Identifier
-
Mp00027:
Dyck paths
—to partition⟶
Integer partitions
Mp00322: Integer partitions —Loehr-Warrington⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001657: Integer partitions ⟶ ℤ
Values
[1,1,0,0,1,0] => [2] => [1,1] => [1] => 0
[1,0,1,0,1,0,1,0] => [3,2,1] => [5,1] => [1] => 0
[1,0,1,0,1,1,0,0] => [2,2,1] => [2,2,1] => [2,1] => 1
[1,0,1,1,0,0,1,0] => [3,1,1] => [4,1] => [1] => 0
[1,0,1,1,0,1,0,0] => [2,1,1] => [2,2] => [2] => 1
[1,0,1,1,1,0,0,0] => [1,1,1] => [2,1] => [1] => 0
[1,1,0,1,0,0,1,0] => [3,1] => [2,1,1] => [1,1] => 0
[1,1,1,0,0,0,1,0] => [3] => [1,1,1] => [1,1] => 0
[1,1,1,0,0,1,0,0] => [2] => [1,1] => [1] => 0
[1,0,1,0,1,0,1,0,1,0] => [4,3,2,1] => [7,3] => [3] => 0
[1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => [3,2,2,2] => [2,2,2] => 3
[1,0,1,0,1,1,0,0,1,0] => [4,2,2,1] => [6,3] => [3] => 0
[1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => [3,2,2,1] => [2,2,1] => 2
[1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => [4,1,1,1] => [1,1,1] => 0
[1,0,1,1,0,0,1,0,1,0] => [4,3,1,1] => [7,2] => [2] => 1
[1,0,1,1,0,0,1,1,0,0] => [3,3,1,1] => [6,2] => [2] => 1
[1,0,1,1,0,1,0,0,1,0] => [4,2,1,1] => [4,4] => [4] => 0
[1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => [5,2] => [2] => 1
[1,0,1,1,0,1,1,0,0,0] => [2,2,1,1] => [4,1,1] => [1,1] => 0
[1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => [3,2,1,1] => [2,1,1] => 1
[1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => [3,3] => [3] => 0
[1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => [3,1,1] => [1,1] => 0
[1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => [3,1] => [1] => 0
[1,1,0,0,1,0,1,0,1,0] => [4,3,2] => [7,1,1] => [1,1] => 0
[1,1,0,0,1,0,1,1,0,0] => [3,3,2] => [2,2,2,2] => [2,2,2] => 3
[1,1,0,0,1,1,0,0,1,0] => [4,2,2] => [6,1,1] => [1,1] => 0
[1,1,0,0,1,1,0,1,0,0] => [3,2,2] => [2,2,2,1] => [2,2,1] => 2
[1,1,0,0,1,1,1,0,0,0] => [2,2,2] => [2,2,2] => [2,2] => 2
[1,1,0,1,0,0,1,0,1,0] => [4,3,1] => [7,1] => [1] => 0
[1,1,0,1,0,0,1,1,0,0] => [3,3,1] => [6,1] => [1] => 0
[1,1,0,1,0,1,0,0,1,0] => [4,2,1] => [5,1,1] => [1,1] => 0
[1,1,0,1,0,1,0,1,0,0] => [3,2,1] => [5,1] => [1] => 0
[1,1,0,1,0,1,1,0,0,0] => [2,2,1] => [2,2,1] => [2,1] => 1
[1,1,0,1,1,0,0,0,1,0] => [4,1,1] => [3,1,1,1] => [1,1,1] => 0
[1,1,0,1,1,0,0,1,0,0] => [3,1,1] => [4,1] => [1] => 0
[1,1,0,1,1,0,1,0,0,0] => [2,1,1] => [2,2] => [2] => 1
[1,1,0,1,1,1,0,0,0,0] => [1,1,1] => [2,1] => [1] => 0
[1,1,1,0,0,1,0,0,1,0] => [4,2] => [2,2,1,1] => [2,1,1] => 1
[1,1,1,0,1,0,0,0,1,0] => [4,1] => [2,1,1,1] => [1,1,1] => 0
[1,1,1,0,1,0,0,1,0,0] => [3,1] => [2,1,1] => [1,1] => 0
[1,1,1,1,0,0,0,0,1,0] => [4] => [1,1,1,1] => [1,1,1] => 0
[1,1,1,1,0,0,0,1,0,0] => [3] => [1,1,1] => [1,1] => 0
[1,1,1,1,0,0,1,0,0,0] => [2] => [1,1] => [1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => [9,5,1] => [5,1] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [4,4,3,2,1] => [5,2,2,2,2,1] => [2,2,2,2,1] => 4
[1,0,1,0,1,0,1,1,0,0,1,0] => [5,3,3,2,1] => [8,5,1] => [5,1] => 0
[1,0,1,0,1,0,1,1,0,1,0,0] => [4,3,3,2,1] => [7,2,2,2] => [2,2,2] => 3
[1,0,1,0,1,0,1,1,1,0,0,0] => [3,3,3,2,1] => [6,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,0] => [5,4,2,2,1] => [9,2,2,1] => [2,2,1] => 2
[1,0,1,0,1,1,0,0,1,1,0,0] => [4,4,2,2,1] => [6,2,2,1,1,1] => [2,2,1,1,1] => 2
[1,0,1,0,1,1,0,1,0,0,1,0] => [5,3,2,2,1] => [6,6,1] => [6,1] => 0
[1,0,1,0,1,1,0,1,0,1,0,0] => [4,3,2,2,1] => [6,2,2,1,1] => [2,2,1,1] => 2
[1,0,1,0,1,1,0,1,1,0,0,0] => [3,3,2,2,1] => [6,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => [5,2,2,2,1] => [7,2,2,1] => [2,2,1] => 2
[1,0,1,0,1,1,1,0,0,1,0,0] => [4,2,2,2,1] => [3,3,3,1,1] => [3,3,1,1] => 0
[1,0,1,0,1,1,1,0,1,0,0,0] => [3,2,2,2,1] => [5,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => [5,4] => [4] => 0
[1,0,1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,1] => [9,4,1] => [4,1] => 0
[1,0,1,1,0,0,1,0,1,1,0,0] => [4,4,3,1,1] => [4,2,2,2,2,1] => [2,2,2,2,1] => 4
[1,0,1,1,0,0,1,1,0,0,1,0] => [5,3,3,1,1] => [8,4,1] => [4,1] => 0
[1,0,1,1,0,0,1,1,0,1,0,0] => [4,3,3,1,1] => [4,2,2,2,2] => [2,2,2,2] => 4
[1,0,1,1,0,0,1,1,1,0,0,0] => [3,3,3,1,1] => [4,2,2,2,1] => [2,2,2,1] => 3
[1,0,1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,1] => [9,2,2] => [2,2] => 2
[1,0,1,1,0,1,0,0,1,1,0,0] => [4,4,2,1,1] => [8,2,2] => [2,2] => 2
[1,0,1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,1] => [7,4,1] => [4,1] => 0
[1,0,1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,1] => [7,2,2] => [2,2] => 2
[1,0,1,1,0,1,0,1,1,0,0,0] => [3,3,2,1,1] => [6,2,2] => [2,2] => 2
[1,0,1,1,0,1,1,0,0,0,1,0] => [5,2,2,1,1] => [6,2,2,1] => [2,2,1] => 2
[1,0,1,1,0,1,1,0,0,1,0,0] => [4,2,2,1,1] => [3,3,2,2] => [3,2,2] => 2
[1,0,1,1,0,1,1,0,1,0,0,0] => [3,2,2,1,1] => [3,3,3] => [3,3] => 0
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,2,2,1,1] => [5,3] => [3] => 0
[1,0,1,1,1,0,0,0,1,0,1,0] => [5,4,1,1,1] => [9,2,1] => [2,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => [4,4,1,1,1] => [8,2,1] => [2,1] => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [5,3,1,1,1] => [5,5,1] => [5,1] => 0
[1,0,1,1,1,0,0,1,0,1,0,0] => [4,3,1,1,1] => [7,2,1] => [2,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => [3,3,1,1,1] => [5,2,1,1] => [2,1,1] => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => [5,2,1,1,1] => [4,2,2,1,1] => [2,2,1,1] => 2
[1,0,1,1,1,0,1,0,0,1,0,0] => [4,2,1,1,1] => [6,2,1] => [2,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => [3,3,1,1] => [3,1,1] => 0
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => [4,3] => [3] => 0
[1,0,1,1,1,1,0,0,0,0,1,0] => [5,1,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 1
[1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => [5,2,1] => [2,1] => 1
[1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => [3,2,2] => [2,2] => 2
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => [4,2] => [2] => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => [3,2] => [2] => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2] => [9,5] => [5] => 0
[1,1,0,0,1,0,1,0,1,1,0,0] => [4,4,3,2] => [3,3,2,2,2,1] => [3,2,2,2,1] => 3
[1,1,0,0,1,0,1,1,0,0,1,0] => [5,3,3,2] => [8,5] => [5] => 0
[1,1,0,0,1,0,1,1,0,1,0,0] => [4,3,3,2] => [3,3,2,2,2] => [3,2,2,2] => 3
[1,1,0,0,1,0,1,1,1,0,0,0] => [3,3,3,2] => [6,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,1,0,0,1,1,0,0,1,0,1,0] => [5,4,2,2] => [9,4] => [4] => 0
[1,1,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => [8,4] => [4] => 0
[1,1,0,0,1,1,0,1,0,0,1,0] => [5,3,2,2] => [6,6] => [6] => 0
[1,1,0,0,1,1,0,1,0,1,0,0] => [4,3,2,2] => [3,3,2,2,1] => [3,2,2,1] => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => [3,3,2,2] => [6,1,1,1,1] => [1,1,1,1] => 0
[1,1,0,0,1,1,1,0,0,0,1,0] => [5,2,2,2] => [7,4] => [4] => 0
[1,1,0,0,1,1,1,0,0,1,0,0] => [4,2,2,2] => [5,5] => [5] => 0
[1,1,0,0,1,1,1,0,1,0,0,0] => [3,2,2,2] => [5,1,1,1,1] => [1,1,1,1] => 0
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,2,2] => [5,1,1,1] => [1,1,1] => 0
[1,1,0,1,0,0,1,0,1,0,1,0] => [5,4,3,1] => [9,2,1,1] => [2,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [4,4,3,1] => [3,2,2,2,2,1] => [2,2,2,2,1] => 4
>>> Load all 1727 entries. <<<[1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,3,1] => [8,2,1,1] => [2,1,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [4,3,3,1] => [3,2,2,2,2] => [2,2,2,2] => 4
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,3,3,1] => [3,2,2,2,1] => [2,2,2,1] => 3
[1,1,0,1,0,1,0,0,1,0,1,0] => [5,4,2,1] => [9,3] => [3] => 0
[1,1,0,1,0,1,0,0,1,1,0,0] => [4,4,2,1] => [8,3] => [3] => 0
[1,1,0,1,0,1,0,1,0,0,1,0] => [5,3,2,1] => [7,2,1,1] => [2,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => [7,3] => [3] => 0
[1,1,0,1,0,1,0,1,1,0,0,0] => [3,3,2,1] => [3,2,2,2] => [2,2,2] => 3
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,2,2,1] => [3,3,2,1,1] => [3,2,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => [4,2,2,1] => [6,3] => [3] => 0
[1,1,0,1,0,1,1,0,1,0,0,0] => [3,2,2,1] => [3,2,2,1] => [2,2,1] => 2
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,2,2,1] => [4,1,1,1] => [1,1,1] => 0
[1,1,0,1,1,0,0,0,1,0,1,0] => [5,4,1,1] => [9,2] => [2] => 1
[1,1,0,1,1,0,0,0,1,1,0,0] => [4,4,1,1] => [8,2] => [2] => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => [5,3,1,1] => [6,2,1,1] => [2,1,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => [4,3,1,1] => [7,2] => [2] => 1
[1,1,0,1,1,0,0,1,1,0,0,0] => [3,3,1,1] => [6,2] => [2] => 1
[1,1,0,1,1,0,1,0,0,0,1,0] => [5,2,1,1] => [3,3,1,1,1] => [3,1,1,1] => 0
[1,1,0,1,1,0,1,0,0,1,0,0] => [4,2,1,1] => [4,4] => [4] => 0
[1,1,0,1,1,0,1,0,1,0,0,0] => [3,2,1,1] => [5,2] => [2] => 1
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,1,1] => [4,1,1] => [1,1] => 0
[1,1,0,1,1,1,0,0,0,0,1,0] => [5,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,1,0,1,1,1,0,0,0,1,0,0] => [4,1,1,1] => [3,2,1,1] => [2,1,1] => 1
[1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,1,1] => [3,3] => [3] => 0
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,1] => [3,1,1] => [1,1] => 0
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1] => [3,1] => [1] => 0
[1,1,1,0,0,0,1,0,1,0,1,0] => [5,4,3] => [9,1,1,1] => [1,1,1] => 0
[1,1,1,0,0,0,1,0,1,1,0,0] => [4,4,3] => [2,2,2,2,2,1] => [2,2,2,2,1] => 4
[1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => [8,1,1,1] => [1,1,1] => 0
[1,1,1,0,0,0,1,1,0,1,0,0] => [4,3,3] => [2,2,2,2,2] => [2,2,2,2] => 4
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => [2,2,2,2,1] => [2,2,2,1] => 3
[1,1,1,0,0,1,0,0,1,0,1,0] => [5,4,2] => [9,1,1] => [1,1] => 0
[1,1,1,0,0,1,0,0,1,1,0,0] => [4,4,2] => [8,1,1] => [1,1] => 0
[1,1,1,0,0,1,0,1,0,0,1,0] => [5,3,2] => [7,1,1,1] => [1,1,1] => 0
[1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => [7,1,1] => [1,1] => 0
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,3,2] => [2,2,2,2] => [2,2,2] => 3
[1,1,1,0,0,1,1,0,0,0,1,0] => [5,2,2] => [6,1,1,1] => [1,1,1] => 0
[1,1,1,0,0,1,1,0,0,1,0,0] => [4,2,2] => [6,1,1] => [1,1] => 0
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,2] => [2,2,2,1] => [2,2,1] => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [2,2,2] => [2,2,2] => [2,2] => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [5,4,1] => [9,1] => [1] => 0
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,4,1] => [8,1] => [1] => 0
[1,1,1,0,1,0,0,1,0,0,1,0] => [5,3,1] => [3,2,2,1,1] => [2,2,1,1] => 2
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => [7,1] => [1] => 0
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,3,1] => [6,1] => [1] => 0
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,1] => [4,1,1,1,1] => [1,1,1,1] => 0
[1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => [5,1,1] => [1,1] => 0
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1] => [5,1] => [1] => 0
[1,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1] => [2,2,1] => [2,1] => 1
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,1,1] => [3,1,1,1,1] => [1,1,1,1] => 0
[1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,1] => [3,1,1,1] => [1,1,1] => 0
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,1,1] => [4,1] => [1] => 0
[1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,1] => [2,2] => [2] => 1
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1] => [2,1] => [1] => 0
[1,1,1,1,0,0,0,1,0,0,1,0] => [5,3] => [2,2,2,1,1] => [2,2,1,1] => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,2] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,2] => [2,2,1,1] => [2,1,1] => 1
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => [2,1,1,1] => [1,1,1] => 0
[1,1,1,1,0,1,0,0,1,0,0,0] => [3,1] => [2,1,1] => [1,1] => 0
[1,1,1,1,1,0,0,0,0,0,1,0] => [5] => [1,1,1,1,1] => [1,1,1,1] => 0
[1,1,1,1,1,0,0,0,0,1,0,0] => [4] => [1,1,1,1] => [1,1,1] => 0
[1,1,1,1,1,0,0,0,1,0,0,0] => [3] => [1,1,1] => [1,1] => 0
[1,1,1,1,1,0,0,1,0,0,0,0] => [2] => [1,1] => [1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => [11,7,3] => [7,3] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => [8,4,1,1,1,1,1] => [4,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2,1] => [4,3,3,3,2,2] => [3,3,3,2,2] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2,1] => [7,4,1,1,1,1,1] => [4,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2,1] => [8,6,1] => [6,1] => 0
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => [4,4,3,2,2,2] => [4,3,2,2,2] => 3
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2,1] => [7,3,2,2,1,1,1] => [3,2,2,1,1,1] => 2
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => [4,4,3,2,2,1] => [4,3,2,2,1] => 2
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2,1] => [9,3,2,2,1] => [3,2,2,1] => 2
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2,1] => [4,3,3,3,3] => [3,3,3,3] => 0
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => [7,4,1,1,1,1] => [4,1,1,1,1] => 0
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => [7,6,1] => [6,1] => 0
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => [10,4,1,1,1] => [4,1,1,1] => 0
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,2,2,1] => [9,5,1,1,1] => [5,1,1,1] => 0
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2,1] => [9,4,1,1,1] => [4,1,1,1] => 0
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => [8,4,1,1,1] => [4,1,1,1] => 0
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,2,2,1] => [8,3,2,2,1] => [3,2,2,1] => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2,1] => [4,3,3,3,1,1] => [3,3,3,1,1] => 0
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2,1] => [4,3,3,2,2] => [3,3,2,2] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2,1] => [7,5,1] => [5,1] => 0
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2,1] => [6,6,1,1,1] => [6,1,1,1] => 0
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2,1] => [5,5,1,1,1,1] => [5,1,1,1,1] => 0
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2,1] => [5,2,2,2,2] => [2,2,2,2] => 4
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2,1] => [6,5,1] => [5,1] => 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2,1] => [3,3,3,2] => [3,3,2] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1,1] => [8,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 0
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => [8,3,2,2,2] => [3,2,2,2] => 3
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => [8,3,1,1,1,1,1] => [3,1,1,1,1,1] => 0
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1,1] => [9,6,2] => [6,2] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => [7,3,2,2,1,1] => [3,2,2,1,1] => 2
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => [7,3,1,1,1,1,1] => [3,1,1,1,1,1] => 0
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => [7,3,1,1,1,1] => [3,1,1,1,1] => 0
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => [4,4,2,2,2,2,1] => [4,2,2,2,2,1] => 4
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => [4,4,2,2,2,2] => [4,2,2,2,2] => 4
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1,1] => [10,5,2] => [5,2] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,1] => [9,4,4] => [4,4] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,1] => [9,5,2] => [5,2] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1,1] => [4,4,2,2,2,1] => [4,2,2,2,1] => 3
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2,1,1] => [7,7,2] => [7,2] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1,1] => [8,5,2] => [5,2] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1,1] => [6,6,2] => [6,2] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => [6,3,1,1,1,1] => [3,1,1,1,1] => 0
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,2,1,1] => [11,4,1,1] => [4,1,1] => 0
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => [10,4,1,1] => [4,1,1] => 0
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,2,1,1] => [8,4,4] => [4,4] => 0
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2,1,1] => [9,4,1,1] => [4,1,1] => 0
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => [7,5,1,1] => [5,1,1] => 0
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2,1,1] => [5,5,5] => [5,5] => 0
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1,1] => [8,4,1,1] => [4,1,1] => 0
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1,1] => [6,5,1,1] => [5,1,1] => 0
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => [7,3,1,1] => [3,1,1] => 0
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2,1,1] => [7,4,1,1,1] => [4,1,1,1] => 0
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1,1] => [7,4,1,1] => [4,1,1] => 0
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1,1] => [6,2,2,2] => [2,2,2] => 3
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1,1] => [6,4,1] => [4,1] => 0
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => [3,3,3,1] => [3,3,1] => 0
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1,1] => [4,3,2,2,2,2,2] => [3,2,2,2,2,2] => 5
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1,1] => [10,3,2,1,1] => [3,2,1,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => [4,3,2,2,2,2,1] => [3,2,2,2,2,1] => 4
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => [4,3,2,2,2,2] => [3,2,2,2,2] => 4
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,1,1] => [11,3,3] => [3,3] => 0
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1,1] => [10,3,3] => [3,3] => 0
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,1,1] => [9,3,2,1,1] => [3,2,1,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,1,1] => [9,3,3] => [3,3] => 0
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1,1] => [4,3,2,2,2,1] => [3,2,2,2,1] => 3
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1,1,1] => [7,3,2,2,1] => [3,2,2,1] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1,1] => [8,3,3] => [3,3] => 0
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1,1] => [4,3,2,2,2] => [3,2,2,2] => 3
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => [4,3,2,2,1] => [3,2,2,1] => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,1,1] => [11,3,1,1] => [3,1,1] => 0
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1,1] => [10,3,1,1] => [3,1,1] => 0
