,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,2,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,2,1,2,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[2,1,1,1,1,1,1,3] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[2,1,1,1,1,1,2,2] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[2,1,1,1,1,2,1,2] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[2,1,1,1,2,1,1,2] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[2,1,1,2,1,1,1,2] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[2,1,2,1,1,1,1,2] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[2,2,1,1,1,1,1,2] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[3,1,1,1,1,1,1,2] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,2,2,4,2,1] => [4,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[1,2,4,2,2,1] => [4,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[1,2,5,2,2] => [5,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[1,3,5,2,1] => [5,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[1,4,2,2,2,1] => [4,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[1,5,2,2,2] => [5,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[1,5,3,2,1] => [5,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[2,5,2,2,1] => [5,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[2,6,2,2] => [6,2,2,2] => [2,2,2] => [2,2] => 2
[2,2,5,2,1] => [5,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[6,2,2,2] => [6,2,2,2] => [2,2,2] => [2,2] => 2
[2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[1,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[1,2,2,1,2,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,2,1,2,2,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,1,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,2,1,1,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,2,1,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[1,9,1] => [9,1,1] => [1,1] => [1] => 1
[1,1,1,1,1,1,1,2,2,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,2,2,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,2,1,1,2,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,2,1,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,2,2,2,3,1,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,2,2,3,1,2,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,2,2,4,1,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,2,3,1,2,2,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,2,3,1,3,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,2,3,2,1,2,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,2,4,1,1,2,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,2,3,2,2,1,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,2,3,3,1,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,2,4,2,1,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,2,5,1,1,1,1] => [5,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,3,1,2,2,2,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,3,1,3,1,2,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,3,1,3,2,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,3,2,1,3,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,4,1,1,2,2,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,4,1,1,3,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,3,2,2,1,2,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,3,3,1,1,2,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,4,1,2,1,2,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,4,2,1,1,2,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,5,1,1,1,2,1] => [5,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,3,2,3,1,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,3,3,1,2,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,3,4,1,1,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,4,1,2,2,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,4,1,3,1,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,5,1,1,2,1,1] => [5,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,4,2,2,1,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,4,3,1,1,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,5,2,1,1,1,1] => [5,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,6,1,1,1,1,1] => [6,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[2,1,2,2,3,1,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[2,1,2,3,1,2,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[2,1,2,3,2,1,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[2,1,2,4,1,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[2,1,3,1,2,2,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[2,1,3,1,3,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[2,1,3,2,1,2,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[2,1,4,1,1,2,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[2,1,3,2,2,1,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[2,1,3,3,1,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[2,1,4,1,2,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[2,1,4,2,1,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[2,1,5,1,1,1,1] => [5,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[2,2,1,2,3,1,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[2,2,1,3,1,2,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[2,2,1,3,2,1,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[2,2,1,4,1,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[3,1,1,2,2,2,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[3,1,1,3,1,2,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[3,1,1,3,2,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[2,2,2,1,3,1,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[2,3,1,1,2,2,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[2,3,1,1,3,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[3,1,2,1,3,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[3,2,1,1,2,2,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[3,2,1,1,3,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[4,1,1,1,2,2,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[4,1,1,1,3,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[2,2,3,1,1,2,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[2,3,1,2,1,2,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[2,3,2,1,1,2,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[2,4,1,1,1,2,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[3,1,2,2,1,2,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[3,1,3,1,1,2,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[3,2,1,2,1,2,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[4,1,1,2,1,2,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[3,2,2,1,1,2,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[3,3,1,1,1,2,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[4,1,2,1,1,2,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[4,2,1,1,1,2,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[5,1,1,1,1,2,1] => [5,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[2,2,2,3,1,1,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[2,2,3,1,2,1,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[2,2,3,2,1,1,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[2,2,4,1,1,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[2,3,1,2,2,1,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[2,3,1,3,1,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[2,3,2,1,2,1,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[2,4,1,1,2,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[2,3,2,2,1,1,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[2,3,3,1,1,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[2,4,1,2,1,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[2,4,2,1,1,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[2,5,1,1,1,1,1] => [5,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[3,1,2,3,1,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[3,1,3,1,2,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[3,1,4,1,1,