Identifier
-
Mp00044:
Integer partitions
—conjugate⟶
Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
St000420: Dyck paths ⟶ ℤ (values match St000419The number of Dyck paths that are weakly above the Dyck path, except for the path itself.)
Values
[2] => [1,1] => [1] => [1,0,1,0] => 2
[3] => [1,1,1] => [1,1] => [1,0,1,1,0,0] => 3
[2,1] => [2,1] => [1] => [1,0,1,0] => 2
[4] => [1,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 4
[3,1] => [2,1,1] => [1,1] => [1,0,1,1,0,0] => 3
[2,2] => [2,2] => [2] => [1,1,0,0,1,0] => 3
[2,1,1] => [3,1] => [1] => [1,0,1,0] => 2
[5] => [1,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 5
[4,1] => [2,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 4
[3,2] => [2,2,1] => [2,1] => [1,0,1,0,1,0] => 5
[3,1,1] => [3,1,1] => [1,1] => [1,0,1,1,0,0] => 3
[2,2,1] => [3,2] => [2] => [1,1,0,0,1,0] => 3
[2,1,1,1] => [4,1] => [1] => [1,0,1,0] => 2
[6] => [1,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 6
[5,1] => [2,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 5
[4,2] => [2,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 7
[4,1,1] => [3,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 4
[3,3] => [2,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 6
[3,2,1] => [3,2,1] => [2,1] => [1,0,1,0,1,0] => 5
[3,1,1,1] => [4,1,1] => [1,1] => [1,0,1,1,0,0] => 3
[2,2,2] => [3,3] => [3] => [1,1,1,0,0,0,1,0] => 4
[2,2,1,1] => [4,2] => [2] => [1,1,0,0,1,0] => 3
[2,1,1,1,1] => [5,1] => [1] => [1,0,1,0] => 2
[7] => [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] => 7
[6,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 6
[5,2] => [2,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 9
[5,1,1] => [3,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 5
[4,3] => [2,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => 9
[4,2,1] => [3,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 7
[4,1,1,1] => [4,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 4
[3,3,1] => [3,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 6
[3,2,2] => [3,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => 7
[3,2,1,1] => [4,2,1] => [2,1] => [1,0,1,0,1,0] => 5
[3,1,1,1,1] => [5,1,1] => [1,1] => [1,0,1,1,0,0] => 3
[2,2,2,1] => [4,3] => [3] => [1,1,1,0,0,0,1,0] => 4
[2,2,1,1,1] => [5,2] => [2] => [1,1,0,0,1,0] => 3
[2,1,1,1,1,1] => [6,1] => [1] => [1,0,1,0] => 2
[8] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,1] => [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] => 7
[6,2] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 11
[6,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 6
[5,3] => [2,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 12
[5,2,1] => [3,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 9
[5,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 5
[4,4] => [2,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 10
[4,3,1] => [3,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => 9
[4,2,2] => [3,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 10
[4,2,1,1] => [4,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 7
[4,1,1,1,1] => [5,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 4
[3,3,2] => [3,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => 9
[3,3,1,1] => [4,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 6
[3,2,2,1] => [4,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => 7
[3,2,1,1,1] => [5,2,1] => [2,1] => [1,0,1,0,1,0] => 5
[3,1,1,1,1,1] => [6,1,1] => [1,1] => [1,0,1,1,0,0] => 3
[2,2,2,2] => [4,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => 5
[2,2,2,1,1] => [5,3] => [3] => [1,1,1,0,0,0,1,0] => 4
[2,2,1,1,1,1] => [6,2] => [2] => [1,1,0,0,1,0] => 3
[2,1,1,1,1,1,1] => [7,1] => [1] => [1,0,1,0] => 2
[8,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,2] => [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] => 13
[7,1,1] => [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] => 7
[6,3] => [2,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 15
[6,2,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 11
[6,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 6
[5,4] => [2,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 14
[5,3,1] => [3,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 12
[5,2,2] => [3,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 13
[5,2,1,1] => [4,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 9
[5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 5
[4,4,1] => [3,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 10
[4,3,2] => [3,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 14
[4,3,1,1] => [4,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => 9
[4,2,2,1] => [4,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 10
[4,2,1,1,1] => [5,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 7
[4,1,1,1,1,1] => [6,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 4
[3,3,3] => [3,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 10
[3,3,2,1] => [4,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => 9
[3,3,1,1,1] => [5,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 6
[3,2,2,2] => [4,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 9
[3,2,2,1,1] => [5,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => 7
