Identifier
-
Mp00027:
Dyck paths
—to partition⟶
Integer partitions
Mp00321: Integer partitions —2-conjugate⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
St001167: Dyck paths ⟶ ℤ
Values
[1,0,1,0] => [1] => [1] => [1,0,1,0] => 0
[1,0,1,0,1,0] => [2,1] => [3] => [1,1,1,0,0,0,1,0] => 0
[1,0,1,1,0,0] => [1,1] => [1,1] => [1,0,1,1,0,0] => 0
[1,1,0,0,1,0] => [2] => [2] => [1,1,0,0,1,0] => 0
[1,1,0,1,0,0] => [1] => [1] => [1,0,1,0] => 0
[1,0,1,0,1,0,1,0] => [3,2,1] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 0
[1,0,1,0,1,1,0,0] => [2,2,1] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,0,1,1,0,0,1,0] => [3,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 1
[1,0,1,1,0,1,0,0] => [2,1,1] => [3,1] => [1,1,0,1,0,0,1,0] => 1
[1,0,1,1,1,0,0,0] => [1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 0
[1,1,0,0,1,0,1,0] => [3,2] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,0] => [2,2] => [4] => [1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,1,0,0,1,0] => [3,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1
[1,1,0,1,0,1,0,0] => [2,1] => [3] => [1,1,1,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,0] => [1,1] => [1,1] => [1,0,1,1,0,0] => 0
[1,1,1,0,0,0,1,0] => [3] => [2,1] => [1,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,0] => [2] => [2] => [1,1,0,0,1,0] => 0
[1,1,1,0,1,0,0,0] => [1] => [1] => [1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0] => [4,3,2,1] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0
[1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,0] => [4,3,1,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,0] => [3,3,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,0,1,0,0,1,0] => [4,2,1,1] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,0] => [2,2,1,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 0
[1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0] => [4,3,2] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,0] => [3,3,2] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,0] => [4,2,2] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,0] => [3,2,2] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,0] => [2,2,2] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,0,1,0,1,0] => [4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,0] => [3,3,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,0] => [4,2,1] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,0] => [3,2,1] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,0,0] => [2,2,1] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,0,1,0] => [4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,0] => [3,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 1
[1,1,0,1,1,0,1,0,0,0] => [2,1,1] => [3,1] => [1,1,0,1,0,0,1,0] => 1
[1,1,0,1,1,1,0,0,0,0] => [1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,0] => [4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,0] => [3,3] => [3,2,1] => [1,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,1,0,0,1,0] => [4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,0,0] => [3,2] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 1
[1,1,1,0,0,1,1,0,0,0] => [2,2] => [4] => [1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,0,0,1,0] => [4,1] => [3,2] => [1,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,0] => [3,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,0] => [2,1] => [3] => [1,1,1,0,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,0] => [1,1] => [1,1] => [1,0,1,1,0,0] => 0
[1,1,1,1,0,0,0,0,1,0] => [4] => [2,2] => [1,1,0,0,1,1,0,0] => 0
[1,1,1,1,0,0,0,1,0,0] => [3] => [2,1] => [1,0,1,0,1,0] => 1
[1,1,1,1,0,0,1,0,0,0] => [2] => [2] => [1,1,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,0] => [1] => [1] => [1,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,0,1,0] => [5,3,3,2,1] => [3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [4,3,3,2,1] => [5,5,3] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [3,3,3,2,1] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,0,0,1,0] => [5,3,2,2,1] => [5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => [3,3,2,2,1] => [5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,1] => [5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => [4,3,3,1,1] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,0] => [3,3,3,1,1] => [3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,1] => [6,3,3,1] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,1] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,1] => [5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,0] => [3,3,2,1,1] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,0] => [5,2,2,1,1] => [6,3,1,1] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,1,0,1,0,0,0] => [3,2,2,1,1] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,0] => [5,4,1,1,1] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => [4,3,1,1,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,1,0,0,0] => [3,3,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,0] => [5,2,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [4,2,1,1,1] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 0
[1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,1,0,0,1,0] => [5,3,3,2] => [5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => 3
[1,1,0,0,1,0,1,1,1,0,0,0] => [3,3,3,2] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => 3
[1,1,0,1,0,0,1,0,1,0,1,0] => [5,4,3,1] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => 3
[1,1,0,1,0,0,1,0,1,1,0,0] => [4,4,3,1] => [6,5,1] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,3,1] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,0] => [4,3,3,1] => [5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,3,3,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,0] => [5,4,2,1] => [6,3,3] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,0] => [5,3,2,1] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,0] => [3,3,2,1] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,2,2,1] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => 2
[1,1,0,1,0,1,1,0,1,0,0,0] => [3,2,2,1] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,0] => [5,4,1,1] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,0,0,0,1,1,0,0] => [4,4,1,1] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 2
[1,1,0,1,1,0,0,1,0,0,1,0] => [5,3,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,0,1,1,0,0,1,0,1,0,0] => [4,3,1,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 2
[1,1,0,1,1,0,0,1,1,0,0,0] => [3,3,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,0,1,0,0,0,1,0] => [5,2,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
>>> Load all 921 entries. <<<[1,1,0,1,1,0,1,0,0,1,0,0] => [4,2,1,1] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,0] => [3,2,1,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,1,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,0] => [5,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,0] => [4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,0] => [5,4,3] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,0,1,1,0,0] => [4,4,3] => [6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => 2
[1,1,1,0,0,0,1,1,0,1,0,0] => [4,3,3] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,1,0,0,1,0,1,0] => [5,4,2] => [6,4,1] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => [4,4,2] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [5,3,2] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,3,2] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => [5,2,2] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [4,2,2] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 1
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,2] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,1,1,1,0,0,0,0] => [2,2,2] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,0,0,1,0,1,0] => [5,4,1] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,4,1] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [5,3,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,3,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 2
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,1] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,1] => [3,1] => [1,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,0,0,1,0,0,1,0] => [5,3] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 2
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,0] => [3,3] => [3,2,1] => [1,0,1,0,1,0,1,0] => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,2] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 2
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,1,0,0,0] => [3,2] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,1,0,0,0,0] => [2,2] => [4] => [1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => [3,2] => [1,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,0] => [3,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => [3] => [1,1,1,0,0,0,1,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,1] => [1,1] => [1,0,1,1,0,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,0] => [5] => [2,2,1] => [1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [4] => [2,2] => [1,1,0,0,1,1,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,0] => [3] => [2,1] => [1,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => [2] => [2] => [1,1,0,0,1,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,0] => [1] => [1] => [1,0,1,0] => 0
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2,1] => [5,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2,1] => [5,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => [5,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 0
