Identifier
-
Mp00027:
Dyck paths
—to partition⟶
Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001901: Integer partitions ⟶ ℤ
Values
[1,0,1,0,1,0,1,0] => [3,2,1] => [2,1] => [1] => 1
[1,0,1,0,1,1,0,0] => [2,2,1] => [2,1] => [1] => 1
[1,0,1,1,0,0,1,0] => [3,1,1] => [1,1] => [1] => 1
[1,0,1,1,0,1,0,0] => [2,1,1] => [1,1] => [1] => 1
[1,0,1,1,1,0,0,0] => [1,1,1] => [1,1] => [1] => 1
[1,0,1,0,1,0,1,0,1,0] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => [3,2,1] => [2,1] => 1
[1,0,1,0,1,1,0,0,1,0] => [4,2,2,1] => [2,2,1] => [2,1] => 1
[1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => [2,2,1] => [2,1] => 1
[1,0,1,1,0,0,1,0,1,0] => [4,3,1,1] => [3,1,1] => [1,1] => 1
[1,0,1,1,0,0,1,1,0,0] => [3,3,1,1] => [3,1,1] => [1,1] => 1
[1,0,1,1,0,1,0,0,1,0] => [4,2,1,1] => [2,1,1] => [1,1] => 1
[1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => [2,1,1] => [1,1] => 1
[1,0,1,1,0,1,1,0,0,0] => [2,2,1,1] => [2,1,1] => [1,1] => 1
[1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => [1,1,1] => [1,1] => 1
[1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => [1,1,1] => [1,1] => 1
[1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => [1,1,1] => [1,1] => 1
[1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => [1,1,1] => [1,1] => 1
[1,1,0,0,1,0,1,0,1,0] => [4,3,2] => [3,2] => [2] => 1
[1,1,0,0,1,0,1,1,0,0] => [3,3,2] => [3,2] => [2] => 1
[1,1,0,0,1,1,0,0,1,0] => [4,2,2] => [2,2] => [2] => 1
[1,1,0,0,1,1,0,1,0,0] => [3,2,2] => [2,2] => [2] => 1
[1,1,0,0,1,1,1,0,0,0] => [2,2,2] => [2,2] => [2] => 1
[1,1,0,1,0,0,1,0,1,0] => [4,3,1] => [3,1] => [1] => 1
[1,1,0,1,0,0,1,1,0,0] => [3,3,1] => [3,1] => [1] => 1
[1,1,0,1,0,1,0,0,1,0] => [4,2,1] => [2,1] => [1] => 1
[1,1,0,1,0,1,0,1,0,0] => [3,2,1] => [2,1] => [1] => 1
[1,1,0,1,0,1,1,0,0,0] => [2,2,1] => [2,1] => [1] => 1
[1,1,0,1,1,0,0,0,1,0] => [4,1,1] => [1,1] => [1] => 1
[1,1,0,1,1,0,0,1,0,0] => [3,1,1] => [1,1] => [1] => 1
[1,1,0,1,1,0,1,0,0,0] => [2,1,1] => [1,1] => [1] => 1
[1,1,0,1,1,1,0,0,0,0] => [1,1,1] => [1,1] => [1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => [4,3,2,1] => [3,2,1] => 3
[1,0,1,0,1,0,1,0,1,1,0,0] => [4,4,3,2,1] => [4,3,2,1] => [3,2,1] => 3
[1,0,1,0,1,0,1,1,0,0,1,0] => [5,3,3,2,1] => [3,3,2,1] => [3,2,1] => 3
[1,0,1,0,1,0,1,1,0,1,0,0] => [4,3,3,2,1] => [3,3,2,1] => [3,2,1] => 3
[1,0,1,0,1,0,1,1,1,0,0,0] => [3,3,3,2,1] => [3,3,2,1] => [3,2,1] => 3
[1,0,1,0,1,1,0,0,1,0,1,0] => [5,4,2,2,1] => [4,2,2,1] => [2,2,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [4,4,2,2,1] => [4,2,2,1] => [2,2,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,0] => [5,3,2,2,1] => [3,2,2,1] => [2,2,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [4,3,2,2,1] => [3,2,2,1] => [2,2,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => [3,3,2,2,1] => [3,2,2,1] => [2,2,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => [5,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [4,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => [3,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,1] => [4,3,1,1] => [3,1,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [4,4,3,1,1] => [4,3,1,1] => [3,1,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,0] => [5,3,3,1,1] => [3,3,1,1] => [3,1,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,0] => [4,3,3,1,1] => [3,3,1,1] => [3,1,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [3,3,3,1,1] => [3,3,1,1] => [3,1,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,1] => [4,2,1,1] => [2,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,0] => [4,4,2,1,1] => [4,2,1,1] => [2,1,1] => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,0] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[1,0,1,1,0,1,1,0,0,0,1,0] => [5,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,0,1,1,0,1,1,0,1,0,0,0] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,0,1,1,1,0,0,0,1,0,1,0] => [5,4,1,1,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => [4,4,1,1,1] => [4,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [5,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => [4,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => [3,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,1,0,0,0,0,1,0] => [5,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2] => [4,3,2] => [3,2] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [4,4,3,2] => [4,3,2] => [3,2] => 1
[1,1,0,0,1,0,1,1,0,0,1,0] => [5,3,3,2] => [3,3,2] => [3,2] => 1
[1,1,0,0,1,0,1,1,0,1,0,0] => [4,3,3,2] => [3,3,2] => [3,2] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [3,3,3,2] => [3,3,2] => [3,2] => 1
[1,1,0,0,1,1,0,0,1,0,1,0] => [5,4,2,2] => [4,2,2] => [2,2] => 1
[1,1,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => [4,2,2] => [2,2] => 1
[1,1,0,0,1,1,0,1,0,0,1,0] => [5,3,2,2] => [3,2,2] => [2,2] => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [4,3,2,2] => [3,2,2] => [2,2] => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => [3,3,2,2] => [3,2,2] => [2,2] => 1
[1,1,0,0,1,1,1,0,0,0,1,0] => [5,2,2,2] => [2,2,2] => [2,2] => 1
[1,1,0,0,1,1,1,0,0,1,0,0] => [4,2,2,2] => [2,2,2] => [2,2] => 1
[1,1,0,0,1,1,1,0,1,0,0,0] => [3,2,2,2] => [2,2,2] => [2,2] => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,2,2] => [2,2,2] => [2,2] => 1
[1,1,0,1,0,0,1,0,1,0,1,0] => [5,4,3,1] => [4,3,1] => [3,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [4,4,3,1] => [4,3,1] => [3,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,3,1] => [3,3,1] => [3,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [4,3,3,1] => [3,3,1] => [3,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,3,3,1] => [3,3,1] => [3,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => [5,4,2,1] => [4,2,1] => [2,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,0] => [4,4,2,1] => [4,2,1] => [2,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => [5,3,2,1] => [3,2,1] => [2,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,0] => [3,3,2,1] => [3,2,1] => [2,1] => 1
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,2,2,1] => [2,2,1] => [2,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => [4,2,2,1] => [2,2,1] => [2,1] => 1
>>> Load all 2045 entries. <<<[1,1,0,1,0,1,1,0,1,0,0,0] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,2,2,1] => [2,2,1] => [2,1] => 1
[1,1,0,1,1,0,0,0,1,0,1,0] => [5,4,1,1] => [4,1,1] => [1,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,0] => [4,4,1,1] => [4,1,1] => [1,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => [5,3,1,1] => [3,1,1] => [1,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => [4,3,1,1] => [3,1,1] => [1,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,0] => [3,3,1,1] => [3,1,1] => [1,1] => 1
[1,1,0,1,1,0,1,0,0,0,1,0] => [5,2,1,1] => [2,1,1] => [1,1] => 1
[1,1,0,1,1,0,1,0,0,1,0,0] => [4,2,1,1] => [2,1,1] => [1,1] => 1
[1,1,0,1,1,0,1,0,1,0,0,0] => [3,2,1,1] => [2,1,1] => [1,1] => 1
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,1,1] => [2,1,1] => [1,1] => 1
[1,1,0,1,1,1,0,0,0,0,1,0] => [5,1,1,1] => [1,1,1] => [1,1] => 1
[1,1,0,1,1,1,0,0,0,1,0,0] => [4,1,1,1] => [1,1,1] => [1,1] => 1
[1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,1,1] => [1,1,1] => [1,1] => 1
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,1] => [1,1,1] => [1,1] => 1
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1] => [1,1,1] => [1,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => [5,4,3] => [4,3] => [3] => 1
[1,1,1,0,0,0,1,0,1,1,0,0] => [4,4,3] => [4,3] => [3] => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => [3,3] => [3] => 1
[1,1,1,0,0,0,1,1,0,1,0,0] => [4,3,3] => [3,3] => [3] => 1
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => [3,3] => [3] => 1
[1,1,1,0,0,1,0,0,1,0,1,0] => [5,4,2] => [4,2] => [2] => 1
[1,1,1,0,0,1,0,0,1,1,0,0] => [4,4,2] => [4,2] => [2] => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [5,3,2] => [3,2] => [2] => 1
[1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => [3,2] => [2] => 1
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,3,2] => [3,2] => [2] => 1
[1,1,1,0,0,1,1,0,0,0,1,0] => [5,2,2] => [2,2] => [2] => 1
[1,1,1,0,0,1,1,0,0,1,0,0] => [4,2,2] => [2,2] => [2] => 1
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,2] => [2,2] => [2] => 1
[1,1,1,0,0,1,1,1,0,0,0,0] => [2,2,2] => [2,2] => [2] => 1
[1,1,1,0,1,0,0,0,1,0,1,0] => [5,4,1] => [4,1] => [1] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,4,1] => [4,1] => [1] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [5,3,1] => [3,1] => [1] => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => [3,1] => [1] => 1
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,3,1] => [3,1] => [1] => 1
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,1] => [2,1] => [1] => 1
[1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => [2,1] => [1] => 1
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1] => [2,1] => [1] => 1
[1,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1] => [2,1] => [1] => 1
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,1,1] => [1,1] => [1] => 1
[1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,1] => [1,1] => [1] => 1
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,1,1] => [1,1] => [1] => 1
[1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,1] => [1,1] => [1] => 1
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1] => [1,1] => [1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => 34
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [5,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => 34
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => 34
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => 34
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => 34
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,3,2,1] => [5,3,3,2,1] => [3,3,2,1] => 7
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2,1] => [5,3,3,2,1] => [3,3,2,1] => 7
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,3,2,1] => [4,3,3,2,1] => [3,3,2,1] => 7
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2,1] => [4,3,3,2,1] => [3,3,2,1] => 7
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => [4,3,3,2,1] => [3,3,2,1] => 7
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => 7
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => 7
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => 7
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => 7
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2,1] => [5,4,2,2,1] => [4,2,2,1] => 8
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2,1] => [5,4,2,2,1] => [4,2,2,1] => 8
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2,1] => [4,4,2,2,1] => [4,2,2,1] => 8
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2,1] => [4,4,2,2,1] => [4,2,2,1] => 8
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => [4,4,2,2,1] => [4,2,2,1] => 8
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,2,1] => [5,3,2,2,1] => [3,2,2,1] => 4
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2,1] => [5,3,2,2,1] => [3,2,2,1] => 4
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,2,1] => [4,3,2,2,1] => [3,2,2,1] => 4
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2,1] => [4,3,2,2,1] => [3,2,2,1] => 4
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => [4,3,2,2,1] => [3,2,2,1] => 4
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2,1] => [3,3,2,2,1] => [3,2,2,1] => 4
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2,1] => [3,3,2,2,1] => [3,2,2,1] => 4
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => [3,3,2,2,1] => [3,2,2,1] => 4
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => [3,3,2,2,1] => [3,2,2,1] => 4
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2,1] => [5,2,2,2,1] => [2,2,2,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => [5,2,2,2,1] => [2,2,2,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,2,2,1] => [4,2,2,2,1] => [2,2,2,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2,1] => [4,2,2,2,1] => [2,2,2,1] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => [4,2,2,2,1] => [2,2,2,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,1] => [5,4,3,1,1] => [4,3,1,1] => 10
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3,1,1] => [5,4,3,1,1] => [4,3,1,1] => 10
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3,1,1] => [4,4,3,1,1] => [4,3,1,1] => 10
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3,1,1] => [4,4,3,1,1] => [4,3,1,1] => 10
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1,1] => [4,4,3,1,1] => [4,3,1,1] => 10
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3,1,1] => [5,3,3,1,1] => [3,3,1,1] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => [5,3,3,1,1] => [3,3,1,1] => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3,1,1] => [4,3,3,1,1] => [3,3,1,1] => 3
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => [4,3,3,1,1] => [3,3,1,1] => 3
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => [4,3,3,1,1] => [3,3,1,1] => 3
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1,1] => [3,3,3,1,1] => [3,3,1,1] => 3
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => [3,3,3,1,1] => [3,3,1,1] => 3
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => [3,3,3,1,1] => [3,3,1,1] => 3
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => [3,3,3,1,1] => [3,3,1,1] => 3
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1,1] => [5,4,2,1,1] => [4,2,1,1] => 6
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [5,5,4,2,1,1] => [5,4,2,1,1] => [4,2,1,1] => 6
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [6,4,4,2,1,1] => [4,4,2,1,1] => [4,2,1,1] => 6
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => [4,4,2,1,1] => [4,2,1,1] => 6
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => [4,4,2,1,1] => [4,2,1,1] => 6
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1,1] => [5,3,2,1,1] => [3,2,1,1] => 3
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1,1] => [5,3,2,1,1] => [3,2,1,1] => 3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => 3
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => 3
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => 3
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => 3
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => 3
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => 3
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => 3
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,2,1,1] => [5,2,2,1,1] => [2,2,1,1] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => [5,2,2,1,1] => [2,2,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,2,1,1] => [4,2,2,1,1] => [2,2,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2,1,1] => [4,2,2,1,1] => [2,2,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => [4,2,2,1,1] => [2,2,1,1] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,1,1] => [5,4,1,1,1] => [4,1,1,1] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1,1] => [5,4,1,1,1] => [4,1,1,1] => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1,1] => [4,4,1,1,1] => [4,1,1,1] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => [4,4,1,1,1] => [4,1,1,1] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => [4,4,1,1,1] => [4,1,1,1] => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,1,1] => [5,3,1,1,1] => [3,1,1,1] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1,1] => [5,3,1,1,1] => [3,1,1,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,1,1] => [5,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1,1] => [5,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2] => [5,4,3,2] => [4,3,2] => 10
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [5,5,4,3,2] => [5,4,3,2] => [4,3,2] => 10
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [6,4,4,3,2] => [4,4,3,2] => [4,3,2] => 10
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [5,4,4,3,2] => [4,4,3,2] => [4,3,2] => 10
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2] => [4,4,3,2] => [4,3,2] => 10
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,3,2] => [5,3,3,2] => [3,3,2] => 3
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => [5,3,3,2] => [3,3,2] => 3
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,3,2] => [4,3,3,2] => [3,3,2] => 3
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2] => [4,3,3,2] => [3,3,2] => 3
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => [4,3,3,2] => [3,3,2] => 3
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2] => [3,3,3,2] => [3,3,2] => 3
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2] => [3,3,3,2] => [3,3,2] => 3
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2] => [3,3,3,2] => [3,3,2] => 3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2] => [3,3,3,2] => [3,3,2] => 3
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2] => [5,4,2,2] => [4,2,2] => 3
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => [5,4,2,2] => [4,2,2] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => [4,4,2,2] => [4,2,2] => 3
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => [4,4,2,2] => [4,2,2] => 3
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => [4,4,2,2] => [4,2,2] => 3
