Identifier
-
Mp00027:
Dyck paths
—to partition⟶
Integer partitions
Mp00322: Integer partitions —Loehr-Warrington⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001177: 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] => 3
[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] => 0
[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] => 2
[1,1,1,0,0,0,1,0] => [3] => [1,1,1] => [1,1] => 2
[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] => 18
[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] => 12
[1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => [4,1,1,1] => [1,1,1] => 6
[1,0,1,1,0,0,1,0,1,0] => [4,3,1,1] => [7,2] => [2] => 0
[1,0,1,1,0,0,1,1,0,0] => [3,3,1,1] => [6,2] => [2] => 0
[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] => 0
[1,0,1,1,0,1,1,0,0,0] => [2,2,1,1] => [4,1,1] => [1,1] => 2
[1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => [3,2,1,1] => [2,1,1] => 8
[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] => 2
[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] => 2
[1,1,0,0,1,0,1,1,0,0] => [3,3,2] => [2,2,2,2] => [2,2,2] => 18
[1,1,0,0,1,1,0,0,1,0] => [4,2,2] => [6,1,1] => [1,1] => 2
[1,1,0,0,1,1,0,1,0,0] => [3,2,2] => [2,2,2,1] => [2,2,1] => 12
[1,1,0,0,1,1,1,0,0,0] => [2,2,2] => [2,2,2] => [2,2] => 6
[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] => 2
[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] => 3
[1,1,0,1,1,0,0,0,1,0] => [4,1,1] => [3,1,1,1] => [1,1,1] => 6
[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] => 0
[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] => 8
[1,1,1,0,1,0,0,0,1,0] => [4,1] => [2,1,1,1] => [1,1,1] => 6
[1,1,1,0,1,0,0,1,0,0] => [3,1] => [2,1,1] => [1,1] => 2
[1,1,1,1,0,0,0,0,1,0] => [4] => [1,1,1,1] => [1,1,1] => 6
[1,1,1,1,0,0,0,1,0,0] => [3] => [1,1,1] => [1,1] => 2
[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] => 6
[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] => 48
[1,0,1,0,1,0,1,1,0,0,1,0] => [5,3,3,2,1] => [8,5,1] => [5,1] => 6
[1,0,1,0,1,0,1,1,0,1,0,0] => [4,3,3,2,1] => [7,2,2,2] => [2,2,2] => 18
[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] => 24
[1,0,1,0,1,1,0,0,1,0,1,0] => [5,4,2,2,1] => [9,2,2,1] => [2,2,1] => 12
[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] => 30
[1,0,1,0,1,1,0,1,0,0,1,0] => [5,3,2,2,1] => [6,6,1] => [6,1] => 7
[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] => 20
[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] => 15
[1,0,1,0,1,1,1,0,0,0,1,0] => [5,2,2,2,1] => [7,2,2,1] => [2,2,1] => 12
[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] => 30
[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] => 15
[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] => 5
[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] => 48
[1,0,1,1,0,0,1,1,0,0,1,0] => [5,3,3,1,1] => [8,4,1] => [4,1] => 5
[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] => 36
[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] => 27
[1,0,1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,1] => [9,2,2] => [2,2] => 6
[1,0,1,1,0,1,0,0,1,1,0,0] => [4,4,2,1,1] => [8,2,2] => [2,2] => 6
[1,0,1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,1] => [7,4,1] => [4,1] => 5
[1,0,1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,1] => [7,2,2] => [2,2] => 6
[1,0,1,1,0,1,0,1,1,0,0,0] => [3,3,2,1,1] => [6,2,2] => [2,2] => 6
[1,0,1,1,0,1,1,0,0,0,1,0] => [5,2,2,1,1] => [6,2,2,1] => [2,2,1] => 12
[1,0,1,1,0,1,1,0,0,1,0,0] => [4,2,2,1,1] => [3,3,2,2] => [3,2,2] => 22
[1,0,1,1,0,1,1,0,1,0,0,0] => [3,2,2,1,1] => [3,3,3] => [3,3] => 12
[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] => 3
[1,0,1,1,1,0,0,0,1,1,0,0] => [4,4,1,1,1] => [8,2,1] => [2,1] => 3
[1,0,1,1,1,0,0,1,0,0,1,0] => [5,3,1,1,1] => [5,5,1] => [5,1] => 6
[1,0,1,1,1,0,0,1,0,1,0,0] => [4,3,1,1,1] => [7,2,1] => [2,1] => 3
[1,0,1,1,1,0,0,1,1,0,0,0] => [3,3,1,1,1] => [5,2,1,1] => [2,1,1] => 8
[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] => 20
[1,0,1,1,1,0,1,0,0,1,0,0] => [4,2,1,1,1] => [6,2,1] => [2,1] => 3
[1,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => [3,3,1,1] => [3,1,1] => 10
[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] => 15
[1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => [5,2,1] => [2,1] => 3
[1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => [3,2,2] => [2,2] => 6
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => [4,2] => [2] => 0
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => [3,2] => [2] => 0
[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] => 55
[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] => 42
[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] => 20
[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] => 32
[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] => 12
[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] => 12
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,2,2] => [5,1,1,1] => [1,1,1] => 6
[1,1,0,1,0,0,1,0,1,0,1,0] => [5,4,3,1] => [9,2,1,1] => [2,1,1] => 8
[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] => 48
>>> 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] => 8
[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] => 36
[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] => 27
[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] => 8
[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] => 18
[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] => 24
[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] => 12
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,2,2,1] => [4,1,1,1] => [1,1,1] => 6
[1,1,0,1,1,0,0,0,1,0,1,0] => [5,4,1,1] => [9,2] => [2] => 0
[1,1,0,1,1,0,0,0,1,1,0,0] => [4,4,1,1] => [8,2] => [2] => 0
[1,1,0,1,1,0,0,1,0,0,1,0] => [5,3,1,1] => [6,2,1,1] => [2,1,1] => 8
[1,1,0,1,1,0,0,1,0,1,0,0] => [4,3,1,1] => [7,2] => [2] => 0
[1,1,0,1,1,0,0,1,1,0,0,0] => [3,3,1,1] => [6,2] => [2] => 0
[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] => 18
[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] => 0
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,1,1] => [4,1,1] => [1,1] => 2
[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] => 15
[1,1,0,1,1,1,0,0,0,1,0,0] => [4,1,1,1] => [3,2,1,1] => [2,1,1] => 8
[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] => 2
[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] => 6
[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] => 48
[1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => [8,1,1,1] => [1,1,1] => 6
[1,1,1,0,0,0,1,1,0,1,0,0] => [4,3,3] => [2,2,2,2,2] => [2,2,2,2] => 36
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => [2,2,2,2,1] => [2,2,2,1] => 27
[1,1,1,0,0,1,0,0,1,0,1,0] => [5,4,2] => [9,1,1] => [1,1] => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => [4,4,2] => [8,1,1] => [1,1] => 2
[1,1,1,0,0,1,0,1,0,0,1,0] => [5,3,2] => [7,1,1,1] => [1,1,1] => 6
[1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => [7,1,1] => [1,1] => 2
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,3,2] => [2,2,2,2] => [2,2,2] => 18
[1,1,1,0,0,1,1,0,0,0,1,0] => [5,2,2] => [6,1,1,1] => [1,1,1] => 6
[1,1,1,0,0,1,1,0,0,1,0,0] => [4,2,2] => [6,1,1] => [1,1] => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,2] => [2,2,2,1] => [2,2,1] => 12
[1,1,1,0,0,1,1,1,0,0,0,0] => [2,2,2] => [2,2,2] => [2,2] => 6
[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] => 20
[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] => 12
[1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => [5,1,1] => [1,1] => 2
[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] => 3
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,1,1] => [3,1,1,1,1] => [1,1,1,1] => 12
[1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,1] => [3,1,1,1] => [1,1,1] => 6
[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] => 0
[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] => 20
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,2] => [2,2,1,1,1] => [2,1,1,1] => 15
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,2] => [2,2,1,1] => [2,1,1] => 8
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => [2,1,1,1,1] => [1,1,1,1] => 12
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => [2,1,1,1] => [1,1,1] => 6
[1,1,1,1,0,1,0,0,1,0,0,0] => [3,1] => [2,1,1] => [1,1] => 2
[1,1,1,1,1,0,0,0,0,0,1,0] => [5] => [1,1,1,1,1] => [1,1,1,1] => 12
[1,1,1,1,1,0,0,0,0,1,0,0] => [4] => [1,1,1,1] => [1,1,1] => 6
[1,1,1,1,1,0,0,0,1,0,0,0] => [3] => [1,1,1] => [1,1] => 2
[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] => 24
[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] => 45
[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] => 90
[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] => 45
[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] => 7
[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] => 87
[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] => 58
[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] => 72
[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] => 32
[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] => 72
[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] => 32
[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] => 7
[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] => 21
[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] => 24
[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] => 21
[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] => 21
[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] => 32
[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] => 62
[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] => 50
[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] => 6
[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] => 27
[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] => 36
[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] => 36
[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] => 6
[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] => 28
[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] => 54
[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] => 42
[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] => 40
[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] => 14
[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] => 44
[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] => 40
[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] => 28
[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] => 93
[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] => 76
[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] => 12
[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] => 20
[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] => 12
[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] => 62
[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] => 16
[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] => 12
[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] => 14
[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] => 28
[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] => 12
[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] => 12
[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] => 20
[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] => 12
[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] => 14
[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] => 30
[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] => 12
[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] => 14
[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] => 10
[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] => 21
[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] => 12
[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] => 18
[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] => 5
[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] => 20
[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] => 100
[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] => 24
[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] => 84
[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] => 68
[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] => 12
[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] => 12
[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] => 24
