Identifier
-
Mp00202:
Integer partitions
—first row removal⟶
Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00028: Dyck paths —reverse⟶ Dyck paths
St001808: Dyck paths ⟶ ℤ
Values
[1,1] => [1] => [1,0,1,0] => [1,0,1,0] => 2
[2,1] => [1] => [1,0,1,0] => [1,0,1,0] => 2
[1,1,1] => [1,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[3,1] => [1] => [1,0,1,0] => [1,0,1,0] => 2
[2,2] => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 4
[2,1,1] => [1,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[1,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0] => 4
[4,1] => [1] => [1,0,1,0] => [1,0,1,0] => 2
[3,2] => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 4
[3,1,1] => [1,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[2,2,1] => [2,1] => [1,0,1,0,1,0] => [1,0,1,0,1,0] => 6
[2,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0] => 4
[1,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => 5
[5,1] => [1] => [1,0,1,0] => [1,0,1,0] => 2
[4,2] => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 4
[4,1,1] => [1,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[3,3] => [3] => [1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0] => 8
[3,2,1] => [2,1] => [1,0,1,0,1,0] => [1,0,1,0,1,0] => 6
[3,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0] => 4
[2,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => 9
[2,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0] => 8
[2,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => 5
[1,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[6,1] => [1] => [1,0,1,0] => [1,0,1,0] => 2
[5,2] => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 4
[5,1,1] => [1,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[4,3] => [3] => [1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0] => 8
[4,2,1] => [2,1] => [1,0,1,0,1,0] => [1,0,1,0,1,0] => 6
[4,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0] => 4
[3,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0] => 12
[3,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => 9
[3,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0] => 8
[3,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => 5
[2,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0] => 12
[2,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0] => 10
[2,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[7,1] => [1] => [1,0,1,0] => [1,0,1,0] => 2
[6,2] => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 4
[6,1,1] => [1,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[5,3] => [3] => [1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0] => 8
[5,2,1] => [2,1] => [1,0,1,0,1,0] => [1,0,1,0,1,0] => 6
[5,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0] => 4
[4,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0] => 16
[4,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0] => 12
[4,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => 9
[4,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0] => 8
[4,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => 5
[3,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0] => 18
[3,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0] => 16
[3,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0] => 12
[3,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0] => 10
[3,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[2,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0] => 16
[2,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0] => 15
[2,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 12
[2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[8,1] => [1] => [1,0,1,0] => [1,0,1,0] => 2
[7,2] => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 4
[7,1,1] => [1,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[6,3] => [3] => [1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0] => 8
[6,2,1] => [2,1] => [1,0,1,0,1,0] => [1,0,1,0,1,0] => 6
[6,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0] => 4
[5,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0] => 16
[5,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0] => 12
[5,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => 9
[5,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0] => 8
[5,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => 5
[4,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0] => 24
[4,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0] => 18
[4,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0] => 16
[4,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0] => 12
[4,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0] => 10
[4,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[3,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0] => 27
[3,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => 24
[3,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 20
[3,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0] => 16
[3,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0] => 15
[3,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 12
[3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[2,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => 20
[2,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 18
[2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 14
[9,1] => [1] => [1,0,1,0] => [1,0,1,0] => 2
[8,2] => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 4
[8,1,1] => [1,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[7,3] => [3] => [1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0] => 8
[7,2,1] => [2,1] => [1,0,1,0,1,0] => [1,0,1,0,1,0] => 6
[7,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0] => 4
[6,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0] => 16
[6,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0] => 12
[6,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => 9
[6,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0] => 8
[6,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => 5
[5,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 32
[5,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0] => 24
[5,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0] => 18
[5,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0] => 16
[5,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0] => 12
[5,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0] => 10
>>> Load all 1143 entries. <<<[5,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[4,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 36
[4,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0] => 32
[4,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0] => 27
[4,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => 24
[4,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 20
[4,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0] => 16
[4,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0] => 15
[4,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 12
[4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[3,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0] => 36
[3,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0] => 32
[3,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 30
[3,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 24
[3,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => 20
[3,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 18
[3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 14
[2,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 25
[2,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 24
[2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 21
[10,1] => [1] => [1,0,1,0] => [1,0,1,0] => 2
[9,2] => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 4
[9,1,1] => [1,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[8,3] => [3] => [1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0] => 8
[8,2,1] => [2,1] => [1,0,1,0,1,0] => [1,0,1,0,1,0] => 6
[8,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0] => 4
[7,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0] => 16
[7,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0] => 12
[7,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => 9
[7,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0] => 8
[7,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => 5
[6,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 32
[6,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0] => 24
[6,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0] => 18
[6,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0] => 16
[6,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0] => 12
[6,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0] => 10
[6,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[5,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 48
[5,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 36
[5,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0] => 32
[5,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0] => 27
[5,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => 24
[5,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 20
[5,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0] => 16
[5,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0] => 15
[5,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 12
[5,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[4,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0] => 54
[4,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 48
[4,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => 40
[4,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0] => 36
[4,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0] => 32
[4,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 30
[4,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 24
[4,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => 20
[4,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 18