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,1,1] => [8,3,2,1,1] => [3,2,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,1,1] => [9,3,1,1] => [3,1,1] => 0
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1,1] => [8,3,1,1] => [3,1,1] => 0
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,1,1] => [4,4,2,2,1,1] => [4,2,2,1,1] => 2
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1,1] => [7,3,3] => [3,3] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1,1] => [6,3,1,1,1] => [3,1,1,1] => 0
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1,1] => [4,4,1,1,1] => [4,1,1,1] => 0
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1,1] => [5,4,1,1,1,1] => [4,1,1,1,1] => 0
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1,1] => [5,5,1,1] => [5,1,1] => 0
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1,1] => [5,2,2,1,1] => [2,2,1,1] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => [4,2,2,2] => [2,2,2] => 3
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => [3,3,2,1] => [3,2,1] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1,1,1] => [11,3,1] => [3,1] => 0
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1,1] => [10,3,1] => [3,1] => 0
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1,1,1] => [7,3,2,1,1] => [3,2,1,1] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1,1] => [9,3,1] => [3,1] => 0
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1,1] => [8,3,1] => [3,1] => 0
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1,1,1] => [4,3,3,1,1,1] => [3,3,1,1,1] => 0
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1,1] => [4,4,4] => [4,4] => 0
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1,1] => [7,3,1] => [3,1] => 0
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1,1] => [5,4,1] => [4,1] => 0
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1,1] => [5,3,1,1,1,1] => [3,1,1,1,1] => 0
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1,1] => [6,3,1,1] => [3,1,1] => 0
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1,1] => [6,3,1] => [3,1] => 0
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1] => [5,2,2] => [2,2] => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1,1] => [3,3,2] => [3,2] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => 0
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => 0
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1,1] => [4,4,1] => [4,1] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1,1] => [4,2,1,1] => [2,1,1] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => [3,3,1] => [3,1] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => [3,2,1] => [2,1] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2] => [8,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2] => [9,2,2,2,2] => [2,2,2,2] => 4
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => [8,2,2,1,1,1,1] => [2,2,1,1,1,1] => 2
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2] => [10,2,2,2,1] => [2,2,2,1] => 3
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2] => [3,3,3,3,2,2] => [3,3,3,2,2] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2] => [7,2,2,1,1,1,1] => [2,2,1,1,1,1] => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2] => [8,6] => [6] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => [6,2,2,2,2,2,1] => [2,2,2,2,2,1] => 5
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => [8,2,2,2,2] => [2,2,2,2] => 4
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2] => [8,2,2,2,1,1,1] => [2,2,2,1,1,1] => 3
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,2] => [9,6,1,1] => [6,1,1] => 0
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2] => [7,2,2,2,1,1,1] => [2,2,2,1,1,1] => 3
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => [7,2,2,2,1,1] => [2,2,2,1,1] => 3
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2] => [9,2,2,2,1] => [2,2,2,1] => 3
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2] => [3,3,3,3,3] => [3,3,3,3] => 0
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => [7,2,2,1,1,1] => [2,2,1,1,1] => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => [7,6] => [6] => 0
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => [11,2,2,2] => [2,2,2] => 3
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => [10,2,2,2] => [2,2,2] => 3
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,2,2] => [7,7,1,1] => [7,1,1] => 0
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2] => [9,2,2,2] => [2,2,2] => 3
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => [8,2,2,2] => [2,2,2] => 3
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,2,2] => [8,2,2,2,1] => [2,2,2,1] => 3
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2] => [3,3,3,3,1,1] => [3,3,3,1,1] => 0
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2] => [3,3,3,2,2] => [3,3,2,2] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => [7,5] => [5] => 0
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => [7,2,2,2,1] => [2,2,2,1] => 3
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2] => [8,2,2,1] => [2,2,1] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2] => [3,3,3,3] => [3,3,3] => 0
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2] => [6,5] => [5] => 0
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => [6,4] => [4] => 0
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3,1] => [4,3,3,2,2,2,1] => [3,3,2,2,2,1] => 3
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1] => [8,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1] => [10,6,1] => [6,1] => 0
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3,1] => [8,8,1] => [8,1] => 0
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1] => [4,3,3,2,2,2] => [3,3,2,2,2] => 3
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => [8,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1] => [9,6,1] => [6,1] => 0
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1] => [4,3,3,2,2,1] => [3,3,2,2,1] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1] => [7,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1] => [7,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [5,5,4,2,1] => [5,2,2,2,2,2,2] => [2,2,2,2,2,2] => 6
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [6,4,4,2,1] => [10,5,1,1] => [5,1,1] => 0
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1] => [5,2,2,2,2,2,1] => [2,2,2,2,2,1] => 5
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1] => [5,2,2,2,2,2] => [2,2,2,2,2] => 5
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1] => [11,5,1] => [5,1] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1] => [10,5,1] => [5,1] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1] => [9,5,1,1] => [5,1,1] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1] => [9,5,1] => [5,1] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1] => [5,2,2,2,2,1] => [2,2,2,2,1] => 4
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2,1] => [7,7,1] => [7,1] => 0
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1] => [8,5,1] => [5,1] => 0
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1] => [7,2,2,2] => [2,2,2] => 3
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1] => [6,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,2,1] => [11,2,2,1] => [2,2,1] => 2
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1] => [10,2,2,1] => [2,2,1] => 2
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,2,1] => [8,5,1,1] => [5,1,1] => 0
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2,1] => [9,2,2,1] => [2,2,1] => 2
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1] => [6,2,2,1,1,1] => [2,2,1,1,1] => 2
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2,1] => [4,3,3,2,1,1] => [3,3,2,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1] => [6,6,1] => [6,1] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1] => [6,2,2,1,1] => [2,2,1,1] => 2
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => [6,2,1,1,1] => [2,1,1,1] => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2,1] => [5,2,2,2,1,1] => [2,2,2,1,1] => 3
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1] => [7,2,2,1] => [2,2,1] => 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1] => [3,3,3,1,1] => [3,3,1,1] => 0
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1] => [5,2,1,1,1] => [2,1,1,1] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1] => [5,4] => [4] => 0
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,1] => [11,3,1,1,1] => [3,1,1,1] => 0
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1] => [4,2,2,2,2,2,2] => [2,2,2,2,2,2] => 6
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1] => [10,3,1,1,1] => [3,1,1,1] => 0
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1] => [4,2,2,2,2,2,1] => [2,2,2,2,2,1] => 5
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1] => [4,2,2,2,2,2] => [2,2,2,2,2] => 5
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,1] => [11,4,1] => [4,1] => 0
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1] => [10,4,1] => [4,1] => 0
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,1] => [9,3,1,1,1] => [3,1,1,1] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,1] => [9,4,1] => [4,1] => 0
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1] => [4,2,2,2,2,1] => [2,2,2,2,1] => 4
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1,1] => [8,3,1,1,1] => [3,1,1,1] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1] => [8,4,1] => [4,1] => 0
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1] => [4,2,2,2,2] => [2,2,2,2] => 4
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => [4,2,2,2,1] => [2,2,2,1] => 3
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,1] => [11,2,2] => [2,2] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1] => [10,2,2] => [2,2] => 2
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,1] => [6,6,1,1] => [6,1,1] => 0
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,1] => [9,2,2] => [2,2] => 2
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1] => [8,2,2] => [2,2] => 2
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,1] => [7,3,1,1,1] => [3,1,1,1] => 0
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1] => [7,4,1] => [4,1] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1] => [7,2,2] => [2,2] => 2
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1] => [6,2,2] => [2,2] => 2
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1] => [5,2,2,1,1,1] => [2,2,1,1,1] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1] => [6,2,2,1] => [2,2,1] => 2
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1] => [3,3,2,2] => [3,2,2] => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => [3,3,3] => [3,3] => 0
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => [5,3] => [3] => 0
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1,1] => [11,2,1] => [2,1] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1] => [10,2,1] => [2,1] => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1,1] => [4,3,2,2,1,1] => [3,2,2,1,1] => 2
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1] => [9,2,1] => [2,1] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1] => [8,2,1] => [2,1] => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1,1] => [4,4,1,1,1,1] => [4,1,1,1,1] => 0
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1] => [5,5,1] => [5,1] => 0
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1] => [7,2,1] => [2,1] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => [5,2,1,1] => [2,1,1] => 1
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => 2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1] => [4,2,2,1,1] => [2,2,1,1] => 2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1] => [6,2,1] => [2,1] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => [3,3,1,1] => [3,1,1] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1] => [4,3] => [3] => 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] => [2,1,1,1,1] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1] => [5,2,1] => [2,1] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1] => [3,2,2] => [2,2] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1] => [4,2] => [2] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => [3,2] => [2] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3] => [3,3,3,2,2,2,2] => [3,3,2,2,2,2] => 4
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3] => [3,3,3,3,2,2,1] => [3,3,3,2,2,1] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3] => [3,3,3,2,2,2,1] => [3,3,2,2,2,1] => 3
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3] => [8,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => [11,6] => [6] => 0
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => [10,6] => [6] => 0
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3] => [8,8] => [8] => 0
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3] => [3,3,3,2,2,2] => [3,3,2,2,2] => 3
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => [8,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => [9,6] => [6] => 0
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3] => [3,3,3,2,2,1] => [3,3,2,2,1] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3] => [7,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => [7,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2] => [11,2,2,1,1] => [2,2,1,1] => 2
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [5,5,4,2] => [3,3,2,2,2,2,2] => [3,2,2,2,2,2] => 5
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [6,4,4,2] => [10,2,2,1,1] => [2,2,1,1] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2] => [3,3,2,2,2,2,1] => [3,2,2,2,2,1] => 4
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2] => [3,3,2,2,2,2] => [3,2,2,2,2] => 4
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2] => [11,5] => [5] => 0
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2] => [10,5] => [5] => 0
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2] => [9,2,2,1,1] => [2,2,1,1] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2] => [9,5] => [5] => 0
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2] => [3,3,2,2,2,1] => [3,2,2,2,1] => 3
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2] => [7,7] => [7] => 0
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2] => [8,5] => [5] => 0
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2] => [3,3,2,2,2] => [3,2,2,2] => 3
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2] => [6,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [6,5,2,2] => [11,4] => [4] => 0
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2] => [10,4] => [4] => 0
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [6,4,2,2] => [8,2,2,1,1] => [2,2,1,1] => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2] => [9,4] => [4] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2] => [8,4] => [4] => 0
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2] => [3,3,3,2,1,1] => [3,3,2,1,1] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2] => [6,6] => [6] => 0
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2] => [3,3,2,2,1] => [3,2,2,1] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => [6,1,1,1,1] => [1,1,1,1] => 0
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2] => [3,3,3,1,1,1] => [3,3,1,1,1] => 0
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2] => [7,4] => [4] => 0
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2] => [5,5] => [5] => 0
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2] => [5,1,1,1,1] => [1,1,1,1] => 0
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => [5,1,1,1] => [1,1,1] => 0
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1] => [11,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1] => [3,2,2,2,2,2,2] => [2,2,2,2,2,2] => 6
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1] => [10,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1] => [3,2,2,2,2,2,1] => [2,2,2,2,2,1] => 5
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1] => [3,2,2,2,2,2] => [2,2,2,2,2] => 5
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1] => [11,2,1,1] => [2,1,1] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1] => [10,2,1,1] => [2,1,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1] => [9,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1] => [9,2,1,1] => [2,1,1] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1] => [3,2,2,2,2,1] => [2,2,2,2,1] => 4
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1] => [8,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1] => [8,2,1,1] => [2,1,1] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1] => [3,2,2,2,2] => [2,2,2,2] => 4
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1] => [3,2,2,2,1] => [2,2,2,1] => 3
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1] => [11,3] => [3] => 0
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1] => [10,3] => [3] => 0
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1] => [7,2,2,1,1] => [2,2,1,1] => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1] => [9,3] => [3] => 0
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1] => [8,3] => [3] => 0
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1] => [7,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1] => [7,2,1,1] => [2,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1] => [7,3] => [3] => 0
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1] => [3,2,2,2] => [2,2,2] => 3
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1] => [3,3,2,1,1] => [3,2,1,1] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1] => [6,3] => [3] => 0
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => [3,2,2,1] => [2,2,1] => 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1] => [4,1,1,1] => [1,1,1] => 0
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1] => [11,2] => [2] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1] => [10,2] => [2] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1] => [4,2,2,2,1,1] => [2,2,2,1,1] => 3