[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] => 12
[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] => 55
[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] => 32
[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] => 12
[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] => 42
[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] => 32
[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] => 10
[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] => 10
[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] => 24
[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] => 10
[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] => 10
[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] => 50
[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] => 12
[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] => 18
[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] => 21
[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] => 32
[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] => 14
[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] => 20
[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] => 18
[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] => 15
[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] => 4
[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] => 4
[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] => 24
[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] => 4
[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] => 4
[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] => 42
[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] => 20
[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] => 4
[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] => 5
[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] => 28
[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] => 10
[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] => 4
[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] => 6
[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] => 8
[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] => 28
[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] => 18
[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] => 5
[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] => 8
[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] => 4
[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] => 3
[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] => 56
[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] => 36
[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] => 42
[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] => 27
[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] => 90
[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] => 42
[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] => 75
[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] => 36
[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] => 51
[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] => 16
[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] => 51
[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] => 38
[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] => 27
[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] => 72
[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] => 30
[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] => 18
[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] => 18
[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] => 18
[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] => 18
[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] => 18
[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] => 27
[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] => 62
[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] => 50
[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] => 27
[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] => 12
[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] => 36
[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] => 95
[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] => 48
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1] => [10,6,1] => [6,1] => 7
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3,1] => [8,8,1] => [8,1] => 9
[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] => 78
[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] => 35
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1] => [9,6,1] => [6,1] => 7
[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] => 64
[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] => 35
[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] => 24
[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] => 90
[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] => 14
[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] => 75
[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] => 60
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1] => [11,5,1] => [5,1] => 6
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1] => [10,5,1] => [5,1] => 6
[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] => 14
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1] => [9,5,1] => [5,1] => 6
[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] => 48
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2,1] => [7,7,1] => [7,1] => 8
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1] => [8,5,1] => [5,1] => 6
[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] => 18
[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] => 24
[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] => 12
[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] => 12
[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] => 14
[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] => 12
[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] => 30
[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] => 52
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1] => [6,6,1] => [6,1] => 7
[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] => 20
[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] => 15
[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] => 38
[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] => 12
[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] => 30
[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] => 15
[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] => 18
[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] => 90
[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] => 18
[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] => 75
[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] => 60
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,1] => [11,4,1] => [4,1] => 5
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1] => [10,4,1] => [4,1] => 5
[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] => 18
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,1] => [9,4,1] => [4,1] => 5
[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] => 48
[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] => 18
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1] => [8,4,1] => [4,1] => 5
[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] => 36
[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] => 27
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,1] => [11,2,2] => [2,2] => 6
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1] => [10,2,2] => [2,2] => 6
[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] => 16
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,1] => [9,2,2] => [2,2] => 6
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1] => [8,2,2] => [2,2] => 6
[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] => 18
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1] => [7,4,1] => [4,1] => 5
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1] => [7,2,2] => [2,2] => 6
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1] => [6,2,2] => [2,2] => 6
[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] => 30
[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] => 12
[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] => 22
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => [3,3,3] => [3,3] => 12
[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] => 3
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1] => [10,2,1] => [2,1] => 3
[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] => 44
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1] => [9,2,1] => [2,1] => 3
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1] => [8,2,1] => [2,1] => 3
[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] => 32
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1] => [5,5,1] => [5,1] => 6
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1] => [7,2,1] => [2,1] => 3
[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] => 8
[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] => 30
[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] => 20
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1] => [6,2,1] => [2,1] => 3
[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] => 10
[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] => 24
[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] => 15
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1] => [5,2,1] => [2,1] => 3
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1] => [3,2,2] => [2,2] => 6
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1] => [4,2] => [2] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => [3,2] => [2] => 0
[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] => 112
[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] => 108
[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] => 95
[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] => 42
[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] => 78
[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] => 30
[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] => 64
[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] => 30
[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] => 20
[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] => 20
[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] => 100
[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] => 20
[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] => 84
[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] => 68
[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] => 20
[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] => 55
[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] => 42
[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] => 20
[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] => 20
[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] => 52
[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] => 32
[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] => 12
[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] => 42
[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] => 12
[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] => 6
[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] => 15
[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] => 90
[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] => 15
[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] => 75
[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] => 60
[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] => 8
[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] => 8
[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] => 15
[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] => 8
[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] => 48
[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] => 15
[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] => 8
[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] => 36
[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] => 27
[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] => 20
[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] => 15
[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] => 8
[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] => 18
