Identifier
-
Mp00027:
Dyck paths
—to partition⟶
Integer partitions
Mp00323: Integer partitions —Loehr-Warrington inverse⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St001176: Integer partitions ⟶ ℤ
Values
[1,0,1,0] => [1] => [1] => [1] => 0
[1,0,1,0,1,0] => [2,1] => [1,1,1] => [3] => 0
[1,0,1,1,0,0] => [1,1] => [2] => [1,1] => 1
[1,1,0,0,1,0] => [2] => [1,1] => [2] => 0
[1,1,0,1,0,0] => [1] => [1] => [1] => 0
[1,0,1,0,1,0,1,0] => [3,2,1] => [1,1,1,1,1,1] => [6] => 0
[1,0,1,0,1,1,0,0] => [2,2,1] => [2,2,1] => [3,2] => 2
[1,0,1,1,0,0,1,0] => [3,1,1] => [2,1,1,1] => [4,1] => 1
[1,0,1,1,0,1,0,0] => [2,1,1] => [3,1] => [2,1,1] => 2
[1,0,1,1,1,0,0,0] => [1,1,1] => [3] => [1,1,1] => 2
[1,1,0,0,1,0,1,0] => [3,2] => [1,1,1,1,1] => [5] => 0
[1,1,0,0,1,1,0,0] => [2,2] => [2,1,1] => [3,1] => 1
[1,1,0,1,0,0,1,0] => [3,1] => [1,1,1,1] => [4] => 0
[1,1,0,1,0,1,0,0] => [2,1] => [1,1,1] => [3] => 0
[1,1,0,1,1,0,0,0] => [1,1] => [2] => [1,1] => 1
[1,1,1,0,0,0,1,0] => [3] => [2,1] => [2,1] => 1
[1,1,1,0,0,1,0,0] => [2] => [1,1] => [2] => 0
[1,1,1,0,1,0,0,0] => [1] => [1] => [1] => 0
[1,0,1,0,1,0,1,0,1,0] => [4,3,2,1] => [1,1,1,1,1,1,1,1,1,1] => [10] => 0
[1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => [2,2,2,1,1,1] => [6,3] => 3
[1,0,1,0,1,1,0,0,1,0] => [4,2,2,1] => [2,2,1,1,1,1,1] => [7,2] => 2
[1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => [3,2,2,1] => [4,3,1] => 4
[1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => [3,2,2] => [3,3,1] => 4
[1,0,1,1,0,0,1,0,1,0] => [4,3,1,1] => [2,1,1,1,1,1,1,1] => [8,1] => 1
[1,0,1,1,0,0,1,1,0,0] => [3,3,1,1] => [3,2,1,1,1] => [5,2,1] => 3
[1,0,1,1,0,1,0,0,1,0] => [4,2,1,1] => [3,1,1,1,1,1] => [6,1,1] => 2
[1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => [4,1,1,1] => [4,1,1,1] => 3
[1,0,1,1,0,1,1,0,0,0] => [2,2,1,1] => [4,2] => [2,2,1,1] => 4
[1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => [2,2,2,1] => [4,3] => 3
[1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => [4,1,1] => [3,1,1,1] => 3
[1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => [4,1] => [2,1,1,1] => 3
[1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => [4] => [1,1,1,1] => 3
[1,1,0,0,1,0,1,0,1,0] => [4,3,2] => [1,1,1,1,1,1,1,1,1] => [9] => 0
[1,1,0,0,1,0,1,1,0,0] => [3,3,2] => [2,2,1,1,1,1] => [6,2] => 2
[1,1,0,0,1,1,0,0,1,0] => [4,2,2] => [2,1,1,1,1,1,1] => [7,1] => 1
[1,1,0,0,1,1,0,1,0,0] => [3,2,2] => [3,1,1,1,1] => [5,1,1] => 2
[1,1,0,0,1,1,1,0,0,0] => [2,2,2] => [2,2,2] => [3,3] => 3
[1,1,0,1,0,0,1,0,1,0] => [4,3,1] => [1,1,1,1,1,1,1,1] => [8] => 0
[1,1,0,1,0,0,1,1,0,0] => [3,3,1] => [2,1,1,1,1,1] => [6,1] => 1
[1,1,0,1,0,1,0,0,1,0] => [4,2,1] => [1,1,1,1,1,1,1] => [7] => 0
[1,1,0,1,0,1,0,1,0,0] => [3,2,1] => [1,1,1,1,1,1] => [6] => 0
[1,1,0,1,0,1,1,0,0,0] => [2,2,1] => [2,2,1] => [3,2] => 2
[1,1,0,1,1,0,0,0,1,0] => [4,1,1] => [2,2,1,1] => [4,2] => 2
[1,1,0,1,1,0,0,1,0,0] => [3,1,1] => [2,1,1,1] => [4,1] => 1
[1,1,0,1,1,0,1,0,0,0] => [2,1,1] => [3,1] => [2,1,1] => 2
[1,1,0,1,1,1,0,0,0,0] => [1,1,1] => [3] => [1,1,1] => 2
[1,1,1,0,0,0,1,0,1,0] => [4,3] => [2,2,1,1,1] => [5,2] => 2
[1,1,1,0,0,0,1,1,0,0] => [3,3] => [3,1,1,1] => [4,1,1] => 2
[1,1,1,0,0,1,0,0,1,0] => [4,2] => [2,1,1,1,1] => [5,1] => 1
[1,1,1,0,0,1,0,1,0,0] => [3,2] => [1,1,1,1,1] => [5] => 0
[1,1,1,0,0,1,1,0,0,0] => [2,2] => [2,1,1] => [3,1] => 1
[1,1,1,0,1,0,0,0,1,0] => [4,1] => [3,1,1] => [3,1,1] => 2
[1,1,1,0,1,0,0,1,0,0] => [3,1] => [1,1,1,1] => [4] => 0
[1,1,1,0,1,0,1,0,0,0] => [2,1] => [1,1,1] => [3] => 0
[1,1,1,0,1,1,0,0,0,0] => [1,1] => [2] => [1,1] => 1
[1,1,1,1,0,0,0,0,1,0] => [4] => [2,2] => [2,2] => 2
[1,1,1,1,0,0,0,1,0,0] => [3] => [2,1] => [2,1] => 1
[1,1,1,1,0,0,1,0,0,0] => [2] => [1,1] => [2] => 0
[1,1,1,1,0,1,0,0,0,0] => [1] => [1] => [1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [15] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [4,4,3,2,1] => [2,2,2,2,1,1,1,1,1,1] => [10,4] => 4
[1,0,1,0,1,0,1,1,0,0,1,0] => [5,3,3,2,1] => [2,2,2,1,1,1,1,1,1,1,1] => [11,3] => 3
[1,0,1,0,1,0,1,1,0,1,0,0] => [4,3,3,2,1] => [3,2,2,2,2,1,1] => [7,5,1] => 6
[1,0,1,0,1,0,1,1,1,0,0,0] => [3,3,3,2,1] => [2,2,2,2,2,2] => [6,6] => 6
[1,0,1,0,1,1,0,0,1,0,1,0] => [5,4,2,2,1] => [2,2,1,1,1,1,1,1,1,1,1,1] => [12,2] => 2
[1,0,1,0,1,1,0,0,1,1,0,0] => [4,4,2,2,1] => [3,3,2,1,1,1,1,1] => [8,3,2] => 5
[1,0,1,0,1,1,0,1,0,0,1,0] => [5,3,2,2,1] => [3,3,1,1,1,1,1,1,1] => [9,2,2] => 4
[1,0,1,0,1,1,0,1,0,1,0,0] => [4,3,2,2,1] => [3,3,3,1,1,1] => [6,3,3] => 6
[1,0,1,0,1,1,0,1,1,0,0,0] => [3,3,2,2,1] => [4,3,2,2] => [4,4,2,1] => 7
[1,0,1,0,1,1,1,0,0,0,1,0] => [5,2,2,2,1] => [2,2,2,2,2,1,1] => [7,5] => 5
[1,0,1,0,1,1,1,0,0,1,0,0] => [4,2,2,2,1] => [3,3,3,1,1] => [5,3,3] => 6
[1,0,1,0,1,1,1,0,1,0,0,0] => [3,2,2,2,1] => [3,3,3,1] => [4,3,3] => 6
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => [3,3,3] => [3,3,3] => 6
[1,0,1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,1] => [2,1,1,1,1,1,1,1,1,1,1,1,1] => [13,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [4,4,3,1,1] => [3,2,2,1,1,1,1,1,1] => [9,3,1] => 4
[1,0,1,1,0,0,1,1,0,0,1,0] => [5,3,3,1,1] => [3,2,1,1,1,1,1,1,1,1] => [10,2,1] => 3
[1,0,1,1,0,0,1,1,0,1,0,0] => [4,3,3,1,1] => [4,2,2,1,1,1,1] => [7,3,1,1] => 5
[1,0,1,1,0,0,1,1,1,0,0,0] => [3,3,3,1,1] => [4,2,2,2,1] => [5,4,1,1] => 6
[1,0,1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,1] => [3,1,1,1,1,1,1,1,1,1,1] => [11,1,1] => 2
[1,0,1,1,0,1,0,0,1,1,0,0] => [4,4,2,1,1] => [4,2,1,1,1,1,1,1] => [8,2,1,1] => 4
[1,0,1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,1] => [4,1,1,1,1,1,1,1,1] => [9,1,1,1] => 3
[1,0,1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,1] => [5,1,1,1,1,1,1] => [7,1,1,1,1] => 4
[1,0,1,1,0,1,0,1,1,0,0,0] => [3,3,2,1,1] => [5,2,2,1] => [4,3,1,1,1] => 6
[1,0,1,1,0,1,1,0,0,0,1,0] => [5,2,2,1,1] => [4,2,2,1,1,1] => [6,3,1,1] => 5
[1,0,1,1,0,1,1,0,0,1,0,0] => [4,2,2,1,1] => [5,2,1,1,1] => [5,2,1,1,1] => 5
[1,0,1,1,0,1,1,0,1,0,0,0] => [3,2,2,1,1] => [5,3,1] => [3,2,2,1,1] => 6
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,2,2,1,1] => [5,3] => [2,2,2,1,1] => 6
[1,0,1,1,1,0,0,0,1,0,1,0] => [5,4,1,1,1] => [2,2,2,2,1,1,1,1] => [8,4] => 4
[1,0,1,1,1,0,0,0,1,1,0,0] => [4,4,1,1,1] => [3,3,2,1,1,1] => [6,3,2] => 5
[1,0,1,1,1,0,0,1,0,0,1,0] => [5,3,1,1,1] => [3,2,2,1,1,1,1] => [7,3,1] => 4
[1,0,1,1,1,0,0,1,0,1,0,0] => [4,3,1,1,1] => [5,1,1,1,1,1] => [6,1,1,1,1] => 4
[1,0,1,1,1,0,0,1,1,0,0,0] => [3,3,1,1,1] => [5,2,1,1] => [4,2,1,1,1] => 5
[1,0,1,1,1,0,1,0,0,0,1,0] => [5,2,1,1,1] => [3,2,2,2,1] => [5,4,1] => 5
[1,0,1,1,1,0,1,0,0,1,0,0] => [4,2,1,1,1] => [5,1,1,1,1] => [5,1,1,1,1] => 4
[1,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => [5,1,1,1] => [4,1,1,1,1] => 4
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => [5,2] => [2,2,1,1,1] => 5
[1,0,1,1,1,1,0,0,0,0,1,0] => [5,1,1,1,1] => [3,2,2,2] => [4,4,1] => 5
[1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => [5,2,1] => [3,2,1,1,1] => 5
[1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => [5,1,1] => [3,1,1,1,1] => 4
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => [5,1] => [2,1,1,1,1] => 4
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => [5] => [1,1,1,1,1] => 4
>>> Load all 1797 entries. <<<[1,1,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14] => 0
[1,1,0,0,1,0,1,0,1,1,0,0] => [4,4,3,2] => [2,2,2,1,1,1,1,1,1,1] => [10,3] => 3
[1,1,0,0,1,0,1,1,0,0,1,0] => [5,3,3,2] => [2,2,1,1,1,1,1,1,1,1,1] => [11,2] => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => [4,3,3,2] => [3,3,1,1,1,1,1,1] => [8,2,2] => 4
[1,1,0,0,1,0,1,1,1,0,0,0] => [3,3,3,2] => [2,2,2,2,2,1] => [6,5] => 5
[1,1,0,0,1,1,0,0,1,0,1,0] => [5,4,2,2] => [2,1,1,1,1,1,1,1,1,1,1,1] => [12,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => [3,2,1,1,1,1,1,1,1] => [9,2,1] => 3
[1,1,0,0,1,1,0,1,0,0,1,0] => [5,3,2,2] => [3,1,1,1,1,1,1,1,1,1] => [10,1,1] => 2
[1,1,0,0,1,1,0,1,0,1,0,0] => [4,3,2,2] => [4,1,1,1,1,1,1,1] => [8,1,1,1] => 3
[1,1,0,0,1,1,0,1,1,0,0,0] => [3,3,2,2] => [4,2,2,1,1] => [5,3,1,1] => 5
[1,1,0,0,1,1,1,0,0,0,1,0] => [5,2,2,2] => [2,2,2,2,1,1,1] => [7,4] => 4
[1,1,0,0,1,1,1,0,0,1,0,0] => [4,2,2,2] => [3,2,2,1,1,1] => [6,3,1] => 4
[1,1,0,0,1,1,1,0,1,0,0,0] => [3,2,2,2] => [3,3,2,1] => [4,3,2] => 5
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,2,2] => [3,3,2] => [3,3,2] => 5
[1,1,0,1,0,0,1,0,1,0,1,0] => [5,4,3,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1] => [13] => 0
[1,1,0,1,0,0,1,0,1,1,0,0] => [4,4,3,1] => [2,2,1,1,1,1,1,1,1,1] => [10,2] => 2
[1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,3,1] => [2,1,1,1,1,1,1,1,1,1,1] => [11,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [4,3,3,1] => [3,1,1,1,1,1,1,1,1] => [9,1,1] => 2
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,3,3,1] => [2,2,2,2,1,1] => [6,4] => 4
[1,1,0,1,0,1,0,0,1,0,1,0] => [5,4,2,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => [12] => 0
[1,1,0,1,0,1,0,0,1,1,0,0] => [4,4,2,1] => [2,1,1,1,1,1,1,1,1,1] => [10,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => [5,3,2,1] => [1,1,1,1,1,1,1,1,1,1,1] => [11] => 0
[1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => [1,1,1,1,1,1,1,1,1,1] => [10] => 0
[1,1,0,1,0,1,0,1,1,0,0,0] => [3,3,2,1] => [2,2,2,1,1,1] => [6,3] => 3
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,2,2,1] => [2,2,2,1,1,1,1] => [7,3] => 3
[1,1,0,1,0,1,1,0,0,1,0,0] => [4,2,2,1] => [2,2,1,1,1,1,1] => [7,2] => 2
[1,1,0,1,0,1,1,0,1,0,0,0] => [3,2,2,1] => [3,2,2,1] => [4,3,1] => 4
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,2,2,1] => [3,2,2] => [3,3,1] => 4
[1,1,0,1,1,0,0,0,1,0,1,0] => [5,4,1,1] => [2,2,2,1,1,1,1,1] => [8,3] => 3
[1,1,0,1,1,0,0,0,1,1,0,0] => [4,4,1,1] => [3,2,1,1,1,1,1] => [7,2,1] => 3
[1,1,0,1,1,0,0,1,0,0,1,0] => [5,3,1,1] => [2,2,1,1,1,1,1,1] => [8,2] => 2
[1,1,0,1,1,0,0,1,0,1,0,0] => [4,3,1,1] => [2,1,1,1,1,1,1,1] => [8,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,0] => [3,3,1,1] => [3,2,1,1,1] => [5,2,1] => 3
[1,1,0,1,1,0,1,0,0,0,1,0] => [5,2,1,1] => [3,3,1,1,1] => [5,2,2] => 4
[1,1,0,1,1,0,1,0,0,1,0,0] => [4,2,1,1] => [3,1,1,1,1,1] => [6,1,1] => 2
[1,1,0,1,1,0,1,0,1,0,0,0] => [3,2,1,1] => [4,1,1,1] => [4,1,1,1] => 3
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,1,1] => [4,2] => [2,2,1,1] => 4
[1,1,0,1,1,1,0,0,0,0,1,0] => [5,1,1,1] => [2,2,2,2] => [4,4] => 4
[1,1,0,1,1,1,0,0,0,1,0,0] => [4,1,1,1] => [2,2,2,1] => [4,3] => 3
[1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,1,1] => [4,1,1] => [3,1,1,1] => 3
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,1] => [4,1] => [2,1,1,1] => 3
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1] => [4] => [1,1,1,1] => 3
[1,1,1,0,0,0,1,0,1,0,1,0] => [5,4,3] => [2,2,2,1,1,1,1,1,1] => [9,3] => 3
[1,1,1,0,0,0,1,0,1,1,0,0] => [4,4,3] => [3,3,1,1,1,1,1] => [7,2,2] => 4
[1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => [3,2,1,1,1,1,1,1] => [8,2,1] => 3
[1,1,1,0,0,0,1,1,0,1,0,0] => [4,3,3] => [4,1,1,1,1,1,1] => [7,1,1,1] => 3
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => [3,2,2,1,1] => [5,3,1] => 4
[1,1,1,0,0,1,0,0,1,0,1,0] => [5,4,2] => [2,2,1,1,1,1,1,1,1] => [9,2] => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => [4,4,2] => [3,1,1,1,1,1,1,1] => [8,1,1] => 2
[1,1,1,0,0,1,0,1,0,0,1,0] => [5,3,2] => [2,1,1,1,1,1,1,1,1] => [9,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => [1,1,1,1,1,1,1,1,1] => [9] => 0
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,3,2] => [2,2,1,1,1,1] => [6,2] => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => [5,2,2] => [3,2,1,1,1,1] => [6,2,1] => 3
[1,1,1,0,0,1,1,0,0,1,0,0] => [4,2,2] => [2,1,1,1,1,1,1] => [7,1] => 1
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,2] => [3,1,1,1,1] => [5,1,1] => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [2,2,2] => [2,2,2] => [3,3] => 3
[1,1,1,0,1,0,0,0,1,0,1,0] => [5,4,1] => [3,3,1,1,1,1] => [6,2,2] => 4
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,4,1] => [4,1,1,1,1,1] => [6,1,1,1] => 3
[1,1,1,0,1,0,0,1,0,0,1,0] => [5,3,1] => [3,1,1,1,1,1,1] => [7,1,1] => 2
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => [1,1,1,1,1,1,1,1] => [8] => 0
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,3,1] => [2,1,1,1,1,1] => [6,1] => 1
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,1] => [4,1,1,1,1] => [5,1,1,1] => 3
[1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => [1,1,1,1,1,1,1] => [7] => 0
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1] => [1,1,1,1,1,1] => [6] => 0
[1,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1] => [2,2,1] => [3,2] => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,1,1] => [4,2,1] => [3,2,1,1] => 4
[1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,1] => [2,2,1,1] => [4,2] => 2
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,1,1] => [2,1,1,1] => [4,1] => 1
[1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,1] => [3,1] => [2,1,1] => 2
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1] => [3] => [1,1,1] => 2
[1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => [2,2,2,2,1] => [5,4] => 4
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => [4,2,1,1] => [4,2,1,1] => 4
[1,1,1,1,0,0,0,1,0,0,1,0] => [5,3] => [2,2,2,1,1] => [5,3] => 3
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => [2,2,1,1,1] => [5,2] => 2
[1,1,1,1,0,0,0,1,1,0,0,0] => [3,3] => [3,1,1,1] => [4,1,1] => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,2] => [3,2,1,1] => [4,2,1] => 3
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,2] => [2,1,1,1,1] => [5,1] => 1
[1,1,1,1,0,0,1,0,1,0,0,0] => [3,2] => [1,1,1,1,1] => [5] => 0
[1,1,1,1,0,0,1,1,0,0,0,0] => [2,2] => [2,1,1] => [3,1] => 1
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => [3,2,1] => [3,2,1] => 3
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => [3,1,1] => [3,1,1] => 2
[1,1,1,1,0,1,0,0,1,0,0,0] => [3,1] => [1,1,1,1] => [4] => 0
[1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => [1,1,1] => [3] => 0
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,1] => [2] => [1,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => [5] => [3,2] => [2,2,1] => 3
[1,1,1,1,1,0,0,0,0,1,0,0] => [4] => [2,2] => [2,2] => 2
[1,1,1,1,1,0,0,0,1,0,0,0] => [3] => [2,1] => [2,1] => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => [2] => [1,1] => [2] => 0
[1,1,1,1,1,0,1,0,0,0,0,0] => [1] => [1] => [1] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => [4,4,2,2,2,2,1] => [7,6,2,2] => 10
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2,1] => [3,3,3,2,2,2,1,1] => [8,6,3] => 9
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2,1] => [3,3,3,2,2,2,1] => [7,6,3] => 9
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2,1] => [3,3,3,2,2,2] => [6,6,3] => 9
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => [4,3,3,2,2,1,1,1] => [8,5,3,1] => 9
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2,1] => [4,4,3,1,1,1,1,1,1] => [9,3,3,2] => 8
[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] => [6,5,3,2] => 10
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2,1] => [4,3,2,2,2,1,1,1,1] => [9,5,2,1] => 8
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2,1] => [4,4,3,2,1,1,1] => [7,4,3,2] => 9
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => [5,3,3,3,1] => [5,4,4,1,1] => 10
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => [5,3,3,3] => [4,4,4,1,1] => 10
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => [3,3,2,2,2,2,1,1,1] => [9,6,2] => 8
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,2,2,1] => [3,3,2,2,2,1,1,1,1,1] => [10,5,2] => 7
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2,1] => [4,4,3,1,1,1,1,1] => [8,3,3,2] => 8
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => [4,4,3,2,1,1] => [6,4,3,2] => 9
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,2,2,1] => [3,2,2,2,2,2,2,1] => [8,7,1] => 8
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2,1] => [4,4,3,1,1,1,1] => [7,3,3,2] => 8
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2,1] => [4,4,3,1,1,1] => [6,3,3,2] => 8
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2,1] => [4,4,3,2] => [4,4,3,2] => 9
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2,1] => [3,2,2,2,2,2,2] => [7,7,1] => 8
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2,1] => [4,4,3,2,1] => [5,4,3,2] => 9
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2,1] => [4,4,3,1,1] => [5,3,3,2] => 8
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2,1] => [4,4,3,1] => [4,3,3,2] => 8
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2,1] => [4,4,3] => [3,3,3,2] => 8
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1,1] => [4,2,2,2,2,2,1,1,1] => [9,6,1,1] => 8
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => [4,3,3,1,1,1,1,1,1,1] => [10,3,3,1] => 7
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => [5,2,2,2,2,2,1] => [7,6,1,1,1] => 9
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1,1] => [3,2,2,2,2,2,1,1,1,1] => [10,6,1] => 7
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => [4,3,3,2,1,1,1,1] => [8,4,3,1] => 8
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => [5,3,2,2,2,1] => [6,5,2,1,1] => 9
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => [5,3,2,2,2] => [5,5,2,1,1] => 9
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => [5,3,1,1,1,1,1,1,1,1,1] => [11,2,2,1,1] => 6
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => [5,3,2,2,1,1,1,1] => [8,4,2,1,1] => 8
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1,1] => [5,2,1,1,1,1,1,1,1,1,1,1] => [12,2,1,1,1] => 5
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,1] => [5,1,1,1,1,1,1,1,1,1,1,1,1] => [13,1,1,1,1] => 4
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,1] => [6,1,1,1,1,1,1,1,1,1,1] => [11,1,1,1,1,1] => 5
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1,1] => [6,2,2,2,1,1,1] => [7,4,1,1,1,1] => 8
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2,1,1] => [5,2,2,2,1,1,1,1,1] => [9,4,1,1,1] => 7
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1,1] => [6,2,2,1,1,1,1,1] => [8,3,1,1,1,1] => 7
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1,1] => [6,3,2,2,1] => [5,4,2,1,1,1] => 9
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => [6,3,2,2] => [4,4,2,1,1,1] => 9
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,2,1,1] => [3,2,2,2,2,1,1,1,1,1,1] => [11,5,1] => 6
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => [5,3,2,1,1,1,1,1,1] => [9,3,2,1,1] => 7
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,2,1,1] => [4,2,2,2,1,1,1,1,1,1] => [10,4,1,1] => 6
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2,1,1] => [6,2,1,1,1,1,1,1,1] => [9,2,1,1,1,1] => 6
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => [6,3,2,1,1,1] => [6,3,2,1,1,1] => 8
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2,1,1] => [5,3,3,1,1,1,1] => [7,3,3,1,1] => 8
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1,1] => [6,3,1,1,1,1,1] => [7,2,2,1,1,1] => 7
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1,1] => [6,4,1,1,1] => [5,2,2,2,1,1] => 8
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => [6,4,2] => [3,3,2,2,1,1] => 9
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2,1,1] => [4,2,2,2,2,2] => [6,6,1,1] => 8
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1,1] => [6,2,2,2,1] => [5,4,1,1,1,1] => 8
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1,1] => [6,4,1,1] => [4,2,2,2,1,1] => 8
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1,1] => [6,4,1] => [3,2,2,2,1,1] => 8
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => [6,4] => [2,2,2,2,1,1] => 8
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1,1] => [4,2,2,2,2,1,1,1,1,1] => [10,5,1,1] => 7
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1,1] => [3,3,2,2,1,1,1,1,1,1,1] => [11,4,2] => 6
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => [4,4,2,1,1,1,1,1,1] => [9,3,2,2] => 7
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => [4,4,2,2,1,1,1] => [7,4,2,2] => 8
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,1,1] => [3,2,2,2,1,1,1,1,1,1,1,1] => [12,4,1] => 5
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1,1] => [5,2,2,1,1,1,1,1,1,1] => [10,3,1,1,1] => 6
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,1,1] => [4,2,2,1,1,1,1,1,1,1,1] => [11,3,1,1] => 5
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,1,1] => [6,1,1,1,1,1,1,1,1,1] => [10,1,1,1,1,1] => 5
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1,1] => [6,2,2,1,1,1,1] => [7,3,1,1,1,1] => 7
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1,1,1] => [3,3,2,2,2,1,1,1] => [8,5,2] => 7
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1,1] => [6,2,1,1,1,1,1,1] => [8,2,1,1,1,1] => 6
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1,1] => [6,3,1,1,1,1] => [6,2,2,1,1,1] => 7
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => [6,2,2,2] => [4,4,1,1,1,1] => 8
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,1,1] => [3,2,2,2,2,2,1,1,1] => [9,6,1] => 7