[4,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 14
[3,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0] => 48
[3,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 45
[3,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => 40
[3,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 36
[3,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 28
[3,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 25
[3,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 24
[3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 21
[2,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 30
[2,2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 28
[11,1] => [1] => [1,0,1,0] => [1,0,1,0] => 2
[10,2] => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 4
[10,1,1] => [1,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[9,3] => [3] => [1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0] => 8
[9,2,1] => [2,1] => [1,0,1,0,1,0] => [1,0,1,0,1,0] => 6
[9,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0] => 4
[8,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0] => 16
[8,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0] => 12
[8,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => 9
[8,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0] => 8
[8,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => 5
[7,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 32
[7,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0] => 24
[7,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0] => 18
[7,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0] => 16
[7,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0] => 12
[7,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0] => 10
[7,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[6,6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 64
[6,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 48
[6,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 36
[6,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0] => 32
[6,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0] => 27
[6,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => 24
[6,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 20
[6,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0] => 16
[6,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0] => 15
[6,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 12
[6,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[5,5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => 72
[5,5,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 64
[5,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0] => 54
[5,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 48
[5,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => 40
[5,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0] => 36
[5,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0] => 32
[5,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 30
[5,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 24
[5,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => 20
[5,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 18
[5,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 14
[4,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 81
[4,4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 72
[4,4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => 64
[4,4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0] => 60
[4,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 48
[4,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0] => 48
[4,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 45
[4,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => 40
[4,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 36
[4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 28
[4,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 25
[4,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 24
[4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 21
[3,3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => 64
[3,3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0] => 60
[3,3,3,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 54
[3,3,2,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 50
[3,3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 48
[3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 42
[3,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 30
[3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 28
[2,2,2,2,2,2] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 36
[2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 35
[12,1] => [1] => [1,0,1,0] => [1,0,1,0] => 2
[11,2] => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 4
[11,1,1] => [1,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[10,3] => [3] => [1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0] => 8
[10,2,1] => [2,1] => [1,0,1,0,1,0] => [1,0,1,0,1,0] => 6
[10,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0] => 4
[9,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0] => 16
[9,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0] => 12
[9,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => 9
[9,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0] => 8
[9,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => 5
[8,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 32
[8,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0] => 24
[8,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0] => 18
[8,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0] => 16
[8,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0] => 12
[8,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0] => 10
[8,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[7,6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 64
[7,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 48
[7,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 36
[7,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0] => 32
[7,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0] => 27
[7,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => 24
[7,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 20
[7,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0] => 16
[7,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0] => 15
[7,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 12
[7,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,6,1] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 96
[6,5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => 72
[6,5,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 64
[6,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0] => 54
[6,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 48
[6,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => 40
[6,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0] => 36
[6,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0] => 32
[6,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 30
[6,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 24
[6,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => 20
[6,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 18
[6,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 14
[5,5,3] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 108
[5,5,2,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => 96
[5,5,1,1,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => 80
[5,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 81
[5,4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 72
[5,4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => 64
[5,4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0] => 60
[5,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 48
[5,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0] => 48
[5,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 45
[5,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => 40
[5,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 36
[5,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 28
[5,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 25
[5,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 24
[5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 21
[4,4,4,1] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => 108
[4,4,3,2] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 96
[4,4,3,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => 90
[4,4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => 80
[4,4,2,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => 72
[4,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 56
[4,3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => 64
[4,3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0] => 60
[4,3,3,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 54
[4,3,2,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 50
[4,3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 48
[4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 42
[4,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 30
[4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 28
[3,3,3,3,1] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => 80
[3,3,3,2,2] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => 75
[3,3,3,2,1,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 72
[3,3,3,1,1,1,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 63
[3,3,2,2,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 60
[3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 56
[3,2,2,2,2,2] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 36
[3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 35
[2,2,2,2,2,2,1] => [2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 42
[13,1] => [1] => [1,0,1,0] => [1,0,1,0] => 2
[12,2] => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 4