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => [5,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => [5,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 3
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2,1,1] => [6,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 3
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1,1] => [4,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1,1] => [5,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => [3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => [6,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1,1] => [6,3,3,1,1] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1,1] => [5,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,1,1] => [5,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1,1] => [5,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1,1] => [5,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,1,1] => [6,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1,1] => [4,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1,1] => [5,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 0
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1,1] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1,1] => [6,3,1,1,1] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1,1] => [5,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1,1] => [5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1,1] => [6,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1,1] => [4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1,1] => [6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 0
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 0
[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] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2] => [5,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2] => [5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1] => [5,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1] => [5,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1] => [5,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1] => [3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1] => [6,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2,1] => [5,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1] => [3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1] => [5,5,3] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1] => [6,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1] => [5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => [5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1] => [5,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,1] => [6,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,1] => [5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1,1] => [5,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => 3
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => [3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,1] => [6,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 3
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1] => [4,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 2
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,1] => [6,3,3,1] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,1] => [6,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1] => [5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1] => [6,3,1,1] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1,1] => [6,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 3
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1,1] => [5,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1] => [6,2,1,1,1] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 0
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3] => [5,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => [6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => [4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3] => [5,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => [5,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3] => [3,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3] => [5,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2] => [6,3,3,2,1] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2] => [5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => 3
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => 3
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1] => [5,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1] => [6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1] => [6,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 3
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1] => [4,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 3
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => 3
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1] => [6,5,1] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 2
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => 3
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1] => [5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1] => [5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1] => [4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1] => [6,3,3] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1] => [5,5,2] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1] => [6,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 3
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1] => [4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1] => [6,4,1,1] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1] => [5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 2
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,5,4] => [6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 3
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [6,5,3] => [5,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [5,5,3] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 3
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [6,4,3] => [6,5,2] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [5,4,3] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,4,3] => [6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [6,3,3] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 3
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [5,3,3] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,3] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,3,3] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [6,5,2] => [6,4,3] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 2
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,5,2] => [6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 3
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [6,4,2] => [6,4,2] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 2
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,4,2] => [6,4,1] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,4,2] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2] => [6,3,2] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [5,3,2] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,2] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,3,2] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,2,2] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [5,2,2] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,2] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,2,2] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [6,5,1] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,5,1] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [6,4,1] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => 2
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,4,1] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,4,1] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,1] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,3,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [3,3,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,2,1] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,2,1] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,2,1] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 0
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [3,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,1,1] => [3,1] => [1,1,0,1,0,0,1,0] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => [4,3,2,1] => [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] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,3] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,3] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 2
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,3] => [3,2,1] => [1,0,1,0,1,0,1,0] => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,2] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,2] => [4] => [1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [4,1] => [3,2] => [1,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => [3] => [1,1,1,0,0,0,1,0] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1] => [1,1] => [1,0,1,1,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => [2,2,1] => [1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [4] => [2,2] => [1,1,0,0,1,1,0,0] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => [2,1] => [1,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => [2] => [1,1,0,0,1,0] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1] => [1] => [1,0,1,0] => 0
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1,1] => [5,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => [6,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => [5,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1,1,1] => [6,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 2