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1,1] => [4,3,3,1,1,1,1,1] => [8,3,3,1] => 7
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,1,1] => [4,2,2,2,1,1,1,1,1] => [9,4,1,1] => 6
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,1,1] => [6,1,1,1,1,1,1,1,1] => [9,1,1,1,1,1] => 5
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1,1] => [6,2,1,1,1,1,1] => [7,2,1,1,1,1] => 6
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,1,1] => [4,4,2,1,1,1,1] => [7,3,2,2] => 7
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1,1] => [6,1,1,1,1,1,1,1] => [8,1,1,1,1,1] => 5
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1,1] => [6,1,1,1,1,1,1] => [7,1,1,1,1,1] => 5
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1,1] => [6,2,2,1] => [4,3,1,1,1,1] => 7
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1,1] => [4,4,2,2,1] => [5,4,2,2] => 8
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1,1] => [6,2,2,1,1] => [5,3,1,1,1,1] => 7
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1,1] => [6,2,1,1,1] => [5,2,1,1,1,1] => 6
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => [6,3,1] => [3,2,2,1,1,1] => 7
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => [6,3] => [2,2,2,1,1,1] => 7
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1,1,1] => [2,2,2,2,2,2,2,1] => [8,7] => 7
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1,1] => [5,2,2,2,2,1] => [6,5,1,1,1] => 8
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1,1,1] => [4,2,2,2,2,1,1] => [7,5,1,1] => 7
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1,1] => [6,2,2,1,1,1] => [6,3,1,1,1,1] => 7
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1,1] => [6,3,1,1,1] => [5,2,2,1,1,1] => 7
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1,1,1] => [3,3,3,2,1,1] => [6,4,3] => 7
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1,1] => [6,2,1,1,1,1] => [6,2,1,1,1,1] => 6
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1,1] => [6,1,1,1,1,1] => [6,1,1,1,1,1] => 5
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1,1] => [6,2,1,1] => [4,2,1,1,1,1] => 6
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1,1] => [3,3,3,2,1] => [5,4,3] => 7
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1,1] => [6,3,1,1] => [4,2,2,1,1,1] => 7
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1,1] => [6,1,1,1,1] => [5,1,1,1,1,1] => 5
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1] => [6,1,1,1] => [4,1,1,1,1,1] => 5
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1,1] => [6,2] => [2,2,1,1,1,1] => 6
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1,1] => [3,3,3,2] => [4,4,3] => 7
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1,1] => [6,2,2] => [3,3,1,1,1,1] => 7
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1,1] => [6,2,1] => [3,2,1,1,1,1] => 6
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1,1] => [6,1,1] => [3,1,1,1,1,1] => 5
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => [6,1] => [2,1,1,1,1,1] => 5
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => [6] => [1,1,1,1,1,1] => 5
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2] => [2,2,2,2,2,2,2,1,1,1] => [10,7] => 7
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2] => [4,4,1,1,1,1,1,1,1,1,1] => [11,2,2,2] => 6
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => [4,3,2,2,2,1,1,1] => [8,5,2,1] => 8
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2] => [2,2,2,2,2,2,1,1,1,1,1] => [11,6] => 6
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2] => [4,2,2,2,2,1,1,1,1] => [9,5,1,1] => 7
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2] => [3,3,2,2,2,2,1] => [7,6,2] => 8
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2] => [3,3,2,2,2,2] => [6,6,2] => 8
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => [4,3,1,1,1,1,1,1,1,1,1,1] => [12,2,2,1] => 5
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => [3,3,2,2,2,1,1,1,1] => [9,5,2] => 7
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2] => [4,2,1,1,1,1,1,1,1,1,1,1,1] => [13,2,1,1] => 4
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,2] => [4,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14,1,1,1] => 3
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2] => [5,1,1,1,1,1,1,1,1,1,1,1] => [12,1,1,1,1] => 4
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => [5,2,2,2,1,1,1,1] => [8,4,1,1,1] => 7
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2] => [3,2,2,2,2,1,1,1,1,1] => [10,5,1] => 6
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2] => [5,2,2,1,1,1,1,1,1] => [9,3,1,1,1] => 6
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => [4,3,2,2,2,1] => [6,5,2,1] => 8
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => [4,3,2,2,2] => [5,5,2,1] => 8
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => [2,2,2,2,2,1,1,1,1,1,1,1] => [12,5] => 5
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => [3,3,2,2,1,1,1,1,1,1] => [10,4,2] => 6
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,2,2] => [3,2,2,2,1,1,1,1,1,1,1] => [11,4,1] => 5
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2] => [4,2,2,1,1,1,1,1,1,1] => [10,3,1,1] => 5
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => [3,3,3,2,1,1,1] => [7,4,3] => 7
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,2,2] => [3,2,2,2,2,2,1,1] => [8,6,1] => 7
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2] => [3,3,2,2,1,1,1,1] => [8,4,2] => 6
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2] => [4,3,3,1,1,1] => [6,3,3,1] => 7
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => [4,3,3,2] => [4,4,3,1] => 8
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => [2,2,2,2,2,2,2] => [7,7] => 7
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2] => [4,2,2,2,2,1] => [6,5,1,1] => 7
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2] => [4,3,3,1,1] => [5,3,3,1] => 7
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2] => [4,3,3,1] => [4,3,3,1] => 7
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => [4,3,3] => [3,3,3,1] => 7
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3,1] => [3,3,1,1,1,1,1,1,1,1,1,1,1] => [13,2,2] => 4
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1] => [2,2,2,2,2,2,1,1,1,1] => [10,6] => 6
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1] => [3,2,1,1,1,1,1,1,1,1,1,1,1,1] => [14,2,1] => 3
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3,1] => [3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [15,1,1] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1] => [4,1,1,1,1,1,1,1,1,1,1,1,1] => [13,1,1,1] => 3
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => [3,2,2,2,2,1,1,1,1] => [9,5,1] => 6
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1] => [2,2,2,2,2,1,1,1,1,1,1] => [11,5] => 5
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1] => [2,2,2,2,2,1,1,1,1,1] => [10,5] => 5
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1] => [3,2,2,2,2,2,1] => [7,6,1] => 7
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1] => [3,2,2,2,2,2] => [6,6,1] => 7
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [5,5,4,2,1] => [2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] => [15,2] => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [6,4,4,2,1] => [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [16,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1] => [3,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14,1,1] => 2
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1] => [3,2,2,2,1,1,1,1,1,1] => [10,4,1] => 5
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [17] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1] => [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [15,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [16] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [15] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1] => [2,2,2,2,1,1,1,1,1,1] => [10,4] => 4
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2,1] => [2,2,2,2,1,1,1,1,1,1,1] => [11,4] => 4
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1] => [2,2,2,1,1,1,1,1,1,1,1] => [11,3] => 3
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1] => [3,2,2,2,2,1,1] => [7,5,1] => 6
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1] => [2,2,2,2,2,2] => [6,6] => 6
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,2,1] => [2,2,2,2,1,1,1,1,1,1,1,1] => [12,4] => 4
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1] => [3,2,2,1,1,1,1,1,1,1,1] => [11,3,1] => 4
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,2,1] => [2,2,2,1,1,1,1,1,1,1,1,1] => [12,3] => 3
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2,1] => [2,2,1,1,1,1,1,1,1,1,1,1] => [12,2] => 2
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1] => [3,3,2,1,1,1,1,1] => [8,3,2] => 5
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2,1] => [3,3,3,1,1,1,1,1] => [8,3,3] => 6
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1] => [3,3,1,1,1,1,1,1,1] => [9,2,2] => 4
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1] => [3,3,3,1,1,1] => [6,3,3] => 6
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => [4,3,2,2] => [4,4,2,1] => 7
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2,1] => [2,2,2,2,2,2,1] => [7,6] => 6
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1] => [2,2,2,2,2,1,1] => [7,5] => 5
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1] => [3,3,3,1,1] => [5,3,3] => 6
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1] => [3,3,3,1] => [4,3,3] => 6
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1] => [3,3,3] => [3,3,3] => 6
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,1] => [2,2,2,2,1,1,1,1,1,1,1,1,1] => [13,4] => 4
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1] => [3,3,2,1,1,1,1,1,1,1,1] => [11,3,2] => 5
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1] => [3,2,2,1,1,1,1,1,1,1,1,1] => [12,3,1] => 4
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1] => [4,2,1,1,1,1,1,1,1,1,1] => [11,2,1,1] => 4
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1] => [4,2,2,2,1,1,1,1] => [8,4,1,1] => 6
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,1] => [2,2,2,1,1,1,1,1,1,1,1,1,1] => [13,3] => 3
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1] => [3,2,1,1,1,1,1,1,1,1,1,1] => [12,2,1] => 3
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,1] => [2,2,1,1,1,1,1,1,1,1,1,1,1] => [13,2] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,1] => [2,1,1,1,1,1,1,1,1,1,1,1,1] => [13,1] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1] => [3,2,2,1,1,1,1,1,1] => [9,3,1] => 4
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1,1] => [3,3,2,1,1,1,1,1,1] => [9,3,2] => 5
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1] => [3,2,1,1,1,1,1,1,1,1] => [10,2,1] => 3
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1] => [4,2,2,1,1,1,1] => [7,3,1,1] => 5
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => [4,2,2,2,1] => [5,4,1,1] => 6
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,1] => [3,3,3,1,1,1,1,1,1] => [9,3,3] => 6
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1] => [4,3,1,1,1,1,1,1,1] => [9,2,2,1] => 5
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,1] => [3,3,1,1,1,1,1,1,1,1] => [10,2,2] => 4
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,1] => [3,1,1,1,1,1,1,1,1,1,1] => [11,1,1] => 2
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1] => [4,2,1,1,1,1,1,1] => [8,2,1,1] => 4
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,1] => [4,3,2,1,1,1,1] => [7,3,2,1] => 6
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1] => [4,1,1,1,1,1,1,1,1] => [9,1,1,1] => 3
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1] => [5,1,1,1,1,1,1] => [7,1,1,1,1] => 4
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1] => [5,2,2,1] => [4,3,1,1,1] => 6
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1] => [4,3,2,2,1] => [5,4,2,1] => 7
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1] => [4,2,2,1,1,1] => [6,3,1,1] => 5
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1] => [5,2,1,1,1] => [5,2,1,1,1] => 5
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => [5,3,1] => [3,2,2,1,1] => 6
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => [5,3] => [2,2,2,1,1] => 6
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1,1] => [2,2,2,2,2,2,1,1] => [8,6] => 6
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1] => [4,2,2,2,1,1,1] => [7,4,1,1] => 6
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1,1] => [2,2,2,2,2,1,1,1] => [8,5] => 5
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1] => [2,2,2,2,1,1,1,1] => [8,4] => 4
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1] => [3,3,2,1,1,1] => [6,3,2] => 5
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1,1] => [4,3,2,1,1,1] => [6,3,2,1] => 6
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1] => [3,2,2,1,1,1,1] => [7,3,1] => 4
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1] => [5,1,1,1,1,1] => [6,1,1,1,1] => 4
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => [5,2,1,1] => [4,2,1,1,1] => 5
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1] => [3,3,2,2,1] => [5,4,2] => 6
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1] => [3,2,2,2,1] => [5,4,1] => 5
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1] => [5,1,1,1,1] => [5,1,1,1,1] => 4
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => [5,1,1,1] => [4,1,1,1,1] => 4
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1] => [5,2] => [2,2,1,1,1] => 5
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1] => [3,3,2,2] => [4,4,2] => 6
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1] => [3,2,2,2] => [4,4,1] => 5
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1] => [5,2,1] => [3,2,1,1,1] => 5
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1] => [5,1,1] => [3,1,1,1,1] => 4
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1] => [5,1] => [2,1,1,1,1] => 4
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => [5] => [1,1,1,1,1] => 4
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3] => [3,3,3,1,1,1,1,1,1,1,1] => [11,3,3] => 6
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3] => [3,3,2,1,1,1,1,1,1,1,1,1] => [12,3,2] => 5
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3] => [4,4,1,1,1,1,1,1,1,1] => [10,2,2,2] => 6
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3] => [4,3,2,2,1,1,1,1] => [8,4,2,1] => 7
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => [3,2,2,1,1,1,1,1,1,1,1,1,1] => [13,3,1] => 4
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => [4,3,1,1,1,1,1,1,1,1,1] => [11,2,2,1] => 5
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3] => [4,2,1,1,1,1,1,1,1,1,1,1] => [12,2,1,1] => 4
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3] => [5,1,1,1,1,1,1,1,1,1,1] => [11,1,1,1,1] => 4
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => [5,2,2,1,1,1,1,1] => [8,3,1,1,1] => 6
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => [3,3,2,2,1,1,1,1,1] => [9,4,2] => 6
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3] => [3,2,2,2,1,1,1,1,1] => [9,4,1] => 5
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3] => [3,3,3,1,1,1,1] => [7,3,3] => 6
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => [4,2,2,2,2] => [5,5,1,1] => 7
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2] => [2,2,2,1,1,1,1,1,1,1,1,1,1,1] => [14,3] => 3
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [5,5,4,2] => [3,3,1,1,1,1,1,1,1,1,1,1] => [12,2,2] => 4
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [6,4,4,2] => [3,2,1,1,1,1,1,1,1,1,1,1,1] => [13,2,1] => 3
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2] => [4,1,1,1,1,1,1,1,1,1,1,1] => [12,1,1,1] => 3
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2] => [4,2,2,1,1,1,1,1,1] => [9,3,1,1] => 5
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2] => [2,2,1,1,1,1,1,1,1,1,1,1,1,1] => [14,2] => 2
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2] => [3,1,1,1,1,1,1,1,1,1,1,1,1] => [13,1,1] => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2] => [2,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14] => 0
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2] => [2,2,2,1,1,1,1,1,1,1] => [10,3] => 3
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2] => [3,2,2,1,1,1,1,1,1,1] => [10,3,1] => 4
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2] => [2,2,1,1,1,1,1,1,1,1,1] => [11,2] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2] => [3,3,1,1,1,1,1,1] => [8,2,2] => 4
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2] => [2,2,2,2,2,1] => [6,5] => 5
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [6,5,2,2] => [3,3,2,1,1,1,1,1,1,1] => [10,3,2] => 5
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2] => [4,2,1,1,1,1,1,1,1,1] => [10,2,1,1] => 4
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [6,4,2,2] => [3,2,1,1,1,1,1,1,1,1,1] => [11,2,1] => 3
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2] => [2,1,1,1,1,1,1,1,1,1,1,1] => [12,1] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2] => [3,2,1,1,1,1,1,1,1] => [9,2,1] => 3
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2] => [4,3,1,1,1,1,1,1] => [8,2,2,1] => 5
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2] => [3,1,1,1,1,1,1,1,1,1] => [10,1,1] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2] => [4,1,1,1,1,1,1,1] => [8,1,1,1] => 3
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => [4,2,2,1,1] => [5,3,1,1] => 5
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2] => [4,2,2,2,1,1] => [6,4,1,1] => 6
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2] => [2,2,2,2,1,1,1] => [7,4] => 4
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2] => [3,2,2,1,1,1] => [6,3,1] => 4
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2] => [3,3,2,1] => [4,3,2] => 5
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => [3,3,2] => [3,3,2] => 5
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1] => [3,3,3,1,1,1,1,1,1,1] => [10,3,3] => 6
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1] => [4,4,1,1,1,1,1,1,1] => [9,2,2,2] => 6
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1] => [4,3,1,1,1,1,1,1,1,1] => [10,2,2,1] => 5
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1] => [5,1,1,1,1,1,1,1,1,1] => [10,1,1,1,1] => 4
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1] => [5,2,1,1,1,1,1,1] => [8,2,1,1,1] => 5
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1] => [3,3,1,1,1,1,1,1,1,1,1] => [11,2,2] => 4
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1] => [4,1,1,1,1,1,1,1,1,1,1] => [11,1,1,1] => 3
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1] => [3,1,1,1,1,1,1,1,1,1,1,1] => [12,1,1] => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1] => [13] => 0
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1] => [2,2,1,1,1,1,1,1,1,1] => [10,2] => 2
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1] => [4,2,1,1,1,1,1,1,1] => [9,2,1,1] => 4
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1] => [2,1,1,1,1,1,1,1,1,1,1] => [11,1] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1] => [3,1,1,1,1,1,1,1,1] => [9,1,1] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1] => [2,2,2,2,1,1] => [6,4] => 4
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1] => [4,3,2,1,1,1,1,1] => [8,3,2,1] => 6
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1] => [5,1,1,1,1,1,1,1,1] => [9,1,1,1,1] => 4
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1] => [4,1,1,1,1,1,1,1,1,1] => [10,1,1,1] => 3
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => [12] => 0
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1] => [2,1,1,1,1,1,1,1,1,1] => [10,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1] => [5,1,1,1,1,1,1,1] => [8,1,1,1,1] => 4
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1] => [1,1,1,1,1,1,1,1,1,1,1] => [11] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1] => [1,1,1,1,1,1,1,1,1,1] => [10] => 0
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1] => [2,2,2,1,1,1] => [6,3] => 3
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1] => [5,2,2,1,1] => [5,3,1,1,1] => 6
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1] => [2,2,2,1,1,1,1] => [7,3] => 3
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1] => [2,2,1,1,1,1,1] => [7,2] => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => [3,2,2,1] => [4,3,1] => 4
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1] => [3,2,2] => [3,3,1] => 4
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1] => [4,3,2,2,1,1] => [6,4,2,1] => 7
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1] => [5,2,2,1,1,1] => [6,3,1,1,1] => 6
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1] => [3,2,2,2,1,1,1] => [7,4,1] => 5
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1] => [2,2,2,1,1,1,1,1] => [8,3] => 3
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1] => [3,2,1,1,1,1,1] => [7,2,1] => 3