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1] => [9,2] => [2] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1] => [8,2] => [2] => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1] => [5,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1] => [6,2,1,1] => [2,1,1] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1] => [7,2] => [2] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1] => [6,2] => [2] => 1
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 0
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1] => [3,3,1,1,1] => [3,1,1,1] => 0
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1] => [4,4] => [4] => 0
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => [5,2] => [2] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1] => [4,1,1] => [1,1] => 0
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1] => [3,2,1,1] => [2,1,1] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1] => [3,3] => [3] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1] => [3,1,1] => [1,1] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1] => [3,1] => [1] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [6,5,4] => [11,1,1,1,1] => [1,1,1,1] => 0
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,5,4] => [2,2,2,2,2,2,2] => [2,2,2,2,2,2] => 6
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => [10,1,1,1,1] => [1,1,1,1] => 0
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,4,4] => [2,2,2,2,2,2,1] => [2,2,2,2,2,1] => 5
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => [2,2,2,2,2,2] => [2,2,2,2,2] => 5
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [6,5,3] => [11,1,1,1] => [1,1,1] => 0
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [5,5,3] => [10,1,1,1] => [1,1,1] => 0
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [6,4,3] => [9,1,1,1,1] => [1,1,1,1] => 0
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [5,4,3] => [9,1,1,1] => [1,1,1] => 0
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,4,3] => [2,2,2,2,2,1] => [2,2,2,2,1] => 4
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [6,3,3] => [8,1,1,1,1] => [1,1,1,1] => 0
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [5,3,3] => [8,1,1,1] => [1,1,1] => 0
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,3] => [2,2,2,2,2] => [2,2,2,2] => 4
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,3,3] => [2,2,2,2,1] => [2,2,2,1] => 3
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [6,5,2] => [11,1,1] => [1,1] => 0
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,5,2] => [10,1,1] => [1,1] => 0
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [6,4,2] => [3,3,2,2,1,1] => [3,2,2,1,1] => 2
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,4,2] => [9,1,1] => [1,1] => 0
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,4,2] => [8,1,1] => [1,1] => 0
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2] => [7,1,1,1,1] => [1,1,1,1] => 0
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [5,3,2] => [7,1,1,1] => [1,1,1] => 0
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,2] => [7,1,1] => [1,1] => 0
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,3,2] => [2,2,2,2] => [2,2,2] => 3
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,2,2] => [5,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [5,2,2] => [6,1,1,1] => [1,1,1] => 0
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,2] => [6,1,1] => [1,1] => 0
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2] => [2,2,2,1] => [2,2,1] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,2,2] => [2,2,2] => [2,2] => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [6,5,1] => [11,1] => [1] => 0
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,5,1] => [10,1] => [1] => 0
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [6,4,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => 3
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,4,1] => [9,1] => [1] => 0
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,4,1] => [8,1] => [1] => 0
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,3,1] => [3,2,2,1,1] => [2,2,1,1] => 2
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,3,1] => [7,1] => [1] => 0
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [3,3,1] => [6,1] => [1] => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,2,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => [4,1,1,1,1] => [1,1,1,1] => 0
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,2,1] => [5,1,1] => [1,1] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => [5,1] => [1] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,2,1] => [2,2,1] => [2,1] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,1] => [3,1,1,1,1] => [1,1,1,1] => 0
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,1,1] => [3,1,1,1] => [1,1,1] => 0
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [3,1,1] => [4,1] => [1] => 0
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,1,1] => [2,2] => [2] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1] => [2,1] => [1] => 0
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,4] => [2,2,2,2,1,1] => [2,2,2,1,1] => 3
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,3] => [2,2,2,1,1,1] => [2,2,1,1,1] => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,3] => [2,2,2,1,1] => [2,2,1,1] => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,2] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [4,2] => [2,2,1,1] => [2,1,1] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [4,1] => [2,1,1,1] => [1,1,1] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,1] => [2,1,1] => [1,1] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => [1,1,1,1,1] => [1,1,1,1] => 0
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [4] => [1,1,1,1] => [1,1,1] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => [1,1,1] => [1,1] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => [1,1] => [1] => 0
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => [4,3,3,3,3,1] => [3,3,3,3,1] => 0
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2,1] => [8,6,3] => [6,3] => 0
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2,1] => [4,3,3,3,2,1] => [3,3,3,2,1] => 1
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2,1] => [4,4,3,3,2,1] => [4,3,3,2,1] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,2,1] => [6,3,2,2,2,2] => [3,2,2,2,2] => 4
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,2,1] => [4,4,4,4] => [4,4,4] => 0
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2,1] => [4,3,3,3,2] => [3,3,3,2] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,2,1] => [8,5,4] => [5,4] => 0
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,2,1] => [4,4,3,3,1,1] => [4,3,3,1,1] => 0
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,2,1] => [7,5,1,1,1] => [5,1,1,1] => 0
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2,1] => [4,3,3,3,1] => [3,3,3,1] => 0
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => [6,2,2,2,1] => [2,2,2,1] => 3
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => [8,7,2] => [7,2] => 1
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1,1] => [7,3,3,1,1,1,1] => [3,3,1,1,1,1] => 0
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => [8,6,2] => [6,2] => 1
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => [7,3,3,2,1,1] => [3,3,2,1,1] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => [8,3,3,3] => [3,3,3] => 0
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => [8,5,3] => [5,3] => 0
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => [7,6,2] => [6,2] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1,1] => [9,5,3] => [5,3] => 0
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => [7,6,3] => [6,3] => 0
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,1,1] => [8,5,2,1,1] => [5,2,1,1] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1,1] => [7,3,2,2,2] => [3,2,2,2] => 3
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1,1] => [7,4,4] => [4,4] => 0
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1,1] => [7,5,2] => [5,2] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,1,1] => [4,4,4,2,1,1,1] => [4,4,2,1,1,1] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1,1] => [6,5,5] => [5,5] => 0
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1,1] => [6,6,3] => [6,3] => 0
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,1,1] => [6,4,1,1,1,1] => [4,1,1,1,1] => 0
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1,1] => [4,3,3,2,1] => [3,3,2,1] => 1
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => [5,2,2,2,1] => [2,2,2,1] => 3
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => [8,3,2,1,1,1,1] => [3,2,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1,1] => [7,6,2,1,1] => [6,2,1,1] => 1
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => [7,3,2,1,1,1,1] => [3,2,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => [7,3,2,1,1,1] => [3,2,1,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1,1] => [5,3,3,2,2,2] => [3,3,2,2,2] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,1,1] => [9,3,3,1,1] => [3,3,1,1] => 0
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1,1,1] => [5,3,3,2,2,1] => [3,3,2,2,1] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1,1,1] => [7,7,2,1] => [7,2,1] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1,1,1] => [7,3,3,1,1,1] => [3,3,1,1,1] => 0
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1,1] => [8,3,2,2] => [3,2,2] => 2
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1,1] => [4,4,2,2,2] => [4,2,2,2] => 3
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1,1] => [10,4,3] => [4,3] => 0
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,1,1,1] => [4,4,3,3,3] => [4,3,3,3] => 0
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1,1,1] => [9,4,3] => [4,3] => 0
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1,1] => [4,4,4,1,1,1] => [4,4,1,1,1] => 0
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,1,1,1] => [5,3,3,3,1,1,1] => [3,3,3,1,1,1] => 0
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1,1,1] => [8,3,3,1,1] => [3,3,1,1] => 0
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1,1] => [8,4,3] => [4,3] => 0
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1,1,1] => [5,5,4] => [5,4] => 0
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1,1] => [6,5,2] => [5,2] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,1,1,1] => [4,4,3,2,1,1,1] => [4,3,2,1,1,1] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1,1,1] => [4,4,3,2,1,1] => [4,3,2,1,1] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1,1,1] => [7,4,3] => [4,3] => 0
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1,1] => [5,5,1,1,1] => [5,1,1,1] => 0
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1,1] => [6,4,1,1] => [4,1,1] => 0
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1,1] => [5,2,2,2] => [2,2,2] => 3
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1] => [5,3,2,2,2,2,1] => [3,2,2,2,2,1] => 4
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => [5,3,2,2,2,2] => [3,2,2,2,2] => 4
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1,1] => [10,3,2,2] => [3,2,2] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,1,1,1] => [9,5,2,1] => [5,2,1] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1,1,1] => [9,3,2,2] => [3,2,2] => 2
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1,1,1] => [5,3,2,2,2,1] => [3,2,2,2,1] => 3
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1,1,1,1] => [6,5,2,1,1,1,1] => [5,2,1,1,1,1] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1,1] => [6,6,2,1,1] => [6,2,1,1] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1,1,1] => [6,3,2,2,1,1] => [3,2,2,1,1] => 2
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1,1] => [7,3,2,2] => [3,2,2] => 2
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1,1] => [4,3,3,3] => [3,3,3] => 0
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,1,1,1] => [11,4,2] => [4,2] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1,1,1] => [10,4,2] => [4,2] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,1,1,1] => [8,4,2,1,1,1] => [4,2,1,1,1] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,1,1,1] => [8,5,2,1] => [5,2,1] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1,1,1] => [9,4,2] => [4,2] => 1
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1,1,1] => [6,3,2,1,1,1] => [3,2,1,1,1] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,1,1,1] => [6,3,3,1,1,1,1] => [3,3,1,1,1,1] => 0
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,1,1,1] => [7,3,3,1,1] => [3,3,1,1] => 0
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1,1,1] => [8,4,2] => [4,2] => 1
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1,1,1] => [6,3,2,1,1] => [3,2,1,1] => 1
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1,1] => [6,3,3] => [3,3] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1,1,1,1] => [4,4,3,1,1,1,1] => [4,3,1,1,1,1] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1,1,1] => [4,4,3,1,1,1] => [4,3,1,1,1] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1,1] => [5,4,4] => [4,4] => 0
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1,1,1] => [4,3,3,1,1] => [3,3,1,1] => 0
[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] => [3,1,1,1] => 0
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => [5,2,2,1] => [2,2,1] => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1,1] => [12,3,2] => [3,2] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,1,1,1,1] => [5,4,2,2,2,1,1] => [4,2,2,2,1,1] => 3
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1,1,1,1] => [11,3,2] => [3,2] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1,1] => [10,3,2] => [3,2] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,1,1,1,1] => [5,5,2,1,1,1,1] => [5,2,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1,1,1,1] => [6,6,2,1] => [6,2,1] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1,1,1] => [9,3,2] => [3,2] => 1
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1,1] => [8,3,2] => [3,2] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,1,1,1,1] => [5,3,2,2,1,1,1] => [3,2,2,1,1,1] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1,1,1] => [5,3,2,2,1,1] => [3,2,2,1,1] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1,1,1] => [7,4,2] => [4,2] => 1
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1,1,1] => [7,3,2] => [3,2] => 1
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1,1] => [4,4,3] => [4,3] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1,1,1,1] => [4,4,2,1,1,1,1] => [4,2,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1,1,1] => [4,4,2,1,1,1] => [4,2,1,1,1] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1,1,1] => [5,5,2] => [5,2] => 1
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1,1] => [6,3,2] => [3,2] => 1
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1,1] => [4,4,1,1] => [4,1,1] => 0
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => [4,2,2,1] => [2,2,1] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1,1] => [4,3,2,1,1] => [3,2,1,1] => 1
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1,1] => [4,3,3] => [3,3] => 0
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1,1] => [5,3,1] => [3,1] => 0
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => [4,2,2] => [2,2] => 2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => [4,2,1] => [2,1] => 1
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2] => [3,3,3,3,3,2] => [3,3,3,3,2] => 1
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => [8,7,1,1] => [7,1,1] => 0
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => [3,3,3,3,3,1] => [3,3,3,3,1] => 0
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,2] => [7,7,3] => [7,3] => 0
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,2] => [7,2,2,2,2,1,1] => [2,2,2,2,1,1] => 4
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => [8,6,1,1] => [6,1,1] => 0
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => [3,3,3,3,2,1] => [3,3,3,2,1] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,2] => [8,6,1,1,1] => [6,1,1,1] => 0
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2] => [7,6,1,1,1] => [6,1,1,1] => 0
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,2] => [6,6,1,1,1,1,1] => [6,1,1,1,1,1] => 0
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,2] => [6,2,2,2,2,2] => [2,2,2,2,2] => 5
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,2] => [7,6,1,1] => [6,1,1] => 0
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2] => [3,3,3,3,2] => [3,3,3,2] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,2] => [8,5,1,1,1,1] => [5,1,1,1,1] => 0
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,2] => [8,5,1,1,1] => [5,1,1,1] => 0
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,2] => [7,2,2,2,2] => [2,2,2,2] => 4
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,2] => [6,2,2,2,1,1] => [2,2,2,1,1] => 3
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2] => [3,3,3,3,1] => [3,3,3,1] => 0
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => [3,3,3,2,1] => [3,3,2,1] => 1
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3,1] => [9,7,1] => [7,1] => 0
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1] => [8,7,1] => [7,1] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1] => [11,7,3] => [7,3] => 0
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2,1] => [8,4,1,1,1,1,1] => [4,1,1,1,1,1] => 0
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2,1] => [4,3,3,3,2,2] => [3,3,3,2,2] => 2
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1] => [7,4,1,1,1,1,1] => [4,1,1,1,1,1] => 0
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1] => [8,6,1] => [6,1] => 0
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,1] => [4,4,3,2,2,2] => [4,3,2,2,2] => 3
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2,1] => [7,3,2,2,1,1,1] => [3,2,2,1,1,1] => 2
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1] => [4,4,3,2,2,1] => [4,3,2,2,1] => 2
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2,1] => [9,3,2,2,1] => [3,2,2,1] => 2
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1] => [4,3,3,3,3] => [3,3,3,3] => 0
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1] => [7,4,1,1,1,1] => [4,1,1,1,1] => 0