[3,2,1,1,1,1] => [6,2,1] => [2,1] => [1,0,1,0,1,0] => 5
[3,1,1,1,1,1,1] => [7,1,1] => [1,1] => [1,0,1,1,0,0] => 3
[2,2,2,2,1] => [5,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => 5
[2,2,2,1,1,1] => [6,3] => [3] => [1,1,1,0,0,0,1,0] => 4
[2,2,1,1,1,1,1] => [7,2] => [2] => [1,1,0,0,1,0] => 3
[2,1,1,1,1,1,1,1] => [8,1] => [1] => [1,0,1,0] => 2
[8,2] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 15
[8,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,3] => [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] => 18
[7,2,1] => [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] => 13
[7,1,1,1] => [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] => 7
[6,4] => [2,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 18
[6,3,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 15
[6,2,2] => [3,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 16
[6,2,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 11
[6,1,1,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 6
[5,5] => [2,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 15
[5,4,1] => [3,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 14
[5,3,2] => [3,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 19
[5,3,1,1] => [4,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 12
[5,2,2,1] => [4,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 13
>>> Load all 1148 entries. <<<[5,2,1,1,1] => [5,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 9
[5,1,1,1,1,1] => [6,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 5
[4,4,2] => [3,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 16
[4,4,1,1] => [4,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 10
[4,3,3] => [3,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 16
[4,3,2,1] => [4,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 14
[4,3,1,1,1] => [5,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => 9
[4,2,2,2] => [4,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 13
[4,2,2,1,1] => [5,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 10
[4,2,1,1,1,1] => [6,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 7
[4,1,1,1,1,1,1] => [7,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 4
[3,3,3,1] => [4,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 10
[3,3,2,2] => [4,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 12
[3,3,2,1,1] => [5,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => 9
[3,3,1,1,1,1] => [6,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 6
[3,2,2,2,1] => [5,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 9
[3,2,2,1,1,1] => [6,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => 7
[3,2,1,1,1,1,1] => [7,2,1] => [2,1] => [1,0,1,0,1,0] => 5
[3,1,1,1,1,1,1,1] => [8,1,1] => [1,1] => [1,0,1,1,0,0] => 3
[2,2,2,2,2] => [5,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[2,2,2,2,1,1] => [6,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => 5
[2,2,2,1,1,1,1] => [7,3] => [3] => [1,1,1,0,0,0,1,0] => 4
[2,2,1,1,1,1,1,1] => [8,2] => [2] => [1,1,0,0,1,0] => 3
[2,1,1,1,1,1,1,1,1] => [9,1] => [1] => [1,0,1,0] => 2
[8,3] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 21
[8,2,1] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 15
[8,1,1,1] => [4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,4] => [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] => 22
[7,3,1] => [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] => 18
[7,2,2] => [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] => 19
[7,2,1,1] => [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] => 13
[7,1,1,1,1] => [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] => 7
[6,5] => [2,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 20
[6,4,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 18
[6,3,2] => [3,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 24
[6,3,1,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 15
[6,2,2,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 16
[6,2,1,1,1] => [5,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 11
[6,1,1,1,1,1] => [6,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 6
[5,5,1] => [3,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 15
[5,4,2] => [3,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 23
[5,4,1,1] => [4,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 14
[5,3,3] => [3,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 22
[5,3,2,1] => [4,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 19
[5,3,1,1,1] => [5,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 12
[5,2,2,2] => [4,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 17
[5,2,2,1,1] => [5,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 13
[5,2,1,1,1,1] => [6,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 9
[5,1,1,1,1,1,1] => [7,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 5
[4,4,3] => [3,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 19
[4,4,2,1] => [4,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 16
[4,4,1,1,1] => [5,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 10
[4,3,3,1] => [4,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 16
[4,3,2,2] => [4,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 19
[4,3,2,1,1] => [5,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 14
