Identifier
-
Mp00100:
Dyck paths
—touch composition⟶
Integer compositions
Mp00040: Integer compositions —to partition⟶ Integer partitions
St001279: Integer partitions ⟶ ℤ
Values
[1,0] => [1] => [1] => 0
[1,0,1,0] => [1,1] => [1,1] => 0
[1,1,0,0] => [2] => [2] => 2
[1,0,1,0,1,0] => [1,1,1] => [1,1,1] => 0
[1,0,1,1,0,0] => [1,2] => [2,1] => 2
[1,1,0,0,1,0] => [2,1] => [2,1] => 2
[1,1,0,1,0,0] => [3] => [3] => 3
[1,1,1,0,0,0] => [3] => [3] => 3
[1,0,1,0,1,0,1,0] => [1,1,1,1] => [1,1,1,1] => 0
[1,0,1,0,1,1,0,0] => [1,1,2] => [2,1,1] => 2
[1,0,1,1,0,0,1,0] => [1,2,1] => [2,1,1] => 2
[1,0,1,1,0,1,0,0] => [1,3] => [3,1] => 3
[1,0,1,1,1,0,0,0] => [1,3] => [3,1] => 3
[1,1,0,0,1,0,1,0] => [2,1,1] => [2,1,1] => 2
[1,1,0,0,1,1,0,0] => [2,2] => [2,2] => 4
[1,1,0,1,0,0,1,0] => [3,1] => [3,1] => 3
[1,1,0,1,0,1,0,0] => [4] => [4] => 4
[1,1,0,1,1,0,0,0] => [4] => [4] => 4
[1,1,1,0,0,0,1,0] => [3,1] => [3,1] => 3
[1,1,1,0,0,1,0,0] => [4] => [4] => 4
[1,1,1,0,1,0,0,0] => [4] => [4] => 4
[1,1,1,1,0,0,0,0] => [4] => [4] => 4
[1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1] => [1,1,1,1,1] => 0
[1,0,1,0,1,0,1,1,0,0] => [1,1,1,2] => [2,1,1,1] => 2
[1,0,1,0,1,1,0,0,1,0] => [1,1,2,1] => [2,1,1,1] => 2
[1,0,1,0,1,1,0,1,0,0] => [1,1,3] => [3,1,1] => 3
[1,0,1,0,1,1,1,0,0,0] => [1,1,3] => [3,1,1] => 3
[1,0,1,1,0,0,1,0,1,0] => [1,2,1,1] => [2,1,1,1] => 2
[1,0,1,1,0,0,1,1,0,0] => [1,2,2] => [2,2,1] => 4
[1,0,1,1,0,1,0,0,1,0] => [1,3,1] => [3,1,1] => 3
[1,0,1,1,0,1,0,1,0,0] => [1,4] => [4,1] => 4
[1,0,1,1,0,1,1,0,0,0] => [1,4] => [4,1] => 4
[1,0,1,1,1,0,0,0,1,0] => [1,3,1] => [3,1,1] => 3
[1,0,1,1,1,0,0,1,0,0] => [1,4] => [4,1] => 4
[1,0,1,1,1,0,1,0,0,0] => [1,4] => [4,1] => 4
[1,0,1,1,1,1,0,0,0,0] => [1,4] => [4,1] => 4
[1,1,0,0,1,0,1,0,1,0] => [2,1,1,1] => [2,1,1,1] => 2
[1,1,0,0,1,0,1,1,0,0] => [2,1,2] => [2,2,1] => 4
[1,1,0,0,1,1,0,0,1,0] => [2,2,1] => [2,2,1] => 4
[1,1,0,0,1,1,0,1,0,0] => [2,3] => [3,2] => 5
[1,1,0,0,1,1,1,0,0,0] => [2,3] => [3,2] => 5
[1,1,0,1,0,0,1,0,1,0] => [3,1,1] => [3,1,1] => 3
[1,1,0,1,0,0,1,1,0,0] => [3,2] => [3,2] => 5
[1,1,0,1,0,1,0,0,1,0] => [4,1] => [4,1] => 4
[1,1,0,1,0,1,0,1,0,0] => [5] => [5] => 5
[1,1,0,1,0,1,1,0,0,0] => [5] => [5] => 5
[1,1,0,1,1,0,0,0,1,0] => [4,1] => [4,1] => 4
[1,1,0,1,1,0,0,1,0,0] => [5] => [5] => 5
[1,1,0,1,1,0,1,0,0,0] => [5] => [5] => 5
[1,1,0,1,1,1,0,0,0,0] => [5] => [5] => 5
[1,1,1,0,0,0,1,0,1,0] => [3,1,1] => [3,1,1] => 3
[1,1,1,0,0,0,1,1,0,0] => [3,2] => [3,2] => 5
[1,1,1,0,0,1,0,0,1,0] => [4,1] => [4,1] => 4
[1,1,1,0,0,1,0,1,0,0] => [5] => [5] => 5
[1,1,1,0,0,1,1,0,0,0] => [5] => [5] => 5
[1,1,1,0,1,0,0,0,1,0] => [4,1] => [4,1] => 4
[1,1,1,0,1,0,0,1,0,0] => [5] => [5] => 5
[1,1,1,0,1,0,1,0,0,0] => [5] => [5] => 5
[1,1,1,0,1,1,0,0,0,0] => [5] => [5] => 5
[1,1,1,1,0,0,0,0,1,0] => [4,1] => [4,1] => 4
[1,1,1,1,0,0,0,1,0,0] => [5] => [5] => 5
[1,1,1,1,0,0,1,0,0,0] => [5] => [5] => 5
[1,1,1,1,0,1,0,0,0,0] => [5] => [5] => 5
[1,1,1,1,1,0,0,0,0,0] => [5] => [5] => 5
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,2] => [2,1,1,1,1] => 2
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,2,1] => [2,1,1,1,1] => 2
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,3] => [3,1,1,1] => 3
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,3] => [3,1,1,1] => 3
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,2,1,1] => [2,1,1,1,1] => 2
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,2,2] => [2,2,1,1] => 4
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,3,1] => [3,1,1,1] => 3
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,4] => [4,1,1] => 4
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,4] => [4,1,1] => 4
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,3,1] => [3,1,1,1] => 3
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,4] => [4,1,1] => 4
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,4] => [4,1,1] => 4
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,4] => [4,1,1] => 4
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,1,1,1] => [2,1,1,1,1] => 2
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,1,2] => [2,2,1,1] => 4
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,1] => [2,2,1,1] => 4
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3] => [3,2,1] => 5
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3] => [3,2,1] => 5
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,1,1] => [3,1,1,1] => 3
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,2] => [3,2,1] => 5
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,4,1] => [4,1,1] => 4
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,5] => [5,1] => 5
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,5] => [5,1] => 5
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,4,1] => [4,1,1] => 4
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,5] => [5,1] => 5
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,5] => [5,1] => 5
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,5] => [5,1] => 5
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,3,1,1] => [3,1,1,1] => 3
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2] => [3,2,1] => 5
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,1] => [4,1,1] => 4
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,5] => [5,1] => 5
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,5] => [5,1] => 5
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,1] => [4,1,1] => 4
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,5] => [5,1] => 5
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,5] => [5,1] => 5
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,5] => [5,1] => 5
>>> Load all 5234 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [1,4,1] => [4,1,1] => 4
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5] => [5,1] => 5
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5] => [5,1] => 5
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5] => [5,1] => 5
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,5] => [5,1] => 5
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1] => [2,1,1,1,1] => 2
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,2] => [2,2,1,1] => 4
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,2,1] => [2,2,1,1] => 4
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3] => [3,2,1] => 5
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3] => [3,2,1] => 5
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,2,1,1] => [2,2,1,1] => 4
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2] => [2,2,2] => 6
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1] => [3,2,1] => 5
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,4] => [4,2] => 6
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,4] => [4,2] => 6
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1] => [3,2,1] => 5
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,4] => [4,2] => 6
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,4] => [4,2] => 6
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,4] => [4,2] => 6
[1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1] => [3,1,1,1] => 3
[1,1,0,1,0,0,1,0,1,1,0,0] => [3,1,2] => [3,2,1] => 5
[1,1,0,1,0,0,1,1,0,0,1,0] => [3,2,1] => [3,2,1] => 5
[1,1,0,1,0,0,1,1,0,1,0,0] => [3,3] => [3,3] => 6
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,3] => [3,3] => 6
[1,1,0,1,0,1,0,0,1,0,1,0] => [4,1,1] => [4,1,1] => 4
[1,1,0,1,0,1,0,0,1,1,0,0] => [4,2] => [4,2] => 6
[1,1,0,1,0,1,0,1,0,0,1,0] => [5,1] => [5,1] => 5
[1,1,0,1,0,1,0,1,0,1,0,0] => [6] => [6] => 6
[1,1,0,1,0,1,0,1,1,0,0,0] => [6] => [6] => 6
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,1] => [5,1] => 5
[1,1,0,1,0,1,1,0,0,1,0,0] => [6] => [6] => 6
[1,1,0,1,0,1,1,0,1,0,0,0] => [6] => [6] => 6
[1,1,0,1,0,1,1,1,0,0,0,0] => [6] => [6] => 6
[1,1,0,1,1,0,0,0,1,0,1,0] => [4,1,1] => [4,1,1] => 4
[1,1,0,1,1,0,0,0,1,1,0,0] => [4,2] => [4,2] => 6
[1,1,0,1,1,0,0,1,0,0,1,0] => [5,1] => [5,1] => 5
[1,1,0,1,1,0,0,1,0,1,0,0] => [6] => [6] => 6
[1,1,0,1,1,0,0,1,1,0,0,0] => [6] => [6] => 6
[1,1,0,1,1,0,1,0,0,0,1,0] => [5,1] => [5,1] => 5
[1,1,0,1,1,0,1,0,0,1,0,0] => [6] => [6] => 6
[1,1,0,1,1,0,1,0,1,0,0,0] => [6] => [6] => 6
[1,1,0,1,1,0,1,1,0,0,0,0] => [6] => [6] => 6
[1,1,0,1,1,1,0,0,0,0,1,0] => [5,1] => [5,1] => 5
[1,1,0,1,1,1,0,0,0,1,0,0] => [6] => [6] => 6
[1,1,0,1,1,1,0,0,1,0,0,0] => [6] => [6] => 6
[1,1,0,1,1,1,0,1,0,0,0,0] => [6] => [6] => 6
[1,1,0,1,1,1,1,0,0,0,0,0] => [6] => [6] => 6
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1] => [3,1,1,1] => 3
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2] => [3,2,1] => 5
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1] => [3,2,1] => 5
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,3] => [3,3] => 6
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,3] => [3,3] => 6
[1,1,1,0,0,1,0,0,1,0,1,0] => [4,1,1] => [4,1,1] => 4
[1,1,1,0,0,1,0,0,1,1,0,0] => [4,2] => [4,2] => 6
[1,1,1,0,0,1,0,1,0,0,1,0] => [5,1] => [5,1] => 5
[1,1,1,0,0,1,0,1,0,1,0,0] => [6] => [6] => 6
[1,1,1,0,0,1,0,1,1,0,0,0] => [6] => [6] => 6
[1,1,1,0,0,1,1,0,0,0,1,0] => [5,1] => [5,1] => 5
[1,1,1,0,0,1,1,0,0,1,0,0] => [6] => [6] => 6
[1,1,1,0,0,1,1,0,1,0,0,0] => [6] => [6] => 6
[1,1,1,0,0,1,1,1,0,0,0,0] => [6] => [6] => 6
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,1] => [4,1,1] => 4
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,2] => [4,2] => 6
[1,1,1,0,1,0,0,1,0,0,1,0] => [5,1] => [5,1] => 5
[1,1,1,0,1,0,0,1,0,1,0,0] => [6] => [6] => 6
[1,1,1,0,1,0,0,1,1,0,0,0] => [6] => [6] => 6
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,1] => [5,1] => 5
[1,1,1,0,1,0,1,0,0,1,0,0] => [6] => [6] => 6
[1,1,1,0,1,0,1,0,1,0,0,0] => [6] => [6] => 6
[1,1,1,0,1,0,1,1,0,0,0,0] => [6] => [6] => 6
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,1] => [5,1] => 5
[1,1,1,0,1,1,0,0,0,1,0,0] => [6] => [6] => 6
[1,1,1,0,1,1,0,0,1,0,0,0] => [6] => [6] => 6
[1,1,1,0,1,1,0,1,0,0,0,0] => [6] => [6] => 6
[1,1,1,0,1,1,1,0,0,0,0,0] => [6] => [6] => 6
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,1,1] => [4,1,1] => 4
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,2] => [4,2] => 6
[1,1,1,1,0,0,0,1,0,0,1,0] => [5,1] => [5,1] => 5
[1,1,1,1,0,0,0,1,0,1,0,0] => [6] => [6] => 6
[1,1,1,1,0,0,0,1,1,0,0,0] => [6] => [6] => 6
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,1] => [5,1] => 5
[1,1,1,1,0,0,1,0,0,1,0,0] => [6] => [6] => 6
[1,1,1,1,0,0,1,0,1,0,0,0] => [6] => [6] => 6
[1,1,1,1,0,0,1,1,0,0,0,0] => [6] => [6] => 6
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => [5,1] => 5
[1,1,1,1,0,1,0,0,0,1,0,0] => [6] => [6] => 6
[1,1,1,1,0,1,0,0,1,0,0,0] => [6] => [6] => 6
[1,1,1,1,0,1,0,1,0,0,0,0] => [6] => [6] => 6
[1,1,1,1,0,1,1,0,0,0,0,0] => [6] => [6] => 6
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,1] => [5,1] => 5
[1,1,1,1,1,0,0,0,0,1,0,0] => [6] => [6] => 6
[1,1,1,1,1,0,0,0,1,0,0,0] => [6] => [6] => 6
[1,1,1,1,1,0,0,1,0,0,0,0] => [6] => [6] => 6
[1,1,1,1,1,0,1,0,0,0,0,0] => [6] => [6] => 6
[1,1,1,1,1,1,0,0,0,0,0,0] => [6] => [6] => 6
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,2] => [2,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,2,1] => [2,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,3] => [3,1,1,1,1] => 3
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,3] => [3,1,1,1,1] => 3
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,2,1,1] => [2,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,2,2] => [2,2,1,1,1] => 4
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,3,1] => [3,1,1,1,1] => 3
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,4] => [4,1,1,1] => 4
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,4] => [4,1,1,1] => 4
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,3,1] => [3,1,1,1,1] => 3
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,4] => [4,1,1,1] => 4
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,4] => [4,1,1,1] => 4
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,4] => [4,1,1,1] => 4
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,2,1,1,1] => [2,1,1,1,1,1] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,2,1,2] => [2,2,1,1,1] => 4
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,2,2,1] => [2,2,1,1,1] => 4
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,2,3] => [3,2,1,1] => 5
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,2,3] => [3,2,1,1] => 5
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,3,1,1] => [3,1,1,1,1] => 3
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,3,2] => [3,2,1,1] => 5
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,4,1] => [4,1,1,1] => 4
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,5] => [5,1,1] => 5
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,5] => [5,1,1] => 5
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,4,1] => [4,1,1,1] => 4
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,5] => [5,1,1] => 5
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,5] => [5,1,1] => 5
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,5] => [5,1,1] => 5
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,3,1,1] => [3,1,1,1,1] => 3
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,3,2] => [3,2,1,1] => 5
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,4,1] => [4,1,1,1] => 4
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,5] => [5,1,1] => 5
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,5] => [5,1,1] => 5
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,4,1] => [4,1,1,1] => 4
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,5] => [5,1,1] => 5
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,5] => [5,1,1] => 5
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,5] => [5,1,1] => 5
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,4,1] => [4,1,1,1] => 4
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,5] => [5,1,1] => 5
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,5] => [5,1,1] => 5
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,5] => [5,1,1] => 5
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,5] => [5,1,1] => 5
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1] => [2,1,1,1,1,1] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,1,1,2] => [2,2,1,1,1] => 4
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,1,2,1] => [2,2,1,1,1] => 4
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,1,3] => [3,2,1,1] => 5
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,1,3] => [3,2,1,1] => 5
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,2,1,1] => [2,2,1,1,1] => 4
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,2,2] => [2,2,2,1] => 6
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,3,1] => [3,2,1,1] => 5
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4] => [4,2,1] => 6
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,4] => [4,2,1] => 6
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,3,1] => [3,2,1,1] => 5
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,4] => [4,2,1] => 6
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,4] => [4,2,1] => 6
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4] => [4,2,1] => 6
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,1,1,1] => [3,1,1,1,1] => 3
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,1,2] => [3,2,1,1] => 5
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,2,1] => [3,2,1,1] => 5
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,3] => [3,3,1] => 6
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,3] => [3,3,1] => 6
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,4,1,1] => [4,1,1,1] => 4
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,4,2] => [4,2,1] => 6
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,5,1] => [5,1,1] => 5
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,6] => [6,1] => 6
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,6] => [6,1] => 6
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,5,1] => [5,1,1] => 5
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,6] => [6,1] => 6
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,6] => [6,1] => 6
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,6] => [6,1] => 6
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,4,1,1] => [4,1,1,1] => 4
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,4,2] => [4,2,1] => 6
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,5,1] => [5,1,1] => 5
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,6] => [6,1] => 6
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,6] => [6,1] => 6
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,5,1] => [5,1,1] => 5
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,6] => [6,1] => 6
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,6] => [6,1] => 6
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,6] => [6,1] => 6
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,5,1] => [5,1,1] => 5
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,6] => [6,1] => 6
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,6] => [6,1] => 6
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,6] => [6,1] => 6
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,6] => [6,1] => 6
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,3,1,1,1] => [3,1,1,1,1] => 3
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,3,1,2] => [3,2,1,1] => 5
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,3,2,1] => [3,2,1,1] => 5
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,3,3] => [3,3,1] => 6
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,3,3] => [3,3,1] => 6
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,1,1] => [4,1,1,1] => 4
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2] => [4,2,1] => 6
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,5,1] => [5,1,1] => 5
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,6] => [6,1] => 6
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,6] => [6,1] => 6
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,5,1] => [5,1,1] => 5
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,6] => [6,1] => 6
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,6] => [6,1] => 6
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,6] => [6,1] => 6
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,1,1] => [4,1,1,1] => 4
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,2] => [4,2,1] => 6
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,5,1] => [5,1,1] => 5
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,6] => [6,1] => 6
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,6] => [6,1] => 6
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,5,1] => [5,1,1] => 5
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,6] => [6,1] => 6
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,6] => [6,1] => 6
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,6] => [6,1] => 6
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,5,1] => [5,1,1] => 5
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,6] => [6,1] => 6
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,6] => [6,1] => 6
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,6] => [6,1] => 6
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,6] => [6,1] => 6
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,4,1,1] => [4,1,1,1] => 4
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,4,2] => [4,2,1] => 6
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,1] => [5,1,1] => 5
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,6] => [6,1] => 6
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,6] => [6,1] => 6
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,1] => [5,1,1] => 5
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,6] => [6,1] => 6
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,6] => [6,1] => 6
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,6] => [6,1] => 6
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,5,1] => [5,1,1] => 5
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,6] => [6,1] => 6
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,6] => [6,1] => 6
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,6] => [6,1] => 6
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,6] => [6,1] => 6
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,5,1] => [5,1,1] => 5
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6] => [6,1] => 6
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,6] => [6,1] => 6
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6] => [6,1] => 6
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,6] => [6,1] => 6
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,6] => [6,1] => 6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1] => [2,1,1,1,1,1] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,2] => [2,2,1,1,1] => 4
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,2,1] => [2,2,1,1,1] => 4
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,3] => [3,2,1,1] => 5
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,3] => [3,2,1,1] => 5
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,2,1,1] => [2,2,1,1,1] => 4
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,2,2] => [2,2,2,1] => 6
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,1] => [3,2,1,1] => 5
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,4] => [4,2,1] => 6
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,4] => [4,2,1] => 6
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,1] => [3,2,1,1] => 5
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,4] => [4,2,1] => 6
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,4] => [4,2,1] => 6
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,4] => [4,2,1] => 6
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,2,1,1,1] => [2,2,1,1,1] => 4
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,2,1,2] => [2,2,2,1] => 6
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,2,2,1] => [2,2,2,1] => 6
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,2,3] => [3,2,2] => 7
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,2,3] => [3,2,2] => 7
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,1] => [3,2,1,1] => 5
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,3,2] => [3,2,2] => 7
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,4,1] => [4,2,1] => 6
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,5] => [5,2] => 7
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,5] => [5,2] => 7
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,4,1] => [4,2,1] => 6
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,5] => [5,2] => 7
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,5] => [5,2] => 7
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,5] => [5,2] => 7
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,1] => [3,2,1,1] => 5
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,2] => [3,2,2] => 7
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,4,1] => [4,2,1] => 6
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,5] => [5,2] => 7
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,5] => [5,2] => 7
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,4,1] => [4,2,1] => 6
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,5] => [5,2] => 7
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,5] => [5,2] => 7
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,5] => [5,2] => 7
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,4,1] => [4,2,1] => 6
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,5] => [5,2] => 7
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,5] => [5,2] => 7
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,5] => [5,2] => 7
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,5] => [5,2] => 7
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1] => [3,1,1,1,1] => 3
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,1,1,2] => [3,2,1,1] => 5
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,2,1] => [3,2,1,1] => 5
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [3,1,3] => [3,3,1] => 6
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,1,3] => [3,3,1] => 6
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,2,1,1] => [3,2,1,1] => 5
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,2] => [3,2,2] => 7
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [3,3,1] => [3,3,1] => 6
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,4] => [4,3] => 7
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [3,4] => [4,3] => 7
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,3,1] => [3,3,1] => 6
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,4] => [4,3] => 7
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [3,4] => [4,3] => 7
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,4] => [4,3] => 7
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [4,1,1,1] => [4,1,1,1] => 4
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [4,1,2] => [4,2,1] => 6
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [4,2,1] => [4,2,1] => 6
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [4,3] => [4,3] => 7
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [4,3] => [4,3] => 7
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [5,1,1] => [5,1,1] => 5
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [5,2] => [5,2] => 7
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [6,1] => [6,1] => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7] => [7] => 7
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7] => [7] => 7
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [6,1] => [6,1] => 6
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [7] => [7] => 7
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [7] => [7] => 7
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [7] => [7] => 7
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [5,1,1] => [5,1,1] => 5
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [5,2] => [5,2] => 7
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [6,1] => [6,1] => 6
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7] => [7] => 7
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [7] => [7] => 7
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [6,1] => [6,1] => 6
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [7] => [7] => 7
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [7] => [7] => 7
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [7] => [7] => 7
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [6,1] => [6,1] => 6
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7] => [7] => 7
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [7] => [7] => 7
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [7] => [7] => 7
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [7] => [7] => 7
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [4,1,1,1] => [4,1,1,1] => 4
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [4,1,2] => [4,2,1] => 6
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [4,2,1] => [4,2,1] => 6
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [4,3] => [4,3] => 7
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,3] => [4,3] => 7
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [5,1,1] => [5,1,1] => 5
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [5,2] => [5,2] => 7
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [6,1] => [6,1] => 6
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7] => [7] => 7
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [7] => [7] => 7
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [6,1] => [6,1] => 6
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7] => [7] => 7
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [7] => [7] => 7
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [7] => [7] => 7
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [5,1,1] => [5,1,1] => 5
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [5,2] => [5,2] => 7
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [6,1] => [6,1] => 6
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7] => [7] => 7
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [7] => [7] => 7
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [6,1] => [6,1] => 6
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7] => [7] => 7
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [7] => [7] => 7
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [7] => [7] => 7
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [6,1] => [6,1] => 6
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [7] => [7] => 7
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [7] => [7] => 7
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [7] => [7] => 7
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [7] => [7] => 7
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [5,1,1] => [5,1,1] => 5
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [5,2] => [5,2] => 7
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [6,1] => [6,1] => 6
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [7] => [7] => 7
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [7] => [7] => 7
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [6,1] => [6,1] => 6
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [7] => [7] => 7
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [7] => [7] => 7
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [7] => [7] => 7
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [6,1] => [6,1] => 6
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [7] => [7] => 7
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [7] => [7] => 7
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [7] => [7] => 7
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [7] => [7] => 7
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [6,1] => [6,1] => 6
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [7] => [7] => 7
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [7] => [7] => 7
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [7] => [7] => 7
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [7] => [7] => 7
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [7] => [7] => 7
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1] => [3,1,1,1,1] => 3
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,1,2] => [3,2,1,1] => 5
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,1,2,1] => [3,2,1,1] => 5
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,3] => [3,3,1] => 6
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,3] => [3,3,1] => 6
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,1] => [3,2,1,1] => 5
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,2] => [3,2,2] => 7
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,3,1] => [3,3,1] => 6
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,4] => [4,3] => 7
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,4] => [4,3] => 7
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,3,1] => [3,3,1] => 6
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,4] => [4,3] => 7
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,4] => [4,3] => 7
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,4] => [4,3] => 7
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [4,1,1,1] => [4,1,1,1] => 4
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [4,1,2] => [4,2,1] => 6
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [4,2,1] => [4,2,1] => 6
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [4,3] => [4,3] => 7
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,3] => [4,3] => 7
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [5,1,1] => [5,1,1] => 5
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [5,2] => [5,2] => 7
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [6,1] => [6,1] => 6
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7] => [7] => 7
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [7] => [7] => 7