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1,1] => [5,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1,1] => [3,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1,1] => [6,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 0
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1,1] => [5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,1,1,1] => [6,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1,1,1] => [5,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1,1] => [3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1,1] => [6,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 1
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1,1] => [5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => 1
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1,1] => [6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 0
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2] => [5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3,1] => [5,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 3
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1] => [5,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1] => [5,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1] => [5,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1,1] => [5,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1] => [5,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1,1] => [6,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 3
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1,1] => [4,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1] => [5,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1] => [3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1] => [6,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,1,1] => [6,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 2
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1] => [6,3,3,1,1] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 1
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1,1] => [5,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1,1] => [5,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1] => [5,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 3
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1,1] => [5,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,1,1] => [6,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1,1] => [4,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1,1] => [5,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1,1,1] => [6,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1] => [6,3,1,1,1] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 2
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 2
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1,1] => [5,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1,1] => [5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1,1] => [6,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1,1] => [4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1] => [6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 0
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 0
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 0
[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] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3] => [5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 3
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => [3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2] => [5,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2] => [5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1] => [5,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,1] => [5,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1] => [5,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 2
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1] => [3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1] => [6,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1] => [5,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 2
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1] => [3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1] => [5,5,3] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,2,1] => [6,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1] => [6,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,1] => [5,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1] => [5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1] => [5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1] => [5,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,1] => [6,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,1] => [5,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1] => [5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1] => [5,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 3
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => 3
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1] => [3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [7,6,2,1,1] => [6,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,1] => [4,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,1] => [6,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 3
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1] => [4,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,1] => [6,4,3,1,1] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 3
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1] => [6,3,3,1] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,1] => [4,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,1] => [6,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1] => [5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1,1] => [6,4,1,1,1] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1] => [6,3,1,1] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 2
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,1,1] => [6,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 3
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1,1] => [6,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 3
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,1,1] => [5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1] => [5,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 2
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1,1] => [4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1] => [6,2,1,1,1] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 0
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 0
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 0
[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] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3] => [5,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3] => [6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3] => [4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [7,4,3,3] => [5,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 3
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3] => [5,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3] => [5,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3] => [3,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3] => [5,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2] => [6,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2] => [6,3,3,2,1] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 2
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2] => [5,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2] => [5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => 3
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => 3
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [6,5,5,1] => [6,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 2
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1] => [5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [7,5,4,1] => [5,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1] => [5,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [7,4,4,1] => [6,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 3
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1] => [6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [7,6,3,1] => [5,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 3
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1] => [6,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 3
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1] => [4,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 3
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1] => [5,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => 3
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1] => [6,5,1] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 2
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => 3
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1] => [5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [7,6,2,1] => [6,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1] => [4,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1] => [5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1] => [4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1] => [6,3,3,2] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1] => [6,3,3] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1] => [3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1] => [5,5,2] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => 2
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,1] => [4,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1] => [6,4,3,1] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 3