[4,3,1,1,1,1] => [6,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => 9
[4,2,2,2,1] => [5,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 13
[4,2,2,1,1,1] => [6,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 10
[4,2,1,1,1,1,1] => [7,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 7
[4,1,1,1,1,1,1,1] => [8,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 4
[3,3,3,2] => [4,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 14
[3,3,3,1,1] => [5,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 10
[3,3,2,2,1] => [5,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 12
[3,3,2,1,1,1] => [6,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => 9
[3,3,1,1,1,1,1] => [7,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 6
[3,2,2,2,2] => [5,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 11
[3,2,2,2,1,1] => [6,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 9
[3,2,2,1,1,1,1] => [7,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => 7
[3,2,1,1,1,1,1,1] => [8,2,1] => [2,1] => [1,0,1,0,1,0] => 5
[3,1,1,1,1,1,1,1,1] => [9,1,1] => [1,1] => [1,0,1,1,0,0] => 3
[2,2,2,2,2,1] => [6,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[2,2,2,2,1,1,1] => [7,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => 5
[2,2,2,1,1,1,1,1] => [8,3] => [3] => [1,1,1,0,0,0,1,0] => 4
[2,2,1,1,1,1,1,1,1] => [9,2] => [2] => [1,1,0,0,1,0] => 3
[2,1,1,1,1,1,1,1,1,1] => [10,1] => [1] => [1,0,1,0] => 2
[8,4] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 26
[8,3,1] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 21
[8,2,2] => [3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 22
[8,2,1,1] => [4,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 15
[8,1,1,1,1] => [5,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,5] => [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] => 25
[7,4,1] => [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] => 22
[7,3,2] => [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] => 29
[7,3,1,1] => [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] => 18
[7,2,2,1] => [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] => 19
[7,2,1,1,1] => [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] => 13
[7,1,1,1,1,1] => [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] => 7
[6,6] => [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] => 21
[6,5,1] => [3,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 20
[6,4,2] => [3,3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 30
[6,4,1,1] => [4,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 18
[6,3,3] => [3,3,3,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 28
[6,3,2,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 24
[6,3,1,1,1] => [5,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 15
[6,2,2,2] => [4,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 21
[6,2,2,1,1] => [5,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 16
[6,2,1,1,1,1] => [6,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 11
[6,1,1,1,1,1,1] => [7,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 6
[5,5,2] => [3,3,2,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 25
[5,5,1,1] => [4,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 15
[5,4,3] => [3,3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 28
[5,4,2,1] => [4,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 23
[5,4,1,1,1] => [5,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 14
[5,3,3,1] => [4,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 22
[5,3,2,2] => [4,4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 26
[5,3,2,1,1] => [5,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 19
[5,3,1,1,1,1] => [6,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 12
[5,2,2,2,1] => [5,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 17
[5,2,2,1,1,1] => [6,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 13
[5,2,1,1,1,1,1] => [7,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 9
[5,1,1,1,1,1,1,1] => [8,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 5
[4,4,4] => [3,3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 20
[4,4,3,1] => [4,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 19
[4,4,2,2] => [4,4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 22
[4,4,2,1,1] => [5,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 16
[4,4,1,1,1,1] => [6,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 10
[4,3,3,2] => [4,4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 23
[4,3,3,1,1] => [5,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 16
[4,3,2,2,1] => [5,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 19
[4,3,2,1,1,1] => [6,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 14
[4,3,1,1,1,1,1] => [7,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => 9
[4,2,2,2,2] => [5,5,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 16
[4,2,2,2,1,1] => [6,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 13
[4,2,2,1,1,1,1] => [7,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 10
[4,2,1,1,1,1,1,1] => [8,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 7
[4,1,1,1,1,1,1,1,1] => [9,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 4