[12,1,1] => [1,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[11,3] => [3] => [1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0] => 8
[11,2,1] => [2,1] => [1,0,1,0,1,0] => [1,0,1,0,1,0] => 6
[11,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0] => 4
[10,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0] => 16
[10,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0] => 12
[10,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => 9
[10,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0] => 8
[10,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => 5
[9,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 32
[9,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0] => 24
[9,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0] => 18
[9,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0] => 16
[9,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0] => 12
[9,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0] => 10
[9,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[8,6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 64
[8,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 48
[8,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 36
[8,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0] => 32
[8,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0] => 27
[8,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => 24
[8,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 20
[8,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0] => 16
[8,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0] => 15
[8,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 12
[8,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[7,7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 128
[7,6,1] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 96
[7,5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => 72
[7,5,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 64
[7,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0] => 54
[7,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 48
[7,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => 40
[7,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0] => 36
[7,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0] => 32
[7,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 30
[7,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 24
[7,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => 20
[7,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 18
[7,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 14
[6,6,2] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 144
[6,6,1,1] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 128
[6,5,3] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 108
[6,5,2,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => 96
[6,5,1,1,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => 80
[6,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 81
[6,4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 72
[6,4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => 64
[6,4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0] => 60
[6,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 48
[6,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0] => 48
[6,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 45
[6,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => 40
[6,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 36
[6,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 28
[6,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 25
[6,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 24
[6,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 21
[5,5,4] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 162
[5,5,3,1] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => 144
[5,5,2,2] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => 128
[5,5,2,1,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => 120
[5,5,1,1,1,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 96
[5,4,4,1] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => 108
[5,4,3,2] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 96
[5,4,3,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => 90
[5,4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => 80
[5,4,2,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => 72
[5,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 56
[5,3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => 64
[5,3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0] => 60
[5,3,3,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 54
[5,3,2,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 50
[5,3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 48
[5,3,2,1,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 42
[5,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 30
[5,2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 28
[4,4,4,2] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => 144
[4,4,4,1,1] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 135
[4,4,3,3] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => 128
[4,4,3,2,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 120
[4,4,3,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => 108
[4,4,2,2,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 100
[4,4,2,2,1,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => 96
[4,4,2,1,1,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 84
[4,3,3,3,1] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => 80
[4,3,3,2,2] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => 75
[4,3,3,2,1,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 72
[4,3,3,1,1,1,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 63
[4,3,2,2,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 60
[4,3,2,2,1,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 56
[4,2,2,2,2,2] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 36
[4,2,2,2,2,1,1] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 35
[3,3,3,3,2] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => 100
[3,3,3,3,1,1] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 96
[3,3,3,2,2,1] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 90
[3,3,3,2,1,1,1] => [3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 84
[3,3,2,2,2,2] => [3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 72
[3,3,2,2,2,1,1] => [3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 70
[3,2,2,2,2,2,1] => [2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 42
[14,1] => [1] => [1,0,1,0] => [1,0,1,0] => 2
[13,2] => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 4
[13,1,1] => [1,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[12,3] => [3] => [1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0] => 8
[12,2,1] => [2,1] => [1,0,1,0,1,0] => [1,0,1,0,1,0] => 6
[12,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0] => 4
[11,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0] => 16
[11,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0] => 12
[11,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => 9
[11,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0] => 8
[11,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => 5
[10,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 32
[10,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0] => 24
[10,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0] => 18
[10,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0] => 16
[10,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0] => 12
[10,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0] => 10
[10,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[9,6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 64
[9,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 48
[9,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 36
[9,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0] => 32
[9,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0] => 27
[9,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => 24
[9,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 20
[9,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0] => 16
[9,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0] => 15
[9,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 12
[9,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[8,7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 128
[8,6,1] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 96
[8,5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => 72
[8,5,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 64
[8,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0] => 54
[8,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 48
[8,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => 40
[8,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0] => 36
[8,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0] => 32
[8,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 30
[8,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 24
[8,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => 20
[8,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 18
[8,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 14
[7,7,1] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 192
[7,6,2] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 144
[7,6,1,1] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 128
[7,5,3] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 108
[7,5,2,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => 96
[7,5,1,1,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => 80
[7,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 81
[7,4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 72
[7,4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => 64
[7,4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0] => 60
[7,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 48