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1] => [6,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 3
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1] => [4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,1] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1] => [6,4,1,1] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 2
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1] => [5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 2
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 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] => [1,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [7,5,5] => [5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [6,5,5] => [6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 3
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [7,5,4] => [6,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,5,4] => [6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 3
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [7,6,3] => [5,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,6,3] => [6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [7,5,3] => [4,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [6,5,3] => [5,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,5,3] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 3
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [7,4,3] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => 3
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [6,4,3] => [6,5,2] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 2
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => 2
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [4,4,3] => [6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [7,3,3] => [3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [6,3,3] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 3
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,3,3] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => 2
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [4,3,3] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 2
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [7,6,2] => [6,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,6,2] => [6,4,4] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [7,5,2] => [6,3,2,2,1] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 3
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [6,5,2] => [6,4,3] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,5,2] => [6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 3
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [7,4,2] => [6,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 3
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [6,4,2] => [6,4,2] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [5,4,2] => [6,4,1] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 2
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [4,4,2] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [7,3,2] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [6,3,2] => [6,3,2] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 2
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,3,2] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [4,3,2] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [3,3,2] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [7,2,2] => [6,2,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [6,2,2] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,2,2] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 2
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [4,2,2] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [3,2,2] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [2,2,2] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [7,6,1] => [4,4,3,3] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,6,1] => [5,4,4] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [7,5,1] => [4,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 3
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [6,5,1] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [5,5,1] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [7,4,1] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [6,4,1] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => 2
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,4,1] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [4,4,1] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [7,3,1] => [3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [6,3,1] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,3,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [3,3,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,2,1] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [6,2,1] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,2,1] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [4,2,1] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 0
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [2,2,1] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [6,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 0
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [3,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,1,1] => [3,1] => [1,1,0,1,0,0,1,0] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [7,6] => [4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [7,5] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [5,5] => [4,3,2,1] => [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] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,4] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [5,4] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,3] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,3] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [5,3] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 2
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [3,3] => [3,2,1] => [1,0,1,0,1,0,1,0] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,2] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [5,2] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 2
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,2] => [4] => [1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [5,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,1] => [3,2] => [1,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => [3] => [1,1,1,0,0,0,1,0] => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1] => [1,1] => [1,0,1,1,0,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => [2,2,1] => [1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => [2,2] => [1,1,0,0,1,1,0,0] => 0
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => [2,1] => [1,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => [2] => [1,1,0,0,1,0] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1] => [1] => [1,0,1,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [8,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 2
[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] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 0
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0] => [11] => [2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1] => [3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0] => [9,2] => [4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [8,3] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1] => [5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1,1] => [4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0] => [10,2] => [4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 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] => [4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0] => [9,3] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0] => [9,2,1] => [3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0] => [8,4] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => [8,2,2] => [6,2,2,2] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1,1] => [6,2,2,1,1] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 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] => [5,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 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] => [5,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0] => [9,4] => [4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => 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] => [4,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [8,5] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0] => [8,4,1] => [5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2] => [6,3,2,2] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 2
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1,1] => [5,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 1
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1,1,1] => [6,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0] => [9,5] => [4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 3
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,1,0] => [9,3,2] => [5,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 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] => [5,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [8,6] => [4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0] => [8,4,2] => [6,4,2,2] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 2
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,1,0] => [8,3,3] => [5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2,1] => [5,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,7] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 3
