Identifier
-
Mp00027:
Dyck paths
—to partition⟶
Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
St001219: Dyck paths ⟶ ℤ
Values
[1,0,1,0,1,0] => [2,1] => [1] => [1,0] => 0
[1,0,1,1,0,0] => [1,1] => [1] => [1,0] => 0
[1,0,1,0,1,0,1,0] => [3,2,1] => [2,1] => [1,0,1,1,0,0] => 0
[1,0,1,0,1,1,0,0] => [2,2,1] => [2,1] => [1,0,1,1,0,0] => 0
[1,0,1,1,0,0,1,0] => [3,1,1] => [1,1] => [1,1,0,0] => 0
[1,0,1,1,0,1,0,0] => [2,1,1] => [1,1] => [1,1,0,0] => 0
[1,0,1,1,1,0,0,0] => [1,1,1] => [1,1] => [1,1,0,0] => 0
[1,1,0,0,1,0,1,0] => [3,2] => [2] => [1,0,1,0] => 0
[1,1,0,0,1,1,0,0] => [2,2] => [2] => [1,0,1,0] => 0
[1,1,0,1,0,0,1,0] => [3,1] => [1] => [1,0] => 0
[1,1,0,1,0,1,0,0] => [2,1] => [1] => [1,0] => 0
[1,1,0,1,1,0,0,0] => [1,1] => [1] => [1,0] => 0
[1,0,1,0,1,0,1,0,1,0] => [4,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 0
[1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 0
[1,0,1,0,1,1,0,0,1,0] => [4,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 0
[1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 0
[1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 0
[1,0,1,1,0,0,1,0,1,0] => [4,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,0] => [3,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,0] => [4,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,0] => [2,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 0
[1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 0
[1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 0
[1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 0
[1,1,0,0,1,0,1,0,1,0] => [4,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 0
[1,1,0,0,1,0,1,1,0,0] => [3,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 0
[1,1,0,0,1,1,0,0,1,0] => [4,2,2] => [2,2] => [1,1,1,0,0,0] => 0
[1,1,0,0,1,1,0,1,0,0] => [3,2,2] => [2,2] => [1,1,1,0,0,0] => 0
[1,1,0,0,1,1,1,0,0,0] => [2,2,2] => [2,2] => [1,1,1,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,0] => [4,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,1,0,0] => [3,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,0] => [4,2,1] => [2,1] => [1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,0] => [3,2,1] => [2,1] => [1,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,0,0] => [2,2,1] => [2,1] => [1,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,0,1,0] => [4,1,1] => [1,1] => [1,1,0,0] => 0
[1,1,0,1,1,0,0,1,0,0] => [3,1,1] => [1,1] => [1,1,0,0] => 0
[1,1,0,1,1,0,1,0,0,0] => [2,1,1] => [1,1] => [1,1,0,0] => 0
[1,1,0,1,1,1,0,0,0,0] => [1,1,1] => [1,1] => [1,1,0,0] => 0
[1,1,1,0,0,0,1,0,1,0] => [4,3] => [3] => [1,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,0] => [3,3] => [3] => [1,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,0,1,0] => [4,2] => [2] => [1,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,0] => [3,2] => [2] => [1,0,1,0] => 0
[1,1,1,0,0,1,1,0,0,0] => [2,2] => [2] => [1,0,1,0] => 0
[1,1,1,0,1,0,0,0,1,0] => [4,1] => [1] => [1,0] => 0
[1,1,1,0,1,0,0,1,0,0] => [3,1] => [1] => [1,0] => 0
[1,1,1,0,1,0,1,0,0,0] => [2,1] => [1] => [1,0] => 0
[1,1,1,0,1,1,0,0,0,0] => [1,1] => [1] => [1,0] => 0
[1,0,1,0,1,0,1,1,0,0,1,0] => [5,3,3,2,1] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,0] => [4,3,3,2,1] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 0
[1,0,1,0,1,0,1,1,1,0,0,0] => [3,3,3,2,1] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 0
[1,0,1,0,1,1,0,1,0,0,1,0] => [5,3,2,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,0] => [4,3,2,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,0] => [3,3,2,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 0
[1,0,1,0,1,1,1,0,0,0,1,0] => [5,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 0
[1,0,1,0,1,1,1,0,0,1,0,0] => [4,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 0
[1,0,1,0,1,1,1,0,1,0,0,0] => [3,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 0
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 0
[1,0,1,1,0,0,1,1,0,0,1,0] => [5,3,3,1,1] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 0
[1,0,1,1,0,0,1,1,0,1,0,0] => [4,3,3,1,1] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 0
[1,0,1,1,0,0,1,1,1,0,0,0] => [3,3,3,1,1] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 0
[1,0,1,1,0,1,0,1,1,0,0,0] => [3,3,2,1,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 0
[1,0,1,1,0,1,1,0,0,0,1,0] => [5,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 0
[1,0,1,1,0,1,1,0,0,1,0,0] => [4,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,0] => [3,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 0
[1,0,1,1,1,0,0,1,0,0,1,0] => [5,3,1,1,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,0,1,0,0] => [4,3,1,1,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,1,0,0,0] => [3,3,1,1,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,0,0,1,0] => [5,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,0,0] => [4,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,0,0,1,0] => [5,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [4,4,3,2] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,0] => [5,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 0
[1,1,0,0,1,0,1,1,0,1,0,0] => [4,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 0
[1,1,0,0,1,0,1,1,1,0,0,0] => [3,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 0
[1,1,0,0,1,1,0,0,1,0,1,0] => [5,4,2,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,0,1,0] => [5,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,0,1,1,0,1,0,1,0,0] => [4,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,0,1,1,0,1,1,0,0,0] => [3,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,0,1,1,1,0,0,0,1,0] => [5,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => 0
[1,1,0,0,1,1,1,0,0,1,0,0] => [4,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => 0
[1,1,0,0,1,1,1,0,1,0,0,0] => [3,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,0] => [5,4,3,1] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [4,4,3,1] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,1,0,0] => [4,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,0] => [5,4,2,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 1
>>> Load all 992 entries. <<<[1,1,0,1,0,1,0,0,1,1,0,0] => [4,4,2,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => [5,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,0] => [3,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 0
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,0,0] => [4,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,0] => [3,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 0
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 0
[1,1,0,1,1,0,0,0,1,0,1,0] => [5,4,1,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,0,1,1,0,0] => [4,4,1,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,0,0,1,0] => [5,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,0,0,1,0,1,0,0] => [4,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,0,0,1,1,0,0,0] => [3,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,0,1,0,0,0,1,0] => [5,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,0] => [4,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,0] => [3,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,0] => [5,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 0
[1,1,0,1,1,1,0,0,0,1,0,0] => [4,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 0
