Identifier
-
Mp00027:
Dyck paths
—to partition⟶
Integer partitions
St001814: Integer partitions ⟶ ℤ
Values
[1,0] => [] => 1
[1,0,1,0] => [1] => 2
[1,1,0,0] => [] => 1
[1,0,1,0,1,0] => [2,1] => 4
[1,0,1,1,0,0] => [1,1] => 2
[1,1,0,0,1,0] => [2] => 3
[1,1,0,1,0,0] => [1] => 2
[1,1,1,0,0,0] => [] => 1
[1,0,1,0,1,0,1,0] => [3,2,1] => 8
[1,0,1,0,1,1,0,0] => [2,2,1] => 4
[1,0,1,1,0,0,1,0] => [3,1,1] => 6
[1,0,1,1,0,1,0,0] => [2,1,1] => 4
[1,0,1,1,1,0,0,0] => [1,1,1] => 2
[1,1,0,0,1,0,1,0] => [3,2] => 6
[1,1,0,0,1,1,0,0] => [2,2] => 3
[1,1,0,1,0,0,1,0] => [3,1] => 6
[1,1,0,1,0,1,0,0] => [2,1] => 4
[1,1,0,1,1,0,0,0] => [1,1] => 2
[1,1,1,0,0,0,1,0] => [3] => 4
[1,1,1,0,0,1,0,0] => [2] => 3
[1,1,1,0,1,0,0,0] => [1] => 2
[1,1,1,1,0,0,0,0] => [] => 1
[1,0,1,0,1,0,1,0,1,0] => [4,3,2,1] => 16
[1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => 8
[1,0,1,0,1,1,0,0,1,0] => [4,2,2,1] => 12
[1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => 8
[1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => 4
[1,0,1,1,0,0,1,0,1,0] => [4,3,1,1] => 12
[1,0,1,1,0,0,1,1,0,0] => [3,3,1,1] => 6
[1,0,1,1,0,1,0,0,1,0] => [4,2,1,1] => 12
[1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => 8
[1,0,1,1,0,1,1,0,0,0] => [2,2,1,1] => 4
[1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => 8
[1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => 6
[1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => 4
[1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 2
[1,1,0,0,1,0,1,0,1,0] => [4,3,2] => 12
[1,1,0,0,1,0,1,1,0,0] => [3,3,2] => 6
[1,1,0,0,1,1,0,0,1,0] => [4,2,2] => 9
[1,1,0,0,1,1,0,1,0,0] => [3,2,2] => 6
[1,1,0,0,1,1,1,0,0,0] => [2,2,2] => 3
[1,1,0,1,0,0,1,0,1,0] => [4,3,1] => 12
[1,1,0,1,0,0,1,1,0,0] => [3,3,1] => 6
[1,1,0,1,0,1,0,0,1,0] => [4,2,1] => 12
[1,1,0,1,0,1,0,1,0,0] => [3,2,1] => 8
[1,1,0,1,0,1,1,0,0,0] => [2,2,1] => 4
[1,1,0,1,1,0,0,0,1,0] => [4,1,1] => 8
[1,1,0,1,1,0,0,1,0,0] => [3,1,1] => 6
[1,1,0,1,1,0,1,0,0,0] => [2,1,1] => 4
[1,1,0,1,1,1,0,0,0,0] => [1,1,1] => 2
[1,1,1,0,0,0,1,0,1,0] => [4,3] => 8
[1,1,1,0,0,0,1,1,0,0] => [3,3] => 4
[1,1,1,0,0,1,0,0,1,0] => [4,2] => 9
[1,1,1,0,0,1,0,1,0,0] => [3,2] => 6
[1,1,1,0,0,1,1,0,0,0] => [2,2] => 3
[1,1,1,0,1,0,0,0,1,0] => [4,1] => 8
[1,1,1,0,1,0,0,1,0,0] => [3,1] => 6
[1,1,1,0,1,0,1,0,0,0] => [2,1] => 4
[1,1,1,0,1,1,0,0,0,0] => [1,1] => 2
[1,1,1,1,0,0,0,0,1,0] => [4] => 5
[1,1,1,1,0,0,0,1,0,0] => [3] => 4
[1,1,1,1,0,0,1,0,0,0] => [2] => 3
[1,1,1,1,0,1,0,0,0,0] => [1] => 2
[1,1,1,1,1,0,0,0,0,0] => [] => 1
[1,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => 32
[1,0,1,0,1,0,1,0,1,1,0,0] => [4,4,3,2,1] => 16
[1,0,1,0,1,0,1,1,0,0,1,0] => [5,3,3,2,1] => 24
[1,0,1,0,1,0,1,1,0,1,0,0] => [4,3,3,2,1] => 16
[1,0,1,0,1,0,1,1,1,0,0,0] => [3,3,3,2,1] => 8
[1,0,1,0,1,1,0,0,1,0,1,0] => [5,4,2,2,1] => 24
[1,0,1,0,1,1,0,0,1,1,0,0] => [4,4,2,2,1] => 12
[1,0,1,0,1,1,0,1,0,0,1,0] => [5,3,2,2,1] => 24
[1,0,1,0,1,1,0,1,0,1,0,0] => [4,3,2,2,1] => 16
[1,0,1,0,1,1,0,1,1,0,0,0] => [3,3,2,2,1] => 8
[1,0,1,0,1,1,1,0,0,0,1,0] => [5,2,2,2,1] => 16
[1,0,1,0,1,1,1,0,0,1,0,0] => [4,2,2,2,1] => 12
[1,0,1,0,1,1,1,0,1,0,0,0] => [3,2,2,2,1] => 8
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => 4
[1,0,1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,1] => 24
[1,0,1,1,0,0,1,0,1,1,0,0] => [4,4,3,1,1] => 12
[1,0,1,1,0,0,1,1,0,0,1,0] => [5,3,3,1,1] => 18
[1,0,1,1,0,0,1,1,0,1,0,0] => [4,3,3,1,1] => 12
[1,0,1,1,0,0,1,1,1,0,0,0] => [3,3,3,1,1] => 6
[1,0,1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,1] => 24
[1,0,1,1,0,1,0,0,1,1,0,0] => [4,4,2,1,1] => 12
[1,0,1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,1] => 24
[1,0,1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,1] => 16
[1,0,1,1,0,1,0,1,1,0,0,0] => [3,3,2,1,1] => 8
[1,0,1,1,0,1,1,0,0,0,1,0] => [5,2,2,1,1] => 16
[1,0,1,1,0,1,1,0,0,1,0,0] => [4,2,2,1,1] => 12
[1,0,1,1,0,1,1,0,1,0,0,0] => [3,2,2,1,1] => 8
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,2,2,1,1] => 4
[1,0,1,1,1,0,0,0,1,0,1,0] => [5,4,1,1,1] => 16
[1,0,1,1,1,0,0,0,1,1,0,0] => [4,4,1,1,1] => 8
[1,0,1,1,1,0,0,1,0,0,1,0] => [5,3,1,1,1] => 18
[1,0,1,1,1,0,0,1,0,1,0,0] => [4,3,1,1,1] => 12
[1,0,1,1,1,0,0,1,1,0,0,0] => [3,3,1,1,1] => 6
[1,0,1,1,1,0,1,0,0,0,1,0] => [5,2,1,1,1] => 16
[1,0,1,1,1,0,1,0,0,1,0,0] => [4,2,1,1,1] => 12
[1,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => 8
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 4
>>> Load all 1367 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [5,1,1,1,1] => 10
[1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => 8
[1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => 6
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => 4
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 2
[1,1,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2] => 24
[1,1,0,0,1,0,1,0,1,1,0,0] => [4,4,3,2] => 12
[1,1,0,0,1,0,1,1,0,0,1,0] => [5,3,3,2] => 18
[1,1,0,0,1,0,1,1,0,1,0,0] => [4,3,3,2] => 12
[1,1,0,0,1,0,1,1,1,0,0,0] => [3,3,3,2] => 6
[1,1,0,0,1,1,0,0,1,0,1,0] => [5,4,2,2] => 18
[1,1,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => 9
[1,1,0,0,1,1,0,1,0,0,1,0] => [5,3,2,2] => 18
[1,1,0,0,1,1,0,1,0,1,0,0] => [4,3,2,2] => 12
[1,1,0,0,1,1,0,1,1,0,0,0] => [3,3,2,2] => 6
[1,1,0,0,1,1,1,0,0,0,1,0] => [5,2,2,2] => 12
[1,1,0,0,1,1,1,0,0,1,0,0] => [4,2,2,2] => 9
[1,1,0,0,1,1,1,0,1,0,0,0] => [3,2,2,2] => 6
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,2,2] => 3
[1,1,0,1,0,0,1,0,1,0,1,0] => [5,4,3,1] => 24
[1,1,0,1,0,0,1,0,1,1,0,0] => [4,4,3,1] => 12
[1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,3,1] => 18
[1,1,0,1,0,0,1,1,0,1,0,0] => [4,3,3,1] => 12
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,3,3,1] => 6
[1,1,0,1,0,1,0,0,1,0,1,0] => [5,4,2,1] => 24
[1,1,0,1,0,1,0,0,1,1,0,0] => [4,4,2,1] => 12
[1,1,0,1,0,1,0,1,0,0,1,0] => [5,3,2,1] => 24
[1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => 16
[1,1,0,1,0,1,0,1,1,0,0,0] => [3,3,2,1] => 8
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,2,2,1] => 16
[1,1,0,1,0,1,1,0,0,1,0,0] => [4,2,2,1] => 12
[1,1,0,1,0,1,1,0,1,0,0,0] => [3,2,2,1] => 8
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,2,2,1] => 4
[1,1,0,1,1,0,0,0,1,0,1,0] => [5,4,1,1] => 16
[1,1,0,1,1,0,0,0,1,1,0,0] => [4,4,1,1] => 8
[1,1,0,1,1,0,0,1,0,0,1,0] => [5,3,1,1] => 18
[1,1,0,1,1,0,0,1,0,1,0,0] => [4,3,1,1] => 12
[1,1,0,1,1,0,0,1,1,0,0,0] => [3,3,1,1] => 6
[1,1,0,1,1,0,1,0,0,0,1,0] => [5,2,1,1] => 16
[1,1,0,1,1,0,1,0,0,1,0,0] => [4,2,1,1] => 12
[1,1,0,1,1,0,1,0,1,0,0,0] => [3,2,1,1] => 8
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,1,1] => 4
[1,1,0,1,1,1,0,0,0,0,1,0] => [5,1,1,1] => 10
[1,1,0,1,1,1,0,0,0,1,0,0] => [4,1,1,1] => 8
[1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,1,1] => 6
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,1] => 4
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1] => 2
[1,1,1,0,0,0,1,0,1,0,1,0] => [5,4,3] => 16
[1,1,1,0,0,0,1,0,1,1,0,0] => [4,4,3] => 8
[1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => 12
[1,1,1,0,0,0,1,1,0,1,0,0] => [4,3,3] => 8
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => 4
[1,1,1,0,0,1,0,0,1,0,1,0] => [5,4,2] => 18
[1,1,1,0,0,1,0,0,1,1,0,0] => [4,4,2] => 9
[1,1,1,0,0,1,0,1,0,0,1,0] => [5,3,2] => 18
[1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => 12
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,3,2] => 6
[1,1,1,0,0,1,1,0,0,0,1,0] => [5,2,2] => 12
[1,1,1,0,0,1,1,0,0,1,0,0] => [4,2,2] => 9
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,2] => 6
[1,1,1,0,0,1,1,1,0,0,0,0] => [2,2,2] => 3
[1,1,1,0,1,0,0,0,1,0,1,0] => [5,4,1] => 16
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,4,1] => 8
[1,1,1,0,1,0,0,1,0,0,1,0] => [5,3,1] => 18
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => 12
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,3,1] => 6
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,1] => 16
[1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => 12
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1] => 8
[1,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1] => 4
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,1,1] => 10
[1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,1] => 8
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,1,1] => 6
[1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,1] => 4
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1] => 2
[1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => 10
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => 5
[1,1,1,1,0,0,0,1,0,0,1,0] => [5,3] => 12
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => 8
[1,1,1,1,0,0,0,1,1,0,0,0] => [3,3] => 4
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,2] => 12
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,2] => 9
[1,1,1,1,0,0,1,0,1,0,0,0] => [3,2] => 6
[1,1,1,1,0,0,1,1,0,0,0,0] => [2,2] => 3
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => 10
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => 8
[1,1,1,1,0,1,0,0,1,0,0,0] => [3,1] => 6
[1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => 4
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,1] => 2
[1,1,1,1,1,0,0,0,0,0,1,0] => [5] => 6
[1,1,1,1,1,0,0,0,0,1,0,0] => [4] => 5
[1,1,1,1,1,0,0,0,1,0,0,0] => [3] => 4
[1,1,1,1,1,0,0,1,0,0,0,0] => [2] => 3
[1,1,1,1,1,0,1,0,0,0,0,0] => [1] => 2
[1,1,1,1,1,1,0,0,0,0,0,0] => [] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => 64
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [5,5,4,3,2,1] => 32
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,4,3,2,1] => 48
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,4,3,2,1] => 32
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2,1] => 16
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,3,2,1] => 48
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2,1] => 24
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2,1] => 32
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2,1] => 32
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2,1] => 24
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2,1] => 16
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2,1] => 8
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2,1] => 48
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2,1] => 24
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2,1] => 36
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 12
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2,1] => 32
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 8
