Identifier
-
Mp00027:
Dyck paths
—to partition⟶
Integer partitions
St000378: Integer partitions ⟶ ℤ
Values
[1,0] => [] => 0
[1,0,1,0] => [1] => 1
[1,1,0,0] => [] => 0
[1,0,1,0,1,0] => [2,1] => 3
[1,0,1,1,0,0] => [1,1] => 1
[1,1,0,0,1,0] => [2] => 2
[1,1,0,1,0,0] => [1] => 1
[1,1,1,0,0,0] => [] => 0
[1,0,1,0,1,0,1,0] => [3,2,1] => 6
[1,0,1,0,1,1,0,0] => [2,2,1] => 3
[1,0,1,1,0,0,1,0] => [3,1,1] => 4
[1,0,1,1,0,1,0,0] => [2,1,1] => 2
[1,0,1,1,1,0,0,0] => [1,1,1] => 1
[1,1,0,0,1,0,1,0] => [3,2] => 5
[1,1,0,0,1,1,0,0] => [2,2] => 3
[1,1,0,1,0,0,1,0] => [3,1] => 4
[1,1,0,1,0,1,0,0] => [2,1] => 3
[1,1,0,1,1,0,0,0] => [1,1] => 1
[1,1,1,0,0,0,1,0] => [3] => 2
[1,1,1,0,0,1,0,0] => [2] => 2
[1,1,1,0,1,0,0,0] => [1] => 1
[1,1,1,1,0,0,0,0] => [] => 0
[1,0,1,0,1,0,1,0,1,0] => [4,3,2,1] => 10
[1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => 6
[1,0,1,0,1,1,0,0,1,0] => [4,2,2,1] => 7
[1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => 4
[1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => 3
[1,0,1,1,0,0,1,0,1,0] => [4,3,1,1] => 8
[1,0,1,1,0,0,1,1,0,0] => [3,3,1,1] => 5
[1,0,1,1,0,1,0,0,1,0] => [4,2,1,1] => 6
[1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => 4
[1,0,1,1,0,1,1,0,0,0] => [2,2,1,1] => 2
[1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => 4
[1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => 3
[1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => 2
[1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0] => [4,3,2] => 9
[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] => 7
[1,1,0,0,1,1,0,1,0,0] => [3,2,2] => 5
[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] => 8
[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] => 7
[1,1,0,1,0,1,0,1,0,0] => [3,2,1] => 6
[1,1,0,1,0,1,1,0,0,0] => [2,2,1] => 3
[1,1,0,1,1,0,0,0,1,0] => [4,1,1] => 4
[1,1,0,1,1,0,0,1,0,0] => [3,1,1] => 4
[1,1,0,1,1,0,1,0,0,0] => [2,1,1] => 2
[1,1,0,1,1,1,0,0,0,0] => [1,1,1] => 1
[1,1,1,0,0,0,1,0,1,0] => [4,3] => 5
[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] => 5
[1,1,1,0,0,1,0,1,0,0] => [3,2] => 5
[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] => 3
[1,1,1,0,1,0,0,1,0,0] => [3,1] => 4
[1,1,1,0,1,0,1,0,0,0] => [2,1] => 3
[1,1,1,0,1,1,0,0,0,0] => [1,1] => 1
[1,1,1,1,0,0,0,0,1,0] => [4] => 2
[1,1,1,1,0,0,0,1,0,0] => [3] => 2
[1,1,1,1,0,0,1,0,0,0] => [2] => 2
[1,1,1,1,0,1,0,0,0,0] => [1] => 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] => 15
[1,0,1,0,1,0,1,0,1,1,0,0] => [4,4,3,2,1] => 10
[1,0,1,0,1,0,1,1,0,0,1,0] => [5,3,3,2,1] => 11
[1,0,1,0,1,0,1,1,0,1,0,0] => [4,3,3,2,1] => 7
[1,0,1,0,1,0,1,1,1,0,0,0] => [3,3,3,2,1] => 6
[1,0,1,0,1,1,0,0,1,0,1,0] => [5,4,2,2,1] => 12
[1,0,1,0,1,1,0,0,1,1,0,0] => [4,4,2,2,1] => 8
[1,0,1,0,1,1,0,1,0,0,1,0] => [5,3,2,2,1] => 9
[1,0,1,0,1,1,0,1,0,1,0,0] => [4,3,2,2,1] => 6
[1,0,1,0,1,1,0,1,1,0,0,0] => [3,3,2,2,1] => 4
[1,0,1,0,1,1,1,0,0,0,1,0] => [5,2,2,2,1] => 7
[1,0,1,0,1,1,1,0,0,1,0,0] => [4,2,2,2,1] => 5
[1,0,1,0,1,1,1,0,1,0,0,0] => [3,2,2,2,1] => 4
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => 3
[1,0,1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,1] => 13
[1,0,1,1,0,0,1,0,1,1,0,0] => [4,4,3,1,1] => 9
[1,0,1,1,0,0,1,1,0,0,1,0] => [5,3,3,1,1] => 10
[1,0,1,1,0,0,1,1,0,1,0,0] => [4,3,3,1,1] => 7
[1,0,1,1,0,0,1,1,1,0,0,0] => [3,3,3,1,1] => 5
[1,0,1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,1] => 11
[1,0,1,1,0,1,0,0,1,1,0,0] => [4,4,2,1,1] => 8
[1,0,1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,1] => 9
[1,0,1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,1] => 7
[1,0,1,1,0,1,0,1,1,0,0,0] => [3,3,2,1,1] => 4
[1,0,1,1,0,1,1,0,0,0,1,0] => [5,2,2,1,1] => 6
[1,0,1,1,0,1,1,0,0,1,0,0] => [4,2,2,1,1] => 5
[1,0,1,1,0,1,1,0,1,0,0,0] => [3,2,2,1,1] => 3
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,2,2,1,1] => 2
[1,0,1,1,1,0,0,0,1,0,1,0] => [5,4,1,1,1] => 8
[1,0,1,1,1,0,0,0,1,1,0,0] => [4,4,1,1,1] => 6
[1,0,1,1,1,0,0,1,0,0,1,0] => [5,3,1,1,1] => 7
[1,0,1,1,1,0,0,1,0,1,0,0] => [4,3,1,1,1] => 6
[1,0,1,1,1,0,0,1,1,0,0,0] => [3,3,1,1,1] => 4
[1,0,1,1,1,0,1,0,0,0,1,0] => [5,2,1,1,1] => 5
[1,0,1,1,1,0,1,0,0,1,0,0] => [4,2,1,1,1] => 5
[1,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => 4
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 2
>>> Load all 1415 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [5,1,1,1,1] => 4
[1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => 3
[1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => 3
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => 2
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2] => 14
[1,1,0,0,1,0,1,0,1,1,0,0] => [4,4,3,2] => 10
[1,1,0,0,1,0,1,1,0,0,1,0] => [5,3,3,2] => 11
[1,1,0,0,1,0,1,1,0,1,0,0] => [4,3,3,2] => 8
[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] => 12
[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] => 10
[1,1,0,0,1,1,0,1,0,1,0,0] => [4,3,2,2] => 8
[1,1,0,0,1,1,0,1,1,0,0,0] => [3,3,2,2] => 5
[1,1,0,0,1,1,1,0,0,0,1,0] => [5,2,2,2] => 7
[1,1,0,0,1,1,1,0,0,1,0,0] => [4,2,2,2] => 6
[1,1,0,0,1,1,1,0,1,0,0,0] => [3,2,2,2] => 4
[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] => 13
[1,1,0,1,0,0,1,0,1,1,0,0] => [4,4,3,1] => 10
[1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,3,1] => 11
[1,1,0,1,0,0,1,1,0,1,0,0] => [4,3,3,1] => 9
[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] => 12
[1,1,0,1,0,1,0,0,1,1,0,0] => [4,4,2,1] => 10
[1,1,0,1,0,1,0,1,0,0,1,0] => [5,3,2,1] => 11
[1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => 10
[1,1,0,1,0,1,0,1,1,0,0,0] => [3,3,2,1] => 6
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,2,2,1] => 7
[1,1,0,1,0,1,1,0,0,1,0,0] => [4,2,2,1] => 7
[1,1,0,1,0,1,1,0,1,0,0,0] => [3,2,2,1] => 4
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,2,2,1] => 3
[1,1,0,1,1,0,0,0,1,0,1,0] => [5,4,1,1] => 8
[1,1,0,1,1,0,0,0,1,1,0,0] => [4,4,1,1] => 7
[1,1,0,1,1,0,0,1,0,0,1,0] => [5,3,1,1] => 8
[1,1,0,1,1,0,0,1,0,1,0,0] => [4,3,1,1] => 8
[1,1,0,1,1,0,0,1,1,0,0,0] => [3,3,1,1] => 5
[1,1,0,1,1,0,1,0,0,0,1,0] => [5,2,1,1] => 5
[1,1,0,1,1,0,1,0,0,1,0,0] => [4,2,1,1] => 6
[1,1,0,1,1,0,1,0,1,0,0,0] => [3,2,1,1] => 4
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,1,1] => 2
[1,1,0,1,1,1,0,0,0,0,1,0] => [5,1,1,1] => 4
[1,1,0,1,1,1,0,0,0,1,0,0] => [4,1,1,1] => 4
[1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,1,1] => 3
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,1] => 2
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => [5,4,3] => 9
[1,1,1,0,0,0,1,0,1,1,0,0] => [4,4,3] => 7
[1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => 8
[1,1,1,0,0,0,1,1,0,1,0,0] => [4,3,3] => 7
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => 5
[1,1,1,0,0,1,0,0,1,0,1,0] => [5,4,2] => 9
[1,1,1,0,0,1,0,0,1,1,0,0] => [4,4,2] => 8
[1,1,1,0,0,1,0,1,0,0,1,0] => [5,3,2] => 9
[1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => 9
[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] => 6
[1,1,1,0,0,1,1,0,0,1,0,0] => [4,2,2] => 7
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,2] => 5
[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] => 6
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,4,1] => 6
[1,1,1,0,1,0,0,1,0,0,1,0] => [5,3,1] => 7
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => 8
[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] => 5
[1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => 7
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1] => 6
[1,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1] => 3
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,1,1] => 3
[1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,1] => 4
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,1,1] => 4
[1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,1] => 2
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => 5
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => 4
[1,1,1,1,0,0,0,1,0,0,1,0] => [5,3] => 5
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => 5
[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] => 4
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,2] => 5
[1,1,1,1,0,0,1,0,1,0,0,0] => [3,2] => 5
[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] => 3
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => 3
[1,1,1,1,0,1,0,0,1,0,0,0] => [3,1] => 4
[1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => 3
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => [5] => 2
[1,1,1,1,1,0,0,0,0,1,0,0] => [4] => 2
[1,1,1,1,1,0,0,0,1,0,0,0] => [3] => 2
[1,1,1,1,1,0,0,1,0,0,0,0] => [2] => 2
[1,1,1,1,1,0,1,0,0,0,0,0] => [1] => 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] => 21
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [5,5,4,3,2,1] => 15
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,4,3,2,1] => 16
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,4,3,2,1] => 11
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2,1] => 10
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,3,2,1] => 17
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2,1] => 12
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2,1] => 9
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2,1] => 11
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2,1] => 8
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2,1] => 7
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2,1] => 6
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2,1] => 18
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2,1] => 13
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2,1] => 14
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 8
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2,1] => 9
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => 4
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2,1] => 12
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => 9
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2,1] => 8
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2,1] => 7