[1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 0
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,0] => [5,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,0] => [4,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => 0
[1,1,1,0,0,0,1,1,0,1,0,0] => [4,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,0,1,0] => [5,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,0] => [4,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [5,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,1,1,0,0,0,1,0] => [5,2,2] => [2,2] => [1,1,1,0,0,0] => 0
[1,1,1,0,0,1,1,0,0,1,0,0] => [4,2,2] => [2,2] => [1,1,1,0,0,0] => 0
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,2] => [2,2] => [1,1,1,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,0,0,0] => [2,2,2] => [2,2] => [1,1,1,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,0,1,0] => [5,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,0,1,0,0,1,0,0,1,0] => [5,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,1] => [2,1] => [1,0,1,1,0,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => [2,1] => [1,0,1,1,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1] => [2,1] => [1,0,1,1,0,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1] => [2,1] => [1,0,1,1,0,0] => 0
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,1,1] => [1,1] => [1,1,0,0] => 0
[1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,1] => [1,1] => [1,1,0,0] => 0
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,1,1] => [1,1] => [1,1,0,0] => 0
[1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,1] => [1,1] => [1,1,0,0] => 0
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1] => [1,1] => [1,1,0,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => [4] => [1,0,1,0,1,0,1,0] => 2
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => [4] => [1,0,1,0,1,0,1,0] => 2
[1,1,1,1,0,0,0,1,0,0,1,0] => [5,3] => [3] => [1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => [3] => [1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,0] => [3,3] => [3] => [1,0,1,0,1,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,2] => [2] => [1,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,2] => [2] => [1,0,1,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,0] => [3,2] => [2] => [1,0,1,0] => 0
[1,1,1,1,0,0,1,1,0,0,0,0] => [2,2] => [2] => [1,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => [1] => [1,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => [1] => [1,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,0] => [3,1] => [1] => [1,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => [1] => [1,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,1] => [1] => [1,0] => 0
[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] => [1,1,1,1,0,1,0,0,0,1,0,0] => 0
[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] => [1,1,1,1,0,1,0,0,0,1,0,0] => 0
[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] => [1,1,1,1,0,1,0,0,0,1,0,0] => 0
[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] => [1,1,1,1,0,1,0,0,0,1,0,0] => 0
[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] => [1,1,1,1,0,1,0,0,0,1,0,0] => 0
[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] => [1,1,1,1,0,0,0,1,0,1,0,0] => 0
[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] => [1,1,1,1,0,0,0,1,0,1,0,0] => 0
[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] => [1,1,1,1,0,0,0,1,0,1,0,0] => 0
[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] => [1,1,1,1,0,0,0,1,0,1,0,0] => 0
[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] => [1,1,1,1,0,0,0,1,0,1,0,0] => 0
[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] => [1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [1,0,1,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,1,0,1,0,1,0,1,0,0] => 2
[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] => [1,1,0,1,0,1,0,1,0,0] => 2
[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] => [1,1,0,1,0,1,0,1,0,0] => 2
[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] => [1,1,0,1,0,1,0,1,0,0] => 2
[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] => [1,1,0,1,0,1,0,1,0,0] => 2
[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] => [1,1,0,1,0,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2] => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 0
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2] => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 0
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2] => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 0
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2] => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 0
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,2,2] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 0
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2,1] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 0
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 0
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 0
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 0
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 0
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 0
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 0
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1,1] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 0
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 0
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 0
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 0
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 0
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 2
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 2
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3] => [4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3] => [4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3] => [4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [6,4,4,2] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [6,4,2,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 0
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 0
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 0
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 0
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 0
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 0
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 0
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 0
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 3
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 3
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 3
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 2
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 2
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 0
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 0
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 0
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [6,5,4] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,5,4] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,4,4] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [6,5,3] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [5,5,3] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [6,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [5,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [6,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [5,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => 0