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2,1] => 32
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => 16
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2,1] => 24
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2,1] => 24
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2,1] => 16
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2,1] => 8
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2,1] => 20
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2,1] => 16
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2,1] => 8
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2,1] => 4
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,1] => 48
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3,1,1] => 24
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3,1,1] => 36
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1,1] => 12
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3,1,1] => 36
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 18
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1,1] => 24
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 6
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,1] => 32
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1,1] => 24
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 8
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1,1] => 16
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1,1] => 8
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => 4
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,1,1] => 32
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1,1] => 16
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1,1] => 24
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 8
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,1,1] => 24
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,1,1] => 24
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1,1] => 24
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1,1] => 20
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1,1] => 16
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => 8
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => 4
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1,1,1] => 20
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1,1] => 10
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1,1] => 16
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1,1,1] => 24
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1,1] => 18
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1,1] => 12
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1,1] => 6
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1,1] => 20
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1,1] => 16
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1,1] => 12
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1] => 8
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1,1] => 4
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1,1] => 12
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1,1] => 10
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1,1] => 8
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1,1] => 6
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 4
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2] => 48
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [5,5,4,3,2] => 24
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [6,4,4,3,2] => 36
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2] => 12
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,3,2] => 36
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => 18
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => 12
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2] => 24
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2] => 12
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2] => 6
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2] => 36
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => 18
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 27
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 9
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 6
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => 24
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 12
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2] => 18
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => 6
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => 15
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2] => 6
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => 3
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1] => 48
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1] => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1] => 32
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1] => 16
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1] => 24
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1] => 16
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1] => 8
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2,1] => 24
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1] => 12
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1] => 24
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1] => 16
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => 8
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1] => 16
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1] => 12
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1] => 8
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1] => 4
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1] => 8
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,1] => 36
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,1] => 24
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1] => 12
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1] => 18
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1] => 12
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => 6
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,1] => 24
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1] => 12
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1] => 24
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1] => 16
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1] => 8
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1] => 20
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1] => 16
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1] => 12
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => 8
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => 4
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1,1] => 20
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1] => 16
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1] => 8
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1,1] => 24
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1] => 18
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1] => 12
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => 6
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1] => 16
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1] => 12
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => 8
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1] => 4
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1] => 12
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1] => 10
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1] => 8
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1] => 6
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1] => 4
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3] => 32
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3] => 16
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3] => 24
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3] => 16
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3] => 8
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 24
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 12
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3] => 24
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3] => 16
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => 8
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 16
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3] => 12
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3] => 8
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => 4
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2] => 9
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2] => 24
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2] => 12
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2] => 18
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2] => 12
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2] => 6
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [6,4,2,2] => 27
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2] => 18
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2] => 9
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2] => 24
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2] => 18
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2] => 12
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => 6
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2] => 15
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2] => 12
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2] => 9
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2] => 6
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => 3
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1] => 8
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1] => 24
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1] => 12
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1] => 18
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1] => 12
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1] => 6
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1] => 36
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1] => 24
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1] => 12
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1] => 24
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1] => 16
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1] => 8
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1] => 20
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1] => 16
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1] => 12