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2,1] => 6
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2,1] => 4
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2,1] => 7
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2,1] => 5
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2,1] => 4
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2,1] => 3
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,1] => 19
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3,1,1] => 14
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3,1,1] => 15
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1,1] => 9
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3,1,1] => 16
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 12
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1,1] => 10
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 5
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,1] => 11
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1,1] => 7
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 3
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1,1] => 5
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1,1] => 4
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1,1] => 3
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,1,1] => 13
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1,1] => 10
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1,1] => 11
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 7
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,1,1] => 10
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => 4
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,1,1] => 9
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1,1] => 8
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1,1] => 7
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1,1] => 4
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1,1] => 5
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1,1] => 5
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1,1] => 5
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => 3
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => 2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1,1,1] => 8
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1,1] => 6
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1,1] => 6
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1,1] => 5
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1,1,1] => 6
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1,1] => 6
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1,1] => 6
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1,1] => 4
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1,1] => 5
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1,1] => 4
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1,1] => 5
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1] => 4
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1,1] => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1,1] => 4
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1,1] => 3
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1,1] => 3
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1,1] => 3
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2] => 20
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [5,5,4,3,2] => 15
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [6,4,4,3,2] => 16
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2] => 10
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,3,2] => 17
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => 13
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => 8
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2] => 11
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2] => 7
[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] => 18
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => 14
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 15
[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] => 5
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => 12
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 10
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2] => 8
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => 4
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => 7
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2] => 5
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2] => 4
[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] => 19
[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] => 15
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1] => 10
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1] => 11
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1] => 7
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1] => 6
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2,1] => 12
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1] => 8
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1] => 9
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1] => 6
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => 4
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1] => 7
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1] => 5
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1] => 4
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1] => 3
[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] => 13
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,1] => 13
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1] => 9
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1] => 10
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1] => 7
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => 5
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,1] => 11
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1] => 8
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1] => 9
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1] => 7
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1] => 4
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1] => 5
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1] => 6
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1] => 5
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => 3
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1,1] => 8
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1] => 8
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1] => 6
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1,1] => 6
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1] => 7
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1] => 6
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => 4
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1] => 5
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1] => 5
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1] => 5
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => 4
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1] => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1] => 4
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1] => 4
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1] => 3
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1] => 3
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3] => 14
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3] => 11
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3] => 12
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3] => 10
[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] => 13
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 11
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [6,4,3,3] => 12
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3] => 11
[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] => 9
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3] => 9
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3] => 7
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => 5
[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] => 14
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2] => 10
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2] => 11
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2] => 8
[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] => 11
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2] => 12
[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] => 8
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2] => 10
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2] => 8
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => 5
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2] => 6
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2] => 7
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2] => 6
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2] => 4
[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] => 13
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1] => 10
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1] => 11
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1] => 9
[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] => 10
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1] => 12
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1] => 10
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1] => 8
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1] => 11
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1] => 10
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1] => 6
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1] => 5
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1] => 7
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1] => 7
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => 4
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1] => 3
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1] => 6
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1] => 6
