Identifier
-
Mp00027:
Dyck paths
—to partition⟶
Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
St000645: Dyck paths ⟶ ℤ
Values
[1,0] => [] => [] => 0
[1,0,1,0] => [1] => [1,0,1,0] => 1
[1,1,0,0] => [] => [] => 0
[1,0,1,0,1,0] => [2,1] => [1,0,1,0,1,0] => 2
[1,0,1,1,0,0] => [1,1] => [1,0,1,1,0,0] => 2
[1,1,0,0,1,0] => [2] => [1,1,0,0,1,0] => 2
[1,1,0,1,0,0] => [1] => [1,0,1,0] => 1
[1,1,1,0,0,0] => [] => [] => 0
[1,0,1,0,1,0,1,0] => [3,2,1] => [1,0,1,0,1,0,1,0] => 3
[1,0,1,0,1,1,0,0] => [2,2,1] => [1,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,0] => [3,1,1] => [1,0,1,1,0,0,1,0] => 4
[1,0,1,1,0,1,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,0] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[1,1,0,0,1,0,1,0] => [3,2] => [1,1,0,0,1,0,1,0] => 3
[1,1,0,0,1,1,0,0] => [2,2] => [1,1,0,0,1,1,0,0] => 4
[1,1,0,1,0,0,1,0] => [3,1] => [1,1,0,1,0,0,1,0] => 3
[1,1,0,1,0,1,0,0] => [2,1] => [1,0,1,0,1,0] => 2
[1,1,0,1,1,0,0,0] => [1,1] => [1,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,0] => [3] => [1,1,1,0,0,0,1,0] => 3
[1,1,1,0,0,1,0,0] => [2] => [1,1,0,0,1,0] => 2
[1,1,1,0,1,0,0,0] => [1] => [1,0,1,0] => 1
[1,1,1,1,0,0,0,0] => [] => [] => 0
[1,0,1,0,1,0,1,0,1,0] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 4
[1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 4
[1,0,1,0,1,1,0,0,1,0] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
[1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 4
[1,0,1,1,0,0,1,0,1,0] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
[1,0,1,1,0,0,1,1,0,0] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 6
[1,0,1,1,0,1,0,0,1,0] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,1,1,0,0,0] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 4
[1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 6
[1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 5
[1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 4
[1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 4
[1,1,0,0,1,0,1,0,1,0] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 4
[1,1,0,0,1,0,1,1,0,0] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 4
[1,1,0,0,1,1,0,0,1,0] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 6
[1,1,0,0,1,1,0,1,0,0] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 5
[1,1,0,0,1,1,1,0,0,0] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 6
[1,1,0,1,0,0,1,0,1,0] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,0,0,1,1,0,0] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 5
[1,1,0,1,0,1,0,0,1,0] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 4
[1,1,0,1,0,1,0,1,0,0] => [3,2,1] => [1,0,1,0,1,0,1,0] => 3
[1,1,0,1,0,1,1,0,0,0] => [2,2,1] => [1,0,1,0,1,1,0,0] => 3
[1,1,0,1,1,0,0,0,1,0] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 5
[1,1,0,1,1,0,0,1,0,0] => [3,1,1] => [1,0,1,1,0,0,1,0] => 4
[1,1,0,1,1,0,1,0,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => 3
[1,1,0,1,1,1,0,0,0,0] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[1,1,1,0,0,0,1,0,1,0] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,1,0,0] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 6
[1,1,1,0,0,1,0,0,1,0] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 4
[1,1,1,0,0,1,0,1,0,0] => [3,2] => [1,1,0,0,1,0,1,0] => 3
[1,1,1,0,0,1,1,0,0,0] => [2,2] => [1,1,0,0,1,1,0,0] => 4
[1,1,1,0,1,0,0,0,1,0] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 4
[1,1,1,0,1,0,0,1,0,0] => [3,1] => [1,1,0,1,0,0,1,0] => 3
[1,1,1,0,1,0,1,0,0,0] => [2,1] => [1,0,1,0,1,0] => 2
[1,1,1,0,1,1,0,0,0,0] => [1,1] => [1,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,0,1,0] => [4] => [1,1,1,1,0,0,0,0,1,0] => 4
[1,1,1,1,0,0,0,1,0,0] => [3] => [1,1,1,0,0,0,1,0] => 3
[1,1,1,1,0,0,1,0,0,0] => [2] => [1,1,0,0,1,0] => 2
[1,1,1,1,0,1,0,0,0,0] => [1] => [1,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,0] => [] => [] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,0,1,0,1,1,0,0] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 5
[1,0,1,0,1,0,1,1,0,0,1,0] => [5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 6
[1,0,1,0,1,0,1,1,0,1,0,0] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,0,1,0,1,0,1,1,1,0,0,0] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 5
[1,0,1,0,1,1,0,0,1,0,1,0] => [5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 6
[1,0,1,0,1,1,0,0,1,1,0,0] => [4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => 7
[1,0,1,0,1,1,0,1,0,0,1,0] => [5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => 6
[1,0,1,0,1,1,0,1,0,1,0,0] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,0,1,1,0,1,1,0,0,0] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => 5
[1,0,1,0,1,1,1,0,0,0,1,0] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 7
[1,0,1,0,1,1,1,0,0,1,0,0] => [4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 6
[1,0,1,0,1,1,1,0,1,0,0,0] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 5
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 5
[1,0,1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 6
[1,0,1,1,0,0,1,0,1,1,0,0] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => 6
[1,0,1,1,0,0,1,1,0,0,1,0] => [5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 8
[1,0,1,1,0,0,1,1,0,1,0,0] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => 7
[1,0,1,1,0,0,1,1,1,0,0,0] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => 8
[1,0,1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => 6
[1,0,1,1,0,1,0,0,1,1,0,0] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => 7
[1,0,1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => 6
[1,0,1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 5
[1,0,1,1,0,1,0,1,1,0,0,0] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 5
[1,0,1,1,0,1,1,0,0,0,1,0] => [5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => 7
[1,0,1,1,0,1,1,0,0,1,0,0] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 6
[1,0,1,1,0,1,1,0,1,0,0,0] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 5
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 5
[1,0,1,1,1,0,0,0,1,0,1,0] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 7
[1,0,1,1,1,0,0,0,1,1,0,0] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => 9
[1,0,1,1,1,0,0,1,0,0,1,0] => [5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => 7
[1,0,1,1,1,0,0,1,0,1,0,0] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 6
[1,0,1,1,1,0,0,1,1,0,0,0] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 7
[1,0,1,1,1,0,1,0,0,0,1,0] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 7
[1,0,1,1,1,0,1,0,0,1,0,0] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 6
[1,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 5
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 5
>>> Load all 2053 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 8
[1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 7
[1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 6
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 5
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 5
[1,1,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,0,1,0,1,0,1,1,0,0] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 5
[1,1,0,0,1,0,1,1,0,0,1,0] => [5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => 6
[1,1,0,0,1,0,1,1,0,1,0,0] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => 5
[1,1,0,0,1,0,1,1,1,0,0,0] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 5
[1,1,0,0,1,1,0,0,1,0,1,0] => [5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => 7
[1,1,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 8
[1,1,0,0,1,1,0,1,0,0,1,0] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => 7
[1,1,0,0,1,1,0,1,0,1,0,0] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => 6
[1,1,0,0,1,1,0,1,1,0,0,0] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 6
[1,1,0,0,1,1,1,0,0,0,1,0] => [5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => 9
[1,1,0,0,1,1,1,0,0,1,0,0] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 8
[1,1,0,0,1,1,1,0,1,0,0,0] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 7
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 8
[1,1,0,1,0,0,1,0,1,0,1,0] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => 5
[1,1,0,1,0,0,1,0,1,1,0,0] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => 5
[1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => 7
[1,1,0,1,0,0,1,1,0,1,0,0] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => 6
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 7
[1,1,0,1,0,1,0,0,1,0,1,0] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 5
[1,1,0,1,0,1,0,0,1,1,0,0] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => 6
[1,1,0,1,0,1,0,1,0,0,1,0] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => 5
[1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,1,0,1,1,0,0,0] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 4
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => 6
[1,1,0,1,0,1,1,0,0,1,0,0] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
[1,1,0,1,0,1,1,0,1,0,0,0] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 4
[1,1,0,1,1,0,0,0,1,0,1,0] => [5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => 6
[1,1,0,1,1,0,0,0,1,1,0,0] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => 8
[1,1,0,1,1,0,0,1,0,0,1,0] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 6
[1,1,0,1,1,0,0,1,0,1,0,0] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
[1,1,0,1,1,0,0,1,1,0,0,0] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 6
[1,1,0,1,1,0,1,0,0,0,1,0] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 6
[1,1,0,1,1,0,1,0,0,1,0,0] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,0,1,1,0,1,0,1,0,0,0] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 4
[1,1,0,1,1,1,0,0,0,0,1,0] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 7
[1,1,0,1,1,1,0,0,0,1,0,0] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 6
[1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 5
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 4
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 4
[1,1,1,0,0,0,1,0,1,0,1,0] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => 5
[1,1,1,0,0,0,1,0,1,1,0,0] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 5
[1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => 8
[1,1,1,0,0,0,1,1,0,1,0,0] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 7
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 9
[1,1,1,0,0,1,0,0,1,0,1,0] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => 5
[1,1,1,0,0,1,0,0,1,1,0,0] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 6
[1,1,1,0,0,1,0,1,0,0,1,0] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => 5
[1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 4
[1,1,1,0,0,1,1,0,0,0,1,0] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 7
[1,1,1,0,0,1,1,0,0,1,0,0] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 6
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 5
[1,1,1,0,0,1,1,1,0,0,0,0] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 6
[1,1,1,0,1,0,0,0,1,0,1,0] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 5
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 7
[1,1,1,0,1,0,0,1,0,0,1,0] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 5
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 4
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 5
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 5
[1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 4
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1] => [1,0,1,0,1,0,1,0] => 3
[1,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1] => [1,0,1,0,1,1,0,0] => 3
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 6
[1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 5
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,1,1] => [1,0,1,1,0,0,1,0] => 4
[1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => 3
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 5
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 8
[1,1,1,1,0,0,0,1,0,0,1,0] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 5
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 4
[1,1,1,1,0,0,0,1,1,0,0,0] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 6
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 5
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 4
[1,1,1,1,0,0,1,0,1,0,0,0] => [3,2] => [1,1,0,0,1,0,1,0] => 3
[1,1,1,1,0,0,1,1,0,0,0,0] => [2,2] => [1,1,0,0,1,1,0,0] => 4
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 5
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 4
[1,1,1,1,0,1,0,0,1,0,0,0] => [3,1] => [1,1,0,1,0,0,1,0] => 3
[1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => [1,0,1,0,1,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,1] => [1,0,1,1,0,0] => 2
[1,1,1,1,1,0,0,0,0,0,1,0] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,1,1,1,1,0,0,0,0,1,0,0] => [4] => [1,1,1,1,0,0,0,0,1,0] => 4
[1,1,1,1,1,0,0,0,1,0,0,0] => [3] => [1,1,1,0,0,0,1,0] => 3
[1,1,1,1,1,0,0,1,0,0,0,0] => [2] => [1,1,0,0,1,0] => 2
[1,1,1,1,1,0,1,0,0,0,0,0] => [1] => [1,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => [] => [] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 7
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 6
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 7
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 8
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 7
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 6
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 6
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 8
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 7
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 6
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 7
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 7
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 9
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 8
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 9
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 7
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 8
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 7
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 6
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 6
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 8
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 7
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 6
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 6
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 8
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 10
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 8
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 7
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 8
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 8
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 7
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 6
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 6
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 9
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 8
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 7
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 6
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 6
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 7
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 7
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 8
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 7
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 7
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 9
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 10
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 9
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 8
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 8
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 11
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 10
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 9
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 10
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 7
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [5,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 7
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [6,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 9