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => 8
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1] => 4
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1] => 20
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1] => 10
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1] => 24
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1] => 16
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1] => 8
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1] => 24
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1] => 18
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1] => 12
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1] => 6
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1] => 20
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1] => 16
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1] => 12
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => 8
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1] => 4
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1] => 12
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1] => 10
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1] => 8
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1] => 6
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1] => 4
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1] => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [6,5,4] => 20
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,5,4] => 10
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 15
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,4,4] => 10
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => 5
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [6,5,3] => 24
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [5,5,3] => 12
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [6,4,3] => 24
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [5,4,3] => 16
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,4,3] => 8
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [6,3,3] => 16
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [5,3,3] => 12
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,3] => 8
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,3,3] => 4
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [6,5,2] => 24
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,5,2] => 12
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [6,4,2] => 27
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,4,2] => 18
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,4,2] => 9
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2] => 24
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [5,3,2] => 18
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,2] => 12
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,3,2] => 6
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,2,2] => 15
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [5,2,2] => 12
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,2] => 9
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2] => 6
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,2,2] => 3
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [6,5,1] => 20
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,5,1] => 10
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [6,4,1] => 24
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,4,1] => 16
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,4,1] => 8
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,1] => 24
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,3,1] => 18
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,3,1] => 12
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [3,3,1] => 6
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,2,1] => 20
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => 16
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,2,1] => 12
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => 8
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,2,1] => 4
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,1,1] => 12
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,1] => 10
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,1,1] => 8
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [3,1,1] => 6
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,1,1] => 4
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1] => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => 12
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 6
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,4] => 15
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4] => 10
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,4] => 5
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,3] => 16
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,3] => 12
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [4,3] => 8
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,3] => 4
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,2] => 15
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => 12
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [4,2] => 9
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,2] => 6
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,2] => 3
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => 12
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1] => 10
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [4,1] => 8
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,1] => 6
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => 4
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 7
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => 6
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [4] => 5
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => 4
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => 3
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1] => 128
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,6,5,4,3,2,1] => 64
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3,2,1] => 64
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,5,5,4,3,2,1] => 32
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,4,3,2,1] => 64
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,4,4,3,2,1] => 48
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,4,4,3,2,1] => 32
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,2,1] => 16
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,3,2,1] => 64
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,3,3,2,1] => 48
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,3,3,2,1] => 48
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,3,3,3,2,1] => 32
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,2,1] => 64
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2,2,1] => 48
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,2,2,1] => 48
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2,2,1] => 32
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => 4
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,1] => 64
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1,1] => 8
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => 4
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,1,1] => 48
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,1,1] => 48
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1,1] => 24
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1,1] => 4
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,1,1,1] => 32
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1,1,1] => 24
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1,1] => 16
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1,1] => 8
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => 4
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1,1,1] => 16
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1,1,1] => 18
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1,1,1] => 12
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1,1] => 6
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1,1,1] => 16
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1,1] => 8
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => 4
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1,1] => 12
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1,1] => 10
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1,1] => 8
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1,1] => 6
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => 4
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2] => 96
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2] => 6
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 6
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 6
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,2,2,2] => 30
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 15
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2] => 6
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2] => 6
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1] => 64
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,2,1] => 32
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,2,1] => 48
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,2,1] => 32
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,2,1] => 16
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,2,1] => 48
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2,1] => 24
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2,1] => 32
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,2,1] => 32
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2,1] => 24
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1] => 16
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1] => 8
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2,1] => 48
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,2,1] => 24
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,2,1] => 36
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,1] => 12
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2,1] => 32
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1] => 8
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2,1] => 32
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2,1] => 16
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1] => 24
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1] => 24