[3,3,3,3] => [4,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 15
[3,3,3,2,1] => [5,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 14
[3,3,3,1,1,1] => [6,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 10
[3,3,2,2,2] => [5,5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 15
[3,3,2,2,1,1] => [6,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 12
[3,3,2,1,1,1,1] => [7,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => 9
[3,3,1,1,1,1,1,1] => [8,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 6
[3,2,2,2,2,1] => [6,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 11
[3,2,2,2,1,1,1] => [7,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 9
[3,2,2,1,1,1,1,1] => [8,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => 7
[3,2,1,1,1,1,1,1,1] => [9,2,1] => [2,1] => [1,0,1,0,1,0] => 5
[3,1,1,1,1,1,1,1,1,1] => [10,1,1] => [1,1] => [1,0,1,1,0,0] => 3
[2,2,2,2,2,2] => [6,6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[2,2,2,2,2,1,1] => [7,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[2,2,2,2,1,1,1,1] => [8,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => 5
[2,2,2,1,1,1,1,1,1] => [9,3] => [3] => [1,1,1,0,0,0,1,0] => 4
[2,2,1,1,1,1,1,1,1,1] => [10,2] => [2] => [1,1,0,0,1,0] => 3
[2,1,1,1,1,1,1,1,1,1,1] => [11,1] => [1] => [1,0,1,0] => 2
[8,5] => [2,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 30
[8,4,1] => [3,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 26
[8,3,2] => [3,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 34
[8,3,1,1] => [4,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 21
[8,2,2,1] => [4,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 22
[8,2,1,1,1] => [5,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 15
[8,1,1,1,1,1] => [6,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,6] => [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] => 27
[7,5,1] => [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] => 25
[7,4,2] => [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] => 37
[7,4,1,1] => [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] => 22
[7,3,3] => [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] => 34
[7,3,2,1] => [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] => 29
[7,3,1,1,1] => [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] => 18
[7,2,2,2] => [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] => 25
[7,2,2,1,1] => [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] => 19
[7,2,1,1,1,1] => [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] => 13
[7,1,1,1,1,1,1] => [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] => 7
[6,6,1] => [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] => 21
[6,5,2] => [3,3,2,2,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 34
[6,5,1,1] => [4,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 20
[6,4,3] => [3,3,3,2,1,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 37
[6,4,2,1] => [4,3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 30
[6,4,1,1,1] => [5,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 18
[6,3,3,1] => [4,3,3,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 28
[6,3,2,2] => [4,4,2,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 33
[6,3,2,1,1] => [5,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 24
[6,3,1,1,1,1] => [6,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 15
[6,2,2,2,1] => [5,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 21
[6,2,2,1,1,1] => [6,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 16
[6,2,1,1,1,1,1] => [7,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 11
[6,1,1,1,1,1,1,1] => [8,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 6
[5,5,3] => [3,3,3,2,2] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 31
[5,5,2,1] => [4,3,2,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 25
[5,5,1,1,1] => [5,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 15
[5,4,4] => [3,3,3,3,1] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 30
[5,4,3,1] => [4,3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 28
[5,4,2,2] => [4,4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 32
[5,4,2,1,1] => [5,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 23
[5,4,1,1,1,1] => [6,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 14
[5,3,3,2] => [4,4,3,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 32
[5,3,3,1,1] => [5,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 22
[5,3,2,2,1] => [5,4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 26
[5,3,2,1,1,1] => [6,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 19
[5,3,1,1,1,1,1] => [7,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 12
[5,2,2,2,2] => [5,5,1,1,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 21
[5,2,2,2,1,1] => [6,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 17
[5,2,2,1,1,1,1] => [7,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 13
[5,2,1,1,1,1,1,1] => [8,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 9
[5,1,1,1,1,1,1,1,1] => [9,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 5
[4,4,4,1] => [4,3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 20
[4,4,3,2] => [4,4,3,2] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 28