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1] => [5,2,1,1,1,1] => [6,2,1,1,1] => 5
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1] => [2,2,1,1,1,1,1,1] => [8,2] => 2
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1] => [2,1,1,1,1,1,1,1] => [8,1] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1] => [3,2,1,1,1] => [5,2,1] => 3
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1] => [5,3,1,1] => [4,2,2,1,1] => 6
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1] => [3,3,1,1,1] => [5,2,2] => 4
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1] => [3,1,1,1,1,1] => [6,1,1] => 2
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => [4,1,1,1] => [4,1,1,1] => 3
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1] => [4,2] => [2,2,1,1] => 4
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1] => [5,2,2] => [3,3,1,1,1] => 6
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1] => [2,2,2,2] => [4,4] => 4
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1] => [2,2,2,1] => [4,3] => 3
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1] => [4,1,1] => [3,1,1,1] => 3
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1] => [4,1] => [2,1,1,1] => 3
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1] => [4] => [1,1,1,1] => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [6,5,4] => [2,2,2,2,2,2,1,1,1] => [9,6] => 6
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,5,4] => [4,3,2,2,1,1,1] => [7,4,2,1] => 7
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => [3,2,2,2,2,1,1,1] => [8,5,1] => 6
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,4,4] => [5,2,2,1,1,1,1] => [7,3,1,1,1] => 6
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => [5,3,1,1,1,1] => [6,2,2,1,1] => 6
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [6,5,3] => [2,2,2,2,2,1,1,1,1] => [9,5] => 5
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [5,5,3] => [3,2,2,2,1,1,1,1] => [8,4,1] => 5
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [6,4,3] => [2,2,2,2,1,1,1,1,1] => [9,4] => 4
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [5,4,3] => [2,2,2,1,1,1,1,1,1] => [9,3] => 3
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,4,3] => [3,3,1,1,1,1,1] => [7,2,2] => 4
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [6,3,3] => [3,3,2,1,1,1,1] => [7,3,2] => 5
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [5,3,3] => [3,2,1,1,1,1,1,1] => [8,2,1] => 3
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,3] => [4,1,1,1,1,1,1] => [7,1,1,1] => 3
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,3,3] => [3,2,2,1,1] => [5,3,1] => 4
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [6,5,2] => [3,3,2,2,1,1,1] => [7,4,2] => 6
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,5,2] => [5,2,1,1,1,1,1] => [7,2,1,1,1] => 5
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [6,4,2] => [3,2,2,1,1,1,1,1] => [8,3,1] => 4
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,4,2] => [2,2,1,1,1,1,1,1,1] => [9,2] => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,4,2] => [3,1,1,1,1,1,1,1] => [8,1,1] => 2
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2] => [4,2,1,1,1,1,1] => [7,2,1,1] => 4
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [5,3,2] => [2,1,1,1,1,1,1,1,1] => [9,1] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,2] => [1,1,1,1,1,1,1,1,1] => [9] => 0
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,3,2] => [2,2,1,1,1,1] => [6,2] => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,2,2] => [3,3,2,1,1] => [5,3,2] => 5
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [5,2,2] => [3,2,1,1,1,1] => [6,2,1] => 3
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,2] => [2,1,1,1,1,1,1] => [7,1] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2] => [3,1,1,1,1] => [5,1,1] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,2,2] => [2,2,2] => [3,3] => 3
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [6,5,1] => [3,2,2,2,2,1] => [6,5,1] => 6
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,5,1] => [5,3,1,1,1] => [5,2,2,1,1] => 6
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [6,4,1] => [3,2,2,2,1,1] => [6,4,1] => 5
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,4,1] => [3,3,1,1,1,1] => [6,2,2] => 4
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,4,1] => [4,1,1,1,1,1] => [6,1,1,1] => 3
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,1] => [4,2,1,1,1,1] => [6,2,1,1] => 4
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,3,1] => [3,1,1,1,1,1,1] => [7,1,1] => 2
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,3,1] => [1,1,1,1,1,1,1,1] => [8] => 0
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [3,3,1] => [2,1,1,1,1,1] => [6,1] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,2,1] => [4,2,1,1,1] => [5,2,1,1] => 4
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => [4,1,1,1,1] => [5,1,1,1] => 3
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,2,1] => [1,1,1,1,1,1,1] => [7] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => [1,1,1,1,1,1] => [6] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,2,1] => [2,2,1] => [3,2] => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,1,1] => [4,2,2] => [3,3,1,1] => 5
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,1] => [4,2,1] => [3,2,1,1] => 4
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,1,1] => [2,2,1,1] => [4,2] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [3,1,1] => [2,1,1,1] => [4,1] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,1,1] => [3,1] => [2,1,1] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1] => [3] => [1,1,1] => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => [3,2,2,2,2] => [5,5,1] => 6
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => [4,2,2,2] => [4,4,1,1] => 6
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,4] => [2,2,2,2,2] => [5,5] => 5
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4] => [2,2,2,2,1] => [5,4] => 4
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,4] => [4,2,1,1] => [4,2,1,1] => 4
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,3] => [4,2,2,1] => [4,3,1,1] => 5
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,3] => [2,2,2,1,1] => [5,3] => 3
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [4,3] => [2,2,1,1,1] => [5,2] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,3] => [3,1,1,1] => [4,1,1] => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,2] => [3,3,1,1] => [4,2,2] => 4
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => [3,2,1,1] => [4,2,1] => 3
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [4,2] => [2,1,1,1,1] => [5,1] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,2] => [1,1,1,1,1] => [5] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,2] => [2,1,1] => [3,1] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => [3,3,1] => [3,2,2] => 4
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1] => [3,2,1] => [3,2,1] => 3
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [4,1] => [3,1,1] => [3,1,1] => 2
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,1] => [1,1,1,1] => [4] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => [1,1,1] => [3] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1] => [2] => [1,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => [3,3] => [2,2,2] => 4
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => [3,2] => [2,2,1] => 3
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [4] => [2,2] => [2,2] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => [2,1] => [2,1] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => [1,1] => [2] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [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] => [6,4,4,3] => [4,4,4,3,1,1] => 13
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2,1] => [5,4,4,3,1] => [5,4,4,3,1] => 12
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2,1] => [5,4,4,3] => [4,4,4,3,1] => 12
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2,1] => [5,4,4,2,1,1] => [6,4,3,3,1] => 11
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,2,1] => [5,4,4,1,1,1,1] => [7,3,3,3,1] => 10
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,2,1] => [5,4,4,1,1,1] => [6,3,3,3,1] => 10
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2,1] => [5,4,4,2] => [4,4,3,3,1] => 11
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,2,1] => [5,4,4,2,2] => [5,5,3,3,1] => 12
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,2,1] => [5,4,4,2,1] => [5,4,3,3,1] => 11
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,2,1] => [5,4,4,1,1] => [5,3,3,3,1] => 10
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2,1] => [5,4,4,1] => [4,3,3,3,1] => 10
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => [5,4,4] => [3,3,3,3,1] => 10
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => [5,3,3,3,3] => [5,5,5,1,1] => 12
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1,1] => [7,3,3,3,1] => [5,4,4,1,1,1,1] => 12
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => [7,3,3,3] => [4,4,4,1,1,1,1] => 12
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => [7,5,2,2,1] => [5,4,2,2,2,1,1] => 12
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => [7,5,2,1,1,1] => [6,3,2,2,2,1,1] => 11
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => [7,5,3,1] => [4,3,3,2,2,1,1] => 12
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => [7,5,3] => [3,3,3,2,2,1,1] => 12
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1,1] => [7,5,1,1,1,1,1] => [7,2,2,2,2,1,1] => 10
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => [7,5,2,1,1] => [5,3,2,2,2,1,1] => 11
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,1,1] => [7,3,2,2,2,1] => [6,5,2,1,1,1,1] => 11
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1,1] => [7,5,1,1,1,1] => [6,2,2,2,2,1,1] => 10
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1,1] => [7,5,1,1,1] => [5,2,2,2,2,1,1] => 10
[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] => [3,3,2,2,2,1,1] => 11
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,1,1] => [5,3,3,2,2,2] => [6,6,3,1,1] => 11
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1,1] => [7,3,2,2,2] => [5,5,2,1,1,1,1] => 11
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1,1] => [7,5,2,1] => [4,3,2,2,2,1,1] => 11
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,1,1] => [7,5,1,1] => [4,2,2,2,2,1,1] => 10
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1,1] => [7,5,1] => [3,2,2,2,2,1,1] => 10
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => [7,5] => [2,2,2,2,2,1,1] => 10
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => [7,4,2,2,1,1] => [6,4,2,2,1,1,1] => 11
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1,1] => [7,3,2,2,1,1,1] => [7,4,2,1,1,1,1] => 10
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => [7,3,3,2,1] => [5,4,3,1,1,1,1] => 11
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => [7,3,3,2] => [4,4,3,1,1,1,1] => 11
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1,1] => [7,2,2,2,2,1,1] => [7,5,1,1,1,1,1] => 10
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,1,1] => [7,1,1,1,1,1,1,1,1,1,1] => [11,1,1,1,1,1,1] => 6
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1,1,1] => [7,2,2,2,1,1,1] => [7,4,1,1,1,1,1] => 9
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1,1,1] => [7,2,2,2,1,1,1,1] => [8,4,1,1,1,1,1] => 9
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1,1,1] => [7,2,2,1,1,1,1,1] => [8,3,1,1,1,1,1] => 8
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1,1] => [7,3,2,2,1] => [5,4,2,1,1,1,1] => 10
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1,1] => [7,3,2,2] => [4,4,2,1,1,1,1] => 10
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1,1] => [7,3,2,1,1,1,1,1] => [8,3,2,1,1,1,1] => 9
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,1,1,1] => [7,2,2,1,1,1,1,1,1] => [9,3,1,1,1,1,1] => 8
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1,1,1] => [7,2,1,1,1,1,1,1,1] => [9,2,1,1,1,1,1] => 7
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1,1] => [7,3,2,1,1,1] => [6,3,2,1,1,1,1] => 9
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,1,1,1] => [5,4,3,2,2,1] => [6,5,3,2,1] => 11
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1,1,1] => [7,3,3,1,1,1] => [6,3,3,1,1,1,1] => 10
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1,1] => [7,3,1,1,1,1,1] => [7,2,2,1,1,1,1] => 8
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1,1,1] => [7,4,1,1,1] => [5,2,2,2,1,1,1] => 9
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1,1] => [7,4,2] => [3,3,2,2,1,1,1] => 10
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,1,1,1] => [5,4,3,2,2] => [5,5,3,2,1] => 11
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1,1,1] => [7,2,2,2,2] => [5,5,1,1,1,1,1] => 10
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1,1,1] => [7,2,2,2,1] => [5,4,1,1,1,1,1] => 9
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1,1] => [7,4,1,1] => [4,2,2,2,1,1,1] => 9
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1,1] => [7,4,1] => [3,2,2,2,1,1,1] => 9
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1,1] => [7,4] => [2,2,2,2,1,1,1] => 9
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1] => [7,4,1,1,1,1,1,1] => [8,2,2,2,1,1,1] => 9
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => [7,3,2,2,1,1] => [6,4,2,1,1,1,1] => 10
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1,1] => [7,3,1,1,1,1,1,1,1] => [9,2,2,1,1,1,1] => 8
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,1,1,1] => [7,2,1,1,1,1,1,1,1,1] => [10,2,1,1,1,1,1] => 7
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1,1,1] => [7,1,1,1,1,1,1,1,1,1] => [10,1,1,1,1,1,1] => 6
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1,1,1] => [7,2,2,1,1,1,1] => [7,3,1,1,1,1,1] => 8
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1,1,1,1] => [4,3,3,3,2,1,1] => [7,5,4,1] => 10
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1,1] => [7,3,2,1,1,1,1] => [7,3,2,1,1,1,1] => 9
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1,1,1] => [7,2,1,1,1,1,1,1] => [8,2,1,1,1,1,1] => 7
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1,1] => [7,3,1,1,1,1] => [6,2,2,1,1,1,1] => 8
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1,1] => [7,2,2,2] => [4,4,1,1,1,1,1] => 9
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,1,1,1] => [7,3,3,1,1,1,1] => [7,3,3,1,1,1,1] => 10
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1,1,1] => [7,4,1,1,1,1,1] => [7,2,2,2,1,1,1] => 9
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,1,1,1] => [4,3,3,3,1,1,1,1] => [8,4,4,1] => 9
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,1,1,1] => [7,3,1,1,1,1,1,1] => [8,2,2,1,1,1,1] => 8
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1,1,1] => [7,1,1,1,1,1,1,1,1] => [9,1,1,1,1,1,1] => 6
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1,1,1] => [7,2,1,1,1,1,1] => [7,2,1,1,1,1,1] => 7
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,1,1,1] => [4,3,3,3,1,1,1] => [7,4,4,1] => 9
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,1,1,1] => [7,4,1,1,1,1] => [6,2,2,2,1,1,1] => 9
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1,1,1] => [7,1,1,1,1,1,1,1] => [8,1,1,1,1,1,1] => 6
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1,1,1] => [7,1,1,1,1,1,1] => [7,1,1,1,1,1,1] => 6
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1,1] => [7,2,2,1] => [4,3,1,1,1,1,1] => 8
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1,1,1,1] => [4,3,3,3,2] => [5,5,4,1] => 10
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1,1,1] => [7,4,2,1] => [4,3,2,2,1,1,1] => 10
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1,1] => [7,2,2,1,1] => [5,3,1,1,1,1,1] => 8
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1,1,1] => [7,2,1,1,1] => [5,2,1,1,1,1,1] => 7
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1,1] => [7,3,1] => [3,2,2,1,1,1,1] => 8
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => [7,3] => [2,2,2,1,1,1,1] => 8
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1,1] => [6,3,2,2,2,2] => [6,6,2,1,1,1] => 11
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,1,1,1,1] => [4,3,2,2,2,2,2] => [7,7,2,1] => 10
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1,1,1,1] => [7,2,2,2,2,1] => [6,5,1,1,1,1,1] => 10
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1,1] => [7,4,2,1,1] => [5,3,2,2,1,1,1] => 10
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,1,1,1,1] => [4,3,3,3,2,1] => [6,5,4,1] => 10
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1,1,1,1] => [7,2,2,2,1,1] => [6,4,1,1,1,1,1] => 9
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1,1,1] => [7,2,2,1,1,1] => [6,3,1,1,1,1,1] => 8
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1,1] => [7,3,1,1,1] => [5,2,2,1,1,1,1] => 8
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,1,1,1,1] => [4,3,3,3,1,1] => [6,4,4,1] => 9
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1,1,1] => [7,3,2,1,1] => [5,3,2,1,1,1,1] => 9
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1,1,1] => [7,2,1,1,1,1] => [6,2,1,1,1,1,1] => 7
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1,1,1] => [7,1,1,1,1,1] => [6,1,1,1,1,1,1] => 6
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1,1] => [7,2,1,1] => [4,2,1,1,1,1,1] => 7
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1,1,1,1] => [4,3,3,3,1] => [5,4,4,1] => 9
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1,1,1] => [7,3,2,1] => [4,3,2,1,1,1,1] => 9
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1,1,1] => [7,3,1,1] => [4,2,2,1,1,1,1] => 8
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1,1] => [7,1,1,1,1] => [5,1,1,1,1,1,1] => 6
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1,1] => [7,1,1,1] => [4,1,1,1,1,1,1] => 6
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => [7,2] => [2,2,1,1,1,1,1] => 7
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1,1,1] => [4,3,3,3] => [4,4,4,1] => 9
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1,1] => [7,3,2] => [3,3,2,1,1,1,1] => 9
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1,1] => [7,2,2] => [3,3,1,1,1,1,1] => 8
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1,1] => [7,2,1] => [3,2,1,1,1,1,1] => 7
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1,1] => [7,1,1] => [3,1,1,1,1,1,1] => 6
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => [7,1] => [2,1,1,1,1,1,1] => 6
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1] => 6
[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] => [6,6,5] => 11
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => [5,3,3,3,2,1] => [6,5,4,1,1] => 11
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => [5,3,3,3,2] => [5,5,4,1,1] => 11
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,2] => [4,4,4,2,2,1] => [6,5,3,3] => 11
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,2] => [4,4,4,2,1,1,1] => [7,4,3,3] => 10
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => [5,4,3,3,1] => [5,4,4,2,1] => 11
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => [5,4,3,3] => [4,4,4,2,1] => 11
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,2] => [4,4,4,1,1,1,1,1] => [8,3,3,3] => 9
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2] => [4,4,4,2,1,1] => [6,4,3,3] => 10
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,2] => [5,3,2,2,2,2,1] => [7,6,2,1,1] => 10
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,2] => [4,4,4,1,1,1,1] => [7,3,3,3] => 9
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,2] => [4,4,4,1,1,1] => [6,3,3,3] => 9
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2] => [4,4,4,2] => [4,4,3,3] => 10
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,2] => [3,3,3,2,2,2,2] => [7,7,3] => 10
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,2] => [5,3,2,2,2,2] => [6,6,2,1,1] => 10
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,2] => [4,4,4,2,1] => [5,4,3,3] => 10
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,2] => [4,4,4,1,1] => [5,3,3,3] => 9
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2] => [4,4,4,1] => [4,3,3,3] => 9
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => [4,4,4] => [3,3,3,3] => 9
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3,1] => [3,3,3,3,2,2,1] => [7,6,4] => 10
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1] => [3,3,3,3,2,2] => [6,6,4] => 10
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2,1] => [4,4,2,2,2,2,1] => [7,6,2,2] => 10
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2,1] => [3,3,3,2,2,2,1,1] => [8,6,3] => 9
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1] => [3,3,3,2,2,2,1] => [7,6,3] => 9
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1] => [3,3,3,2,2,2] => [6,6,3] => 9
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,1] => [4,3,3,2,2,1,1,1] => [8,5,3,1] => 9