[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] => 35
[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] => 24
[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] => 12
[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] => 6
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1] => [11,2] => [2] => 0
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1] => [10,2] => [2] => 0
[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] => 38
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1] => [9,2] => [2] => 0
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1] => [8,2] => [2] => 0
[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] => 24
[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] => 8
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1] => [7,2] => [2] => 0
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1] => [6,2] => [2] => 0
[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] => 28
[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] => 18
[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] => 0
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1] => [4,1,1] => [1,1] => 2
[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] => 24
[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] => 15
[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] => 8
[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] => 2
[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] => 12
[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] => 90
[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] => 12
[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] => 75
[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] => 60
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [6,5,3] => [11,1,1,1] => [1,1,1] => 6
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [5,5,3] => [10,1,1,1] => [1,1,1] => 6
[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] => 12
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [5,4,3] => [9,1,1,1] => [1,1,1] => 6
[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] => 48
[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] => 12
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [5,3,3] => [8,1,1,1] => [1,1,1] => 6
[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] => 36
[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] => 27
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [6,5,2] => [11,1,1] => [1,1] => 2
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,5,2] => [10,1,1] => [1,1] => 2
[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] => 44
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,4,2] => [9,1,1] => [1,1] => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,4,2] => [8,1,1] => [1,1] => 2
[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] => 12
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [5,3,2] => [7,1,1,1] => [1,1,1] => 6
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,2] => [7,1,1] => [1,1] => 2
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,3,2] => [2,2,2,2] => [2,2,2] => 18
[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] => 20
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [5,2,2] => [6,1,1,1] => [1,1,1] => 6
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,2] => [6,1,1] => [1,1] => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2] => [2,2,2,1] => [2,2,1] => 12
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,2,2] => [2,2,2] => [2,2] => 6
[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] => 38
[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] => 30
[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] => 20
[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] => 20
[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] => 12
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,2,1] => [5,1,1] => [1,1] => 2
[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] => 3
[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] => 20
[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] => 12
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,1,1] => [3,1,1,1] => [1,1,1] => 6
[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] => 0
[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] => 38
[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] => 30
[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] => 20
[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] => 24
[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] => 15
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [4,2] => [2,2,1,1] => [2,1,1] => 8
[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] => 20
[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] => 12
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [4,1] => [2,1,1,1] => [1,1,1] => 6
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,1] => [2,1,1] => [1,1] => 2
[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] => 20
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => [1,1,1,1,1] => [1,1,1,1] => 12
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [4] => [1,1,1,1] => [1,1,1] => 6
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => [1,1,1] => [1,1] => 2
[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] => 88
[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] => 21
[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] => 75
[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] => 84
[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] => 68
[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] => 60
[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] => 60
[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] => 24
[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] => 70
[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] => 24
[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] => 48
[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] => 27
[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] => 16
[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] => 56
[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] => 14
[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] => 52
[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] => 36
[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] => 18
[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] => 14
[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] => 18
[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] => 21
[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] => 32
[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] => 42
[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] => 20
[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] => 12
[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] => 85
[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] => 30
[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] => 21
[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] => 32
[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] => 39
[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] => 27
[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] => 48
[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] => 36
[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] => 48
[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] => 35
[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] => 78
[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] => 30
[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] => 64
[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] => 27
[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] => 42
[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] => 22
[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] => 48
[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] => 15
[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] => 81
[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] => 15
[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] => 56
[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] => 78
[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] => 30
[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] => 15
[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] => 24
[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] => 12
[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] => 75
[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] => 59
[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] => 15
[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] => 24
[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] => 12
[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] => 18
[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] => 84
[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] => 68
[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] => 22
[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] => 21
[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] => 22
[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] => 55
[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] => 60
[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] => 36
[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] => 44
[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] => 22
[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] => 36
[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] => 10
[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] => 10
[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] => 40
[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] => 21
[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] => 10
[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] => 35
[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] => 56
[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] => 30
[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] => 10
[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] => 24
[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] => 12
[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] => 63
[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] => 48
[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] => 20
[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] => 30
[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] => 18
[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] => 12
[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] => 8
[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] => 78
[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] => 8
[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] => 8
[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] => 60
[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] => 24
[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] => 8
[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] => 8
[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] => 58
[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] => 44
[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] => 10
[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] => 8
[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] => 15
[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] => 54
[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] => 40
[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] => 12
[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] => 8
[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] => 12
[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] => 12
[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] => 48
[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] => 35
[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] => 24
[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] => 12
[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] => 4
[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] => 6
[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] => 3
[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] => 104
[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] => 18
[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] => 88
[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] => 24
[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] => 62