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 8
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 9
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 7
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 8
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 7
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 6
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 6
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 8
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 7
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 6
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 6
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 8
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 10
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 8
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 7
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 8
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 8
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 7
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 6
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 6
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 9
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 8
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 7
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 6
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 6
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 8
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 8
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 11
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 10
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 12
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 8
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 9
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 8
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 7
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 7
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 10
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 9
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 8
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 9
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 8
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 10
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 8
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 7
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 8
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 8
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 7
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 6
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 6
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 9
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 8
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 7
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 6
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 6
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 9
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 12
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 9
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 8
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 10
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 9
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 8
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 7
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 8
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 9
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 8
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 7
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 6
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 6
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 10
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 9
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 8
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 7
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 6
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 6
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [6,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 7
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 6
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 7
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 8
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 7
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 6
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 6
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 8
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 7
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 6
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 8
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 8
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 10
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 9
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 10
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 8
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [5,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 9
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 8
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 7
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [4,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 7
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [6,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 9
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 8
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 7
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 7
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 10
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 12
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 10
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 9
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [4,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 10
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 10
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 9
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 8
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 8
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 12
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 11
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 10
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 9
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 10
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 6
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 6
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 7
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 6
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 6
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 8
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 9
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 8
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 7
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 7
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 10
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 9
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 8
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 9
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 6
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [5,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 6
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [6,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 8
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 7
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 8
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 6
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 7
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 5
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2,1] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 7
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 6
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 5
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 7
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 9
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,2,1] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 7
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 6
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => 7
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2,1] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 7
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => 6
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => 5
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2,1] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 8
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 7
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 6
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 5
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 5
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 7
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 7
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 10
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 9
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 11
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 7
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 8
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,1] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 7
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 6
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => 6
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1,1] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 9
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 8
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => 7
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => 8
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 7
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 9
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,1] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 7
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => 6
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => 7
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 7
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => 6
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 5
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 5
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 8
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => 7
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 6
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 5
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 5
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 8
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 11
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1,1] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 8
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 7
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => 9
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1,1] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 8
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => 7
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 6
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 7
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 8
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 7
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 6
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 5
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 5
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 9
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 8
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 7
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 6
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 5
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 5
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 6
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 6
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 7
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 6
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 9
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 10
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 9
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 8
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 8
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 12
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 11
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 10
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 12
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 6
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [5,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 6
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [6,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 8
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [5,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 7
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 8
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 6
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [5,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 7
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 6
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 5
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [6,3,3,2] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 7
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => 6
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => 5
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 5
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [6,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 8
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [5,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 10
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [6,4,2,2] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 8
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => 7
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 8
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 8
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => 7
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => 6
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 6
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 10
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => 9
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 8
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 7
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 8
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 6
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 6
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 9
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 8
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 10
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 6
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 7
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 6
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => 5
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => 5
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [6,3,3,1] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 8
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => 7
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => 6
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 7
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 6
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 8
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 6
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 5
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => 6
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 6
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => 5
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 4
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 7
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => 6
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 4
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 7