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,2] => [5,3,2,2] => [3,2,2] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2] => [5,3,2,2] => [3,2,2] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,2] => [4,3,2,2] => [3,2,2] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2] => [4,3,2,2] => [3,2,2] => 2
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => [4,3,2,2] => [3,2,2] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2] => [3,3,2,2] => [3,2,2] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2] => [3,3,2,2] => [3,2,2] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => [3,3,2,2] => [3,2,2] => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => [3,3,2,2] => [3,2,2] => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => [5,2,2,2] => [2,2,2] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => [5,2,2,2] => [2,2,2] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,2,2] => [4,2,2,2] => [2,2,2] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2] => [4,2,2,2] => [2,2,2] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => [4,2,2,2] => [2,2,2] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,2,2] => [3,2,2,2] => [2,2,2] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2] => [3,2,2,2] => [2,2,2] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2] => [3,2,2,2] => [2,2,2] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => [3,2,2,2] => [2,2,2] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => [2,2,2,2] => [2,2,2] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2] => [2,2,2,2] => [2,2,2] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2] => [2,2,2,2] => [2,2,2] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => [2,2,2,2] => [2,2,2] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1] => [5,4,3,1] => [4,3,1] => 8
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3,1] => [5,4,3,1] => [4,3,1] => 8
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3,1] => [4,4,3,1] => [4,3,1] => 8
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3,1] => [4,4,3,1] => [4,3,1] => 8
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1] => [4,4,3,1] => [4,3,1] => 8
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3,1] => [5,3,3,1] => [3,3,1] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1] => [5,3,3,1] => [3,3,1] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3,1] => [4,3,3,1] => [3,3,1] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1] => [4,3,3,1] => [3,3,1] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => [4,3,3,1] => [3,3,1] => 2
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1] => [3,3,3,1] => [3,3,1] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1] => [3,3,3,1] => [3,3,1] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1] => [3,3,3,1] => [3,3,1] => 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1] => [3,3,3,1] => [3,3,1] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1] => [5,4,2,1] => [4,2,1] => 5
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [5,5,4,2,1] => [5,4,2,1] => [4,2,1] => 5
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [6,4,4,2,1] => [4,4,2,1] => [4,2,1] => 5
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1] => [4,4,2,1] => [4,2,1] => 5
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1] => [4,4,2,1] => [4,2,1] => 5
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1] => [5,3,2,1] => [3,2,1] => 3
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1] => [5,3,2,1] => [3,2,1] => 3
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1] => [4,3,2,1] => [3,2,1] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1] => [4,3,2,1] => [3,2,1] => 3
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1] => [4,3,2,1] => [3,2,1] => 3
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2,1] => [3,3,2,1] => [3,2,1] => 3
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1] => [3,3,2,1] => [3,2,1] => 3
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1] => [3,3,2,1] => [3,2,1] => 3
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1] => [3,3,2,1] => [3,2,1] => 3
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,2,1] => [5,2,2,1] => [2,2,1] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1] => [5,2,2,1] => [2,2,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,2,1] => [4,2,2,1] => [2,2,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2,1] => [4,2,2,1] => [2,2,1] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1] => [4,2,2,1] => [2,2,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2,1] => [3,2,2,1] => [2,2,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1] => [3,2,2,1] => [2,2,1] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1] => [3,2,2,1] => [2,2,1] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => [3,2,2,1] => [2,2,1] => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,1] => [5,4,1,1] => [4,1,1] => 2
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1] => [5,4,1,1] => [4,1,1] => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1] => [4,4,1,1] => [4,1,1] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1] => [4,4,1,1] => [4,1,1] => 2
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1] => [4,4,1,1] => [4,1,1] => 2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,1] => [5,3,1,1] => [3,1,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1] => [5,3,1,1] => [3,1,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,1] => [4,3,1,1] => [3,1,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,1] => [4,3,1,1] => [3,1,1] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1] => [4,3,1,1] => [3,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1,1] => [3,3,1,1] => [3,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1] => [3,3,1,1] => [3,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1] => [3,3,1,1] => [3,1,1] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => [3,3,1,1] => [3,1,1] => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,1] => [5,2,1,1] => [2,1,1] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1] => [5,2,1,1] => [2,1,1] => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,1] => [4,2,1,1] => [2,1,1] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,1] => [4,2,1,1] => [2,1,1] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1] => [4,2,1,1] => [2,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1,1] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1] => [5,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1,1] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1] => [4,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3] => [5,4,3] => [4,3] => 3
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3] => [5,4,3] => [4,3] => 3
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3] => [4,4,3] => [4,3] => 3
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3] => [4,4,3] => [4,3] => 3
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3] => [4,4,3] => [4,3] => 3
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => [5,3,3] => [3,3] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => [5,3,3] => [3,3] => 1
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3] => [4,3,3] => [3,3] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3] => [4,3,3] => [3,3] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => [4,3,3] => [3,3] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => [3,3,3] => [3,3] => 1
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3] => [3,3,3] => [3,3] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3] => [3,3,3] => [3,3] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => [3,3,3] => [3,3] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2] => [5,4,2] => [4,2] => 2
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [5,5,4,2] => [5,4,2] => [4,2] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [6,4,4,2] => [4,4,2] => [4,2] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2] => [4,4,2] => [4,2] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2] => [4,4,2] => [4,2] => 2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2] => [5,3,2] => [3,2] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2] => [5,3,2] => [3,2] => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2] => [4,3,2] => [3,2] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2] => [4,3,2] => [3,2] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2] => [4,3,2] => [3,2] => 1
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2] => [3,3,2] => [3,2] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2] => [3,3,2] => [3,2] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2] => [3,3,2] => [3,2] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2] => [3,3,2] => [3,2] => 1
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [6,5,2,2] => [5,2,2] => [2,2] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2] => [5,2,2] => [2,2] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [6,4,2,2] => [4,2,2] => [2,2] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2] => [4,2,2] => [2,2] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2] => [4,2,2] => [2,2] => 1
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2] => [3,2,2] => [2,2] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2] => [3,2,2] => [2,2] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2] => [3,2,2] => [2,2] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => [3,2,2] => [2,2] => 1
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2] => [2,2,2] => [2,2] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2] => [2,2,2] => [2,2] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2] => [2,2,2] => [2,2] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2] => [2,2,2] => [2,2] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => [2,2,2] => [2,2] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1] => [5,4,1] => [4,1] => 2
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1] => [5,4,1] => [4,1] => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1] => [4,4,1] => [4,1] => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1] => [4,4,1] => [4,1] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1] => [4,4,1] => [4,1] => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1] => [5,3,1] => [3,1] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1] => [5,3,1] => [3,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1] => [4,3,1] => [3,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1] => [4,3,1] => [3,1] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1] => [4,3,1] => [3,1] => 1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1] => [3,3,1] => [3,1] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1] => [3,3,1] => [3,1] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1] => [3,3,1] => [3,1] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1] => [3,3,1] => [3,1] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1] => [5,2,1] => [2,1] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1] => [5,2,1] => [2,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1] => [4,2,1] => [2,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1] => [4,2,1] => [2,1] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1] => [4,2,1] => [2,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1] => [3,2,1] => [2,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1] => [3,2,1] => [2,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1] => [3,2,1] => [2,1] => 1
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1] => [2,2,1] => [2,1] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1] => [2,2,1] => [2,1] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1] => [2,2,1] => [2,1] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1] => [2,2,1] => [2,1] => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1] => [5,1,1] => [1,1] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1] => [5,1,1] => [1,1] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1] => [4,1,1] => [1,1] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1] => [4,1,1] => [1,1] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1] => [4,1,1] => [1,1] => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1] => [3,1,1] => [1,1] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1] => [3,1,1] => [1,1] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1] => [3,1,1] => [1,1] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1] => [3,1,1] => [1,1] => 1
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1] => [2,1,1] => [1,1] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1] => [2,1,1] => [1,1] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1] => [2,1,1] => [1,1] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => [2,1,1] => [1,1] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1] => [2,1,1] => [1,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1] => [1,1,1] => [1,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1] => [1,1,1] => [1,1] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1] => [1,1,1] => [1,1] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1] => [1,1,1] => [1,1] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1] => [1,1,1] => [1,1] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1] => [1,1,1] => [1,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [6,5,4] => [5,4] => [4] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,5,4] => [5,4] => [4] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => [4,4] => [4] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,4,4] => [4,4] => [4] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => [4,4] => [4] => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [6,5,3] => [5,3] => [3] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [5,5,3] => [5,3] => [3] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [6,4,3] => [4,3] => [3] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [5,4,3] => [4,3] => [3] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,4,3] => [4,3] => [3] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [6,3,3] => [3,3] => [3] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [5,3,3] => [3,3] => [3] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,3] => [3,3] => [3] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,3,3] => [3,3] => [3] => 1
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [6,5,2] => [5,2] => [2] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,5,2] => [5,2] => [2] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [6,4,2] => [4,2] => [2] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,4,2] => [4,2] => [2] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,4,2] => [4,2] => [2] => 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2] => [3,2] => [2] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [5,3,2] => [3,2] => [2] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,2] => [3,2] => [2] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,3,2] => [3,2] => [2] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,2,2] => [2,2] => [2] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [5,2,2] => [2,2] => [2] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,2] => [2,2] => [2] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2] => [2,2] => [2] => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,2,2] => [2,2] => [2] => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [6,5,1] => [5,1] => [1] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,5,1] => [5,1] => [1] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [6,4,1] => [4,1] => [1] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,4,1] => [4,1] => [1] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,4,1] => [4,1] => [1] => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,1] => [3,1] => [1] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,3,1] => [3,1] => [1] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,3,1] => [3,1] => [1] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [3,3,1] => [3,1] => [1] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,2,1] => [2,1] => [1] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => [2,1] => [1] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,2,1] => [2,1] => [1] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => [2,1] => [1] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,2,1] => [2,1] => [1] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,1,1] => [1,1] => [1] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,1] => [1,1] => [1] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,1,1] => [1,1] => [1] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [3,1,1] => [1,1] => [1] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,1,1] => [1,1] => [1] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1] => [1,1] => [1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1] => [6,5,4,3,2,1] => [5,4,3,2,1] => 2526
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,6,5,4,3,2,1] => [6,5,4,3,2,1] => [5,4,3,2,1] => 2526
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,5,5,4,3,2,1] => [5,5,4,3,2,1] => [5,4,3,2,1] => 2526
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3,2,1] => [5,5,4,3,2,1] => [5,4,3,2,1] => 2526
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,5,5,4,3,2,1] => [5,5,4,3,2,1] => [5,4,3,2,1] => 2526