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1] => [7,6,1] => [6,1] => 0
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2,1] => [10,4,1,1,1] => [4,1,1,1] => 0
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,2,1] => [9,5,1,1,1] => [5,1,1,1] => 0
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1] => [9,4,1,1,1] => [4,1,1,1] => 0
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1] => [8,4,1,1,1] => [4,1,1,1] => 0
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,2,1] => [6,3,2,2,2,1,1] => [3,2,2,2,1,1] => 3
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,1] => [8,3,2,2,1] => [3,2,2,1] => 2
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1] => [4,3,3,3,1,1] => [3,3,3,1,1] => 0
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1] => [4,3,3,2,2] => [3,3,2,2] => 2
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1] => [7,5,1] => [5,1] => 0
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,1] => [6,5,1,1,1,1,1] => [5,1,1,1,1,1] => 0
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1] => [6,6,1,1,1] => [6,1,1,1] => 0
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1] => [5,5,1,1,1,1] => [5,1,1,1,1] => 0
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,1] => [5,2,2,2,2] => [2,2,2,2] => 4
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1] => [6,5,1] => [5,1] => 0
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1] => [3,3,3,2] => [3,3,2] => 1
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1,1] => [8,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 0
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1,1] => [8,3,2,2,2] => [3,2,2,2] => 3
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => [8,3,1,1,1,1,1] => [3,1,1,1,1,1] => 0
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,1,1] => [9,6,2] => [6,2] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1] => [7,3,2,2,1,1] => [3,2,2,1,1] => 2
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1] => [7,3,1,1,1,1,1] => [3,1,1,1,1,1] => 0
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1] => [7,3,1,1,1,1] => [3,1,1,1,1] => 0
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1,1] => [4,4,2,2,2,2,1] => [4,2,2,2,2,1] => 4
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1] => [4,4,2,2,2,2] => [4,2,2,2,2] => 4
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,1,1] => [10,5,2] => [5,2] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,1] => [9,4,4] => [4,4] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,1] => [9,5,2] => [5,2] => 1
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1,1] => [4,4,2,2,2,1] => [4,2,2,2,1] => 3
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,1,1] => [8,3,3,1,1,1] => [3,3,1,1,1] => 0
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1,1] => [7,7,2] => [7,2] => 1
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1,1] => [8,5,2] => [5,2] => 1
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1] => [6,6,2] => [6,2] => 1
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1] => [6,3,1,1,1,1] => [3,1,1,1,1] => 0
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,1,1] => [11,4,1,1] => [4,1,1] => 0
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1] => [10,4,1,1] => [4,1,1] => 0
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,2,1,1] => [4,4,3,3,1,1,1] => [4,3,3,1,1,1] => 0
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,1,1] => [8,4,4] => [4,4] => 0
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1,1] => [9,4,1,1] => [4,1,1] => 0
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1] => [7,5,1,1] => [5,1,1] => 0
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,1,1] => [4,4,4,1,1,1,1] => [4,4,1,1,1,1] => 0
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1,1] => [5,5,5] => [5,5] => 0
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1] => [8,4,1,1] => [4,1,1] => 0
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1,1] => [6,5,1,1] => [5,1,1] => 0
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => [7,3,1,1] => [3,1,1] => 0
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,1,1] => [6,4,1,1,1,1,1] => [4,1,1,1,1,1] => 0
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1,1] => [7,4,1,1,1] => [4,1,1,1] => 0
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1,1] => [7,4,1,1] => [4,1,1] => 0
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1] => [6,2,2,2] => [2,2,2] => 3
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1] => [6,4,1] => [4,1] => 0
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1] => [3,3,3,1] => [3,3,1] => 0
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1,1] => [4,3,2,2,2,2,2] => [3,2,2,2,2,2] => 5
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1,1,1] => [10,3,2,1,1] => [3,2,1,1] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1] => [4,3,2,2,2,2,1] => [3,2,2,2,2,1] => 4
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1] => [4,3,2,2,2,2] => [3,2,2,2,2] => 4
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,1,1] => [11,3,3] => [3,3] => 0
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1] => [10,3,3] => [3,3] => 0
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,1,1] => [9,3,2,1,1,1] => [3,2,1,1,1] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,1,1] => [9,3,2,1,1] => [3,2,1,1] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1,1] => [9,3,3] => [3,3] => 0
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1,1] => [4,3,2,2,2,1] => [3,2,2,2,1] => 3
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1,1,1] => [6,3,2,2,1,1,1] => [3,2,2,1,1,1] => 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1] => [7,3,2,2,1] => [3,2,2,1] => 2
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1,1] => [8,3,3] => [3,3] => 0
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1] => [4,3,2,2,2] => [3,2,2,2] => 3
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1] => [4,3,2,2,1] => [3,2,2,1] => 2
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1,1,1] => [12,3,1,1] => [3,1,1] => 0
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,1,1] => [5,3,3,2,2,1,1] => [3,3,2,2,1,1] => 2
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,1,1] => [11,3,1,1] => [3,1,1] => 0
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1,1] => [10,3,1,1] => [3,1,1] => 0
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,1,1] => [8,3,2,1,1,1] => [3,2,1,1,1] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,1,1] => [8,3,2,1,1] => [3,2,1,1] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1,1] => [9,3,1,1] => [3,1,1] => 0
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1,1] => [8,3,1,1] => [3,1,1] => 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,1,1] => [4,4,2,2,1,1,1] => [4,2,2,1,1,1] => 2
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,1,1] => [4,4,2,2,1,1] => [4,2,2,1,1] => 2
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1,1] => [7,3,3] => [3,3] => 0
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1,1] => [6,3,1,1,1] => [3,1,1,1] => 0
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1] => [4,4,1,1,1] => [4,1,1,1] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1,1,1] => [5,4,1,1,1,1,1] => [4,1,1,1,1,1] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1,1] => [5,4,1,1,1,1] => [4,1,1,1,1] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1] => [5,5,1,1] => [5,1,1] => 0
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1,1] => [5,2,2,1,1] => [2,2,1,1] => 2
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1] => [4,2,2,2] => [2,2,2] => 3
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1] => [3,3,2,1] => [3,2,1] => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,1,1,1] => [13,3,1] => [3,1] => 0
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1] => [12,3,1] => [3,1] => 0
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,1,1,1] => [5,3,2,2,2,1,1] => [3,2,2,2,1,1] => 3
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1,1,1] => [11,3,1] => [3,1] => 0
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1] => [10,3,1] => [3,1] => 0
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,1,1,1] => [6,3,2,1,1,1,1] => [3,2,1,1,1,1] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1,1,1] => [7,3,2,1,1] => [3,2,1,1] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1,1] => [9,3,1] => [3,1] => 0
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1] => [8,3,1] => [3,1] => 0
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,1,1,1] => [4,3,3,1,1,1,1] => [3,3,1,1,1,1] => 0
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1,1] => [4,3,3,1,1,1] => [3,3,1,1,1] => 0
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1,1] => [4,4,4] => [4,4] => 0
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1,1] => [7,3,1] => [3,1] => 0
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1] => [5,4,1] => [4,1] => 0
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1,1,1] => [5,3,1,1,1,1,1] => [3,1,1,1,1,1] => 0
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1,1] => [5,3,1,1,1,1] => [3,1,1,1,1] => 0
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1,1] => [6,3,1,1] => [3,1,1] => 0
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1] => [6,3,1] => [3,1] => 0
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1] => [5,2,2] => [2,2] => 2
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1] => [3,3,2] => [3,2] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => 0
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1] => [4,4,1] => [4,1] => 0
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1] => [4,2,1,1] => [2,1,1] => 1
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1] => [3,3,1] => [3,1] => 0
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => [3,2,1] => [2,1] => 1
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => [9,8] => [8] => 0
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,3,3,3] => [3,3,3,3,3,1,1] => [3,3,3,3,1,1] => 0
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3] => [9,7] => [7] => 0
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => [8,7] => [7] => 0
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,2] => [8,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2] => [9,2,2,2,2] => [2,2,2,2] => 4
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2] => [8,2,2,1,1,1,1] => [2,2,1,1,1,1] => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,2] => [10,2,2,2,1] => [2,2,2,1] => 3
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2] => [3,3,3,3,2,2] => [3,3,3,2,2] => 2
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2] => [7,2,2,1,1,1,1] => [2,2,1,1,1,1] => 2
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2] => [8,6] => [6] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2] => [6,2,2,2,2,2,1] => [2,2,2,2,2,1] => 5
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2] => [8,2,2,2,2] => [2,2,2,2] => 4
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,2] => [8,2,2,2,1,1,1] => [2,2,2,1,1,1] => 3
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,2] => [9,6,1,1] => [6,1,1] => 0
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2] => [7,2,2,2,1,1,1] => [2,2,2,1,1,1] => 3
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2] => [7,2,2,2,1,1] => [2,2,2,1,1] => 3
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,2] => [8,2,2,2,2,1] => [2,2,2,2,1] => 4
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2] => [9,2,2,2,1] => [2,2,2,1] => 3
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2] => [3,3,3,3,3] => [3,3,3,3] => 0
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2] => [7,2,2,1,1,1] => [2,2,1,1,1] => 2
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2] => [7,6] => [6] => 0
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2] => [11,2,2,2] => [2,2,2] => 3
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2] => [10,2,2,2] => [2,2,2] => 3
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,2,2] => [7,7,1,1,1] => [7,1,1,1] => 0
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,2] => [7,7,1,1] => [7,1,1] => 0
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2] => [9,2,2,2] => [2,2,2] => 3
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => [8,2,2,2] => [2,2,2] => 3
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,2] => [6,2,2,2,2,1,1] => [2,2,2,2,1,1] => 4
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2] => [8,2,2,2,1] => [2,2,2,1] => 3
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2] => [3,3,3,3,1,1] => [3,3,3,1,1] => 0
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2] => [3,3,3,2,2] => [3,3,2,2] => 2
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2] => [7,5] => [5] => 0
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2] => [6,2,2,2,1,1,1] => [2,2,2,1,1,1] => 3
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2] => [7,2,2,2,1] => [2,2,2,1] => 3
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2] => [8,2,2,1] => [2,2,1] => 2
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2] => [3,3,3,3] => [3,3,3] => 0
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2] => [6,5] => [5] => 0
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2] => [6,4] => [4] => 0
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,1] => [9,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,1] => [4,3,3,2,2,2,1] => [3,3,2,2,2,1] => 3
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1] => [8,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1] => [10,6,1] => [6,1] => 0
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3,1] => [8,8,1] => [8,1] => 0
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1] => [4,3,3,2,2,2] => [3,3,2,2,2] => 3
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1] => [8,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [7,3,3,3,1] => [4,3,3,3,2,1,1] => [3,3,3,2,1,1] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,1] => [9,6,1] => [6,1] => 0
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1] => [4,3,3,2,2,1] => [3,3,2,2,1] => 2
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1] => [7,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1] => [7,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,1] => [5,2,2,2,2,2,2] => [2,2,2,2,2,2] => 6
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,1] => [10,5,1,1] => [5,1,1] => 0
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1] => [5,2,2,2,2,2,1] => [2,2,2,2,2,1] => 5
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1] => [5,2,2,2,2,2] => [2,2,2,2,2] => 5
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1] => [11,5,1] => [5,1] => 0
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,1] => [10,5,1] => [5,1] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,1] => [9,4,1,1,1,1] => [4,1,1,1,1] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1] => [9,5,1,1] => [5,1,1] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1] => [9,5,1] => [5,1] => 0
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1] => [5,2,2,2,2,1] => [2,2,2,2,1] => 4
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,1] => [4,3,3,3,1,1,1] => [3,3,3,1,1,1] => 0
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1] => [7,7,1] => [7,1] => 0
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1] => [8,5,1] => [5,1] => 0
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1] => [7,2,2,2] => [2,2,2] => 3
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1] => [6,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,1] => [12,2,2,1] => [2,2,1] => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,2,1] => [4,4,3,2,2,1,1] => [4,3,2,2,1,1] => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,1] => [11,2,2,1] => [2,2,1] => 2
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1] => [10,2,2,1] => [2,2,1] => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,2,1] => [8,4,1,1,1,1] => [4,1,1,1,1] => 0
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,1] => [8,5,1,1] => [5,1,1] => 0
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1] => [9,2,2,1] => [2,2,1] => 2
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1] => [6,2,2,1,1,1] => [2,2,1,1,1] => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,1] => [4,3,3,2,1,1,1] => [3,3,2,1,1,1] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1] => [4,3,3,2,1,1] => [3,3,2,1,1] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1] => [6,6,1] => [6,1] => 0
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1] => [6,2,2,1,1] => [2,2,1,1] => 2
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1] => [6,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,1] => [5,2,2,2,1,1,1] => [2,2,2,1,1,1] => 3
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1] => [5,2,2,2,1,1] => [2,2,2,1,1] => 3
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1] => [7,2,2,1] => [2,2,1] => 2
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1] => [3,3,3,1,1] => [3,3,1,1] => 0
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1] => [5,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1] => [5,4] => [4] => 0
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1,1] => [4,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => 6
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,1] => [11,3,1,1,1] => [3,1,1,1] => 0
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1] => [4,2,2,2,2,2,2] => [2,2,2,2,2,2] => 6
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [7,4,4,1,1] => [10,3,1,1,1,1] => [3,1,1,1,1] => 0
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1,1] => [10,3,1,1,1] => [3,1,1,1] => 0
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1] => [4,2,2,2,2,2,1] => [2,2,2,2,2,1] => 5
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1] => [4,2,2,2,2,2] => [2,2,2,2,2] => 5
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [6,6,3,1,1] => [12,4,1] => [4,1] => 0
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1,1] => [8,3,2,2,1,1] => [3,2,2,1,1] => 2
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,1] => [11,4,1] => [4,1] => 0
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1] => [10,4,1] => [4,1] => 0
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,1] => [9,3,1,1,1,1] => [3,1,1,1,1] => 0