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [6,5,2] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,5,2] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [6,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [5,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,2,2] => [2,2] => [1,1,1,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [5,2,2] => [2,2] => [1,1,1,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,2] => [2,2] => [1,1,1,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2] => [2,2] => [1,1,1,0,0,0] => 0
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,2,2] => [2,2] => [1,1,1,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [6,5,1] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 3
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,5,1] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 3
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [6,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [3,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,2,1] => [2,1] => [1,0,1,1,0,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => [2,1] => [1,0,1,1,0,0] => 0
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,2,1] => [2,1] => [1,0,1,1,0,0] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => [2,1] => [1,0,1,1,0,0] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,2,1] => [2,1] => [1,0,1,1,0,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,1,1] => [1,1] => [1,1,0,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,1] => [1,1] => [1,1,0,0] => 0
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,1,1] => [1,1] => [1,1,0,0] => 0
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [3,1,1] => [1,1] => [1,1,0,0] => 0
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,1,1] => [1,1] => [1,1,0,0] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1] => [1,1] => [1,1,0,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => 3
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => 3
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,4] => [4] => [1,0,1,0,1,0,1,0] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4] => [4] => [1,0,1,0,1,0,1,0] => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,4] => [4] => [1,0,1,0,1,0,1,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,3] => [3] => [1,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,3] => [3] => [1,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [4,3] => [3] => [1,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,3] => [3] => [1,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,2] => [2] => [1,0,1,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => [2] => [1,0,1,0] => 0
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [4,2] => [2] => [1,0,1,0] => 0
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,2] => [2] => [1,0,1,0] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,2] => [2] => [1,0,1,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => [1] => [1,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1] => [1] => [1,0] => 0
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [4,1] => [1] => [1,0] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,1] => [1] => [1,0] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => [1] => [1,0] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1] => [1] => [1,0] => 0
[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] => [1,1,0,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,1,0,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,1,0,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,1,0,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,1,0,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,1,0,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,1,0,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,1,1,1,0,1,0,1,0,0,0,0] => 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] => [1,1,1,1,0,1,0,1,0,0,0,0] => 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] => [1,1,1,1,0,1,0,1,0,0,0,0] => 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] => [1,1,1,1,0,1,0,1,0,0,0,0] => 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] => [1,1,1,1,0,1,0,1,0,0,0,0] => 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] => [1,1,1,1,0,1,0,1,0,0,0,0] => 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] => [1,1,1,1,0,1,0,0,0,1,0,0] => 0
[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] => [1,1,1,1,0,1,0,0,0,1,0,0] => 0
[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] => [1,1,1,1,0,1,0,0,0,1,0,0] => 0
[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] => [1,1,1,1,0,1,0,0,0,1,0,0] => 0
[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] => [1,1,1,1,0,1,0,0,0,1,0,0] => 0
[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] => [1,1,1,1,0,1,0,0,0,1,0,0] => 0
[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] => [1,1,1,1,0,0,0,1,0,1,0,0] => 0
[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] => [1,1,1,1,0,0,0,1,0,1,0,0] => 0
[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] => [1,1,1,1,0,0,0,1,0,1,0,0] => 0
[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] => [1,1,1,1,0,0,0,1,0,1,0,0] => 0
[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] => [1,1,1,1,0,0,0,1,0,1,0,0] => 0
[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] => [1,1,1,1,0,0,0,1,0,1,0,0] => 0
[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] => [1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [1,0,1,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,1,0,1,0,1,0,1,0,0] => 2
[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] => [1,1,0,1,0,1,0,1,0,0] => 2
[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] => [1,1,0,1,0,1,0,1,0,0] => 2
[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] => [1,1,0,1,0,1,0,1,0,0] => 2
[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] => [1,1,0,1,0,1,0,1,0,0] => 2
[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] => [1,1,0,1,0,1,0,1,0,0] => 2
[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] => [1,1,0,1,0,1,0,1,0,0] => 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] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[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] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[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] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[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] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[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] => [1,1,1,1,1,0,0,1,0,0,0,0] => 0
[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] => [1,1,1,1,1,0,0,1,0,0,0,0] => 0
[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] => [1,1,1,1,1,0,0,1,0,0,0,0] => 0
[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] => [1,1,1,1,1,0,0,1,0,0,0,0] => 0