[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] => 16
[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] => 75
[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] => 27
[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] => 27
[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] => 55
[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] => 60
[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] => 16
[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] => 60
[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] => 36
[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] => 24
[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] => 36
[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] => 38
[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] => 48
[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] => 39
[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] => 8
[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] => 8
[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] => 24
[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] => 45
[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] => 90
[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] => 45
[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] => 7
[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] => 87
[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] => 58
[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] => 72
[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] => 32
[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] => 72
[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] => 32
[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] => 7
[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] => 21
[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] => 24
[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] => 21
[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] => 21
[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] => 70
[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] => 32
[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] => 62
[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] => 50
[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] => 6
[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] => 50
[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] => 27
[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] => 36
[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] => 36
[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] => 6
[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] => 28
[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] => 54
[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] => 42
[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] => 40
[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] => 14
[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] => 44
[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] => 40
[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] => 28
[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] => 93
[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] => 76
[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] => 12
[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] => 20
[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] => 12
[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] => 62
[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] => 42
[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] => 16
[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] => 12
[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] => 14
[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] => 28
[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] => 12
[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] => 12
[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] => 87
[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] => 20
[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] => 12
[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] => 14
[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] => 72
[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] => 30
[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] => 12
[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] => 14
[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] => 10
[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] => 45
[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] => 21
[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] => 12
[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] => 18
[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] => 5
[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] => 20
[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] => 100
[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] => 24
[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] => 84
[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] => 68
[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] => 12
[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] => 12
[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] => 35
[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] => 24
[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] => 12
[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] => 55
[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] => 58
[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] => 32
[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] => 12
[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] => 42
[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] => 32
[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] => 10
[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] => 80
[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] => 10
[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] => 10
[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] => 35
[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] => 24
[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] => 10
[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] => 10
[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] => 65
[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] => 50
[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] => 12
[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] => 18
[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] => 21
[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] => 45
[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] => 32
[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] => 14
[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] => 20
[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] => 18
[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] => 15
[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] => 4
[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] => 4
[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] => 70
[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] => 4
[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] => 4
[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] => 48
[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] => 24
[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] => 4
[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] => 4
[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] => 56
[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] => 42
[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] => 20
[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] => 4
[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] => 5
[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] => 40
[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] => 28
[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] => 10
[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] => 4
[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] => 6
[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] => 8
[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] => 40
[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] => 28
[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] => 18
[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] => 5
[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] => 8
[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] => 4
[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] => 3
[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] => 106
[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] => 56
[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] => 36
[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] => 42
[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] => 27
[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] => 90
[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] => 42
[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] => 75
[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] => 36
[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] => 51
[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] => 16
[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] => 51
[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] => 38
[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] => 48
[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] => 27
[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] => 72
[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] => 30
[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] => 18
[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] => 18
[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] => 30
[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] => 18
[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] => 18
[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] => 18
[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] => 62
[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] => 27
[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] => 62
[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] => 50
[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] => 51
[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] => 27
[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] => 12
[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] => 36
[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] => 48
[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] => 95
[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] => 48
[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] => 7
[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] => 9
[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] => 78
[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] => 35
[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] => 92
[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] => 7
[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] => 64
[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] => 35
[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] => 24
[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] => 90
[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] => 14
[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] => 75
[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] => 60
[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] => 6
[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] => 6
[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] => 32
[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] => 14
[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] => 6
[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] => 48
[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] => 78
[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] => 8
[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] => 6
[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] => 18
[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] => 24
[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] => 12
[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] => 89
[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] => 12