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 10
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 7
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => 6
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => 8
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 7
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 6
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 6
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 7
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 6
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 4
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 8
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 7
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 6
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 4
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 4
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 6
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 6
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 10
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,4,4] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 9
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 12
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 6
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [5,5,3] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 7
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [6,4,3] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 6
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => 5
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 5
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [6,3,3] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 9
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => 8
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 7
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 9
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [6,5,2] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 6
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,5,2] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 8
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [6,4,2] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 6
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => 5
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 6
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 6
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => 5
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 4
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 8
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 7
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 6
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 5
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 6
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [6,5,1] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 6
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 9
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [6,4,1] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 6
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 5
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 7
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 6
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 5
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 4
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 5
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 6
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 5
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 4
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => [1,0,1,0,1,0,1,0] => 3
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,2,1] => [1,0,1,0,1,1,0,0] => 3
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 7
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 6
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 5
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [3,1,1] => [1,0,1,1,0,0,1,0] => 4
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => 3
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 10
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 6
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 5
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 8
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 6
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 5
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 4
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 6
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 6
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 5
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 4
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,2] => [1,1,0,0,1,0,1,0] => 3
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,2] => [1,1,0,0,1,1,0,0] => 4
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 6
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 5
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 4
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,1] => [1,1,0,1,0,0,1,0] => 3
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => [1,0,1,0,1,0] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1] => [1,0,1,1,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [4] => [1,1,1,1,0,0,0,0,1,0] => 4
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => [1,1,1,0,0,0,1,0] => 3
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => [1,1,0,0,1,0] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1] => [1,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [] => [] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 8
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 7
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 7
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 8
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [6,6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 9
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 8
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 7
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [5,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 7
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [7,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 9
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 8
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 7
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 7
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [6,6,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 8
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 7
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 8
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 8
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 7
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 9
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [6,6,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 8
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [6,5,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 8
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 9
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 7
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 7
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 7
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 9
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 8
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 8
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 8
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 7
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 7
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 7
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 9
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 9
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 8
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 7
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 7
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 11
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 10
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 9
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 8
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 7
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 7
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 8
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [6,6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 8
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 8
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 12
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [6,6,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 8
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [6,5,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 8
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 11
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 7
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 7
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 7
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 7
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 7
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 8
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 7
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 7
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 8
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 9
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 9
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 8
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 7
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 7
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 11
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 10
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 9
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 8
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 7
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 7
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 9
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [6,5,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 9
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 8
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 9
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 11
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 10
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 11
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 9
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [5,5,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 13
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 9
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 8
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 10
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 9
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 9
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 8
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 7
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 7
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 9
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 8
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 7
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 7
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 11
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 9
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 8
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 9
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 10
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 9
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 8
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 7
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 7
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 11
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 10
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 9
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 8
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 7
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 7
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 9
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 11
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 13
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 10
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 9
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 8
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 8
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 12
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 11
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 10
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 9
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 10
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 13
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 9
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 11
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 10
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 9
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 8
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 9
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 10
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 9
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 8
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 7
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 7
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 11
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 10
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 9
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 8
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 7
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 7
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 11
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 15
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 10
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 13
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 11
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 10
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 9
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 11
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 11
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 10
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 9
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 8
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 9
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 11
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 10
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 9
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 8
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 7
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 7
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 12
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 11
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 10
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 9
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 8
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 7
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 7
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 8
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 7
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 7
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 8
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 7
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 7
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => 7
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => 7
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 8
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 8
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 8
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 8
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 11
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 10
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 9
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 9
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 10
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 9