[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] => [1,1,1,0,1,1,0,1,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,0,1,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,0,1,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,0,1,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,0,1,0,0,0,0] => 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] => [1,0,1,1,1,1,0,1,0,0,0,0] => 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] => [1,0,1,1,1,1,0,1,0,0,0,0] => 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] => [1,0,1,1,1,1,0,1,0,0,0,0] => 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] => [1,0,1,1,1,1,0,1,0,0,0,0] => 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] => [1,0,1,1,1,1,0,1,0,0,0,0] => 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] => [1,1,1,1,0,1,0,0,0,0] => 0
[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] => [1,1,1,1,0,1,0,0,0,0] => 0
[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] => [1,1,1,1,0,1,0,0,0,0] => 0
[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] => [1,1,1,1,0,1,0,0,0,0] => 0
[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] => [1,1,1,1,0,1,0,0,0,0] => 0
[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] => [1,1,1,1,0,1,0,0,0,0] => 0
[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] => [1,1,1,1,1,0,0,0,0,1,0,0] => 0
[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] => [1,1,1,1,1,0,0,0,0,1,0,0] => 0
[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] => [1,1,1,1,1,0,0,0,0,1,0,0] => 0
[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] => [1,1,1,1,1,0,0,0,0,1,0,0] => 0
[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] => [1,1,1,1,1,0,0,0,0,1,0,0] => 0
[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] => [1,1,1,0,1,1,0,0,0,1,0,0] => 0
[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] => [1,1,1,0,1,1,0,0,0,1,0,0] => 0
[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] => [1,1,1,0,1,1,0,0,0,1,0,0] => 0
[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] => [1,1,1,0,1,1,0,0,0,1,0,0] => 0
[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] => [1,1,1,0,1,1,0,0,0,1,0,0] => 0
[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] => [1,0,1,1,1,1,0,0,0,1,0,0] => 0
[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] => [1,0,1,1,1,1,0,0,0,1,0,0] => 0
[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] => [1,0,1,1,1,1,0,0,0,1,0,0] => 0
[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] => [1,0,1,1,1,1,0,0,0,1,0,0] => 0
[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] => [1,0,1,1,1,1,0,0,0,1,0,0] => 0
[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] => [1,1,1,1,0,0,0,1,0,0] => 0
[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] => [1,1,1,1,0,0,0,1,0,0] => 0
[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] => [1,1,1,1,0,0,0,1,0,0] => 0
[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] => [1,1,1,1,0,0,0,1,0,0] => 0
[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] => [1,1,1,1,0,0,0,1,0,0] => 0
[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] => [1,1,1,1,0,0,0,1,0,0] => 0
[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] => [1,1,1,0,1,0,0,1,0,1,0,0] => 0
[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] => [1,1,1,0,1,0,0,1,0,1,0,0] => 0
[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] => [1,1,1,0,1,0,0,1,0,1,0,0] => 0
[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] => [1,1,1,0,1,0,0,1,0,1,0,0] => 0
[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] => [1,1,1,0,1,0,0,1,0,1,0,0] => 0
[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] => [1,0,1,1,1,0,0,1,0,1,0,0] => 0
[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] => [1,0,1,1,1,0,0,1,0,1,0,0] => 0
[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] => [1,0,1,1,1,0,0,1,0,1,0,0] => 0
[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] => [1,0,1,1,1,0,0,1,0,1,0,0] => 0
[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] => [1,0,1,1,1,0,0,1,0,1,0,0] => 0
[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] => [1,1,1,0,0,1,0,1,0,0] => 0
[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] => [1,1,1,0,0,1,0,1,0,0] => 0
[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] => [1,1,1,0,0,1,0,1,0,0] => 0
[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] => [1,1,1,0,0,1,0,1,0,0] => 0
[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] => [1,1,1,0,0,1,0,1,0,0] => 0
[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] => [1,1,1,0,0,1,0,1,0,0] => 0
[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] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,0,1,0,1,0,0] => 2
[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] => [1,0,1,1,0,1,0,1,0,0] => 2
[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] => [1,0,1,1,0,1,0,1,0,0] => 2
[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] => [1,0,1,1,0,1,0,1,0,0] => 2
[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] => [1,0,1,1,0,1,0,1,0,0] => 2
[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] => [1,0,1,1,0,1,0,1,0,0] => 2
[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] => [1,1,0,1,0,1,0,0] => 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] => [1,1,0,1,0,1,0,0] => 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] => [1,1,0,1,0,1,0,0] => 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] => [1,1,0,1,0,1,0,0] => 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] => [1,1,0,1,0,1,0,0] => 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] => [1,1,0,1,0,1,0,0] => 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] => [1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4] => [4,4,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => [4,4,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3] => [4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3] => [4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3] => [4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [7,4,3,3] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [7,3,3,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [7,4,4,2] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [7,4,4,1] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 0
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 0
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 0
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 0
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 0
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 0
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 0
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 0
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 0
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 0
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 0
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 3
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 3
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 3
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 3
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 2
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 2
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 0
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 0
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 0
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 0