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [6,1] => [6,1] => 6
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [7] => [7] => 7
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [7] => [7] => 7
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [7] => [7] => 7
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [5,1,1] => [5,1,1] => 5
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [5,2] => [5,2] => 7
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [6,1] => [6,1] => 6
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [7] => [7] => 7
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [7] => [7] => 7
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [6,1] => [6,1] => 6
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [7] => [7] => 7
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [7] => [7] => 7
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [7] => [7] => 7
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [6,1] => [6,1] => 6
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [7] => [7] => 7
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [7] => [7] => 7
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [7] => [7] => 7
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [7] => [7] => 7
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,1,1,1] => [4,1,1,1] => 4
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,1,2] => [4,2,1] => 6
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,2,1] => [4,2,1] => 6
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,3] => [4,3] => 7
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,3] => [4,3] => 7
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [5,1,1] => [5,1,1] => 5
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [5,2] => [5,2] => 7
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [6,1] => [6,1] => 6
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7] => [7] => 7
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [7] => [7] => 7
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [6,1] => [6,1] => 6
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [7] => [7] => 7
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [7] => [7] => 7
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [7] => [7] => 7
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [5,1,1] => [5,1,1] => 5
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,2] => [5,2] => 7
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [6,1] => [6,1] => 6
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [7] => [7] => 7
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [7] => [7] => 7
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,1] => [6,1] => 6
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [7] => [7] => 7
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7] => [7] => 7
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [7] => [7] => 7
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,1] => [6,1] => 6
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [7] => [7] => 7
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [7] => [7] => 7
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [7] => [7] => 7
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [7] => [7] => 7
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,1,1] => [5,1,1] => 5
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,2] => [5,2] => 7
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [6,1] => [6,1] => 6
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [7] => [7] => 7
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [7] => [7] => 7
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,1] => [6,1] => 6
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [7] => [7] => 7
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7] => [7] => 7
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7] => [7] => 7
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,1] => [6,1] => 6
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [7] => [7] => 7
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7] => [7] => 7
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7] => [7] => 7
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7] => [7] => 7
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,1] => [6,1] => 6
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [7] => [7] => 7
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [7] => [7] => 7
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [7] => [7] => 7
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [7] => [7] => 7
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [7] => [7] => 7
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,1,1] => [4,1,1,1] => 4
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,1,2] => [4,2,1] => 6
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,2,1] => [4,2,1] => 6
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3] => [4,3] => 7
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3] => [4,3] => 7
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [5,1,1] => [5,1,1] => 5
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [5,2] => [5,2] => 7
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [6,1] => [6,1] => 6
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7] => [7] => 7
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [7] => [7] => 7
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [6,1] => [6,1] => 6
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7] => [7] => 7
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [7] => [7] => 7
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [7] => [7] => 7
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,1,1] => [5,1,1] => 5
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,2] => [5,2] => 7
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [6,1] => [6,1] => 6
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [7] => [7] => 7
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [7] => [7] => 7
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,1] => [6,1] => 6
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [7] => [7] => 7
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [7] => [7] => 7
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [7] => [7] => 7
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,1] => [6,1] => 6
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [7] => [7] => 7
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [7] => [7] => 7
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [7] => [7] => 7
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [7] => [7] => 7
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,1,1] => [5,1,1] => 5
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,2] => [5,2] => 7
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [6,1] => [6,1] => 6
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7] => [7] => 7
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [7] => [7] => 7
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,1] => [6,1] => 6
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7] => [7] => 7
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7] => [7] => 7
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7] => [7] => 7
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,1] => [6,1] => 6
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [7] => [7] => 7
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7] => [7] => 7
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7] => [7] => 7
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7] => [7] => 7
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,1] => [6,1] => 6
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [7] => [7] => 7
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [7] => [7] => 7
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [7] => [7] => 7
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [7] => [7] => 7
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [7] => [7] => 7
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,1,1] => [5,1,1] => 5
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,2] => [5,2] => 7
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,1] => [6,1] => 6
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7] => [7] => 7
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [7] => [7] => 7
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,1] => [6,1] => 6
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [7] => [7] => 7
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [7] => [7] => 7
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [7] => [7] => 7
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,1] => [6,1] => 6
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [7] => [7] => 7
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [7] => [7] => 7
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [7] => [7] => 7
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [7] => [7] => 7
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => [6,1] => 6
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [7] => [7] => 7
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [7] => [7] => 7
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [7] => [7] => 7
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [7] => [7] => 7
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7] => [7] => 7
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,1] => [6,1] => 6
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7] => [7] => 7
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [7] => [7] => 7
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [7] => [7] => 7
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [7] => [7] => 7
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7] => [7] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7] => [7] => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,2] => [2,1,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,2,1] => [2,1,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,3] => [3,1,1,1,1,1] => 3
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,3] => [3,1,1,1,1,1] => 3
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,2,1,1] => [2,1,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,2,2] => [2,2,1,1,1,1] => 4
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,3,1] => [3,1,1,1,1,1] => 3
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,4] => [4,1,1,1,1] => 4
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,4] => [4,1,1,1,1] => 4
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,3,1] => [3,1,1,1,1,1] => 3
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,4] => [4,1,1,1,1] => 4
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,4] => [4,1,1,1,1] => 4
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,4] => [4,1,1,1,1] => 4
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,2,1,1,1] => [2,1,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,2,1,2] => [2,2,1,1,1,1] => 4
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,2,2,1] => [2,2,1,1,1,1] => 4
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,2,3] => [3,2,1,1,1] => 5
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,2,3] => [3,2,1,1,1] => 5
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,3,1,1] => [3,1,1,1,1,1] => 3
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,3,2] => [3,2,1,1,1] => 5
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,4,1] => [4,1,1,1,1] => 4
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,5] => [5,1,1,1] => 5
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,5] => [5,1,1,1] => 5
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,4,1] => [4,1,1,1,1] => 4
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,5] => [5,1,1,1] => 5
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,5] => [5,1,1,1] => 5
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,5] => [5,1,1,1] => 5
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,3,1,1] => [3,1,1,1,1,1] => 3
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,3,2] => [3,2,1,1,1] => 5
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,4,1] => [4,1,1,1,1] => 4
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,5] => [5,1,1,1] => 5
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,5] => [5,1,1,1] => 5
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,4,1] => [4,1,1,1,1] => 4
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,5] => [5,1,1,1] => 5
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,5] => [5,1,1,1] => 5
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,5] => [5,1,1,1] => 5
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,4,1] => [4,1,1,1,1] => 4
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,5] => [5,1,1,1] => 5
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,5] => [5,1,1,1] => 5
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,5] => [5,1,1,1] => 5
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,5] => [5,1,1,1] => 5
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,2,1,1,1,1] => [2,1,1,1,1,1,1] => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,2,1,1,2] => [2,2,1,1,1,1] => 4
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,2,1,2,1] => [2,2,1,1,1,1] => 4
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,2,1,3] => [3,2,1,1,1] => 5
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,2,1,3] => [3,2,1,1,1] => 5
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,2,2,1,1] => [2,2,1,1,1,1] => 4
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,2,2,2] => [2,2,2,1,1] => 6
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,2,3,1] => [3,2,1,1,1] => 5
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,2,4] => [4,2,1,1] => 6
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,2,4] => [4,2,1,1] => 6
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,2,3,1] => [3,2,1,1,1] => 5
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,2,4] => [4,2,1,1] => 6
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,2,4] => [4,2,1,1] => 6
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,2,4] => [4,2,1,1] => 6
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,3,1,1,1] => [3,1,1,1,1,1] => 3
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,3,1,2] => [3,2,1,1,1] => 5
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,3,2,1] => [3,2,1,1,1] => 5
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,3,3] => [3,3,1,1] => 6
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,3,3] => [3,3,1,1] => 6
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,4,1,1] => [4,1,1,1,1] => 4
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,4,2] => [4,2,1,1] => 6
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,5,1] => [5,1,1,1] => 5
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,6] => [6,1,1] => 6
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,6] => [6,1,1] => 6
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,5,1] => [5,1,1,1] => 5
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,6] => [6,1,1] => 6
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,6] => [6,1,1] => 6
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,6] => [6,1,1] => 6
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,4,1,1] => [4,1,1,1,1] => 4
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,4,2] => [4,2,1,1] => 6
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,5,1] => [5,1,1,1] => 5
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,6] => [6,1,1] => 6
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,6] => [6,1,1] => 6
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,5,1] => [5,1,1,1] => 5
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,6] => [6,1,1] => 6
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,6] => [6,1,1] => 6
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,6] => [6,1,1] => 6
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,5,1] => [5,1,1,1] => 5
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,6] => [6,1,1] => 6
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,6] => [6,1,1] => 6
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,6] => [6,1,1] => 6
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,6] => [6,1,1] => 6
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,3,1,1,1] => [3,1,1,1,1,1] => 3
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,3,1,2] => [3,2,1,1,1] => 5
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,3,2,1] => [3,2,1,1,1] => 5
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,3,3] => [3,3,1,1] => 6
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,3,3] => [3,3,1,1] => 6
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,4,1,1] => [4,1,1,1,1] => 4
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,4,2] => [4,2,1,1] => 6
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,5,1] => [5,1,1,1] => 5
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,6] => [6,1,1] => 6
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,6] => [6,1,1] => 6
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,5,1] => [5,1,1,1] => 5
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,6] => [6,1,1] => 6
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,6] => [6,1,1] => 6
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,6] => [6,1,1] => 6
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,4,1,1] => [4,1,1,1,1] => 4
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,4,2] => [4,2,1,1] => 6
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,5,1] => [5,1,1,1] => 5
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,6] => [6,1,1] => 6
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,6] => [6,1,1] => 6
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,5,1] => [5,1,1,1] => 5
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,6] => [6,1,1] => 6
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,6] => [6,1,1] => 6
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,6] => [6,1,1] => 6
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,5,1] => [5,1,1,1] => 5
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,6] => [6,1,1] => 6
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,6] => [6,1,1] => 6
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,6] => [6,1,1] => 6
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,6] => [6,1,1] => 6
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,4,1,1] => [4,1,1,1,1] => 4
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,4,2] => [4,2,1,1] => 6
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,5,1] => [5,1,1,1] => 5
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,6] => [6,1,1] => 6
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,6] => [6,1,1] => 6
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,5,1] => [5,1,1,1] => 5
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,6] => [6,1,1] => 6
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,6] => [6,1,1] => 6
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,6] => [6,1,1] => 6
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,5,1] => [5,1,1,1] => 5
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,6] => [6,1,1] => 6
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,6] => [6,1,1] => 6
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,6] => [6,1,1] => 6
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,6] => [6,1,1] => 6
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,5,1] => [5,1,1,1] => 5
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,6] => [6,1,1] => 6
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,6] => [6,1,1] => 6
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,6] => [6,1,1] => 6
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,6] => [6,1,1] => 6
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,6] => [6,1,1] => 6
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1] => [2,1,1,1,1,1,1] => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,2,1,1,1,2] => [2,2,1,1,1,1] => 4
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,2,1,1,2,1] => [2,2,1,1,1,1] => 4
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,2,1,1,3] => [3,2,1,1,1] => 5
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,2,1,1,3] => [3,2,1,1,1] => 5
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,2,1,2,1,1] => [2,2,1,1,1,1] => 4
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,2,1,2,2] => [2,2,2,1,1] => 6
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,2,1,3,1] => [3,2,1,1,1] => 5
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,2,1,4] => [4,2,1,1] => 6
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,2,1,4] => [4,2,1,1] => 6
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,2,1,3,1] => [3,2,1,1,1] => 5
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,2,1,4] => [4,2,1,1] => 6
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,2,1,4] => [4,2,1,1] => 6
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,2,1,4] => [4,2,1,1] => 6
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,2,2,1,1,1] => [2,2,1,1,1,1] => 4
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,2,2,1,2] => [2,2,2,1,1] => 6
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,2,1] => [2,2,2,1,1] => 6
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,2,2,3] => [3,2,2,1] => 7
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,2,2,3] => [3,2,2,1] => 7
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,1,1] => [3,2,1,1,1] => 5
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,2] => [3,2,2,1] => 7
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,1] => [4,2,1,1] => 6
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,2,5] => [5,2,1] => 7
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,2,5] => [5,2,1] => 7
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,1] => [4,2,1,1] => 6
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,2,5] => [5,2,1] => 7
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,2,5] => [5,2,1] => 7
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,2,5] => [5,2,1] => 7
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,1,1] => [3,2,1,1,1] => 5
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,2] => [3,2,2,1] => 7
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,2,4,1] => [4,2,1,1] => 6
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5] => [5,2,1] => 7
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5] => [5,2,1] => 7
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,2,4,1] => [4,2,1,1] => 6
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,2,5] => [5,2,1] => 7
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,2,5] => [5,2,1] => 7
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5] => [5,2,1] => 7
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,2,4,1] => [4,2,1,1] => 6
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,2,5] => [5,2,1] => 7
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,2,5] => [5,2,1] => 7
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,2,5] => [5,2,1] => 7
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,5] => [5,2,1] => 7
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,1,1,1,1] => [3,1,1,1,1,1] => 3
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,1,1,2] => [3,2,1,1,1] => 5
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,3,1,2,1] => [3,2,1,1,1] => 5
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,1,3] => [3,3,1,1] => 6
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,3,1,3] => [3,3,1,1] => 6
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,1,1] => [3,2,1,1,1] => 5
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,2] => [3,2,2,1] => 7
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,3,1] => [3,3,1,1] => 6
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4] => [4,3,1] => 7
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,3,4] => [4,3,1] => 7
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,3,3,1] => [3,3,1,1] => 6
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,3,4] => [4,3,1] => 7
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,3,4] => [4,3,1] => 7
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4] => [4,3,1] => 7
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,4,1,1,1] => [4,1,1,1,1] => 4
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,4,1,2] => [4,2,1,1] => 6
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,4,2,1] => [4,2,1,1] => 6
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,4,3] => [4,3,1] => 7
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,4,3] => [4,3,1] => 7
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,5,1,1] => [5,1,1,1] => 5
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,5,2] => [5,2,1] => 7
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,6,1] => [6,1,1] => 6
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,6,1] => [6,1,1] => 6
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,5,1,1] => [5,1,1,1] => 5
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,5,2] => [5,2,1] => 7
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,6,1] => [6,1,1] => 6
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,6,1] => [6,1,1] => 6
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,6,1] => [6,1,1] => 6
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,4,1,1,1] => [4,1,1,1,1] => 4
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,4,1,2] => [4,2,1,1] => 6
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,4,2,1] => [4,2,1,1] => 6
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3] => [4,3,1] => 7
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3] => [4,3,1] => 7
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,5,1,1] => [5,1,1,1] => 5
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,5,2] => [5,2,1] => 7
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,6,1] => [6,1,1] => 6
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,6,1] => [6,1,1] => 6
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,5,1,1] => [5,1,1,1] => 5
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,5,2] => [5,2,1] => 7
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,6,1] => [6,1,1] => 6
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,6,1] => [6,1,1] => 6
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,6,1] => [6,1,1] => 6
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,5,1,1] => [5,1,1,1] => 5
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,5,2] => [5,2,1] => 7
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,6,1] => [6,1,1] => 6
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,6,1] => [6,1,1] => 6
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,6,1] => [6,1,1] => 6
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,6,1] => [6,1,1] => 6
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,3,1,1,1,1] => [3,1,1,1,1,1] => 3
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,3,1,1,2] => [3,2,1,1,1] => 5
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,3,1,2,1] => [3,2,1,1,1] => 5
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,3,1,3] => [3,3,1,1] => 6
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,3,1,3] => [3,3,1,1] => 6
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,3,2,1,1] => [3,2,1,1,1] => 5
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,3,2,2] => [3,2,2,1] => 7
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,3,3,1] => [3,3,1,1] => 6
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,3,4] => [4,3,1] => 7
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,3,4] => [4,3,1] => 7
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,3,3,1] => [3,3,1,1] => 6
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,3,4] => [4,3,1] => 7
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,3,4] => [4,3,1] => 7
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,3,4] => [4,3,1] => 7
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,4,1,1,1] => [4,1,1,1,1] => 4
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,4,1,2] => [4,2,1,1] => 6
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,2,1] => [4,2,1,1] => 6
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,4,3] => [4,3,1] => 7
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,4,3] => [4,3,1] => 7
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,5,1,1] => [5,1,1,1] => 5
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,5,2] => [5,2,1] => 7
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,6,1] => [6,1,1] => 6
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,6,1] => [6,1,1] => 6
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,5,1,1] => [5,1,1,1] => 5
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,5,2] => [5,2,1] => 7
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,6,1] => [6,1,1] => 6
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,6,1] => [6,1,1] => 6
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,6,1] => [6,1,1] => 6
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,4,1,1,1] => [4,1,1,1,1] => 4
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,4,1,2] => [4,2,1,1] => 6
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,4,2,1] => [4,2,1,1] => 6
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,4,3] => [4,3,1] => 7
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,4,3] => [4,3,1] => 7
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,5,1,1] => [5,1,1,1] => 5
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,5,2] => [5,2,1] => 7
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,6,1] => [6,1,1] => 6
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,6,1] => [6,1,1] => 6
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,5,1,1] => [5,1,1,1] => 5
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,5,2] => [5,2,1] => 7
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,6,1] => [6,1,1] => 6
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,6,1] => [6,1,1] => 6
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,6,1] => [6,1,1] => 6
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,5,1,1] => [5,1,1,1] => 5
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,5,2] => [5,2,1] => 7
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,6,1] => [6,1,1] => 6
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,6,1] => [6,1,1] => 6
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,6,1] => [6,1,1] => 6
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,6,1] => [6,1,1] => 6
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,4,1,1,1] => [4,1,1,1,1] => 4
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,4,1,2] => [4,2,1,1] => 6
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,4,2,1] => [4,2,1,1] => 6
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,4,3] => [4,3,1] => 7
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,4,3] => [4,3,1] => 7
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,5,1,1] => [5,1,1,1] => 5
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,5,2] => [5,2,1] => 7
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,6,1] => [6,1,1] => 6
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,6,1] => [6,1,1] => 6
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,5,1,1] => [5,1,1,1] => 5
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,5,2] => [5,2,1] => 7
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,6,1] => [6,1,1] => 6
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,6,1] => [6,1,1] => 6
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,6,1] => [6,1,1] => 6
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,5,1,1] => [5,1,1,1] => 5
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,5,2] => [5,2,1] => 7
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,6,1] => [6,1,1] => 6
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,6,1] => [6,1,1] => 6
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,6,1] => [6,1,1] => 6
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,6,1] => [6,1,1] => 6