[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] => 12
[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] => 32
[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] => 14
[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] => 12
[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] => 30
[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] => 67
[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] => 52
[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] => 7
[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] => 20
[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] => 15
[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] => 51
[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] => 38
[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] => 12
[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] => 30
[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] => 15
[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] => 108
[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] => 18
[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] => 90
[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] => 28
[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] => 18
[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] => 75
[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] => 60
[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] => 5
[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] => 44
[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] => 5
[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] => 5
[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] => 28
[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] => 18
[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] => 5
[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] => 48
[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] => 28
[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] => 18
[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] => 5
[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] => 36
[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] => 27
[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] => 6
[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] => 6
[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] => 78
[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] => 6
[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] => 6
[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] => 50
[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] => 16
[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] => 6
[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] => 6
[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] => 40
[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] => 18
[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] => 5
[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] => 6
[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] => 6
[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] => 42
[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] => 30
[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] => 12
[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] => 22
[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] => 12
[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] => 3
[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] => 3
[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] => 70
[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] => 3
[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] => 3
[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] => 58
[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] => 44
[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] => 3
[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] => 3
[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] => 45
[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] => 32
[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] => 6
[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] => 3
[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] => 8
[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] => 42
[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] => 30
[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] => 20
[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] => 3
[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] => 10
[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] => 35
[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] => 24
[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] => 15
[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] => 3
[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] => 6
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1] => [4,2] => [2] => 0
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1] => [3,2] => [2] => 0
[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] => 56
[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] => 42
[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] => 112
[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] => 108
[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] => 95
[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] => 42
[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] => 78
[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] => 30
[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] => 92
[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] => 64
[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] => 30
[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] => 20
[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] => 119
[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] => 20
[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] => 100
[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] => 30
[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] => 20
[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] => 84
[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] => 68
[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] => 38
[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] => 30
[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] => 20
[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] => 55
[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] => 78
[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] => 42
[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] => 20
[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] => 38
[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] => 30
[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] => 20
[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] => 67
[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] => 52
[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] => 32
[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] => 12
[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] => 56
[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] => 42
[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] => 12
[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] => 6
[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] => 126
[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] => 108
[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] => 15
[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] => 24
[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] => 15
[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] => 90
[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] => 24
[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] => 15
[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] => 75
[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] => 60
[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] => 8
[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] => 8
[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] => 80
[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] => 8
[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] => 8
[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] => 24
[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] => 15
[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] => 8
[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] => 48
[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] => 24
[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] => 15
[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] => 8
[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] => 36
[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] => 27
[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] => 62
[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] => 42
[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] => 20
[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] => 35
[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] => 15
[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] => 8
[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] => 18
[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] => 48
[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] => 35
[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] => 24
[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] => 12
[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] => 6
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,1] => [13,2] => [2] => 0
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1] => [12,2] => [2] => 0
[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] => 62
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1] => [11,2] => [2] => 0
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1] => [10,2] => [2] => 0
[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] => 51
[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] => 38
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1] => [9,2] => [2] => 0
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1] => [8,2] => [2] => 0
[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] => 35
[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] => 24
[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] => 8
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1] => [7,2] => [2] => 0
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1] => [6,2] => [2] => 0
[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] => 40
[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] => 28
[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] => 18
[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] => 0
[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] => 2
[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] => 35
[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] => 24
[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] => 15
[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] => 8
[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] => 2
[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] => 147
[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] => 20
[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] => 126
[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] => 108
[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] => 12
[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] => 12
[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] => 20
[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] => 12
[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] => 90
[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] => 20
[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] => 12
[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] => 75
[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] => 60
[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] => 6
[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] => 6
[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] => 80
[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] => 6
[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] => 6
[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] => 20
[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] => 12
[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] => 6