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [7,5,5] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [6,5,5] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [7,5,4] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [6,5,4] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,5,4] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [7,4,4] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [6,4,4] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,4] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [4,4,4] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [7,5,3] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [6,5,3] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,5,3] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [7,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [6,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [4,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [7,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [6,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [4,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [7,5,2] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [6,5,2] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,5,2] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [7,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [6,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [5,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [4,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [7,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [6,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [4,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [3,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [7,2,2] => [2,2] => [1,1,1,0,0,0] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [6,2,2] => [2,2] => [1,1,1,0,0,0] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,2,2] => [2,2] => [1,1,1,0,0,0] => 0
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [4,2,2] => [2,2] => [1,1,1,0,0,0] => 0
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [3,2,2] => [2,2] => [1,1,1,0,0,0] => 0
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [2,2,2] => [2,2] => [1,1,1,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [7,5,1] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 3
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [6,5,1] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 3
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [5,5,1] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 3
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [7,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [6,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [4,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [7,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [6,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [4,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [3,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,2,1] => [2,1] => [1,0,1,1,0,0] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [6,2,1] => [2,1] => [1,0,1,1,0,0] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,2,1] => [2,1] => [1,0,1,1,0,0] => 0
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [4,2,1] => [2,1] => [1,0,1,1,0,0] => 0
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => [2,1] => [1,0,1,1,0,0] => 0
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [2,2,1] => [2,1] => [1,0,1,1,0,0] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,1,1] => [1,1] => [1,1,0,0] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [6,1,1] => [1,1] => [1,1,0,0] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,1,1] => [1,1] => [1,1,0,0] => 0
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [4,1,1] => [1,1] => [1,1,0,0] => 0
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [3,1,1] => [1,1] => [1,1,0,0] => 0
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,1,1] => [1,1] => [1,1,0,0] => 0
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1] => [1,1] => [1,1,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [7,6] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [7,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => 3
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => 3
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [5,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => 3
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,4] => [4] => [1,0,1,0,1,0,1,0] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,4] => [4] => [1,0,1,0,1,0,1,0] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [5,4] => [4] => [1,0,1,0,1,0,1,0] => 2
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [4,4] => [4] => [1,0,1,0,1,0,1,0] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,3] => [3] => [1,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,3] => [3] => [1,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [5,3] => [3] => [1,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [4,3] => [3] => [1,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [3,3] => [3] => [1,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,2] => [2] => [1,0,1,0] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,2] => [2] => [1,0,1,0] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [5,2] => [2] => [1,0,1,0] => 0
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [4,2] => [2] => [1,0,1,0] => 0
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => [2] => [1,0,1,0] => 0
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,2] => [2] => [1,0,1,0] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => [1] => [1,0] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1] => [1] => [1,0] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [5,1] => [1] => [1,0] => 0
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,1] => [1] => [1,0] => 0
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => [1] => [1,0] => 0
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => [1] => [1,0] => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1] => [1] => [1,0] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1] => [1] => [1,0] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => [1] => [1,0] => 0
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [8,2] => [2] => [1,0,1,0] => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1] => [1,1] => [1,1,0,0] => 0
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1] => [1] => [1,0] => 0
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0] => [9,2] => [2] => [1,0,1,0] => 0
[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] => [1,1,0,0] => 0
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [8,3] => [3] => [1,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1] => [2,1] => [1,0,1,1,0,0] => 0
[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] => [1,1,0,1,0,0] => 0
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0] => [11,1] => [1] => [1,0] => 0
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0] => [10,2] => [2] => [1,0,1,0] => 0
[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] => [1,1,0,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0] => [9,3] => [3] => [1,0,1,0,1,0] => 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] => [1,0,1,1,0,0] => 0
[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] => [1,1,0,1,0,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0] => [8,4] => [4] => [1,0,1,0,1,0,1,0] => 2
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => [8,2,2] => [2,2] => [1,1,1,0,0,0] => 0