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 9
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 16
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 11
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 12
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 12
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 11
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 10
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 10
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 15
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 14
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 13
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 12
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 11
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 12
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [6,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 7
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 7
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 7
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => 10
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => 11
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 7
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [5,5,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => 7
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => 10
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 7
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [6,6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => 7
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [5,5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => 9
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 7
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [6,6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 7
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 7
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 6
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 7
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 8
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 7
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 6
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 6
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 8
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 7
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 6
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => 8
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 7
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 7
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 9
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 8
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 9
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 7
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 8
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 7
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 6
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 6
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 8
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 7
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 6
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 6
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 8
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 10
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 8
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 7
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 8
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 8
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 7
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 6
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 6
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,1] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => 10
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 9
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 8
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 7
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 6
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 6
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => 8
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 7
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 7
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 8
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 7
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 7
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 9
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 10
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 9
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 8
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 8
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 11
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 10
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 9
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 10
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 7
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 7
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 9
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 8
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 9
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => 8
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 7
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 8
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => 8
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 7
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 6
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 6
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 8
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 7
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 6
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 6
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 8
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 10
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 8
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 7
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 8
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,1,1] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 9
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 8
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 7
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 6
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 6
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 9
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 8
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 7
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 6
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 6
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 8
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 8
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 11
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 10
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 12
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 8
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 9
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 8
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 7
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 7
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 10
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 9
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 8
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 9
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 8
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 10
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,1,1] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 9
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 8
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 7
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 8
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 8
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 7
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 6
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 6
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 9
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 8
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 7
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 6
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 6
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => 14
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 9
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 12
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 9
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 8
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 10
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 9
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 8
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 7
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 8
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 9
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 8
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 7
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 6
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 6
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 10
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 9
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 8
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 7
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 6
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [6,6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 7
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => 7
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [5,4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => 7
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => 11
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => 11
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [7,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 16
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => 13
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 15
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => 7
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => 10
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => 7
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => 7
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => 7
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 6
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 7
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 6
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 7
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 8
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 7
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 6
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 6
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 8
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 7
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 6
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 8
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 8
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 10
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 9
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 10
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 8
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 9
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 8
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 7
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 7
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 9
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 8
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 7
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 7
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 10
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 12
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 10
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 9
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 10
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 10
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 9
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 8
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 8
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 12
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 11
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 10
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 9
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 10
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => 7
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => 13
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => 7
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 6
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 6
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 7
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 6
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 8
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 9
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 8
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 7
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 7
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 10
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 9
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 8
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 9
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => 7
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [6,6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => 7
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => 7
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [6,6,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => 8
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => 7
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 6
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 6
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 8
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 7
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 8
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => 7
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [6,6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => 9
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 6
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 7
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 7
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 6
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 5
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 7
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 6
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 5
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => 11
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 7
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 9
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,1] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 7
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 6
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => 7
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 7
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => 6
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => 5
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 8
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 7
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 6
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 5
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 5
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 7
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 7
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 10
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 9
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 11
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [6,6,3,1,1] => [1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => 10
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 7
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 8