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2,1] => [4,4,3,1,1,1,1,1,1] => [9,3,3,2] => 8
[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] => [6,5,3,2] => 10
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2,1] => [4,3,2,2,2,1,1,1,1] => [9,5,2,1] => 8
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1] => [4,4,3,2,1,1,1] => [7,4,3,2] => 9
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1] => [5,3,3,3,1] => [5,4,4,1,1] => 10
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1] => [5,3,3,3] => [4,4,4,1,1] => 10
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2,1] => [3,3,2,2,2,2,1,1,1] => [9,6,2] => 8
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,2,1] => [3,3,2,2,2,1,1,1,1,1] => [10,5,2] => 7
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1] => [4,4,3,1,1,1,1,1] => [8,3,3,2] => 8
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1] => [4,4,3,2,1,1] => [6,4,3,2] => 9
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,2,1] => [3,3,2,2,2,2,2,1] => [8,7,2] => 9
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,1] => [3,2,2,2,2,2,2,1] => [8,7,1] => 8
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1] => [4,4,3,1,1,1,1] => [7,3,3,2] => 8
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1] => [4,4,3,1,1,1] => [6,3,3,2] => 8
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1] => [4,4,3,2] => [4,4,3,2] => 9
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,1] => [3,3,2,2,2,2,2] => [7,7,2] => 9
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1] => [3,2,2,2,2,2,2] => [7,7,1] => 8
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1] => [4,4,3,2,1] => [5,4,3,2] => 9
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,1] => [4,4,3,1,1] => [5,3,3,2] => 8
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1] => [4,4,3,1] => [4,3,3,2] => 8
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1] => [4,4,3] => [3,3,3,2] => 8
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1,1] => [4,2,2,2,2,2,1,1,1] => [9,6,1,1] => 8
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1,1] => [4,3,3,1,1,1,1,1,1,1] => [10,3,3,1] => 7
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => [5,2,2,2,2,2,1] => [7,6,1,1,1] => 9
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,1,1] => [3,2,2,2,2,2,1,1,1,1] => [10,6,1] => 7
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1] => [4,3,3,2,1,1,1,1] => [8,4,3,1] => 8
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1] => [5,3,2,2,2,1] => [6,5,2,1,1] => 9
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1] => [5,3,2,2,2] => [5,5,2,1,1] => 9
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1,1] => [5,3,1,1,1,1,1,1,1,1,1] => [11,2,2,1,1] => 6
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1] => [5,3,2,2,1,1,1,1] => [8,4,2,1,1] => 8
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,1,1] => [5,2,1,1,1,1,1,1,1,1,1,1] => [12,2,1,1,1] => 5
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,1] => [5,1,1,1,1,1,1,1,1,1,1,1,1] => [13,1,1,1,1] => 4
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,1] => [6,1,1,1,1,1,1,1,1,1,1] => [11,1,1,1,1,1] => 5
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1,1] => [6,2,2,2,1,1,1] => [7,4,1,1,1,1] => 8
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,1,1] => [4,4,3,2,2,1,1] => [7,5,3,2] => 10
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1,1] => [5,2,2,2,1,1,1,1,1] => [9,4,1,1,1] => 7
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1,1] => [6,2,2,1,1,1,1,1] => [8,3,1,1,1,1] => 7
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1] => [6,3,2,2,1] => [5,4,2,1,1,1] => 9
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1] => [6,3,2,2] => [4,4,2,1,1,1] => 9
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,1,1] => [3,2,2,2,2,1,1,1,1,1,1] => [11,5,1] => 6
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1] => [5,3,2,1,1,1,1,1,1] => [9,3,2,1,1] => 7
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,2,1,1] => [4,4,3,2,1,1,1,1] => [8,4,3,2] => 9
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,1,1] => [4,2,2,2,1,1,1,1,1,1] => [10,4,1,1] => 6
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1,1] => [6,2,1,1,1,1,1,1,1] => [9,2,1,1,1,1] => 6
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1] => [6,3,2,1,1,1] => [6,3,2,1,1,1] => 8
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,1,1] => [5,3,3,3,1,1] => [6,4,4,1,1] => 10
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1,1] => [5,3,3,1,1,1,1] => [7,3,3,1,1] => 8
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1] => [6,3,1,1,1,1,1] => [7,2,2,1,1,1] => 7
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1,1] => [6,4,1,1,1] => [5,2,2,2,1,1] => 8
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => [6,4,2] => [3,3,2,2,1,1] => 9
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,1,1] => [4,4,3,2,2] => [5,5,3,2] => 10
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1,1] => [4,2,2,2,2,2] => [6,6,1,1] => 8
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1,1] => [6,2,2,2,1] => [5,4,1,1,1,1] => 8
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1] => [6,4,1,1] => [4,2,2,2,1,1] => 8
[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] => [3,2,2,2,1,1] => 8
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1] => [6,4] => [2,2,2,2,1,1] => 8
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1,1] => [4,2,2,2,2,1,1,1,1,1] => [10,5,1,1] => 7
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1,1,1] => [3,3,2,2,1,1,1,1,1,1,1] => [11,4,2] => 6
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1] => [4,4,2,1,1,1,1,1,1] => [9,3,2,2] => 7
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1] => [4,4,2,2,1,1,1] => [7,4,2,2] => 8
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,1,1] => [3,2,2,2,1,1,1,1,1,1,1,1] => [12,4,1] => 5
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1] => [5,2,2,1,1,1,1,1,1,1] => [10,3,1,1,1] => 6
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,1,1] => [4,3,3,2,1,1,1,1,1] => [9,4,3,1] => 8
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,1,1] => [4,2,2,1,1,1,1,1,1,1,1] => [11,3,1,1] => 5
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1,1] => [6,1,1,1,1,1,1,1,1,1] => [10,1,1,1,1,1] => 5
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1,1] => [6,2,2,1,1,1,1] => [7,3,1,1,1,1] => 7
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1,1,1] => [5,3,3,2,1,1,1] => [7,4,3,1,1] => 9
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1] => [3,3,2,2,2,1,1,1] => [8,5,2] => 7
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1,1] => [6,2,1,1,1,1,1,1] => [8,2,1,1,1,1] => 6
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1] => [6,3,1,1,1,1] => [6,2,2,1,1,1] => 7
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1] => [6,2,2,2] => [4,4,1,1,1,1] => 8
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1,1,1] => [4,3,2,2,2,2,1,1] => [8,6,2,1] => 9
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,1,1] => [3,2,2,2,2,2,2,1,1] => [9,7,1] => 8
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,1,1] => [3,2,2,2,2,2,1,1,1] => [9,6,1] => 7
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1,1] => [4,3,3,1,1,1,1,1] => [8,3,3,1] => 7
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,1,1] => [3,3,3,3,1,1,1,1] => [8,4,4] => 8
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,1,1] => [4,2,2,2,1,1,1,1,1] => [9,4,1,1] => 6
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1,1] => [6,1,1,1,1,1,1,1,1] => [9,1,1,1,1,1] => 5
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1,1] => [6,2,1,1,1,1,1] => [7,2,1,1,1,1] => 6
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,1,1] => [3,3,3,3,1,1,1] => [7,4,4] => 8
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,1,1] => [4,4,2,1,1,1,1] => [7,3,2,2] => 7
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1,1] => [6,1,1,1,1,1,1,1] => [8,1,1,1,1,1] => 5
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1,1] => [6,1,1,1,1,1,1] => [7,1,1,1,1,1] => 5
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1] => [6,2,2,1] => [4,3,1,1,1,1] => 7
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1,1,1] => [4,3,3,2,2] => [5,5,3,1] => 9
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1,1] => [4,4,2,2,1] => [5,4,2,2] => 8
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1] => [6,2,2,1,1] => [5,3,1,1,1,1] => 7
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1,1] => [6,2,1,1,1] => [5,2,1,1,1,1] => 6
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1] => [6,3,1] => [3,2,2,1,1,1] => 7
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1] => [6,3] => [2,2,2,1,1,1] => 7
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,1,1,1] => [3,2,2,2,2,2,2,2] => [8,8,1] => 9
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1] => [4,2,2,2,2,2,2] => [7,7,1,1] => 9
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,1,1,1] => [2,2,2,2,2,2,2,2] => [8,8] => 8
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1,1,1] => [2,2,2,2,2,2,2,1] => [8,7] => 7
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1] => [5,2,2,2,2,1] => [6,5,1,1,1] => 8
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,1,1,1] => [4,3,3,2,2,1] => [6,5,3,1] => 9
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1,1,1] => [4,2,2,2,2,1,1] => [7,5,1,1] => 7
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1,1] => [6,2,2,1,1,1] => [6,3,1,1,1,1] => 7
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1] => [6,3,1,1,1] => [5,2,2,1,1,1] => 7
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,1,1,1] => [3,3,3,3,1,1] => [6,4,4] => 8
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1,1] => [3,3,3,2,1,1] => [6,4,3] => 7
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1,1] => [6,2,1,1,1,1] => [6,2,1,1,1,1] => 6
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1,1] => [6,1,1,1,1,1] => [6,1,1,1,1,1] => 5
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1] => [6,2,1,1] => [4,2,1,1,1,1] => 6
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1,1,1] => [3,3,3,3,1] => [5,4,4] => 8
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1,1] => [3,3,3,2,1] => [5,4,3] => 7
[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] => [4,2,2,1,1,1] => 7
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1] => [6,1,1,1,1] => [5,1,1,1,1,1] => 5
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1] => [6,1,1,1] => [4,1,1,1,1,1] => 5
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1] => [6,2] => [2,2,1,1,1,1] => 6
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1,1] => [3,3,3,3] => [4,4,4] => 8
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1] => [3,3,3,2] => [4,4,3] => 7
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1] => [6,2,2] => [3,3,1,1,1,1] => 7
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1] => [6,2,1] => [3,2,1,1,1,1] => 6
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1] => [6,1,1] => [3,1,1,1,1,1] => 5
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1] => [6,1] => [2,1,1,1,1,1] => 5
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => [6] => [1,1,1,1,1,1] => 5
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => [6,4,2,2,1,1,1] => [7,4,2,2,1,1] => 10
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,3,3,3] => [4,4,2,2,2,1,1,1] => [8,5,2,2] => 9
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3] => [5,3,3,2,2,1] => [6,5,3,1,1] => 10
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => [5,3,3,2,2] => [5,5,3,1,1] => 10
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,2] => [2,2,2,2,2,2,2,1,1,1] => [10,7] => 7
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2] => [4,4,1,1,1,1,1,1,1,1,1] => [11,2,2,2] => 6
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2] => [4,3,2,2,2,1,1,1] => [8,5,2,1] => 8
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,2] => [2,2,2,2,2,2,1,1,1,1,1] => [11,6] => 6
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2] => [4,2,2,2,2,1,1,1,1] => [9,5,1,1] => 7
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2] => [3,3,2,2,2,2,1] => [7,6,2] => 8
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2] => [3,3,2,2,2,2] => [6,6,2] => 8
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2] => [4,3,1,1,1,1,1,1,1,1,1,1] => [12,2,2,1] => 5
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2] => [3,3,2,2,2,1,1,1,1] => [9,5,2] => 7
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,2] => [4,2,1,1,1,1,1,1,1,1,1,1,1] => [13,2,1,1] => 4
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,2] => [4,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14,1,1,1] => 3
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2] => [5,1,1,1,1,1,1,1,1,1,1,1] => [12,1,1,1,1] => 4
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2] => [5,2,2,2,1,1,1,1] => [8,4,1,1,1] => 7
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,2] => [5,3,2,2,2,1,1,1] => [8,5,2,1,1] => 9
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2] => [3,2,2,2,2,1,1,1,1,1] => [10,5,1] => 6
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2] => [5,2,2,1,1,1,1,1,1] => [9,3,1,1,1] => 6
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2] => [4,3,2,2,2,1] => [6,5,2,1] => 8
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2] => [4,3,2,2,2] => [5,5,2,1] => 8
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2] => [2,2,2,2,2,1,1,1,1,1,1,1] => [12,5] => 5
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2] => [3,3,2,2,1,1,1,1,1,1] => [10,4,2] => 6
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,2,2] => [3,3,3,3,1,1,1,1,1] => [9,4,4] => 8
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,2] => [3,2,2,2,1,1,1,1,1,1,1] => [11,4,1] => 5
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2] => [4,2,2,1,1,1,1,1,1,1] => [10,3,1,1] => 5
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => [3,3,3,2,1,1,1] => [7,4,3] => 7
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,2] => [5,3,2,2,2,1,1] => [7,5,2,1,1] => 9
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2] => [3,2,2,2,2,2,1,1] => [8,6,1] => 7
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2] => [3,3,2,2,1,1,1,1] => [8,4,2] => 6
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2] => [4,3,3,1,1,1] => [6,3,3,1] => 7
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2] => [4,3,3,2] => [4,4,3,1] => 8
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2] => [5,2,2,2,2,2] => [6,6,1,1,1] => 9
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2] => [2,2,2,2,2,2,2] => [7,7] => 7
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2] => [4,2,2,2,2,1] => [6,5,1,1] => 7
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2] => [4,3,3,1,1] => [5,3,3,1] => 7
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2] => [4,3,3,1] => [4,3,3,1] => 7
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2] => [4,3,3] => [3,3,3,1] => 7
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,1] => [5,2,2,2,2,2,1,1] => [8,6,1,1,1] => 9
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,1] => [3,3,1,1,1,1,1,1,1,1,1,1,1] => [13,2,2] => 4
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1] => [2,2,2,2,2,2,1,1,1,1] => [10,6] => 6
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1] => [3,2,1,1,1,1,1,1,1,1,1,1,1,1] => [14,2,1] => 3
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3,1] => [3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [15,1,1] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1] => [4,1,1,1,1,1,1,1,1,1,1,1,1] => [13,1,1,1] => 3
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1] => [3,2,2,2,2,1,1,1,1] => [9,5,1] => 6
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [7,3,3,3,1] => [5,2,2,2,2,1,1,1,1] => [9,5,1,1,1] => 8
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,1] => [2,2,2,2,2,1,1,1,1,1,1] => [11,5] => 5
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1] => [2,2,2,2,2,1,1,1,1,1] => [10,5] => 5
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1] => [3,2,2,2,2,2,1] => [7,6,1] => 7
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1] => [3,2,2,2,2,2] => [6,6,1] => 7
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,1] => [2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] => [15,2] => 2
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,1] => [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [16,1] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1] => [3,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14,1,1] => 2
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1] => [3,2,2,2,1,1,1,1,1,1] => [10,4,1] => 5
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [17] => 0
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,1] => [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [15,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,1] => [6,1,1,1,1,1,1,1,1,1,1,1] => [12,1,1,1,1,1] => 5
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [16] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [15] => 0
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1] => [2,2,2,2,1,1,1,1,1,1] => [10,4] => 4
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,1] => [6,2,2,2,1,1,1,1] => [8,4,1,1,1,1] => 8
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1] => [2,2,2,2,1,1,1,1,1,1,1] => [11,4] => 4
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1] => [2,2,2,1,1,1,1,1,1,1,1] => [11,3] => 3
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1] => [3,2,2,2,2,1,1] => [7,5,1] => 6
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1] => [2,2,2,2,2,2] => [6,6] => 6
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,1] => [6,2,2,2,1,1,1,1,1] => [9,4,1,1,1,1] => 8
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,2,1] => [5,2,2,2,1,1,1,1,1,1] => [10,4,1,1,1] => 7
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,1] => [2,2,2,2,1,1,1,1,1,1,1,1] => [12,4] => 4
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1] => [3,2,2,1,1,1,1,1,1,1,1] => [11,3,1] => 4
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,2,1] => [6,2,2,1,1,1,1,1,1] => [9,3,1,1,1,1] => 7
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,1] => [2,2,2,1,1,1,1,1,1,1,1,1] => [12,3] => 3
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1] => [2,2,1,1,1,1,1,1,1,1,1,1] => [12,2] => 2
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1] => [3,3,2,1,1,1,1,1] => [8,3,2] => 5
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,1] => [6,3,3,1,1,1] => [6,3,3,1,1,1] => 9
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1] => [3,3,3,1,1,1,1,1] => [8,3,3] => 6
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1] => [3,3,1,1,1,1,1,1,1] => [9,2,2] => 4
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1] => [3,3,3,1,1,1] => [6,3,3] => 6
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1] => [4,3,2,2] => [4,4,2,1] => 7
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,1] => [6,2,2,2,2] => [5,5,1,1,1,1] => 9
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1] => [2,2,2,2,2,2,1] => [7,6] => 6
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1] => [2,2,2,2,2,1,1] => [7,5] => 5
[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] => [5,3,3] => 6
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1] => [3,3,3,1] => [4,3,3] => 6
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1] => [3,3,3] => [3,3,3] => 6
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1,1] => [6,3,2,1,1,1,1,1,1] => [9,3,2,1,1,1] => 8
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,1] => [2,2,2,2,1,1,1,1,1,1,1,1,1] => [13,4] => 4
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1] => [3,3,2,1,1,1,1,1,1,1,1] => [11,3,2] => 5
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [7,4,4,1,1] => [5,3,2,1,1,1,1,1,1,1] => [10,3,2,1,1] => 7
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1,1] => [3,2,2,1,1,1,1,1,1,1,1,1] => [12,3,1] => 4
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1] => [4,2,1,1,1,1,1,1,1,1,1] => [11,2,1,1] => 4
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1] => [4,2,2,2,1,1,1,1] => [8,4,1,1] => 6
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [6,6,3,1,1] => [6,2,2,1,1,1,1,1,1,1] => [10,3,1,1,1,1] => 7
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1,1] => [4,2,2,2,1,1,1,1,1,1,1] => [11,4,1,1] => 6
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,1] => [2,2,2,1,1,1,1,1,1,1,1,1,1] => [13,3] => 3
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1] => [3,2,1,1,1,1,1,1,1,1,1,1] => [12,2,1] => 3
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,1] => [6,2,1,1,1,1,1,1,1,1] => [10,2,1,1,1,1] => 6
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,1] => [2,2,1,1,1,1,1,1,1,1,1,1,1] => [13,2] => 2
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1] => [2,1,1,1,1,1,1,1,1,1,1,1,1] => [13,1] => 1
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1] => [3,2,2,1,1,1,1,1,1] => [9,3,1] => 4