[7,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0] => 48
[7,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 45
[7,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => 40
[7,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 36
[7,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 28
[7,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 25
[7,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 24
[7,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 21
[6,6,3] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 216
[6,6,2,1] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 192
[6,6,1,1,1] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 160
[6,5,4] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 162
[6,5,3,1] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => 144
[6,5,2,2] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => 128
[6,5,2,1,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => 120
[6,5,1,1,1,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 96
[6,4,4,1] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => 108
[6,4,3,2] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 96
[6,4,3,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => 90
[6,4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => 80
[6,4,2,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => 72
[6,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 56
[6,3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => 64
[6,3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0] => 60
[6,3,3,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 54
[6,3,2,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 50
[6,3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 48
[6,3,2,1,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 42
[6,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 30
[6,2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 28
[5,5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 243
[5,5,4,1] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => 216
[5,5,3,2] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => 192
[5,5,3,1,1] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => 180
[5,5,2,2,1] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => 160
[5,5,2,1,1,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => 144
[5,5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 112
[5,4,4,2] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => 144
[5,4,4,1,1] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 135
[5,4,3,3] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => 128
[5,4,3,2,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 120
[5,4,3,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => 108
[5,4,2,2,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 100
[5,4,2,2,1,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => 96
[5,4,2,1,1,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 84
[5,3,3,3,1] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => 80
[5,3,3,2,2] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => 75
[5,3,3,2,1,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 72
[5,3,3,1,1,1,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 63
[5,3,2,2,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 60
[5,3,2,2,1,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 56
[5,2,2,2,2,2] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 36
[5,2,2,2,2,1,1] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 35
[4,4,4,3] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => 192
[4,4,4,2,1] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 180
[4,4,4,1,1,1] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 162
[4,4,3,3,1] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 160
[4,4,3,2,2] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => 150
[4,4,3,2,1,1] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 144
[4,4,3,1,1,1,1] => [4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 126
[4,4,2,2,2,1] => [4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 120
[4,4,2,2,1,1,1] => [4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 112
[4,3,3,3,2] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => 100
[4,3,3,3,1,1] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 96
[4,3,3,2,2,1] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 90
[4,3,3,2,1,1,1] => [3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 84
[4,3,2,2,2,2] => [3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 72
[4,3,2,2,2,1,1] => [3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 70
[4,2,2,2,2,2,1] => [2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 42
[3,3,3,3,3] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 125
[3,3,3,3,2,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 120
[3,3,3,3,1,1,1] => [3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 112
[3,3,3,2,2,2] => [3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 108
[3,3,3,2,2,1,1] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 105
[3,3,2,2,2,2,1] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 84
[15,1] => [1] => [1,0,1,0] => [1,0,1,0] => 2
[14,2] => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 4
[14,1,1] => [1,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[13,3] => [3] => [1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0] => 8
[13,2,1] => [2,1] => [1,0,1,0,1,0] => [1,0,1,0,1,0] => 6
[13,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0] => 4
[12,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0] => 16
[12,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0] => 12
[12,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => 9
[12,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0] => 8
[12,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => 5
[11,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 32
[11,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0] => 24
[11,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0] => 18
[11,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0] => 16
[11,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0] => 12
[11,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0] => 10
[11,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[10,6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 64
[10,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 48
[10,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 36
[10,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0] => 32
[10,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0] => 27
[10,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => 24
[10,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 20
[10,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0] => 16
[10,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0] => 15
[10,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 12
[10,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[9,7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 128
[9,6,1] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 96
[9,5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => 72
[9,5,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 64
[9,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0] => 54
[9,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 48
[9,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => 40
[9,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0] => 36
[9,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0] => 32
[9,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 30
[9,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 24
[9,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => 20
[9,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 18
[9,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 14
[8,7,1] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 192
[8,6,2] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 144
[8,6,1,1] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 128
[8,5,3] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 108
[8,5,2,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => 96
[8,5,1,1,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => 80
[8,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 81
[8,4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 72
[8,4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => 64
[8,4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0] => 60
[8,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 48
[8,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0] => 48
[8,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 45
[8,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => 40
[8,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 36
[8,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 28
[8,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 25
[8,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 24
[8,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 21
[7,7,2] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 288
[7,7,1,1] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 256
[7,6,3] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 216
[7,6,2,1] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 192
[7,6,1,1,1] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 160
[7,5,4] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 162
[7,5,3,1] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => 144
[7,5,2,2] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => 128
[7,5,2,1,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => 120
[7,5,1,1,1,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 96
[7,4,4,1] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => 108
[7,4,3,2] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 96
[7,4,3,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => 90