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,1] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 7
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 6
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => 6
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 9
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 8
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => 7
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => 8
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => 8
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 7
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 9
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,1] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 7
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => 6
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => 7
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 7
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => 6
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 5
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 5
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 8
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => 7
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 6
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 5
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 5
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 13
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 8
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 11
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1,1] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 8
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 7
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => 9
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 8
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => 7
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 6
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 7
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 8
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 7
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 6
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 5
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 5
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 10
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 9
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 8
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 7
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 6
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 5
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 5
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 7
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [6,5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => 7
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => 13
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 16
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => 7
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => 7
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => 7
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 6
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 6
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 7
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 6
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 9
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 10
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 9
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 8
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 8
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 12
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 11
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 10
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 12
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => 7
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,5,5,2] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => 11
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 6
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 6
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 8
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 7
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 8
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 6
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 7
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 6
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 5
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 7
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => 6
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => 5
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 5
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 8
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 10
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 8
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => 7
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 8
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 8
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => 7
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => 6
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 6
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 10
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => 9
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 8
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 7
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 8
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => 13
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 6
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 6
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 9
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 8
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 10
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => 7
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 6
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 7
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 6
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => 5
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => 5
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 8
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => 7
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => 6
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 7
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => 10
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 6
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 8
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 6
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 5
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => 6
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 6
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => 5
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 4
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => 8
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 7
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => 6
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 4
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => 12
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 7
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 10
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 7
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => 6
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => 8
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 7
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 6
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 6
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 7
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 6
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 4
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 9
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 8
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 7
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 6
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 4
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 4
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [7,6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 7
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [6,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => 11
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 15
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [7,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => 7
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [7,5,4] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => 7
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 6
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 6
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [6,4,4] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 10
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,4] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 9
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 12
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [7,6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => 7
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => 9
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 6
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,5,3] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 7
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [6,4,3] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 6
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => 5
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 5
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [7,3,3] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => 10
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [6,3,3] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 9
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => 8
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 7
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 9
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => 10
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [6,5,2] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 6
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,5,2] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 8
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [6,4,2] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 6
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => 5
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 6
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [6,3,2] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 6
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => 5
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 4
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [7,2,2] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => 9
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 8
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 7
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 6
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 5
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 6
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => 11
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [6,5,1] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 6
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 9
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [6,4,1] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 6
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 5
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 7
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 6
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 5
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 4
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 5
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => 7
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 6
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 5
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 4
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => [1,0,1,0,1,0,1,0] => 3
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [2,2,1] => [1,0,1,0,1,1,0,0] => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 8
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 7
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 6
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 5
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [3,1,1] => [1,0,1,1,0,0,1,0] => 4
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => 3
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [7,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 7
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 12
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => 7
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 10
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,4] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => 7
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 6
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 5
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 8
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 7
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 6
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 5
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 4
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 6
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 7
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 6
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 5
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 4
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => [1,1,0,0,1,0,1,0] => 3
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,2] => [1,1,0,0,1,1,0,0] => 4
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 7
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 6
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 5
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 4
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => [1,1,0,1,0,0,1,0] => 3
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => [1,0,1,0,1,0] => 2
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1] => [1,0,1,1,0,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => [1,1,1,1,0,0,0,0,1,0] => 4
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => [1,1,1,0,0,0,1,0] => 3
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => [1,1,0,0,1,0] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1] => [1,0,1,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [] => [] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 8
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 8
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 9
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => 8
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 8
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 9
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => 10
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => 9
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => 8
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => 9
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 9
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 8
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 9
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 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] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0] => 11
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0] => 10
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,1] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => 10
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1,1] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => 10
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 8
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 10
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => [8,2,2] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => 10
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => 9
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => 9