[4,4,3,1,1] => [5,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 19
[4,4,2,2,1] => [5,4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 22
[4,4,2,1,1,1] => [6,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 16
[4,4,1,1,1,1,1] => [7,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 10
[4,3,3,3] => [4,4,4,1] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 25
[4,3,3,2,1] => [5,4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 23
[4,3,3,1,1,1] => [6,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 16
[4,3,2,2,2] => [5,5,2,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 24
[4,3,2,2,1,1] => [6,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 19
[4,3,2,1,1,1,1] => [7,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 14
[4,3,1,1,1,1,1,1] => [8,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => 9
[4,2,2,2,2,1] => [6,5,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 16
[4,2,2,2,1,1,1] => [7,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 13
[4,2,2,1,1,1,1,1] => [8,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 10
[4,2,1,1,1,1,1,1,1] => [9,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 7
[4,1,1,1,1,1,1,1,1,1] => [10,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 4
[3,3,3,3,1] => [5,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 15
[3,3,3,2,2] => [5,5,3] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 18
[3,3,3,2,1,1] => [6,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 14
[3,3,3,1,1,1,1] => [7,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 10
[3,3,2,2,2,1] => [6,5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 15
[3,3,2,2,1,1,1] => [7,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 12
[3,3,2,1,1,1,1,1] => [8,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => 9
[3,3,1,1,1,1,1,1,1] => [9,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 6
[3,2,2,2,2,2] => [6,6,1] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 13
[3,2,2,2,2,1,1] => [7,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 11
[3,2,2,2,1,1,1,1] => [8,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 9
[3,2,2,1,1,1,1,1,1] => [9,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => 7
[3,2,1,1,1,1,1,1,1,1] => [10,2,1] => [2,1] => [1,0,1,0,1,0] => 5
[3,1,1,1,1,1,1,1,1,1,1] => [11,1,1] => [1,1] => [1,0,1,1,0,0] => 3
[2,2,2,2,2,2,1] => [7,6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[2,2,2,2,2,1,1,1] => [8,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[2,2,2,2,1,1,1,1,1] => [9,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => 5
[2,2,2,1,1,1,1,1,1,1] => [10,3] => [3] => [1,1,1,0,0,0,1,0] => 4
[2,2,1,1,1,1,1,1,1,1,1] => [11,2] => [2] => [1,1,0,0,1,0] => 3
[2,1,1,1,1,1,1,1,1,1,1,1] => [12,1] => [1] => [1,0,1,0] => 2
[8,6] => [2,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 33
[8,5,1] => [3,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 30
[8,4,2] => [3,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 44
[8,4,1,1] => [4,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 26
[8,3,3] => [3,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 40
[8,3,2,1] => [4,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 34
[8,3,1,1,1] => [5,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 21
[8,2,2,2] => [4,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 29
[8,2,2,1,1] => [5,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 22
[8,2,1,1,1,1] => [6,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 15
[8,1,1,1,1,1,1] => [7,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,7] => [2,2,2,2,2,2,2] => [2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 28
[7,6,1] => [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] => 27
[7,5,2] => [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] => 43
[7,5,1,1] => [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] => 25
[7,4,3] => [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] => 46
[7,4,2,1] => [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] => 37
[7,4,1,1,1] => [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] => 22
[7,3,3,1] => [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] => 34
[7,3,2,2] => [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] => 40
[7,3,2,1,1] => [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] => 29
[7,3,1,1,1,1] => [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] => 18
[7,2,2,2,1] => [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] => 25
[7,2,2,1,1,1] => [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] => 19
[7,2,1,1,1,1,1] => [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] => 13
[7,1,1,1,1,1,1,1] => [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] => 7
[6,6,2] => [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] => 36
[6,6,1,1] => [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] => 21
[6,5,3] => [3,3,3,2,2,1] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => 43
[6,5,2,1] => [4,3,2,2,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 34
[6,5,1,1,1] => [5,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 20
[6,4,4] => [3,3,3,3,1,1] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => 40
[6,4,3,1] => [4,3,3,2,1,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 37