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,5,1,1] => [5,1,1,1] => 5
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,5,2] => [5,2,1] => 7
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,6,1] => [6,1,1] => 6
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,6,1] => [6,1,1] => 6
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,1] => [6,1,1] => 6
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,6,1] => [6,1,1] => 6
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,6,1] => [6,1,1] => 6
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,7] => [7,1] => 7
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,7] => [7,1] => 7
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,2] => [2,2,1,1,1,1] => 4
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,2,1] => [2,2,1,1,1,1] => 4
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,3] => [3,2,1,1,1] => 5
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,1,3] => [3,2,1,1,1] => 5
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,1,2,1,1] => [2,2,1,1,1,1] => 4
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,1,2,2] => [2,2,2,1,1] => 6
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,1,3,1] => [3,2,1,1,1] => 5
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,1,4] => [4,2,1,1] => 6
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,1,1,4] => [4,2,1,1] => 6
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,1,3,1] => [3,2,1,1,1] => 5
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,1,4] => [4,2,1,1] => 6
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,1,4] => [4,2,1,1] => 6
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,1,4] => [4,2,1,1] => 6
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,2,1,1,1] => [2,2,1,1,1,1] => 4
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,2,1,2] => [2,2,2,1,1] => 6
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,2,2,1] => [2,2,2,1,1] => 6
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,2,3] => [3,2,2,1] => 7
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,2,3] => [3,2,2,1] => 7
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,3,1,1] => [3,2,1,1,1] => 5
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,2] => [3,2,2,1] => 7
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,1] => [4,2,1,1] => 6
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,5] => [5,2,1] => 7
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,1,5] => [5,2,1] => 7
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,1] => [4,2,1,1] => 6
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,1,5] => [5,2,1] => 7
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,1,5] => [5,2,1] => 7
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,1,5] => [5,2,1] => 7
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,1,1] => [3,2,1,1,1] => 5
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,2] => [3,2,2,1] => 7
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,4,1] => [4,2,1,1] => 6
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5] => [5,2,1] => 7
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5] => [5,2,1] => 7
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,4,1] => [4,2,1,1] => 6
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,1,5] => [5,2,1] => 7
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,5] => [5,2,1] => 7
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,1,5] => [5,2,1] => 7
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,1] => [4,2,1,1] => 6
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,1,5] => [5,2,1] => 7
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,5] => [5,2,1] => 7
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,5] => [5,2,1] => 7
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,5] => [5,2,1] => 7
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => [2,2,1,1,1,1] => 4
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,2,1,1,2] => [2,2,2,1,1] => 6
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,2,1,2,1] => [2,2,2,1,1] => 6
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,2,1,3] => [3,2,2,1] => 7
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,2,1,3] => [3,2,2,1] => 7
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,2,2,1,1] => [2,2,2,1,1] => 6
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2] => [2,2,2,2] => 8
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,2,3,1] => [3,2,2,1] => 7
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,2,4] => [4,2,2] => 8
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,2,4] => [4,2,2] => 8
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,2,3,1] => [3,2,2,1] => 7
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,2,4] => [4,2,2] => 8
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,2,4] => [4,2,2] => 8
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,4] => [4,2,2] => 8
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,1,1] => [3,2,1,1,1] => 5
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,2] => [3,2,2,1] => 7
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,2,1] => [3,2,2,1] => 7
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,3] => [3,3,2] => 8
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,3] => [3,3,2] => 8
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,4,1,1] => [4,2,1,1] => 6
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,4,2] => [4,2,2] => 8
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,5,1] => [5,2,1] => 7
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,6] => [6,2] => 8
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,6] => [6,2] => 8
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,5,1] => [5,2,1] => 7
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,6] => [6,2] => 8
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,6] => [6,2] => 8
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,6] => [6,2] => 8
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,1,1] => [4,2,1,1] => 6
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,2] => [4,2,2] => 8
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,5,1] => [5,2,1] => 7
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,6] => [6,2] => 8
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,6] => [6,2] => 8
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,5,1] => [5,2,1] => 7
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,6] => [6,2] => 8
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,6] => [6,2] => 8
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,6] => [6,2] => 8
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,1] => [5,2,1] => 7
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,6] => [6,2] => 8
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,6] => [6,2] => 8
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,6] => [6,2] => 8
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,6] => [6,2] => 8
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,1,1,1] => [3,2,1,1,1] => 5
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,1,2] => [3,2,2,1] => 7
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,2,1] => [3,2,2,1] => 7
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,3,3] => [3,3,2] => 8
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,3] => [3,3,2] => 8
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,4,1,1] => [4,2,1,1] => 6
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,4,2] => [4,2,2] => 8
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,5,1] => [5,2,1] => 7
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,6] => [6,2] => 8
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,6] => [6,2] => 8
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,5,1] => [5,2,1] => 7
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,6] => [6,2] => 8
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,6] => [6,2] => 8
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,6] => [6,2] => 8
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,4,1,1] => [4,2,1,1] => 6
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,4,2] => [4,2,2] => 8
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,5,1] => [5,2,1] => 7
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,6] => [6,2] => 8
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,6] => [6,2] => 8
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,5,1] => [5,2,1] => 7
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,6] => [6,2] => 8
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,6] => [6,2] => 8
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,6] => [6,2] => 8
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,5,1] => [5,2,1] => 7
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,6] => [6,2] => 8
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,6] => [6,2] => 8
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,6] => [6,2] => 8
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,6] => [6,2] => 8
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,4,1,1] => [4,2,1,1] => 6
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,4,2] => [4,2,2] => 8
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,5,1] => [5,2,1] => 7
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,6] => [6,2] => 8
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,6] => [6,2] => 8
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,5,1] => [5,2,1] => 7
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,6] => [6,2] => 8
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,6] => [6,2] => 8
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,6] => [6,2] => 8
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,5,1] => [5,2,1] => 7
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,6] => [6,2] => 8
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,6] => [6,2] => 8
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,6] => [6,2] => 8
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,6] => [6,2] => 8
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,5,1] => [5,2,1] => 7
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,6] => [6,2] => 8
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,6] => [6,2] => 8
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,6] => [6,2] => 8
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,6] => [6,2] => 8
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,6] => [6,2] => 8
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => [3,1,1,1,1,1] => 3
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,1,1,2] => [3,2,1,1,1] => 5
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,1,2,1] => [3,2,1,1,1] => 5
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,1,3] => [3,3,1,1] => 6
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [3,1,1,3] => [3,3,1,1] => 6
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,2,1,1] => [3,2,1,1,1] => 5
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [3,1,2,2] => [3,2,2,1] => 7
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,3,1] => [3,3,1,1] => 6
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [3,1,4] => [4,3,1] => 7
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [3,1,4] => [4,3,1] => 7
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,3,1] => [3,3,1,1] => 6
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [3,1,4] => [4,3,1] => 7
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [3,1,4] => [4,3,1] => 7
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,1,4] => [4,3,1] => 7
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,1,1] => [3,2,1,1,1] => 5
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [3,2,1,2] => [3,2,2,1] => 7
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,2,1] => [3,2,2,1] => 7
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [3,2,3] => [3,3,2] => 8
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => [3,2,3] => [3,3,2] => 8
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [3,3,1,1] => [3,3,1,1] => 6
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [3,3,2] => [3,3,2] => 8
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [3,4,1] => [4,3,1] => 7
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [3,5] => [5,3] => 8
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [3,5] => [5,3] => 8
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [3,4,1] => [4,3,1] => 7
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [3,5] => [5,3] => 8
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [3,5] => [5,3] => 8
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,5] => [5,3] => 8
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [3,3,1,1] => [3,3,1,1] => 6
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [3,3,2] => [3,3,2] => 8
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [3,4,1] => [4,3,1] => 7
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [3,5] => [5,3] => 8
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [3,5] => [5,3] => 8
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [3,4,1] => [4,3,1] => 7
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [3,5] => [5,3] => 8
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [3,5] => [5,3] => 8
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,5] => [5,3] => 8
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [3,4,1] => [4,3,1] => 7
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [3,5] => [5,3] => 8
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [3,5] => [5,3] => 8
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,5] => [5,3] => 8
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,5] => [5,3] => 8
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1] => [4,1,1,1,1] => 4
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [4,1,1,2] => [4,2,1,1] => 6
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => [4,2,1,1] => 6
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [4,1,3] => [4,3,1] => 7
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => [4,3,1] => 7
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [4,2,1,1] => [4,2,1,1] => 6
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [4,2,2] => [4,2,2] => 8
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [4,3,1] => [4,3,1] => 7
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [4,4] => [4,4] => 8
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4] => [4,4] => 8
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [4,3,1] => [4,3,1] => 7
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [4,4] => [4,4] => 8
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [4,4] => [4,4] => 8
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4] => [4,4] => 8
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [5,1,1,1] => [5,1,1,1] => 5
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [5,1,2] => [5,2,1] => 7
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [5,2,1] => [5,2,1] => 7
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [5,3] => [5,3] => 8
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [5,3] => [5,3] => 8
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => 6
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [6,2] => [6,2] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8] => [8] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [8] => [8] => 8
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [8] => [8] => 8
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [8] => [8] => 8
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [8] => [8] => 8
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => 6
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [6,2] => [6,2] => 8
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [8] => [8] => 8
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [8] => [8] => 8
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [8] => [8] => 8
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [8] => [8] => 8
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [8] => [8] => 8
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [8] => [8] => 8
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [8] => [8] => 8
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [8] => [8] => 8
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [8] => [8] => 8
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => [5,1,1,1] => 5
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [5,1,2] => [5,2,1] => 7
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [5,2,1] => [5,2,1] => 7
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [5,3] => [5,3] => 8
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [5,3] => [5,3] => 8
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => 6
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [6,2] => [6,2] => 8
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [8] => [8] => 8
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [8] => [8] => 8
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [8] => [8] => 8
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [8] => [8] => 8
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [8] => [8] => 8
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => 6
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [6,2] => [6,2] => 8
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [8] => [8] => 8
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [8] => [8] => 8
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [8] => [8] => 8
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [8] => [8] => 8
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [8] => [8] => 8
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [8] => [8] => 8
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [8] => [8] => 8
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [8] => [8] => 8
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [8] => [8] => 8
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => 6
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [6,2] => [6,2] => 8
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [8] => [8] => 8
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [8] => [8] => 8
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [8] => [8] => 8
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [8] => [8] => 8
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [8] => [8] => 8
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [8] => [8] => 8
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [8] => [8] => 8
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [8] => [8] => 8
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [8] => [8] => 8
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [8] => [8] => 8
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [8] => [8] => 8
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [8] => [8] => 8
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [8] => [8] => 8
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1] => [4,1,1,1,1] => 4
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [4,1,1,2] => [4,2,1,1] => 6
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => [4,2,1,1] => 6
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [4,1,3] => [4,3,1] => 7
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => [4,3,1] => 7
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [4,2,1,1] => [4,2,1,1] => 6
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [4,2,2] => [4,2,2] => 8
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [4,3,1] => [4,3,1] => 7
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [4,4] => [4,4] => 8
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4] => [4,4] => 8
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [4,3,1] => [4,3,1] => 7
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [4,4] => [4,4] => 8
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,4] => [4,4] => 8
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4] => [4,4] => 8
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [5,1,1,1] => [5,1,1,1] => 5
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [5,1,2] => [5,2,1] => 7
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [5,2,1] => [5,2,1] => 7
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [5,3] => [5,3] => 8
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [5,3] => [5,3] => 8
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => 6
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [6,2] => [6,2] => 8
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [8] => [8] => 8
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [8] => [8] => 8
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => 6
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [6,2] => [6,2] => 8
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [8] => [8] => 8
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [8] => [8] => 8
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [8] => [8] => 8
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => [5,1,1,1] => 5
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [5,1,2] => [5,2,1] => 7
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [5,2,1] => [5,2,1] => 7
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [5,3] => [5,3] => 8
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [5,3] => [5,3] => 8
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => 6
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [6,2] => [6,2] => 8
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [8] => [8] => 8
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [8] => [8] => 8
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => 6
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [6,2] => [6,2] => 8
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [8] => [8] => 8
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [8] => [8] => 8
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [8] => [8] => 8
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => 6
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [6,2] => [6,2] => 8
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [8] => [8] => 8
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [8] => [8] => 8
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [8] => [8] => 8
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [8] => [8] => 8
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => [5,1,1,1] => 5
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,1,2] => [5,2,1] => 7
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [5,2,1] => [5,2,1] => 7
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,3] => [5,3] => 8
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,3] => [5,3] => 8
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => 6
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [6,2] => [6,2] => 8
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [8] => [8] => 8
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [8] => [8] => 8
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => 6
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [6,2] => [6,2] => 8
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [8] => [8] => 8
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [8] => [8] => 8
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [8] => [8] => 8
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => 6
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,2] => [6,2] => 8
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [8] => [8] => 8
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [8] => [8] => 8
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [8] => [8] => 8
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [8] => [8] => 8
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => 6
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,2] => [6,2] => 8
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [8] => [8] => 8
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [8] => [8] => 8
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [8] => [8] => 8
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [8] => [8] => 8
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [8] => [8] => 8
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [8] => [8] => 8
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => [3,1,1,1,1,1] => 3
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,1,1,2] => [3,2,1,1,1] => 5
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,1,2,1] => [3,2,1,1,1] => 5
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,1,3] => [3,3,1,1] => 6
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,1,1,3] => [3,3,1,1] => 6
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,2,1,1] => [3,2,1,1,1] => 5
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [3,1,2,2] => [3,2,2,1] => 7
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,3,1] => [3,3,1,1] => 6
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,1,4] => [4,3,1] => 7
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,1,4] => [4,3,1] => 7
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,3,1] => [3,3,1,1] => 6
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [3,1,4] => [4,3,1] => 7
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,1,4] => [4,3,1] => 7
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,1,4] => [4,3,1] => 7
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,1,1] => [3,2,1,1,1] => 5
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [3,2,1,2] => [3,2,2,1] => 7
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,2,1] => [3,2,2,1] => 7
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [3,2,3] => [3,3,2] => 8
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [3,2,3] => [3,3,2] => 8
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,3,1,1] => [3,3,1,1] => 6
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [3,3,2] => [3,3,2] => 8
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [3,4,1] => [4,3,1] => 7
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,5] => [5,3] => 8
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,5] => [5,3] => 8
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,4,1] => [4,3,1] => 7
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [3,5] => [5,3] => 8
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,5] => [5,3] => 8
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,5] => [5,3] => 8
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [3,3,1,1] => [3,3,1,1] => 6
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,3,2] => [3,3,2] => 8
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [3,4,1] => [4,3,1] => 7
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,5] => [5,3] => 8
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,5] => [5,3] => 8
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [3,4,1] => [4,3,1] => 7
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,5] => [5,3] => 8
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,5] => [5,3] => 8
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,5] => [5,3] => 8
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,4,1] => [4,3,1] => 7
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [3,5] => [5,3] => 8
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,5] => [5,3] => 8
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,5] => [5,3] => 8
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,5] => [5,3] => 8
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1] => [4,1,1,1,1] => 4
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [4,1,1,2] => [4,2,1,1] => 6
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => [4,2,1,1] => 6
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [4,1,3] => [4,3,1] => 7
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => [4,3,1] => 7
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [4,2,1,1] => [4,2,1,1] => 6
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [4,2,2] => [4,2,2] => 8
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [4,3,1] => [4,3,1] => 7
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [4,4] => [4,4] => 8
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4] => [4,4] => 8
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [4,3,1] => [4,3,1] => 7
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [4,4] => [4,4] => 8
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [4,4] => [4,4] => 8
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4] => [4,4] => 8
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [5,1,1,1] => [5,1,1,1] => 5
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [5,1,2] => [5,2,1] => 7
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [5,2,1] => [5,2,1] => 7
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [5,3] => [5,3] => 8
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [5,3] => [5,3] => 8
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => 6
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [6,2] => [6,2] => 8
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8] => [8] => 8
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [8] => [8] => 8
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => 6
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [6,2] => [6,2] => 8
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [8] => [8] => 8
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [8] => [8] => 8
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => [5,1,1,1] => 5
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [5,1,2] => [5,2,1] => 7
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [5,2,1] => [5,2,1] => 7
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [5,3] => [5,3] => 8
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [5,3] => [5,3] => 8
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => 6
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [6,2] => [6,2] => 8
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [8] => [8] => 8
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [8] => [8] => 8
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => 6
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [6,2] => [6,2] => 8
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [8] => [8] => 8
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [8] => [8] => 8
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => 6
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [6,2] => [6,2] => 8
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [8] => [8] => 8
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [8] => [8] => 8
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1] => [4,1,1,1,1] => 4
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [4,1,1,2] => [4,2,1,1] => 6
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => [4,2,1,1] => 6
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [4,1,3] => [4,3,1] => 7
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => [4,3,1] => 7
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [4,2,1,1] => [4,2,1,1] => 6
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [4,2,2] => [4,2,2] => 8
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [4,3,1] => [4,3,1] => 7
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [4,4] => [4,4] => 8
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4] => [4,4] => 8
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [4,3,1] => [4,3,1] => 7
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [4,4] => [4,4] => 8
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [4,4] => [4,4] => 8
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4] => [4,4] => 8
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [5,1,1,1] => [5,1,1,1] => 5
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [5,1,2] => [5,2,1] => 7
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [5,2,1] => [5,2,1] => 7
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [5,3] => [5,3] => 8
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [5,3] => [5,3] => 8