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1] => 7
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1] => 8
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1] => 7
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1] => 6
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1] => 8
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1] => 8
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1] => 5
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1] => 4
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1] => 5
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1] => 6
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => 4
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1] => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1] => 3
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1] => 4
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1] => 4
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1] => 3
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [6,5,4] => 9
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,5,4] => 7
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 8
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,4,4] => 7
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => 6
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [6,5,3] => 9
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [5,5,3] => 8
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [6,4,3] => 9
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [5,4,3] => 9
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,4,3] => 7
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [6,3,3] => 7
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [5,3,3] => 8
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,3] => 7
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,3,3] => 5
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [6,5,2] => 7
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,5,2] => 7
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [6,4,2] => 8
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,4,2] => 9
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,4,2] => 8
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2] => 7
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [5,3,2] => 9
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,2] => 9
[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] => 5
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [5,2,2] => 6
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,2] => 7
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2] => 5
[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] => 6
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,5,1] => 5
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [6,4,1] => 6
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,4,1] => 6
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,4,1] => 6
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,1] => 6
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,3,1] => 7
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,3,1] => 8
[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] => 5
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => 5
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,2,1] => 7
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => 6
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,2,1] => 3
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,1,1] => 3
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,1] => 3
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,1,1] => 4
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [3,1,1] => 4
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,1,1] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => 5
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 4
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,4] => 5
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4] => 5
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,4] => 4
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,3] => 4
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,3] => 5
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [4,3] => 5
[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] => 4
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => 4
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [4,2] => 5
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,2] => 5
[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] => 3
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1] => 3
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [4,1] => 3
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,1] => 4
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [4] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1] => 28
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,6,5,4,3,2,1] => 21
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3,2,1] => 16
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,5,5,4,3,2,1] => 15
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,4,3,2,1] => 13
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,4,4,3,2,1] => 12
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,4,4,3,2,1] => 11
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,2,1] => 10
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,3,2,1] => 12
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,3,3,2,1] => 11
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,3,3,2,1] => 10
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,3,3,3,2,1] => 8
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,2,1] => 13
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2,2,1] => 12
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,2,2,1] => 11
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2,2,1] => 8
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => 3
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,1] => 16
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1,1] => 3
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,1,1] => 15
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,1,1] => 14
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1,1] => 7
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1,1] => 3
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1,1] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,1,1,1] => 10
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1,1,1] => 8
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1,1] => 4
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1,1] => 5
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1,1,1] => 5
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1,1] => 3
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => 2
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1,1,1] => 6
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1,1,1] => 6
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1,1,1] => 6
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1,1] => 4
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1,1,1] => 4
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1,1] => 5
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1,1] => 4
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1,1] => 3
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1,1] => 3
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1,1] => 3
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1,1] => 3
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => 2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2] => 27
[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] => 5
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 4
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,2,2,2] => 12
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2] => 10
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2] => 4
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2] => 4
[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] => 21
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,2,1] => 15
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,2,1] => 16
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,2,1] => 11
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,2,1] => 10
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,2,1] => 17
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2,1] => 12
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2,1] => 9
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,2,1] => 11
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2,1] => 8
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1] => 7
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1] => 6
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2,1] => 18
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,2,1] => 13
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,2,1] => 14
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,1] => 8
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2,1] => 9
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1] => 4
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2,1] => 12
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2,1] => 9
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1] => 8
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1] => 7
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1] => 6
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1] => 4
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1] => 7
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1] => 5
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1] => 4
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1] => 3
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,1] => 19
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,1,1] => 14
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,1,1] => 15