[6,4,2,2] => [4,4,2,2,1,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 42
[6,4,2,1,1] => [5,3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 30
[6,4,1,1,1,1] => [6,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 18
[6,3,3,2] => [4,4,3,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 41
[6,3,3,1,1] => [5,3,3,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 28
[6,3,2,2,1] => [5,4,2,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 33
[6,3,2,1,1,1] => [6,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 24
[6,3,1,1,1,1,1] => [7,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 15
[6,2,2,2,2] => [5,5,1,1,1,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 26
[6,2,2,2,1,1] => [6,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 21
[6,2,2,1,1,1,1] => [7,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 16
[6,2,1,1,1,1,1,1] => [8,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 11
[6,1,1,1,1,1,1,1,1] => [9,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 6
[5,5,4] => [3,3,3,3,2] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 34
[5,5,3,1] => [4,3,3,2,2] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 31
[5,5,2,2] => [4,4,2,2,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 35
[5,5,2,1,1] => [5,3,2,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 25
[5,5,1,1,1,1] => [6,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 15
[5,4,4,1] => [4,3,3,3,1] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 30
[5,4,3,2] => [4,4,3,2,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 42
[5,4,3,1,1] => [5,3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 28
[5,4,2,2,1] => [5,4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 32
[5,4,2,1,1,1] => [6,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 23
[5,4,1,1,1,1,1] => [7,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 14
[5,3,3,3] => [4,4,4,1,1] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => 35
[5,3,3,2,1] => [5,4,3,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 32
[5,3,3,1,1,1] => [6,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 22
[5,3,2,2,2] => [5,5,2,1,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 33
[5,3,2,2,1,1] => [6,4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 26
[5,3,2,1,1,1,1] => [7,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 19
[5,3,1,1,1,1,1,1] => [8,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 12
[5,2,2,2,2,1] => [6,5,1,1,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 21
[5,2,2,2,1,1,1] => [7,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 17
[5,2,2,1,1,1,1,1] => [8,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 13
[5,2,1,1,1,1,1,1,1] => [9,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 9
[5,1,1,1,1,1,1,1,1,1] => [10,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 5
[4,4,4,2] => [4,4,3,3] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 30
[4,4,4,1,1] => [5,3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 20
[4,4,3,3] => [4,4,4,2] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 31
[4,4,3,2,1] => [5,4,3,2] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 28
[4,4,3,1,1,1] => [6,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 19
[4,4,2,2,2] => [5,5,2,2] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 28
[4,4,2,2,1,1] => [6,4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 22
[4,4,2,1,1,1,1] => [7,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 16
[4,4,1,1,1,1,1,1] => [8,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 10
[4,3,3,3,1] => [5,4,4,1] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 25
[4,3,3,2,2] => [5,5,3,1] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 30
[4,3,3,2,1,1] => [6,4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 23
[4,3,3,1,1,1,1] => [7,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 16
[4,3,2,2,2,1] => [6,5,2,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 24
[4,3,2,2,1,1,1] => [7,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 19
[4,3,2,1,1,1,1,1] => [8,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 14
[4,3,1,1,1,1,1,1,1] => [9,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => 9
[4,2,2,2,2,2] => [6,6,1,1] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 19
[4,2,2,2,2,1,1] => [7,5,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 16
[4,2,2,2,1,1,1,1] => [8,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 13
[4,2,2,1,1,1,1,1,1] => [9,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 10
[4,2,1,1,1,1,1,1,1,1] => [10,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 7
[4,1,1,1,1,1,1,1,1,1,1] => [11,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 4
[3,3,3,3,2] => [5,5,4] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 20
[3,3,3,3,1,1] => [6,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 15
[3,3,3,2,2,1] => [6,5,3] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 18
[3,3,3,2,1,1,1] => [7,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 14
[3,3,3,1,1,1,1,1] => [8,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 10
[3,3,2,2,2,2] => [6,6,2] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 18
[3,3,2,2,2,1,1] => [7,5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 15