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => 6
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [6,2] => [6,2] => 8
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [8] => [8] => 8
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => 6
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [6,2] => [6,2] => 8
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [8] => [8] => 8
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => [5,1,1,1] => 5
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [5,1,2] => [5,2,1] => 7
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [5,2,1] => [5,2,1] => 7
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [5,3] => [5,3] => 8
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [5,3] => [5,3] => 8
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => 6
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [6,2] => [6,2] => 8
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [8] => [8] => 8
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => 6
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [6,2] => [6,2] => 8
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [8] => [8] => 8
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => 6
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [6,2] => [6,2] => 8
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [8] => [8] => 8
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => [5,1,1,1] => 5
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [5,1,2] => [5,2,1] => 7
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [5,2,1] => [5,2,1] => 7
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [5,3] => [5,3] => 8
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,3] => [5,3] => 8
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => 6
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [6,2] => [6,2] => 8
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [8] => [8] => 8
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => 6
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [6,2] => [6,2] => 8
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [8] => [8] => 8
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => 6
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [6,2] => [6,2] => 8
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [8] => [8] => 8
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => 6
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [6,2] => [6,2] => 8
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [8] => [8] => 8
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1] => [4,1,1,1,1] => 4
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,1,1,2] => [4,2,1,1] => 6
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => [4,2,1,1] => 6
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,1,3] => [4,3,1] => 7
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => [4,3,1] => 7
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,2,1,1] => [4,2,1,1] => 6
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,2,2] => [4,2,2] => 8
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,3,1] => [4,3,1] => 7
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,4] => [4,4] => 8
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,4] => [4,4] => 8
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,3,1] => [4,3,1] => 7
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,4] => [4,4] => 8
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,4] => [4,4] => 8
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4] => [4,4] => 8
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [5,1,1,1] => [5,1,1,1] => 5
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [5,1,2] => [5,2,1] => 7
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [5,2,1] => [5,2,1] => 7
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [5,3] => [5,3] => 8
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [5,3] => [5,3] => 8
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => 6
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [6,2] => [6,2] => 8
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [8] => [8] => 8
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => 6
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [6,2] => [6,2] => 8
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [8] => [8] => 8
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => [5,1,1,1] => 5
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [5,1,2] => [5,2,1] => 7
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [5,2,1] => [5,2,1] => 7
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [5,3] => [5,3] => 8
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,3] => [5,3] => 8
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => 6
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [6,2] => [6,2] => 8
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [8] => [8] => 8
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => 6
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [6,2] => [6,2] => 8
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [8] => [8] => 8
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => 6
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,2] => [6,2] => 8
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [8] => [8] => 8
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => [5,1,1,1] => 5
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [5,1,2] => [5,2,1] => 7
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [5,2,1] => [5,2,1] => 7
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [5,3] => [5,3] => 8
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,3] => [5,3] => 8
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => 6
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [6,2] => [6,2] => 8
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [8] => [8] => 8
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => 6
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [6,2] => [6,2] => 8
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [8] => [8] => 8
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => 6
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [6,2] => [6,2] => 8
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [8] => [8] => 8
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => 6
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,2] => [6,2] => 8
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [8] => [8] => 8
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => [5,1,1,1] => 5
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,1,2] => [5,2,1] => 7
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,2,1] => [5,2,1] => 7
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,3] => [5,3] => 8
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,3] => [5,3] => 8
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => 6
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [6,2] => [6,2] => 8
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [8] => [8] => 8
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => 6
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,2] => [6,2] => 8
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [8] => [8] => 8
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => 6
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,2] => [6,2] => 8
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [8] => [8] => 8
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => 6
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,2] => [6,2] => 8
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [8] => [8] => 8
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => 6
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,2] => [6,2] => 8
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [8] => [8] => 8
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,1] => [7,1] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [8] => [8] => 8
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8] => [8] => 8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,8] => [8,1] => 8
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,9] => [9,1] => 9
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10,1] => [10,1] => 10
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,10] => [10,1] => 10
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1] => [10,1] => 10
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1,10] => [10,1] => 10
[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] => [11,1] => 11
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0] => [10,1] => [10,1] => 10
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1] => [10,1] => 10
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [1,10] => [10,1] => 10
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [1,10] => [10,1] => 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] => [1,11] => [11,1] => 11
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,1,0] => [10,1] => [10,1] => 10
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [1,10] => [10,1] => 10
[1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [1,10] => [10,1] => 10
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10] => [10,1] => 10
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,2] => [7,2] => 9
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [1,9] => [9,1] => 9
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,7] => [7,2] => 9
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10] => [10,1] => 10
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => 7
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,7,1] => [7,1,1] => 7
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [7,2] => [7,2] => 9
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [1,9] => [9,1] => 9
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,7] => [7,2] => 9
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,7] => [7,1,1] => 7
[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10] => [10,1] => 10
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,2] => [8,2] => 10
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => 7
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,7,1] => [7,1,1] => 7
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,9] => [9,1] => 9
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0] => [7,2] => [7,2] => 9
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => [7,2] => [7,2] => 9
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [1,8] => [8,1] => 8
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,7] => [7,2] => 9
[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [1,9] => [9,1] => 9
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,7] => [7,2] => 9
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,7] => [7,1,1] => 7
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,8] => [8,2] => 10
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10] => [10,1] => 10
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [8,1,1] => [8,1,1] => 8
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,8,1] => [8,1,1] => 8
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0] => [8,2] => [8,2] => 10
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => 7
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => 7
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,1] => [7,1,1] => 7
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,7,1] => [7,1,1] => 7
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,1,0,0] => [7,2] => [7,2] => 9
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0] => [7,2] => [7,2] => 9
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,2] => [7,2] => 9
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,8] => [8,1] => 8
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,7] => [7,2] => 9
[1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,7] => [7,1,1] => 7
[1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [1,8] => [8,1] => 8
[1,1,0,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,7] => [7,2] => 9
[1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,7] => [7,1,1] => 7
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,8] => [8,2] => 10
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,8] => [8,1,1] => 8
[1,0,1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10] => [10,1] => 10
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [9] => [9] => 9
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [9] => [9] => 9
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [9] => [9] => 9
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [9] => [9] => 9
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [9] => [9] => 9
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [9] => [9] => 9
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [9] => [9] => 9
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [9] => [9] => 9
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [9] => [9] => 9
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [9] => [9] => 9
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [9] => [9] => 9
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [9] => [9] => 9
[1,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [9] => [9] => 9
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [9] => [9] => 9
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [9] => [9] => 9
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [9] => [9] => 9
[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [9] => [9] => 9
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [9] => [9] => 9
[1,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [9] => [9] => 9
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [9] => [9] => 9
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [9] => [9] => 9
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [9] => [9] => 9
[1,1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [9] => [9] => 9
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [9] => [9] => 9
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [9] => [9] => 9
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [9] => [9] => 9
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [9] => [9] => 9
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [9] => [9] => 9
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [9] => [9] => 9
[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [9] => [9] => 9
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [9] => [9] => 9
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [9] => [9] => 9
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [9] => [9] => 9
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [9] => [9] => 9
[1,1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [9] => [9] => 9
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [9] => [9] => 9
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9] => [9] => 9
[1,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [9] => [9] => 9
[1,1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [9] => [9] => 9
[1,1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [9] => [9] => 9
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [9] => [9] => 9
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [9] => [9] => 9
[1,1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [9] => [9] => 9
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [9] => [9] => 9
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [9] => [9] => 9
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [9] => [9] => 9
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [9] => [9] => 9
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [9] => [9] => 9
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [9] => [9] => 9
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [9] => [9] => 9
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [9] => [9] => 9
[1,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [9] => [9] => 9
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [9] => [9] => 9
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [9] => [9] => 9
[1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [9] => [9] => 9
[1,1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [9] => [9] => 9
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [9] => [9] => 9
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [9] => [9] => 9
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [9] => [9] => 9
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [9] => [9] => 9
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [9] => [9] => 9
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [9] => [9] => 9
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [9] => [9] => 9
[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [9] => [9] => 9
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [9] => [9] => 9
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [9] => [9] => 9
[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [9] => [9] => 9
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [9] => [9] => 9
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [9] => [9] => 9
[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [9] => [9] => 9
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [9] => [9] => 9
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0] => [9] => [9] => 9
[1,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,0] => [9] => [9] => 9
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,0] => [9] => [9] => 9
[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0,0] => [9] => [9] => 9
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,0] => [9] => [9] => 9
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [9] => [9] => 9
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,0] => [9] => [9] => 9
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0] => [9] => [9] => 9
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0] => [9] => [9] => 9
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,0] => [9] => [9] => 9
[1,1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0,0] => [9] => [9] => 9
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0] => [9] => [9] => 9
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [9] => [9] => 9
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0,0] => [9] => [9] => 9
[1,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0] => [9] => [9] => 9
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [9] => [9] => 9
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [9] => [9] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,3] => [3,1,1,1,1,1,1] => 3
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,4] => [4,1,1,1,1,1] => 4
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,5] => [5,1,1,1,1] => 5
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,6] => [6,1,1,1] => 6
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,7] => [7,1,1] => 7
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,8] => [8,1] => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,3] => [3,1,1,1,1,1,1] => 3
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,1,3] => [3,1,1,1,1,1,1,1] => 3
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,4] => [4,1,1,1,1,1] => 4
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,4] => [4,1,1,1,1,1,1] => 4
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,5] => [5,1,1,1,1] => 5
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,5] => [5,1,1,1,1,1] => 5
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,6] => [6,1,1,1] => 6
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,6] => [6,1,1,1,1] => 6
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,7] => [7,1,1] => 7
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,7] => [7,1,1,1] => 7
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,8] => [8,1] => 8
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,8] => [8,1,1] => 8
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,9] => [9,1] => 9
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10] => [10] => 10
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,3] => [3,1,1,1,1,1,1,1] => 3
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,1,1,3] => [3,1,1,1,1,1,1,1,1] => 3
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,4] => [4,1,1,1,1,1] => 4
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,1,4] => [4,1,1,1,1,1,1] => 4
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,5] => [5,1,1,1,1] => 5
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,4] => [4,1,1,1,1,1] => 4
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,6] => [6,1,1,1] => 6
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,5] => [5,1,1,1,1] => 5
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,6] => [6,1,1,1,1,1] => 6
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,7] => [7,1,1] => 7
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,6] => [6,1,1,1] => 6
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,9] => [9,1] => 9
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,9] => [9,1,1] => 9
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10] => [10] => 10
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,10] => [10,1] => 10
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [11] => [11] => 11
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,1,3] => [3,1,1,1,1,1,1,1,1] => 3
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,1,4] => [4,1,1,1,1,1,1] => 4
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,5] => [5,1,1,1,1] => 5
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,1,5] => [5,1,1,1,1,1] => 5
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,4] => [4,1,1,1,1,1,1] => 4
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,6] => [6,1,1,1] => 6
[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,5] => [5,1,1,1,1] => 5
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,6] => [6,1,1,1,1] => 6
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,7] => [7,1,1] => 7
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,7] => [7,1,1,1] => 7
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,5] => [5,1,1,1,1] => 5
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,8] => [8,1] => 8
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,7] => [7,1,1] => 7
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,8] => [8,1,1] => 8
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,6] => [6,1,1,1] => 6
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,9] => [9,1] => 9
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,7] => [7,1,1] => 7
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10] => [10] => 10
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [1,8] => [8,1] => 8
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10] => [10] => 10
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [11] => [11] => 11
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,11] => [11,1] => 11
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,5] => [5,1,1,1,1,1] => 5
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,6] => [6,1,1,1] => 6
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,1,5] => [5,1,1,1,1,1] => 5
[1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,6] => [6,1,1,1] => 6
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,5] => [5,1,1,1,1] => 5
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,5] => [5,1,1,1,1,1] => 5
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [1,8] => [8,1] => 8
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,7] => [7,1,1] => 7
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,7] => [7,1,1] => 7
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [10] => [10] => 10
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,7] => [7,1,1] => 7
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [11] => [11] => 11
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,6] => [6,1,1,1,1] => 6
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,7] => [7,1,1] => 7
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,6] => [6,1,1,1,1] => 6
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,5] => [5,1,1,1,1,1] => 5
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,8] => [8,1] => 8
[1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,7] => [7,1,1] => 7
[1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,6] => [6,1,1,1] => 6
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [10] => [10] => 10
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [1,8] => [8,1] => 8
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,7] => [7,1,1] => 7
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [10] => [10] => 10
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,8] => [8,1] => 8
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,7] => [7,1,1,1] => 7
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,7] => [7,1,1,1] => 7
[1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,6] => [6,1,1,1] => 6
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [10] => [10] => 10
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,7] => [7,1,1] => 7
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,6] => [6,1,1,1] => 6
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,8] => [8,1] => 8
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0] => [10] => [10] => 10
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,8] => [8,1,1] => 8
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,8] => [8,1,1] => 8
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,6] => [6,1,1,1,1] => 6
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [10] => [10] => 10
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,6] => [6,1,1,1,1] => 6
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [11] => [11] => 11
[1,0,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,8] => [8,1,1] => 8
[1,0,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,7] => [7,1,1] => 7
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0] => [10] => [10] => 10
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,9] => [9,1] => 9
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [10] => [10] => 10
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,7] => [7,1,1] => 7
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,1,2,1,1] => [2,1,1,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,1,2,2] => [2,2,1,1,1,1,1] => 4
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,1,3,1] => [3,1,1,1,1,1,1] => 3
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,1,2,1,2] => [2,2,1,1,1,1,1] => 4
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,1,2,2,1] => [2,2,1,1,1,1,1] => 4
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,1,2,3] => [3,2,1,1,1,1] => 5
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,3,1,1] => [3,1,1,1,1,1,1] => 3
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,3,2] => [3,2,1,1,1,1] => 5
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,4,1] => [4,1,1,1,1,1] => 4
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,2,1,1,1,1] => [2,1,1,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,2,1,2,1] => [2,2,1,1,1,1,1] => 4
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,2,2,1,1] => [2,2,1,1,1,1,1] => 4
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,2,2,2] => [2,2,2,1,1,1] => 6
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,2,4] => [4,2,1,1,1] => 6
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,3,1,1,1] => [3,1,1,1,1,1,1] => 3
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,3,2,1] => [3,2,1,1,1,1] => 5
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,3,3] => [3,3,1,1,1] => 6
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,5,1] => [5,1,1,1,1] => 5
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,2,1,1,1,2] => [2,2,1,1,1,1,1] => 4
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,2,1,1,2,1] => [2,2,1,1,1,1,1] => 4
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,2,1,1,3] => [3,2,1,1,1,1] => 5
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,2,1,2,2] => [2,2,2,1,1,1] => 6
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,2,2,1,1,1] => [2,2,1,1,1,1,1] => 4
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,2,2,2,1] => [2,2,2,1,1,1] => 6
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,2,2,3] => [3,2,2,1,1] => 7
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,2,3,2] => [3,2,2,1,1] => 7
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,2,4,1] => [4,2,1,1,1] => 6
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,2,5] => [5,2,1,1] => 7
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,3,1,1,1,1] => [3,1,1,1,1,1,1] => 3
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,3,2,2] => [3,2,2,1,1] => 7
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,4,1,1,1] => [4,1,1,1,1,1] => 4
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,4,3] => [4,3,1,1] => 7
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,5,1,1] => [5,1,1,1,1] => 5
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,5,2] => [5,2,1,1] => 7
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,6,1] => [6,1,1,1] => 6
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,1,1,1,1,2] => [2,2,1,1,1,1,1] => 4
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,1,1,1,2,1] => [2,2,1,1,1,1,1] => 4
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,1,1,1,3] => [3,2,1,1,1,1] => 5
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,1,1,2,1,1] => [2,2,1,1,1,1,1] => 4
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,1,2,1,1,1] => [2,2,1,1,1,1,1] => 4
[1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,1,5] => [5,2,1,1] => 7
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,2,1,1,1,1] => [2,2,1,1,1,1,1] => 4
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,2,1,1,2] => [2,2,2,1,1,1] => 6
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,2,2,1,1] => [2,2,2,1,1,1] => 6
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,2,2,2] => [2,2,2,2,1] => 8
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,2,3,1] => [3,2,2,1,1] => 7
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,2,4] => [4,2,2,1] => 8
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,3,1,1,1] => [3,2,1,1,1,1] => 5
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,3,3] => [3,3,2,1] => 8
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,5,1] => [5,2,1,1] => 7
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,6] => [6,2,1] => 8
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,1,1,1,1,1] => [3,1,1,1,1,1,1] => 3
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,2,1] => [3,2,2,1,1] => 7
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,3,1,1] => [3,3,1,1,1] => 6
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,3,2] => [3,3,2,1] => 8
[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,5] => [5,3,1] => 8
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,4,1,1,1,1] => [4,1,1,1,1,1] => 4
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,4,1,3] => [4,3,1,1] => 7
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,4,2,1,1] => [4,2,1,1,1] => 6
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,4,4] => [4,4,1] => 8
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,5,1,1,1] => [5,1,1,1,1] => 5
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,5,3] => [5,3,1] => 8
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,6,1,1] => [6,1,1,1] => 6
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,6,2] => [6,2,1] => 8
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,1,2] => [2,2,1,1,1,1,1] => 4
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,1,2,1] => [2,2,1,1,1,1,1] => 4
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,1,1,3] => [3,2,1,1,1,1] => 5
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,1,1,2,1,1] => [2,2,1,1,1,1,1] => 4
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,1,1,2,2] => [2,2,2,1,1,1] => 6
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,1,1,3,1] => [3,2,1,1,1,1] => 5