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [8,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => 8
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1,1,1,1,1] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 13
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 14
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => 8
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 14
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [8,7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 8
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 14
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [7,7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => 13
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => 9
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 13
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 16
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0] => [7,7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0] => 12
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => [7,7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => 14
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 14
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 12
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 16
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [9,8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 9
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 16
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0] => [8,8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0] => 15
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => 9
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,2,2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 15
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[] => [] => [] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 7
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 7
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 7
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 8
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [6,6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 9
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 8
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 7
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [5,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 7
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 9
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [6,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 8
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [5,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 7
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [4,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 7
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 7
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [6,5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 8
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 7
[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 7
[1,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 7
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 9
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 8
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 7
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [6,5,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 9
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 11
[1,1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 9
[1,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 7
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 7
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 8
[1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 12
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 7
[1,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [5,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 7
[1,1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 7
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [5,3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 8
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [4,3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 7
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 7
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 9
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 8
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [7,5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 9
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 8
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 9
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 9
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 7
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [6,5,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 9
[1,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [4,4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 13
[1,1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 8
[1,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 7
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 7
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 7
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [7,6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 11
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 15
[1,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [5,5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 13
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 10
[1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 9
[1,1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 11
[1,1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 8
[1,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 9
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 11
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 9
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 7
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 7
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 12
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 11
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 9
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 8
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 7
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 7
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 7
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 7
[1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [4,3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => 7
[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 8
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 11
[1,1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 9
[1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 10
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 15
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 11
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 12
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 7
[1,1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [4,4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 7
[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => 11
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 7
[1,1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,4,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => 10
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 7
[1,1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [5,5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => 9
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 7
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [6,6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 8
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 7
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 7
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 6
[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 6
[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => 8
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 7
[1,1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 6
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [6,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 8
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [6,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 8
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 6
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 9
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 6
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => 8
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 7
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [6,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 8
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [5,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 10
[1,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [4,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 8
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 7
[1,1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [5,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 8
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 7
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 6
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 6
[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 6
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [6,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 8
[1,1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [5,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 10
[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [4,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 12
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [6,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 8
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [6,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 8
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [6,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 8
[1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 7
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 6
[1,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 6
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 8
[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 6
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 9
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [5,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 12
[1,1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 8
[1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 10
[1,1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 7
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 9
[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 6
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 6
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1,1,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 10
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 9
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 8
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 7
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 6
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0] => [4,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => 13
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 15
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => 7
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => 7
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => 7
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0] => [5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 6
[1,1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 6
[1,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0,0] => [5,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 8
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0,0] => [6,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 7
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0] => [4,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 6
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 8
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 7
[1,1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 8
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 12
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 10
[1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 9
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 10
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => 7
[1,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => 13
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => 7
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 6
[1,1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0,0] => [5,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 9
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => 7
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 6
[1,1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 8
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => 7
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0,0] => [6,6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => 9
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 6
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => [5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 7
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 7
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 6
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 5
[1,1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0,0] => [5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 6
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 5
[1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 6
[1,1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => 6
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 5
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 5
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => 6
[1,1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => 6
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0] => [6,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 7
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 5
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 5
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 5
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 8
[1,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 7
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => 9
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1,1,1] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 8
[1,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 6
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 7
[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 7
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 5
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 5
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 10
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 9
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 8
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 5
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 5
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 7
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0,0] => [6,5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => 7
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [4,4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 16
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => 7
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 6
[1,1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0,0] => [5,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 6
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0] => [6,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 7
[1,1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0,0] => [4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 6
[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0] => [5,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 10
[1,1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 10
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 6
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 6
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 5