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,4,3,2,1] => [6,4,4,3,2,1] => [4,4,3,2,1] => 397
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [6,6,4,4,3,2,1] => [6,4,4,3,2,1] => [4,4,3,2,1] => 397
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,4,3,2,1] => [5,4,4,3,2,1] => [4,4,3,2,1] => 397
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,4,3,2,1] => [5,4,4,3,2,1] => [4,4,3,2,1] => 397
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [5,5,4,4,3,2,1] => [5,4,4,3,2,1] => [4,4,3,2,1] => 397
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [7,4,4,4,3,2,1] => [4,4,4,3,2,1] => [4,4,3,2,1] => 397
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,4,4,3,2,1] => [4,4,4,3,2,1] => [4,4,3,2,1] => 397
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,4,4,3,2,1] => [4,4,4,3,2,1] => [4,4,3,2,1] => 397
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,2,1] => [4,4,4,3,2,1] => [4,4,3,2,1] => 397
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [6,6,5,3,3,2,1] => [6,5,3,3,2,1] => [5,3,3,2,1] => 422
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,3,2,1] => [5,4,3,3,2,1] => [4,3,3,2,1] => 161
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,3,3,2,1] => [5,3,3,3,2,1] => [3,3,3,2,1] => 24
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,3,3,2,1] => [4,3,3,3,2,1] => [3,3,3,2,1] => 24
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,3,3,2,1] => [4,3,3,3,2,1] => [3,3,3,2,1] => 24
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,3,3,3,2,1] => [3,3,3,3,2,1] => [3,3,3,2,1] => 24
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2,1] => [3,3,3,3,2,1] => [3,3,3,2,1] => 24
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [6,6,5,4,2,2,1] => [6,5,4,2,2,1] => [5,4,2,2,1] => 494
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [6,5,5,4,2,2,1] => [5,5,4,2,2,1] => [5,4,2,2,1] => 494
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,4,2,2,1] => [5,4,4,2,2,1] => [4,4,2,2,1] => 90
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,2,1] => [5,4,3,2,2,1] => [4,3,2,2,1] => 78
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,2,2,1] => [5,4,3,2,2,1] => [4,3,2,2,1] => 78
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => [3,3,3,2,2,1] => [3,3,2,2,1] => 19
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,2,2,1] => [6,5,2,2,2,1] => [5,2,2,2,1] => 32
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2,2,1] => [5,4,2,2,2,1] => [4,2,2,2,1] => 14
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,2,2,1] => [5,3,2,2,2,1] => [3,2,2,2,1] => 6
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,2,2,1] => [4,3,2,2,2,1] => [3,2,2,2,1] => 6
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2,2,1] => [4,3,2,2,2,1] => [3,2,2,2,1] => 6
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2,1] => [3,3,2,2,2,1] => [3,2,2,2,1] => 6
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2,1] => [3,3,2,2,2,1] => [3,2,2,2,1] => 6
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2,2,1] => [5,2,2,2,2,1] => [2,2,2,2,1] => 1
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2,1] => [4,2,2,2,2,1] => [2,2,2,2,1] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,2,1] => [3,2,2,2,2,1] => [2,2,2,2,1] => 1
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,2,1] => [3,2,2,2,2,1] => [2,2,2,2,1] => 1
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2,1] => [3,2,2,2,2,1] => [2,2,2,2,1] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => 1
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => 1
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => 1
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,1,1] => [6,5,4,3,1,1] => [5,4,3,1,1] => 631
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [6,6,5,4,3,1,1] => [6,5,4,3,1,1] => [5,4,3,1,1] => 631
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3,1,1] => [5,5,4,3,1,1] => [5,4,3,1,1] => 631
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => [3,3,3,3,1,1] => [3,3,3,1,1] => 8
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [6,6,5,4,2,1,1] => [6,5,4,2,1,1] => [5,4,2,1,1] => 273
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [6,5,5,4,2,1,1] => [5,5,4,2,1,1] => [5,4,2,1,1] => 273
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,2,1,1] => [4,4,4,2,1,1] => [4,4,2,1,1] => 62
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,1] => [5,4,3,2,1,1] => [4,3,2,1,1] => 50
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,2,1,1] => [5,4,3,2,1,1] => [4,3,2,1,1] => 50
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,2,1,1] => [4,4,3,2,1,1] => [4,3,2,1,1] => 50
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1,1] => [3,3,3,2,1,1] => [3,3,2,1,1] => 12
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => [3,3,3,2,1,1] => [3,3,2,1,1] => 12
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => [4,3,2,2,1,1] => [3,2,2,1,1] => 5
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => [3,3,2,2,1,1] => [3,2,2,1,1] => 5
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => [3,3,2,2,1,1] => [3,2,2,1,1] => 5
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => [3,3,2,2,1,1] => [3,2,2,1,1] => 5
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1,1] => [4,2,2,2,1,1] => [2,2,2,1,1] => 1
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => [4,2,2,2,1,1] => [2,2,2,1,1] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,1,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => 1
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => 1
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1,1,1] => [6,5,4,1,1,1] => [5,4,1,1,1] => 67
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [6,5,5,4,1,1,1] => [5,5,4,1,1,1] => [5,4,1,1,1] => 67
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,1,1] => [5,4,3,1,1,1] => [4,3,1,1,1] => 11
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => [4,3,3,1,1,1] => [3,3,1,1,1] => 3
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1,1] => [3,3,3,1,1,1] => [3,3,1,1,1] => 3
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => [3,3,3,1,1,1] => [3,3,1,1,1] => 3
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => [3,3,3,1,1,1] => [3,3,1,1,1] => 3
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,1,1,1] => [6,5,2,1,1,1] => [5,2,1,1,1] => 12
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [5,5,5,2,1,1,1] => [5,5,2,1,1,1] => [5,2,1,1,1] => 12
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,1,1,1] => [5,4,2,1,1,1] => [4,2,1,1,1] => 6
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,1,1] => [5,4,2,1,1,1] => [4,2,1,1,1] => 6
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1,1] => [4,4,2,1,1,1] => [4,2,1,1,1] => 6
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,1,1,1] => [6,3,2,1,1,1] => [3,2,1,1,1] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,1,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => 3
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => 3
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => 3
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => 3
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => 3
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => 3
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1,1] => [5,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,1,1,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1,1,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,1,1,1] => [5,4,1,1,1,1] => [4,1,1,1,1] => 2
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1] => [4,4,1,1,1,1] => [4,1,1,1,1] => 2
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => [4,4,1,1,1,1] => [4,1,1,1,1] => 2
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1,1] => [5,3,1,1,1,1] => [3,1,1,1,1] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,1,1,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1,1,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => 1
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1,1,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 1
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 1
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1,1,1,1] => [6,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,1,1,1] => [5,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1,1,1] => [5,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,1,1,1,1] => [6,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1,1] => [6,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2] => [6,5,4,3,2] => [5,4,3,2] => 631
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,6,5,4,3,2] => [6,5,4,3,2] => [5,4,3,2] => 631
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,5,5,4,3,2] => [5,5,4,3,2] => [5,4,3,2] => 631
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3,2] => [5,5,4,3,2] => [5,4,3,2] => 631
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,5,5,4,3,2] => [5,5,4,3,2] => [5,4,3,2] => 631
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,4,3,2] => [6,4,4,3,2] => [4,4,3,2] => 120
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,4,3,2] => [5,4,4,3,2] => [4,4,3,2] => 120
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,3,2] => [5,4,3,3,2] => [4,3,3,2] => 56
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,3,3,2] => [4,3,3,3,2] => [3,3,3,2] => 8
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3,2] => [3,3,3,3,2] => [3,3,3,2] => 8
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2] => [3,3,3,3,2] => [3,3,3,2] => 8
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,2] => [5,4,3,2,2] => [4,3,2,2] => 28
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,2,2] => [4,4,3,2,2] => [4,3,2,2] => 28
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => [3,3,3,2,2] => [3,3,2,2] => 6
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => [3,3,3,2,2] => [3,3,2,2] => 6
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,2,2] => [6,5,2,2,2] => [5,2,2,2] => 11
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2,2] => [5,4,2,2,2] => [4,2,2,2] => 4
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2,2] => [4,3,2,2,2] => [3,2,2,2] => 2
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,2] => [4,3,2,2,2] => [3,2,2,2] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,2] => [3,3,2,2,2] => [3,2,2,2] => 2
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => [3,3,2,2,2] => [3,2,2,2] => 2
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => [3,3,2,2,2] => [3,2,2,2] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => [6,2,2,2,2] => [2,2,2,2] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,2] => [4,2,2,2,2] => [2,2,2,2] => 1
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2] => [4,2,2,2,2] => [2,2,2,2] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,2] => [3,2,2,2,2] => [2,2,2,2] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,2] => [3,2,2,2,2] => [2,2,2,2] => 1
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,2] => [3,2,2,2,2] => [2,2,2,2] => 1
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2] => [3,2,2,2,2] => [2,2,2,2] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 1
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 1
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,1] => [6,5,4,3,1] => [5,4,3,1] => 368
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [6,6,5,4,3,1] => [6,5,4,3,1] => [5,4,3,1] => 368
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3,1] => [5,5,4,3,1] => [5,4,3,1] => 368
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,1] => [4,4,4,3,1] => [4,4,3,1] => 84
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3,1] => [3,3,3,3,1] => [3,3,3,1] => 5
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1] => [3,3,3,3,1] => [3,3,3,1] => 5
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,1] => [6,5,4,2,1] => [5,4,2,1] => 196
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [5,5,5,4,2,1] => [5,5,4,2,1] => [5,4,2,1] => 196
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,2,1] => [4,4,4,2,1] => [4,4,2,1] => 39
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,1] => [6,5,3,2,1] => [5,3,2,1] => 85
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [6,6,5,3,2,1] => [6,5,3,2,1] => [5,3,2,1] => 85
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [5,5,5,3,2,1] => [5,5,3,2,1] => [5,3,2,1] => 85
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,1] => [6,4,3,2,1] => [4,3,2,1] => 34
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [6,6,4,3,2,1] => [6,4,3,2,1] => [4,3,2,1] => 34
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => 34
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => 34
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => 34
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [7,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => 34
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => 34
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => 34
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => 34
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,3,2,1] => [6,3,3,2,1] => [3,3,2,1] => 7
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,2,1] => [5,3,3,2,1] => [3,3,2,1] => 7
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2,1] => [5,3,3,2,1] => [3,3,2,1] => 7
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,3,2,1] => [4,3,3,2,1] => [3,3,2,1] => 7
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3,2,1] => [4,3,3,2,1] => [3,3,2,1] => 7
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2,1] => [4,3,3,2,1] => [3,3,2,1] => 7
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2,1] => [4,3,3,2,1] => [3,3,2,1] => 7
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [7,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => 7
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => 7
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => 7
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => 7
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => 7
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,2,1] => [6,5,2,2,1] => [5,2,2,1] => 19
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2,1] => [5,4,2,2,1] => [4,2,2,1] => 8
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,2,1] => [5,4,2,2,1] => [4,2,2,1] => 8
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,2,1] => [4,4,2,2,1] => [4,2,2,1] => 8
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2,1] => [4,4,2,2,1] => [4,2,2,1] => 8
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,1] => [4,4,2,2,1] => [4,2,2,1] => 8
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,2,1] => [6,3,2,2,1] => [3,2,2,1] => 4
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,2,1] => [5,3,2,2,1] => [3,2,2,1] => 4
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,2,1] => [5,3,2,2,1] => [3,2,2,1] => 4
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,2,1] => [4,3,2,2,1] => [3,2,2,1] => 4
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2,1] => [4,3,2,2,1] => [3,2,2,1] => 4
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1] => [4,3,2,2,1] => [3,2,2,1] => 4
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2,1] => [3,3,2,2,1] => [3,2,2,1] => 4
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1] => [3,3,2,2,1] => [3,2,2,1] => 4
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1] => [3,3,2,2,1] => [3,2,2,1] => 4
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1] => [3,3,2,2,1] => [3,2,2,1] => 4
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,2,2,1] => [6,2,2,2,1] => [2,2,2,1] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2,1] => [5,2,2,2,1] => [2,2,2,1] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2,1] => [5,2,2,2,1] => [2,2,2,1] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,2,1] => [4,2,2,2,1] => [2,2,2,1] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1] => [4,2,2,2,1] => [2,2,2,1] => 1
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1] => [4,2,2,2,1] => [2,2,2,1] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 1
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 1
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 1
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 1
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 1
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1,1] => [6,5,4,1,1] => [5,4,1,1] => 62
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,1] => [5,4,3,1,1] => [4,3,1,1] => 10
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,1,1] => [5,4,3,1,1] => [4,3,1,1] => 10
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,1,1] => [4,4,3,1,1] => [4,3,1,1] => 10
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,1,1] => [4,4,3,1,1] => [4,3,1,1] => 10
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1,1] => [4,4,3,1,1] => [4,3,1,1] => 10
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,1,1] => [5,3,3,1,1] => [3,3,1,1] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1,1] => [5,3,3,1,1] => [3,3,1,1] => 3
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3,1,1] => [4,3,3,1,1] => [3,3,1,1] => 3
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1,1] => [4,3,3,1,1] => [3,3,1,1] => 3
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => [4,3,3,1,1] => [3,3,1,1] => 3