[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] => 48
[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] => 20
[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] => 12
[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] => 6
[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] => 36
[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] => 27
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [7,6,2] => [13,1,1] => [1,1] => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,6,2] => [12,1,1] => [1,1] => 2
[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] => 70
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [6,5,2] => [11,1,1] => [1,1] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,5,2] => [10,1,1] => [1,1] => 2
[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] => 58
[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] => 44
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [5,4,2] => [9,1,1] => [1,1] => 2
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [4,4,2] => [8,1,1] => [1,1] => 2
[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] => 30
[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] => 12
[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] => 6
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [4,3,2] => [7,1,1] => [1,1] => 2
[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] => 18
[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] => 30
[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] => 20
[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] => 6
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [4,2,2] => [6,1,1] => [1,1] => 2
[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] => 12
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [2,2,2] => [2,2,2] => [2,2] => 6
[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] => 62
[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] => 51
[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] => 38
[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] => 42
[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] => 30
[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] => 20
[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] => 30
[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] => 20
[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] => 12
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [4,2,1] => [5,1,1] => [1,1] => 2
[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] => 3
[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] => 30
[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] => 20
[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] => 12
[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] => 6
[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] => 0
[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] => 62
[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] => 51
[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] => 38
[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] => 42
[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] => 30
[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] => 20
[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] => 35
[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] => 24
[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] => 15
[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] => 8
[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] => 30
[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] => 20
[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] => 12
[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] => 6
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => [2,1,1] => [1,1] => 2
[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] => 30
[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] => 20
[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] => 12
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => [1,1,1,1] => [1,1,1] => 6
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => [1,1,1] => [1,1] => 2
[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] => 42
[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] => 4
[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] => 56
[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] => 42
[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] => 10
[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] => 8
[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] => 72
[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] => 56
[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] => 48
[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] => 42
[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] => 10
[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] => 10
[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] => 8
[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] => 15
[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] => 90
[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] => 72
[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] => 63
[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] => 56
[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] => 56
[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] => 42
[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] => 48
[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] => 22
[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] => 12
[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] => 20
[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] => 12
[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] => 10
[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] => 18
[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] => 90
[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] => 80
[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] => 72
[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] => 72
[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] => 56
[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] => 63
[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] => 66
[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] => 56
[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] => 42
[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] => 54
[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] => 48
[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] => 15
[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] => 28
[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] => 24
[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] => 28
[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] => 10
[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] => 26
[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] => 22
[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] => 21
[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] => 15
[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] => 24
[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] => 20
[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] => 72
[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] => 83
[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] => 72
[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] => 70
[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] => 63
[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] => 78
[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] => 66
[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] => 42
[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] => 48
[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] => 63
[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] => 56
[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] => 54
[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] => 35
[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] => 30
[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] => 21
[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] => 22
[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] => 15
[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] => 20
[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] => 18
[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] => 37
[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] => 32
[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] => 18
[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] => 35
[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] => 30
[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] => 21
[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] => 15
[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] => 33
[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] => 96
[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] => 56
[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] => 80
[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] => 70
[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] => 92
[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] => 74
[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] => 42
[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] => 48
[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] => 56
[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] => 63
[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] => 48
[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] => 40
[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] => 20
[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] => 15
[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] => 21
[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] => 32
[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] => 40
[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] => 42
[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] => 30
[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] => 20
[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] => 36
[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] => 24
[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] => 18
[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] => 45
[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] => 111
[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] => 56
[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] => 63
[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] => 90
[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] => 80
[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] => 92
[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] => 56
[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] => 74
[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] => 48
[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] => 84
[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] => 54
[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] => 63
[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] => 56
[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] => 54
[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] => 28
[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] => 15
[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] => 20
[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] => 57
[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] => 21
[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] => 35
[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] => 45
[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] => 50
[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] => 26
[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] => 28
[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] => 36
[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] => 48
[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] => 42
[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] => 36
[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] => 24
[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] => 48
[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] => 128
[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] => 80
[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] => 98
[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] => 78