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,1] => [9,3,1,1,1] => [3,1,1,1] => 0
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1] => [9,4,1] => [4,1] => 0
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1] => [4,2,2,2,2,1] => [2,2,2,2,1] => 4
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1,1] => [8,3,1,1,1,1] => [3,1,1,1,1] => 0
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1] => [8,3,1,1,1] => [3,1,1,1] => 0
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1] => [8,4,1] => [4,1] => 0
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1] => [4,2,2,2,2] => [2,2,2,2] => 4
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1] => [4,2,2,2,1] => [2,2,2,1] => 3
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [7,6,2,1,1] => [13,2,2] => [2,2] => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1,1] => [12,2,2] => [2,2] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,1] => [4,4,2,2,2,1,1] => [4,2,2,2,1,1] => 3
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,1] => [11,2,2] => [2,2] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1] => [10,2,2] => [2,2] => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,1] => [5,5,1,1,1,1,1] => [5,1,1,1,1,1] => 0
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,1] => [6,6,1,1] => [6,1,1] => 0
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1] => [9,2,2] => [2,2] => 2
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1] => [8,2,2] => [2,2] => 2
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,1] => [6,3,1,1,1,1,1] => [3,1,1,1,1,1] => 0
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,1] => [7,3,1,1,1] => [3,1,1,1] => 0
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1] => [7,4,1] => [4,1] => 0
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1] => [7,2,2] => [2,2] => 2
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1] => [6,2,2] => [2,2] => 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1,1] => [5,2,2,1,1,1,1] => [2,2,1,1,1,1] => 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1] => [5,2,2,1,1,1] => [2,2,1,1,1] => 2
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1] => [6,2,2,1] => [2,2,1] => 2
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1] => [3,3,2,2] => [3,2,2] => 2
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => [3,3,3] => [3,3] => 0
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1] => [5,3] => [3] => 0
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,1,1] => [13,2,1] => [2,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1] => [12,2,1] => [2,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,1,1] => [4,3,2,2,2,1,1] => [3,2,2,2,1,1] => 3
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1,1] => [11,2,1] => [2,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1] => [10,2,1] => [2,1] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,1,1] => [4,3,2,2,1,1,1] => [3,2,2,1,1,1] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1,1] => [4,3,2,2,1,1] => [3,2,2,1,1] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1] => [9,2,1] => [2,1] => 1
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1] => [8,2,1] => [2,1] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,1,1] => [4,4,1,1,1,1,1] => [4,1,1,1,1,1] => 0
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1] => [4,4,1,1,1,1] => [4,1,1,1,1] => 0
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1] => [5,5,1] => [5,1] => 0
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1] => [7,2,1] => [2,1] => 1
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1] => [5,2,1,1] => [2,1,1] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1] => [4,2,2,1,1] => [2,2,1,1] => 2
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1] => [6,2,1] => [2,1] => 1
[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] => [3,1,1] => 0
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => [4,3] => [3] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1] => [4,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1] => [5,2,1] => [2,1] => 1
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1] => [3,2,2] => [2,2] => 2
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1] => [4,2] => [2] => 1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1] => [3,2] => [2] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4] => [9,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => [9,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3] => [3,3,3,2,2,2,2] => [3,3,2,2,2,2] => 4
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3] => [3,3,3,3,2,2,1] => [3,3,3,2,2,1] => 2
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3] => [3,3,3,2,2,2,1] => [3,3,2,2,2,1] => 3
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3] => [8,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3] => [11,6] => [6] => 0
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3] => [10,6] => [6] => 0
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [7,4,3,3] => [10,7] => [7] => 0
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3] => [8,8] => [8] => 0
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3] => [3,3,3,2,2,2] => [3,3,2,2,2] => 3
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3] => [8,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [7,3,3,3] => [3,3,3,3,2,1,1] => [3,3,3,2,1,1] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3] => [9,6] => [6] => 0
[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] => [3,3,2,2,1] => 2
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3] => [7,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3] => [7,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,5,5,2] => [3,3,2,2,2,2,2,1] => [3,2,2,2,2,2,1] => 5
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2] => [11,2,2,1,1] => [2,2,1,1] => 2
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2] => [3,3,2,2,2,2,2] => [3,2,2,2,2,2] => 5
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [7,4,4,2] => [10,2,2,1,1,1] => [2,2,1,1,1] => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2] => [10,2,2,1,1] => [2,2,1,1] => 2
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2] => [3,3,2,2,2,2,1] => [3,2,2,2,2,1] => 4
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2] => [3,3,2,2,2,2] => [3,2,2,2,2] => 4
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [6,6,3,2] => [12,5] => [5] => 0
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2] => [9,2,2,2,1,1] => [2,2,2,1,1] => 3
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2] => [11,5] => [5] => 0
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2] => [10,5] => [5] => 0
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2] => [9,2,2,1,1,1] => [2,2,1,1,1] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2] => [9,2,2,1,1] => [2,2,1,1] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2] => [9,5] => [5] => 0
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2] => [3,3,2,2,2,1] => [3,2,2,2,1] => 3
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2] => [3,3,3,3,1,1,1] => [3,3,3,1,1,1] => 0
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2] => [7,7] => [7] => 0
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2] => [8,5] => [5] => 0
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2] => [3,3,2,2,2] => [3,2,2,2] => 3
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2] => [6,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [7,6,2,2] => [13,4] => [4] => 0
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2] => [12,4] => [4] => 0
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,2] => [8,2,2,2,1,1] => [2,2,2,1,1] => 3
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2] => [11,4] => [4] => 0
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2] => [10,4] => [4] => 0
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,2] => [8,2,2,1,1,1] => [2,2,1,1,1] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2] => [8,2,2,1,1] => [2,2,1,1] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2] => [9,4] => [4] => 0
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2] => [8,4] => [4] => 0
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2] => [3,3,3,2,1,1,1] => [3,3,2,1,1,1] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2] => [3,3,3,2,1,1] => [3,3,2,1,1] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2] => [6,6] => [6] => 0
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2] => [3,3,2,2,1] => [3,2,2,1] => 2
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => [6,1,1,1,1] => [1,1,1,1] => 0
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2] => [3,3,3,1,1,1,1] => [3,3,1,1,1,1] => 0
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2] => [3,3,3,1,1,1] => [3,3,1,1,1] => 0
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2] => [7,4] => [4] => 0
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2] => [5,5] => [5] => 0
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2] => [5,1,1,1,1] => [1,1,1,1] => 0
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2] => [5,1,1,1] => [1,1,1] => 0
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [6,5,5,1] => [3,2,2,2,2,2,2,2] => [2,2,2,2,2,2,2] => 7
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1] => [3,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => 6
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [6,6,4,1] => [12,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [7,5,4,1] => [11,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1] => [11,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1] => [3,2,2,2,2,2,2] => [2,2,2,2,2,2] => 6
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [7,4,4,1] => [10,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1] => [10,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1] => [3,2,2,2,2,2,1] => [2,2,2,2,2,1] => 5
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1] => [3,2,2,2,2,2] => [2,2,2,2,2] => 5
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [7,6,3,1] => [13,2,1,1] => [2,1,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [6,6,3,1] => [12,2,1,1] => [2,1,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1] => [4,3,3,2,2,1,1] => [3,3,2,2,1,1] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1] => [11,2,1,1] => [2,1,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1] => [10,2,1,1] => [2,1,1] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1] => [9,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1] => [9,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1] => [9,2,1,1] => [2,1,1] => 1
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1] => [3,2,2,2,2,1] => [2,2,2,2,1] => 4
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1] => [8,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1] => [8,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1] => [8,2,1,1] => [2,1,1] => 1
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1] => [3,2,2,2,2] => [2,2,2,2] => 4
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1] => [3,2,2,2,1] => [2,2,2,1] => 3
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [7,6,2,1] => [13,3] => [3] => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1] => [12,3] => [3] => 0
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1] => [5,2,2,2,2,1,1] => [2,2,2,2,1,1] => 4
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1] => [11,3] => [3] => 0
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1] => [10,3] => [3] => 0
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1] => [6,2,2,1,1,1,1] => [2,2,1,1,1,1] => 2
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1] => [7,2,2,1,1] => [2,2,1,1] => 2
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1] => [9,3] => [3] => 0
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1] => [8,3] => [3] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1] => [6,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1] => [7,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1] => [7,2,1,1] => [2,1,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1] => [7,3] => [3] => 0
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1] => [3,2,2,2] => [2,2,2] => 3
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1] => [3,3,2,1,1] => [3,2,1,1] => 1
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1] => [6,3] => [3] => 0
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => [3,2,2,1] => [2,2,1] => 2
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1] => [4,1,1,1] => [1,1,1] => 0
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,1] => [13,2] => [2] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1] => [12,2] => [2] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,1] => [4,2,2,2,2,1,1] => [2,2,2,2,1,1] => 4
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1] => [11,2] => [2] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1] => [10,2] => [2] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,1] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => 3
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1] => [4,2,2,2,1,1] => [2,2,2,1,1] => 3
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1] => [9,2] => [2] => 1
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1] => [8,2] => [2] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,1] => [5,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1] => [5,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1] => [6,2,1,1] => [2,1,1] => 1
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1] => [7,2] => [2] => 1
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1] => [6,2] => [2] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => 0
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 0
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1] => [3,3,1,1,1] => [3,1,1,1] => 0
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1] => [4,4] => [4] => 0
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1] => [5,2] => [2] => 1
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1] => [4,1,1] => [1,1] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1] => [3,2,1,1] => [2,1,1] => 1
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1] => [3,3] => [3] => 0
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1] => [3,1,1] => [1,1] => 0
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1] => [3,1] => [1] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [6,6,5] => [2,2,2,2,2,2,2,2,1] => [2,2,2,2,2,2,2,1] => 7
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [7,5,5] => [12,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [6,5,5] => [2,2,2,2,2,2,2,2] => [2,2,2,2,2,2,2] => 7
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => [2,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => 6
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [7,6,4] => [13,1,1,1,1] => [1,1,1,1] => 0
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [6,6,4] => [12,1,1,1,1] => [1,1,1,1] => 0
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [7,5,4] => [11,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [6,5,4] => [11,1,1,1,1] => [1,1,1,1] => 0
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,5,4] => [2,2,2,2,2,2,2] => [2,2,2,2,2,2] => 6
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [7,4,4] => [10,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [6,4,4] => [10,1,1,1,1] => [1,1,1,1] => 0
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,4] => [2,2,2,2,2,2,1] => [2,2,2,2,2,1] => 5
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [4,4,4] => [2,2,2,2,2,2] => [2,2,2,2,2] => 5
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [7,6,3] => [13,1,1,1] => [1,1,1] => 0
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,6,3] => [12,1,1,1] => [1,1,1] => 0
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [7,5,3] => [3,3,3,2,2,1,1] => [3,3,2,2,1,1] => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [6,5,3] => [11,1,1,1] => [1,1,1] => 0
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,5,3] => [10,1,1,1] => [1,1,1] => 0
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [7,4,3] => [9,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [6,4,3] => [9,1,1,1,1] => [1,1,1,1] => 0
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3] => [9,1,1,1] => [1,1,1] => 0
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [4,4,3] => [2,2,2,2,2,1] => [2,2,2,2,1] => 4
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [7,3,3] => [8,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [6,3,3] => [8,1,1,1,1] => [1,1,1,1] => 0
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,3,3] => [8,1,1,1] => [1,1,1] => 0
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [4,3,3] => [2,2,2,2,2] => [2,2,2,2] => 4
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => [2,2,2,2,1] => [2,2,2,1] => 3
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [7,6,2] => [13,1,1] => [1,1] => 0
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,6,2] => [12,1,1] => [1,1] => 0
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [7,5,2] => [3,3,2,2,2,1,1] => [3,2,2,2,1,1] => 3
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [6,5,2] => [11,1,1] => [1,1] => 0
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,5,2] => [10,1,1] => [1,1] => 0
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [7,4,2] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [6,4,2] => [3,3,2,2,1,1] => [3,2,2,1,1] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [5,4,2] => [9,1,1] => [1,1] => 0
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [4,4,2] => [8,1,1] => [1,1] => 0
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [7,3,2] => [6,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [6,3,2] => [7,1,1,1,1] => [1,1,1,1] => 0
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,3,2] => [7,1,1,1] => [1,1,1] => 0
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [4,3,2] => [7,1,1] => [1,1] => 0
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [3,3,2] => [2,2,2,2] => [2,2,2] => 3
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [7,2,2] => [5,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [6,2,2] => [5,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,2,2] => [6,1,1,1] => [1,1,1] => 0