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1,1] => 9
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,1,1] => 16
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1,1] => 12
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,1,1] => 10
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1] => 5
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,1] => 11
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1] => 7
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => 3
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1,1] => 5
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1] => 4
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1] => 3
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1] => 2
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,1,1] => 13
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1,1] => 10
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1,1,1] => 11
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1] => 7
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1,1] => 10
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1] => 4
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1,1] => 9
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1,1] => 8
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1,1] => 7
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1] => 4
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1,1] => 5
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1] => 5
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1,1] => 5
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1] => 3
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1,1,1] => 8
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1] => 6
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1,1] => 6
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1] => 5
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1,1] => 6
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1,1] => 6
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1,1] => 6
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1] => 4
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1,1] => 5
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1,1] => 4
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1] => 5
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1] => 4
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1,1] => 4
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1] => 4
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1] => 3
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1] => 3
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1] => 3
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1] => 2
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[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] => 7
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3] => 6
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 5
[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] => 20
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,2] => 15
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,2] => 16
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,2] => 10
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,2] => 17
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2] => 13
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2] => 8
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,2] => 11
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2] => 7
[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] => 18
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,2] => 14
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,2] => 15
[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] => 5
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2] => 12
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2] => 10
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2] => 8
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2] => 4
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2] => 7
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2] => 5
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2] => 4
[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] => 18
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1] => 19
[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] => 15
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1] => 10
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1] => 11
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1] => 7
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1] => 6
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1] => 12
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1] => 8
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1] => 9
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1] => 6
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1] => 4
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1] => 7
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1] => 5
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1] => 4
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1] => 3
[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] => 13
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1] => 13
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1] => 9
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1] => 10
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1] => 7
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1] => 5
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1] => 11
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1] => 8
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1] => 9
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1] => 7
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1] => 4
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1] => 5
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1] => 6
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1] => 5
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => 3
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1] => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1,1] => 8
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1] => 8
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1] => 6
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1] => 6
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1] => 7
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1] => 6
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1] => 4
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1,1] => 4
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1] => 5
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1] => 5
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1] => 5
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1] => 4
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1] => 3
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1] => 4
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1] => 4
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1] => 3
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1] => 3
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1] => 2
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [6,6,5,4] => 11
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 9
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [6,4,4,4] => 10
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4] => 9
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 7
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3] => 14
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3] => 11
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3] => 12
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3] => 10
[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] => 13
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3] => 11
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3] => 12
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3] => 11
[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] => 9
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3] => 9
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3] => 7
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3] => 5
[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] => 12
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2] => 14
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2] => 10
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2] => 11
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2] => 8
[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] => 8
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2] => 11
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2] => 12
[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] => 8
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2] => 10
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2] => 8
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => 5
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2] => 6
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2] => 7
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2] => 6
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2] => 4
[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] => 10
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1] => 13
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1] => 10
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1] => 11
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1] => 9
[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] => 10
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1] => 12
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1] => 10
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1] => 8
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1] => 11
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1] => 10