[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] => 82
[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] => 80
[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] => 72
[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] => 70
[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] => 2
[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] => 0
[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] => 34
[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] => 52
[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] => 28
[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] => 68
[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] => 40
[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] => 28
[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] => 30
[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] => 48
[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] => 55
[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] => 36
[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] => 24
[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] => 64
[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] => 128
[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] => 88
[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] => 2
[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] => 0
[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] => 92
[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] => 30
[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] => 87
[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] => 42
[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] => 111
[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] => 96
[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] => 70
[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] => 84
[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] => 6
[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] => 3
[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] => 15
[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] => 30
[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] => 39
[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] => 28
[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] => 28
[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] => 76
[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] => 50
[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] => 50
[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] => 50
[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] => 30
[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] => 24
[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] => 60
[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] => 55
[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] => 40
[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] => 45
[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] => 28
[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] => 78
[1,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,2,2,1] => [4,3,3,3,3,1] => [3,3,3,3,1] => 88
[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] => 70
[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] => 48
[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] => 27
[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] => 16
[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] => 14
[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] => 36
[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] => 18
[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] => 27
[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] => 30
[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] => 68
[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] => 22
[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] => 24
[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] => 18
[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] => 12
[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] => 8
[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] => 8
[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] => 24
[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] => 8
[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] => 8
[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] => 8
[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] => 15
[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] => 54
[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] => 12
[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] => 12
[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] => 12
[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] => 48
[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] => 35
[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] => 12
[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] => 4
[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] => 6
[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] => 3
[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] => 104
[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] => 60
[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] => 36
[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] => 48
[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] => 39
[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] => 8
[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] => 24
[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] => 7
[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] => 58
[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] => 32
[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] => 50
[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] => 27
[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] => 28
[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] => 40
[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] => 12
[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] => 20
[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] => 12
[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] => 62
[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] => 87
[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] => 45
[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] => 20
[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] => 84
[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] => 68
[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] => 10
[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] => 24
[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] => 50
[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] => 12
[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] => 18
[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] => 21
[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] => 45
[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] => 14
[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] => 15
[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] => 4
[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] => 4
[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] => 4
[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] => 4
[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] => 4
[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] => 28
[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] => 6
[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] => 8
[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] => 40
[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] => 28
[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] => 18
[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] => 5
[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] => 8
[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] => 4
[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] => 3
[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] => 56
[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] => 42
[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] => 27
[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] => 51
[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] => 50
[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] => 27
[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] => 36
[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] => 48
[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] => 95
[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] => 24
[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] => 60
[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] => 6
[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] => 6
[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] => 32
[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] => 14
[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] => 6
[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] => 48
[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] => 78
[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] => 6
[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] => 18
[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] => 24
[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] => 12
[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] => 67
[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] => 7
[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] => 20
[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] => 51
[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] => 15
[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] => 44
[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] => 48
[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] => 6
[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] => 18
[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] => 6
[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] => 12
[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] => 3
[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] => 3
[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] => 58
[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] => 3
[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] => 3
[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] => 32
[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] => 3
[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] => 8
[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] => 42
[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] => 20
[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] => 10
[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] => 35
[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] => 24
[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] => 15
[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] => 0
[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] => 0
[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] => 42
[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] => 112
[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] => 108
[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] => 42
[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] => 30
[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] => 20
[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] => 20
[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] => 55
[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] => 12
[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] => 108
[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] => 80
[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] => 8
[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] => 8
[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] => 15
[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] => 36
[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] => 27
[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] => 62
[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] => 15
[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] => 8
[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] => 18
[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] => 12
[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] => 6
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 2