[1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,1,1,4] => [4,2,1,1,1] => 6
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,1,2,1,1,1] => [2,2,1,1,1,1,1] => 4
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,1,2,3] => [3,2,2,1,1] => 7
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,1,4,1] => [4,2,1,1,1] => 6
[1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,1,5] => [5,2,1,1] => 7
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,2,1,1,1,1] => [2,2,1,1,1,1,1] => 4
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,2,2,2] => [2,2,2,2,1] => 8
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,3,3] => [3,3,2,1] => 8
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,5,1] => [5,2,1,1] => 7
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,6] => [6,2,1] => 8
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 4
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,2,1,1,1,2] => [2,2,2,1,1,1] => 6
[1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,2,1,4] => [4,2,2,1] => 8
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,2,2,1,1,1] => [2,2,2,1,1,1] => 6
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,2,2,1,2] => [2,2,2,2,1] => 8
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,2,2,2,1] => [2,2,2,2,1] => 8
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,2,2,3] => [3,2,2,2] => 9
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,2,3,1,1] => [3,2,2,1,1] => 7
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,2,3,2] => [3,2,2,2] => 9
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,5] => [5,2,2] => 9
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,3,1,1,1,1] => [3,2,1,1,1,1] => 5
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,3,3,1] => [3,3,2,1] => 8
[1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4] => [4,3,2] => 9
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,4,1,1,1] => [4,2,1,1,1] => 6
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,4,3] => [4,3,2] => 9
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,5,1,1] => [5,2,1,1] => 7
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,5,2] => [5,2,2] => 9
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,6,1] => [6,2,1] => 8
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 3
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,1,1,1,1,2] => [3,2,1,1,1,1] => 5
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [3,1,1,1,2,1] => [3,2,1,1,1,1] => 5
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [3,1,1,1,3] => [3,3,1,1,1] => 6
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [3,1,2,1,2] => [3,2,2,1,1] => 7
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,2,1] => [3,2,2,1,1] => 7
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,1] => [4,3,1,1] => 7
[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,5] => [5,3,1] => 8
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,2,1,1,1,1] => [3,2,1,1,1,1] => 5
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,2,2,2] => [3,2,2,2] => 9
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [3,3,1,1,1] => [3,3,1,1,1] => 6
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => [3,3,3] => 9
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [3,4,2] => [4,3,2] => 9
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [3,5,1] => [5,3,1] => 8
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,6] => [6,3] => 9
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => 4
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,1,0,0] => [4,1,1,1,2] => [4,2,1,1,1] => 6
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,0,0,0] => [4,1,1,3] => [4,3,1,1] => 7
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,0] => [4,1,3,1] => [4,3,1,1] => 7
[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0] => [4,1,4] => [4,4,1] => 8
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0] => [4,2,1,1,1] => [4,2,1,1,1] => 6
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [4,2,2,1] => [4,2,2,1] => 8
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0] => [4,2,3] => [4,3,2] => 9
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0] => [4,3,1,1] => [4,3,1,1] => 7
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0] => [4,3,2] => [4,3,2] => 9
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [4,4,1] => [4,4,1] => 8
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5] => [5,4] => 9
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => 5
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,1,0,0] => [5,1,1,2] => [5,2,1,1] => 7
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,1,0] => [5,1,2,1] => [5,2,1,1] => 7
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0] => [5,1,3] => [5,3,1] => 8
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [5,2,1,1] => [5,2,1,1] => 7
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [5,3,1] => [5,3,1] => 8
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,4] => [5,4] => 9
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => [6,1,1,1] => 6
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0] => [6,1,2] => [6,2,1] => 8
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [6,2,1] => [6,2,1] => 8
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,3] => [6,3] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,1,1,2,1,1] => [2,1,1,1,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,1,1,2,2] => [2,2,1,1,1,1,1,1] => 4
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,1,1,3,1] => [3,1,1,1,1,1,1,1] => 3
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,1,1,2,2,1] => [2,2,1,1,1,1,1,1] => 4
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,4,1] => [4,1,1,1,1,1,1] => 4
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,2,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,2,2,2] => [2,2,2,1,1,1,1] => 6
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,3,1,1,1] => [3,1,1,1,1,1,1,1] => 3
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,5,1] => [5,1,1,1,1,1] => 5
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,2,1,1,1,2] => [2,2,1,1,1,1,1,1] => 4
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,2,2,1,1,1] => [2,2,1,1,1,1,1,1] => 4
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,2,2,2,1] => [2,2,2,1,1,1,1] => 6
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,3,1,1,1,1] => [3,1,1,1,1,1,1,1] => 3
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,1,4,2,1] => [4,2,1,1,1,1] => 6
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,6,1] => [6,1,1,1,1] => 6
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,7] => [7,1,1,1] => 7
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,2,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => 4
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,2,2,2,2] => [2,2,2,2,1,1] => 8
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,3,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 3
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,4,4] => [4,4,1,1] => 8
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,1,5,1,1,1] => [5,1,1,1,1,1] => 5
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,6,2] => [6,2,1,1] => 8
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,1,7,1] => [7,1,1,1] => 7
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => 4
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1] => 4
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,1,1,1,1,3] => [3,2,1,1,1,1,1] => 5
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,1,3,1,2] => [3,2,2,1,1,1] => 7
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 4
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,2,2,2,1,1,1] => [2,2,2,1,1,1,1] => 6
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,2,2,1] => [2,2,2,2,1,1] => 8
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,2,2,2,3] => [3,2,2,2,1] => 9
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,2,3,2,2] => [3,2,2,2,1] => 9
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,2,3,4] => [4,3,2,1] => 9
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,2,4,1,1,1] => [4,2,1,1,1,1] => 6
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,7] => [7,2,1] => 9
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 3
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,2,2] => [3,2,2,2,1] => 9
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,3,3,3] => [3,3,3,1] => 9
[1,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,3,6] => [6,3,1] => 9
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,4,1,1,1,1,1] => [4,1,1,1,1,1,1] => 4
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,4,5] => [5,4,1] => 9
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [1,5,1,1,1,1] => [5,1,1,1,1,1] => 5
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,5,4] => [5,4,1] => 9
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [1,6,1,1,1] => [6,1,1,1,1] => 6
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [1,7,1,1] => [7,1,1,1] => 7
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [1,7,2] => [7,2,1] => 9
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => 4
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1] => 4
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,1,1,1,3] => [3,2,1,1,1,1,1] => 5
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1] => 4
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,1,1,1,3,1] => [3,2,1,1,1,1,1] => 5
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,1,1,1,4] => [4,2,1,1,1,1] => 6
[1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,1,1,5] => [5,2,1,1,1] => 7
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 4
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,1,4,1,2] => [4,2,2,1,1] => 8
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,6,1] => [6,2,1,1] => 8
[1,1,0,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,7] => [7,2,1] => 9
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 4
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,2,1,1,2,2] => [2,2,2,2,1,1] => 8
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 6
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,2,2,1,2,1] => [2,2,2,2,1,1] => 8
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,2,2,2,1,1] => [2,2,2,2,1,1] => 8
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2,2] => [2,2,2,2,2] => 10
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,2,2,3,1] => [3,2,2,2,1] => 9
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,2,4] => [4,2,2,2] => 10
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,2,3,1,1,1] => [3,2,2,1,1,1] => 7
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,2,3,3] => [3,3,2,2] => 10
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,1,1,1,1] => [3,2,1,1,1,1,1] => 5
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,3,2] => [3,3,2,2] => 10
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [2,4,3,1] => [4,3,2,1] => 9
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,4,4] => [4,4,2] => 10
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [2,6,1,1] => [6,2,1,1] => 8
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,6,2] => [6,2,2] => 10
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,7,1] => [7,2,1] => 9
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 3
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,1,1,1,1,1,2] => [3,2,1,1,1,1,1] => 5
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [3,1,1,1,1,2,1] => [3,2,1,1,1,1,1] => 5
[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [3,1,5,1] => [5,3,1,1] => 8
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => 5
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,2,2,1] => [3,2,2,2,1] => 9
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [3,2,2,3] => [3,3,2,2] => 10
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,3,2,2] => [3,3,2,2] => 10
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,4] => [4,3,3] => 10
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [3,4,3] => [4,3,3] => 10
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,6,1] => [6,3,1] => 9
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,7] => [7,3] => 10
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => 4
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [4,1,1,1,1,2] => [4,2,1,1,1,1] => 6
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,1,1,4] => [4,4,1,1] => 8
[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [4,1,4,1] => [4,4,1,1] => 8
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,2,2,2] => [4,2,2,2] => 10
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,2,4] => [4,4,2] => 10
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,3,3] => [4,3,3] => 10
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [4,4,1,1] => [4,4,1,1] => 8
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,4,2] => [4,4,2] => 10
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [4,5,1] => [5,4,1] => 9
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,6] => [6,4] => 10
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1,1] => [5,1,1,1,1,1] => 5
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,1,0,0] => [5,1,1,1,2] => [5,2,1,1,1] => 7
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0,1,0] => [5,1,3,1] => [5,3,1,1] => 8
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,1,0,0,0,0] => [5,1,4] => [5,4,1] => 9
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [5,2,2,1] => [5,2,2,1] => 9
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [5,4,1] => [5,4,1] => 9
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,5] => [5,5] => 10
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,1,1,1,1] => [6,1,1,1,1] => 6
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,1,0,0] => [6,1,1,2] => [6,2,1,1] => 8
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0,1,0] => [6,1,2,1] => [6,2,1,1] => 8
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,1,0,0,0] => [6,1,3] => [6,3,1] => 9
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0] => [6,3,1] => [6,3,1] => 9
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,4] => [6,4] => 10
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [7,1,1,1] => [7,1,1,1] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,1,0,0] => [7,1,2] => [7,2,1] => 9
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [7,2,1] => [7,2,1] => 9
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [7,3] => [7,3] => 10
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 3
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => 4
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => 5
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [6,1,1,1] => [6,1,1,1] => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => 7
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 3
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => 4
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => 4
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => 5
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1,1] => [5,1,1,1,1,1] => 5
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => [6,1,1,1] => 6
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [6,1,1,1,1] => [6,1,1,1,1] => 6
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => 7
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [7,1,1,1] => [7,1,1,1] => 7
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [8,1,1] => [8,1,1] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [11] => [11] => 11
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [10] => [10] => 10
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,1,3] => [3,2,1,1,1,1] => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [11] => [11] => 11
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [11] => [11] => 11
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,1,1,3] => [3,2,1,1,1,1,1] => 5
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [3,1,1,1,3] => [3,3,1,1,1] => 6
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,1,1,1,3] => [3,2,1,1,1,1] => 5
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,1,1,1,1,2] => [3,2,1,1,1,1] => 5
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => 7
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => [6,1,1,1] => 6
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => 5
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => 4
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [10] => [10] => 10
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [11] => [11] => 11
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [10] => [10] => 10
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => 7
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [6,1,1,1] => [6,1,1,1] => 6
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => 5
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => 4
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [7,2] => [7,2] => 9
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,7] => [7,2] => 9
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [11] => [11] => 11
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,6] => [6,3] => 9
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5] => [5,4] => 9
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,4] => [5,4] => 9
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => [6,3] => [6,3] => 9
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,4,1,1,1,1] => [4,1,1,1,1,1] => 4
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,3,1,1,1,1] => [3,1,1,1,1,1,1] => 3
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,3,1,1] => [3,1,1,1,1,1,1,1] => 3
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,4,1] => [4,1,1,1,1,1,1] => 4
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [5,1,1,2] => [5,2,1,1] => 7
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,1,1,1] => [3,2,1,1,1,1] => 5
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [10] => [10] => 10
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [10] => [10] => 10
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [10] => [10] => 10
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,8] => [8,1] => 8
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,1] => [8,1] => 8
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,8] => [8,1] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,2] => [7,2] => 9
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,7] => [7,2] => 9
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [6,3] => [6,3] => 9
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [10] => [10] => 10
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,4] => [5,4] => 9
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [10] => [10] => 10
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,5] => [5,4] => 9
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,6] => [6,3] => 9
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,7] => [7,2] => 9
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [10] => [10] => 10
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7] => [7,2] => 9
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,2] => [7,2] => 9
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,6] => [6,3] => 9
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,3] => [6,3] => 9
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,5] => [5,4] => 9
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [6,3] => [6,3] => 9
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4] => [5,4] => 9
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,6] => [6,3] => 9
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [10] => [10] => 10
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,2,1,4] => [4,2,1,1,1] => 6
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0] => [7,2] => [7,2] => 9
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,7] => [7,2] => 9
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,1,0,0,0] => [6,3] => [6,3] => 9
[1,1,1,0,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,6] => [6,3] => 9
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,4,1] => [4,1,1,1,1,1] => 4
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,3,1,1] => [3,1,1,1,1,1,1] => 3
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,3,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 3
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,4,1,1,1,1,1] => [4,1,1,1,1,1,1] => 4
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,1,5] => [5,2,1,1] => 7
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [10] => [10] => 10
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,3,2] => [3,2,1,1,1,1] => 5
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [10] => [10] => 10
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [10] => [10] => 10
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [10] => [10] => 10
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0] => [11] => [11] => 11
[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [11] => [11] => 11
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [6,2,1] => [6,2,1] => 8
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [5,2,1,1] => [5,2,1,1] => 7
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [4,2,1,1,1] => [4,2,1,1,1] => 6
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,2,1,1,1,1] => [3,2,1,1,1,1] => 5
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [4,2,2,1] => [4,2,2,1] => 8
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [6,2,1] => [6,2,1] => 8
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [7,2] => [7,2] => 9
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [5,2,2] => [5,2,2] => 9
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,2,2,2] => [3,2,2,2] => 9
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,2,2,2] => [4,2,2,2] => 10
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [6,2,1] => [6,2,1] => 8
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [6,2,2] => [6,2,2] => 10
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [8,2] => [8,2] => 10
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [10] => [10] => 10
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => 7
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [5,4] => [5,4] => 9
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [7,2,1] => [7,2,1] => 9
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [3,4,2] => [4,3,2] => 9
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [5,2,2,1] => [5,2,2,1] => 9
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,4,2,2] => [4,2,2,1] => 8
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,2,2,1] => [3,2,2,2,1] => 9
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [10] => [10] => 10
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [4,1,4] => [4,4,1] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [10] => [10] => 10
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [10] => [10] => 10
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [10] => [10] => 10
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10] => [10] => 10
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10] => [10] => 10
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [11] => [11] => 11
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [11] => [11] => 11
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10] => [10] => 10
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [11] => [11] => 11
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0] => [10] => [10] => 10
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [1,9] => [9,1] => 9
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,7] => [7,3] => 10
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [3,7] => [7,3] => 10
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,7] => [7,3] => 10
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,7] => [7,3] => 10
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [3,7] => [7,3] => 10
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [5,5] => [5,5] => 10
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [5,5] => [5,5] => 10
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [5,5] => [5,5] => 10
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [5,5] => [5,5] => 10
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [7,3] => [7,3] => 10
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [7,3] => [7,3] => 10
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [7,3] => [7,3] => 10
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => [7,3] => [7,3] => 10
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => [7,3] => [7,3] => 10
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [9,1] => [9,1] => 9
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [1,11] => [11,1] => 11
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0] => [7,5] => [7,5] => 12
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0] => [7,5] => [7,5] => 12
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [7,5] => [7,5] => 12
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [7,5] => [7,5] => 12
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [7,5] => [7,5] => 12
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [7,5] => [7,5] => 12
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [7,5] => [7,5] => 12
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [7,5] => [7,5] => 12
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [7,5] => [7,5] => 12
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [7,5] => [7,5] => 12
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [11] => [11] => 11
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,9] => [9,2] => 11
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [11] => [11] => 11
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0] => [10] => [10] => 10
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,1,1,1,1,1,2] => [3,2,1,1,1,1,1] => 5
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [3,1,1,1,2,1] => [3,2,1,1,1,1] => 5
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,7] => [7,1,1] => 7
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,6] => [6,1,1,1] => 6
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,5] => [5,1,1,1,1] => 5
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,4] => [4,1,1,1,1,1] => 4
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [3,6] => [6,3] => 9
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0] => [4,5] => [5,4] => 9
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,1,0,0] => [5,4] => [5,4] => 9
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => [9,2] => [9,2] => 11
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => 7
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [4,1,2,1,1] => [4,2,1,1,1] => 6
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,0,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,6] => [6,3] => 9
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,7] => [7,3] => 10
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [3,6] => [6,3] => 9
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [4,6] => [6,4] => 10
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0,1,0] => [4,4,1] => [4,4,1] => 8
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,5] => [5,3,1] => 8
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [10] => [10] => 10
[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,8] => [8,1,1] => 8
[1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,7] => [7,1,1,1] => 7
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => [6,1,1,1] => 6
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => 5
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0] => [6,3] => [6,3] => 9
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [10] => [10] => 10
[1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,8] => [8,1] => 8
[1,1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [4,1,1,1,2] => [4,2,1,1,1] => 6
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,1,0,0] => [5,1,1,2] => [5,2,1,1] => 7
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,1,0,0] => [6,1,2] => [6,2,1] => 8
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [10] => [10] => 10
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [10] => [10] => 10
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,4,1] => [4,1,1,1,1,1] => 4
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,8] => [8,1] => 8
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,5,1,1] => [5,1,1,1,1] => 5
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,7] => [7,1,1] => 7
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [10] => [10] => 10
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,1,1,1,1,1] => [3,1,1,1,1,1,1] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [11] => [11] => 11
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,8] => [8,2] => 10
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [3,6] => [6,3] => 9
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0] => [11] => [11] => 11
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [10] => [10] => 10
[1,0,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,7] => [7,1,1] => 7
[1,0,1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,6] => [6,1,1,1] => 6
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,1,1,1,3,1] => [3,1,1,1,1,1,1,1,1] => 3
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1,1,1] => 2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [1,5,1,1,1] => [5,1,1,1,1] => 5
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,4,1,1,1] => [4,1,1,1,1,1] => 4
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [10] => [10] => 10
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [10] => [10] => 10
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [5,4] => [5,4] => 9
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [6,4] => [6,4] => 10
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0] => [10] => [10] => 10
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [10] => [10] => 10
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [10] => [10] => 10
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,3,1] => [3,1,1,1,1,1,1] => 3
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,6] => [6,1,1,1] => 6
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,1,3,1] => [3,1,1,1,1,1,1,1] => 3
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [6,1,2] => [6,2,1] => 8
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,6,2] => [6,2,1] => 8
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,7] => [7,1,1] => 7
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,7,1,1] => [7,1,1,1] => 7
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,7,1] => [7,1,1,1] => 7
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,3,1,1,1,2] => [3,2,1,1,1,1,1] => 5
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => 5
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,4,1,1,1,2] => [4,2,1,1,1,1] => 6
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [5,1,1,1,2] => [5,2,1,1,1] => 7
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1] => [10,1] => 10
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,7] => [7,1,1] => 7
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,2] => [6,2,1] => 8
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,6,1] => [6,2,1] => 8
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => 7
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [1,10] => [10,1] => 10
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [10,1] => [10,1] => 10
[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0] => [11] => [11] => 11
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,1,1,1] => [4,2,1,1,1] => 6
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,2,4,1] => [4,2,2,1] => 8
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [5,2,2] => [5,2,2] => 9
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,6] => [6,3] => 9
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,6,1] => [6,2,1] => 8
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,7] => [7,2] => 9
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,7,1] => [7,1,1] => 7
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,3,4] => [4,3,1,1] => 7