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1,1] => [6,3,2,1,1,1,1] => [7,3,2,1,1,1] => 8
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1] => [3,3,2,1,1,1,1,1,1] => [9,3,2] => 5
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1] => [3,2,1,1,1,1,1,1,1,1] => [10,2,1] => 3
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1] => [4,2,2,1,1,1,1] => [7,3,1,1] => 5
[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] => [5,4,1,1] => 6
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [7,6,2,1,1] => [5,3,3,3,1,1,1] => [7,4,4,1,1] => 10
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1,1] => [6,3,3,1,1,1,1] => [7,3,3,1,1,1] => 9
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,1] => [5,3,3,1,1,1,1,1] => [8,3,3,1,1] => 8
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,1] => [3,3,3,1,1,1,1,1,1] => [9,3,3] => 6
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1] => [4,3,1,1,1,1,1,1,1] => [9,2,2,1] => 5
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,1] => [6,3,1,1,1,1,1,1] => [8,2,2,1,1,1] => 7
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,1] => [3,3,1,1,1,1,1,1,1,1] => [10,2,2] => 4
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1] => [3,1,1,1,1,1,1,1,1,1,1] => [11,1,1] => 2
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1] => [4,2,1,1,1,1,1,1] => [8,2,1,1] => 4
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,1] => [6,4,1,1,1,1] => [6,2,2,2,1,1] => 8
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,1] => [4,3,2,1,1,1,1] => [7,3,2,1] => 6
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1] => [4,1,1,1,1,1,1,1,1] => [9,1,1,1] => 3
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1] => [5,1,1,1,1,1,1] => [7,1,1,1,1] => 4
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1] => [5,2,2,1] => [4,3,1,1,1] => 6
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1,1] => [6,4,2,1] => [4,3,2,2,1,1] => 9
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1] => [4,3,2,2,1] => [5,4,2,1] => 7
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1] => [4,2,2,1,1,1] => [6,3,1,1] => 5
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1] => [5,2,1,1,1] => [5,2,1,1,1] => 5
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => [5,3,1] => [3,2,2,1,1] => 6
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1] => [5,3] => [2,2,2,1,1] => 6
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,1,1] => [4,4,2,2,2,2] => [6,6,2,2] => 10
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1] => [6,2,2,2,2,1] => [6,5,1,1,1,1] => 9
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,1,1] => [4,2,2,2,2,2,1] => [7,6,1,1] => 8
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1,1] => [2,2,2,2,2,2,1,1] => [8,6] => 6
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1] => [4,2,2,2,1,1,1] => [7,4,1,1] => 6
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,1,1] => [6,2,2,2,1,1] => [6,4,1,1,1,1] => 8
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1,1] => [2,2,2,2,2,1,1,1] => [8,5] => 5
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1] => [2,2,2,2,1,1,1,1] => [8,4] => 4
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1] => [3,3,2,1,1,1] => [6,3,2] => 5
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,1,1] => [6,3,2,1,1] => [5,3,2,1,1,1] => 8
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1] => [4,3,2,1,1,1] => [6,3,2,1] => 6
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1] => [3,2,2,1,1,1,1] => [7,3,1] => 4
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1] => [5,1,1,1,1,1] => [6,1,1,1,1] => 4
[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] => [4,2,1,1,1] => 5
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1,1] => [6,3,2,1] => [4,3,2,1,1,1] => 8
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1] => [3,3,2,2,1] => [5,4,2] => 6
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1] => [3,2,2,2,1] => [5,4,1] => 5
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1] => [5,1,1,1,1] => [5,1,1,1,1] => 4
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1] => [5,1,1,1] => [4,1,1,1,1] => 4
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => [5,2] => [2,2,1,1,1] => 5
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1] => [6,3,2] => [3,3,2,1,1,1] => 8
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1] => [3,3,2,2] => [4,4,2] => 6
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1] => [3,2,2,2] => [4,4,1] => 5
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1] => [5,2,1] => [3,2,1,1,1] => 5
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1] => [5,1,1] => [3,1,1,1,1] => 4
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1] => [5,1] => [2,1,1,1,1] => 4
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1] => [5] => [1,1,1,1,1] => 4
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4] => [3,3,3,2,2,1,1,1,1] => [9,5,3] => 8
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => [4,3,2,2,2,2,1] => [7,6,2,1] => 9
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3] => [3,3,3,1,1,1,1,1,1,1,1] => [11,3,3] => 6
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3] => [3,3,2,1,1,1,1,1,1,1,1,1] => [12,3,2] => 5
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3] => [4,4,1,1,1,1,1,1,1,1] => [10,2,2,2] => 6
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3] => [4,3,2,2,1,1,1,1] => [8,4,2,1] => 7
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3] => [3,2,2,1,1,1,1,1,1,1,1,1,1] => [13,3,1] => 4
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3] => [4,3,1,1,1,1,1,1,1,1,1] => [11,2,2,1] => 5
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [7,4,3,3] => [4,3,2,2,1,1,1,1,1,1] => [10,4,2,1] => 7
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3] => [4,2,1,1,1,1,1,1,1,1,1,1] => [12,2,1,1] => 4
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3] => [5,1,1,1,1,1,1,1,1,1,1] => [11,1,1,1,1] => 4
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3] => [5,2,2,1,1,1,1,1] => [8,3,1,1,1] => 6
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [7,3,3,3] => [3,3,2,2,2,2,1,1] => [8,6,2] => 8
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3] => [3,3,2,2,1,1,1,1,1] => [9,4,2] => 6
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3] => [3,2,2,2,1,1,1,1,1] => [9,4,1] => 5
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3] => [3,3,3,1,1,1,1] => [7,3,3] => 6
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3] => [4,2,2,2,2] => [5,5,1,1] => 7
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,5,5,2] => [6,3,1,1,1,1,1,1,1,1] => [10,2,2,1,1,1] => 7
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2] => [2,2,2,1,1,1,1,1,1,1,1,1,1,1] => [14,3] => 3
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2] => [3,3,1,1,1,1,1,1,1,1,1,1] => [12,2,2] => 4
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [7,4,4,2] => [4,3,2,1,1,1,1,1,1,1,1] => [11,3,2,1] => 6
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2] => [3,2,1,1,1,1,1,1,1,1,1,1,1] => [13,2,1] => 3
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2] => [4,1,1,1,1,1,1,1,1,1,1,1] => [12,1,1,1] => 3
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2] => [4,2,2,1,1,1,1,1,1] => [9,3,1,1] => 5
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [6,6,3,2] => [6,2,1,1,1,1,1,1,1,1,1] => [11,2,1,1,1,1] => 6
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2] => [4,2,2,1,1,1,1,1,1,1,1,1] => [12,3,1,1] => 5
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2] => [2,2,1,1,1,1,1,1,1,1,1,1,1,1] => [14,2] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2] => [3,1,1,1,1,1,1,1,1,1,1,1,1] => [13,1,1] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2] => [5,2,1,1,1,1,1,1,1,1,1] => [11,2,1,1,1] => 5
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2] => [2,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14,1] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14] => 0
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2] => [2,2,2,1,1,1,1,1,1,1] => [10,3] => 3
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2] => [3,3,3,2,1,1,1,1] => [8,4,3] => 7
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2] => [3,2,2,1,1,1,1,1,1,1] => [10,3,1] => 4
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2] => [2,2,1,1,1,1,1,1,1,1,1] => [11,2] => 2
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2] => [3,3,1,1,1,1,1,1] => [8,2,2] => 4
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2] => [2,2,2,2,2,1] => [6,5] => 5
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [7,6,2,2] => [5,3,3,2,1,1,1,1] => [8,4,3,1,1] => 9
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2] => [6,3,2,1,1,1,1,1] => [8,3,2,1,1,1] => 8
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,2] => [3,3,3,2,1,1,1,1,1] => [9,4,3] => 7
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2] => [3,3,2,1,1,1,1,1,1,1] => [10,3,2] => 5
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2] => [4,2,1,1,1,1,1,1,1,1] => [10,2,1,1] => 4
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,2] => [4,3,2,1,1,1,1,1,1] => [9,3,2,1] => 6
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2] => [3,2,1,1,1,1,1,1,1,1,1] => [11,2,1] => 3
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2] => [2,1,1,1,1,1,1,1,1,1,1,1] => [12,1] => 1
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2] => [3,2,1,1,1,1,1,1,1] => [9,2,1] => 3
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2] => [4,3,3,1,1,1,1] => [7,3,3,1] => 7
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2] => [4,3,1,1,1,1,1,1] => [8,2,2,1] => 5
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2] => [3,1,1,1,1,1,1,1,1,1] => [10,1,1] => 2
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2] => [4,1,1,1,1,1,1,1] => [8,1,1,1] => 3
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => [4,2,2,1,1] => [5,3,1,1] => 5
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2] => [4,3,3,2,1] => [5,4,3,1] => 8
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2] => [4,2,2,2,1,1] => [6,4,1,1] => 6
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2] => [2,2,2,2,1,1,1] => [7,4] => 4
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2] => [3,2,2,1,1,1] => [6,3,1] => 4
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2] => [3,3,2,1] => [4,3,2] => 5
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2] => [3,3,2] => [3,3,2] => 5
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [6,5,5,1] => [6,3,3,1,1,1,1,1] => [8,3,3,1,1,1] => 9
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1] => [6,4,1,1,1,1,1,1] => [8,2,2,2,1,1] => 8
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [6,6,4,1] => [5,3,3,1,1,1,1,1,1] => [9,3,3,1,1] => 8
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [7,5,4,1] => [3,3,3,2,1,1,1,1,1,1] => [10,4,3] => 7
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1] => [3,3,3,1,1,1,1,1,1,1] => [10,3,3] => 6
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1] => [4,4,1,1,1,1,1,1,1] => [9,2,2,2] => 6
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [7,4,4,1] => [4,3,2,2,1,1,1,1,1] => [9,4,2,1] => 7
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1] => [4,3,1,1,1,1,1,1,1,1] => [10,2,2,1] => 5
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1] => [5,1,1,1,1,1,1,1,1,1] => [10,1,1,1,1] => 4
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1] => [5,2,1,1,1,1,1,1] => [8,2,1,1,1] => 5
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [7,6,3,1] => [4,4,2,2,1,1,1,1,1] => [9,4,2,2] => 8
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [6,6,3,1] => [6,3,1,1,1,1,1,1,1] => [9,2,2,1,1,1] => 7
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1] => [4,3,2,1,1,1,1,1,1,1] => [10,3,2,1] => 6
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1] => [3,3,1,1,1,1,1,1,1,1,1] => [11,2,2] => 4
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1] => [4,1,1,1,1,1,1,1,1,1,1] => [11,1,1,1] => 3
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1] => [5,2,1,1,1,1,1,1,1,1] => [10,2,1,1,1] => 5
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1] => [3,1,1,1,1,1,1,1,1,1,1,1] => [12,1,1] => 2
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1] => [13] => 0
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1] => [2,2,1,1,1,1,1,1,1,1] => [10,2] => 2
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1] => [5,3,1,1,1,1,1,1] => [8,2,2,1,1] => 6
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1] => [4,2,1,1,1,1,1,1,1] => [9,2,1,1] => 4
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1] => [2,1,1,1,1,1,1,1,1,1,1] => [11,1] => 1
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1] => [3,1,1,1,1,1,1,1,1] => [9,1,1] => 2
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1] => [2,2,2,2,1,1] => [6,4] => 4
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [7,6,2,1] => [3,3,3,2,2,1,1,1] => [8,5,3] => 8
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1] => [6,4,1,1,1,1,1] => [7,2,2,2,1,1] => 8
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1] => [4,4,2,1,1,1,1,1] => [8,3,2,2] => 7
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1] => [4,3,2,1,1,1,1,1] => [8,3,2,1] => 6
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1] => [5,1,1,1,1,1,1,1,1] => [9,1,1,1,1] => 4
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1] => [5,2,1,1,1,1,1,1,1] => [9,2,1,1,1] => 5
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1] => [4,1,1,1,1,1,1,1,1,1] => [10,1,1,1] => 3
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => [12] => 0
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1] => [2,1,1,1,1,1,1,1,1,1] => [10,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1] => [4,2,2,1,1,1,1,1] => [8,3,1,1] => 5
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1] => [5,1,1,1,1,1,1,1] => [8,1,1,1,1] => 4
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1] => [1,1,1,1,1,1,1,1,1,1,1] => [11] => 0
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1] => [1,1,1,1,1,1,1,1,1,1] => [10] => 0
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1] => [2,2,2,1,1,1] => [6,3] => 3
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1] => [5,2,2,2,1] => [5,4,1,1,1] => 7
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1] => [5,2,2,1,1] => [5,3,1,1,1] => 6
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1] => [2,2,2,1,1,1,1] => [7,3] => 3
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1] => [2,2,1,1,1,1,1] => [7,2] => 2
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => [3,2,2,1] => [4,3,1] => 4
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1] => [3,2,2] => [3,3,1] => 4
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,1] => [4,3,2,2,2,2] => [6,6,2,1] => 9
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1] => [6,4,2,1,1] => [5,3,2,2,1,1] => 9
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,1] => [4,4,2,2,1,1] => [6,4,2,2] => 8
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1] => [4,3,2,2,1,1] => [6,4,2,1] => 7
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1] => [5,2,2,1,1,1] => [6,3,1,1,1] => 6
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,1] => [5,2,2,2,1,1] => [6,4,1,1,1] => 7
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1] => [3,2,2,2,1,1,1] => [7,4,1] => 5
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1] => [2,2,2,1,1,1,1,1] => [8,3] => 3
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1] => [3,2,1,1,1,1,1] => [7,2,1] => 3
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,1] => [3,3,2,2,1,1] => [6,4,2] => 6
[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] => [6,2,1,1,1] => 5
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1] => [2,2,1,1,1,1,1,1] => [8,2] => 2
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1] => [2,1,1,1,1,1,1,1] => [8,1] => 1
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1] => [3,2,1,1,1] => [5,2,1] => 3
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1] => [5,3,2,1] => [4,3,2,1,1] => 7
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1] => [5,3,1,1] => [4,2,2,1,1] => 6
[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] => [5,2,2] => 4
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1] => [3,1,1,1,1,1] => [6,1,1] => 2
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1] => [4,1,1,1] => [4,1,1,1] => 3
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1] => [4,2] => [2,2,1,1] => 4
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1] => [5,3,2] => [3,3,2,1,1] => 7
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1] => [5,2,2] => [3,3,1,1,1] => 6
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1] => [2,2,2,2] => [4,4] => 4
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1] => [2,2,2,1] => [4,3] => 3
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1] => [4,1,1] => [3,1,1,1] => 3
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1] => [4,1] => [2,1,1,1] => 3
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1] => [4] => [1,1,1,1] => 3
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [6,6,5] => [5,2,2,2,2,2,2] => [7,7,1,1,1] => 10
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [7,5,5] => [4,2,2,2,2,2,2,1] => [8,7,1,1] => 9
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [6,5,5] => [6,2,2,2,2,1,1] => [7,5,1,1,1,1] => 9
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => [6,3,2,2,1,1] => [6,4,2,1,1,1] => 9
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [7,6,4] => [2,2,2,2,2,2,2,2,1] => [9,8] => 8
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [6,6,4] => [4,2,2,2,2,2,1,1] => [8,6,1,1] => 8
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [7,5,4] => [2,2,2,2,2,2,2,1,1] => [9,7] => 7
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [6,5,4] => [2,2,2,2,2,2,1,1,1] => [9,6] => 6
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,5,4] => [4,3,2,2,1,1,1] => [7,4,2,1] => 7
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [7,4,4] => [4,3,2,2,2,1,1] => [7,5,2,1] => 8
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [6,4,4] => [3,2,2,2,2,1,1,1] => [8,5,1] => 6
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,4] => [5,2,2,1,1,1,1] => [7,3,1,1,1] => 6
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [4,4,4] => [5,3,1,1,1,1] => [6,2,2,1,1] => 6
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [7,6,3] => [4,4,2,2,2,1,1] => [7,5,2,2] => 9
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,6,3] => [5,2,2,2,2,1,1] => [7,5,1,1,1] => 8
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [7,5,3] => [4,2,2,2,2,1,1,1] => [8,5,1,1] => 7
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [6,5,3] => [2,2,2,2,2,1,1,1,1] => [9,5] => 5
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,5,3] => [3,2,2,2,1,1,1,1] => [8,4,1] => 5
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [7,4,3] => [5,2,2,2,1,1,1] => [7,4,1,1,1] => 7
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [6,4,3] => [2,2,2,2,1,1,1,1,1] => [9,4] => 4
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3] => [2,2,2,1,1,1,1,1,1] => [9,3] => 3
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [4,4,3] => [3,3,1,1,1,1,1] => [7,2,2] => 4
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [7,3,3] => [5,3,2,1,1,1] => [6,3,2,1,1] => 7
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [6,3,3] => [3,3,2,1,1,1,1] => [7,3,2] => 5
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,3,3] => [3,2,1,1,1,1,1,1] => [8,2,1] => 3
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [4,3,3] => [4,1,1,1,1,1,1] => [7,1,1,1] => 3
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => [3,2,2,1,1] => [5,3,1] => 4
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [7,6,2] => [3,3,3,2,2,1,1] => [7,5,3] => 8
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,6,2] => [4,3,3,2,1,1] => [6,4,3,1] => 8
[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] => [7,5,2] => 7
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [6,5,2] => [3,3,2,2,1,1,1] => [7,4,2] => 6
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,5,2] => [5,2,1,1,1,1,1] => [7,2,1,1,1] => 5
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [7,4,2] => [5,3,1,1,1,1,1] => [7,2,2,1,1] => 6
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [6,4,2] => [3,2,2,1,1,1,1,1] => [8,3,1] => 4
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [5,4,2] => [2,2,1,1,1,1,1,1,1] => [9,2] => 2
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [4,4,2] => [3,1,1,1,1,1,1,1] => [8,1,1] => 2
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [7,3,2] => [4,3,1,1,1,1,1] => [7,2,2,1] => 5
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [6,3,2] => [4,2,1,1,1,1,1] => [7,2,1,1] => 4
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,3,2] => [2,1,1,1,1,1,1,1,1] => [9,1] => 1
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [4,3,2] => [1,1,1,1,1,1,1,1,1] => [9] => 0
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [3,3,2] => [2,2,1,1,1,1] => [6,2] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [7,2,2] => [4,3,2,1,1] => [5,3,2,1] => 6