[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] => 35
[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] => 24
[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] => 15
[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] => 8
[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] => 2
[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] => 147
[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] => 126
[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] => 108
[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] => 12
[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] => 75
[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] => 60
[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] => 80
[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] => 6
[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] => 48
[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] => 12
[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] => 36
[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] => 27
[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] => 44
[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] => 2
[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] => 2
[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] => 6
[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] => 2
[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] => 18
[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] => 30
[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] => 2
[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] => 12
[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] => 6
[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] => 30
[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] => 20
[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] => 30
[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] => 20
[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] => 12
[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] => 2
[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] => 3
[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] => 30
[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] => 20
[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] => 6
[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] => 0
[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] => 62
[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] => 42
[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] => 35
[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] => 8
[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] => 30
[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] => 20
[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] => 12
[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] => 6
[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] => 2
[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] => 30
[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] => 20
[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] => 12
[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] => 6
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [3] => [1,1,1] => [1,1] => 2
[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] => 123
[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] => 168
[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] => 48
[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] => 3
[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] => 4
[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] => 42
[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] => 56
[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] => 42
[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] => 0
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => [3,2,1] => [2,1] => 3
[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] => 3
[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] => 24
[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] => 30
[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] => 20
[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] => 12
[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] => 6
[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] => 2
[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] => 56
[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] => 42
[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] => 12
[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] => 8
[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] => 36
[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] => 27
[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] => 60
[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] => 42
[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] => 35
[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] => 0
[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] => 10
[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] => 8
[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] => 42
[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] => 10
[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] => 10
[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] => 15
[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] => 6
[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] => 2
[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] => 2
[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] => 21
[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] => 168
[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] => 4
[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] => 8
[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] => 5
[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] => 18
[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] => 2
[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] => 30
[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] => 12
[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] => 42
[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] => 12
[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] => 7
[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] => 27
[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] => 123
[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] => 36
[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] => 22
[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] => 24
[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] => 28
[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] => 35
[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] => 48
[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] => 12
[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] => 8
[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] => 30
[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] => 8
[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] => 2
[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] => 8
[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] => 28
[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] => 14
[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] => 14
[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] => 15
[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] => 18
[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] => 12
[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] => 18
[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] => 20
[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] => 32
[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] => 6
[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] => 24
[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] => 6
[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] => 51
[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] => 39
[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] => 30
[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] => 20
[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] => 12
[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] => 6
[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] => 2
[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] => 0
[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => [4,2,2] => [2,2] => 6
[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] => 0
[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0] => [3,2,2,1] => [3,2,2,1] => [2,2,1] => 12
[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] => 48
[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] => 18
[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] => 80
[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] => 63
[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] => 20
[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] => 70
[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] => 50
[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] => 63
[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] => 48
[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] => 22
[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] => 72
[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] => 2
[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] => 0
[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] => 6
[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] => 12
[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] => 24
[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] => 45
[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] => 50
[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] => 50
[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] => 30
[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] => 2
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0,0] => [5,5,3,2,1] => [10,5,1] => [5,1] => 6
[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] => 6
[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] => 0
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0,0] => [8,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 42
[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] => 3
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 30
[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] => 4
[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] => 20
[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] => 8
[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] => 12
[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] => 6
[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] => 20
[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] => 6
[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] => 18
search for individual values
searching the database for the individual values of this statistic
Description
Twice the mean value of the major index among all standard Young tableaux of a partition.
For a partition $\lambda$ of $n$, this mean value is given in [1, Proposition 3.1] by
$$\frac{1}{2}\Big(\binom{n}{2} - \sum_i\binom{\lambda_i}{2} + \sum_i\binom{\lambda_i'}{2}\Big),$$
where $\lambda_i$ is the size of the $i$-th row of $\lambda$ and $\lambda_i'$ is the size of the $i$-th column.
For a partition $\lambda$ of $n$, this mean value is given in [1, Proposition 3.1] by
$$\frac{1}{2}\Big(\binom{n}{2} - \sum_i\binom{\lambda_i}{2} + \sum_i\binom{\lambda_i'}{2}\Big),$$
where $\lambda_i$ is the size of the $i$-th row of $\lambda$ and $\lambda_i'$ is the size of the $i$-th column.
Map
Loehr-Warrington
Description
Return a partition whose diagonal inversion number is the length of the preimage.
Map
first row removal
Description
Removes the first entry of an integer partition
Map
to partition
Description
The cut-out partition of a Dyck path.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ is the number of down-steps before the $(n+1-i)$-th up-step of $D$.
This map is a bijection between Dyck paths of size $n$ and partitions inside the staircase partition $(n-1,\ldots,2,1)$.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ is the number of down-steps before the $(n+1-i)$-th up-step of $D$.
This map is a bijection between Dyck paths of size $n$ and partitions inside the staircase partition $(n-1,\ldots,2,1)$.
searching the database
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