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1] => 16
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1] => 8
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1] => 20
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1] => 16
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1] => 8
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1] => 4
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,1] => 48
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,1,1] => 24
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,1,1] => 36
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1,1] => 12
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,1,1] => 36
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1,1] => 18
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,1,1] => 24
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1] => 6
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,1] => 32
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1] => 24
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => 8
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1,1] => 16
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1] => 8
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1] => 4
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,1,1] => 32
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1,1] => 16
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1,1,1] => 24
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1] => 8
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1,1] => 24
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1,1] => 24
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1,1] => 24
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1,1] => 20
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1] => 16
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1] => 8
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1] => 4
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1,1,1] => 20
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1] => 10
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1,1] => 16
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1,1] => 24
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1,1] => 18
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1,1] => 12
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1] => 6
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1,1] => 20
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1,1] => 16
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1] => 12
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1] => 8
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1] => 4
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1] => 12
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1] => 10
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1] => 8
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1] => 6
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1] => 4
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 2
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3] => 8
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 8
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 8
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3] => 8
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 4
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,2] => 9
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2] => 48
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,2] => 24
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,2] => 36
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,2] => 12
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,2] => 36
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2] => 18
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2] => 12
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,2] => 24
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2] => 12
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2] => 6
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2] => 36
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,2] => 18
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,2] => 27
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2] => 9
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2] => 6
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2] => 24
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2] => 12
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2] => 18
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2] => 6
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2] => 15
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2] => 6
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2] => 3
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,1] => 72
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1] => 48
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1] => 6
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1] => 32
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1] => 16
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1] => 24
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1] => 16
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1] => 8
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1] => 24
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1] => 12
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1] => 24
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1] => 16
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1] => 8
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1] => 16
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1] => 12
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1] => 8
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1] => 4
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1] => 8
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,1] => 36
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1] => 24
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1] => 12
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1] => 18
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1] => 12
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1] => 6
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1] => 24
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1] => 12
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1] => 24
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1] => 16
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1] => 8
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1] => 20
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1] => 16
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1] => 12
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => 8
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1] => 4
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1,1] => 20
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1] => 16
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1] => 8
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1] => 24
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1] => 18
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1] => 12
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1] => 6
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1] => 16
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1] => 12
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1] => 8
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => 4
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1] => 14
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1] => 12
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1] => 10
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1] => 8
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1] => 6
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1] => 4
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1] => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [6,6,5,4] => 20
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 10
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [6,4,4,4] => 15
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4] => 10
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 5
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3] => 32
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3] => 16
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3] => 24
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3] => 16
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3] => 8
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3] => 24
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3] => 12
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3] => 24
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3] => 16
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3] => 8
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3] => 16
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3] => 12
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3] => 8
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3] => 4
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2] => 9
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2] => 54
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2] => 24
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2] => 12
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2] => 18
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2] => 12
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2] => 6
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2] => 15
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2] => 27
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2] => 18
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2] => 9
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2] => 24
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2] => 18
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2] => 12
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => 6
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2] => 15
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2] => 12
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2] => 9
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2] => 6
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2] => 3
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1] => 8
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1] => 54