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,1,1] => [3,3,3,1,1] => [3,3,1,1] => 3
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1] => [3,3,3,1,1] => [3,3,1,1] => 3
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1] => [3,3,3,1,1] => [3,3,1,1] => 3
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1] => [3,3,3,1,1] => [3,3,1,1] => 3
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,1,1] => [6,5,2,1,1] => [5,2,1,1] => 11
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,1] => [5,4,2,1,1] => [4,2,1,1] => 6
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,1,1] => [5,4,2,1,1] => [4,2,1,1] => 6
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,1,1] => [4,4,2,1,1] => [4,2,1,1] => 6
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1,1] => [4,4,2,1,1] => [4,2,1,1] => 6
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1] => [4,4,2,1,1] => [4,2,1,1] => 6
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,1,1] => [6,3,2,1,1] => [3,2,1,1] => 3
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1,1] => [5,3,2,1,1] => [3,2,1,1] => 3
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,1,1] => [5,3,2,1,1] => [3,2,1,1] => 3
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => 3
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => 3
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => 3
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => 3
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => 3
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => 3
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => 3
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => 3
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => 3
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,1,1] => [5,2,2,1,1] => [2,2,1,1] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1] => [5,2,2,1,1] => [2,2,1,1] => 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,2,1,1] => [4,2,2,1,1] => [2,2,1,1] => 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,1,1] => [4,2,2,1,1] => [2,2,1,1] => 1
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1,1] => [4,2,2,1,1] => [2,2,1,1] => 1
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1] => [4,2,2,1,1] => [2,2,1,1] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 1
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 1
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 1
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [7,6,5,1,1,1] => [6,5,1,1,1] => [5,1,1,1] => 4
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,1,1] => [5,4,1,1,1] => [4,1,1,1] => 2
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1,1] => [5,4,1,1,1] => [4,1,1,1] => 2
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1,1,1] => [4,4,1,1,1] => [4,1,1,1] => 2
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1] => [4,4,1,1,1] => [4,1,1,1] => 2
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1] => [4,4,1,1,1] => [4,1,1,1] => 2
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,1,1] => [5,3,1,1,1] => [3,1,1,1] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1] => [5,3,1,1,1] => [3,1,1,1] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => 1
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 1
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 1
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 1
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1,1,1] => [6,2,1,1,1] => [2,1,1,1] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,1,1] => [5,2,1,1,1] => [2,1,1,1] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,1,1] => [5,2,1,1,1] => [2,1,1,1] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1,1] => [5,2,1,1,1] => [2,1,1,1] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 1
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,1,1,1] => [6,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1] => [6,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3] => [6,5,4,3] => [5,4,3] => 132
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [6,6,5,4,3] => [6,5,4,3] => [5,4,3] => 132
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3] => [5,5,4,3] => [5,4,3] => 132
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [5,4,4,4,3] => [4,4,4,3] => [4,4,3] => 25
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,3,3] => [4,3,3,3] => [3,3,3] => 2
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => [4,3,3,3] => [3,3,3] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [7,3,3,3,3] => [3,3,3,3] => [3,3,3] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,3,3,3] => [3,3,3,3] => [3,3,3] => 2
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3] => [3,3,3,3] => [3,3,3] => 2
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => [3,3,3,3] => [3,3,3] => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2] => [6,5,4,2] => [5,4,2] => 62
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,2] => [4,4,4,2] => [4,4,2] => 12
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2] => [6,5,3,2] => [5,3,2] => 27
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2] => [6,4,3,2] => [4,3,2] => 10
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2] => [5,4,3,2] => [4,3,2] => 10
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2] => [5,4,3,2] => [4,3,2] => 10
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,2] => [5,4,3,2] => [4,3,2] => 10
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,2] => [4,4,3,2] => [4,3,2] => 10
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,2] => [4,4,3,2] => [4,3,2] => 10
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,2] => [4,4,3,2] => [4,3,2] => 10
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,2] => [5,3,3,2] => [3,3,2] => 3
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2] => [5,3,3,2] => [3,3,2] => 3
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3,2] => [4,3,3,2] => [3,3,2] => 3
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2] => [4,3,3,2] => [3,3,2] => 3
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2] => [4,3,3,2] => [3,3,2] => 3
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,2] => [3,3,3,2] => [3,3,2] => 3
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2] => [3,3,3,2] => [3,3,2] => 3
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2] => [3,3,3,2] => [3,3,2] => 3
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2] => [3,3,3,2] => [3,3,2] => 3
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2] => [5,4,2,2] => [4,2,2] => 3
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,2] => [5,4,2,2] => [4,2,2] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,2] => [4,4,2,2] => [4,2,2] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2] => [4,4,2,2] => [4,2,2] => 3
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2] => [4,4,2,2] => [4,2,2] => 3
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,2] => [5,3,2,2] => [3,2,2] => 2
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,2] => [5,3,2,2] => [3,2,2] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,2] => [4,3,2,2] => [3,2,2] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2] => [4,3,2,2] => [3,2,2] => 2
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2] => [4,3,2,2] => [3,2,2] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,2] => [3,3,2,2] => [3,2,2] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2] => [3,3,2,2] => [3,2,2] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2] => [3,3,2,2] => [3,2,2] => 2
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2] => [3,3,2,2] => [3,2,2] => 2
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2] => [3,3,2,2] => [3,2,2] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2] => [5,2,2,2] => [2,2,2] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2] => [5,2,2,2] => [2,2,2] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,2,2] => [4,2,2,2] => [2,2,2] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,2] => [4,2,2,2] => [2,2,2] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2] => [4,2,2,2] => [2,2,2] => 1
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => [4,2,2,2] => [2,2,2] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,2] => [3,2,2,2] => [2,2,2] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2] => [3,2,2,2] => [2,2,2] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2] => [3,2,2,2] => [2,2,2] => 1
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2] => [3,2,2,2] => [2,2,2] => 1
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2] => [3,2,2,2] => [2,2,2] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2] => [2,2,2,2] => [2,2,2] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2] => [2,2,2,2] => [2,2,2] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2] => [2,2,2,2] => [2,2,2] => 1
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 1
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2] => [2,2,2,2] => [2,2,2] => 1
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2] => [2,2,2,2] => [2,2,2] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1] => [6,5,4,1] => [5,4,1] => 38
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,1] => [4,4,4,1] => [4,4,1] => 7
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,1] => [5,4,3,1] => [4,3,1] => 8
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1] => [5,4,3,1] => [4,3,1] => 8
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,1] => [5,4,3,1] => [4,3,1] => 8
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,1] => [4,4,3,1] => [4,3,1] => 8
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,1] => [4,4,3,1] => [4,3,1] => 8
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1] => [4,4,3,1] => [4,3,1] => 8
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,1] => [5,3,3,1] => [3,3,1] => 2
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1] => [5,3,3,1] => [3,3,1] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3,1] => [4,3,3,1] => [3,3,1] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1] => [4,3,3,1] => [3,3,1] => 2
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1] => [4,3,3,1] => [3,3,1] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [7,3,3,3,1] => [3,3,3,1] => [3,3,1] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,1] => [3,3,3,1] => [3,3,1] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1] => [3,3,3,1] => [3,3,1] => 2
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1] => [3,3,3,1] => [3,3,1] => 2
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1] => [3,3,3,1] => [3,3,1] => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,1] => [6,5,2,1] => [5,2,1] => 9
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [6,6,5,2,1] => [6,5,2,1] => [5,2,1] => 9
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,1] => [6,4,2,1] => [4,2,1] => 5
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [6,6,4,2,1] => [6,4,2,1] => [4,2,1] => 5
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,1] => [5,4,2,1] => [4,2,1] => 5
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1] => [5,4,2,1] => [4,2,1] => 5
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,1] => [5,4,2,1] => [4,2,1] => 5
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,1] => [4,4,2,1] => [4,2,1] => 5
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1] => [4,4,2,1] => [4,2,1] => 5
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1] => [4,4,2,1] => [4,2,1] => 5
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,1] => [6,3,2,1] => [3,2,1] => 3
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [6,6,3,2,1] => [6,3,2,1] => [3,2,1] => 3
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1] => [5,3,2,1] => [3,2,1] => 3
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,1] => [5,3,2,1] => [3,2,1] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,1] => [4,3,2,1] => [3,2,1] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1] => [4,3,2,1] => [3,2,1] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1] => [4,3,2,1] => [3,2,1] => 3
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1] => [4,3,2,1] => [3,2,1] => 3
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,1] => [3,3,2,1] => [3,2,1] => 3
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1] => [3,3,2,1] => [3,2,1] => 3
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1] => [3,3,2,1] => [3,2,1] => 3
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1] => [3,3,2,1] => [3,2,1] => 3
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1] => [3,3,2,1] => [3,2,1] => 3
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,1] => [6,2,2,1] => [2,2,1] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,2,1] => [5,2,2,1] => [2,2,1] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,1] => [5,2,2,1] => [2,2,1] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1] => [5,2,2,1] => [2,2,1] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,2,1] => [4,2,2,1] => [2,2,1] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,1] => [4,2,2,1] => [2,2,1] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1] => [4,2,2,1] => [2,2,1] => 1
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1] => [4,2,2,1] => [2,2,1] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,1] => [3,2,2,1] => [2,2,1] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1] => [3,2,2,1] => [2,2,1] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1] => [3,2,2,1] => [2,2,1] => 1
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1] => [3,2,2,1] => [2,2,1] => 1
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1] => [3,2,2,1] => [2,2,1] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1,1] => [5,5,1,1] => [5,1,1] => 4
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,1] => [5,4,1,1] => [4,1,1] => 2
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1] => [5,4,1,1] => [4,1,1] => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [7,4,4,1,1] => [4,4,1,1] => [4,1,1] => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1,1] => [4,4,1,1] => [4,1,1] => 2
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1] => [4,4,1,1] => [4,1,1] => 2
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1] => [4,4,1,1] => [4,1,1] => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [6,6,3,1,1] => [6,3,1,1] => [3,1,1] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1,1] => [5,3,1,1] => [3,1,1] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,1] => [5,3,1,1] => [3,1,1] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1] => [5,3,1,1] => [3,1,1] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,1] => [4,3,1,1] => [3,1,1] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,1] => [4,3,1,1] => [3,1,1] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1] => [4,3,1,1] => [3,1,1] => 1
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1] => [4,3,1,1] => [3,1,1] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1,1] => [3,3,1,1] => [3,1,1] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1] => [3,3,1,1] => [3,1,1] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1] => [3,3,1,1] => [3,1,1] => 1
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1] => [3,3,1,1] => [3,1,1] => 1
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1] => [3,3,1,1] => [3,1,1] => 1
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [7,6,2,1,1] => [6,2,1,1] => [2,1,1] => 1
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1,1] => [6,2,1,1] => [2,1,1] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,1] => [5,2,1,1] => [2,1,1] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,1] => [5,2,1,1] => [2,1,1] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1] => [5,2,1,1] => [2,1,1] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,1] => [4,2,1,1] => [2,1,1] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,1] => [4,2,1,1] => [2,1,1] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1] => [4,2,1,1] => [2,1,1] => 1
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1] => [4,2,1,1] => [2,1,1] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,1,1] => [6,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1] => [6,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,1,1] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1,1] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,1,1] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1,1] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4] => [6,5,4] => [5,4] => 11
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [6,5,5,4] => [5,5,4] => [5,4] => 11
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4] => [4,4,4] => [4,4] => 3
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => [4,4,4] => [4,4] => 3
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3] => [6,5,3] => [5,3] => 6
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3] => [6,4,3] => [4,3] => 3
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3] => [5,4,3] => [4,3] => 3
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3] => [5,4,3] => [4,3] => 3
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3] => [5,4,3] => [4,3] => 3
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3] => [4,4,3] => [4,3] => 3
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3] => [4,4,3] => [4,3] => 3