[7,4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => 80
[7,4,2,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => 72
[7,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 56
[7,3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => 64
[7,3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0] => 60
[7,3,3,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 54
[7,3,2,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 50
[7,3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 48
[7,3,2,1,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 42
[7,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 30
[7,2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 28
[6,6,4] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 324
[6,6,3,1] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 288
[6,6,2,2] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 256
[6,6,2,1,1] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 240
[6,6,1,1,1,1] => [6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 192
[6,5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 243
[6,5,4,1] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => 216
[6,5,3,2] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => 192
[6,5,3,1,1] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => 180
[6,5,2,2,1] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => 160
[6,5,2,1,1,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => 144
[6,5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 112
[6,4,4,2] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => 144
[6,4,4,1,1] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 135
[6,4,3,3] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => 128
[6,4,3,2,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 120
[6,4,3,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => 108
[6,4,2,2,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 100
[6,4,2,2,1,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => 96
[6,4,2,1,1,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 84
[6,3,3,3,1] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => 80
[6,3,3,2,2] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => 75
[6,3,3,2,1,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 72
[6,3,3,1,1,1,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 63
[6,3,2,2,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 60
[6,3,2,2,1,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 56
[6,2,2,2,2,2] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 36
[6,2,2,2,2,1,1] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 35
[5,5,5,1] => [5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 324
[5,5,4,2] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => 288
[5,5,4,1,1] => [5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => 270
[5,5,3,3] => [5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 256
[5,5,3,2,1] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 240
[5,5,3,1,1,1] => [5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => 216
[5,5,2,2,2] => [5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 200
[5,5,2,2,1,1] => [5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 192
[5,5,2,1,1,1,1] => [5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 168
[5,4,4,3] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => 192
[5,4,4,2,1] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 180
[5,4,4,1,1,1] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 162
[5,4,3,3,1] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 160
[5,4,3,2,2] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => 150
[5,4,3,2,1,1] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 144
[5,4,3,1,1,1,1] => [4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 126
[5,4,2,2,2,1] => [4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 120
[5,4,2,2,1,1,1] => [4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 112
[5,3,3,3,2] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => 100
[5,3,3,3,1,1] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 96
[5,3,3,2,2,1] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 90
[5,3,3,2,1,1,1] => [3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 84
[5,3,2,2,2,2] => [3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 72
[5,3,2,2,2,1,1] => [3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 70
[5,2,2,2,2,2,1] => [2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 42
[4,4,4,4] => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 256
[4,4,4,3,1] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 240
[4,4,4,2,2] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 225
[4,4,4,2,1,1] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 216
[4,4,4,1,1,1,1] => [4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 189
[4,4,3,3,2] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 200
[4,4,3,3,1,1] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 192
[4,4,3,2,2,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 180
[4,4,3,2,1,1,1] => [4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 168
[4,4,2,2,2,2] => [4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 144
[4,4,2,2,2,1,1] => [4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 140
[4,3,3,3,3] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 125
[4,3,3,3,2,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 120
[4,3,3,3,1,1,1] => [3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 112
[4,3,3,2,2,2] => [3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 108
[4,3,3,2,2,1,1] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 105
[4,3,2,2,2,2,1] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 84
[3,3,3,3,3,1] => [3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 150
[3,3,3,3,2,2] => [3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 144
[3,3,3,3,2,1,1] => [3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 140
[3,3,3,2,2,2,1] => [3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 126
[16,1] => [1] => [1,0,1,0] => [1,0,1,0] => 2
[15,2] => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 4
[15,1,1] => [1,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[14,3] => [3] => [1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0] => 8
[14,2,1] => [2,1] => [1,0,1,0,1,0] => [1,0,1,0,1,0] => 6
[14,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0] => 4
[13,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0] => 16
[13,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0] => 12
[13,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => 9
[13,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0] => 8
[13,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => 5
[12,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 32
[12,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0] => 24
[12,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0] => 18
[12,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0] => 16
[12,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0] => 12
[12,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0] => 10
[12,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[11,6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 64
[11,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 48
[11,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 36
[11,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0] => 32
[11,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0] => 27
[11,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => 24
[11,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 20
[11,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0] => 16
[11,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0] => 15
[11,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 12
[11,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[10,7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 128
[10,6,1] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 96
[10,5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => 72
[10,5,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 64
[10,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0] => 54
[10,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 48
[10,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => 40
[10,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0] => 36
[10,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0] => 32
[10,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 30
[10,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 24
[10,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => 20
[10,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 18
[10,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 14
[9,7,1] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 192
[9,6,2] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 144
[9,6,1,1] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 128
[9,5,3] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 108
[9,5,2,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => 96
[9,5,1,1,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => 80
[9,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 81
[9,4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 72
[9,4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => 64
[9,4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0] => 60
[9,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 48
[9,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0] => 48
[9,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 45
[9,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => 40
[9,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 36
[9,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 28
[9,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 25
[9,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 24
[9,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 21