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,5,3] => [5,3,1] => 8
[1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [6,3] => [6,3] => 9
[1,1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,0,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5] => [5,4] => 9
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [10] => [10] => 10
[1,0,1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,3,4] => [4,3,1,1] => 7
[1,0,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,7] => [7,1,1] => 7
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,6,1] => [6,1,1,1] => 6
[1,1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0,0] => [10] => [10] => 10
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [5,3,1] => [5,3,1] => 8
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [1,7,1] => [7,1,1] => 7
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [10] => [10] => 10
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,6] => [6,2,1] => 8
[1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0] => [11] => [11] => 11
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,1,1,3,1] => [3,2,1,1,1,1] => 5
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,1,1,3,1] => [3,1,1,1,1,1,1,1,1] => 3
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,1,1,1,3,1] => [3,2,1,1,1,1,1] => 5
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [3,1,1,3,1] => [3,3,1,1,1] => 6
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,1,1,3,1] => [3,2,1,1,1,1] => 5
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,5] => [5,1,1,1,1] => 5
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => 4
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [8,2] => [8,2] => 10
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [6,3] => [6,3] => 9
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,1,0,0] => [6,1,2] => [6,2,1] => 8
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,1,0,0] => [4,1,1,3] => [4,3,1,1] => 7
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,1,1,1,1] => [6,1,1,1,1] => 6
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => 7
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => 7
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => 7
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0] => [7,1,1,1] => [7,1,1,1] => 7
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => [10] => [10] => 10
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,4,1,1,1,1] => [4,1,1,1,1,1] => 4
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [4,1,1,2,1] => [4,2,1,1,1] => 6
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,5,1,1] => [5,1,1,1,1] => 5
[1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,6] => [6,2,1] => 8
[1,0,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,1,5] => [5,2,1,1] => 7
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,1,1,4] => [4,2,1,1,1] => 6
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,2,2,3] => [3,2,2,2] => 9
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,2,3,1,1] => [3,2,2,1,1] => 7
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,2,2,3,1] => [3,2,2,2,1] => 9
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,2,2,2,2] => [2,2,2,2,2,1] => 10
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [5,2,2] => [5,2,2] => 9
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [4,2,2,1] => [4,2,2,1] => 8
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,2,2,2] => [4,2,2,2] => 10
[1,1,1,0,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,4] => [5,4] => 9
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [3,6] => [6,3] => 9
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,5] => [5,1,1,1,1] => 5
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,6] => [6,1,1,1] => 6
[1,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,7] => [7,1,1] => 7
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,10] => [10,1] => 10
[1,0,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,8] => [8,1] => 8
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [6,3] => [6,3] => 9
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [7,2] => [7,2] => 9
[1,0,1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,9] => [9,1] => 9
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,0,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,9] => [9,1] => 9
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => 7
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,1,4,1] => [4,1,1,1,1,1] => 4
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,3,1,1,1] => [3,1,1,1,1,1,1] => 3
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,3,1,1,1] => [3,1,1,1,1,1,1,1] => 3
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,3,1,1,1,1] => [3,1,1,1,1,1,1,1] => 3
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,1,1,4] => [4,2,1,1,1] => 6
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 3
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,1,1,1,1] => [4,1,1,1,1,1] => 4
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,4,1,1,1] => [4,1,1,1,1,1] => 4
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,4,1,1] => [4,1,1,1,1,1] => 4
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,4] => [6,4] => 10
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,1,0,0,0] => [6,3] => [6,3] => 9
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,8,1] => [8,1,1] => 8
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,5,1,1,1,1] => [5,1,1,1,1,1] => 5
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,4,1,1,1,1] => [4,1,1,1,1,1,1] => 4
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [3,1,2,1,1,1] => [3,2,1,1,1,1] => 5
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [6,1,1,1] => [6,1,1,1] => 6
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => 7
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [11] => [11] => 11
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,1,6] => [6,2,1] => 8
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [3,1,5] => [5,3,1] => 8
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,1,0,0] => [4,1,4] => [4,4,1] => 8
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [4,5] => [5,4] => 9
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,1,5] => [5,1,1,1,1] => 5
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,1,4] => [4,1,1,1,1,1,1] => 4
[1,0,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,7] => [7,1,1] => 7
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,6] => [6,1,1,1] => 6
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => [6,1,1,1] => 6
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,5,1,1] => [5,2,1,1] => 7
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,2,4,1] => [4,2,2,1] => 8
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => 5
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => 5
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => 7
[1,1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [10] => [10] => 10
[1,0,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,1,1,1] => [3,2,1,1,1,1] => 5
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [3,3,1,1,1] => [3,3,1,1,1] => 6
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,3,1,1,1] => [3,2,1,1,1,1] => 5
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,1,1,1,1] => [3,2,1,1,1,1,1] => 5
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,5,1,1] => [5,1,1,1,1] => 5
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,6,1] => [6,1,1,1] => 6
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,5,1,1] => [5,1,1,1,1,1] => 5
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,4,1,1] => [4,1,1,1,1,1] => 4
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,5,1] => [5,1,1,1,1] => 5
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,1,6,1] => [6,1,1,1,1] => 6
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,6,1,1] => [6,1,1,1,1] => 6
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [1,6,1,1] => [6,1,1,1] => 6
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,4,1,1] => [4,2,1,1,1] => 6
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [1,7,1] => [7,1,1] => 7
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,1] => [4,3,1,1] => 7
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,7,1] => [7,1,1,1] => 7
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,7,1] => [7,1,1,1,1] => 7
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,9,1] => [9,1,1] => 9
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,1,0,0,0] => [6,3] => [6,3] => 9
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [7,3] => [7,3] => 10
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,8] => [8,1] => 8
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,1,0,0] => [5,2,2] => [5,2,2] => 9
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,7] => [7,1,1] => 7
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,8] => [8,1,1] => 8
[1,1,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,1,5] => [5,3,1] => 8
[1,1,0,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,5] => [5,2,1,1] => 7
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,6] => [6,1,1,1,1] => 6
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [3,6] => [6,3] => 9
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,7,2] => [7,2,1] => 9
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,5,1,2] => [5,2,1,1] => 7
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [11] => [11] => 11
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,2,3,1,1] => [3,2,1,1,1,1,1] => 5
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,1,0,0] => [8,2] => [8,2] => 10
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [4,2,2,1] => [4,2,2,1] => 8
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [6,2,1] => [6,2,1] => 8
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,2,2] => [5,2,2] => 9
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,2,2,2] => [4,2,2,2] => 10
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [6,2,1] => [6,2,1] => 8
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [6,2,2] => [6,2,2] => 10
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [8,2] => [8,2] => 10
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [10] => [10] => 10
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,2] => [4,2,2,1] => 8
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => 7
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => 7
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => [6,1,1,1] => 6
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => 7
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => 7
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => [6,1,1,1] => 6
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => 7
[1,1,0,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,1,1,5] => [5,2,1,1] => 7
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [8,1] => [8,1] => 8
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,5,1] => [5,1,1,1,1] => 5
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,1] => [7,1,1] => 7
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,7,1] => [7,1,1] => 7
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [4,1,1,1,2] => [4,2,1,1,1] => 6
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,4,1,1,1,1] => [4,1,1,1,1,1,1] => 4
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,5,1,1,1,1] => [5,1,1,1,1,1] => 5
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [6,1,1,1,1] => [6,1,1,1,1] => 6
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [1,9] => [9,1] => 9
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0] => [10] => [10] => 10
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [5,1,2,1] => [5,2,1,1] => 7
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [4,1,3,1] => [4,3,1,1] => 7
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [3,1,4,1] => [4,3,1,1] => 7
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,5,1] => [5,2,1,1] => 7
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,6,1] => [6,1,1,1] => 6
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [6,1,2,1] => [6,2,1,1] => 8
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [4,1,1,3] => [4,3,1,1] => 7
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [5,1,3,1] => [5,3,1,1] => 8
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [3,1,1,4] => [4,3,1,1] => 7
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [4,1,4,1] => [4,4,1,1] => 8
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [3,1,5,1] => [5,3,1,1] => 8
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,6,1] => [6,2,1,1] => 8
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => 7
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0] => [8,1,1] => [8,1,1] => 8
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => [6,1,1,1] => 6
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,0] => [10] => [10] => 10
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,5] => [5,3,1] => 8
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,4,1] => [4,1,1,1,1,1] => 4
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,4,1,1] => [4,1,1,1,1,1] => 4
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,5,1] => [5,1,1,1,1] => 5
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,1,4,1] => [4,1,1,1,1,1,1] => 4
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,8] => [8,2] => 10
[1,1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => [11] => [11] => 11
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [11] => [11] => 11
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,3] => [6,3] => 9
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,0] => [5,4] => [5,4] => 9
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,1,0,0] => [5,4] => [5,4] => 9
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [10] => [10] => 10
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,8] => [8,1] => 8
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [10] => [10] => 10
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [1,8] => [8,1] => 8
[1,1,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,7] => [7,2] => 9
[1,1,0,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,4] => [5,4] => 9
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [3,3,3] => [3,3,3] => 9
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,6] => [6,4] => 10
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,1,0,0,0] => [5,5] => [5,5] => 10
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,1,0,0,0,0] => [5,5] => [5,5] => 10
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,7] => [7,3] => 10
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,9] => [9,1] => 9
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,6,1] => [6,2,1] => 8
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0] => [10] => [10] => 10
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0] => [10] => [10] => 10
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,2,4] => [4,2,2,1] => 8
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,2,6] => [6,2,1] => 8
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,8] => [8,1] => 8
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,7] => [7,2] => 9
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,2,5] => [5,2,2] => 9
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,2,2,4] => [4,2,2,2] => 10
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,2,6] => [6,2,1] => 8
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,2,6] => [6,2,2] => 10
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [1,8] => [8,1] => 8
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,8] => [8,2] => 10
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,7] => [7,1,1] => 7
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,9] => [9,1] => 9
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [4,5] => [5,4] => 9
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,2,7] => [7,2,1] => 9
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3] => [4,3,2] => 9
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,2,2,5] => [5,2,2,1] => 9
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,2,2,2,3] => [3,2,2,2,1] => 9
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,5] => [5,1,1,1,1] => 5
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => 4
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,1,0,0] => [5,1,3] => [5,3,1] => 8
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [3,1,1,1,3] => [3,3,1,1,1] => 6
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,8] => [8,1] => 8
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,2,5] => [5,2,2] => 9
[1,1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,0] => [11] => [11] => 11
[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,1,1,4] => [4,2,1,1,1] => 6
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => 7
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [3,1,5] => [5,3,1] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [11] => [11] => 11
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [6,1,1,1,1,1] => [6,1,1,1,1,1] => 6
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,6] => [6,2,1] => 8
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,2,5] => [5,2,1,1] => 7
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,2,4] => [4,2,1,1,1] => 6
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,1,2,3] => [3,2,1,1,1,1] => 5
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [11] => [11] => 11
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [10] => [10] => 10
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,5,1] => [5,1,1,1,1] => 5
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,4,2,1] => [4,2,1,1,1] => 6
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,2,4,1,1] => [4,2,1,1,1] => 6
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [1,5,1,1,1] => [5,1,1,1,1] => 5
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [10] => [10] => 10
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [11] => [11] => 11
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,7,1] => [7,2,1] => 9
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => 4
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,1,5] => [5,2,1,1] => 7
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,6,1,1] => [6,1,1,1] => 6
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [5,4] => [5,4] => 9
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,6] => [6,3] => 9
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,8] => [8,1] => 8
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,8] => [8,2] => 10
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [4,6] => [6,4] => 10
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [6,4] => [6,4] => 10
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => [6,1,1,1] => 6
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [8,1,1] => [8,1,1] => 8
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [10] => [10] => 10
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [10] => [10] => 10
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [3,6] => [6,3] => 9
[1,1,0,1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [10] => [10] => 10
[1,0,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,8] => [8,1] => 8
[1,1,0,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [10] => [10] => 10
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,8] => [8,1] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [9,1] => [9,1] => 9
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,4,1,2] => [4,2,1,1,1] => 6
[1,1,1,0,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,4] => [5,4] => 9
[1,1,0,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5] => [5,4] => 9
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [9,1] => [9,1] => 9
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,5] => [5,1,1,1,1] => 5
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0] => [10] => [10] => 10
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => 5
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [8,1] => [8,1] => 8
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [1,6,2] => [6,2,1] => 8
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [2,7,1] => [7,2,1] => 9
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [2,7] => [7,2] => 9
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,6,1] => [6,1,1,1] => 6
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [1,6,1,1] => [6,1,1,1] => 6
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [7,2] => [7,2] => 9
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [1,7,2] => [7,2,1] => 9
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [10] => [10] => 10
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,7] => [7,1,1] => 7
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,1,5] => [5,2,1,1] => 7
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,2,4,2] => [4,2,2,1] => 8
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => 7
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,1,1,5] => [5,2,1,1,1] => 7
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => 5
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => [6,1,1,1] => 6
[1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0] => [11] => [11] => 11
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,4,2] => [4,2,1,1,1] => 6
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,4,2] => [4,2,1,1,1] => 6
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,1,4,2] => [4,2,1,1,1,1] => 6
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,4,2] => [4,2,1,1,1,1] => 6
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,4,2,1] => [4,2,1,1,1,1] => 6
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,5,2] => [5,2,1,1] => 7
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,5,2] => [5,2,1,1] => 7
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,5,2] => [5,2,1,1] => 7
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,5,2] => [5,2,1,1] => 7
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,1,4,2,1] => [4,2,1,1,1,1] => 6
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [10] => [10] => 10
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,7,1] => [7,1,1] => 7
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,6,1] => [6,1,1,1] => 6
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,8,1] => [8,1,1] => 8
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,7,1] => [7,1,1,1] => 7
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,1,1,1,1,3,1] => [3,2,1,1,1,1,1,1] => 5
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [3,1,1,1,3,1] => [3,3,1,1,1,1] => 6
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,3,1,3,1] => [3,3,1,1,1] => 6
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,2,1,3,1] => [3,2,1,1,1,1] => 5
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,1,1,2,1] => [3,2,1,1,1,1] => 5
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1] => 4
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [3,6] => [6,3] => 9
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [3,3,3] => [3,3,3] => 9
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,5,2] => [5,2,2] => 9
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,4,3] => [4,3,2] => 9
[1,1,0,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4] => [4,3,2] => 9
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,4,3] => [4,3,1,1] => 7
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [1,6,2] => [6,2,1] => 8
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [1,5,3] => [5,3,1] => 8
[1,0,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,4] => [4,4,1] => 8
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [4,5] => [5,4] => 9
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [6,2,2] => [6,2,2] => 10
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [2,4,2,2] => [4,2,2,2] => 10
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [2,6,2] => [6,2,2] => 10
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [8,2] => [8,2] => 10
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [8,2] => [8,2] => 10
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [8,2] => [8,2] => 10
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,2,4,2] => [4,2,2,2] => 10
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [4,4,2] => [4,4,2] => 10
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [8,2] => [8,2] => 10
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [2,6,2] => [6,2,2] => 10
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,2,6] => [6,2,2] => 10
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [4,6] => [6,4] => 10
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [10] => [10] => 10
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [2,8] => [8,2] => 10
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [10] => [10] => 10
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [10] => [10] => 10
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [10] => [10] => 10
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [10] => [10] => 10
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [10] => [10] => 10
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [2,8] => [8,2] => 10
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [10] => [10] => 10
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [10] => [10] => 10
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [2,8] => [8,2] => 10
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [10] => [10] => 10
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [4,2,4] => [4,4,2] => 10
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [6,4] => [6,4] => 10
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [2,4,4] => [4,4,2] => 10
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [6,4] => [6,4] => 10
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [2,8] => [8,2] => 10
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [10] => [10] => 10
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [10] => [10] => 10
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [10] => [10] => 10
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [4,6] => [6,4] => 10
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [10] => [10] => 10
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => 12
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,2,2,2,2] => [4,2,2,2,2] => 12
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [6,2,2,2] => [6,2,2,2] => 12
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,2,2,2] => [4,2,2,2,2] => 12
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [6,2,2,2] => [6,2,2,2] => 12
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [2,6,2,2] => [6,2,2,2] => 12
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [2,2,4,2,2] => [4,2,2,2,2] => 12
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => [4,4,2,2] => 12
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [2,6,2,2] => [6,2,2,2] => 12
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,6,2] => [6,4,2] => 12
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,2,2,4,2] => [4,2,2,2,2] => 12
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [4,2,4,2] => [4,4,2,2] => 12
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [6,4,2] => [6,4,2] => 12
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,4,4,2] => [4,4,2,2] => 12
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [6,4,2] => [6,4,2] => 12
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [4,6,2] => [6,4,2] => 12
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [6,6] => [6,6] => 12
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [6,6] => [6,6] => 12
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [4,2,2,4] => [4,4,2,2] => 12
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [6,2,4] => [6,4,2] => 12
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,4,2,4] => [4,4,2,2] => 12
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [6,2,4] => [6,4,2] => 12
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [2,6,4] => [6,4,2] => 12
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [2,2,4,4] => [4,4,2,2] => 12
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [4,4,4] => [4,4,4] => 12
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [2,6,4] => [6,4,2] => 12
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [6,6] => [6,6] => 12
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [6,6] => [6,6] => 12
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [4,4,1] => [4,4,1] => 8
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [3,5,1] => [5,3,1] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [7,2,1] => [7,2,1] => 9
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [5,3,1] => [5,3,1] => 8
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [6,3,1] => [6,3,1] => 9
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [4,4,1] => [4,4,1] => 8
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [5,4,1] => [5,4,1] => 9
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [3,5,1] => [5,3,1] => 8
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [4,5,1] => [5,4,1] => 9
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,6,1] => [6,2,1] => 8
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,6,1] => [6,3,1] => 9
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,7,1] => [7,1,1] => 7
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [6,3,1] => [6,3,1] => 9
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [4,4,1] => [4,4,1] => 8
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [5,4,1] => [5,4,1] => 9
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [3,5,1] => [5,3,1] => 8
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [4,4,1] => [4,4,1] => 8
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [4,5,1] => [5,4,1] => 9
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,6,1] => [6,2,1] => 8
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [3,5,1] => [5,3,1] => 8
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,6,1] => [6,3,1] => 9
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [1,7,1] => [7,1,1] => 7
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,6,1] => [6,2,1] => 8
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [2,7,1] => [7,2,1] => 9
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,7,1] => [7,3,1] => 10
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [1,7,1] => [7,1,1] => 7
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,8,1] => [8,1,1] => 8
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,8,1] => [8,2,1] => 10
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,9,1] => [9,1,1] => 9
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10] => [10] => 10
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [6,2,1] => [6,2,1] => 8
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [8,1] => [8,1] => 8
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [1,8] => [8,1] => 8
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [7,2] => [7,2] => 9
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [10] => [10] => 10
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,7] => [7,2] => 9
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,1,0,0] => [8,2] => [8,2] => 10
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0] => [10] => [10] => 10
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,1,0,0] => [10] => [10] => 10
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [1,7,1] => [7,1,1] => 7
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0,0,0] => [10] => [10] => 10
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,1,0,0] => [4,5] => [5,4] => 9
[1,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,9] => [9,1,1] => 9
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,1,1,1,1] => [4,1,1,1,1,1] => 4
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0] => [10] => [10] => 10
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [10] => [10] => 10
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [10] => [10] => 10
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,0] => [6,2,1] => [6,2,1] => 8
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [6,2,2] => [6,2,2] => 10