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3] => [4,4,3] => [4,3] => 3
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3] => [5,3,3] => [3,3] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3] => [5,3,3] => [3,3] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [7,4,3,3] => [4,3,3] => [3,3] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3] => [4,3,3] => [3,3] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3] => [4,3,3] => [3,3] => 1
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3] => [4,3,3] => [3,3] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [7,3,3,3] => [3,3,3] => [3,3] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3] => [3,3,3] => [3,3] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3] => [3,3,3] => [3,3] => 1
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3] => [3,3,3] => [3,3] => 1
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3] => [3,3,3] => [3,3] => 1
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2] => [6,5,2] => [5,2] => 4
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,5,5,2] => [5,5,2] => [5,2] => 4
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2] => [5,4,2] => [4,2] => 2
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2] => [5,4,2] => [4,2] => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [7,4,4,2] => [4,4,2] => [4,2] => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2] => [4,4,2] => [4,2] => 2
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2] => [4,4,2] => [4,2] => 2
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2] => [4,4,2] => [4,2] => 2
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [6,6,3,2] => [6,3,2] => [3,2] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2] => [5,3,2] => [3,2] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2] => [5,3,2] => [3,2] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2] => [5,3,2] => [3,2] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2] => [4,3,2] => [3,2] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2] => [4,3,2] => [3,2] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2] => [4,3,2] => [3,2] => 1
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2] => [4,3,2] => [3,2] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2] => [3,3,2] => [3,2] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2] => [3,3,2] => [3,2] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2] => [3,3,2] => [3,2] => 1
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2] => [3,3,2] => [3,2] => 1
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2] => [3,3,2] => [3,2] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [7,6,2,2] => [6,2,2] => [2,2] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2] => [6,2,2] => [2,2] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,2] => [5,2,2] => [2,2] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2] => [5,2,2] => [2,2] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2] => [5,2,2] => [2,2] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,2] => [4,2,2] => [2,2] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2] => [4,2,2] => [2,2] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2] => [4,2,2] => [2,2] => 1
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2] => [4,2,2] => [2,2] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2] => [3,2,2] => [2,2] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2] => [3,2,2] => [2,2] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2] => [3,2,2] => [2,2] => 1
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2] => [3,2,2] => [2,2] => 1
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => [3,2,2] => [2,2] => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2] => [2,2,2] => [2,2] => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2] => [2,2,2] => [2,2] => 1
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2] => [2,2,2] => [2,2] => 1
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2] => [2,2,2] => [2,2] => 1
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2] => [2,2,2] => [2,2] => 1
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2] => [2,2,2] => [2,2] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [6,5,5,1] => [5,5,1] => [5,1] => 3
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1] => [5,5,1] => [5,1] => 3
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [6,6,4,1] => [6,4,1] => [4,1] => 2
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [7,5,4,1] => [5,4,1] => [4,1] => 2
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1] => [5,4,1] => [4,1] => 2
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1] => [5,4,1] => [4,1] => 2
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [7,4,4,1] => [4,4,1] => [4,1] => 2
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1] => [4,4,1] => [4,1] => 2
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1] => [4,4,1] => [4,1] => 2
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1] => [4,4,1] => [4,1] => 2
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [7,6,3,1] => [6,3,1] => [3,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [6,6,3,1] => [6,3,1] => [3,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1] => [5,3,1] => [3,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1] => [5,3,1] => [3,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1] => [5,3,1] => [3,1] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1] => [4,3,1] => [3,1] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1] => [4,3,1] => [3,1] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1] => [4,3,1] => [3,1] => 1
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1] => [4,3,1] => [3,1] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1] => [3,3,1] => [3,1] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1] => [3,3,1] => [3,1] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1] => [3,3,1] => [3,1] => 1
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1] => [3,3,1] => [3,1] => 1
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1] => [3,3,1] => [3,1] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [7,6,2,1] => [6,2,1] => [2,1] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1] => [6,2,1] => [2,1] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1] => [5,2,1] => [2,1] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1] => [5,2,1] => [2,1] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1] => [5,2,1] => [2,1] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1] => [4,2,1] => [2,1] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1] => [4,2,1] => [2,1] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1] => [4,2,1] => [2,1] => 1
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1] => [4,2,1] => [2,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1] => [3,2,1] => [2,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1] => [3,2,1] => [2,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1] => [3,2,1] => [2,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1] => [3,2,1] => [2,1] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1] => [2,2,1] => [2,1] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1] => [2,2,1] => [2,1] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1] => [2,2,1] => [2,1] => 1
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1] => [2,2,1] => [2,1] => 1
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1] => [2,2,1] => [2,1] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,1] => [6,1,1] => [1,1] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1] => [6,1,1] => [1,1] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,1] => [5,1,1] => [1,1] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1] => [5,1,1] => [1,1] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1] => [5,1,1] => [1,1] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,1] => [4,1,1] => [1,1] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1] => [4,1,1] => [1,1] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1] => [4,1,1] => [1,1] => 1
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1] => [4,1,1] => [1,1] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,1] => [3,1,1] => [1,1] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1] => [3,1,1] => [1,1] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1] => [3,1,1] => [1,1] => 1
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1] => [3,1,1] => [1,1] => 1
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1] => [3,1,1] => [1,1] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1] => [2,1,1] => [1,1] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1] => [2,1,1] => [1,1] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1] => [2,1,1] => [1,1] => 1
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1] => [2,1,1] => [1,1] => 1
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1] => [2,1,1] => [1,1] => 1
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1] => [2,1,1] => [1,1] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1] => [1,1,1] => [1,1] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1] => [1,1,1] => [1,1] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1] => [1,1,1] => [1,1] => 1
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1] => [1,1,1] => [1,1] => 1
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1] => [1,1,1] => [1,1] => 1
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1] => [1,1,1] => [1,1] => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1] => [1,1,1] => [1,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [7,6,5] => [6,5] => [5] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [6,6,5] => [6,5] => [5] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [7,5,5] => [5,5] => [5] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [6,5,5] => [5,5] => [5] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => [5,5] => [5] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [7,6,4] => [6,4] => [4] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [6,6,4] => [6,4] => [4] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [7,5,4] => [5,4] => [4] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [6,5,4] => [5,4] => [4] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,5,4] => [5,4] => [4] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [7,4,4] => [4,4] => [4] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [6,4,4] => [4,4] => [4] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,4] => [4,4] => [4] => 1
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [4,4,4] => [4,4] => [4] => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [7,6,3] => [6,3] => [3] => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,6,3] => [6,3] => [3] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [7,5,3] => [5,3] => [3] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [6,5,3] => [5,3] => [3] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,5,3] => [5,3] => [3] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [7,4,3] => [4,3] => [3] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [6,4,3] => [4,3] => [3] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3] => [4,3] => [3] => 1
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [4,4,3] => [4,3] => [3] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [7,3,3] => [3,3] => [3] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [6,3,3] => [3,3] => [3] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,3,3] => [3,3] => [3] => 1
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [4,3,3] => [3,3] => [3] => 1
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => [3,3] => [3] => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [7,6,2] => [6,2] => [2] => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,6,2] => [6,2] => [2] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [7,5,2] => [5,2] => [2] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [6,5,2] => [5,2] => [2] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,5,2] => [5,2] => [2] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [7,4,2] => [4,2] => [2] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [6,4,2] => [4,2] => [2] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [5,4,2] => [4,2] => [2] => 1
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [4,4,2] => [4,2] => [2] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [7,3,2] => [3,2] => [2] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [6,3,2] => [3,2] => [2] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,3,2] => [3,2] => [2] => 1
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [4,3,2] => [3,2] => [2] => 1
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [3,3,2] => [3,2] => [2] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [7,2,2] => [2,2] => [2] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [6,2,2] => [2,2] => [2] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,2,2] => [2,2] => [2] => 1
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [4,2,2] => [2,2] => [2] => 1
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [3,2,2] => [2,2] => [2] => 1
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [2,2,2] => [2,2] => [2] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [7,6,1] => [6,1] => [1] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,6,1] => [6,1] => [1] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [7,5,1] => [5,1] => [1] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [6,5,1] => [5,1] => [1] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [5,5,1] => [5,1] => [1] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [7,4,1] => [4,1] => [1] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [6,4,1] => [4,1] => [1] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,4,1] => [4,1] => [1] => 1
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [4,4,1] => [4,1] => [1] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [7,3,1] => [3,1] => [1] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [6,3,1] => [3,1] => [1] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,3,1] => [3,1] => [1] => 1
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [4,3,1] => [3,1] => [1] => 1
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [3,3,1] => [3,1] => [1] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,2,1] => [2,1] => [1] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [6,2,1] => [2,1] => [1] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,2,1] => [2,1] => [1] => 1
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [4,2,1] => [2,1] => [1] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => [2,1] => [1] => 1
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [2,2,1] => [2,1] => [1] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,1,1] => [1,1] => [1] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [6,1,1] => [1,1] => [1] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,1,1] => [1,1] => [1] => 1
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [4,1,1] => [1,1] => [1] => 1
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [3,1,1] => [1,1] => [1] => 1
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,1,1] => [1,1] => [1] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1] => [1,1] => [1] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1] => [1,1] => [1] => 1
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [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
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,1] => [1,1] => [1] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1] => [2,1] => [1] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1,1] => [1,1,1] => [1,1] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [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
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [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
[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [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
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1,1] => [1,1] => [1] => 1
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0] => [9,2,1] => [2,1] => [1] => 1
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,1,1] => [1,1,1] => [1,1] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1] => [3,1] => [1] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => [8,2,2] => [2,2] => [2] => 1
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1,1] => [2,1,1] => [1,1] => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [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
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [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
[1,0,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [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
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [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
[1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [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
[1,0,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [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
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,1,0] => [10,2,1] => [2,1] => [1] => 1