[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] => [1,0,1,1,0,1,0,0] => 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] => [1,1,0,1,0,1,0,0] => 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] => [1,0,1,1,0,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0] => [9,4] => [4] => [1,0,1,0,1,0,1,0] => 2
[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] => [1,0,1,0,1,1,0,0] => 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] => [1,0,1,1,0,1,0,0] => 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] => [1,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [8,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => 3
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0] => [8,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 0
[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] => [1,0,1,0,1,1,0,1,0,0] => 2
[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] => [1,1,1,0,0,1,0,0] => 0
[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] => [1,0,1,1,0,1,0,1,0,0] => 2
[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] => [1,1,0,1,0,1,0,1,0,0] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0] => [9,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => 3
[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] => [1,0,1,1,1,0,0,0] => 0
[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] => [1,1,1,0,0,1,0,0] => 0
[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] => [1,1,0,1,0,1,0,1,0,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [8,6] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0] => [8,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,1,0] => [8,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => 0
[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] => [1,0,1,1,1,0,0,1,0,0] => 0
[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] => [1,1,1,0,0,1,0,1,0,0] => 0
[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] => [1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0] => [9,6] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 4
[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] => [1,1,1,0,1,0,0,0] => 0
[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] => [1,0,1,1,1,0,0,1,0,0] => 0
[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] => [1,1,1,1,0,0,0,0] => 0
[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] => [1,1,0,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,0,1,1,1,0,0,1,0,0] => 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] => [1,1,1,0,1,0,0,1,0,0] => 0
[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] => [1,0,1,1,1,1,0,0,0,0] => 0
[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] => [1,0,1,1,1,0,0,1,0,1,0,0] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,1,0] => [8,5,3] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,0] => [8,5,4] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => 2
[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] => [1,0,1,1,1,0,1,1,0,0,0,0] => 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] => [1,1,1,1,1,0,0,0,0,0] => 0
[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] => [1,1,1,0,1,1,0,0,0,1,0,0] => 0
[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] => [1,1,0,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,1,0,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,1,0,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,1,0,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,1,0,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,1,0,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,1,1,1,0,1,0,1,0,0,0,0] => 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] => [1,1,1,1,0,1,0,1,0,0,0,0] => 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] => [1,1,1,1,0,1,0,1,0,0,0,0] => 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] => [1,1,1,1,0,1,0,0,0,1,0,0] => 0
[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] => [1,1,1,1,0,1,0,0,0,1,0,0] => 0
[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] => [1,1,1,1,0,0,0,1,0,1,0,0] => 0
[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] => [1,1,1,1,0,0,0,1,0,1,0,0] => 0
[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] => [1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [1,1,1,0,0,1,0,1,0,1,0,0] => 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] => [1,0,1,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,1,0,1,0,1,0,1,0,0] => 2
[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] => [1,1,0,1,0,1,0,1,0,0] => 2
[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] => [1,1,0,1,0,1,0,1,0,0] => 2
[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] => [1,1,0,1,0,1,0,1,0,0] => 2
[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] => [1,1,0,1,0,1,0,1,0,0] => 2
[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] => [1,1,0,1,0,1,0,1,0,0] => 2
[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] => [1,1,0,1,0,1,0,1,0,0] => 2
[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] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[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] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[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] => [1,1,1,1,1,0,0,1,0,0,0,0] => 0
[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] => [1,0,1,1,1,1,0,1,0,0,0,0] => 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] => [1,1,1,1,0,1,0,0,0,0] => 0
[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] => [1,1,1,1,0,1,0,0,0,0] => 0
[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] => [1,1,1,1,0,1,0,0,0,0] => 0
[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] => [1,1,1,1,0,1,0,0,0,0] => 0
[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] => [1,1,1,1,1,0,0,0,0,1,0,0] => 0
[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] => [1,1,1,0,1,1,0,0,0,1,0,0] => 0
[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] => [1,1,1,0,1,1,0,0,0,1,0,0] => 0
[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] => [1,1,1,0,1,1,0,0,0,1,0,0] => 0
[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] => [1,1,1,0,1,1,0,0,0,1,0,0] => 0
[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] => [1,0,1,1,1,1,0,0,0,1,0,0] => 0
[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] => [1,0,1,1,1,1,0,0,0,1,0,0] => 0
[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] => [1,0,1,1,1,1,0,0,0,1,0,0] => 0
[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] => [1,1,1,1,0,0,0,1,0,0] => 0
[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] => [1,1,1,1,0,0,0,1,0,0] => 0
[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] => [1,1,1,1,0,0,0,1,0,0] => 0
[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] => [1,0,1,1,1,0,0,1,0,1,0,0] => 0
[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] => [1,0,1,1,1,0,0,1,0,1,0,0] => 0
[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] => [1,1,1,0,0,1,0,1,0,0] => 0
[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] => [1,1,1,0,0,1,0,1,0,0] => 0
[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] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,0,1,0,1,0,0] => 2
[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] => [1,0,1,1,0,1,0,1,0,0] => 2
[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] => [1,0,1,1,0,1,0,1,0,0] => 2
[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] => [1,0,1,1,0,1,0,1,0,0] => 2