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1] => 24
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1] => 12
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1] => 18
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1] => 12
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1] => 6
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1] => 36
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1] => 24
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1] => 12
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1] => 24
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1] => 16
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1] => 8
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1] => 20
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1] => 16
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1] => 12
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => 8
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1] => 4
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1] => 12
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1] => 20
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1] => 10
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1] => 24
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1] => 16
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1] => 8
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1] => 24
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1] => 18
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1] => 12
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1] => 6
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1] => 20
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1] => 16
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1] => 12
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1] => 8
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1] => 4
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1] => 14
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1] => 12
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1] => 10
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1] => 8
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1] => 6
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1] => 4
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [6,5,5] => 12
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 6
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [6,6,4] => 15
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [6,5,4] => 20
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,5,4] => 10
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [6,4,4] => 15
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,4] => 10
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [4,4,4] => 5
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [7,6,3] => 32
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,6,3] => 16
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [7,5,3] => 36
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [6,5,3] => 24
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,5,3] => 12
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [7,4,3] => 32
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [6,4,3] => 24
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3] => 16
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [4,4,3] => 8
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [7,3,3] => 20
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [6,3,3] => 16
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,3,3] => 12
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [4,3,3] => 8
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => 4
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,6,2] => 15
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [7,5,2] => 36
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [6,5,2] => 24
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,5,2] => 12
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [7,4,2] => 36
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [6,4,2] => 27
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [5,4,2] => 18
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [4,4,2] => 9
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [6,3,2] => 24
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,3,2] => 18
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [4,3,2] => 12
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [3,3,2] => 6
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [7,2,2] => 18
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [6,2,2] => 15
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,2,2] => 12
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [4,2,2] => 9
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [3,2,2] => 6
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [2,2,2] => 3
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,6,1] => 12
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [7,5,1] => 30
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [6,5,1] => 20
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [5,5,1] => 10
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [7,4,1] => 32
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [6,4,1] => 24
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,4,1] => 16
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [4,4,1] => 8
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [6,3,1] => 24
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,3,1] => 18
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [4,3,1] => 12
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [3,3,1] => 6
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,2,1] => 24
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [6,2,1] => 20
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,2,1] => 16
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [4,2,1] => 12
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => 8
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [2,2,1] => 4
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,1,1] => 14
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [6,1,1] => 12
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,1,1] => 10
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [4,1,1] => 8
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [3,1,1] => 6
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,1,1] => 4
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [7,6] => 14
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => 7
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [7,5] => 18
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5] => 12
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [5,5] => 6
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,4] => 20
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,4] => 15
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [5,4] => 10
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [4,4] => 5
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,3] => 20
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,3] => 16
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [5,3] => 12
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [4,3] => 8
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [3,3] => 4
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,2] => 18
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,2] => 15
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [5,2] => 12
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [4,2] => 9
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => 6
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,2] => 3
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => 14
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1] => 12
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [5,1] => 10
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,1] => 8
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => 6
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 4
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 8
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => 6
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => 5
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => 4
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 3
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 9
[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] => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => 10
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1] => 16
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1] => 4
[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] => 2
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10] => 11
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => 18
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [8,2] => 21
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1] => 16
[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] => 6
[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] => 4
[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] => 4
[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] => 2
[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] => 12
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1] => 20
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,1] => 18
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [8,3] => 24
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1] => 28
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1,1] => 16
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1,1,1,1,1] => 8
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1,1,1,1] => 8
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1,1,1,1,1,1,1] => 6
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1,1,1,1] => 4
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1,1,1,1,1,1,1] => 4
[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1,1,1] => 4
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0] => [11,1] => 22
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0] => [10,2] => 27
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1,1] => 20
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0] => [9,3] => 28
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0] => [8,4] => 25
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1] => 36