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[3,2,1,2,2,1,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[3,2,1,3,1,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[4,1,1,2,2,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[4,1,1,3,1,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[3,3,1,1,2,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[4,1,2,1,2,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[4,2,1,1,2,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[5,1,1,1,2,1,1] => [5,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[3,2,2,2,1,1,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[3,2,3,1,1,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[3,4,1,1,1,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[4,1,2,2,1,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[4,1,3,1,1,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[4,2,1,2,1,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[4,2,2,1,1,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[4,3,1,1,1,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[5,1,2,1,1,1,1] => [5,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[5,2,1,1,1,1,1] => [5,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[6,1,1,1,1,1,1] => [6,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,2,2,4,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,3,1,3,1,3,1] => [3,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 1
[1,3,1,2,3,2,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,3,1,2,1,4,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,3,1,1,1,5,1] => [5,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,2,3,2,1,3,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,2,3,1,3,2,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,2,3,1,1,4,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,2,2,3,2,2,1] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[1,2,2,1,4,2,1] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,2,2,1,2,4,1] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,2,1,4,1,3,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,2,1,3,3,2,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,2,1,3,1,4,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,2,1,2,1,5,1] => [5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,2,1,1,5,2,1] => [5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,2,1,1,3,4,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,2,1,1,1,6,1] => [6,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,5,1,3,1] => [5,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,4,3,2,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,4,1,4,1] => [4,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,3,1,5,1] => [5,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,2,5,2,1] => [5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,2,3,4,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,2,1,6,1] => [6,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,7,1] => [7,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[1,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,2,2,1,1,1,1,2,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,1,1,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[1,1,2,3,2,3] => [3,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 1
[1,2,2,2,2,3] => [3,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 1
[5,1,1,1,1,2] => [5,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,2,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,3,1] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,3,1,1,1] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,5,1] => [5,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,2,1,2,1] => [2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,3,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,3,1,3,1] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,5,1,1,1] => [5,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,7,1] => [7,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,1,1,4,1,2,1] => [4,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,2,1,2,1,1,1] => [2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,2,1,4,1] => [4,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,2,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,2,3,2,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,3,1,1,1,3,1] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,3,1,3,1,1,1] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,3,1,5,1] => [5,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[1,3,1,2,1,2,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,5,1,1,1,1,1] => [5,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,5,1,3,1] => [5,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[1,7,1,1,1] => [7,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,6,1,2,1] => [6,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,4,1,2,1,1,1] => [4,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,4,1,4,1] => [4,4,1,1,1] => [4,1,1,1] => [1,1,1] => 1
[1,4,1,1,1,2,1] => [4,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,4,3,2,1] => [4,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[1,2,1,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,2,1,2,1,3,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,2,1,4,1,1,1] => [4,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,2,1,6,1] => [6,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,2,1,3,1,2,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,2,1,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,2,1,1,1,4,1] => [4,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,2,1,1,3,2,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,2,3,2,1,1,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,2,3,4,1] => [4,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[1,2,3,1,1,2,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,2,5,2,1] => [5,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,2,2,1,2,2,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,3,1] => [3,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,3,1,1,1] => [3,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,5,1] => [5,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,2,1,2,1] => [2,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,3,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,3,1,3,1] => [3,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,5,1,1,1] => [5,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,4,1,2,1] => [4,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,2,1,2,1,1,1] => [2,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,2,1,4,1] => [4,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,2,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,2,3,2,1] => [3,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,1,1,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[1,1,1,3,1,1,1,3,1] => [3,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,3,1,3,1,1,1] => [3,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,3,1,2,1,2,1] => [3,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,1,1,5,1,1,1,1,1] => [5,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,7,1,1,1] => [7,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,9,1] => [9,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,1,1,6,1,2,1] => [6,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,4,1,2,1,1,1] => [4,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,4,1,1,1,2,1] => [4,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,2,1,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[1,1,1,2,1,2,1,3,1] => [3,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,1,1,2,1,4,1,1,1] => [4,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,2,1,3,1,2,1] => [3,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,1,1,2,1,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[1,1,1,2,1,1,1,4,1] => [4,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,2,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[1,1,1,2,1,1,3,2,1] => [3,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,1,1,2,3,2,1,1,1] => [3,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,1,1,2,3,1,1,2,1] => [3,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,1,1,2,2,1,2,2,1] => [2,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 1