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0] => [6,3,3,2] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 7
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 8
[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 6
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0] => [5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => 9
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,0] => [5,5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => 13
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [7,5,3,1] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => 7
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,0] => [6,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 6
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => 5
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0] => [6,3,3,1] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 8
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => 6
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 7
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0] => [6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 6
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 5
[1,1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => 6
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0] => [6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 6
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => 5
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 4
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 4
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 7
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 6
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 4
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 9
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 8
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 7
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 6
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 4
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 4
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0] => [7,6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 7
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0] => [6,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => 11
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => [5,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 15
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,0] => [7,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => 7
[1,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0,0] => [5,4,4] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 9
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0] => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 12
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => 5
[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 5
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0] => [6,3,3] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 9
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 7
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 9
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [6,4,2] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 6
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => 5
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 6
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => 5
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 4
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0] => [7,2,2] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => 9
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 6
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 5
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 6
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0] => [6,6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => 11
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 6
[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 5
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 7
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 6
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 5
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 4
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 5
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => 7
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 6
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 5
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 4
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1] => [1,0,1,0,1,0,1,0] => 3
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1] => [1,0,1,0,1,1,0,0] => 3
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 8
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 7
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 5
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1] => [1,0,1,1,0,0,1,0] => 4
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => 3
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [7,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 12
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 10
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 8
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 7
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 4
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 6
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 7
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 4
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [3,2] => [1,1,0,0,1,0,1,0] => 3
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [2,2] => [1,1,0,0,1,1,0,0] => 4
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 7
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 6
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 5
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 4
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [3,1] => [1,1,0,1,0,0,1,0] => 3
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => [1,0,1,0,1,0] => 2
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1] => [1,0,1,1,0,0] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 7
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [4] => [1,1,1,1,0,0,0,0,1,0] => 4
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [3] => [1,1,1,0,0,0,1,0] => 3
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2] => [1,1,0,0,1,0] => 2
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1] => [1,0,1,0] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [] => [] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [7,6,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 8
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 8
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 8
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 8
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 8
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,8,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,6,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,7,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 9
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [7,5,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [8,7,6,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 9
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 9
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [8,7,6,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 9
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 9
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 9
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 9
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 9
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 9
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 9
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 9
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [9,9,8,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 10
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [9,8,8,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 10
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 9
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 9
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 8
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 8
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 9
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 8
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 9
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 8
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => 8
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => 8
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 8
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => 8
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0] => [8,7,6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => 8
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [8,7,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 8
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => 8
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0] => [8,7,4,3,2,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => 8
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 9
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [8,6,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 8
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => 9
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0] => [8,5,4,3,2,1] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 8
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,7,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 10
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 9
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 9
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,7,6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 9
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 11
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 10
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,7,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 18
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 8
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 8
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 9
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 18
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 8
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 18
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => 8
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,4,4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 20
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => 8
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,5,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => 20
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [8,7,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => 8
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => 18
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [9,8,7,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 10
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 9
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,8,7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 9
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 9
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,3,3,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 21
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 9
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,4,4,4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 24
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => 9
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,5,5,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 25
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => 9
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,6,6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => 24
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [9,8,7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => 9
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [7,7,7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => 21
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [] => [] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 8
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 8
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 9
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,7,6,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 9
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 5
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 10
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [7,6,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 8
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [1,1] => [1,0,1,1,0,0] => 2
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [2] => [1,1,0,0,1,0] => 2
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1] => [1,0,1,1,0,0] => 2
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1] => [1,0,1,0,1,1,0,0] => 3
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [3,2] => [1,1,0,0,1,0,1,0] => 3
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [2] => [1,1,0,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,7,7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 9
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [7,6,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 8
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [7,6,6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 9
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,7,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 8
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,1] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 8
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => 8
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => 8
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => 8
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 8
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 8
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 8
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 9
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => 8
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [8,7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => 8
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => 8
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => 8
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 8
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1] => [1,0,1,0] => 1
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 4
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 5
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 7
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [7,7,4,3,2,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => 10
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 10
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 9
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 8
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [1] => [1,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 13
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,4,4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 16
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,5,5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => 17
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => [6,6,6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => 16
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 9
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 9
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [9,8,6,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 10
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [9,7,6,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 10
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [7,7,6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => 8
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 10
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 9
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 9
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 9
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => 9