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,1,0] => [9,3,1] => [3,1] => [1] => 1
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,1,0] => [9,2,1,1] => [2,1,1] => [1,1] => 1
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0] => [8,4,1] => [4,1] => [1] => 1
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2] => [3,2] => [2] => 1
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1,1] => [3,1,1] => [1,1] => 1
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0] => [8,2,2,1] => [2,2,1] => [2,1] => 1
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [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
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [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
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [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
[1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [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
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [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
[1,0,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [3,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => 1
[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [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
[1,0,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [2,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,1,0] => [9,3,2] => [3,2] => [2] => 1
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,1,0] => [9,2,2,1] => [2,2,1] => [2,1] => 1
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0] => [8,4,2] => [4,2] => [2] => 1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,1,0] => [8,3,3] => [3,3] => [3] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2,1] => [3,2,1] => [2,1] => 1
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0] => [8,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [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
[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [4,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [4,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [3,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => 1
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => 1
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => 1
[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,2,2,2,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,1,0] => [9,3,3] => [3,3] => [3] => 1
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0] => [9,3,2,1] => [3,2,1] => [2,1] => 1
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,2,2] => [2,2,2] => [2,2] => 1
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0] => [8,6,1] => [6,1] => [1] => 1
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,1,0] => [8,4,2,1] => [4,2,1] => [2,1] => 1
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,1,0] => [8,4,1,1,1] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,0] => [8,3,3,1] => [3,3,1] => [3,1] => 1
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,2] => [3,2,2] => [2,2] => 1
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [7,7,1] => [7,1] => [1] => 1
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [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
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [5,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [4,4,2,1,1,1,1,1] => [4,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [4,4,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => 1
[1,0,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [3,3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => 3
[1,0,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [3,3,2,2,1,1,1,1,1] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 1
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => 1
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => 1
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => [2,2,2,2,2,1] => 1
[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2,1,1,1] => [2,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => 1
[1,0,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,2,2,2,2,1,1,1,1,1] => [2,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => 1
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [8,7,1] => [7,1] => [1] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,1,0] => [8,5,3] => [5,3] => [3] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0] => [8,5,2,1] => [5,2,1] => [2,1] => 1
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [8,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [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
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0] => [7,7,2] => [7,2] => [2] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => [7,7,1,1] => [7,1,1] => [1,1] => 1
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [6,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [5,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 1
[1,0,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,4,2,2,1,1,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,2,2,1,1,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => 1
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => 1
[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => 1
[1,0,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [3,3,3,2,1,1,1,1,1] => [3,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => 3
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2,2,2,2,2] => [3,2,2,2,2,2] => [2,2,2,2,2] => 1
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => [2,2,2,2,2,1] => 1
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2,2] => [2,2,2,2,2,2,2] => [2,2,2,2,2,2] => 1
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2,1,1] => [2,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => 1
[1,0,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2,1,1,1,1] => [2,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,1,0] => [9,7,1] => [7,1] => [1] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0] => [8,8,1] => [8,1] => [1] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0] => [8,7,2] => [7,2] => [2] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0] => [8,7,1,1] => [7,1,1] => [1,1] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,1,0] => [8,6,2,1] => [6,2,1] => [2,1] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,0] => [8,5,4] => [5,4] => [4] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [8,5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,1,0] => [8,4,3,2] => [4,3,2] => [3,2] => 1
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,1,0] => [8,3,3,3] => [3,3,3] => [3,3] => 1
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0] => [8,3,3,2,1] => [3,3,2,1] => [3,2,1] => 3
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [8,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,1,0,0] => [7,7,3] => [7,3] => [3] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0] => [7,7,2,1] => [7,2,1] => [2,1] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,7,1,1,1] => [7,1,1,1] => [1,1,1] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1,1,1,1,1,1] => [5,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [6,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => 1
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3,1,1,1,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => 1
[1,0,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,2,1,1,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [4,4,4,1,1,1,1,1] => [4,4,1,1,1,1,1] => [4,1,1,1,1,1] => 2
[1,0,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,4,3,2,1,1,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => 3
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,2,2,2,2] => [3,2,2,2,2,2] => [2,2,2,2,2] => 1
[1,0,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,2,2,2,1,1] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => 1
[1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => [2,2,2,2,2,1] => 1
[1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,2,1,1,1] => [3,3,3,2,1,1,1] => [3,3,2,1,1,1] => 13
[1,1,0,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,3,3,2,2,2,2] => [3,3,2,2,2,2] => [3,2,2,2,2] => 2
[1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2,2,2,2,2,1] => [3,2,2,2,2,2,1] => [2,2,2,2,2,1] => 1
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,2,2,2,2,2,2,2] => [2,2,2,2,2,2,2] => [2,2,2,2,2,2] => 1
[1,0,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,2,2,2,2,2,2,1,1] => [2,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => 1
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2,2,1] => [2,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => 1
[1,0,1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2,1,1,1] => [2,2,2,2,2,2,1,1,1] => [2,2,2,2,2,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,1] => [6,5,4,3,2,1] => [5,4,3,2,1] => 2526
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,6,5,4,3,2,1] => [6,5,4,3,2,1] => [5,4,3,2,1] => 2526
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,5,4,3,2,1] => [5,5,4,3,2,1] => [5,4,3,2,1] => 2526
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,5,4,3,2,1] => [5,5,4,3,2,1] => [5,4,3,2,1] => 2526
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,5,5,4,3,2,1] => [5,5,4,3,2,1] => [5,4,3,2,1] => 2526
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,4,3,2,1] => [6,4,4,3,2,1] => [4,4,3,2,1] => 397
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [6,6,4,4,3,2,1] => [6,4,4,3,2,1] => [4,4,3,2,1] => 397
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,4,3,2,1] => [5,4,4,3,2,1] => [4,4,3,2,1] => 397
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,4,3,2,1] => [5,4,4,3,2,1] => [4,4,3,2,1] => 397
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [5,5,4,4,3,2,1] => [5,4,4,3,2,1] => [4,4,3,2,1] => 397
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,4,4,3,2,1] => [4,4,4,3,2,1] => [4,4,3,2,1] => 397
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [6,4,4,4,3,2,1] => [4,4,4,3,2,1] => [4,4,3,2,1] => 397
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [5,4,4,4,3,2,1] => [4,4,4,3,2,1] => [4,4,3,2,1] => 397
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [4,4,4,4,3,2,1] => [4,4,4,3,2,1] => [4,4,3,2,1] => 397
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,3,2,1] => [5,4,3,3,2,1] => [4,3,3,2,1] => 161
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [6,5,3,3,3,2,1] => [5,3,3,3,2,1] => [3,3,3,2,1] => 24
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,3,3,2,1] => [4,3,3,3,2,1] => [3,3,3,2,1] => 24
[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,2,1] => [3,3,3,3,2,1] => [3,3,3,2,1] => 24
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,2,1] => [5,4,3,2,2,1] => [4,3,2,2,1] => 78
[1,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,2,2,1] => [3,3,3,2,2,1] => [3,3,2,2,1] => 19
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,2,2,1] => [6,5,2,2,2,1] => [5,2,2,2,1] => 32
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,2,2,1] => [5,4,2,2,2,1] => [4,2,2,2,1] => 14
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,2,2,1] => [4,3,2,2,2,1] => [3,2,2,2,1] => 6
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [6,5,2,2,2,2,1] => [5,2,2,2,2,1] => [2,2,2,2,1] => 1
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => 1
[1,1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => 1
[1,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => 1
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,1,1] => [6,5,4,3,1,1] => [5,4,3,1,1] => 631
[1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,1,1] => [3,3,3,3,1,1] => [3,3,3,1,1] => 8
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,1,1] => [5,4,3,2,1,1] => [4,3,2,1,1] => 50
[1,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [5,5,4,3,2,1,1] => [5,4,3,2,1,1] => [4,3,2,1,1] => 50
[1,1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,4,3,2,1,1] => [4,4,3,2,1,1] => [4,3,2,1,1] => 50
[1,1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,2,1,1] => [3,3,3,2,1,1] => [3,3,2,1,1] => 12
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [5,3,3,2,2,1,1] => [3,3,2,2,1,1] => [3,2,2,1,1] => 5
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [4,3,3,2,2,1,1] => [3,3,2,2,1,1] => [3,2,2,1,1] => 5
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,1,1,1] => [6,5,4,1,1,1] => [5,4,1,1,1] => 67
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,1,1,1] => [5,4,3,1,1,1] => [4,3,1,1,1] => 11
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [7,5,4,2,1,1,1] => [5,4,2,1,1,1] => [4,2,1,1,1] => 6
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,1,1,1] => [5,4,2,1,1,1] => [4,2,1,1,1] => 6
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,1,1,1] => [6,3,2,1,1,1] => [3,2,1,1,1] => 3
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,1,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => 3
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => 3
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [6,5,4,1,1,1,1] => [5,4,1,1,1,1] => [4,1,1,1,1] => 2
[1,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [4,4,4,1,1,1,1] => [4,4,1,1,1,1] => [4,1,1,1,1] => 2
[1,1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3,1,1,1,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => 1
[1,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [7,6,1,1,1,1,1] => [6,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,6,1,1,1,1,1] => [6,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [5,5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2] => [6,5,4,3,2] => [5,4,3,2] => 631
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,6,5,4,3,2] => [6,5,4,3,2] => [5,4,3,2] => 631
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,5,4,3,2] => [5,5,4,3,2] => [5,4,3,2] => 631
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,4,3,2] => [5,4,4,3,2] => [4,4,3,2] => 120
[1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [4,3,3,3,3,2] => [3,3,3,3,2] => [3,3,3,2] => 8
[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,2] => [3,3,3,3,2] => [3,3,3,2] => 8
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,2] => [5,4,3,2,2] => [4,3,2,2] => 28
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,2,2] => [6,5,2,2,2] => [5,2,2,2] => 11
[1,1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,2,2] => [4,3,2,2,2] => [3,2,2,2] => 2
[1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2,2,2,2] => [3,2,2,2,2] => [2,2,2,2] => 1
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 1
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 1
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,1] => [6,5,4,3,1] => [5,4,3,1] => 368
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,5,4,3,1] => [5,5,4,3,1] => [5,4,3,1] => 368
[1,1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [4,4,4,4,3,1] => [4,4,4,3,1] => [4,4,3,1] => 84
[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,1] => [3,3,3,3,1] => [3,3,3,1] => 5
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,1] => [6,5,4,2,1] => [5,4,2,1] => 196
[1,1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,4,4,4,2,1] => [4,4,4,2,1] => [4,4,2,1] => 39
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,1] => [6,5,3,2,1] => [5,3,2,1] => 85
[1,1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [5,5,5,3,2,1] => [5,5,3,2,1] => [5,3,2,1] => 85
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,1] => [6,4,3,2,1] => [4,3,2,1] => 34
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [6,6,4,3,2,1] => [6,4,3,2,1] => [4,3,2,1] => 34
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => 34
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => 34
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [5,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => 34
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [7,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => 34
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [6,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => 34
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => 34
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => 34
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [7,6,3,3,2,1] => [6,3,3,2,1] => [3,3,2,1] => 7
[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,3,2,1] => [4,3,3,2,1] => [3,3,2,1] => 7
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [7,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => 7
[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => 7
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,2,1] => [6,5,2,2,1] => [5,2,2,1] => 19
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,2,1] => [4,3,2,2,1] => [3,2,2,1] => 4
[1,1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,2,1] => [4,3,2,2,1] => [3,2,2,1] => 4
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,2,2,1] => [6,2,2,2,1] => [2,2,2,1] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [6,5,2,2,2,1] => [5,2,2,2,1] => [2,2,2,1] => 1
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [6,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 1
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 1
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 1