[3,3,2,2,1,1,1,1] => [8,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 12
[3,3,2,1,1,1,1,1,1] => [9,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => 9
[3,3,1,1,1,1,1,1,1,1] => [10,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 6
[3,2,2,2,2,2,1] => [7,6,1] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 13
[3,2,2,2,2,1,1,1] => [8,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 11
[3,2,2,2,1,1,1,1,1] => [9,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 9
[3,2,2,1,1,1,1,1,1,1] => [10,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => 7
[3,2,1,1,1,1,1,1,1,1,1] => [11,2,1] => [2,1] => [1,0,1,0,1,0] => 5
[3,1,1,1,1,1,1,1,1,1,1,1] => [12,1,1] => [1,1] => [1,0,1,1,0,0] => 3
[2,2,2,2,2,2,1,1] => [8,6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[2,2,2,2,2,1,1,1,1] => [9,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[2,2,2,2,1,1,1,1,1,1] => [10,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => 5
[2,2,2,1,1,1,1,1,1,1,1] => [11,3] => [3] => [1,1,1,0,0,0,1,0] => 4
[2,2,1,1,1,1,1,1,1,1,1,1] => [12,2] => [2] => [1,1,0,0,1,0] => 3
[2,1,1,1,1,1,1,1,1,1,1,1,1] => [13,1] => [1] => [1,0,1,0] => 2
[8,7] => [2,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 35
[8,6,1] => [3,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 33
[8,5,2] => [3,3,2,2,2,1,1,1] => [3,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 52
[8,5,1,1] => [4,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 30
[8,4,3] => [3,3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 55
[8,4,2,1] => [4,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 44
[8,4,1,1,1] => [5,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 26
[8,3,3,1] => [4,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 40
[8,3,2,2] => [4,4,2,1,1,1,1,1] => [4,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 47
[8,3,2,1,1] => [5,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 34
[8,3,1,1,1,1] => [6,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 21
[8,2,2,2,1] => [5,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 29
[8,2,2,1,1,1] => [6,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 22
[8,2,1,1,1,1,1] => [7,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 15
[8,1,1,1,1,1,1,1] => [8,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,7,1] => [3,2,2,2,2,2,2] => [2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 28
[7,6,2] => [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] => 47
[7,6,1,1] => [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] => 27
[7,5,3] => [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] => 55
[7,5,2,1] => [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] => 43
[7,5,1,1,1] => [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] => 25
[7,4,4] => [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] => 50
[7,4,3,1] => [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] => 46
[7,4,2,2] => [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] => 52
[7,4,2,1,1] => [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] => 37
[7,4,1,1,1,1] => [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] => 22
[7,3,3,2] => [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] => 50
[7,3,3,1,1] => [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] => 34
[7,3,2,2,1] => [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] => 40
[7,3,2,1,1,1] => [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] => 29
[7,3,1,1,1,1,1] => [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] => 18
[7,2,2,2,2] => [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] => 31
[7,2,2,2,1,1] => [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] => 25
[7,2,2,1,1,1,1] => [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] => 19
[7,2,1,1,1,1,1,1] => [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] => 13
[7,1,1,1,1,1,1,1,1] => [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] => 7
[6,6,3] => [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] => 46
[6,6,2,1] => [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] => 36
[6,6,1,1,1] => [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] => 21
[6,5,4] => [3,3,3,3,2,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 48
[6,5,3,1] => [4,3,3,2,2,1] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => 43
[6,5,2,2] => [4,4,2,2,2,1] => [4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 48
[6,5,2,1,1] => [5,3,2,2,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 34
[6,5,1,1,1,1] => [6,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 20
[6,4,4,1] => [4,3,3,3,1,1] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => 40
[6,4,3,2] => [4,4,3,2,1,1] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 56
[6,4,3,1,1] => [5,3,3,2,1,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 37
[6,4,2,2,1] => [5,4,2,2,1,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 42
[6,4,2,1,1,1] => [6,3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 30
[6,4,1,1,1,1,1] => [7,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 18
[6,3,3,3] => [4,4,4,1,1,1] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => 45
[6,3,3,2,1] => [5,4,3,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 41
[6,3,3,1,1,1] => [6,3,3,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 28