[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] => [1,1,0,1,0,1,0,0] => 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] => [1,1,0,1,0,1,0,0] => 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] => [1,1,0,1,0,1,0,0] => 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] => [1,1,0,1,0,1,0,0] => 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] => [1,1,0,1,0,1,0,0] => 1
[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] => [1,1,1,1,1,0,1,0,0,0,0,0] => 0
[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] => [1,1,1,0,1,1,1,0,0,0,0,0] => 0
[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] => [1,1,1,0,1,1,1,0,0,0,0,0] => 0
[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] => [1,1,1,1,1,0,0,0,0,0] => 0
[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] => [1,0,1,1,1,0,1,1,0,0,0,0] => 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] => [1,0,1,1,1,0,1,1,0,0,0,0] => 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] => [1,0,1,1,1,0,1,1,0,0,0,0] => 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] => [1,1,1,0,1,1,0,0,0,0] => 0
[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] => [1,0,1,0,1,1,1,1,0,0,0,0] => 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] => [1,0,1,1,1,1,0,0,0,0] => 0
[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] => [1,1,1,1,0,0,0,0] => 0
[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] => [1,0,1,1,1,0,1,0,0,1,0,0] => 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] => [1,1,1,0,1,0,0,1,0,0] => 0
[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] => [1,1,1,0,1,0,0,1,0,0] => 0
[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] => [1,1,1,0,1,0,0,1,0,0] => 0
[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] => [1,0,1,0,1,1,1,0,0,1,0,0] => 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] => [1,0,1,0,1,1,1,0,0,1,0,0] => 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] => [1,0,1,1,1,0,0,1,0,0] => 0
[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] => [1,0,1,1,1,0,0,1,0,0] => 0
[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] => [1,0,1,1,1,0,0,1,0,0] => 0
[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] => [1,0,1,1,1,0,0,1,0,0] => 0
[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] => [1,1,1,0,0,1,0,0] => 0
[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] => [1,1,1,0,0,1,0,0] => 0
[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] => [1,1,1,0,0,1,0,0] => 0
[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] => [1,0,1,0,1,1,0,1,0,0] => 2
[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] => [1,0,1,0,1,1,0,1,0,0] => 2
[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] => [1,0,1,1,0,1,0,0] => 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] => [1,0,1,1,0,1,0,0] => 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] => [1,0,1,1,0,1,0,0] => 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] => [1,1,0,1,0,0] => 0
[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] => [1,1,0,1,0,0] => 0
[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] => [1,1,0,1,0,0] => 0
[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] => [1,1,0,1,0,0] => 0
[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] => [1,1,0,1,0,0] => 0
[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] => [1,1,0,1,0,0] => 0
[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] => [1,1,0,1,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0] => [6,5,5] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => [5,5,5] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0,0] => [5,4,4] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0] => [4,4,4] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => [7,5,3] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0] => [4,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0] => [6,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => 0
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [6,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0] => [4,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 0
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 0
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 0
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0] => [7,2,2] => [2,2] => [1,1,1,0,0,0] => 0
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2] => [2,2] => [1,1,1,0,0,0] => 0
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2] => [2,2] => [1,1,1,0,0,0] => 0
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2] => [2,2] => [1,1,1,0,0,0] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 3
[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1] => [2,1] => [1,0,1,1,0,0] => 0
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1] => [2,1] => [1,0,1,1,0,0] => 0
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1] => [2,1] => [1,0,1,1,0,0] => 0
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1] => [2,1] => [1,0,1,1,0,0] => 0
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1] => [2,1] => [1,0,1,1,0,0] => 0
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1] => [2,1] => [1,0,1,1,0,0] => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1] => [1,1] => [1,1,0,0] => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1] => [1,1] => [1,1,0,0] => 0
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1] => [1,1] => [1,1,0,0] => 0
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1] => [1,1] => [1,1,0,0] => 0
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1] => [1,1] => [1,1,0,0] => 0
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1] => [1,1] => [1,1,0,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [7,6] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [6,6] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [7,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => 3
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [5,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => 3
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0] => [4,4] => [4] => [1,0,1,0,1,0,1,0] => 2
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0] => [7,3] => [3] => [1,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [4,3] => [3] => [1,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [3,3] => [3] => [1,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [7,2] => [2] => [1,0,1,0] => 0
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [4,2] => [2] => [1,0,1,0] => 0
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [3,2] => [2] => [1,0,1,0] => 0
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [2,2] => [2] => [1,0,1,0] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [7,1] => [1] => [1,0] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0] => [6,1] => [1] => [1,0] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0] => [5,1] => [1] => [1,0] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0] => [4,1] => [1] => [1,0] => 0
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [3,1] => [1] => [1,0] => 0
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => [1] => [1,0] => 0
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1] => [1] => [1,0] => 0
[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] => [1,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [1,1] => [1] => [1,0] => 0