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,1,1] => [6,5,4,1,1] => [5,4,1,1] => 62
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,1,1] => [5,4,3,1,1] => [4,3,1,1] => 10
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [6,4,4,3,1,1] => [4,4,3,1,1] => [4,3,1,1] => 10
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [5,5,3,3,1,1] => [5,3,3,1,1] => [3,3,1,1] => 3
[1,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [4,4,3,3,1,1] => [4,3,3,1,1] => [3,3,1,1] => 3
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,1,1] => [5,3,2,1,1] => [3,2,1,1] => 3
[1,1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [5,5,3,2,1,1] => [5,3,2,1,1] => [3,2,1,1] => 3
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => 3
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => 3
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => 3
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [7,4,2,2,1,1] => [4,2,2,1,1] => [2,2,1,1] => 1
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [7,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [7,6,5,1,1,1] => [6,5,1,1,1] => [5,1,1,1] => 4
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [6,5,4,1,1,1] => [5,4,1,1,1] => [4,1,1,1] => 2
[1,1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [5,4,4,1,1,1] => [4,4,1,1,1] => [4,1,1,1] => 2
[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [4,4,4,1,1,1] => [4,4,1,1,1] => [4,1,1,1] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [6,5,2,1,1,1] => [5,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [6,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [6,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [7,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [5,5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3] => [6,5,4,3] => [5,4,3] => 132
[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0] => [4,3,3,3,3] => [3,3,3,3] => [3,3,3] => 2
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3] => [3,3,3,3] => [3,3,3] => 2
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2] => [6,5,4,2] => [5,4,2] => 62
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2] => [6,5,3,2] => [5,3,2] => 27
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2] => [5,4,3,2] => [4,3,2] => 10
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2] => [5,4,3,2] => [4,3,2] => 10
[1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0] => [5,5,4,3,2] => [5,4,3,2] => [4,3,2] => 10
[1,1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,4,3,2] => [4,4,3,2] => [4,3,2] => 10
[1,1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,4,4,3,2] => [4,4,3,2] => [4,3,2] => 10
[1,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0,0] => [5,5,3,3,2] => [5,3,3,2] => [3,3,2] => 3
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0,0] => [6,4,3,3,2] => [4,3,3,2] => [3,3,2] => 3
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0] => [4,4,3,3,2] => [4,3,3,2] => [3,3,2] => 3
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,3,3,2] => [3,3,3,2] => [3,3,2] => 3
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,2] => [4,3,2,2] => [3,2,2] => 2
[1,1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,2,2] => [3,2,2,2] => [2,2,2] => 1
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,2,2,2] => [2,2,2,2] => [2,2,2] => 1
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 1
[1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,2] => [2,2,2,2] => [2,2,2] => 1
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2] => [2,2,2,2] => [2,2,2] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,1] => [6,5,4,1] => [5,4,1] => 38
[1,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,4,4,4,1] => [4,4,4,1] => [4,4,1] => 7
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,1] => [5,4,3,1] => [4,3,1] => 8
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,1] => [5,4,3,1] => [4,3,1] => 8
[1,1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0,0] => [5,4,4,3,1] => [4,4,3,1] => [4,3,1] => 8
[1,1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,1] => [3,3,3,1] => [3,3,1] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,1] => [6,5,2,1] => [5,2,1] => 9
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,1] => [5,4,2,1] => [4,2,1] => 5
[1,1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,4,4,2,1] => [4,4,2,1] => [4,2,1] => 5
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,1] => [6,3,2,1] => [3,2,1] => 3
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0,0] => [6,6,3,2,1] => [6,3,2,1] => [3,2,1] => 3
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,1] => [5,3,2,1] => [3,2,1] => 3
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => [5,5,3,2,1] => [5,3,2,1] => [3,2,1] => 3
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,1] => [4,3,2,1] => [3,2,1] => 3
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,1] => [4,3,2,1] => [3,2,1] => 3
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1] => [4,3,2,1] => [3,2,1] => 3
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,4,3,2,1] => [4,3,2,1] => [3,2,1] => 3
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,0] => [7,3,3,2,1] => [3,3,2,1] => [3,2,1] => 3
[1,1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0,0] => [5,3,3,2,1] => [3,3,2,1] => [3,2,1] => 3
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,3,3,2,1] => [3,3,2,1] => [3,2,1] => 3
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [3,3,3,2,1] => [3,3,2,1] => [3,2,1] => 3
[1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,2,1] => [4,2,2,1] => [2,2,1] => 1
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0,0] => [7,3,2,2,1] => [3,2,2,1] => [2,2,1] => 1
[1,1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,2,1] => [3,2,2,1] => [2,2,1] => 1
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,2,1] => [3,2,2,1] => [2,2,1] => 1
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0] => [7,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [7,5,3,1,1] => [5,3,1,1] => [3,1,1] => 1
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0] => [4,4,3,1,1] => [4,3,1,1] => [3,1,1] => 1
[1,1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1,1] => [4,2,1,1] => [2,1,1] => 1
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0] => [6,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0,0] => [7,6,1,1,1] => [6,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1,1,1] => [5,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0,0] => [7,4,1,1,1] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,1,1] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1,1,1] => [4,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4] => [6,5,4] => [5,4] => 11
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0,0] => [6,5,5,4] => [5,5,4] => [5,4] => 11
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [4,4,4,4] => [4,4,4] => [4,4] => 3
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3] => [6,5,3] => [5,3] => 6
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3] => [5,4,3] => [4,3] => 3
[1,1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0,0] => [5,5,4,3] => [5,4,3] => [4,3] => 3
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0] => [6,4,4,3] => [4,4,3] => [4,3] => 3
[1,1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0,0] => [4,4,4,3] => [4,4,3] => [4,3] => 3
[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0] => [5,5,3,3] => [5,3,3] => [3,3] => 1
[1,1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,3,3] => [3,3,3] => [3,3] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2] => [5,4,2] => [4,2] => 2
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2] => [4,3,2] => [3,2] => 1
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2] => [4,3,2] => [3,2] => 1
[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0] => [4,4,3,2] => [4,3,2] => [3,2] => 1
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0] => [6,3,3,2] => [3,3,2] => [3,2] => 1
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [4,4,2,2] => [4,2,2] => [2,2] => 1
[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2,2] => [3,2,2] => [2,2] => 1
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0] => [5,2,2,2] => [2,2,2] => [2,2] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,0] => [5,5,5,1] => [5,5,1] => [5,1] => 3
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [7,5,3,1] => [5,3,1] => [3,1] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,0] => [6,5,3,1] => [5,3,1] => [3,1] => 1
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3,1] => [4,3,1] => [3,1] => 1
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0] => [6,3,3,1] => [3,3,1] => [3,1] => 1
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3,1] => [3,3,1] => [3,1] => 1
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3,1] => [3,3,1] => [3,1] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0] => [7,5,2,1] => [5,2,1] => [2,1] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0] => [6,5,2,1] => [5,2,1] => [2,1] => 1
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1] => [4,2,1] => [2,1] => 1
[1,1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0] => [4,4,2,1] => [4,2,1] => [2,1] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0] => [6,3,2,1] => [3,2,1] => [2,1] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1] => [3,2,1] => [2,1] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2,1] => [3,2,1] => [2,1] => 1
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2,1] => [2,2,1] => [2,1] => 1
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1] => [2,2,1] => [2,1] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0] => [7,6,1,1] => [6,1,1] => [1,1] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1,1] => [5,1,1] => [1,1] => 1
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1] => [3,1,1] => [1,1] => 1
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1] => [3,1,1] => [1,1] => 1
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,1] => [2,1,1] => [1,1] => 1
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1] => [2,1,1] => [1,1] => 1
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1] => [2,1,1] => [1,1] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1] => [1,1,1] => [1,1] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1] => [1,1,1] => [1,1] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1] => [1,1,1] => [1,1] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1] => [1,1,1] => [1,1] => 1
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1] => [1,1,1] => [1,1] => 1
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1] => [1,1,1] => [1,1] => 1
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1] => [1,1,1] => [1,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0] => [7,6,5] => [6,5] => [5] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0] => [6,6,5] => [6,5] => [5] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0] => [6,5,5] => [5,5] => [5] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => [5,5,5] => [5,5] => [5] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,0] => [7,6,4] => [6,4] => [4] => 1
[1,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0,0] => [5,4,4] => [4,4] => [4] => 1
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0] => [4,4,4] => [4,4] => [4] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => [7,5,3] => [5,3] => [3] => 1
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3] => [4,3] => [3] => 1
[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0] => [4,4,3] => [4,3] => [3] => 1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0] => [6,3,3] => [3,3] => [3] => 1
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3] => [3,3] => [3] => 1
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3] => [3,3] => [3] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [6,4,2] => [4,2] => [2] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2] => [4,2] => [2] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0] => [4,4,2] => [4,2] => [2] => 1
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2] => [3,2] => [2] => 1
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2] => [3,2] => [2] => 1
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2] => [3,2] => [2] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0] => [7,2,2] => [2,2] => [2] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2] => [2,2] => [2] => 1
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2] => [2,2] => [2] => 1
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2] => [2,2] => [2] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0] => [7,6,1] => [6,1] => [1] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0] => [6,6,1] => [6,1] => [1] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1] => [5,1] => [1] => 1
[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1] => [4,1] => [1] => 1
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1] => [4,1] => [1] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1] => [3,1] => [1] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1] => [3,1] => [1] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1] => [3,1] => [1] => 1
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1] => [3,1] => [1] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1] => [2,1] => [1] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1] => [2,1] => [1] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1] => [2,1] => [1] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1] => [2,1] => [1] => 1
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1] => [2,1] => [1] => 1
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1] => [2,1] => [1] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1] => [1,1] => [1] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1] => [1,1] => [1] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1] => [1,1] => [1] => 1
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1] => [1,1] => [1] => 1
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1] => [1,1] => [1] => 1
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1] => [1,1] => [1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,1,1] => [6,5,4,3,2,1,1] => [5,4,3,2,1,1] => 4924
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,2,2,1] => [6,5,4,2,2,2,1] => [5,4,2,2,2,1] => 1322
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,1,1,1] => [6,5,4,3,1,1,1] => [5,4,3,1,1,1] => 778
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,2,2,1] => [6,4,3,2,2,2,1] => [4,3,2,2,2,1] => 136
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,3,3,2,1] => [5,4,3,3,3,2,1] => [4,3,3,3,2,1] => 993
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,1] => [7,6,5,4,1] => [6,5,4,1] => 9616
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,2,2,1] => [5,4,3,2,2,2,1] => [4,3,2,2,2,1] => 136
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,1,1,1] => [5,4,3,2,1,1,1] => [4,3,2,1,1,1] => 57
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4] => [7,6,5,4] => [6,5,4] => 2430
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,2,1] => [7,6,5,2,1] => [6,5,2,1] => 1244
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,1,1,1] => [5,4,3,2,1,1,1] => [4,3,2,1,1,1] => 57
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [8,7,6,4,3,2,1] => [7,6,4,3,2,1] => [6,4,3,2,1] => 8552
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1,1,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => 3
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0] => [8,7,6,3,2,1] => [7,6,3,2,1] => [6,3,2,1] => 216
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [8,7,5,4,3,2,1] => [7,5,4,3,2,1] => [5,4,3,2,1] => 2526
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5] => [7,6,5] => [6,5] => 77
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0] => [8,7,4,3,2,1] => [7,4,3,2,1] => [4,3,2,1] => 34
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [8,6,5,4,3,2,1] => [6,5,4,3,2,1] => [5,4,3,2,1] => 2526
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,1,1,1,1] => [5,4,3,2,1,1,1,1] => [4,3,2,1,1,1,1] => 57
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0] => [8,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => 34
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,7,1,1,1,1,1,1] => [7,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => 1
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,3] => [3,3,3,3,3] => [3,3,3,3] => 4
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4] => [7,6,5,4] => [6,5,4] => 2430
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,4,4,4,4] => [4,4,4,4] => [4,4,4] => 20
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5] => [7,6,5] => [6,5] => 77
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,5,5,5] => [5,5,5] => [5,5] => 15
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [8,7,6] => [7,6] => [6] => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,6,6] => [6,6] => [6] => 3
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,3,3,3,3,3,3] => [3,3,3,3,3,3] => [3,3,3,3,3] => 12
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,4,4,4,4,4] => [4,4,4,4,4] => [4,4,4,4] => 188
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,5,5,5,5] => [5,5,5,5] => [5,5,5] => 389