[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] => [5,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[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] => [5,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0] => [9,6] => [4,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [8,7] => [4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0] => [8,6,1] => [5,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,0] => [8,3,3,1] => [5,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [7,7,1] => [4,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 3
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => [9,7] => [4,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [8,7,1] => [4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,1,0] => [8,5,3] => [5,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 3
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0] => [8,5,2,1] => [5,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0] => [7,7,2] => [6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 4
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0] => [8,7,2] => [6,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0] => [8,7,1,1] => [6,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 4
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,1,0] => [8,3,3,3] => [5,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0] => [8,3,3,2,1] => [5,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,1,0,0] => [7,7,3] => [4,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3
[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] => [6,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 0
[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] => [5,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 0
[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] => [5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => 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] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0
[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] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[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] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,2] => [5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [6,3,2,1,1,1] => [6,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 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] => [4,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 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] => [5,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2,1,1,1] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => 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] => [6,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 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] => [6,3,1,1,1] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 2
[1,1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,1,1,1] => [5,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 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] => [5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 2
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1,1,1,1] => [6,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 2
[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 0
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 0
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 0
[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] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0] => [4,3,3,3,3] => [5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 3
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3] => [3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,1] => [3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,1] => [6,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0,0] => [5,3,3,2,1] => [3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,3,3,2,1] => [5,5,3] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [3,3,3,2,1] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0,0] => [7,3,2,2,1] => [5,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2
[1,1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,2,1] => [5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1,1] => [6,3,3,1] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0] => [6,3,2,1,1] => [6,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,1] => [5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1,1] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0,0] => [7,6,1,1,1] => [6,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 3
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1,1,1] => [6,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 3
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0,0] => [7,4,1,1,1] => [5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,1,1] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1,1,1] => [5,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2
[1,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 2
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1,1,1] => [4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0
[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 0
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 0
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 0
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0,0] => [5,5,4,3] => [5,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0] => [5,5,3,3] => [4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,3,3] => [5,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,0] => [5,5,5,1] => [5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 4
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,0] => [6,5,3,1] => [6,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 3
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3,1] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => 3
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0] => [6,3,3,1] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => 3
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3,1] => [5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0] => [7,5,2,1] => [4,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0] => [6,5,2,1] => [5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1] => [6,3,3] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 0
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0] => [6,3,2,1] => [5,5,2] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2,1] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0] => [7,6,1,1] => [4,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1,1] => [6,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 3
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 2
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,1] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 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] => [1,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0] => [6,5,5] => [6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 3
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => [5,5,5] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => [7,5,3] => [4,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => 2
[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0] => [4,4,3] => [6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0] => [6,3,3] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 3
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 2
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [6,4,2] => [6,4,2] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 2
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2] => [6,4,1] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 2
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0] => [4,4,2] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 2
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0] => [7,2,2] => [6,2,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0] => [7,6,1] => [4,4,3,3] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0] => [6,6,1] => [5,4,4] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => 0
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 2
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 0
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 0
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 0
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1] => [3,1] => [1,1,0,1,0,0,1,0] => 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] => [1,0,1,1,1,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [7,6] => [4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [6,6] => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [7,5] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [5,5] => [4,3,2,1] => [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] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0] => [7,3] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [3,3] => [3,2,1] => [1,0,1,0,1,0,1,0] => 2
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [7,2] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [3,2] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [2,2] => [4] => [1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [7,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0] => [6,1] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0] => [5,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0] => [4,1] => [3,2] => [1,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [3,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => [3] => [1,1,1,0,0,0,1,0] => 0