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => [8,2,2] => 21
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1,1] => 28
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1,1,1] => 16
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1,1,1,1] => 10
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1,1,1,1,1] => 6
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1,1,1,1,1] => 8
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1,1,1,1] => 4
[1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [2,2,1,1,1,1,1,1,1,1] => 4
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [8,5] => 24
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0] => [8,4,1] => 40
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2] => 36
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1,1] => 36
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1,1,1,1,1] => 12
[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,1,1,1,1,1] => 16
[1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2,1,1,1,1,1] => 8
[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,1,1,1,1,1] => 4
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0] => [9,5] => 30
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [8,6] => 21
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0] => [8,4,2] => 45
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,7] => 8
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [6,1,1,1,1,1,1,1,1] => 12
[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1,1,1,1,1,1] => 18
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,2,1,1,1] => 8
[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] => 3
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0] => [9,6] => 28
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [8,7] => 16
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1,1,1,1,1,1] => 24
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,8] => 9
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,1,0] => [8,5,3] => 48
[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] => 6
[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] => 3
[1,0,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2,1,1,1,1] => 4
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [9,8] => 18
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0] => [8,8,1] => 16
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,2,2,2,2,2,2,2] => 6
[] => [] => 1
[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] => 128
[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] => 64
[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] => 64
[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] => 32
[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] => 64
[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] => 48
[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] => 32
[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] => 16
[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] => 64
[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] => 48
[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] => 64
[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] => 48
[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] => 32
[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] => 4
[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] => 64
[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] => 4
[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] => 48
[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] => 48
[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] => 32
[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] => 8
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => 4
[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] => 16
[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] => 12
[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] => 6
[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] => 16
[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] => 8
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => 4
[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] => 12
[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] => 8
[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] => 6
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => 4
[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] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2] => 96
[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,2] => 6
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,2,2,2] => 30
[1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2,2,2,2] => 6
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,2,2] => 6
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,1] => 64
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [5,5,4,3,2,1] => 32
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [6,4,4,3,2,1] => 48
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,4,3,2,1] => 32
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,4,4,3,2,1] => 16
[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,3,2,1] => 32
[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,2,1] => 8
[1,1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,2,1] => 32
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [6,5,2,2,2,1] => 32
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,2,2,1] => 16
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,2,2,2,1] => 20
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,1] => 4
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,1,1] => 48
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [6,4,4,3,1,1] => 36
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [5,5,3,3,1,1] => 18
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1,1] => 32
[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1,1] => 4
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [6,5,4,1,1,1] => 32
[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [4,4,4,1,1,1] => 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] => 24
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,2,2,1,1,1] => 16
[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1,1] => 4
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1,1,1,1] => 20
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [5,5,1,1,1,1] => 10
[1,1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,1,1,1] => 16
[1,1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1,1,1] => 12
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1,1,1,1] => 20
[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1,1] => 8
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1,1] => 4
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1,1,1] => 12
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1,1] => 10
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1,1,1] => 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] => 6
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1] => 4
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 2
[1,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,0] => [4,4,4,4,3] => 8
[1,1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0,0] => [4,4,4,3,3] => 8
[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0] => [4,3,3,3,3] => 8
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3] => 4
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2] => 48
[1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0] => [5,5,4,3,2] => 24
[1,1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,4,4,3,2] => 12
[1,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0,0] => [5,5,3,3,2] => 18
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0] => [4,4,3,3,2] => 12
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,3,3,2] => 24
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,2,2,2] => 15
[1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,2] => 6
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2] => 3
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,1] => 72
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,1] => 48
[1,1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,1] => 6
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1] => 32
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,4,3,2,1] => 16
[1,1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0,0] => [5,3,3,2,1] => 24
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,3,3,2,1] => 16
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [3,3,3,2,1] => 8
[1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,2,1] => 24
[1,1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,2,1] => 24
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,2,1] => 16
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,1] => 8
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1] => 4
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0] => [4,4,3,1,1] => 12
[1,1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1,1] => 24
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,1] => 16
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1,1] => 8
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1] => 4
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1,1,1] => 20
[1,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,1,1] => 16
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1,1,1] => 8
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1,1,1] => 24
[1,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1,1] => 12
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1,1] => 6
[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,1,1] => 16
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1] => 8
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1] => 4
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1,1] => 14
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1,1] => 12
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1] => 10
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1] => 4
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1] => 2
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [4,4,4,4] => 5
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3] => 32
[1,1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0,0] => [5,5,4,3] => 16
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0] => [6,4,4,3] => 24
[1,1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0,0] => [4,4,4,3] => 8