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1] => 6
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1] => 5
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1] => 5
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1] => 7
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1] => 7
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => 4
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1] => 3
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1] => 5
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1] => 6
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1] => 6
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1] => 7
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1] => 8
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1] => 7
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,1] => 6
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1] => 6
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1] => 8
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1] => 8
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1] => 5
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1] => 4
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1] => 4
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1] => 5
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1] => 6
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1] => 4
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1] => 3
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1] => 3
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1] => 4
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1] => 4
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1] => 3
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1] => 2
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [6,5,5] => 7
[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] => 8
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [6,5,4] => 9
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,5,4] => 7
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [6,4,4] => 8
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,4] => 7
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [4,4,4] => 6
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [7,6,3] => 7
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,6,3] => 7
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [7,5,3] => 8
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [6,5,3] => 9
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,5,3] => 8
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [7,4,3] => 7
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [6,4,3] => 9
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3] => 9
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [4,4,3] => 7
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [7,3,3] => 6
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [6,3,3] => 7
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,3,3] => 8
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [4,3,3] => 7
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => 5
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,6,2] => 6
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [7,5,2] => 7
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [6,5,2] => 7
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,5,2] => 7
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [7,4,2] => 7
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [6,4,2] => 8
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [5,4,2] => 9
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [4,4,2] => 8
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [7,3,2] => 7
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [6,3,2] => 7
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,3,2] => 9
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [4,3,2] => 9
[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] => 5
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [6,2,2] => 5
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,2,2] => 6
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [4,2,2] => 7
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [3,2,2] => 5
[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] => 5
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [7,5,1] => 6
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [6,5,1] => 6
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [5,5,1] => 5
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [7,4,1] => 5
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [6,4,1] => 6
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,4,1] => 6
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [4,4,1] => 6
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [7,3,1] => 6
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [6,3,1] => 6
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,3,1] => 7
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [4,3,1] => 8
[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] => 5
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [6,2,1] => 5
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,2,1] => 5
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [4,2,1] => 7
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => 6
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [2,2,1] => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,1,1] => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [6,1,1] => 3
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,1,1] => 3
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [4,1,1] => 4
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [3,1,1] => 4
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,1,1] => 2
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [7,6] => 5
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => 4
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [7,5] => 5
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5] => 5
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [5,5] => 4
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,4] => 4
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,4] => 5
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [5,4] => 5
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [4,4] => 4
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,3] => 4
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,3] => 4
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [5,3] => 5
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [4,3] => 5
[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] => 4
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,2] => 4
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [5,2] => 4
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [4,2] => 5
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => 5
[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] => 3
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1] => 3
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [5,1] => 3
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,1] => 3
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => 4
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 3
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => 2
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => 2
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => 2
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1] => 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] => 2
[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
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1] => 3
[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] => 2
[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
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10] => 2
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => 3
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [8,2] => 4
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1] => 3
[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] => 3
[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] => 2
[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] => 2
[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
[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] => 2
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1] => 3
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0] => [9,2] => 4
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,1] => 3
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [8,3] => 4
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1] => 5
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1,1] => 3
[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] => 3
[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] => 4
[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] => 3
[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] => 2
[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] => 2
[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] => 2
[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] => 3
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0] => [10,2] => 4
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1,1] => 3
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0] => [9,3] => 4
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0] => [9,2,1] => 5
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,1,1] => 3
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0] => [8,4] => 4
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1] => 6
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => [8,2,2] => 5
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1,1] => 4
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1,1,1] => 3
[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] => 3
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,1,1,1,1,1] => 5