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [4,2,2] => [6,1,1] => [1,1] => 0
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [3,2,2] => [2,2,2,1] => [2,2,1] => 2
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [2,2,2] => [2,2,2] => [2,2] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [7,6,1] => [13,1] => [1] => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,6,1] => [12,1] => [1] => 0
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [7,5,1] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => 4
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [6,5,1] => [11,1] => [1] => 0
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [5,5,1] => [10,1] => [1] => 0
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [7,4,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => 3
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [6,4,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => 3
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,4,1] => [9,1] => [1] => 0
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [4,4,1] => [8,1] => [1] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [7,3,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => 2
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [6,3,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 2
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,3,1] => [3,2,2,1,1] => [2,2,1,1] => 2
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [4,3,1] => [7,1] => [1] => 0
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [3,3,1] => [6,1] => [1] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,2,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [6,2,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,2,1] => [4,1,1,1,1] => [1,1,1,1] => 0
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [4,2,1] => [5,1,1] => [1,1] => 0
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => [5,1] => [1] => 0
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [2,2,1] => [2,2,1] => [2,1] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [6,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,1,1] => [3,1,1,1,1] => [1,1,1,1] => 0
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [4,1,1] => [3,1,1,1] => [1,1,1] => 0
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [3,1,1] => [4,1] => [1] => 0
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,1,1] => [2,2] => [2] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1] => [2,1] => [1] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [7,5] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => 4
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,4] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => 3
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,4] => [2,2,2,2,1,1] => [2,2,2,1,1] => 3
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,3] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,3] => [2,2,2,1,1,1] => [2,2,1,1,1] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [5,3] => [2,2,2,1,1] => [2,2,1,1] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,2] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,2] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [5,2] => [2,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [4,2] => [2,2,1,1] => [2,1,1] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [5,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,1] => [2,1,1,1] => [1,1,1] => 0
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => [2,1,1] => [1,1] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => [1,1,1,1,1] => [1,1,1,1] => 0
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => [1,1,1,1] => [1,1,1] => 0
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => [1,1,1] => [1,1] => 0
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => [1,1] => [1] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => [4,3,1] => [3,1] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1] => [4,3,1,1] => [3,1,1] => 0
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1] => [4,3,2] => [3,2] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [8,2] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1,1,1,1,1] => [4,4,2] => [4,2] => 1
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1,1,1,1] => [5,3,1,1] => [3,1,1] => 0
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1,1] => [5,3,2] => [3,2] => 1
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1] => [4,3,2,1] => [3,2,1] => 1
[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] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0] => [9,2] => [2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,1] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [8,3] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 2
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1] => [4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1,1] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1,1,1,1,1] => [4,3,2,2] => [3,2,2] => 2
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1,1,1,1] => [5,3,3] => [3,3] => 0
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1,1,1,1,1,1,1] => [4,3,3,1] => [3,3,1] => 0
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1,1,1,1] => [5,4,1,1] => [4,1,1] => 0
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1,1,1,1,1,1,1] => [5,4,2] => [4,2] => 1
[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1,1,1] => [4,4,2,1] => [4,2,1] => 1
[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] => [2,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0] => [10,2] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1,1] => [3,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0] => [9,3] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0] => [9,2,1] => [4,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,1,1] => [3,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0] => [8,4] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 3
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 2
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => [8,2,2] => [5,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1,1] => [3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 0
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1,1,1] => [4,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1,1,1,1] => [6,3,2,1] => [3,2,1] => 1
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,1,1,1,1,1] => [4,4,2,1,1] => [4,2,1,1] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [4,1,1,1,1,1,1,1,1] => [5,3,2,1,1] => [3,2,1,1] => 1
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1,1,1,1,1] => [4,3,3,2] => [3,3,2] => 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] => [6,4,2] => [4,2] => 1
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1,1,1,1,1,1] => [4,4,2,2] => [4,2,2] => 2
[1,0,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [3,1,1,1,1,1,1,1,1,1] => [5,3,2,2] => [3,2,2] => 2
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1,1,1,1] => [5,4,1,1,1] => [4,1,1,1] => 0
[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,1,1,1,1,1,1] => [5,4,3] => [4,3] => 0
[1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [2,2,1,1,1,1,1,1,1,1] => [4,4,3,1] => [4,3,1] => 0
[1,0,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1,1,1,1] => [5,3,3,1] => [3,3,1] => 0
[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] => [4,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0] => [9,4] => [2,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => 3
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,1,0] => [9,3,1] => [3,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,1,0] => [9,2,1,1] => [3,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 0
[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] => [4,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [8,5] => [2,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => 4
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0] => [8,4,1] => [3,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 3
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2] => [6,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1,1] => [5,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0] => [8,2,2,1] => [3,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => 1
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1,1,1] => [4,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 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] => [4,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 0
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1,1,1,1,1] => [5,3,2,1,1,1] => [3,2,1,1,1] => 1
[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,1,1,1,1,1] => [4,4,4,1] => [4,4,1] => 0
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [5,1,1,1,1,1,1,1,1] => [5,5,2,1] => [5,2,1] => 1
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1,1,1,1,1] => [6,3,2,2] => [3,2,2] => 2
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2,1,1,1,1,1] => [7,3,2,1] => [3,2,1] => 1
[1,0,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [4,2,1,1,1,1,1,1,1] => [6,3,3,1] => [3,3,1] => 0
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [4,1,1,1,1,1,1,1,1,1] => [6,4,2,1] => [4,2,1] => 1
[1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2,1,1,1,1,1] => [4,4,2,2,1] => [4,2,2,1] => 2
[1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [3,3,1,1,1,1,1,1,1] => [5,3,2,2,1] => [3,2,2,1] => 2
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,1,1,1,1] => [5,5,3] => [5,3] => 0
[1,0,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [3,2,2,1,1,1,1,1,1] => [4,4,3,1,1] => [4,3,1,1] => 0
[1,0,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [3,2,1,1,1,1,1,1,1,1] => [5,3,3,1,1] => [3,3,1,1] => 0
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,1,1,1] => [6,4,1,1,1] => [4,1,1,1] => 0
[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,1,1,1,1,1] => [6,4,3] => [4,3] => 0
[1,0,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [2,2,2,1,1,1,1,1,1,1] => [4,4,3,2] => [4,3,2] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0] => [9,5] => [2,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => 4
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,1,0] => [9,3,2] => [6,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,1,0] => [9,2,2,1] => [3,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => 1
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,1,1,1,1] => [4,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [8,6] => [2,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => 5
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0] => [8,4,2] => [3,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => 2
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,1,0] => [8,3,3] => [7,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2,1] => [6,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0] => [8,2,2,1,1] => [5,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 2
[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] => [4,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1,1,1,1,1] => [5,3,2,1,1,1,1] => [3,2,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [6,1,1,1,1,1,1,1,1] => [5,4,2,1,1,1] => [4,2,1,1,1] => 1
[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1,1,1,1,1,1] => [7,3,3,1] => [3,3,1] => 0
[1,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1,1,1,1,1,1] => [8,3,2,1] => [3,2,1] => 1
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,1,1,1,1] => [6,5,2,1] => [5,2,1] => 1
[1,0,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [4,3,1,1,1,1,1,1,1] => [5,5,2,1,1] => [5,2,1,1] => 1
[1,0,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [4,2,2,1,1,1,1,1,1] => [4,4,4,2] => [4,4,2] => 1
[1,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2,2,1,1,1,1] => [5,3,2,2,2] => [3,2,2,2] => 3
[1,0,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [3,3,2,1,1,1,1,1,1] => [6,3,3,1,1] => [3,3,1,1] => 0
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,2,1,1,1] => [6,4,4] => [4,4] => 0
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2] => [6,2,2,2,2] => [2,2,2,2] => 4
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,1,1] => [6,5,1,1,1] => [5,1,1,1] => 0
[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,1,1,1,1] => [6,5,3] => [5,3] => 0
[1,0,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,2,2,2,1,1,1,1,1,1] => [4,4,3,2,1] => [4,3,2,1] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0] => [9,6] => [2,2,2,2,2,2,1,1,1] => [2,2,2,2,2,1,1,1] => 5
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,1,0] => [9,3,3] => [7,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0] => [9,3,2,1] => [6,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,2,2] => [3,3,3,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1] => 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] => [4,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0] => [8,6,1] => [3,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => 5
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,1,0] => [8,4,2,1] => [6,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 2
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,1,0] => [8,4,1,1,1] => [4,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => 2
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,0] => [8,3,3,1] => [7,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,2] => [3,3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => 1
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2,1,1] => [6,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 0
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1,1,1,1,1,1] => [5,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [7,7,1] => [14,1] => [1] => 0
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1,1,1,1,1,1] => [5,3,3,1,1,1,1] => [3,3,1,1,1,1] => 0
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [7,1,1,1,1,1,1,1,1] => [5,4,2,1,1,1,1] => [4,2,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1,1,1,1,1,1] => [7,4,2,1,1] => [4,2,1,1] => 1
[1,0,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,1,1,1,1,1] => [9,3,2,1] => [3,2,1] => 1
[1,0,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1,1,1,1,1] => [8,3,3,1] => [3,3,1] => 0
[1,0,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [5,2,2,2,1,1,1,1] => [4,4,3,2,2] => [4,3,2,2] => 2
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [4,4,2,1,1,1,1,1] => [7,5,2,1] => [5,2,1] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [4,4,1,1,1,1,1,1,1] => [5,5,4,1] => [5,4,1] => 0
[1,0,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3,1,1,1,1,1] => [5,5,2,1,1,1] => [5,2,1,1,1] => 1
[1,0,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,2,1,1,1,1] => [4,4,4,3] => [4,4,3] => 0
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1,1,1,1,1,1] => [7,4,2,2] => [4,2,2] => 2
[1,0,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [3,3,3,2,1,1,1,1] => [7,3,3,2] => [3,3,2] => 1
[1,0,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [3,3,2,2,1,1,1,1,1] => [6,3,3,3] => [3,3,3] => 0
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,2,2,2] => [6,2,2,2,2,1] => [2,2,2,2,1] => 4
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,2,2,1,1] => [6,3,2,2,2] => [3,2,2,2] => 3
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2,1] => [6,5,1,1,1,1] => [5,1,1,1,1] => 0
[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2,1,1,1] => [6,5,4] => [5,4] => 0
[1,0,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,2,2,2,2,1,1,1,1,1] => [5,3,3,3,1] => [3,3,3,1] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => [9,7] => [2,2,2,2,2,2,2,1,1] => [2,2,2,2,2,2,1,1] => 6
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,1,1,1,1,1,1] => [5,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [8,7,1] => [15,1] => [1] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,1,0] => [8,5,3] => [3,3,3,2,2,1,1,1] => [3,3,2,2,1,1,1] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0] => [8,5,2,1] => [5,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => 4
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2,1,1,1] => [4,4,2,2,1,1,1,1] => [4,2,2,1,1,1,1] => 2
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [8,2,2,1,1,1,1] => [4,4,3,1,1,1,1,1] => [4,3,1,1,1,1,1] => 0
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1,1,1,1,1,1] => [5,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => 0
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,1,1,1,1,1,1,1] => [5,4,2,1,1,1,1,1] => [4,2,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0] => [7,7,2] => [14,1,1] => [1,1] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => [7,7,1,1] => [14,2] => [2] => 1
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [6,3,2,1,1,1,1,1] => [6,6,2,2] => [6,2,2] => 2
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [5,2,2,2,1,1,1,1,1] => [6,3,3,2,1,1] => [3,3,2,1,1] => 1
[1,0,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,4,2,2,1,1,1,1] => [8,4,2,1,1] => [4,2,1,1] => 1
[1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,2,2,1,1,1] => [4,4,3,3,2] => [4,3,3,2] => 1
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,2,2,2,2,2] => [6,6,1,1,1,1] => [6,1,1,1,1] => 0
[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,2,2,2,2,1,1] => [6,6,4] => [6,4] => 0
[1,0,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [3,3,3,2,1,1,1,1,1] => [7,5,2,2] => [5,2,2] => 2
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2,2,2,2,2] => [7,2,2,2,2,1] => [2,2,2,2,1] => 4
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,2,2,2,1] => [6,3,2,2,2,1] => [3,2,2,2,1] => 3
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2,2] => [7,5,1,1,1,1] => [5,1,1,1,1] => 0
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2,1,1] => [7,5,4] => [5,4] => 0
[1,0,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2,1,1,1,1] => [4,4,4,3,1] => [4,4,3,1] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,1,0] => [9,7,1] => [3,2,2,2,2,2,2,1,1] => [2,2,2,2,2,2,1,1] => 6