[8,7,2] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 288
[8,7,1,1] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 256
[8,6,3] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 216
[8,6,2,1] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 192
[8,6,1,1,1] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 160
[8,5,4] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 162
[8,5,3,1] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => 144
[8,5,2,2] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => 128
[8,5,2,1,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => 120
[8,5,1,1,1,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 96
[8,4,4,1] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => 108
[8,4,3,2] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 96
[8,4,3,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => 90
[8,4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => 80
[8,4,2,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => 72
[8,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 56
[8,3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => 64
[8,3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0] => 60
[8,3,3,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 54
[8,3,2,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 50
[8,3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 48
[8,3,2,1,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 42
[8,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 30
[8,2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 28
[7,7,3] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 432
[7,7,2,1] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 384
[7,7,1,1,1] => [7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 320
[7,6,4] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 324
[7,6,3,1] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 288
[7,6,2,2] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 256
[7,6,2,1,1] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 240
[7,6,1,1,1,1] => [6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 192
[7,5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 243
[7,5,4,1] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => 216
[7,5,3,2] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => 192
[7,5,3,1,1] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => 180
[7,5,2,2,1] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => 160
[7,5,2,1,1,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => 144
[7,5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 112
[7,4,4,2] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => 144
[7,4,4,1,1] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 135
[7,4,3,3] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => 128
[7,4,3,2,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 120
[7,4,3,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => 108
[7,4,2,2,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 100
[7,4,2,2,1,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => 96
[7,4,2,1,1,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 84
[7,3,3,3,1] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => 80
[7,3,3,2,2] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => 75
[7,3,3,2,1,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 72
[7,3,3,1,1,1,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 63
[7,3,2,2,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 60
[7,3,2,2,1,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 56
[7,2,2,2,2,2] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 36
[7,2,2,2,2,1,1] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 35
[6,6,5] => [6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 486
[6,6,4,1] => [6,4,1] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 432
[6,6,3,2] => [6,3,2] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 384
[6,6,3,1,1] => [6,3,1,1] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 360
[6,6,2,2,1] => [6,2,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 320
[6,6,2,1,1,1] => [6,2,1,1,1] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 288
[6,6,1,1,1,1,1] => [6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 224
[6,5,5,1] => [5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 324
[6,5,4,2] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => 288
[6,5,4,1,1] => [5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => 270
[6,5,3,3] => [5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 256
[6,5,3,2,1] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 240
[6,5,3,1,1,1] => [5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => 216
[6,5,2,2,2] => [5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 200
[6,5,2,2,1,1] => [5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 192
[6,5,2,1,1,1,1] => [5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 168
[6,4,4,3] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => 192
[6,4,4,2,1] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 180
[6,4,4,1,1,1] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 162
[6,4,3,3,1] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 160
[6,4,3,2,2] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => 150
[6,4,3,2,1,1] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 144
[6,4,3,1,1,1,1] => [4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 126
[6,4,2,2,2,1] => [4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 120
[6,4,2,2,1,1,1] => [4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 112
[6,3,3,3,2] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => 100
[6,3,3,3,1,1] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 96
[6,3,3,2,2,1] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 90
[6,3,3,2,1,1,1] => [3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 84
[6,3,2,2,2,2] => [3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 72
[6,3,2,2,2,1,1] => [3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 70
[6,2,2,2,2,2,1] => [2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 42
[5,5,5,2] => [5,5,2] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 432
[5,5,5,1,1] => [5,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 405
[5,5,4,3] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 384
[5,5,4,2,1] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 360
[5,5,4,1,1,1] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => 324
[5,5,3,3,1] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 320
[5,5,3,2,2] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 300
[5,5,3,2,1,1] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 288
[5,5,3,1,1,1,1] => [5,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 252
[5,5,2,2,2,1] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 240
[5,5,2,2,1,1,1] => [5,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 224
[5,4,4,4] => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 256
[5,4,4,3,1] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 240
[5,4,4,2,2] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 225
[5,4,4,2,1,1] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 216
[5,4,4,1,1,1,1] => [4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 189
[5,4,3,3,2] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 200
[5,4,3,3,1,1] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 192
[5,4,3,2,2,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 180
[5,4,3,2,1,1,1] => [4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 168
[5,4,2,2,2,2] => [4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 144
[5,4,2,2,2,1,1] => [4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 140
[5,3,3,3,3] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 125
[5,3,3,3,2,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 120
[5,3,3,3,1,1,1] => [3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 112
[5,3,3,2,2,2] => [3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 108
[5,3,3,2,2,1,1] => [3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 105
[5,3,2,2,2,2,1] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 84
[4,4,4,4,1] => [4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 320
[4,4,4,3,2] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 300
[4,4,4,3,1,1] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 288
[4,4,4,2,2,1] => [4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 270
[4,4,4,2,1,1,1] => [4,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 252
[4,4,3,3,3] => [4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 250
[4,4,3,3,2,1] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 240
[4,4,3,3,1,1,1] => [4,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 224
[4,4,3,2,2,2] => [4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 216
[4,4,3,2,2,1,1] => [4,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 210
[4,4,2,2,2,2,1] => [4,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 168
[4,3,3,3,3,1] => [3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 150
[4,3,3,3,2,2] => [3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 144
[4,3,3,3,2,1,1] => [3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 140
[4,3,3,2,2,2,1] => [3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 126
[3,3,3,3,3,2] => [3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 180
[3,3,3,3,3,1,1] => [3,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 175
[3,3,3,3,2,2,1] => [3,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 168
[6,5,4,3,2,1] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 720
[5,5,4,3,2,1] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 720
[6,4,4,3,2,1] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 360
[5,4,4,3,2,1] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 360
[4,4,4,3,2,1] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 360
[6,5,3,3,2,1] => [5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 480