[1,3,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[1,3,1,1,1,1,1,3,1] => [3,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,3,1,1,1,3,1,1,1] => [3,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,3,1,1,1,2,1,2,1] => [3,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,3,1,3,1,1,1,1,1] => [3,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,3,1,5,1,1,1] => [5,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,3,1,7,1] => [7,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[1,3,1,4,1,2,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,3,1,2,1,2,1,1,1] => [3,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,3,1,2,1,1,1,2,1] => [3,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,5,1,1,1,1,1,1,1] => [5,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,5,1,1,1,3,1] => [5,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,5,1,3,1,1,1] => [5,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,5,1,5,1] => [5,5,1,1,1] => [5,1,1,1] => [1,1,1] => 1
[1,5,1,2,1,2,1] => [5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,7,1,1,1,1,1] => [7,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,7,1,3,1] => [7,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[1,9,1,1,1] => [9,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,11,1] => [11,1,1] => [1,1] => [1] => 1
[1,8,1,2,1] => [8,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,6,1,2,1,1,1] => [6,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,6,1,4,1] => [6,4,1,1,1] => [4,1,1,1] => [1,1,1] => 1
[1,6,1,1,1,2,1] => [6,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,6,3,2,1] => [6,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[1,4,1,2,1,1,1,1,1] => [4,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,4,1,2,1,3,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,4,1,4,1,1,1] => [4,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,4,1,6,1] => [6,4,1,1,1] => [4,1,1,1] => [1,1,1] => 1
[1,4,1,3,1,2,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,4,1,1,1,2,1,1,1] => [4,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,4,1,1,1,4,1] => [4,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,4,1,1,1,1,1,2,1] => [4,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,4,1,1,3,2,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,4,3,2,1,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,4,3,4,1] => [4,4,3,1,1] => [4,3,1,1] => [3,1,1] => 1
[1,4,3,1,1,2,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,4,5,2,1] => [5,4,2,1,1] => [4,2,1,1] => [2,1,1] => 1
[1,4,2,1,2,2,1] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,2,1,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[1,2,1,2,1,1,1,3,1] => [3,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,2,1,2,1,3,1,1,1] => [3,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,2,1,2,1,2,1,2,1] => [2,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 1
[1,2,1,4,1,1,1,1,1] => [4,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,2,1,6,1,1,1] => [6,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,2,1,8,1] => [8,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,2,1,5,1,2,1] => [5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,2,1,3,1,2,1,1,1] => [3,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,2,1,3,1,1,1,2,1] => [3,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,2,1,1,1,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[1,2,1,1,1,2,1,3,1] => [3,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,2,1,1,1,4,1,1,1] => [4,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,2,1,1,1,3,1,2,1] => [3,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,2,1,1,1,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[1,2,1,1,1,1,1,4,1] => [4,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,2,1,1,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[1,2,1,1,1,1,3,2,1] => [3,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,2,1,1,3,2,1,1,1] => [3,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,2,1,1,3,1,1,2,1] => [3,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,2,1,1,2,1,2,2,1] => [2,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 1
[1,2,3,2,1,1,1,1,1] => [3,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,2,3,4,1,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,2,3,6,1] => [6,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[1,2,3,3,1,2,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,2,3,1,1,2,1,1,1] => [3,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,2,3,1,1,1,1,2,1] => [3,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,2,5,2,1,1,1] => [5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,2,5,4,1] => [5,4,2,1,1] => [4,2,1,1] => [2,1,1] => 1
[1,2,5,1,1,2,1] => [5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,2,7,2,1] => [7,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,2,4,1,2,2,1] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,2,2,1,2,2,1,1,1] => [2,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 1
[1,2,2,1,2,1,1,2,1] => [2,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 1
[1,2,2,1,1,1,2,2,1] => [2,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 1
[1,1,9] => [9,1,1] => [1,1] => [1] => 1
[1,1,1,1,1,1,1,1,3] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[1,1,2,2,1,2,3] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,1,1,1,2,2,2,1,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,2,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,2,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[1,1,1,2,2,2,3] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,6,4] => [6,4,1] => [4,1] => [1] => 1
[1,5,5] => [5,5,1] => [5,1] => [1] => 1
[1,4,6] => [6,4,1] => [4,1] => [1] => 1
[1,3,7] => [7,3,1] => [3,1] => [1] => 1
[1,2,8] => [8,2,1] => [2,1] => [1] => 1
[1,2,1,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,2,1,1,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,2,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,2,1,2,1,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,2,1,2,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,2,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,2,2,2,2,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,1,2,2,2,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,1,2,2,3,1,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,2,2,1,2,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,1,2,3,2,1,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,2,1,2,2,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,1,3,2,2,1,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,2,2,2,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,2,2,2,2,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,1,2,2,2,4] => [4,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[1,1,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,2,5,1,1] => [5,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,5,2,1,1] => [5,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,2,2,1,1] => [2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,4,2,2,1,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
search for individual values
searching the database for the individual values of this statistic
Description
The greatest common divisor of the parts of the partition.
Map
to partition
Description
Sends a composition to the partition obtained by sorting the entries.
Map
first row removal
Description
Removes the first entry of an integer partition
searching the database
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