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [6,2,2] => [3,3,2,1,1] => [5,3,2] => 5
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,2,2] => [3,2,1,1,1,1] => [6,2,1] => 3
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [4,2,2] => [2,1,1,1,1,1,1] => [7,1] => 1
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [3,2,2] => [3,1,1,1,1] => [5,1,1] => 2
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [2,2,2] => [2,2,2] => [3,3] => 3
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [7,6,1] => [3,3,3,2,2,1] => [6,5,3] => 8
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,6,1] => [5,3,2,2,1] => [5,4,2,1,1] => 8
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [7,5,1] => [3,3,2,2,2,1] => [6,5,2] => 7
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [6,5,1] => [3,2,2,2,2,1] => [6,5,1] => 6
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [5,5,1] => [5,3,1,1,1] => [5,2,2,1,1] => 6
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [7,4,1] => [5,3,2,1,1] => [5,3,2,1,1] => 7
[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] => [6,4,1] => 5
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,4,1] => [3,3,1,1,1,1] => [6,2,2] => 4
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [4,4,1] => [4,1,1,1,1,1] => [6,1,1,1] => 3
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [7,3,1] => [4,3,1,1,1,1] => [6,2,2,1] => 5
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [6,3,1] => [4,2,1,1,1,1] => [6,2,1,1] => 4
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,3,1] => [3,1,1,1,1,1,1] => [7,1,1] => 2
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [4,3,1] => [1,1,1,1,1,1,1,1] => [8] => 0
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [3,3,1] => [2,1,1,1,1,1] => [6,1] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,2,1] => [4,3,1,1,1] => [5,2,2,1] => 5
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [6,2,1] => [4,2,1,1,1] => [5,2,1,1] => 4
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,2,1] => [4,1,1,1,1] => [5,1,1,1] => 3
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [4,2,1] => [1,1,1,1,1,1,1] => [7] => 0
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => [1,1,1,1,1,1] => [6] => 0
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [2,2,1] => [2,2,1] => [3,2] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,1,1] => [4,3,2] => [3,3,2,1] => 6
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [6,1,1] => [4,2,2] => [3,3,1,1] => 5
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,1,1] => [4,2,1] => [3,2,1,1] => 4
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [4,1,1] => [2,2,1,1] => [4,2] => 2
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [3,1,1] => [2,1,1,1] => [4,1] => 1
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,1,1] => [3,1] => [2,1,1] => 2
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1] => [3] => [1,1,1] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [7,6] => [3,3,3,2,2] => [5,5,3] => 8
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => [5,3,2,2] => [4,4,2,1,1] => 8
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [7,5] => [3,3,2,2,2] => [5,5,2] => 7
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5] => [3,2,2,2,2] => [5,5,1] => 6
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [5,5] => [4,2,2,2] => [4,4,1,1] => 6
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,4] => [5,2,2,2] => [4,4,1,1,1] => 7
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,4] => [2,2,2,2,2] => [5,5] => 5
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [5,4] => [2,2,2,2,1] => [5,4] => 4
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [4,4] => [4,2,1,1] => [4,2,1,1] => 4
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,3] => [4,3,2,1] => [4,3,2,1] => 6
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,3] => [4,2,2,1] => [4,3,1,1] => 5
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [5,3] => [2,2,2,1,1] => [5,3] => 3
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [4,3] => [2,2,1,1,1] => [5,2] => 2
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [3,3] => [3,1,1,1] => [4,1,1] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,2] => [4,3,1,1] => [4,2,2,1] => 5
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,2] => [3,3,1,1] => [4,2,2] => 4
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [5,2] => [3,2,1,1] => [4,2,1] => 3
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [4,2] => [2,1,1,1,1] => [5,1] => 1
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => [1,1,1,1,1] => [5] => 0
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,2] => [2,1,1] => [3,1] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => [4,3,1] => [3,2,2,1] => 5
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1] => [3,3,1] => [3,2,2] => 4
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [5,1] => [3,2,1] => [3,2,1] => 3
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,1] => [3,1,1] => [3,1,1] => 2
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => [1,1,1,1] => [4] => 0
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => [1,1,1] => [3] => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1] => [2] => [1,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => [4,3] => [2,2,2,1] => 5
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => [3,3] => [2,2,2] => 4
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => [3,2] => [2,2,1] => 3
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => [2,2] => [2,2] => 2
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => [2,1] => [2,1] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => [1,1] => [2] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1] => [1] => [1] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => [4,4] => [2,2,2,2] => 6
[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] => [8] => [1,1,1,1,1,1,1,1] => 7
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => [5,4] => [2,2,2,2,1] => 7
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1] => [4,4,1] => [3,2,2,2] => 6
[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] => [8,1] => [2,1,1,1,1,1,1,1] => 7
[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] => [9] => [1,1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10] => [5,5] => [2,2,2,2,2] => 8
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => [5,4,1] => [3,2,2,2,1] => 7
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [8,2] => [4,4,1,1] => [4,2,2,2] => 6
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1] => [4,4,2] => [3,3,2,2] => 7
[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] => [8,1,1] => [3,1,1,1,1,1,1,1] => 7
[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] => [8,2] => [2,2,1,1,1,1,1,1] => 8
[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] => [9,1] => [2,1,1,1,1,1,1,1,1] => 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] => [10] => [1,1,1,1,1,1,1,1,1,1] => 9
[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] => [6,5] => [2,2,2,2,2,1] => 9
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1] => [5,5,1] => [3,2,2,2,2] => 8
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0] => [9,2] => [5,4,1,1] => [4,2,2,2,1] => 7
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,1] => [5,4,2] => [3,3,2,2,1] => 8
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [8,3] => [4,4,2,1] => [4,3,2,2] => 7
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1] => [4,4,1,1,1] => [5,2,2,2] => 6
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1,1] => [5,3,3] => [3,3,3,1,1] => 8
[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] => [8,2,1] => [3,2,1,1,1,1,1,1] => 8
[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] => [8,1,1,1] => [4,1,1,1,1,1,1,1] => 7
[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] => [9,1,1] => [3,1,1,1,1,1,1,1,1] => 8
[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] => [8,3] => [2,2,2,1,1,1,1,1] => 9
[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] => [9,2] => [2,2,1,1,1,1,1,1,1] => 9
[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] => [10,1] => [2,1,1,1,1,1,1,1,1,1] => 9
[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] => [6,5,1] => [3,2,2,2,2,1] => 9
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0] => [10,2] => [5,5,1,1] => [4,2,2,2,2] => 8
[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] => [5,5,2] => [3,3,2,2,2] => 9
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0] => [9,3] => [5,4,2,1] => [4,3,2,2,1] => 8
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0] => [9,2,1] => [5,4,1,1,1] => [5,2,2,2,1] => 7
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,1,1] => [5,4,3] => [3,3,3,2,1] => 9
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0] => [8,4] => [4,4,2,2] => [4,4,2,2] => 8
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1] => [4,4,1,1,1,1] => [6,2,2,2] => 6
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => [8,2,2] => [4,4,2,1,1] => [5,3,2,2] => 7
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1,1] => [5,3,3,1] => [4,3,3,1,1] => 8
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1,1,1] => [6,3,3] => [3,3,3,1,1,1] => 9
[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] => [8,2,2] => [3,3,1,1,1,1,1,1] => 9
[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] => [8,1,1,1,1] => [5,1,1,1,1,1,1,1] => 7
[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] => [9,2,1] => [3,2,1,1,1,1,1,1,1] => 9
[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] => [8,2,1,1] => [4,2,1,1,1,1,1,1] => 8
[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] => [8,3,1] => [3,2,2,1,1,1,1,1] => 9
[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] => [9,1,1,1] => [4,1,1,1,1,1,1,1,1] => 8
[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] => [10,1,1] => [3,1,1,1,1,1,1,1,1,1] => 9
[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] => [8,4] => [2,2,2,2,1,1,1,1] => 10
[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] => [9,3] => [2,2,2,1,1,1,1,1,1] => 10
[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] => [10,2] => [2,2,1,1,1,1,1,1,1,1] => 10
[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] => [11,1] => [2,1,1,1,1,1,1,1,1,1,1] => 10
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,1,0] => [10,2,1] => [5,5,1,1,1] => [5,2,2,2,2] => 8
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0] => [9,4] => [5,4,2,2] => [4,4,2,2,1] => 9
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,1,0] => [9,3,1] => [5,4,1,1,1,1] => [6,2,2,2,1] => 7
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,1,0] => [9,2,1,1] => [5,4,3,1] => [4,3,3,2,1] => 9
[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] => [6,4,3] => [3,3,3,2,1,1] => 10
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [8,5] => [5,3,3,2] => [4,4,3,1,1] => 9
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0] => [8,4,1] => [5,3,3,1,1] => [5,3,3,1,1] => 8
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2] => [4,4,1,1,1,1,1] => [7,2,2,2] => 6
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1,1] => [4,4,2,1,1,1] => [6,3,2,2] => 7
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0] => [8,2,2,1] => [5,2,2,2,2] => [5,5,1,1,1] => 8
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1,1,1] => [6,3,3,1] => [4,3,3,1,1,1] => 9
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1,1,1,1] => [7,3,3] => [3,3,3,1,1,1,1] => 10
[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] => [8,3,2] => [3,3,2,1,1,1,1,1] => 10
[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] => [8,3,1,1] => [4,2,2,1,1,1,1,1] => 9
[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] => [9,2,2] => [3,3,1,1,1,1,1,1,1] => 10
[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] => [8,1,1,1,1,1] => [6,1,1,1,1,1,1,1] => 7
[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] => [8,2,1,1,1] => [5,2,1,1,1,1,1,1] => 8
[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] => [9,1,1,1,1] => [5,1,1,1,1,1,1,1,1] => 8
[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] => [10,2,1] => [3,2,1,1,1,1,1,1,1,1] => 10
[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] => [8,2,2,1] => [4,3,1,1,1,1,1,1] => 9
[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] => [9,2,1,1] => [4,2,1,1,1,1,1,1,1] => 9
[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] => [8,4,1] => [3,2,2,2,1,1,1,1] => 10
[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] => [9,3,1] => [3,2,2,1,1,1,1,1,1] => 10
[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] => [10,1,1,1] => [4,1,1,1,1,1,1,1,1,1] => 9
[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] => [8,5] => [2,2,2,2,2,1,1,1] => 11
[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] => [9,4] => [2,2,2,2,1,1,1,1,1] => 11
[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] => [10,3] => [2,2,2,1,1,1,1,1,1,1] => 11
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0] => [9,5] => [5,4,3,2] => [4,4,3,2,1] => 10
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,1,0] => [9,3,2] => [5,4,1,1,1,1,1] => [7,2,2,2,1] => 7
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,1,0] => [9,2,2,1] => [5,4,2,2,1] => [5,4,2,2,1] => 9
[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] => [7,4,3] => [3,3,3,2,1,1,1] => 11
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [8,6] => [3,3,3,3,2] => [5,5,4] => 9
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0] => [8,4,2] => [5,3,2,1,1,1,1] => [7,3,2,1,1] => 7
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,1,0] => [8,3,3] => [5,3,3,1,1,1] => [6,3,3,1,1] => 8
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2,1] => [4,4,1,1,1,1,1,1] => [8,2,2,2] => 6
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0] => [8,2,2,1,1] => [6,4,2,2] => [4,4,2,2,1,1] => 10
[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] => [4,4,3,3] => [4,4,4,2] => 10
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,7] => [6,3,3,2] => [4,4,3,1,1,1] => 10
[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] => [8,3,3] => [3,3,3,1,1,1,1,1] => 11
[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] => [9,3,2] => [3,3,2,1,1,1,1,1,1] => 11
[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] => [8,2,1,1,1,1] => [6,2,1,1,1,1,1,1] => 8
[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] => [8,3,1,1,1] => [5,2,2,1,1,1,1,1] => 9
[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] => [8,1,1,1,1,1,1] => [7,1,1,1,1,1,1,1] => 7
[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] => [9,1,1,1,1,1] => [6,1,1,1,1,1,1,1,1] => 8
[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] => [9,2,1,1,1] => [5,2,1,1,1,1,1,1,1] => 9
[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] => [8,4,2] => [3,3,2,2,1,1,1,1] => 11
[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] => [9,2,2,1] => [4,3,1,1,1,1,1,1,1] => 10
[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] => [8,5,1] => [3,2,2,2,2,1,1,1] => 11
[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] => [5,5,4] => [3,3,3,3,2] => 11
[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] => [8,6] => [2,2,2,2,2,2,1,1] => 12
[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] => [9,5] => [2,2,2,2,2,1,1,1,1] => 12
[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] => [10,4] => [2,2,2,2,1,1,1,1,1,1] => 12
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0] => [9,6] => [6,3,3,3] => [4,4,4,1,1,1] => 11
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,1,0] => [9,3,3] => [5,4,3,1,1,1] => [6,3,3,2,1] => 9
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0] => [9,3,2,1] => [5,4,1,1,1,1,1,1] => [8,2,2,2,1] => 7
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,2,2] => [5,4,2,2,2] => [5,5,2,2,1] => 10
[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] => [8,4,3] => [3,3,3,2,1,1,1,1] => 12
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [8,7] => [3,3,3,3,3] => [5,5,5] => 10
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0] => [8,6,1] => [3,3,3,3,2,1] => [6,5,4] => 9
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,1,0] => [8,4,2,1] => [5,3,1,1,1,1,1,1,1] => [9,2,2,1,1] => 6
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,1,0] => [8,4,1,1,1] => [4,4,2,2,2,1] => [6,5,2,2] => 9
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,0] => [8,3,3,1] => [5,3,2,1,1,1,1,1] => [8,3,2,1,1] => 7
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,2] => [4,3,3,2,1,1,1] => [7,4,3,1] => 8
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2,1,1] => [6,4,2,1,1,1] => [6,3,2,2,1,1] => 9
[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] => [4,4,4,3] => [4,4,4,3] => 11
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [7,7,1] => [6,3,3,2,1] => [5,4,3,1,1,1] => 10
[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] => [8,3,3,1] => [4,3,3,1,1,1,1,1] => 11
[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] => [9,3,3] => [3,3,3,1,1,1,1,1,1] => 12
[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] => [8,3,2,1,1] => [5,3,2,1,1,1,1,1] => 10
[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] => [8,2,2,1,1,1] => [6,3,1,1,1,1,1,1] => 9
[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] => [8,1,1,1,1,1,1,1] => [8,1,1,1,1,1,1,1] => 7
[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] => [8,2,2,2,1] => [5,4,1,1,1,1,1,1] => 10
[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] => [8,2,1,1,1,1,1] => [7,2,1,1,1,1,1,1] => 8
[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] => [9,3,1,1,1] => [5,2,2,1,1,1,1,1,1] => 10
[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] => [8,3,1,1,1,1] => [6,2,2,1,1,1,1,1] => 9
[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] => [8,4,1,1,1] => [5,2,2,2,1,1,1,1] => 10
[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] => [9,1,1,1,1,1,1] => [7,1,1,1,1,1,1,1,1] => 8
[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] => [8,3,2,2] => [4,4,2,1,1,1,1,1] => 11
[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] => [9,4,2] => [3,3,2,2,1,1,1,1,1] => 12
[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] => [5,5,4,1] => [4,3,3,3,2] => 11
[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] => [8,6,1] => [3,2,2,2,2,2,1,1] => 12
[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] => [5,5,5] => [3,3,3,3,3] => 12
[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] => [9,6] => [2,2,2,2,2,2,1,1,1] => 13
[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] => [10,5] => [2,2,2,2,2,1,1,1,1,1] => 13
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => [9,7] => [4,3,3,3,3] => [5,5,5,1] => 11
[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] => [4,4,4,4] => [4,4,4,4] => 12
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,8] => [6,4,3,3] => [4,4,4,2,1,1] => 12
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [8,7,1] => [3,3,3,3,3,1] => [6,5,5] => 10
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,1,0] => [8,5,3] => [4,3,3,2,2,1,1] => [7,5,3,1] => 9
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0] => [8,5,2,1] => [6,4,2,1,1,1,1] => [7,3,2,2,1,1] => 9
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2,1,1,1] => [7,4,2,1,1,1] => [6,3,2,2,1,1,1] => 10
[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] => [4,4,3,3,2] => [5,5,4,2] => 11
[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] => [4,4,4,3,1] => [5,4,4,3] => 11
[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] => [9,4,3] => [3,3,3,2,1,1,1,1,1] => 13
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0] => [7,7,2] => [6,3,3,2,1,1] => [6,4,3,1,1,1] => 10
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => [7,7,1,1] => [6,4,2,2,2] => [5,5,2,2,1,1] => 11
[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] => [8,4,1,1,1,1] => [6,2,2,2,1,1,1,1] => 10
[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] => [9,2,2,2,1] => [5,4,1,1,1,1,1,1,1] => 11
[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] => [8,3,2,1,1,1] => [6,3,2,1,1,1,1,1] => 10
[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] => [8,5,1,1,1] => [5,2,2,2,2,1,1,1] => 11
[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] => [5,5,4,1,1] => [5,3,3,3,2] => 11
[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] => [8,6,1,1] => [4,2,2,2,2,2,1,1] => 12
[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] => [9,3,2,2] => [4,4,2,1,1,1,1,1,1] => 12
[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] => [5,5,4,2] => [4,4,3,3,2] => 12
[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] => [5,5,5,1] => [4,3,3,3,3] => 12
[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] => [6,5,5] => [3,3,3,3,3,1] => 13
[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] => [9,7] => [2,2,2,2,2,2,2,1,1] => 14
[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] => [10,6] => [2,2,2,2,2,2,1,1,1,1] => 14
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [9,8] => [4,4,3,3,3] => [5,5,5,2] => 12
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,1,0] => [9,7,1] => [4,3,3,3,3,1] => [6,5,5,1] => 11