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1] => [1] => [1,0] => 0
[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] => [1,0,1,1,0,0] => 0
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [3,2] => [2] => [1,0,1,0] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [8,1] => [1] => [1,0] => 0
[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] => [1,1,0,0] => 0
[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] => [1,1,0,1,0,0] => 0
[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] => [1,1,0,1,0,1,0,0] => 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] => [1,1,0,1,0,1,0,1,0,0] => 2
[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] => [1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0] => [9,1] => [1] => [1,0] => 0
[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] => [1,0,1,1,0,0] => 0
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [2,2] => [2] => [1,0,1,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0] => [3,3] => [3] => [1,0,1,0,1,0] => 1
[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] => [1,1,1,0,1,0,0,0] => 0
[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] => [1,1,1,0,1,0,1,0,0,0] => 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] => [1,1,1,1,1,0,1,0,0,0,0,0] => 0
[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] => [1,1,0,0] => 0
[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] => [1,1,0,0] => 0
[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] => [1,0,1,1,1,0,0,0] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [3,1] => [1] => [1,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0] => [6,6] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 4
[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] => [1,1,0,1,0,1,0,1,0,0] => 2
[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] => [1,1,0,1,0,1,0,1,0,0] => 2
[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] => [1,1,0,1,0,1,0,1,0,0] => 2
[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] => [1,1,0,1,0,1,0,1,0,0] => 2
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [2,1] => [1] => [1,0] => 0
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1] => [1] => [1,0] => 0
[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] => [1,0,1,1,1,0,0,1,0,0] => 0
[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] => [1,0,1,1,0,0] => 0
[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] => [1,0,1,1,0,0] => 0
[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] => [1,0,1,1,0,0] => 0
[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] => [1,1,0,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,1,0,1,0,1,0,1,0,0] => 2
[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] => [1,1,0,1,0,1,0,0] => 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] => [1,1,0,1,0,0] => 0
[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] => [1,0,1,1,1,0,0,1,0,0] => 0
[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] => [1,0,1,0,1,1,1,0,0,1,0,0] => 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] => [1,0,1,1,1,0,1,0,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0] => [3,1] => [1] => [1,0] => 0
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0] => [4,2] => [2] => [1,0,1,0] => 0
[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] => [1,1,1,1,0,1,0,0,0,1,0,0] => 0
[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] => [1,0,1,1,1,0,0,1,0,0] => 0
[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] => [1,1,1,0,1,1,0,0,0,1,0,0] => 0
[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] => [1,0,1,1,1,1,0,0,0,1,0,0] => 0
[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] => [1,0,1,1,1,0,0,1,0,1,0,0] => 0
[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] => [1,0,1,0,1,0,1,0,1,1,0,0] => 3
[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] => [1,0,1,0,1,0,1,1,0,0] => 2
[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] => [1,0,1,0,1,1,0,0] => 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] => [1,1,1,0,0,0] => 0
[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] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0] => [7,1] => [1] => [1,0] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0] => [6,1] => [1] => [1,0] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0] => [5,1] => [1] => [1,0] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0] => [4,1] => [1] => [1,0] => 0
[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] => [1,1,0,1,0,0] => 0
[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] => [1,1,0,1,0,1,0,0] => 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] => [1,1,0,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,1,0,0] => 0
[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] => [1,1,1,0,0,1,0,0] => 0
[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] => [1,1,0,0] => 0
[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] => [1,1,0,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,1,0,0] => 0
[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] => [1,0,1,1,1,0,0,1,0,0] => 0
[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] => [1,0,1,1,0,1,0,0] => 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] => [1,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0] => [2,2] => [2] => [1,0,1,0] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0] => [3,3] => [3] => [1,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,1] => [1] => [1,0] => 0
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0,0] => [8,1] => [1] => [1,0] => 0
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0,0] => [7,1] => [1] => [1,0] => 0
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0,0] => [6,1] => [1] => [1,0] => 0
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0,0] => [5,1] => [1] => [1,0] => 0
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0] => [4,1] => [1] => [1,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0] => [5,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => 3
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0] => [4,4] => [4] => [1,0,1,0,1,0,1,0] => 2
[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] => [1,0,1,0,1,1,0,0] => 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] => [1,1,1,0,0,1,0,0] => 0
[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] => [1,0,1,1,1,0,0,0] => 0
search for individual values
searching the database for the individual values of this statistic
Description
Number of simple modules S in the corresponding Nakayama algebra such that the Auslander-Reiten sequence ending at S has the property that all modules in the exact sequence are reflexive.
Map
parallelogram polyomino
Description
Return the Dyck path corresponding to the partition interpreted as a parallogram polyomino.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
Map
to partition
Description
The cut-out partition of a Dyck path.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ 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 $(n-1,\ldots,2,1)$.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ 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 $(n-1,\ldots,2,1)$.
Map
first row removal
Description
Removes the first entry of an integer partition
searching the database
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