[1,0,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [4,1,1,1,1,1,1,1,1] => 3
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1,1,1,1,1] => 4
[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] => 3
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1,1,1,1,1,1] => 4
[1,0,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [3,1,1,1,1,1,1,1,1,1] => 3
[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] => 2
[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,1,1,1,1,1,1] => 2
[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] => 2
[1,0,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [8,5] => 4
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0] => [8,4,1] => 5
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2] => 7
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1,1] => 6
[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] => 3
[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,1,1,1,1,1] => 4
[1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2,1,1,1,1,1] => 4
[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] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0] => [9,5] => 4
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [8,6] => 5
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0] => [8,4,2] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,7] => 4
[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] => 3
[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] => 6
[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] => 3
[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] => 4
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [8,7] => 5
[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] => 5
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,8] => 4
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,1,0] => [8,5,3] => 7
[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] => 4
[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] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [9,8] => 5
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0] => [8,8,1] => 5
[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] => 4
[] => [] => 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] => 28
[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] => 21
[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] => 16
[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] => 15
[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] => 13
[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] => 12
[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] => 11
[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] => 10
[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] => 12
[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] => 11
[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] => 13
[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] => 12
[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] => 8
[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] => 3
[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] => 16
[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] => 2
[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] => 15
[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] => 14
[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] => 10
[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] => 3
[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] => 2
[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] => 6
[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] => 6
[1,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1,1,1,1] => 4
[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] => 4
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1,1,1] => 4
[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] => 2
[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] => 3
[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] => 3
[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] => 3
[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] => 2
[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
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2] => 27
[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] => 12
[1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2,2,2,2] => 4
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,2,2] => 4
[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] => 21
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [5,5,4,3,2,1] => 15
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [6,4,4,3,2,1] => 16
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,4,3,2,1] => 11
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,4,4,3,2,1] => 10
[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,3,2,1] => 9
[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,2,1] => 6
[1,1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,2,1] => 9
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [6,5,2,2,2,1] => 12
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,2,2,1] => 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] => 7
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,1] => 3
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,1,1] => 19
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [6,4,4,3,1,1] => 15
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [5,5,3,3,1,1] => 12
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1,1] => 11
[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1,1] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [6,5,4,1,1,1] => 13
[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [4,4,4,1,1,1] => 7
[1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1,1,1] => 8
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,1,1] => 7
[1,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2,1,1,1] => 4
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,2,2,1,1,1] => 5
[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1,1] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1,1,1,1] => 8
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [5,5,1,1,1,1] => 6
[1,1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,1,1,1] => 6
[1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1,1,1,1] => 5
[1,1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1,1,1] => 6
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1,1,1,1] => 5
[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1,1] => 4
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1,1] => 2
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1,1,1] => 4
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1,1,1] => 4
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1,1] => 3
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1,1,1] => 3
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1,1,1] => 3
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1] => 2
[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
[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] => 6
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3] => 5
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2] => 20
[1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0] => [5,5,4,3,2] => 15
[1,1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,4,4,3,2] => 10
[1,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0,0] => [5,5,3,3,2] => 13
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0] => [4,4,3,3,2] => 8
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,3,3,2] => 11
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,2,2,2] => 7
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,2,2,2] => 5
[1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,2] => 4
[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] => 18
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,1] => 19
[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] => 15
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,4,3,2,1] => 10
[1,1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0,0] => [5,3,3,2,1] => 11
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,3,3,2,1] => 7
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [3,3,3,2,1] => 6
[1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,2,1] => 12
[1,1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,2,1] => 9
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,2,1] => 6
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,1] => 4
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1] => 3
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0] => [4,4,3,1,1] => 9
[1,1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1,1] => 11
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,1] => 7
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1,1] => 3
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1,1,1] => 8
[1,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,1,1] => 8
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1,1,1] => 6
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1,1,1] => 6
[1,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1,1] => 6
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1,1] => 4
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1,1,1] => 4
[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,1,1] => 5
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1] => 4
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1] => 2
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1,1] => 3
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1,1] => 4
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1] => 4
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1] => 2
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [4,4,4,4] => 7
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3] => 14
[1,1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0,0] => [5,5,4,3] => 11
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0] => [6,4,4,3] => 12