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,1,1,1,1,1,1,1] => [5,4,2,1,1,1,1,1,1] => [4,2,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0] => [8,8,1] => [16,1] => [1] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0] => [8,7,2] => [15,1,1] => [1,1] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0] => [8,7,1,1] => [15,2] => [2] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,1,0] => [8,6,2,1] => [5,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => 5
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,0] => [8,5,4] => [11,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [8,5,1,1,1,1] => [5,3,2,2,2,1,1,1] => [3,2,2,2,1,1,1] => 3
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,1,0] => [8,4,3,2] => [9,2,2,1,1,1,1] => [2,2,1,1,1,1] => 2
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,1,0] => [8,3,3,3] => [3,3,3,3,2,1,1,1] => [3,3,3,2,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0] => [8,3,3,2,1] => [4,3,3,3,1,1,1,1] => [3,3,3,1,1,1,1] => 0
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1,1,1,1,1,1] => [6,4,2,1,1,1,1,1] => [4,2,1,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [8,2,2,1,1,1,1,1] => [5,3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,1,0,0] => [7,7,3] => [14,1,1,1] => [1,1,1] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0] => [7,7,2,1] => [14,3] => [3] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,7,1,1,1] => [14,2,1] => [2,1] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1,1,1,1,1,1] => [11,3,2,1] => [3,2,1] => 1
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [6,3,2,2,1,1,1,1] => [8,5,2,2] => [5,2,2] => 2
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,2,2,2,1,1,1] => [8,3,3,2,1] => [3,3,2,1] => 1
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3,1,1,1,1,1] => [9,4,2,1,1] => [4,2,1,1] => 1
[1,0,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,2,1,1,1,1] => [9,3,3,2] => [3,3,2] => 1
[1,0,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [4,4,4,1,1,1,1,1] => [5,4,2,2,2,2] => [4,2,2,2,2] => 4
[1,0,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,4,3,2,1,1,1,1] => [7,4,2,2,1,1] => [4,2,2,1,1] => 2
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,2,2,2,2] => [7,5,1,1,1,1,1] => [5,1,1,1,1,1] => 0
[1,0,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,2,2,2,1,1] => [6,6,2,1,1,1] => [6,2,1,1,1] => 1
[1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,2,2,2,2,2,1] => [7,5,5] => [5,5] => 0
[1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,2,1,1,1] => [8,6,2,1] => [6,2,1] => 1
[1,1,0,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,3,3,2,2,2,2] => [7,2,2,2,2,2] => [2,2,2,2,2] => 5
[1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2,2,2,2,2,1] => [7,3,2,2,2,1] => [3,2,2,2,1] => 3
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,2,2,2,2,2,2,2] => [7,6,1,1,1,1] => [6,1,1,1,1] => 0
[1,0,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,2,2,2,2,2,2,1,1] => [7,5,2,1,1,1] => [5,2,1,1,1] => 1
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2,2,1] => [7,6,4] => [6,4] => 0
[1,0,1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2,1,1,1] => [4,4,4,3,2] => [4,4,3,2] => 1
[1,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,2,2,1] => [4,3,3,3,3,1] => [3,3,3,3,1] => 0
[1,1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,2,2,2,2,1] => [4,4,3,3,1,1] => [4,3,3,1,1] => 0
[1,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,2,2,1] => [4,3,3,3,1] => [3,3,3,1] => 0
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => [6,2,2,2,1] => [2,2,2,1] => 3
[1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,1,1] => [8,7,2] => [7,2] => 1
[1,1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,2,1,1] => [8,6,2] => [6,2] => 1
[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] => [8,3,3,3] => [3,3,3] => 0
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [4,3,3,2,2,1,1] => [8,5,3] => [5,3] => 0
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => [5,2,2,2,1] => [2,2,2,1] => 3
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1,1,1] => [9,3,3,1,1] => [3,3,1,1] => 0
[1,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [4,4,4,1,1,1,1] => [5,3,2,2,2,2] => [3,2,2,2,2] => 4
[1,1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3,1,1,1,1] => [9,3,2,2] => [3,2,2] => 2
[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] => [6,3,2,1,1] => [3,2,1,1] => 1
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1,1,1,1] => [5,3,1,1,1] => [3,1,1,1] => 0
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => [5,2,2,1] => [2,2,1] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,6,1,1,1,1,1] => [12,3,2] => [3,2] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [5,5,1,1,1,1,1] => [10,3,2] => [3,2] => 1
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,4,1,1,1,1,1] => [6,6,2,1] => [6,2,1] => 1
[1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,1,1,1,1] => [9,3,2] => [3,2] => 1
[1,1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1,1,1,1,1] => [8,3,2] => [3,2] => 1
[1,1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1,1,1,1] => [7,3,2] => [3,2] => 1
[1,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1,1,1,1] => [4,4,3] => [4,3] => 0
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1,1,1,1,1] => [4,4,2,1,1,1,1] => [4,2,1,1,1,1] => 1
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,1,1,1,1] => [5,5,2] => [5,2] => 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] => [4,4,1,1] => [4,1,1] => 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] => [4,2,2,1] => [2,2,1] => 2
[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] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1,1,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => 1
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1,1,1,1] => [4,3,3] => [3,3] => 0
[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] => [5,3,1] => [3,1] => 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] => [4,2,2] => [2,2] => 2
[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] => [4,2,1] => [2,1] => 1
[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,2] => [3,3,3,3,3,2] => [3,3,3,3,2] => 1
[1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2,2,2,2] => [3,3,3,3,2] => [3,3,3,2] => 1
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,2,2,2,2] => [8,5,1,1,1,1] => [5,1,1,1,1] => 0
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,2,2] => [3,3,3,3,1] => [3,3,3,1] => 0
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2] => [3,3,3,2,1] => [3,3,2,1] => 1
[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,1] => [8,7,1] => [7,1] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,1] => [11,7,3] => [7,3] => 0
[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,2,1] => [8,6,1] => [6,1] => 0
[1,1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,2,1] => [7,3,2,2,1,1,1] => [3,2,2,1,1,1] => 2
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [6,3,2,2,2,1] => [8,3,2,2,1] => [3,2,2,1] => 2
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,2,2,1] => [4,3,3,2,2] => [3,3,2,2] => 2
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,2,2,2,1] => [6,6,1,1,1] => [6,1,1,1] => 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] => [3,3,3,2] => [3,3,2] => 1
[1,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [4,4,3,3,1,1] => [8,3,1,1,1,1,1] => [3,1,1,1,1,1] => 0
[1,1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [5,5,3,2,1,1] => [10,5,2] => [5,2] => 1
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,1,1] => [9,4,4] => [4,4] => 0
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1,1] => [9,5,2] => [5,2] => 1
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,4,3,2,1,1] => [4,4,2,2,2,1] => [4,2,2,2,1] => 3
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [7,4,2,2,1,1] => [4,4,3,3,1,1,1] => [4,3,3,1,1,1] => 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] => [6,4,1,1,1,1,1] => [4,1,1,1,1,1] => 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] => [3,3,3,1] => [3,3,1] => 0
[1,1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [5,4,4,1,1,1] => [4,3,2,2,2,2,1] => [3,2,2,2,2,1] => 4
[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [4,4,4,1,1,1] => [4,3,2,2,2,2] => [3,2,2,2,2] => 4
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [6,5,2,1,1,1] => [11,3,1,1] => [3,1,1] => 0
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [6,4,2,1,1,1] => [8,3,2,1,1] => [3,2,1,1] => 1
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [6,3,2,1,1,1] => [4,4,2,2,1,1] => [4,2,2,1,1] => 2
[1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1,1,1] => [7,3,3] => [3,3] => 0
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,1,1] => [6,3,1,1,1] => [3,1,1,1] => 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] => [4,4,1,1,1] => [4,1,1,1] => 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] => [5,4,1,1,1,1,1] => [4,1,1,1,1,1] => 0
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,2,2,1,1,1] => [5,5,1,1] => [5,1,1] => 0
[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1,1] => [3,3,2,1] => [3,2,1] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1,1,1,1] => [11,3,1] => [3,1] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [5,5,1,1,1,1] => [10,3,1] => [3,1] => 0
[1,1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,1,1,1] => [9,3,1] => [3,1] => 0
[1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1,1,1,1] => [8,3,1] => [3,1] => 0
[1,1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1,1,1] => [7,3,1] => [3,1] => 0
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1,1,1,1] => [5,3,1,1,1,1] => [3,1,1,1,1] => 0
[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1,1] => [5,2,2] => [2,2] => 2
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1,1] => [3,3,2] => [3,2] => 1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => 0
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1,1,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => 0
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => 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] => [4,4,1] => [4,1] => 0
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1,1,1] => [4,2,1,1] => [2,1,1] => 1
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1] => [3,3,1] => [3,1] => 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] => [3,2,1] => [2,1] => 1
[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0] => [4,3,3,3,3] => [9,7] => [7] => 0
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3] => [8,7] => [7] => 0
[1,1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,4,4,3,2] => [8,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 2
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0] => [4,4,3,3,2] => [8,2,2,1,1,1,1] => [2,2,1,1,1,1] => 2
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,3,3,2] => [10,2,2,2,1] => [2,2,2,1] => 3
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,2] => [7,2,2,2,1,1,1] => [2,2,2,1,1,1] => 3
[1,1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,2,2] => [3,3,3,2,2] => [3,3,2,2] => 2
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,2,2,2] => [7,2,2,2,1] => [2,2,2,1] => 3
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,2,2,2] => [3,3,3,3] => [3,3,3] => 0
[1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,2] => [6,5] => [5] => 0
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2] => [6,4] => [4] => 0
[1,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,4,4,4,1] => [9,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0,0] => [5,4,4,3,1] => [4,3,3,2,2,2,1] => [3,3,2,2,2,1] => 3
[1,1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,1] => [7,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,4,4,2,1] => [5,2,2,2,2,2] => [2,2,2,2,2] => 5
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,1] => [11,5,1] => [5,1] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => [5,5,3,2,1] => [10,5,1] => [5,1] => 0
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,1] => [9,4,1,1,1,1] => [4,1,1,1,1] => 0
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,1] => [9,5,1,1] => [5,1,1] => 0
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1] => [9,5,1] => [5,1] => 0
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,4,3,2,1] => [5,2,2,2,2,1] => [2,2,2,2,1] => 4
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,0] => [7,3,3,2,1] => [4,3,3,3,1,1,1] => [3,3,3,1,1,1] => 0
[1,1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0,0] => [5,3,3,2,1] => [8,5,1] => [5,1] => 0
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,3,3,2,1] => [7,2,2,2] => [2,2,2] => 3
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [3,3,3,2,1] => [6,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,2,1] => [9,2,2,1] => [2,2,1] => 2
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0,0] => [7,3,2,2,1] => [4,3,3,2,1,1,1] => [3,3,2,1,1,1] => 1
[1,1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,2,1] => [6,6,1] => [6,1] => 0
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,2,1] => [6,2,2,1,1] => [2,2,1,1] => 2
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0] => [7,2,2,2,1] => [5,2,2,2,1,1,1] => [2,2,2,1,1,1] => 3
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,1] => [5,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1] => [5,4] => [4] => 0
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [7,5,3,1,1] => [8,3,2,2,1,1] => [3,2,2,1,1] => 2
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0] => [4,4,3,1,1] => [4,2,2,2,2,1] => [2,2,2,2,1] => 4
[1,1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1,1] => [9,2,2] => [2,2] => 2
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0] => [6,3,2,1,1] => [7,3,1,1,1] => [3,1,1,1] => 0
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,1] => [7,2,2] => [2,2] => 2
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1,1] => [3,3,3] => [3,3] => 0
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1] => [5,3] => [3] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0,0] => [7,6,1,1,1] => [13,2,1] => [2,1] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1,1,1] => [11,2,1] => [2,1] => 1
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0,0] => [7,4,1,1,1] => [4,3,2,2,1,1,1] => [3,2,2,1,1,1] => 2
[1,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,1,1] => [9,2,1] => [2,1] => 1
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1,1,1] => [8,2,1] => [2,1] => 1
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1,1,1] => [4,4,1,1,1,1] => [4,1,1,1,1] => 0
[1,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1,1] => [7,2,1] => [2,1] => 1
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1,1] => [5,2,1,1] => [2,1,1] => 1
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => 2
[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,1,1] => [4,2,2,1,1] => [2,2,1,1] => 2
[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] => [3,1,1] => 0
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1] => [4,3] => [3] => 0
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1,1] => [4,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1] => [4,2] => [2] => 1
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1] => [3,2] => [2] => 1
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [4,4,4,4] => [9,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[1,1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0,0] => [5,5,4,3] => [3,3,3,2,2,2,2] => [3,3,2,2,2,2] => 4
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0] => [6,4,4,3] => [3,3,3,3,2,2,1] => [3,3,3,2,2,1] => 2
[1,1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0,0] => [4,4,4,3] => [8,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0] => [5,5,3,3] => [10,6] => [6] => 0
[1,1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,3,3] => [7,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2] => [11,2,2,1,1] => [2,2,1,1] => 2
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2] => [9,2,2,1,1] => [2,2,1,1] => 2
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2] => [9,5] => [5] => 0
[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0] => [4,4,3,2] => [3,3,2,2,2,1] => [3,2,2,2,1] => 3
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0] => [6,3,3,2] => [7,7] => [7] => 0
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [4,4,2,2] => [8,4] => [4] => 0
[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2,2] => [6,1,1,1,1] => [1,1,1,1] => 0
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0] => [5,2,2,2] => [7,4] => [4] => 0
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,0] => [5,5,5,1] => [3,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => 6
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [7,5,3,1] => [4,3,3,2,2,1,1] => [3,3,2,2,1,1] => 2
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,0] => [6,5,3,1] => [11,2,1,1] => [2,1,1] => 1
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3,1] => [9,2,1,1] => [2,1,1] => 1
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0] => [6,3,3,1] => [8,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3,1] => [3,2,2,2,2] => [2,2,2,2] => 4
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3,1] => [3,2,2,2,1] => [2,2,2,1] => 3
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0] => [7,5,2,1] => [5,2,2,2,2,1,1] => [2,2,2,2,1,1] => 4
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0] => [6,5,2,1] => [11,3] => [3] => 0
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1] => [9,3] => [3] => 0
[1,1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0] => [4,4,2,1] => [8,3] => [3] => 0
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0] => [6,3,2,1] => [7,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1] => [7,2,1,1] => [2,1,1] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1] => [7,3] => [3] => 0
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2,1] => [3,2,2,2] => [2,2,2] => 3
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2,1] => [6,3] => [3] => 0
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1] => [3,2,2,1] => [2,2,1] => 2
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1] => [4,1,1,1] => [1,1,1] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0] => [7,6,1,1] => [13,2] => [2] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1,1] => [11,2] => [2] => 1