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,0] => [6,2,1] => [6,2,1] => 8
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [6,2,1] => [6,2,1] => 8
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0] => [6,2,1] => [6,2,1] => 8
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [6,2,1] => [6,2,1] => 8
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => 7
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [11] => [11] => 11
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [11] => [11] => 11
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,2,2] => [3,2,2,2,1] => 9
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [3,5,1] => [5,3,1] => 8
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [4,4,1] => [4,4,1] => 8
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,1,0] => [5,3,1] => [5,3,1] => 8
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0] => [6,2,1] => [6,2,1] => 8
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [2,8,1] => [8,2,1] => 10
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,6,1] => [6,3,1] => 9
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [3,7,1] => [7,3,1] => 10
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [4,4,1] => [4,4,1] => 8
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [4,5,1] => [5,4,1] => 9
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0] => [5,3,1] => [5,3,1] => 8
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,4,1] => [4,3,1,1] => 7
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [5,4,1] => [5,4,1] => 9
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,1,0] => [6,2,1] => [6,2,1] => 8
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,1] => [4,3,1,1] => 7
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [6,3,1] => [6,3,1] => 9
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [1,5,2,1] => [5,2,1,1] => 7
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0,1,0] => [7,2,1] => [7,2,1] => 9
[1,1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [9,2] => [9,2] => 11
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [8,2] => [8,2] => 10
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [5,4] => [5,4] => 9
[1,0,1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [1,8,1] => [8,1,1] => 8
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,2,1,6] => [6,2,1,1] => 8
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => [1,8,1] => [8,1,1] => 8
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,8,1] => [8,1,1] => 8
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [1,6,1,2] => [6,2,1,1] => 8
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,5,1,2,1] => [5,2,1,1,1] => 7
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [1,8,1] => [8,1,1] => 8
[1,0,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,2,1,6] => [6,2,1,1] => 8
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => [1,8,1] => [8,1,1] => 8
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [1,8,1] => [8,1,1] => 8
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,2,1,6] => [6,2,1,1] => 8
[1,0,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0] => [1,8,1] => [8,1,1] => 8
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,4,1,4] => [4,4,1,1] => 8
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,1,4,1] => [4,3,1,1,1] => 7
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [1,5,1,3] => [5,3,1,1] => 8
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,4,1,3,1] => [4,3,1,1,1] => 7
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [1,8,1] => [8,1,1] => 8
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,1,0] => [1,8,1] => [8,1,1] => 8
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [1,8,1] => [8,1,1] => 8
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,2,1,6] => [6,2,1,1] => 8
[1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0] => [1,8,1] => [8,1,1] => 8
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,8,1] => [8,1,1] => 8
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [1,6,1,2] => [6,2,1,1] => 8
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,1,0] => [1,5,1,2,1] => [5,2,1,1,1] => 7
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [1,8,1] => [8,1,1] => 8
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,2,1,6] => [6,2,1,1] => 8
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [1,8,1] => [8,1,1] => 8
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,0,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0,1,1,0,0] => [1,8,1,2] => [8,2,1,1] => 10
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,0,1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,1,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0,1,1,0,0] => [1,8,1,2] => [8,2,1,1] => 10
[1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,1,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,1,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [1,8,1,2] => [8,2,1,1] => 10
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,1,2,1,3,1] => [3,3,2,1,1,1,1] => 8
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,8,1,2] => [8,2,1,1] => 10
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,1,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0,1,1,0,0] => [1,8,1,2] => [8,2,1,1] => 10
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,1,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,1,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,1,1,0,0] => [1,8,1,2] => [8,2,1,1] => 10
[1,0,1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0] => [7,3] => [7,3] => 10
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,1,0,0] => [6,4] => [6,4] => 10
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,1,0,0] => [5,5] => [5,5] => 10
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [4,6] => [6,4] => 10
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [3,1,5] => [5,3,1] => 8
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,7] => [7,3] => 10
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1,1] => 4
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,1,1,1,1,3] => [3,2,1,1,1,1,1] => 5
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,1,1,4] => [4,2,1,1,1] => 6
[1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,10] => [10,1] => 10
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,5,2] => [5,2,2] => 9
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,2,1] => [4,2,2,1] => 8
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,2,2] => [4,2,2,2] => 10
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,2,4,2] => [4,2,2,2] => 10
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,2,2,4] => [4,2,2,2] => 10
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,6,1] => [6,2,1] => 8
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,2,5,1] => [5,2,2,1] => 9
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [4,4,1] => [4,4,1] => 8
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,5,2,1] => [5,2,2,1] => 9
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [6,2,1] => [6,2,1] => 8
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,7] => [7,1,1] => 7
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => 7
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [1,7,1,1] => [7,1,1,1] => 7
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,1,7,1] => [7,1,1,1] => 7
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [1,8,1] => [8,1,1] => 8
[1,0,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1,8] => [8,1,1] => 8
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,3] => [6,3] => 9
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,2] => [7,2] => 9
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => 7
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0,0] => [12] => [12] => 12
[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0] => [11] => [11] => 11
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0] => [6,2,2] => [6,2,2] => 10
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0] => [10] => [10] => 10
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,2,6] => [6,2,1] => 8
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,8] => [8,1] => 8
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,2,5] => [5,2,2] => 9
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,2,6] => [6,2,2] => 10
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,8] => [8,1] => 8
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,8] => [8,2] => 10
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [2,8] => [8,2] => 10
[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [10] => [10] => 10
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [8,2] => [8,2] => 10
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => 7
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [6,1,1,1] => [6,1,1,1] => 6
[1,0,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,9] => [9,1] => 9
[1,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,6] => [6,3] => 9
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [6,1,1,2] => [6,2,1,1] => 8
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,10] => [10,1] => 10
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,10] => [10,1] => 10
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [2,6,1] => [6,2,1] => 8
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,1,0,0] => [5,2,2] => [5,2,2] => 9
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,2] => [4,3,2] => 9
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,6,2] => [6,2,1] => 8
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,4,2,2,1] => [4,2,2,1,1] => 8
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => 7
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0,0] => [10] => [10] => 10
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0,1,0] => [8,1,1] => [8,1,1] => 8
[1,1,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0,0] => [10] => [10] => 10
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,1,0] => [8,1,1] => [8,1,1] => 8
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0] => [1,8,1] => [8,1,1] => 8
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [6,3,1] => [6,3,1] => 9
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [6,1,3] => [6,3,1] => 9
[1,1,0,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [10] => [10] => 10
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,6,1] => [6,3,1] => 9
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [8,1,1] => [8,1,1] => 8
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [1,8,1] => [8,1,1] => 8
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,4,3] => [4,3,3] => 10
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [1,8,1] => [8,1,1] => 8
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,1,8] => [8,1,1] => 8
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0,1,0] => [6,3,1] => [6,3,1] => 9
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,1,0,1,0,0] => [6,1,3] => [6,3,1] => 9
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => [1,8,1] => [8,1,1] => 8
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => [1,6,3] => [6,3,1] => 9
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => [10] => [10] => 10
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [3,6,1] => [6,3,1] => 9
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [1,8,1] => [8,1,1] => 8
[1,1,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [3,1,6] => [6,3,1] => 9
[1,0,1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,3,6] => [6,3,1] => 9
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [8,1,1] => [8,1,1] => 8
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [1,8,1] => [8,1,1] => 8
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [3,4,3] => [4,3,3] => 10
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [1,8,1] => [8,1,1] => 8
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [1,1,8] => [8,1,1] => 8
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,6,3] => [6,3,1] => 9
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,1,0,0] => [10] => [10] => 10
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [3,1,6] => [6,3,1] => 9
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,3,6] => [6,3,1] => 9
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [1,8,1] => [8,1,1] => 8
[1,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0] => [10] => [10] => 10
[1,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,8] => [8,1,1] => 8
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [10] => [10] => 10
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,1,0,1,0,0] => [1,8,3] => [8,3,1] => 11
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,4,5] => [5,4,3] => 12
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,4,5] => [5,4,3] => 12
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,1,0,1,0,0] => [1,8,3] => [8,3,1] => 11
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0,0] => [12] => [12] => 12
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,6,5] => [6,5,1] => 11
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,6,5] => [6,5,1] => 11
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,1,1,0,1,0,0,0] => [12] => [12] => 12
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,1,1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0,0] => [12] => [12] => 12
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,1,0,1,0,0] => [1,8,3] => [8,3,1] => 11
[1,1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0,0] => [12] => [12] => 12
[1,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0,0] => [12] => [12] => 12
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [3,8,1] => [8,3,1] => 11
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,6,5] => [6,5,1] => 11
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,6,5] => [6,5,1] => 11
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,0] => [12] => [12] => 12
[1,1,1,0,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,0] => [12] => [12] => 12
[1,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0] => [12] => [12] => 12
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0,0] => [12] => [12] => 12
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [12] => [12] => 12
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [12] => [12] => 12
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0,0] => [12] => [12] => 12
[1,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0,1,0,0,0] => [12] => [12] => 12
[1,1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,6,1] => [6,5,1] => 11
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,6,1] => [6,5,1] => 11
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,1,0,0] => [1,8,3] => [8,3,1] => 11
[1,1,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0,0,0] => [12] => [12] => 12
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0,0] => [12] => [12] => 12
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0] => [3,8,1] => [8,3,1] => 11
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0,1,1,0,1,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,0,0] => [12] => [12] => 12
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,1,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [12] => [12] => 12
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [5,6,1] => [6,5,1] => 11
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [5,6,1] => [6,5,1] => 11
[1,1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [3,8,1] => [8,3,1] => 11
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [5,4,3] => [5,4,3] => 12
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [5,4,3] => [5,4,3] => 12
[1,1,0,1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,0,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [3,8,1] => [8,3,1] => 11
[1,0,1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0] => [10] => [10] => 10
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [1,8] => [8,1] => 8
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,0,0] => [10] => [10] => 10
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,9] => [9,1] => 9
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0] => [8,1] => [8,1] => 8
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,1,5] => [5,2,1,1] => 7
[1,0,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,9] => [9,1] => 9
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,1,2,2] => [5,2,2,1] => 9
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,2,2] => [3,2,2,2,1] => 9
[1,0,1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10] => [10,1] => 10
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [2,6,1] => [6,2,1] => 8
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,6] => [6,2,2] => 10
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,4] => [4,4,2] => 10
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,6,2] => [6,2,2] => 10
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,6,2] => [6,2,2] => 10
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,8] => [8,2] => 10
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,8] => [8,2] => 10
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,8] => [8,2] => 10
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,2,4] => [4,4,2] => 10
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [4,4,2] => [4,4,2] => 10
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,6] => [6,4] => 10
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [6,2,2] => [6,2,2] => 10
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [6,4] => [6,4] => 10
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [8,2] => [8,2] => 10
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [8,2] => [8,2] => 10
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [8,2] => [8,2] => 10
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [8,2] => [8,2] => 10
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [10] => [10] => 10
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [10] => [10] => 10
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [10] => [10] => 10
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [10] => [10] => 10
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [10] => [10] => 10
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [10] => [10] => 10
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [10] => [10] => 10
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [10] => [10] => 10
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [10] => [10] => 10
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [10] => [10] => 10
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [10] => [10] => 10
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [10] => [10] => 10
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,2,2,4,2] => [4,2,2,2,2] => 12
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,2,4,2,2] => [4,2,2,2,2] => 12
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,2,4,4] => [4,4,2,2] => 12
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,2,2,2] => [4,2,2,2,2] => 12
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,4,2,4] => [4,4,2,2] => 12
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,4,2] => [4,4,2,2] => 12
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,6,2,2] => [6,2,2,2] => 12
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,6,4] => [6,4,2] => 12
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [2,6,2,2] => [6,2,2,2] => 12
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [2,6,4] => [6,4,2] => 12
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,2,2,2,2] => [4,2,2,2,2] => 12
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,2,2,4] => [4,4,2,2] => 12
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [4,2,4,2] => [4,4,2,2] => 12
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => [4,4,2,2] => 12
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,4] => [4,4,4] => 12
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [4,6,2] => [6,4,2] => 12
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [4,6,2] => [6,4,2] => 12
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [6,2,2,2] => [6,2,2,2] => 12
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [6,2,4] => [6,4,2] => 12
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [6,4,2] => [6,4,2] => 12
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [6,6] => [6,6] => 12
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [6,6] => [6,6] => 12
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [6,2,2,2] => [6,2,2,2] => 12
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [6,2,4] => [6,4,2] => 12
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [6,4,2] => [6,4,2] => 12
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [6,6] => [6,6] => 12
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [6,6] => [6,6] => 12
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [12] => [12] => 12
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,6,2] => [6,2,1] => 8
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,7,1] => [7,1,1] => 7
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,5,2,1] => [5,2,1,1] => 7
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,2,1] => [3,2,2,1,1] => 7
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,4,2,2,1] => [4,2,2,1,1] => 8
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,6,2] => [6,2,1] => 8
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [1,6,2,1] => [6,2,1,1] => 8
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [1,8,1] => [8,1,1] => 8
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,5,3] => [5,3,1] => 8
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,7,2] => [7,2,1] => 9
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,4,1] => [4,3,1,1] => 7
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,5,2,2] => [5,2,2,1] => 9
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,4,2,1] => [4,2,1,1,1] => 6
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [1,6,2,1] => [6,2,1,1] => 8
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,8] => [8,1] => 8
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0] => [10,1] => [10,1] => 10
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [10,1] => [10,1] => 10
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,2,4,2] => [4,2,2,1] => 8
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [10] => [10] => 10
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [7,3] => [7,3] => 10
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [8,1,1] => [8,1,1] => 8
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,5,1,1] => [5,1,1,1,1] => 5
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,3,1,1,2] => [3,2,1,1,1,1] => 5
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => 7
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => 7
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => 7
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => 7
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0,1,0] => [6,1,1,1] => [6,1,1,1] => 6
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,8] => [8,2] => 10
[1,1,0,0,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,8] => [8,2] => 10
[1,1,0,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [2,8] => [8,2] => 10
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [2,8] => [8,2] => 10
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [10] => [10] => 10
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [10] => [10] => 10
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [10] => [10] => 10
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [10] => [10] => 10
[1,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0] => [9,1] => [9,1] => 9
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,2,6] => [6,2,1,1] => 8
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,2,6] => [6,2,1,1] => 8
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,8] => [8,1,1] => 8
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,7,1] => [7,1,1,1] => 7
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [1,1,7,1] => [7,1,1,1] => 7
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,5,4] => [5,4,1] => 9
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,8,1] => [8,1,1] => 8
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [4,2,4] => [4,4,2] => 10
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [1,7,1,1] => [7,1,1,1] => 7
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [1,7,1,1] => [7,1,1,1] => 7
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [8,1,1] => [8,1,1] => 8
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [6,2,1,1] => [6,2,1,1] => 8
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [6,2,1,1] => [6,2,1,1] => 8
[1,0,1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,0] => [1,9] => [9,1] => 9
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [10] => [10] => 10
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [10] => [10] => 10
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [10] => [10] => 10
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [10] => [10] => 10
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [8,2] => [8,2] => 10
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,1,0,0] => [8,2] => [8,2] => 10
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0] => [8,2] => [8,2] => 10
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [8,2] => [8,2] => 10
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,0,0,1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [12] => [12] => 12
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,0] => [12] => [12] => 12
[1,1,1,0,0,1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [12] => [12] => 12
[1,1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [12] => [12] => 12
[1,1,1,0,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,0,0,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,0,0,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,0,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,0,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0,1,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [11,1] => [11,1] => 11
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [6,2,4] => [6,4,2] => 12
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [6,5,1] => [6,5,1] => 11
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [6,2,4] => [6,4,2] => 12
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [6,5,1] => [6,5,1] => 11
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,0,1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,1,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,1,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,1,1,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0,0] => [1,11] => [11,1] => 11
[1,0,1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,0] => [1,11] => [11,1] => 11
[1,1,0,1,0,1,1,0,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [12] => [12] => 12
[1,1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,1,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0,0] => [12] => [12] => 12
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0,1,1,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0,1,1,0,0,0] => [12] => [12] => 12
[1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [12] => [12] => 12
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,1,1,0,0,0] => [12] => [12] => 12
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,0,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,0,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [10] => [10] => 10
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [10] => [10] => 10
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [7,2] => [7,2] => 9
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [10] => [10] => 10
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,4,1,1,1,1] => [4,2,1,1,1,1] => 6
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [11] => [11] => 11
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,7] => [7,2] => 9
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,1,1,1,1] => [3,2,1,1,1,1,1] => 5
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [11] => [11] => 11
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [11] => [11] => 11
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [11] => [11] => 11
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,7] => [7,2] => 9
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0] => [9,1] => [9,1] => 9
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,2,2,2,1] => [2,2,2,2,2,1,1] => 10
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,1,0,0] => [8,2] => [8,2] => 10
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [8,1] => [8,1] => 8
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [1,6,2] => [6,2,1] => 8
[1,1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0] => [11] => [11] => 11
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0] => [12] => [12] => 12
[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0] => [12] => [12] => 12
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,8] => [8,1,1] => 8
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,4,4] => [4,4,1] => 8
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,7] => [7,1,1,1] => 7
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,1,4] => [4,3,1,1] => 7
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,6] => [6,1,1,1,1] => 6
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,1,1,4] => [4,2,1,1,1] => 6
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,5] => [5,1,1,1,1,1] => 5
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,6] => [6,1,1,1,1,1] => 6
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,9] => [9,1,1] => 9
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,9] => [9,1] => 9
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => [6,3] => [6,3] => 9
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [4,5] => [5,4] => 9
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [2,7] => [7,2] => 9
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,8] => [8,1] => 8
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [3,6] => [6,3] => 9
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [5,4] => [5,4] => 9
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [7,2] => [7,2] => 9
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [4,5] => [5,4] => 9
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,7] => [7,2] => 9
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [1,8] => [8,1] => 8
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [3,6] => [6,3] => 9
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [7,2] => [7,2] => 9
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,2,6] => [6,2,2] => 10
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [5,2,2] => [5,2,2] => 9
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,2,2,4] => [4,2,2,2] => 10
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [4,4,1] => [4,4,1] => 8
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [2,8] => [8,2] => 10
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,9] => [9,1] => 9
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [4,2,2,1] => [4,2,2,1] => 8
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [5,2,2,1] => [5,2,2,1] => 9
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,1,1,4] => [4,2,1,1,1] => 6
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,6,2] => [6,2,1] => 8
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,4,2,2] => [4,2,2,1] => 8
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0] => [7,2] => [7,2] => 9
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [1,8,1] => [8,1,1] => 8
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [1,8,1] => [8,1,1] => 8
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0] => [7,2] => [7,2] => 9
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [1,6,2,1] => [6,2,1,1] => 8
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [5,2,2] => [5,2,2] => 9
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,4,2,2,1] => [4,2,2,1,1] => 8
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,2,1] => [3,2,2,1,1] => 7