[5,5,3,3,2,1] => [5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 480
[6,4,3,3,2,1] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 240
[5,4,3,3,2,1] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 240
[6,3,3,3,2,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 120
[6,5,4,2,2,1] => [5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 540
[5,5,4,2,2,1] => [5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 540
[6,4,4,2,2,1] => [4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 270
[5,4,4,2,2,1] => [4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 270
[6,5,3,2,2,1] => [5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 360
[5,5,3,2,2,1] => [5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 360
[6,4,3,2,2,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 180
[6,5,2,2,2,1] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 240
[6,5,4,3,1,1] => [5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 576
[5,5,4,3,1,1] => [5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 576
[6,4,4,3,1,1] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 288
[5,4,4,3,1,1] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 288
[6,5,3,3,1,1] => [5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 384
[5,5,3,3,1,1] => [5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 384
[6,4,3,3,1,1] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 192
[6,5,4,2,1,1] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 432
[5,5,4,2,1,1] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 432
[6,4,4,2,1,1] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 216
[6,5,3,2,1,1] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 288
[6,5,4,1,1,1] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => 324
[6,5,4,3,2] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 600
[5,5,4,3,2] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 600
[6,4,4,3,2] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 300
[5,4,4,3,2] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 300
[6,5,3,3,2] => [5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => 400
[5,5,3,3,2] => [5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => 400
[6,4,3,3,2] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 200
[6,5,4,2,2] => [5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => 450
[5,5,4,2,2] => [5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => 450
[6,4,4,2,2] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 225
[6,5,3,2,2] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 300
[6,5,4,3,1] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 480
[5,5,4,3,1] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 480
[6,4,4,3,1] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 240
[6,5,3,3,1] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 320
[6,5,4,2,1] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 360
[6,5,4,3] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 384
[7,6,5,4,3,2,1] => [6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 5040
[6,6,5,4,3,2,1] => [6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 5040
[7,5,5,4,3,2,1] => [5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2520
[6,5,5,4,3,2,1] => [5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2520
[5,5,5,4,3,2,1] => [5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2520
[7,6,4,4,3,2,1] => [6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 3360
[6,6,4,4,3,2,1] => [6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 3360
[7,5,4,4,3,2,1] => [5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 1680
[6,5,4,4,3,2,1] => [5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 1680
[5,5,4,4,3,2,1] => [5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 1680
[7,4,4,4,3,2,1] => [4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 840
[6,4,4,4,3,2,1] => [4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 840
[5,4,4,4,3,2,1] => [4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 840
[4,4,4,4,3,2,1] => [4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 840
[6,6,5,3,3,2,1] => [6,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 3780
[6,5,4,3,3,2,1] => [5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1260
[6,5,3,3,3,2,1] => [5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 840
[6,4,3,3,3,2,1] => [4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 420
[5,4,3,3,3,2,1] => [4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 420
[6,3,3,3,3,2,1] => [3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 210
[3,3,3,3,3,2,1] => [3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 210
[6,6,5,4,2,2,1] => [6,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 4032
[6,5,5,4,2,2,1] => [5,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2016
[6,5,4,4,2,2,1] => [5,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1344
[6,5,4,3,2,2,1] => [5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1008
[5,5,4,3,2,2,1] => [5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1008
[7,6,5,2,2,2,1] => [6,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2268
[6,5,4,2,2,2,1] => [5,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 756
[6,5,3,2,2,2,1] => [5,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 504
[6,4,3,2,2,2,1] => [4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 252
[5,4,3,2,2,2,1] => [4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 252
[6,5,2,2,2,2,1] => [5,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 336
[7,2,2,2,2,2,1] => [2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 42
[7,6,5,4,3,1,1] => [6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 4200
[6,6,5,4,3,1,1] => [6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 4200
[6,5,5,4,3,1,1] => [5,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2100
[6,6,5,4,2,1,1] => [6,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3360
[6,5,5,4,2,1,1] => [5,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1680
[4,4,4,4,2,1,1] => [4,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 560
[6,5,4,3,2,1,1] => [5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 840
[5,5,4,3,2,1,1] => [5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 840
[5,4,4,3,2,1,1] => [4,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 420
[7,6,5,4,1,1,1] => [6,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2688
[6,5,5,4,1,1,1] => [5,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1344
[6,5,4,3,1,1,1] => [5,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 672
[7,6,5,2,1,1,1] => [6,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 1512
[5,5,5,2,1,1,1] => [5,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 756
[7,5,4,2,1,1,1] => [5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 504
[6,5,4,2,1,1,1] => [5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 504
[7,6,3,2,1,1,1] => [6,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 672
[7,4,3,2,1,1,1] => [4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 168
[6,4,3,2,1,1,1] => [4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 168
[6,5,4,1,1,1,1] => [5,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 378
[6,6,2,1,1,1,1] => [6,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 336
[7,6,1,1,1,1,1] => [6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 224
[7,6,5,4,3,2] => [6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 4320
[6,6,5,4,3,2] => [6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 4320
[7,5,5,4,3,2] => [5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2160
[6,5,5,4,3,2] => [5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2160
[5,5,5,4,3,2] => [5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2160
[7,6,4,4,3,2] => [6,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2880
[6,5,4,4,3,2] => [5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1440
[6,5,4,3,3,2] => [5,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1080
[5,4,3,3,3,2] => [4,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 360
[4,3,3,3,3,2] => [3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 180
[6,5,4,3,2,2] => [5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 864
[4,4,4,3,2,2] => [4,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 432
[7,6,5,2,2,2] => [6,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1944
[6,5,4,2,2,2] => [5,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 648
[5,4,3,2,2,2] => [4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 216
[6,6,2,2,2,2] => [6,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 576
[7,6,5,4,3,1] => [6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 3600
[6,6,5,4,3,1] => [6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 3600
[6,5,5,4,3,1] => [5,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1800
[4,4,4,4,3,1] => [4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 600
[7,6,5,4,2,1] => [6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2880
[5,5,5,4,2,1] => [5,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1440
[4,4,4,4,2,1] => [4,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 480
[7,6,5,3,2,1] => [6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 2160
[6,6,5,3,2,1] => [6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 2160
[5,5,5,3,2,1] => [5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 1080
[7,6,4,3,2,1] => [6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1440
[6,6,4,3,2,1] => [6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1440
[7,5,4,3,2,1] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 720
[7,4,4,3,2,1] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 360
[7,6,3,3,2,1] => [6,3,3,2,1] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 960
[7,4,3,3,2,1] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 240
[7,3,3,3,2,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 120