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 9
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 8
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,6,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,7,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 9
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 9
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [6,6,6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => 10
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [6,6,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 8
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,5,5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => 11
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [5,4,4,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => 11
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 11
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 11
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 8
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 9
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,7,1,1,1,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 16
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [4,4,4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 12
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,6,6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => 17
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [5,4,4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => 17
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [7,6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => 13
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 7
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [6,5,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => 16
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 16
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [4] => [1,1,1,1,0,0,0,0,1,0] => 4
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [3] => [1,1,1,0,0,0,1,0] => 3
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 9
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 8
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => 9
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 8
[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 9
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [7,6,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [7,6,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 8
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 8
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 8
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [8,8,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 9
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [8,7,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 9
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 8
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [2,2] => [1,1,0,0,1,1,0,0] => 4
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 6
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 9
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0] => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 12
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [4,4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 16
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0] => [5,5,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => 20
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [9,7,5,3,1] => [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => 9
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [11,9,7,5,3,1] => [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
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [] => [] => 0
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 18
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => 3
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 8
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 9
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => 9
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 9
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 8
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 10
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => [9,9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => 18
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [3,1] => [1,1,0,1,0,0,1,0] => 3
[1,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => 8
[1,1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => 8
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0] => [6,6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => 18
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0] => [6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 12
[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 6
[1,1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 7
[1,1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 8
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 9
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 9
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [9,8,7,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 10
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [2,1] => [1,0,1,0,1,0] => 2
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1] => [1,0,1,0,1,0] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [6,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 7
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1] => [1,0,1,0,1,0,1,0] => 3
[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0] => [3] => [1,1,1,0,0,0,1,0] => 3
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => 7
[1,1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 7
[1,1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [3,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 8
[1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 6
[1,1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 7
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [7,7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 14
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [4,4,4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 20
[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,3,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 18
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 14
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [5,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 10
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 10
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [7,1,1,1,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 10
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,1,1] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => 10
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 6
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => 5
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 7
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 5
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => 5
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0] => [3,1] => [1,1,0,1,0,0,1,0] => 3
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 4
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0] => [7,6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 7
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => [5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 6
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 6
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0] => [6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 6
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0] => [6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 6
[1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 6
[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 6
[1,1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0,0] => [7,4,3,2,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 7
[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 5
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 6
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [9,8,6,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 10
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0,0] => [6,5,1] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 6
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 5
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 4
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 6
[1,1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 7
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 6
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => [6,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 7
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [6,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 7
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 12
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 7
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 6
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 5
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 4
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 4
[1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 5
[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0] => [8,7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 8
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0] => [8,7,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => 8
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 6
[1,1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 7
[1,1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => 3
[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 13
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [4,3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 7
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0] => [7,5,3,1] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => 7
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 8
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [7,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 8
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [5,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 7
[1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 14
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [7,7,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 9
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 9
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [6,6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 9
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [6,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 7
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [6,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 8
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,1,1,1,1,1] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 13
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1] => [1,0,1,1,0,0,1,0] => 4
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => [7,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 7
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [5,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 7
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [6,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 7
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [6,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 7
[1,1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [4,3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => 9
[1,1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [4,4,4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 16
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 4
[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0] => [2,2] => [1,1,0,0,1,1,0,0] => 4
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [4,3,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 16
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [7,6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 7
[1,1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [3,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 7
[1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [4,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 8
[1,1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 6
[1,1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 6
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => [8,6,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 8
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [6,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 7
[1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [5,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 7
[1,1,1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [5,4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 7
[1,1,1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 7
[1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 7
[1,1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 6
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0] => [3] => [1,1,1,0,0,0,1,0] => 3
[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,1] => [1,0,1,1,0,0] => 2
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0,0] => [5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 7
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0,0] => [6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 6
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0,0] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => 8
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0,0] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 7
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0,0] => [6,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 9
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0,0] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 6
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [5,4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 9
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0,0] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 5
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 4
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 10
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 8
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 5
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 4
[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 4
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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:
1,1 1,1,3 1,1,3,7,2 1,1,3,7,18,7,5 1,1,3,7,18,43,28,19,9,3 1,1,3,7,18,43,108,87,79,41,28,6,7
$F_{1} = 1$
$F_{2} = 1 + q$
$F_{3} = 1 + q + 3\ q^{2}$
$F_{4} = 1 + q + 3\ q^{2} + 7\ q^{3} + 2\ q^{4}$
$F_{5} = 1 + q + 3\ q^{2} + 7\ q^{3} + 18\ q^{4} + 7\ q^{5} + 5\ q^{6}$
$F_{6} = 1 + q + 3\ q^{2} + 7\ q^{3} + 18\ q^{4} + 43\ q^{5} + 28\ q^{6} + 19\ q^{7} + 9\ q^{8} + 3\ q^{9}$
$F_{7} = 1 + q + 3\ q^{2} + 7\ q^{3} + 18\ q^{4} + 43\ q^{5} + 108\ q^{6} + 87\ q^{7} + 79\ q^{8} + 41\ q^{9} + 28\ q^{10} + 6\ q^{11} + 7\ q^{12}$
Description
The sum of the areas of the rectangles formed by two consecutive peaks and the valley in between.
For a Dyck path $D = D_1 \cdots D_{2n}$ with peaks in positions $i_1 < \ldots < i_k$ and valleys in positions $j_1 < \ldots < j_{k-1}$, this statistic is given by
$$ \sum_{a=1}^{k-1} (j_a-i_a)(i_{a+1}-j_a) $$
For a Dyck path $D = D_1 \cdots D_{2n}$ with peaks in positions $i_1 < \ldots < i_k$ and valleys in positions $j_1 < \ldots < j_{k-1}$, this statistic is given by
$$ \sum_{a=1}^{k-1} (j_a-i_a)(i_{a+1}-j_a) $$
Map
to partition
Description
The cut-out partition of a Dyck path.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ is the number of down-steps before the $(n+1-i)$-th up-step of $D$.
This map is a bijection between Dyck paths of size $n$ and partitions inside the staircase partition $(n-1,\ldots,2,1)$.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ is the number of down-steps before the $(n+1-i)$-th up-step of $D$.
This map is a bijection between Dyck paths of size $n$ and partitions inside the staircase partition $(n-1,\ldots,2,1)$.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.
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