[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] => 11
[1,1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,3,3] => 7
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2] => 14
[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0] => [4,4,3,2] => 10
[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] => 5
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0] => [5,2,2,2] => 7
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [7,5,3,1] => 10
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3,1] => 13
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3,1] => 9
[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] => 12
[1,1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0] => [4,4,2,1] => 10
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0] => [6,3,2,1] => 8
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1] => 11
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1] => 10
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2,1] => 6
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2,1] => 7
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1] => 4
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1] => 3
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1,1] => 6
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1] => 8
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1] => 5
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,1] => 6
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1] => 4
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1] => 2
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1] => 3
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1] => 3
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1] => 4
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1] => 4
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1] => 3
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1] => 2
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0] => [6,5,5] => 7
[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] => 7
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0] => [4,4,4] => 6
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => [7,5,3] => 8
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3] => 9
[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0] => [4,4,3] => 7
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0] => [6,3,3] => 7
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3] => 7
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3] => 5
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [6,4,2] => 8
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2] => 9
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0] => [4,4,2] => 8
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2] => 9
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2] => 9
[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] => 5
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2] => 7
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2] => 5
[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] => 5
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1] => 6
[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1] => 6
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1] => 6
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1] => 6
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1] => 7
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1] => 8
[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] => 5
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1] => 5
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1] => 5
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1] => 7
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1] => 6
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1] => 3
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1] => 3
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1] => 3
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1] => 4
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1] => 4
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1] => 2
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [7,6] => 5
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [6,6] => 4
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [7,5] => 5
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [5,5] => 4
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0] => [4,4] => 4
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0] => [7,3] => 4
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [4,3] => 5
[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] => 4
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [4,2] => 5
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [3,2] => 5
[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] => 3
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0] => [6,1] => 3
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0] => [5,1] => 3
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0] => [4,1] => 3
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [3,1] => 4
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => 3
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [6] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [5] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [4] => 2
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [3] => 2
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2] => 2
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1] => 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] => 36
[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] => 28
[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] => 22
[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] => 18
[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] => 16
[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] => 16
[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] => 18
[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] => 22
[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] => 45
[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] => 36
[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] => 21
[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] => 29
[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] => 17
[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] => 24
[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] => 15
[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] => 21
[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] => 15
[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] => 20
[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] => 17
[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] => 21
[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] => 21
[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] => 24
[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] => 29
[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] => 36
[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] => 45
[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] => 7
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,3] => 5
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,4,4,4,4] => 7
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,5,5,5] => 8
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [8,6,6] => 8
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,6,6] => 6
[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] => 5
[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] => 7
[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] => 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] => 8
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [] => 0
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [4,4,3,2,1] => 10
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2] => 14
[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] => 15
[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] => 15
[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] => 20
[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] => 20
[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] => 28
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [1,1] => 1
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [2] => 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
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1] => 3
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [3,2] => 5
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [2] => 2
[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
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [8] => 2
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [9] => 2
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [8,1] => 3
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1] => 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
[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
[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
[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
[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
[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] => 22
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [6,6,6,5,4,3,2,1] => 21
[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] => 21
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,7,1,1,1,1] => 6
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [4,4,4,3,3,3] => 7
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [7,6,6] => 7
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [7] => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [6] => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [5] => 2
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,3,3,3,3] => 6
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [4] => 2
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [3] => 2