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [3,6] => [6,3] => 9
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [5,4] => [5,4] => 9
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [3,1,1,4] => [4,3,1,1] => 7
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,1,0,0,0] => [4,1,4] => [4,4,1] => 8
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [1,8,2] => [8,2,1] => 10
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0,0,0] => [10] => [10] => 10
[1,1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [10] => [10] => 10
[1,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0,0,0] => [10] => [10] => 10
[1,1,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [10] => [10] => 10
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [10] => [10] => 10
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [10] => [10] => 10
[1,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [10] => [10] => 10
[1,1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [10] => [10] => 10
[1,1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0,0,0] => [10] => [10] => 10
[1,1,1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [10] => [10] => 10
[1,1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [10] => [10] => 10
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [10] => [10] => 10
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [10] => [10] => 10
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => [10] => [10] => 10
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0,0] => [10] => [10] => 10
[1,1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0,0] => [10] => [10] => 10
[1,1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0] => [10] => [10] => 10
[1,1,0,1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => [10] => [10] => 10
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [10] => [10] => 10
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [10] => [10] => 10
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [10] => [10] => 10
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [10] => [10] => 10
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0,1,0,0] => [10] => [10] => 10
[1,1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0,0] => [10] => [10] => 10
[1,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0,0] => [10] => [10] => 10
[1,1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [10] => [10] => 10
[1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [10] => [10] => 10
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,0] => [10] => [10] => 10
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0,0,0] => [10] => [10] => 10
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0,0] => [10] => [10] => 10
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,0,0] => [10] => [10] => 10
[1,1,1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0,0] => [10] => [10] => 10
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0,0] => [10] => [10] => 10
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,0] => [10] => [10] => 10
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [10] => [10] => 10
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [10] => [10] => 10
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,0,0] => [10] => [10] => 10
[1,1,1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,0] => [10] => [10] => 10
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0,0] => [10] => [10] => 10
[1,1,1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0,0] => [12] => [12] => 12
[1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0,0,1,0,0,0] => [12] => [12] => 12
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0,0,0] => [12] => [12] => 12
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,0,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0,0,1,0,0,0] => [12] => [12] => 12
[1,1,1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,1,0,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0,0,0] => [12] => [12] => 12
[1,1,1,1,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [12] => [12] => 12
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0,0,0] => [12] => [12] => 12
[1,1,1,0,0,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0,0,0] => [12] => [12] => 12
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0,0] => [12] => [12] => 12
[1,1,1,0,0,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,0,1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0,0] => [12] => [12] => 12
[1,1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,0,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,0,1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,0,0] => [12] => [12] => 12
[1,1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,1,0,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0,0,0] => [12] => [12] => 12
[1,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,1,0,0,1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0,0,0] => [12] => [12] => 12
[1,1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,0,0] => [12] => [12] => 12
[1,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,1,0,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0] => [12] => [12] => 12
[1,1,1,0,0,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0,0] => [12] => [12] => 12
[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,1,0,0,1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0,0,0] => [12] => [12] => 12
[1,1,1,0,0,1,1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0] => [12] => [12] => 12
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0,1,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,0,0,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0,1,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,0,0,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [12] => [12] => 12
[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0,0] => [12] => [12] => 12
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0] => [12] => [12] => 12
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [12] => [12] => 12
[1,1,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [12] => [12] => 12
[1,1,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0] => [12] => [12] => 12
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,1,1,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,1,1,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,0] => [12] => [12] => 12
[1,1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0,0,1,1,0,0,0] => [12] => [12] => 12
[1,1,1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0] => [12] => [12] => 12
[1,1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0,1,1,0,0,0] => [12] => [12] => 12
[1,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,0] => [12] => [12] => 12
[1,1,1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0,0] => [12] => [12] => 12
[1,1,1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0] => [12] => [12] => 12
[1,1,1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0,0] => [12] => [12] => 12
[1,1,1,0,1,1,0,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,1,1,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0,0,0] => [12] => [12] => 12
[1,1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0,1,1,0,0,0] => [12] => [12] => 12
[1,1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,1,1,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [12] => [12] => 12
[1,1,1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0,1,1,0,0,0] => [12] => [12] => 12
[1,1,1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,1,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0] => [12] => [12] => 12
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,0,0] => [12] => [12] => 12
[1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0,0,0] => [12] => [12] => 12
[1,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0,0,0] => [12] => [12] => 12
[1,1,1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [12] => [12] => 12
[1,1,1,0,1,1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,0] => [12] => [12] => 12
[1,1,1,0,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [12] => [12] => 12
[1,1,0,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2,8] => [8,2] => 10
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [7,2] => [7,2] => 9
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [6,3] => [6,3] => 9
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,1,8] => [8,1,1] => 8
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,8] => [8,1] => 8
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,1,1,1,4] => [4,2,1,1,1,1] => 6
[1,1,0,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,8] => [8,2] => 10
[1,1,0,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,7] => [7,2] => 9
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,8] => [8,2] => 10
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,7] => [7,2] => 9
[1,0,1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,7] => [7,1,1] => 7
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [3,4,1,1] => [4,3,1,1] => 7
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [6,3] => [6,3] => 9
[1,1,0,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [4,5] => [5,4] => 9
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [7,2] => [7,2] => 9
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [7,2] => [7,2] => 9
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,7] => [7,2] => 9
[1,1,0,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,7] => [7,2] => 9
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,7] => [7,2] => 9
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,7] => [7,2] => 9
[1,1,0,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,7] => [7,2] => 9
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [4,4,1,1] => [4,4,1,1] => 8
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,1,5,2] => [5,2,2,1] => 9
[1,1,1,0,0,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [5,4,1] => [5,4,1] => 9
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [3,5,2] => [5,3,2] => 10
[1,1,1,0,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [4,1,4,1] => [4,4,1,1] => 8
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [5,4,1] => [5,4,1] => 9
[1,1,1,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [3,1,6] => [6,3,1] => 9
[1,1,1,0,1,0,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,5] => [5,4,1] => 9
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [8,2] => [8,2] => 10
[1,1,1,0,0,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [5,5] => [5,5] => 10
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [8,2] => [8,2] => 10
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [4,6] => [6,4] => 10
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [7,3] => [7,3] => 10
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,1,0,0,1,0] => [6,1,2,1] => [6,2,1,1] => 8
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,1,0] => [7,2,1] => [7,2,1] => 9
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,1,0,1,0,0] => [6,1,3] => [6,3,1] => 9
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0,1,1,0,0] => [8,2] => [8,2] => 10
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => [7,3] => [7,3] => 10
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,1,7] => [7,2,1] => 9
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,7] => [7,3] => 10
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [2,1,7] => [7,2,1] => 9
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [3,7] => [7,3] => 10
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [10] => [10] => 10
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [10] => [10] => 10
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [10] => [10] => 10
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [10] => [10] => 10
[1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0,1,0,0] => [10] => [10] => 10
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0,0] => [10] => [10] => 10
[1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [10] => [10] => 10
[1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0] => [10] => [10] => 10
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,0] => [10] => [10] => 10
[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [10] => [10] => 10
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0,0] => [10] => [10] => 10
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [10] => [10] => 10
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,0] => [10] => [10] => 10
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,2,1,4] => [5,4,2,1] => 11
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [3,4,4,1] => [4,4,3,1] => 11
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,1,2,1,5] => [5,3,2,1,1] => 10
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,1,3,5] => [5,3,3,1] => 11
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [9,2,1] => [9,2,1] => 11
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,3,4] => [5,4,3] => 12
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [9,2,1] => [9,2,1] => 11
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4] => [4,4,4] => 12
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [4,3,5] => [5,4,3] => 12
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [7,4,1] => [7,4,1] => 11
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [3,5,4] => [5,4,3] => 12
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [7,4,1] => [7,4,1] => 11
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [7,5] => [7,5] => 12
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [6,6] => [6,6] => 12
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [6,6] => [6,6] => 12
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [7,5] => [7,5] => 12
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [7,5] => [7,5] => 12
[1,1,1,0,0,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,6,1] => [6,5,1] => 11
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,6,1] => [6,5,1] => 11
[1,1,0,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,0,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,1,1,0,0,1,0] => [9,2,1] => [9,2,1] => 11
[1,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,1,0,0,1,0] => [9,2,1] => [9,2,1] => 11
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0,0,1,1,0,0] => [10,2] => [10,2] => 12
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0,1,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,1,0,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,0,0,1,0] => [11,1] => [11,1] => 11
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,1,1,0,0,0,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,1,1,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,1,1,0,1,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [12] => [12] => 12
[1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0] => [12] => [12] => 12
[1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,0] => [12] => [12] => 12
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [12] => [12] => 12
[1,1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0,1,1,0,0,0] => [12] => [12] => 12
[1,1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [12] => [12] => 12
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [12] => [12] => 12
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [12] => [12] => 12
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0,0] => [12] => [12] => 12
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0,0] => [10] => [10] => 10
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0,0] => [11] => [11] => 11
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0,0] => [11] => [11] => 11
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0,0] => [11] => [11] => 11
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [4,5] => [5,4] => 9
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0,0] => [11] => [11] => 11
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0] => [11] => [11] => 11
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0] => [10] => [10] => 10
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,2,1,3] => [3,2,1,1,1,1] => 5
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0,1,0] => [6,2,1] => [6,2,1] => 8
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0,1,0] => [6,2,1] => [6,2,1] => 8
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => 7
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,6,1] => [6,1,1,1] => 6
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [10] => [10] => 10
[1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [10] => [10] => 10
[1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [10] => [10] => 10
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => 2
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,2,2] => [5,2,2] => 9
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0] => [5,2,2] => [5,2,2] => 9
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [8,1,1] => [8,1,1] => 8
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [1,6,1,1] => [6,1,1,1] => 6
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [7,1,1,1] => [7,1,1,1] => 7
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [1,5,1,1,1] => [5,1,1,1,1] => 5
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [6,1,1,1,1] => [6,1,1,1,1] => 6
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1,1] => [5,1,1,1,1,1] => 5
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,5,5] => [5,5,1] => 10
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,0,1,0] => [8,1,1] => [8,1,1] => 8
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [5,3,1] => [5,3,1] => 8
[1,1,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [2,7,1] => [7,2,1] => 9
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3] => [4,3,2] => 9
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => 7
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,2,6] => [6,2,2] => 10
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [3,2,4] => [4,3,2] => 9
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,6,1] => [6,2,1] => 8
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [6,2,2] => [6,2,2] => 10
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [4,3,2] => [4,3,2] => 9
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [3,5,2] => [5,3,2] => 10
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,3,4] => [4,3,3] => 10
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0] => [10] => [10] => 10
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [3,1,1,1,3,1] => [3,3,1,1,1,1] => 6
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,1,1,1,3,1] => [3,2,1,1,1,1,1] => 5
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [3,1,1,3,1] => [3,3,1,1,1] => 6
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [3,1,1,1,1,2,1] => [3,2,1,1,1,1,1] => 5
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1,1,1,1] => 2
[1,0,1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,8] => [8,1,1] => 8
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,7] => [7,1,1] => 7
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,5,3] => [5,3,1] => 8
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,5,3] => [5,3,1] => 8
[1,0,1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,8] => [8,1,1] => 8
[1,0,1,0,1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,8] => [8,1,1] => 8
[1,0,1,0,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,3,5] => [5,3,1,1] => 8
[1,0,1,1,0,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,3,6] => [6,3,1] => 9
[1,0,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,8] => [8,1,1] => 8
[1,0,1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,1,7] => [7,1,1,1] => 7
[1,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6] => [6,3,1] => 9
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,1,7] => [7,1,1,1] => 7
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,2,2,4] => [4,2,2,1,1] => 8
[1,1,0,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [3,1,6] => [6,3,1] => 9
[1,1,0,1,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [3,1,6] => [6,3,1] => 9
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [3,1,2,4] => [4,3,2,1] => 9
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [5,1,4] => [5,4,1] => 9
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [5,1,4] => [5,4,1] => 9
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [1,8,1] => [8,1,1] => 8
[1,0,1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,7,1] => [7,1,1,1] => 7
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,8,1] => [8,1,1] => 8
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [1,5,3,1] => [5,3,1,1] => 8
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,3,1] => [3,3,2,1,1] => 8
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [3,6,1] => [6,3,1] => 9
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,3,3,1] => [3,3,3,1] => 9
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [5,4,1] => [5,4,1] => 9
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [5,4,1] => [5,4,1] => 9
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [1,6,2,1] => [6,2,1,1] => 8
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [1,1,5,2,1] => [5,2,1,1,1] => 7
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,4,2,1] => [4,3,2,1] => 9
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [1,1,5,2,1] => [5,2,1,1,1] => 7
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,5,5] => [5,5,1,1] => 10
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,2,2,2,4] => [4,2,2,2,1,1] => 10
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [3,1,3,5] => [5,3,3,1] => 11
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,10,1] => [10,1,1] => 10
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,6,3,1] => [6,3,1,1,1] => 9
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,5,2,3,1] => [5,3,2,1,1] => 10
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,2,3,1] => [3,3,2,2,1,1] => 10
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [3,8,1] => [8,3,1] => 11
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [3,8,1] => [8,3,1] => 11
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [3,5,3,1] => [5,3,3,1] => 11
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [3,3,2,3,1] => [3,3,3,2,1] => 11
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [5,6,1] => [6,5,1] => 11
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [5,3,3,1] => [5,3,3,1] => 11
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [5,6,1] => [6,5,1] => 11
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [5,3,3,1] => [5,3,3,1] => 11
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,0,0,1,0] => [7,4,1] => [7,4,1] => 11
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [7,4,1] => [7,4,1] => 11
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [7,4,1] => [7,4,1] => 11
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [7,4,1] => [7,4,1] => 11
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [7,4,1] => [7,4,1] => 11
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [5,4,2,1] => [5,4,2,1] => 11
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [5,4,2,1] => [5,4,2,1] => 11
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,5,1] => [5,1,1,1,1] => 5
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,1,4,1] => [4,1,1,1,1,1,1] => 4
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,5,1] => [5,1,1,1,1,1] => 5
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,6,1] => [6,1,1,1,1] => 6
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5] => [5,4] => 9
[1,1,1,1,0,0,0,1,0,0,1,1,1,1,0,0,0,0] => [5,4] => [5,4] => 9
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,1,0,0,0] => [6,3] => [6,3] => 9
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [5,2,3] => [5,3,2] => 10
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,2,3] => [5,3,2] => 10
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,1,1,0,1,0,0] => [7,2,3] => [7,3,2] => 12
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [7,2,3] => [7,3,2] => 12
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [7,2,3] => [7,3,2] => 12
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [7,2,3] => [7,3,2] => 12
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [7,2,3] => [7,3,2] => 12
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => [10] => [10] => 10
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [8,1] => [8,1] => 8
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0,0] => [10] => [10] => 10
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [1,7,1] => [7,1,1] => 7
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [5,2,1,1] => [5,2,1,1] => 7
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [9,1] => [9,1] => 9
[1,1,1,1,0,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,5] => [5,4] => 9
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [6,3] => [6,3] => 9
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,1,0,0] => [7,2] => [7,2] => 9
[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,7] => [7,2] => 9
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [10] => [10] => 10
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,2,1,1,3] => [3,2,1,1,1,1] => 5
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [5,4] => [5,4] => 9
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [6,2,2] => [6,2,2] => 10
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,2,2,2] => [4,2,2,2] => 10
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [11,1] => [11,1] => 11
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,5,3] => [5,3,1] => 8
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,5,4] => [5,4,1] => 9
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,4,1,3] => [4,3,1,1] => 7
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,4,1,4] => [4,4,1,1] => 8
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,1,1,3] => [3,3,1,1,1] => 6
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [1,4,4] => [4,4,1] => 8
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,3,1,1,4] => [4,3,1,1,1] => 7
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,1,4] => [4,3,1,1] => 7
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,1,1,1,4] => [4,2,1,1,1,1] => 6
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [5,1,2,1] => [5,2,1,1] => 7
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,2,2,5] => [5,2,2,1] => 9
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,2,4,3] => [4,3,2,1] => 9
[1,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,2,7] => [7,2,1] => 9
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,2,7] => [7,2,1] => 9
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,4,2,3] => [4,3,2,1] => 9
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5] => [5,4,1] => 9
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [1,6,3] => [6,3,1] => 9
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [1,6,3] => [6,3,1] => 9
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [3,2,2,3] => [3,3,2,2] => 10
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [3,2,5] => [5,3,2] => 10
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,3] => [4,3,3] => 10
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [10] => [10] => 10
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [10] => [10] => 10
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [10] => [10] => 10
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [10] => [10] => 10
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [10] => [10] => 10
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [10] => [10] => 10
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0,0] => [10] => [10] => 10
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,1,0,0] => [10] => [10] => 10
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,0] => [10] => [10] => 10
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0] => [10] => [10] => 10
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,1,0,0] => [10] => [10] => 10
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,1,0,0] => [10] => [10] => 10
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0,0] => [10] => [10] => 10
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,2,2,2,2,3] => [3,2,2,2,2,1] => 11
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,2,2,2,5] => [5,2,2,2,1] => 11
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,2,2,4,3] => [4,3,2,2,1] => 11
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,2,3] => [4,3,2,2,1] => 11
[1,0,1,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [1,2,9] => [9,2,1] => 11
[1,0,1,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [1,2,9] => [9,2,1] => 11
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [1,2,9] => [9,2,1] => 11
[1,0,1,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [1,2,9] => [9,2,1] => 11
[1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [1,2,9] => [9,2,1] => 11
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,4,2,2,3] => [4,3,2,2,1] => 11
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,4,4,3] => [4,4,3,1] => 11
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,4,7] => [7,4,1] => 11
[1,0,1,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,4,7] => [7,4,1] => 11
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,6,5] => [6,5,1] => 11
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,6,5] => [6,5,1] => 11
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0] => [1,8,3] => [8,3,1] => 11
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0] => [1,8,3] => [8,3,1] => 11
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [1,8,3] => [8,3,1] => 11
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0] => [1,8,3] => [8,3,1] => 11
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [1,8,3] => [8,3,1] => 11
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [3,2,2,2,3] => [3,3,2,2,2] => 12
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,2,4,3] => [4,3,3,2] => 12
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,2,7] => [7,3,2] => 12
[1,1,0,1,0,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [3,2,7] => [7,3,2] => 12
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [3,4,2,3] => [4,3,3,2] => 12
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,4,5] => [5,4,3] => 12
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [3,6,3] => [6,3,3] => 12
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [3,6,3] => [6,3,3] => 12
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,2,2,3] => [5,3,2,2] => 12
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [5,2,5] => [5,5,2] => 12
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [5,4,3] => [5,4,3] => 12
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,2,2,3] => [5,3,2,2] => 12
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [5,2,5] => [5,5,2] => 12
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [5,4,3] => [5,4,3] => 12
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,1,0,0] => [12] => [12] => 12
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,1,0,0] => [12] => [12] => 12
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,1,0,0] => [12] => [12] => 12
[1,0,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,8] => [8,1] => 8
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [1,9] => [9,1] => 9
[1,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,8] => [8,1] => 8
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,0,1 1,0,2,2 1,0,3,4,6 1,0,4,6,13,18 1,0,5,8,21,40,57 1,0,6,10,30,66,130,186 1,0,7,12,40,96,220,432,622
F1=1
F2=1+q2
F3=1+2 q2+2 q3
F4=1+3 q2+4 q3+6 q4
F5=1+4 q2+6 q3+13 q4+18 q5
F6=1+5 q2+8 q3+21 q4+40 q5+57 q6
F7=1+6 q2+10 q3+30 q4+66 q5+130 q6+186 q7
F8=1+7 q2+12 q3+40 q4+96 q5+220 q6+432 q7+622 q8
Description
The sum of the parts of an integer partition that are at least two.
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to partition
Description
Sends a composition to the partition obtained by sorting the entries.
Map
touch composition
Description
Sends a Dyck path to its touch composition given by the composition of lengths of its touch points.
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