[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0] => [5,5,3,3] => 12
[1,1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,3,3] => 8
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2] => 24
[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0] => [4,4,3,2] => 12
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [4,4,2,2] => 9
[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2,2] => 6
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0] => [5,2,2,2] => 12
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [7,5,3,1] => 54
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3,1] => 24
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3,1] => 12
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3,1] => 6
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1] => 24
[1,1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0] => [4,4,2,1] => 12
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1] => 24
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1] => 16
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2,1] => 8
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2,1] => 12
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1] => 8
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1] => 4
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1,1] => 20
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1] => 12
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1] => 6
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,1] => 12
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1] => 8
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1] => 4
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1] => 14
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1] => 12
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1] => 10
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1] => 8
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1] => 6
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1] => 4
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0] => [6,5,5] => 12
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => [5,5,5] => 6
[1,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0,0] => [5,4,4] => 10
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0] => [4,4,4] => 5
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => [7,5,3] => 36
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3] => 16
[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0] => [4,4,3] => 8
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0] => [6,3,3] => 16
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3] => 8
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3] => 4
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [6,4,2] => 27
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2] => 18
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0] => [4,4,2] => 9
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2] => 18
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2] => 12
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2] => 6
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0] => [7,2,2] => 18
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2] => 9
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2] => 6
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2] => 3
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0] => [6,6,1] => 12
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1] => 20
[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1] => 16
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1] => 8
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1] => 24
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1] => 18
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1] => 12
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1] => 6
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1] => 24
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1] => 20
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1] => 16
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1] => 12
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1] => 8
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1] => 4
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1] => 14
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1] => 12
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1] => 8
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1] => 6
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1] => 4
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [7,6] => 14
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [6,6] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [7,5] => 18
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [5,5] => 6
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0] => [4,4] => 5
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0] => [7,3] => 20
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [4,3] => 8
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [3,3] => 4
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [7,2] => 18
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [4,2] => 9
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [3,2] => 6
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [2,2] => 3
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [7,1] => 14
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0] => [6,1] => 12
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0] => [5,1] => 10
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0] => [4,1] => 8
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [3,1] => 6
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => 4
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => 8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [6] => 7
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [5] => 6
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [4] => 5
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [3] => 4
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2] => 3
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1] => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [] => 1
[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] => 256
[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] => 128
[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] => 128
[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] => 128
[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] => 128
[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] => 128
[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] => 128
[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] => 128
[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] => 512
[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] => 256
[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] => 64
[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] => 256
[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] => 96
[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] => 256
[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] => 96
[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] => 256
[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] => 96
[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] => 256
[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] => 96
[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] => 256
[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] => 96
[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] => 256
[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] => 256
[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] => 256
[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] => 512
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,3,2] => 6
[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] => 21
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,3] => 4
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,4,4,4,4] => 5
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,5,5,5] => 6
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [8,6,6] => 21
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,6,6] => 7
[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] => 4
[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] => 5
[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] => 6
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,6,6,6] => 7
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [4,4,3,2,1] => 16
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2] => 24
[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] => 32
[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] => 32
[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] => 48
[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] => 48
[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] => 128
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [1,1] => 2
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [2] => 3
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1] => 2
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1] => 4
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [3,2] => 6
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [2] => 3
[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] => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [8] => 9
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [9] => 10
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [8,1] => 16
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1] => 2
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1] => 2
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 128
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [1] => 2
[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] => 64
[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] => 64
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,7,1,1,1,1] => 14
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [4,4,4,3,3,3] => 8
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [7,6,6] => 14
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [7] => 8
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [6] => 7
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [5] => 6
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,3,3,3,3] => 8
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [4] => 5
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [3] => 4