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1] => [1,1] => [1,0,1,1,0,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [6] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [5] => [2,2,1] => [1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [4] => [2,2] => [1,1,0,0,1,1,0,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [3] => [2,1] => [1,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2] => [2] => [1,1,0,0,1,0] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1] => [1] => [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] => [1,1] => [1,1] => [1,0,1,1,0,0] => 0
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [2] => [2] => [1,1,0,0,1,0] => 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] => [1,0,1,1,0,0] => 0
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [3,2] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [2] => [2] => [1,1,0,0,1,0] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [8] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [9] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [8,1] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1] => [1] => [1,0,1,0] => 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] => [1,0,1,1,1,0,0,0] => 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] => [1,0,1,1,1,1,0,0,0,0] => 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] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[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] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [1] => [1] => [1,0,1,0] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [7] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [6] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [5] => [2,2,1] => [1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [4] => [2,2] => [1,1,0,0,1,1,0,0] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [3] => [2,1] => [1,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0] => [9,1] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0] => [8,2,1] => [5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [2,2] => [4] => [1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0] => [3,3] => [3,2,1] => [1,0,1,0,1,0,1,0] => 2
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [3,3,3] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1] => [3,1] => [1,1,0,1,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 2
[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] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 0
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [3,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1
[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] => [5,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0] => [6,6] => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[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] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 0
[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] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 0
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [2,1] => [3] => [1,1,1,0,0,0,1,0] => 0
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1] => [3] => [1,1,1,0,0,0,1,0] => 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] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 0
[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0] => [3] => [2,1] => [1,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0] => [7,2,1] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 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] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 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] => [5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [7,7] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 3
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,1,1] => [4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0] => [5,3,2,1] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0] => [5,4,2,1] => [6,3,3] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 0
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,1] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => 3
[1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0] => [3,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0] => [4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0] => [6,3,2,1] => [5,5,2] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 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] => [5,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 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] => [5,5,3] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1
[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] => [5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,0] => [8,7,1] => [4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0,0] => [7,6,1] => [4,4,3,3] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0,0] => [6,5,1] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0] => [5,4,1] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0] => [4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0] => [7,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0] => [6,1] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0] => [5,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0] => [4,1] => [3,2] => [1,1,0,0,1,0,1,0] => 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] => [3,1,1] => [1,0,1,1,0,0,1,0] => 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] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 0
[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] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0] => [8,7] => [4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[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] => [3,1] => [1,1,0,1,0,0,1,0] => 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] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 1
[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] => [1,0,1,1,1,0,0,0] => 0
[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] => [6,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0,0] => [8,3,2,1] => [5,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 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] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 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] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 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] => [4] => [1,1,1,1,0,0,0,0,1,0] => 0
[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] => [5,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 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] => [3,2,1] => [1,0,1,0,1,0,1,0] => 2
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0] => [3] => [2,1] => [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] => [1,0,1,1,0,0] => 0
[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] => [6,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0,0] => [8,7,1,1] => [6,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 4
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0,0] => [8,1] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 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] => [6,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 3
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0,0] => [7,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0,0] => [6,1] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0,0] => [5,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0] => [4,1] => [3,2] => [1,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0] => [5,5] => [4,3,2,1] => [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] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0] => [5,3,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0] => [3,3,2] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 2
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Description
The number of simple modules that appear as the top of an indecomposable non-projective modules that is reflexive in the corresponding Nakayama algebra.
The top of a module is the cokernel of the inclusion of the radical of the module into the module.
For Nakayama algebras with at most 8 simple modules, the statistic also coincides with the number of simple modules with projective dimension at least 3 in the corresponding Nakayama algebra.
The top of a module is the cokernel of the inclusion of the radical of the module into the module.
For Nakayama algebras with at most 8 simple modules, the statistic also coincides with the number of simple modules with projective dimension at least 3 in the corresponding Nakayama algebra.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.
Map
2-conjugate
Description
Return a partition with the same number of odd parts and number of even parts interchanged with the number of cells with zero leg and odd arm length.
This is a special case of an involution that preserves the sequence of non-zero remainders of the parts under division by $s$ and interchanges the number of parts divisible by $s$ and the number of cells with zero leg length and arm length congruent to $s-1$ modulo $s$.
In particular, for $s=1$ the involution is conjugation, hence the name.
This is a special case of an involution that preserves the sequence of non-zero remainders of the parts under division by $s$ and interchanges the number of parts divisible by $s$ and the number of cells with zero leg length and arm length congruent to $s-1$ modulo $s$.
In particular, for $s=1$ the involution is conjugation, hence the name.
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 $(n-1,\ldots,2,1)$.
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