[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] => [5,4,4,4] => [4,4,4,4,1] => 13
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0] => [8,8,1] => [6,4,3,3,1] => [5,4,4,2,1,1] => 12
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0] => [8,7,2] => [3,3,3,3,3,1,1] => [7,5,5] => 10
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0] => [8,7,1,1] => [4,3,3,3,2,2] => [6,6,4,1] => 11
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,1,0] => [8,6,2,1] => [3,3,3,3,2,1,1,1] => [8,5,4] => 9
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,0] => [8,5,4] => [6,2,2,2,2,2,1] => [7,6,1,1,1,1] => 10
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [8,5,1,1,1,1] => [7,2,2,2,2,2] => [6,6,1,1,1,1,1] => 11
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,1,0] => [8,4,3,2] => [5,2,2,1,1,1,1,1,1,1,1] => [11,3,1,1,1] => 6
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,1,0] => [8,3,3,3] => [5,3,3,2,2,1,1] => [7,5,3,1,1] => 10
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0] => [8,3,3,2,1] => [6,2,2,2,2,1,1,1] => [8,5,1,1,1,1] => 9
[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] => [4,4,4,3,1,1] => [6,4,4,3] => 11
[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] => [4,4,4,3,2] => [5,5,4,3] => 12
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,1,0,0] => [7,7,3] => [4,4,3,2,2,2] => [6,6,3,2] => 11
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0] => [7,7,2,1] => [6,3,3,2,1,1,1] => [7,4,3,1,1,1] => 10
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,7,1,1,1] => [7,4,2,2,2] => [5,5,2,2,1,1,1] => 12
[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] => [8,2,2,2,2,1] => [6,5,1,1,1,1,1,1] => 11
[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] => [8,3,3,1,1,1] => [6,3,3,1,1,1,1,1] => 11
[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] => [8,3,2,2,2] => [5,5,2,1,1,1,1,1] => 12
[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] => [8,1,1,1,1,1,1,1,1,1] => [10,1,1,1,1,1,1,1] => 7
[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] => [8,2,1,1,1,1,1,1,1] => [9,2,1,1,1,1,1,1] => 8
[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] => [8,3,2,2,1,1] => [6,4,2,1,1,1,1,1] => 11
[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] => [8,2,2,2,1,1,1] => [7,4,1,1,1,1,1,1] => 10
[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] => [5,5,4,1,1,1] => [6,3,3,3,2] => 11
[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] => [8,6,1,1,1] => [5,2,2,2,2,2,1,1] => 12
[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] => [5,5,5,1,1] => [5,3,3,3,3] => 12
[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] => [8,3,3,3] => [4,4,4,1,1,1,1,1] => 13
[1,1,0,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,3,3,2,2,2,2] => [5,5,4,3] => [4,4,4,3,2] => 13
[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] => [5,5,5,2] => [4,4,3,3,3] => 13
[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] => [6,5,5,1] => [4,3,3,3,3,1] => 13
[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] => [9,7,1] => [3,2,2,2,2,2,2,1,1] => 14
[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] => [6,6,5] => [3,3,3,3,3,2] => 14
[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] => [6,4,4,3] => [4,4,4,3,1,1] => 13
[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] => [5,4,4,2,1] => [5,4,3,3,1] => 11
[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] => [5,4,4,1] => [4,3,3,3,1] => 10
[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] => [5,4,4] => [3,3,3,3,1] => 10
[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] => [5,3,3,3,3] => [5,5,5,1,1] => 12
[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] => [7,3,3,3] => [4,4,4,1,1,1,1] => 12
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [5,3,3,2,2,1,1] => [7,5,2,1,1,1] => [6,3,2,2,2,1,1] => 11
[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] => [7,5,3,1] => [4,3,3,2,2,1,1] => 12
[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] => [7,5] => [2,2,2,2,2,1,1] => 10
[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] => [7,1,1,1,1,1,1,1,1,1,1] => [11,1,1,1,1,1,1] => 6
[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] => [7,3,2,2,1,1] => [6,4,2,1,1,1,1] => 10
[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] => [7,1,1,1,1,1,1,1,1,1] => [10,1,1,1,1,1,1] => 6
[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] => [7,1,1,1,1,1,1] => [7,1,1,1,1,1,1] => 6
[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] => [7,3,1] => [3,2,2,1,1,1,1] => 8
[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] => [7,3] => [2,2,2,1,1,1,1] => 8
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,6,1,1,1,1,1] => [6,3,2,2,2,2] => [6,6,2,1,1,1] => 11
[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] => [7,4,2,1,1] => [5,3,2,2,1,1,1] => 10
[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] => [7,2,2,2,1,1] => [6,4,1,1,1,1,1] => 9
[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] => [7,2,2,1,1,1] => [6,3,1,1,1,1,1] => 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] => [7,3,1,1,1] => [5,2,2,1,1,1,1] => 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] => [7,1,1,1,1,1] => [6,1,1,1,1,1,1] => 6
[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] => [7,2,1,1] => [4,2,1,1,1,1,1] => 7
[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] => [4,3,3,3,1] => [5,4,4,1] => 9
[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] => [7,3,1,1] => [4,2,2,1,1,1,1] => 8
[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] => [7,1,1,1] => [4,1,1,1,1,1,1] => 6
[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] => [7,2] => [2,2,1,1,1,1,1] => 7
[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] => [4,3,3,3] => [4,4,4,1] => 9
[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] => [7,3,2] => [3,3,2,1,1,1,1] => 9
[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] => [7,2,1] => [3,2,1,1,1,1,1] => 7
[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] => [7,1,1] => [3,1,1,1,1,1,1] => 6
[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] => [7,1] => [2,1,1,1,1,1,1] => 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] => [7] => [1,1,1,1,1,1,1] => 6
[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] => [6,6,5] => 11
[1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2,2,2,2] => [4,4,4,2] => [4,4,3,3] => 10
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,2,2,2,2] => [3,3,3,2,2,2,2] => [7,7,3] => 10
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,2,2] => [4,4,4,1] => [4,3,3,3] => 9
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2] => [4,4,4] => [3,3,3,3] => 9
[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,1] => [3,3,3,3,2,2] => [6,6,4] => 10
[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,2,1] => [3,3,3,2,2,2] => [6,6,3] => 9
[1,1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,2,1] => [4,4,3,1,1,1,1,1,1] => [9,3,3,2] => 8
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [6,3,2,2,2,1] => [3,2,2,2,2,2,2,1] => [8,7,1] => 8
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,2,2,1] => [4,4,3,1,1,1] => [6,3,3,2] => 8
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,2,2,2,1] => [3,2,2,2,2,2,2] => [7,7,1] => 8
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,1] => [4,4,3] => [3,3,3,2] => 8
[1,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [4,4,3,3,1,1] => [5,2,2,2,2,2,1] => [7,6,1,1,1] => 9
[1,1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [5,5,3,2,1,1] => [5,2,1,1,1,1,1,1,1,1,1,1] => [12,2,1,1,1] => 5
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,1,1] => [5,1,1,1,1,1,1,1,1,1,1,1,1] => [13,1,1,1,1] => 4
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1,1] => [6,1,1,1,1,1,1,1,1,1,1] => [11,1,1,1,1,1] => 5
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,4,3,2,1,1] => [6,2,2,2,1,1,1] => [7,4,1,1,1,1] => 8
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [7,4,2,2,1,1] => [4,4,3,2,1,1,1,1] => [8,4,3,2] => 9
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [7,2,2,2,1,1] => [4,4,3,2,2] => [5,5,3,2] => 10
[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1,1] => [6,4] => [2,2,2,2,1,1] => 8
[1,1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [5,4,4,1,1,1] => [4,4,2,1,1,1,1,1,1] => [9,3,2,2] => 7
[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [4,4,4,1,1,1] => [4,4,2,2,1,1,1] => [7,4,2,2] => 8
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [6,5,2,1,1,1] => [3,2,2,2,2,2,1,1,1] => [9,6,1] => 7
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [6,4,2,1,1,1] => [4,2,2,2,1,1,1,1,1] => [9,4,1,1] => 6
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [6,3,2,1,1,1] => [4,4,2,1,1,1,1] => [7,3,2,2] => 7
[1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1,1,1] => [6,1,1,1,1,1,1,1] => [8,1,1,1,1,1] => 5
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,1,1] => [6,1,1,1,1,1,1] => [7,1,1,1,1,1] => 5
[1,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2,1,1,1] => [6,2,2,1] => [4,3,1,1,1,1] => 7
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [7,2,2,1,1,1] => [4,3,3,2,2] => [5,5,3,1] => 9
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,2,2,1,1,1] => [6,2,2,1,1] => [5,3,1,1,1,1] => 7
[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1,1] => [6,3] => [2,2,2,1,1,1] => 7
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1,1,1,1] => [2,2,2,2,2,2,2,1] => [8,7] => 7
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [5,5,1,1,1,1] => [5,2,2,2,2,1] => [6,5,1,1,1] => 8
[1,1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,1,1,1] => [6,2,2,1,1,1] => [6,3,1,1,1,1] => 7
[1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1,1,1,1] => [6,3,1,1,1] => [5,2,2,1,1,1] => 7
[1,1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1,1,1] => [6,1,1,1,1,1] => [6,1,1,1,1,1] => 5
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1,1,1,1] => [3,3,3,2,1] => [5,4,3] => 7
[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1,1] => [6,1,1,1] => [4,1,1,1,1,1] => 5
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1,1] => [6,2] => [2,2,1,1,1,1] => 6
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1,1,1] => [3,3,3,3] => [4,4,4] => 8
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1,1,1] => [3,3,3,2] => [4,4,3] => 7
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1,1] => [6,2,2] => [3,3,1,1,1,1] => 7
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1,1,1] => [6,2,1] => [3,2,1,1,1,1] => 6
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1,1,1] => [6,1,1] => [3,1,1,1,1,1] => 5
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1] => [6,1] => [2,1,1,1,1,1] => 5
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => [6] => [1,1,1,1,1,1] => 5
[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0] => [4,3,3,3,3] => [5,3,3,2,2,1] => [6,5,3,1,1] => 10
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3] => [5,3,3,2,2] => [5,5,3,1,1] => 10
[1,1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,4,4,3,2] => [2,2,2,2,2,2,2,1,1,1] => [10,7] => 7
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0] => [4,4,3,3,2] => [4,3,2,2,2,1,1,1] => [8,5,2,1] => 8
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,3,3,2] => [2,2,2,2,2,2,1,1,1,1,1] => [11,6] => 6
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,2] => [5,1,1,1,1,1,1,1,1,1,1,1] => [12,1,1,1,1] => 4
[1,1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,2,2] => [4,3,3,1,1,1] => [6,3,3,1] => 7
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,2,2,2] => [2,2,2,2,2,2,2] => [7,7] => 7
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,2,2,2] => [4,3,3,1,1] => [5,3,3,1] => 7
[1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,2] => [4,3,3,1] => [4,3,3,1] => 7
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2] => [4,3,3] => [3,3,3,1] => 7
[1,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,4,4,4,1] => [5,2,2,2,2,2,1,1] => [8,6,1,1,1] => 9
[1,1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0,0] => [5,4,4,3,1] => [3,3,1,1,1,1,1,1,1,1,1,1,1] => [13,2,2] => 4
[1,1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,1] => [3,2,2,2,2,2] => [6,6,1] => 7
[1,1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,4,4,2,1] => [3,2,2,2,1,1,1,1,1,1] => [10,4,1] => 5
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [17] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => [5,5,3,2,1] => [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [15,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,1] => [6,1,1,1,1,1,1,1,1,1,1,1] => [12,1,1,1,1,1] => 5
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [16] => 0
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [15] => 0
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,4,3,2,1] => [2,2,2,2,1,1,1,1,1,1] => [10,4] => 4
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,0] => [7,3,3,2,1] => [6,2,2,2,1,1,1,1] => [8,4,1,1,1,1] => 8
[1,1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0,0] => [5,3,3,2,1] => [2,2,2,1,1,1,1,1,1,1,1] => [11,3] => 3
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,3,3,2,1] => [3,2,2,2,2,1,1] => [7,5,1] => 6
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [3,3,3,2,1] => [2,2,2,2,2,2] => [6,6] => 6
[1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,2,1] => [2,2,1,1,1,1,1,1,1,1,1,1] => [12,2] => 2
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0,0] => [7,3,2,2,1] => [6,3,3,1,1,1] => [6,3,3,1,1,1] => 9
[1,1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,2,1] => [3,3,1,1,1,1,1,1,1] => [9,2,2] => 4
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,2,1] => [3,3,3,1,1,1] => [6,3,3] => 6
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0] => [7,2,2,2,1] => [6,2,2,2,2] => [5,5,1,1,1,1] => 9
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,1] => [3,3,3,1] => [4,3,3] => 6
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1] => [3,3,3] => [3,3,3] => 6
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [7,5,3,1,1] => [4,2,2,2,1,1,1,1,1,1,1] => [11,4,1,1] => 6
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0] => [4,4,3,1,1] => [3,2,2,1,1,1,1,1,1] => [9,3,1] => 4
[1,1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1,1] => [3,1,1,1,1,1,1,1,1,1,1] => [11,1,1] => 2
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0] => [6,3,2,1,1] => [4,3,2,1,1,1,1] => [7,3,2,1] => 6
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,1] => [5,1,1,1,1,1,1] => [7,1,1,1,1] => 4
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1,1] => [5,3,1] => [3,2,2,1,1] => 6
[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] => [2,2,2,1,1] => 6
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0,0] => [7,6,1,1,1] => [4,4,2,2,2,2] => [6,6,2,2] => 10
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1,1,1] => [2,2,2,2,2,2,1,1] => [8,6] => 6
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0,0] => [7,4,1,1,1] => [6,2,2,2,1,1] => [6,4,1,1,1,1] => 8
[1,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,1,1] => [2,2,2,2,1,1,1,1] => [8,4] => 4
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1,1,1] => [3,3,2,1,1,1] => [6,3,2] => 5
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1,1,1] => [4,3,2,1,1,1] => [6,3,2,1] => 6
[1,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1,1] => [5,1,1,1,1,1] => [6,1,1,1,1] => 4
[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] => [4,2,1,1,1] => 5
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1,1,1] => [6,3,2,1] => [4,3,2,1,1,1] => 8
[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,1,1] => [3,2,2,2,1] => [5,4,1] => 5
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1] => [5,1,1,1] => [4,1,1,1,1] => 4
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1] => [5,2] => [2,2,1,1,1] => 5
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1,1] => [6,3,2] => [3,3,2,1,1,1] => 8
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1,1] => [3,3,2,2] => [4,4,2] => 6
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1] => [3,2,2,2] => [4,4,1] => 5
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1] => [5,1] => [2,1,1,1,1] => 4
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1] => [5] => [1,1,1,1,1] => 4
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [4,4,4,4] => [4,3,2,2,2,2,1] => [7,6,2,1] => 9
[1,1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0,0] => [5,5,4,3] => [3,3,3,1,1,1,1,1,1,1,1] => [11,3,3] => 6
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0] => [6,4,4,3] => [3,3,2,1,1,1,1,1,1,1,1,1] => [12,3,2] => 5
[1,1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0,0] => [4,4,4,3] => [4,3,2,2,1,1,1,1] => [8,4,2,1] => 7
[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0] => [5,5,3,3] => [4,3,1,1,1,1,1,1,1,1,1] => [11,2,2,1] => 5
[1,1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,3,3] => [3,3,3,1,1,1,1] => [7,3,3] => 6
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2] => [2,2,2,1,1,1,1,1,1,1,1,1,1,1] => [14,3] => 3
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2] => [2,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14,1] => 1
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14] => 0
[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0] => [4,4,3,2] => [2,2,2,1,1,1,1,1,1,1] => [10,3] => 3
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0] => [6,3,3,2] => [3,2,2,1,1,1,1,1,1,1] => [10,3,1] => 4
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [4,4,2,2] => [3,2,1,1,1,1,1,1,1] => [9,2,1] => 3
[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2,2] => [4,2,2,1,1] => [5,3,1,1] => 5
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0] => [5,2,2,2] => [2,2,2,2,1,1,1] => [7,4] => 4
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,0] => [5,5,5,1] => [6,4,1,1,1,1,1,1] => [8,2,2,2,1,1] => 8
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [7,5,3,1] => [4,3,2,1,1,1,1,1,1,1] => [10,3,2,1] => 6
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,0] => [6,5,3,1] => [3,3,1,1,1,1,1,1,1,1,1] => [11,2,2] => 4
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1] => [13] => 0
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0] => [6,3,3,1] => [4,2,1,1,1,1,1,1,1] => [9,2,1,1] => 4
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3,1] => [3,1,1,1,1,1,1,1,1] => [9,1,1] => 2
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3,1] => [2,2,2,2,1,1] => [6,4] => 4
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0] => [7,5,2,1] => [4,4,2,1,1,1,1,1] => [8,3,2,2] => 7
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0] => [6,5,2,1] => [4,3,2,1,1,1,1,1] => [8,3,2,1] => 6
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => [12] => 0
[1,1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0] => [4,4,2,1] => [2,1,1,1,1,1,1,1,1,1] => [10,1] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0] => [6,3,2,1] => [5,1,1,1,1,1,1,1] => [8,1,1,1,1] => 4
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1] => [1,1,1,1,1,1,1,1,1,1,1] => [11] => 0
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1] => [1,1,1,1,1,1,1,1,1,1] => [10] => 0
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2,1] => [2,2,2,1,1,1] => [6,3] => 3
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2,1] => [2,2,1,1,1,1,1] => [7,2] => 2
[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] => [4,3,1] => 4
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1] => [3,2,2] => [3,3,1] => 4
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0] => [7,6,1,1] => [4,3,2,2,2,2] => [6,6,2,1] => 9
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1,1] => [4,3,2,2,1,1] => [6,4,2,1] => 7
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1] => [2,1,1,1,1,1,1,1] => [8,1] => 1
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1] => [3,2,1,1,1] => [5,2,1] => 3
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,1] => [3,1,1,1,1,1] => [6,1,1] => 2
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1] => [4,1,1,1] => [4,1,1,1] => 3
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1] => [4,2] => [2,2,1,1] => 4
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1] => [5,3,2] => [3,3,2,1,1] => 7
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1] => [5,2,2] => [3,3,1,1,1] => 6
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1] => [2,2,2,2] => [4,4] => 4
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1] => [2,2,2,1] => [4,3] => 3
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1] => [4,1,1] => [3,1,1,1] => 3
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1] => [4,1] => [2,1,1,1] => 3
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1] => [4] => [1,1,1,1] => 3
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0] => [6,6,5] => [5,2,2,2,2,2,2] => [7,7,1,1,1] => 10
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0] => [6,5,5] => [6,2,2,2,2,1,1] => [7,5,1,1,1,1] => 9
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => [5,5,5] => [6,3,2,2,1,1] => [6,4,2,1,1,1] => 9