[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] => 128
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0] => [9,1] => 18
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0] => [8,2,1] => 28
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1,1] => 4
[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] => 128
[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] => 128
[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] => 128
[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] => 128
[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] => 128
[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] => 256
[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] => 256
[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] => 96
[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] => 256
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [2,2] => 3
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0] => [3,3] => 4
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [3,3,3] => 4
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0] => [4,4,4] => 5
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [4,4,4,4] => 5
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0] => [5,5,5,5] => 6
[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] => 162
[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] => 486
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [] => 1
[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] => 3
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1] => 4
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1] => 4
[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] => 2
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,1] => 16
[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] => 6
[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] => 4
[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] => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => [9,9] => 10
[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] => 32
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2] => 12
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [3,1] => 6
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0] => [6,6,6] => 7
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0] => [6,6] => 7
[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] => 4
[1,1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1,1,1,1] => 6
[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] => 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] => 10
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [2,1] => 4
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1] => 4
[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] => 64
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1] => 16
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1] => 8
[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0] => [3] => 4
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0] => [7,2,1] => 24
[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] => 8
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0,0] => [8,2,1] => 28
[1,1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [3,2,1,1,1,1,1,1] => 8
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,2,2,2,2,2] => 18
[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] => 16
[1,1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [3,3,3,3,2,1] => 8
[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] => 4
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [7,7] => 8
[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] => 5
[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] => 4
[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] => 3
[1,1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [4,1,1,1,1,1,1,1] => 8
[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] => 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] => 12
[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] => 14
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,1,1] => 16
[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] => 32
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0] => [5,3,2,1] => 24
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0] => [5,4,2,1] => 24
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,1] => 24
[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] => 128
[1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0] => [3,1] => 6
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0] => [4,2] => 9
[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] => 32
[1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,1] => 4
[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] => 32
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [6,6,6,6,6] => 7
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,1,0,0,0] => [6,6,6,2] => 15
[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] => 16
[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] => 16
[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] => 16
[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] => 24
[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] => 64
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0,0] => [6,5,1] => 20
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0] => [5,4,1] => 16
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0] => [4,3,1] => 12
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2] => 3
[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] => 48
[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] => 64
[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] => 64
[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2] => 3
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0] => [7,1] => 14
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0] => [6,1] => 12
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0] => [5,1] => 10
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0] => [4,1] => 8
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1] => 4
[1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1] => 4
[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => 4
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0] => [8,7] => 16
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3] => 32
[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] => 48
[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] => 4
[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0] => [3,2,2,1] => 8
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0] => [7,5,3,1] => 54
[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] => 128
[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] => 32
[1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1] => 2
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [8,6,4,2] => 81
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [10,8,6,4,2] => 243
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0] => [10,10] => 11
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1] => 6
[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] => 32
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0] => [8,7,7] => 16
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [5,5,5,5,5,5] => 6
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1,1] => 4
[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1] => 8
[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0] => [2,2] => 3
[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] => 32
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [8,6,2,2,2,2] => 45
[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] => 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] => 16
[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] => 16
[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] => 64
[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] => 32
[1,1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0] => [3,3] => 4
[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] => 4
[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,1] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2] => 81
[1,1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,3,3,3,3,3,2] => 6
[1,1,0,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [4,2,2,2,2,2,2,2] => 9
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0,0] => [8,1] => 16
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0,0] => [7,1] => 14
[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] => 20
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0,0] => [6,1] => 12
[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] => 16
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0,0] => [5,1] => 10
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0] => [4,1] => 8
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0] => [5,5] => 6
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0] => [4,4] => 5
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0] => [5,3,1] => 18
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,1] => 4
[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0] => [3,3,2] => 6
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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 1,2,1,1 1,3,2,4,0,3,0,1 1,4,3,8,1,8,0,8,2,0,0,6,0,0,0,1 1,5,4,13,2,16,0,20,5,5,0,25,0,0,0,15,0,10,0,0,0,0,0,10,0,0,0,0,0,0,0,1
$F_{1} = q$
$F_{2} = q + q^{2}$
$F_{3} = q + 2\ q^{2} + q^{3} + q^{4}$
$F_{4} = q + 3\ q^{2} + 2\ q^{3} + 4\ q^{4} + 3\ q^{6} + q^{8}$
$F_{5} = q + 4\ q^{2} + 3\ q^{3} + 8\ q^{4} + q^{5} + 8\ q^{6} + 8\ q^{8} + 2\ q^{9} + 6\ q^{12} + q^{16}$
$F_{6} = q + 5\ q^{2} + 4\ q^{3} + 13\ q^{4} + 2\ q^{5} + 16\ q^{6} + 20\ q^{8} + 5\ q^{9} + 5\ q^{10} + 25\ q^{12} + 15\ q^{16} + 10\ q^{18} + 10\ q^{24} + q^{32}$
Description
The number of partitions interlacing the given partition.
Map
to partition
Description
The cut-out partition of a Dyck path.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ is the number of down-steps before the $(n+1-i)$-th up-step of $D$.
This map is a bijection between Dyck paths of size $n$ and partitions inside the staircase partition $(n-1,\ldots,2,1)$.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ is the number of down-steps before the $(n+1-i)$-th up-step of $D$.
This map is a bijection between Dyck paths of size $n$ and partitions inside the staircase partition $(n-1,\ldots,2,1)$.
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