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6] => [8,7,6] => [7,6] => 513
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,6,6,6] => [6,6,6] => [6,6] => 109
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [9,8,7] => [8,7] => [7] => 5
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [7,7,7] => [7,7] => [7] => 5
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,2,1] => [7,6,4,3,2,1] => [6,4,3,2,1] => 8552
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,2,1] => [7,5,4,3,2,1] => [5,4,3,2,1] => 2526
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,2,1] => [6,5,4,3,2,1] => [5,4,3,2,1] => 2526
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,2,1] => [7,6,5,2,2,1] => [6,5,2,2,1] => 5153
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,3,2,1] => [7,6,3,3,2,1] => [6,3,3,2,1] => 1460
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,4,3,2,1] => [7,4,4,3,2,1] => [4,4,3,2,1] => 397
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [8,5,5,4,3,2,1] => [5,5,4,3,2,1] => [5,4,3,2,1] => 2526
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [4,4,3,2,1] => [4,3,2,1] => [3,2,1] => 3
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2] => [4,3,2] => [3,2] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [5,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => 34
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => 34
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2] => [5,4,3,2] => [4,3,2] => 10
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,5,4,3,2] => [5,4,3,2] => [4,3,2] => 10
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1] => [2,1] => [1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => 34
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,1] => [7,4,3,2,1] => [4,3,2,1] => 34
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,1] => [7,6,3,2,1] => [6,3,2,1] => 216
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,1] => [7,6,5,2,1] => [6,5,2,1] => 1244
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,1] => [7,6,5,4,1] => [6,5,4,1] => 9616
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [8,7,5] => [7,5] => [5] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4] => [7,6,4] => [6,4] => 32
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3] => [7,6,5,3] => [6,5,3] => 783
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1] => [1,1] => [1] => 1
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1] => [1,1,1] => [1,1] => 1
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [7,7,4,3,2,1] => [7,4,3,2,1] => [4,3,2,1] => 34
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,2,2] => [5,4,3,2,2,2] => [4,3,2,2,2] => 43
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,1,1] => [5,4,3,2,1,1] => [4,3,2,1,1] => 50
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,2,1,1] => [6,5,4,3,2,1,1] => [5,4,3,2,1,1] => 4924
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,3,1] => [3,3,3,3,3,1] => [3,3,3,3,1] => 12
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,4,4,4,4,1] => [4,4,4,4,1] => [4,4,4,1] => 59
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,5,5,5,1] => [5,5,5,1] => [5,5,1] => 46
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => [6,6,6,1] => [6,6,1] => [6,1] => 6
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,1,1,1,1,1] => [4,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => 3
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,1,1,1,1] => [5,4,3,1,1,1,1] => [4,3,1,1,1,1] => 11
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,2] => [6,5,4,3,2] => [5,4,3,2] => 631
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,6,5,4,3,2,1,1] => [6,5,4,3,2,1,1] => [5,4,3,2,1,1] => 4924
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,7,5,4,3,2,1] => [7,5,4,3,2,1] => [5,4,3,2,1] => 2526
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,2] => [6,5,4,3,2,2] => [5,4,3,2,2] => 2643
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [6,6,6,4,3,2,1] => [6,6,4,3,2,1] => [6,4,3,2,1] => 8552
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,5,5,5,3,2,1] => [5,5,5,3,2,1] => [5,5,3,2,1] => 4086
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [5,4,4,4,4,2,1] => [4,4,4,4,2,1] => [4,4,4,2,1] => 380
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,3,3,3,1] => [4,3,3,3,3,1] => [3,3,3,3,1] => 12
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,3,3,2,1] => [5,4,3,3,3,2,1] => [4,3,3,3,2,1] => 993
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,2,2,2] => [4,3,2,2,2,2] => [3,2,2,2,2] => 2
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,2,2,1] => [5,4,3,2,2,2,1] => [4,3,2,2,2,1] => 136
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,1,1,1] => [5,4,3,2,1,1,1] => [4,3,2,1,1,1] => 57
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => 34
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,2,2] => [3,3,3,3,2,2] => [3,3,3,2,2] => 18
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,7,1,1,1,1] => [7,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [4,4,4,3,3,3] => [4,4,3,3,3] => [4,3,3,3] => 37
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,6,6,1,1] => [6,6,1,1] => [6,1,1] => 8
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [5,4,4,4,4] => [4,4,4,4] => [4,4,4] => 20
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [7,6,6] => [6,6] => [6] => 3
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [6,5,5,5] => [5,5,5] => [5,5] => 15
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,3,3,3,3] => [3,3,3,3,3] => [3,3,3,3] => 4
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0] => [8,2,1] => [2,1] => [1] => 1
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [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
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => [2,2,2,2,2,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,2,1] => [6,5,4,3,2,1] => [5,4,3,2,1] => 2526
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,2] => [6,5,4,3,2] => [5,4,3,2] => 631
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [3,3,3] => [3,3] => [3] => 1
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0] => [4,4,4] => [4,4] => [4] => 1
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [4,4,4,4] => [4,4,4] => [4,4] => 3
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0] => [5,5,5,5] => [5,5,5] => [5,5] => 15
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [9,7,5,3,1] => [7,5,3,1] => [5,3,1] => 15
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [11,9,7,5,3,1] => [9,7,5,3,1] => [7,5,3,1] => 11214
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [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
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1] => [1,1] => [1] => 1
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,1] => [1,1] => [1] => 1
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,1] => [4,3,2,1] => [3,2,1] => 3
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2] => [3,2] => [2] => 1
[1,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,1,1,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => 3
[1,1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0] => [6,6,6] => [6,6] => [6] => 3
[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [4,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [5,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [6,6,5,4,3,2,1] => [6,5,4,3,2,1] => [5,4,3,2,1] => 2526
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1] => [2,1] => [1] => 1
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0] => [7,2,1] => [2,1] => [1] => 1
[1,1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0,0] => [8,2,1] => [2,1] => [1] => 1
[1,1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [4,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => 34
[1,1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [3,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => 7
[1,1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,3,3,3,3,2,1] => [3,3,3,3,2,1] => [3,3,3,2,1] => 24
[1,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => 1
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [4,4,4,4,4] => [4,4,4,4] => [4,4,4] => 20
[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,3,3,3,3,3] => [3,3,3,3,3] => [3,3,3,3] => 4
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => 1
[1,1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [5,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [6,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [7,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,1,1] => [1,1,1] => [1,1] => 1
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => 3
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0] => [5,3,2,1] => [3,2,1] => [2,1] => 1
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,1,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => 3
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0] => [5,4,2,1] => [4,2,1] => [2,1] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,1] => [4,3,1] => [3,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,3,2,1] => [6,5,4,3,2,1] => [5,4,3,2,1] => 2526
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0] => [7,6,4,3,2,1] => [6,4,3,2,1] => [4,3,2,1] => 34
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => [5,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => 34
[1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [6,4,3,2,1] => [4,3,2,1] => [3,2,1] => 3
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0] => [6,4,3,2,1] => [4,3,2,1] => [3,2,1] => 3
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0] => [6,3,2,1] => [3,2,1] => [2,1] => 1
[1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => 3
[1,1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [4,3,3,2,1] => [3,3,2,1] => [3,2,1] => 3
[1,1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,2,1] => [3,2,2,1] => [2,2,1] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0,0] => [7,4,3,2,1] => [4,3,2,1] => [3,2,1] => 3
[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,5,4,3,2] => [5,4,3,2] => [4,3,2] => 10
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => 34
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,0] => [8,7,1] => [7,1] => [1] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0,0] => [7,6,1] => [6,1] => [1] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0,0] => [6,5,1] => [5,1] => [1] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0] => [5,4,1] => [4,1] => [1] => 1
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0] => [4,3,1] => [3,1] => [1] => 1
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2] => [2,2] => [2] => 1
[1,1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,2] => [4,3,2,2] => [3,2,2] => 2
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,1] => [5,4,3,1] => [4,3,1] => 8
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => [6,5,5,4,3,2,1] => [5,5,4,3,2,1] => [5,4,3,2,1] => 2526
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [6,5,5,4,3,2,1] => [5,5,4,3,2,1] => [5,4,3,2,1] => 2526
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,1] => [6,5,4,3,1] => [5,4,3,1] => 368
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,3,1] => [6,5,4,3,1] => [5,4,3,1] => 368
[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 1
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1] => [1,1,1] => [1,1] => 1
[1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0] => [8,7,6] => [7,6] => [6] => 3
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3] => [5,4,3] => [4,3] => 3
[1,1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,1,1] => [5,4,3,1,1] => [4,3,1,1] => 10
[1,1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,1] => [1,1] => [1] => 1
[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[1,1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => 1
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [4,3,3,2,2,1,1] => [3,3,2,2,1,1] => [3,2,2,1,1] => 5
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0] => [7,5,3,1] => [5,3,1] => [3,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [5,5,5,4,3,2,1] => [5,5,4,3,2,1] => [5,4,3,2,1] => 2526
[1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1] => [1,1] => [1] => 1
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [7,7,5,4,3,2,1] => [7,5,4,3,2,1] => [5,4,3,2,1] => 2526
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,2,2] => [6,5,4,3,2,2] => [5,4,3,2,2] => 2643
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [8,6,4,2] => [6,4,2] => [4,2] => 2
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [10,8,6,4,2] => [8,6,4,2] => [6,4,2] => 163
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [6,6,4,4,3,2,1] => [6,4,4,3,2,1] => [4,4,3,2,1] => 397
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [6,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => 3
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0,0,0] => [7,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 1
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [6,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1] => [1,1] => [1] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => [7,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => 34
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0,0] => [8,3,2,1] => [3,2,1] => [2,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [5,5,5,4,3,2,1] => [5,5,4,3,2,1] => [5,4,3,2,1] => 2526
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [6,6,5,4,3,2] => [6,5,4,3,2] => [5,4,3,2] => 631
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [6,6,5,4,3,2] => [6,5,4,3,2] => [5,4,3,2] => 631
[1,1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [4,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [8,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [4,4,4,4,4,1] => [4,4,4,4,1] => [4,4,4,1] => 59
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1,1] => [2,1,1] => [1,1] => 1
[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1] => [2,1,1] => [1,1] => 1
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,4,3,2,1] => [4,3,2,1] => [3,2,1] => 3
[1,1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [4,3,3,3,3,3] => [3,3,3,3,3] => [3,3,3,3] => 4
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [7,6,5,3,2,1] => [6,5,3,2,1] => [5,3,2,1] => 85
[1,1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [4,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => 7
[1,1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => [8,6,5,4,3,2,1] => [6,5,4,3,2,1] => [5,4,3,2,1] => 2526
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [6,6,5,4,3,2,1] => [6,5,4,3,2,1] => [5,4,3,2,1] => 2526
[1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [5,4,4,4,3,2,1] => [4,4,4,3,2,1] => [4,4,3,2,1] => 397
[1,1,1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [5,4,3,3,3,2,1] => [4,3,3,3,2,1] => [3,3,3,2,1] => 24
[1,1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,2,2,2,2] => [3,2,2,2,2,2] => [2,2,2,2,2] => 1
[1,1,1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,4,3,2,2,2,1] => [4,3,2,2,2,1] => [3,2,2,2,1] => 6
[1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,4,3,2,1,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => 3
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2] => [6,4,2] => [4,2] => 2
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0,0] => [5,5,3,2,1] => [5,3,2,1] => [3,2,1] => 3
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0,0] => [6,5,3,2,1] => [5,3,2,1] => [3,2,1] => 3
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3] => [6,5,4,3] => [5,4,3] => 132
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0,0] => [8,7,1,1] => [7,1,1] => [1,1] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0,0,0] => [7,6,1,1,1] => [6,1,1,1] => [1,1,1] => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0,0] => [6,5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [5,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0] => [5,3,1] => [3,1] => [1] => 1
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,1] => [2,2,1] => [2,1] => 1
[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0] => [3,3,2] => [3,2] => [2] => 1
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Description
The largest multiplicity of an irreducible representation contained in the higher Lie character for an integer partition.
Map
first row removal
Description
Removes the first entry of an integer partition
Map
to partition
Description
The cut-out partition of a Dyck path.
The partition λ associated to a Dyck path is defined to be the complementary partition inside the staircase partition (n−1,…,2,1) when cutting out D considered as a path from (0,0) to (n,n).
In other words, λi is the number of down-steps before the (n+1−i)-th up-step of D.
This map is a bijection between Dyck paths of size n and partitions inside the staircase partition (n−1,…,2,1).
The partition λ associated to a Dyck path is defined to be the complementary partition inside the staircase partition (n−1,…,2,1) when cutting out D considered as a path from (0,0) to (n,n).
In other words, λi is the number of down-steps before the (n+1−i)-th up-step of D.
This map is a bijection between Dyck paths of size n and partitions inside the staircase partition (n−1,…,2,1).
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