[7,6,5,2,2,1] => [6,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 1620
[7,6,3,2,2,1] => [6,3,2,2,1] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 720
[7,6,2,2,2,1] => [6,2,2,2,1] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 480
[7,6,5,4,1,1] => [6,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2304
[7,6,5,2,1,1] => [6,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 1296
[7,6,3,2,1,1] => [6,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 576
[7,4,3,2,1,1] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 144
[7,6,5,1,1,1] => [6,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 972
[7,6,5,4,3] => [6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3000
[6,6,5,4,3] => [6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3000
[6,5,5,4,3] => [5,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1500
[5,4,4,4,3] => [4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 500
[5,4,3,3,3] => [4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 250
[7,3,3,3,3] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 125
[7,6,5,4,2] => [6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 2400
[4,4,4,4,2] => [4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 400
[7,6,5,3,2] => [6,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 1800
[7,6,4,3,2] => [6,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1200
[7,5,4,3,2] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 600
[7,6,5,4,1] => [6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 1920
[7,5,4,3,1] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 480
[7,6,5,2,1] => [6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 1080
[6,6,5,2,1] => [6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 1080
[7,6,4,2,1] => [6,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 720
[6,6,4,2,1] => [6,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 720
[7,5,4,2,1] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 360
[7,6,3,2,1] => [6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 480
[6,6,3,2,1] => [6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 480
[7,6,5,4] => [6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1536
[6,5,5,4] => [5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 768
[7,6,5,3] => [6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 1152
[7,6,4,3] => [6,4,3] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 768
[7,5,4,3] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 384
[7,6,5,2] => [6,5,2] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 864
[7,6,5] => [6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 486
[6,6,6] => [6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 729
[7,6,6] => [6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 729
[10,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 81
[11,7,3] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 432
[9,6,3] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 216
[8,6,4,2] => [6,4,2] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 576
[8,6,4] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 324
[10,6,4] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 324
[8,7,6] => [7,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1458
[15,5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 243
[11,7,5,1] => [7,5,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 1296
[9,7,5,3,1] => [7,5,3,1] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 2880
[8,7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 40320
[7,7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 40320
[7,6,6,5,4,3,2,1] => [6,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 20160
[7,6,5,5,4,3,2,1] => [6,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 13440
[6,6,6,5,4,3,2,1] => [6,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 20160
[8,7,6,5,4,3,2] => [7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 35280
[8,7,6,5,4,3,1] => [7,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 30240
[8,7,6,5,4,2,1] => [7,6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 25200
[8,7,6,5,3,2,1] => [7,6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 20160
[8,7,6,4,3,2,1] => [7,6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 15120
[8,7,5,4,3,2,1] => [7,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 10080
[8,6,5,4,3,2,1] => [6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 5040
[8,7,6,5,4,3] => [7,6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 25920
[8,7,6,5,4,1,1] => [7,6,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 21000
[8,7,6,5,2,2,1] => [7,6,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 16128
[8,5,5,4,3,2,1] => [5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2520
[9,7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 40320
[9,6,4] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 324
[10,7,3] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 432
[8,5,4,2] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => 288
[9,6,5,3] => [6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 1152
[10,7,5,3] => [7,5,3] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 2304
[9,6,4,3] => [6,4,3] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 768
[9,7,4] => [7,4] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 648
[9,7,5,4,1] => [7,5,4,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 3840
[8,6,5,3,1] => [6,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 1440
[8,5,5,1] => [5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 324
[9,5,5,1] => [5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 324
[9,7,5,3] => [7,5,3] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 2304
[7,7,1,1,1,1] => [7,1,1,1,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 384
[8,5,4,3,2,1] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 720
[8,7,4,3,2,1] => [7,4,3,2,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 2880
[7,7,1,1,1,1,1,1] => [7,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 512
[8,6,5,4,3,2] => [6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 4320
[7,6,5,5,4,2,2,1] => [6,5,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 11200
[7,6,6,5,4,3,1,1] => [6,6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 17280
[7,7,6,5,4,3,2] => [7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 35280
[6,6,6,4,3,2,1] => [6,6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 7560
[8,7,6,3,2,1] => [7,6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 6480
[8,7,6,5,2,1] => [7,6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 11520
[8,7,6,5,4,1] => [7,6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 18000
[7,6,6,5,4,3,2] => [6,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 17640
[7,6,6,5,4,3,1] => [6,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 15120
[7,7,6,5,4,3,1] => [7,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 30240
[7,7,6,5,4,3,1,1] => [7,6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 34560
[7,7,6,5,3,2,1] => [7,6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 20160
[8,7,6,5,4,1,1,1] => [7,6,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 24000
[8,6,6,5,4,3,2] => [6,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 17640
[8,7,6,5] => [7,6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 6144
[8,7,6,5,4] => [7,6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 15000
[8,7,5] => [7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 972
[8,7,6,4] => [7,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 4608
[8,7,6,5,3] => [7,6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 12000
[8,7,6,5,4,2] => [7,6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 21600
[6,6,6,1] => [6,6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 972
[7,7,5,5,4,3,2,1] => [7,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 26880
[7,7,5,4,3,2,1] => [7,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 10080
[6,6,6,1,1] => [6,6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 1215
[7,7,4,3,2,1] => [7,4,3,2,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 2880
[8,5,4,3,2,1,1] => [5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 840
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searching the database for the individual values of this statistic
Description
The box weight or horizontal decoration of a Dyck path.
Let a Dyck path $D = (d_1,d_2,\dots,d_n)$ with steps $d_i \in \{N=(0,1),E=(1,0)\}$ be given.
For the $i$th step $d_i \in D$ we define the weight
$$ \beta(d_i) = 1, \quad \text{ if } d_i=N, $$
and
$$ \beta(d_i) = \sum_{k = 1}^{i} [\![ d_k = N]\!], \quad \text{ if } d_i=E, $$
where we use the Iverson bracket $[\![ A ]\!]$ that is equal to $1$ if $A$ is true, and $0$ otherwise.
The box weight or horizontal deocration of $D$ is defined as
$$ \prod_{i=1}^{n} \beta(d_i). $$
The name describes the fact that between each $E$ step and the line $y=-1$ exactly one unit box is marked.
Let a Dyck path $D = (d_1,d_2,\dots,d_n)$ with steps $d_i \in \{N=(0,1),E=(1,0)\}$ be given.
For the $i$th step $d_i \in D$ we define the weight
$$ \beta(d_i) = 1, \quad \text{ if } d_i=N, $$
and
$$ \beta(d_i) = \sum_{k = 1}^{i} [\![ d_k = N]\!], \quad \text{ if } d_i=E, $$
where we use the Iverson bracket $[\![ A ]\!]$ that is equal to $1$ if $A$ is true, and $0$ otherwise.
The box weight or horizontal deocration of $D$ is defined as
$$ \prod_{i=1}^{n} \beta(d_i). $$
The name describes the fact that between each $E$ step and the line $y=-1$ exactly one unit box is marked.
Map
first row removal
Description
Removes the first entry of an integer partition
Map
reverse
Description
The reversal of a Dyck path.
This is the Dyck path obtained by reading the path backwards.
This is the Dyck path obtained by reading the path backwards.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.
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