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,0] => [7,6,4] => [2,2,2,2,2,2,2,2,1] => [9,8] => 8
[1,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0,0] => [5,4,4] => [5,2,2,1,1,1,1] => [7,3,1,1,1] => 6
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0] => [4,4,4] => [5,3,1,1,1,1] => [6,2,2,1,1] => 6
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => [7,5,3] => [4,2,2,2,2,1,1,1] => [8,5,1,1] => 7
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3] => [2,2,2,1,1,1,1,1,1] => [9,3] => 3
[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0] => [4,4,3] => [3,3,1,1,1,1,1] => [7,2,2] => 4
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0] => [6,3,3] => [3,3,2,1,1,1,1] => [7,3,2] => 5
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3] => [4,1,1,1,1,1,1] => [7,1,1,1] => 3
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3] => [3,2,2,1,1] => [5,3,1] => 4
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [6,4,2] => [3,2,2,1,1,1,1,1] => [8,3,1] => 4
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2] => [2,2,1,1,1,1,1,1,1] => [9,2] => 2
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0] => [4,4,2] => [3,1,1,1,1,1,1,1] => [8,1,1] => 2
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2] => [2,1,1,1,1,1,1,1,1] => [9,1] => 1
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2] => [1,1,1,1,1,1,1,1,1] => [9] => 0
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2] => [2,2,1,1,1,1] => [6,2] => 2
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0] => [7,2,2] => [4,3,2,1,1] => [5,3,2,1] => 6
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2] => [2,1,1,1,1,1,1] => [7,1] => 1
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2] => [3,1,1,1,1] => [5,1,1] => 2
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2] => [2,2,2] => [3,3] => 3
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0] => [7,6,1] => [3,3,3,2,2,1] => [6,5,3] => 8
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0] => [6,6,1] => [5,3,2,2,1] => [5,4,2,1,1] => 8
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1] => [3,2,2,2,2,1] => [6,5,1] => 6
[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1] => [3,3,1,1,1,1] => [6,2,2] => 4
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1] => [4,1,1,1,1,1] => [6,1,1,1] => 3
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1] => [4,2,1,1,1,1] => [6,2,1,1] => 4
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1] => [3,1,1,1,1,1,1] => [7,1,1] => 2
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1] => [1,1,1,1,1,1,1,1] => [8] => 0
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1] => [2,1,1,1,1,1] => [6,1] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1] => [4,3,1,1,1] => [5,2,2,1] => 5
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1] => [4,2,1,1,1] => [5,2,1,1] => 4
[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] => [5,1,1,1] => 3
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1] => [1,1,1,1,1,1,1] => [7] => 0
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1] => [1,1,1,1,1,1] => [6] => 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] => [3,2] => 2
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1] => [4,3,2] => [3,3,2,1] => 6
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1] => [4,2,2] => [3,3,1,1] => 5
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1] => [2,2,1,1] => [4,2] => 2
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1] => [2,1,1,1] => [4,1] => 1
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1] => [3,1] => [2,1,1] => 2
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1] => [3] => [1,1,1] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [7,6] => [3,3,3,2,2] => [5,5,3] => 8
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [6,6] => [5,3,2,2] => [4,4,2,1,1] => 8
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [7,5] => [3,3,2,2,2] => [5,5,2] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [5,5] => [4,2,2,2] => [4,4,1,1] => 6
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0] => [4,4] => [4,2,1,1] => [4,2,1,1] => 4
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0] => [7,3] => [4,3,2,1] => [4,3,2,1] => 6
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [4,3] => [2,2,1,1,1] => [5,2] => 2
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [3,3] => [3,1,1,1] => [4,1,1] => 2
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [7,2] => [4,3,1,1] => [4,2,2,1] => 5
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [4,2] => [2,1,1,1,1] => [5,1] => 1
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [3,2] => [1,1,1,1,1] => [5] => 0
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [2,2] => [2,1,1] => [3,1] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [7,1] => [4,3,1] => [3,2,2,1] => 5
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0] => [6,1] => [3,3,1] => [3,2,2] => 4
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0] => [5,1] => [3,2,1] => [3,2,1] => 3
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0] => [4,1] => [3,1,1] => [3,1,1] => 2
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [3,1] => [1,1,1,1] => [4] => 0
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => [1,1,1] => [3] => 0
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1] => [2] => [1,1] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => [4,3] => [2,2,2,1] => 5
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [6] => [3,3] => [2,2,2] => 4
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [5] => [3,2] => [2,2,1] => 3
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [4] => [2,2] => [2,2] => 2
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [3] => [2,1] => [2,1] => 1
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2] => [1,1] => [2] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1] => [1] => [1] => 0
[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] => [2,2,2,2,1,1,1,1,1,1] => [10,4] => 4
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14] => 0
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [1,1] => [2] => [1,1] => 1
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [2] => [1,1] => [2] => 0
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1] => [2] => [1,1] => 1
[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] => [3,2] => 2
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [3,2] => [1,1,1,1,1] => [5] => 0
[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] => [2] => 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] => [8] => [1,1,1,1,1,1,1,1] => 7
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [8] => [4,4] => [2,2,2,2] => 6
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [9] => [5,4] => [2,2,2,2,1] => 7
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [8,1] => [4,4,1] => [3,2,2,2] => 6
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1] => [1] => [1] => 0
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1] => [3] => [1,1,1] => 2
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1] => [4] => [1,1,1,1] => 3
[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] => [5] => [1,1,1,1,1] => 4
[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] => [6] => [1,1,1,1,1,1] => 5
[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] => [7] => [1,1,1,1,1,1,1] => 6
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [1] => [1] => [1] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [7] => [4,3] => [2,2,2,1] => 5
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [6] => [3,3] => [2,2,2] => 4
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [5] => [3,2] => [2,2,1] => 3
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [4] => [2,2] => [2,2] => 2
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [3] => [2,1] => [2,1] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0] => [9,1] => [5,4,1] => [3,2,2,2,1] => 7
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0] => [8,2,1] => [4,4,1,1,1] => [5,2,2,2] => 6
[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] => [8,1,1,1] => [4,1,1,1,1,1,1,1] => 7
[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] => [9,1] => [2,1,1,1,1,1,1,1,1] => 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] => [5,5,5] => [3,3,3,3,3] => 12
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [2,2] => [2,1,1] => [3,1] => 1
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0] => [3,3] => [3,1,1,1] => [4,1,1] => 2
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [3,3,3] => [3,2,2,1,1] => [5,3,1] => 4
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0] => [4,4,4] => [5,3,1,1,1,1] => [6,2,2,1,1] => 6
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [4,4,4,4] => [4,3,2,2,2,2,1] => [7,6,2,1] => 9
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1] => [3,1] => [2,1,1] => 2
[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] => [8,1] => [2,1,1,1,1,1,1,1] => 7
[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] => [9] => [1,1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,1] => [4,4,2] => [3,3,2,2] => 7
[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] => [8,1,1] => [3,1,1,1,1,1,1,1] => 7
[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] => [8,2] => [2,2,1,1,1,1,1,1] => 8
[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] => [10] => [1,1,1,1,1,1,1,1,1,1] => 9
[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] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [15] => 0
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2] => [1,1,1,1,1,1,1,1,1] => [9] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [3,1] => [1,1,1,1] => [4] => 0
[1,1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1,1,1,1,1] => [8,1,1,1,1,1,1] => [7,1,1,1,1,1,1,1] => 7
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0] => [6,6] => [5,3,2,2] => [4,4,2,1,1] => 8
[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1] => [6,1] => [2,1,1,1,1,1] => 5
[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] => [6,1,1] => [3,1,1,1,1,1] => 5
[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] => [6,2,1] => [3,2,1,1,1,1] => 6
[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] => [6,2,2] => [3,3,1,1,1,1] => 7
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [2,1] => [1,1,1] => [3] => 0
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1] => [1,1,1] => [3] => 0
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1] => [1,1,1,1,1,1,1,1,1,1] => [10] => 0
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1] => [1,1,1,1,1,1] => [6] => 0
[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0] => [3] => [2,1] => [2,1] => 1
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0] => [7,2,1] => [4,3,1,1,1] => [5,2,2,1] => 5
[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] => [7,1,1,1] => [4,1,1,1,1,1,1] => 6
[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] => [4,4,1,1,1] => [5,2,2,2] => 6
[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] => [8,1,1,1] => [4,1,1,1,1,1,1,1] => 7
[1,1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [3,3,3,3,2,1] => [3,3,3,2,2,2] => [6,6,3] => 9
[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] => [5,4,4] => [3,3,3,3,1] => 10
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [7,7] => [6,3,3,2] => [4,4,3,1,1,1] => 10
[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] => [5,5,4] => [3,3,3,3,2] => 11
[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] => [8,2,1] => [3,2,1,1,1,1,1,1] => 8
[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] => [7,2,2] => [3,3,1,1,1,1,1] => 8
[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] => [3,3,3,2] => [4,4,3] => 7
[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] => [6,3,2] => [3,3,2,1,1,1] => 8
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,1,1] => [5,3,3] => [3,3,3,1,1] => 8
[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] => [6,1,1,1,1,1,1,1,1,1,1] => [11,1,1,1,1,1] => 5
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0] => [5,3,2,1] => [1,1,1,1,1,1,1,1,1,1,1] => [11] => 0
[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] => [7,1,1,1,1,1,1,1,1,1,1] => [11,1,1,1,1,1,1] => 6
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0] => [5,4,2,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => [12] => 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] => [1,1,1,1,1,1,1,1,1,1,1,1,1] => [13] => 0
[1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0] => [3,1] => [1,1,1,1] => [4] => 0
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0] => [4,2] => [2,1,1,1,1] => [5,1] => 1
[1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,1] => [4,4,3] => [3,3,3,2] => 8
[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] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [16] => 0
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0] => [6,4,3,2,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [16] => 0
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0] => [6,3,2,1] => [5,1,1,1,1,1,1,1] => [8,1,1,1,1] => 4
[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] => [6,1,1,1,1,1,1] => [7,1,1,1,1,1] => 5
[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] => [6,1,1,1,1,1,1,1,1,1,1] => [11,1,1,1,1,1] => 5
[1,1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [4,3,3,2,1] => [3,2,2,2,2,1,1] => [7,5,1] => 6
[1,1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,2,1] => [3,3,3,1,1,1] => [6,3,3] => 6
[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] => [6,1,1,1,1,1,1,1,1,1,1,1] => [12,1,1,1,1,1] => 5
[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1,1] => [5,1,1,1,1,1,1] => [7,1,1,1,1] => 4
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,0] => [8,7,1] => [3,3,3,3,3,1] => [6,5,5] => 10
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0,0] => [7,6,1] => [3,3,3,2,2,1] => [6,5,3] => 8
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0,0] => [6,5,1] => [3,2,2,2,2,1] => [6,5,1] => 6
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0] => [5,4,1] => [3,3,1,1,1,1] => [6,2,2] => 4
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0] => [4,3,1] => [1,1,1,1,1,1,1,1] => [8] => 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] => [3,3] => 3
[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] => [5,1,1,1,1,1,1,1,1,1,1,1] => [12,1,1,1,1] => 4
[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] => [4,4,4] => [3,3,3,3] => 9
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0] => [7,1] => [4,3,1] => [3,2,2,1] => 5
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0] => [6,1] => [3,3,1] => [3,2,2] => 4
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0] => [5,1] => [3,2,1] => [3,2,1] => 3
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0] => [4,1] => [3,1,1] => [3,1,1] => 2
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1] => [4,1] => [2,1,1,1] => 3
[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] => [5,1] => [2,1,1,1,1] => 4
[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] => [7,1] => [2,1,1,1,1,1,1] => 6
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0] => [8,7] => [3,3,3,3,3] => [5,5,5] => 10
[1,1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,1] => [3,1] => [2,1,1] => 2
[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] => [4,3,1] => 4
[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] => [5,5,4,1] => [4,3,3,3,2] => 11
[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] => [7,5,3,1] => [4,3,3,2,2,1,1] => 12
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0] => [7,5,3,1] => [4,3,2,1,1,1,1,1,1,1] => [10,3,2,1] => 6
[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] => [3] => [1,1,1] => 2
[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] => [4,4,4,3] => [4,4,4,3] => 11
[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] => [5,1,1,1,1,1,1,1,1,1,1,1,1] => [13,1,1,1,1] => 4
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0,0,0] => [7,3,2,2,2,1] => [3,3,2,2,2,2,2,1] => [8,7,2] => 9
[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] => [4,4,2,1,1,1,1] => [7,3,2,2] => 7
[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] => [4,4,3,3] => [4,4,4,2] => 10
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1] => [2,1,1,1] => [4,1] => 1
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0,0] => [8,3,2,1] => [4,4,1,1,1,1,1,1] => [8,2,2,2] => 6
[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] => [8,1,1,1,1,1] => [6,1,1,1,1,1,1,1] => 7
[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] => [4,4,4,3,1] => [5,4,4,3] => 11
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1,1] => [4,2] => [2,2,1,1] => 4
[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1] => [4,1,1,1] => [4,1,1,1] => 3
[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0] => [2,2] => [2,1,1] => [3,1] => 1
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,4,3,2,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [15] => 0
[1,1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [3,2,2,2,1,1,1] => [7,4,1] => [3,2,2,2,1,1,1] => 9
[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] => [7,4,1,1] => [4,2,2,2,1,1,1] => 9
[1,1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [4,3,3,3,2,1] => [3,3,3,2,2,2,1] => [7,6,3] => 9
[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] => [4,4,3,1,1,1] => [6,3,3,2] => 8
[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] => [5,5,4,1,1,1] => [6,3,3,3,2] => 11
[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] => [7,1,1,1,1,1,1,1,1,1,1] => [11,1,1,1,1,1,1] => 6
[1,1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0] => [3,3] => [3,1,1,1] => [4,1,1] => 2
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0] => [3] => [2,1] => [2,1] => 1
[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,1] => [2] => [1,1] => 1
[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] => [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [15,1] => 1
[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] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [17] => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0,0] => [8,7,1,1] => [4,3,3,3,2,2] => [6,6,4,1] => 11
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0,0] => [8,1] => [4,4,1] => [3,2,2,2] => 6
[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] => [4,4,2,2,2,2] => [6,6,2,2] => 10
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0,0] => [7,1] => [4,3,1] => [3,2,2,1] => 5
[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] => [2,2,2,2,2,2,2,1] => [8,7] => 7
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0,0] => [6,1] => [3,3,1] => [3,2,2] => 4
[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] => [7,2,2,1,1,1] => [6,3,1,1,1,1,1] => 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] => [3,2,1] => [3,2,1] => 3
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0] => [4,1] => [3,1,1] => [3,1,1] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0] => [5,5] => [4,2,2,2] => [4,4,1,1] => 6
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0] => [4,4] => [4,2,1,1] => [4,2,1,1] => 4
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0] => [5,3,1] => [3,1,1,1,1,1,1] => [7,1,1] => 2
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,1] => [3,2,2] => [3,3,1] => 4
[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0] => [3,3,2] => [2,2,1,1,1,1] => [6,2] => 2
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Description
The size of a partition minus its first part.
This is the number of boxes in its diagram that are not in the first row.
This is the number of boxes in its diagram that are not in the first row.
Map
to partition
Description
The cut-out partition of a Dyck path.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ is the number of down-steps before the $(n+1-i)$-th up-step of $D$.
This map is a bijection between Dyck paths of size $n$ and partitions inside the staircase partition $(n-1,\ldots,2,1)$.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ is the number of down-steps before the $(n+1-i)$-th up-step of $D$.
This map is a bijection between Dyck paths of size $n$ and partitions inside the staircase partition $(n-1,\ldots,2,1)$.
Map
conjugate
Description
Return the conjugate partition of the partition.
The conjugate partition of the partition $\lambda$ of $n$ is the partition $\lambda^*$ whose Ferrers diagram is obtained from the diagram of $\lambda$ by interchanging rows with columns.
This is also called the associated partition or the transpose in the literature.
The conjugate partition of the partition $\lambda$ of $n$ is the partition $\lambda^*$ whose Ferrers diagram is obtained from the diagram of $\lambda$ by interchanging rows with columns.
This is also called the associated partition or the transpose in the literature.
Map
Loehr-Warrington inverse
Description
Return a partition whose length is the diagonal inversion number of the preimage.
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