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1] => [7,2] => [2] => 1
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1] => [6,2] => [2] => 1
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,1] => [4,4] => [4] => 0
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1] => [5,2] => [2] => 1
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1] => [4,1,1] => [1,1] => 0
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1] => [3,2,1,1] => [2,1,1] => 1
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1] => [3,3] => [3] => 0
[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] => [1,1] => 0
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1] => [3,1] => [1] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0] => [6,6,5] => [2,2,2,2,2,2,2,2,1] => [2,2,2,2,2,2,2,1] => 7
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0] => [6,5,5] => [2,2,2,2,2,2,2,2] => [2,2,2,2,2,2,2] => 7
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => [5,5,5] => [2,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => 6
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,0] => [7,6,4] => [13,1,1,1,1] => [1,1,1,1] => 0
[1,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0,0] => [5,4,4] => [2,2,2,2,2,2,1] => [2,2,2,2,2,1] => 5
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0] => [4,4,4] => [2,2,2,2,2,2] => [2,2,2,2,2] => 5
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => [7,5,3] => [3,3,3,2,2,1,1] => [3,3,2,2,1,1] => 2
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3] => [9,1,1,1] => [1,1,1] => 0
[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0] => [4,4,3] => [2,2,2,2,2,1] => [2,2,2,2,1] => 4
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0] => [6,3,3] => [8,1,1,1,1] => [1,1,1,1] => 0
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3] => [2,2,2,2,2] => [2,2,2,2] => 4
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3] => [2,2,2,2,1] => [2,2,2,1] => 3
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [6,4,2] => [3,3,2,2,1,1] => [3,2,2,1,1] => 2
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2] => [9,1,1] => [1,1] => 0
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0] => [4,4,2] => [8,1,1] => [1,1] => 0
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2] => [7,1,1,1] => [1,1,1] => 0
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2] => [7,1,1] => [1,1] => 0
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2] => [2,2,2,2] => [2,2,2] => 3
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0] => [7,2,2] => [5,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2] => [6,1,1] => [1,1] => 0
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2] => [2,2,2,1] => [2,2,1] => 2
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2] => [2,2,2] => [2,2] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0] => [7,6,1] => [13,1] => [1] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0] => [6,6,1] => [12,1] => [1] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1] => [11,1] => [1] => 0
[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1] => [9,1] => [1] => 0
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1] => [8,1] => [1] => 0
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 2
[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] => [2,2,1,1] => 2
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1] => [7,1] => [1] => 0
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1] => [6,1] => [1] => 0
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1] => [4,1,1,1,1] => [1,1,1,1] => 0
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1] => [5,1,1] => [1,1] => 0
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1] => [5,1] => [1] => 0
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1] => [2,2,1] => [2,1] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1] => [3,1,1,1] => [1,1,1] => 0
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1] => [4,1] => [1] => 0
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1] => [2,2] => [2] => 1
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1] => [2,1] => [1] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [7,5] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => 4
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0] => [7,3] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 2
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [7,2] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [4,2] => [2,2,1,1] => [2,1,1] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0] => [6,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0] => [5,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0] => [4,1] => [2,1,1,1] => [1,1,1] => 0
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [3,1] => [2,1,1] => [1,1] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [5] => [1,1,1,1,1] => [1,1,1,1] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [4] => [1,1,1,1] => [1,1,1] => 0
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [3] => [1,1,1] => [1,1] => 0
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2] => [1,1] => [1] => 0
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,3] => [3,3,3,3,3,2,1] => [3,3,3,3,2,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,6,6] => [2,2,2,2,2,2,2,2,2] => [2,2,2,2,2,2,2,2] => 8
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [4,4,3,2,1] => [5,2,2,2,2,1] => [2,2,2,2,1] => 4
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2] => [9,5] => [5] => 0
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [2] => [1,1] => [1] => 0
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1] => [2,2,1] => [2,1] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [2] => [1,1] => [1] => 0
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => [4,3,1] => [3,1] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [8] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [9] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [8,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1] => [2,1] => [1] => 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] => [3,1] => [1] => 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] => [3,2] => [2] => 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] => [3,2,1] => [2,1] => 1
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => [4,2,1] => [2,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,1] => [11,7,3] => [7,3] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [5] => [1,1,1,1,1] => [1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [4] => [1,1,1,1] => [1,1,1] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [3] => [1,1,1] => [1,1] => 0
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0] => [9,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0] => [8,2,1] => [4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1,1,1,1,1] => [5,3,3] => [3,3] => 0
[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1,1] => [5,3,2] => [3,2] => 1
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2,1] => [6,5,1,1,1,1] => [5,1,1,1,1] => 0
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [3,3,3] => [2,2,2,2,1] => [2,2,2,1] => 3
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0] => [4,4,4] => [2,2,2,2,2,2] => [2,2,2,2,2] => 5
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [4,4,4,4] => [9,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2,2,2] => [7,6,5] => [6,5] => 0
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1] => [2,2] => [2] => 1
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1] => [4,3,1,1] => [3,1,1] => 0
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1] => [4,3,2] => [3,2] => 1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1,1,1,1,1,1] => [4,4,2] => [4,2] => 1
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1,1,1,1,1,1] => [5,3,1,1] => [3,1,1] => 0
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1] => [4,3,2,1] => [3,2,1] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,1] => [9,5,1] => [5,1] => 0
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2] => [7,1,1] => [1,1] => 0
[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] => [1,1] => 0
[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] => [6,5,2,1] => [5,2,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0] => [6,6,6] => [2,2,2,2,2,2,2,2,2] => [2,2,2,2,2,2,2,2] => 8
[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] => [3,3,1] => [3,1] => 0
[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] => [4,2,1,1] => [2,1,1] => 1
[1,1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [4,1,1,1,1,1] => [4,4,1] => [4,1] => 0
[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] => [4,3,1,1,1] => [3,1,1,1] => 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] => [7,3] => [3] => 0
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1] => [5,1] => [1] => 0
[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0] => [3] => [1,1,1] => [1,1] => 0
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0] => [7,2,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[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] => [4,4,1,1] => [4,1,1] => 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] => [4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[1,1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [3,2,1,1,1,1,1,1] => [5,3,3] => [3,3] => 0
[1,1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [3,3,3,3,2,1] => [8,6,1] => [6,1] => 0
[1,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => [6,2,2,2,1] => [2,2,2,1] => 3
[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,3,3,3,3,3] => [3,3,3,3,3,2,1] => [3,3,3,3,2,1] => 1
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2] => [6,2,2,2,2] => [2,2,2,2] => 4
[1,1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [4,1,1,1,1,1,1,1] => [4,3,2,2] => [3,2,2] => 2
[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] => [4,3,2,1,1] => [3,2,1,1] => 1
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [6,1,1,1,1,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => 0
[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] => [4,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,1,1] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,1,1] => [9,5,2] => [5,2] => 1
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0] => [5,3,2,1] => [7,2,1,1] => [2,1,1] => 1
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,1,1,1] => [9,3,3,1,1] => [3,3,1,1] => 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] => [9,3] => [3] => 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] => [9,2,1,1] => [2,1,1] => 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] => [2,1,1] => [1,1] => 0
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0] => [4,2] => [2,2,1,1] => [2,1,1] => 1
[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] => [3,3,3,2] => [3,3,2] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [6,4,3,2,1] => [9,5,1,1] => [5,1,1] => 0
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0] => [6,4,3,2,1] => [9,5,1,1] => [5,1,1] => 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] => [7,2,1,1,1] => [2,1,1,1] => 1
[1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1,1,1] => [6,3,1,1,1] => [3,1,1,1] => 0
[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,4,3,2,1,1] => [9,5,2] => [5,2] => 1
[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] => [7,2,2,2] => [2,2,2] => 3
[1,1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,2,1] => [6,2,2,1,1] => [2,2,1,1] => 2
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0,0] => [7,4,3,2,1] => [9,4,1,1,1,1] => [4,1,1,1,1] => 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] => [7,2,2] => [2,2] => 2
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,5,4,3,2,1] => [11,7,3] => [7,3] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,0] => [8,7,1] => [15,1] => [1] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0,0] => [7,6,1] => [13,1] => [1] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0,0] => [6,5,1] => [11,1] => [1] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0] => [5,4,1] => [9,1] => [1] => 0
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0] => [4,3,1] => [7,1] => [1] => 0
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2] => [2,2,2] => [2,2] => 2
[1,1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,2] => [7,2,2,2,1,1,1] => [2,2,2,1,1,1] => 3
[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] => [3,3,3,2,1] => [3,3,2,1] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0] => [6,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0] => [5,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0] => [4,1] => [2,1,1,1] => [1,1,1] => 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] => [3,1,1] => [1,1] => 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] => [4,2] => [2] => 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] => [4,2,2] => [2,2] => 2
[1,1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,1] => [2,2] => [2] => 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] => [3,2,2,1] => [2,2,1] => 2
[1,1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,2,2,2,2,2,2] => [6,2,2,2,2,1] => [2,2,2,2,1] => 4
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [4,3,3,2,2,1,1] => [8,5,3] => [5,3] => 0
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0] => [7,5,3,1] => [4,3,3,2,2,1,1] => [3,3,2,2,1,1] => 2
[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] => [2,1] => [1] => 0
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,1,1,1,1,1,1] => [5,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => 1
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [6,4,3,2,1,1] => [9,4,4] => [4,4] => 0
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0,0,0] => [7,3,2,2,2,1] => [6,3,2,2,2,1,1] => [3,2,2,2,1,1] => 3
[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] => [4,4,2,2,1,1] => [4,2,2,1,1] => 2
[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] => [4,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1] => [4,1] => [1] => 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] => [6,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [4,3,1,1,1,1,1,1] => [6,3,2,2] => [3,2,2] => 2
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [8,2,1,1,1,1,1,1] => [5,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => 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] => [4,1,1] => [1,1] => 0
[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1] => [5,2] => [2] => 1
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,4,3,2,1] => [9,5,1] => [5,1] => 0
[1,1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [3,2,2,2,1,1,1] => [6,4,1,1] => [4,1,1] => 0
[1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [4,2,2,2,1,1,1] => [5,5,1,1,1] => [5,1,1,1] => 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] => [7,4,1,1,1,1,1] => [4,1,1,1,1,1] => 0
[1,1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,2,2,1] => [4,3,3,2,2] => [3,3,2,2] => 2
[1,1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,2,2,2,2] => [7,5,1,1,1,1,1] => [5,1,1,1,1,1] => 0
[1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,4,3,2,1,1,1] => [9,3,3,1,1] => [3,3,1,1] => 0
[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] => [1,1,1] => [1,1] => 0
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0,0] => [5,5,3,2,1] => [10,5,1] => [5,1] => 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] => [11,5,1] => [5,1] => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0,0] => [8,7,1,1] => [15,2] => [2] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0,0] => [8,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0,0,0] => [7,6,1,1,1] => [13,2,1] => [2,1] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0,0] => [6,5,1,1,1,1] => [11,3,1] => [3,1] => 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] => [2,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [5,4,1,1,1,1,1] => [9,3,2] => [3,2] => 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] => [2,1,1,1,1] => [1,1,1,1] => 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] => [2,1,1,1] => [1,1,1] => 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] => [2,2,1,1] => 2
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,1] => [4,1,1,1] => [1,1,1] => 0
[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0] => [3,3,2] => [2,2,2,2] => [2,2,2] => 3
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searching the database for the individual values of this statistic
Description
The number of twos in an integer partition.
The total number of twos in all partitions of n is equal to the total number of singletons St001484The number of singletons of an integer partition. in all partitions of n−1, see [1].
The total number of twos in all partitions of n is equal to the total number of singletons St001484The number of singletons of an integer partition. in all partitions of n−1, see [1].
Map
to partition
Description
The cut-out partition of a Dyck path.
The partition λ associated to a Dyck path is defined to be the complementary partition inside the staircase partition (n−1,…,2,1) when cutting out D considered as a path from (0,0) to (n,n).
In other words, λi is the number of down-steps before the (n+1−i)-th up-step of D.
This map is a bijection between Dyck paths of size n and partitions inside the staircase partition (n−1,…,2,1).
The partition λ associated to a Dyck path is defined to be the complementary partition inside the staircase partition (n−1,…,2,1) when cutting out D considered as a path from (0,0) to (n,n).
In other words, λi is the number of down-steps before the (n+1−i)-th up-step of D.
This map is a bijection between Dyck paths of size n and partitions inside the staircase partition (n−1,…,2,1).
Map
first row removal
Description
Removes the first entry of an integer partition
Map
Loehr-Warrington
Description
Return a partition whose diagonal inversion number is the length of the preimage.
searching the database
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