[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] => 16
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0] => [9,1] => 3
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0] => [8,2,1] => 5
[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] => 4
[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] => 2
[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] => 22
[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] => 18
[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] => 16
[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] => 18
[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] => 28
[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] => 36
[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] => 29
[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] => 27
[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] => 36
[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] => 5
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0] => [4,4,4] => 6
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [4,4,4,4] => 7
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0] => [5,5,5,5] => 8
[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] => 13
[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] => 16
[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] => 3
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1] => 2
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1] => 2
[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
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,1] => 3
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1,1,1,1,1,1] => 3
[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] => 2
[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
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => [9,9] => 4
[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] => 15
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2] => 9
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [3,1] => 4
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0] => [6,6,6] => 6
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0] => [6,6] => 4
[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] => 2
[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] => 3
[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] => 3
[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] => 3
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [2,1] => 3
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1] => 3
[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] => 21
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1] => 10
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1] => 6
[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0] => [3] => 2
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0] => [7,2,1] => 5
[1,1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1,1,1,1] => 4
[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] => 5
[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] => 4
[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] => 6
[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] => 10
[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] => 6
[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] => 3
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [7,7] => 4
[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] => 7
[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] => 5
[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] => 3
[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] => 3
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [6,1,1,1,1,1] => 4
[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] => 3
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,1,1] => 3
[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] => 11
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0] => [5,3,2,1] => 11
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0] => [5,4,2,1] => 12
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,1] => 13
[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] => 28
[1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0] => [3,1] => 4
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0] => [4,2] => 5
[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] => 11
[1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,1] => 3
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0] => [6,3,2,1] => 8
[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] => 7
[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] => 11
[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] => 10
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,1,0,0,0] => [6,6,6,2] => 9
[1,1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [4,3,3,2,1] => 7
[1,1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,2,1] => 6
[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1,1] => 7
[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] => 15
[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] => 21
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0,0] => [6,5,1] => 6
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0] => [5,4,1] => 6
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0] => [4,3,1] => 8
[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] => 19
[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] => 16
[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] => 16
[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] => 3
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0] => [6,1] => 3
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0] => [5,1] => 3
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0] => [4,1] => 3
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1] => 2
[1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1] => 2
[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] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0] => [8,7] => 5
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3] => 14
[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] => 19
[1,1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,1] => 2
[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0] => [3,2,2,1] => 4
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0] => [7,5,3,1] => 10
[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] => 28
[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] => 15
[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
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [8,6,4,2] => 11
[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] => 14
[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] => 4
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1] => 4
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [5,5,5,4,3,2,1] => 15
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0] => [8,7,7] => 7
[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] => 9
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1,1] => 2
[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1] => 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] => 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] => 15
[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] => 11
[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] => 6
[1,1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [3,2,2,2,1,1,1] => 3
[1,1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [4,3,3,3,2,1] => 7
[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] => 6
[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] => 21
[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] => 11
[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] => 2
[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
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2] => 11
[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] => 5
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0,0] => [8,1] => 3
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0,0] => [7,1] => 3
[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] => 8
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0,0] => [6,1] => 3
[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] => 6
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0,0] => [5,1] => 3
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0] => [4,1] => 3
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0] => [5,5] => 4
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0] => [4,4] => 4
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0] => [5,3,1] => 7
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,1] => 3
[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 1,3,3,3,2,1,1 1,4,6,7,7,5,5,3,2,1,1 1,5,10,14,17,16,16,14,11,9,7,5,3,2,1,1
$F_{1} = 1$
$F_{2} = 1 + q$
$F_{3} = 1 + 2\ q + q^{2} + q^{3}$
$F_{4} = 1 + 3\ q + 3\ q^{2} + 3\ q^{3} + 2\ q^{4} + q^{5} + q^{6}$
$F_{5} = 1 + 4\ q + 6\ q^{2} + 7\ q^{3} + 7\ q^{4} + 5\ q^{5} + 5\ q^{6} + 3\ q^{7} + 2\ q^{8} + q^{9} + q^{10}$
$F_{6} = 1 + 5\ q + 10\ q^{2} + 14\ q^{3} + 17\ q^{4} + 16\ q^{5} + 16\ q^{6} + 14\ q^{7} + 11\ q^{8} + 9\ q^{9} + 7\ q^{10} + 5\ q^{11} + 3\ q^{12} + 2\ q^{13} + q^{14} + q^{15}$
Description
The diagonal inversion number of an integer partition.
The dinv of a partition is the number of cells $c$ in the diagram of an integer partition $\lambda$ for which $\operatorname{arm}(c)-\operatorname{leg}(c) \in \{0,1\}$.
See also exercise 3.19 of [2].
This statistic is equidistributed with the length of the partition, see [3].
The dinv of a partition is the number of cells $c$ in the diagram of an integer partition $\lambda$ for which $\operatorname{arm}(c)-\operatorname{leg}(c) \in \{0,1\}$.
See also exercise 3.19 of [2].
This statistic is equidistributed with the length of the partition, see [3].
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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