[6,3,2,2,2] => [5,5,2,1,1,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 42
[6,3,2,2,1,1] => [6,4,2,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 33
[6,3,2,1,1,1,1] => [7,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 24
[6,3,1,1,1,1,1,1] => [8,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 15
[6,2,2,2,2,1] => [6,5,1,1,1,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 26
[6,2,2,2,1,1,1] => [7,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 21
[6,2,2,1,1,1,1,1] => [8,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 16
[6,2,1,1,1,1,1,1,1] => [9,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 11
[6,1,1,1,1,1,1,1,1,1] => [10,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 6
[5,5,5] => [3,3,3,3,3] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 35
[5,5,4,1] => [4,3,3,3,2] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 34
[5,5,3,2] => [4,4,3,2,2] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => 47
[5,5,3,1,1] => [5,3,3,2,2] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 31
[5,5,2,2,1] => [5,4,2,2,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 35
[5,5,2,1,1,1] => [6,3,2,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 25
[5,5,1,1,1,1,1] => [7,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 15
[5,4,4,2] => [4,4,3,3,1] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => 46
[5,4,4,1,1] => [5,3,3,3,1] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 30
[5,4,3,3] => [4,4,4,2,1] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => 47
[5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 42
[5,4,3,1,1,1] => [6,3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 28
[5,4,2,2,2] => [5,5,2,2,1] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => 41
[5,4,2,2,1,1] => [6,4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 32
[5,4,2,1,1,1,1] => [7,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 23
[5,4,1,1,1,1,1,1] => [8,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 14
[5,3,3,3,1] => [5,4,4,1,1] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => 35
[5,3,3,2,2] => [5,5,3,1,1] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 42
[5,3,3,2,1,1] => [6,4,3,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 32
[5,3,3,1,1,1,1] => [7,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 22
[5,3,2,2,2,1] => [6,5,2,1,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 33
[5,3,2,2,1,1,1] => [7,4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 26
[5,3,2,1,1,1,1,1] => [8,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 19
[5,3,1,1,1,1,1,1,1] => [9,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 12
[5,2,2,2,2,2] => [6,6,1,1,1] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 25
[5,2,2,2,2,1,1] => [7,5,1,1,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 21
[5,2,2,2,1,1,1,1] => [8,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 17
[5,2,2,1,1,1,1,1,1] => [9,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 13
[5,2,1,1,1,1,1,1,1,1] => [10,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 9
[5,1,1,1,1,1,1,1,1,1,1] => [11,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 5
[4,4,4,3] => [4,4,4,3] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 34
[4,4,4,2,1] => [5,4,3,3] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 30
[4,4,4,1,1,1] => [6,3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 20
[4,4,3,3,1] => [5,4,4,2] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 31
[4,4,3,2,2] => [5,5,3,2] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => 37
[4,4,3,2,1,1] => [6,4,3,2] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 28
[4,4,3,1,1,1,1] => [7,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 19
[4,4,2,2,2,1] => [6,5,2,2] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 28
[4,4,2,2,1,1,1] => [7,4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 22
[4,4,2,1,1,1,1,1] => [8,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 16
[4,4,1,1,1,1,1,1,1] => [9,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 10
[4,3,3,3,2] => [5,5,4,1] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 34
[4,3,3,3,1,1] => [6,4,4,1] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 25
[4,3,3,2,2,1] => [6,5,3,1] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 30
[4,3,3,2,1,1,1] => [7,4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 23
[4,3,3,1,1,1,1,1] => [8,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 16
[4,3,2,2,2,2] => [6,6,2,1] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 29
[4,3,2,2,2,1,1] => [7,5,2,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 24
[4,3,2,2,1,1,1,1] => [8,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 19
[4,3,2,1,1,1,1,1,1] => [9,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 14
[4,3,1,1,1,1,1,1,1,1] => [10,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => 9
[4,2,2,2,2,2,1] => [7,6,1,1] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 19
[4,2,2,2,2,1,1,1] => [8,5,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 16
[4,2,2,2,1,1,1,1,1] => [9,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 13
[4,2,2,1,1,1,1,1,1,1] => [10,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 10
[4,2,1,1,1,1,1,1,1,1,1] => [11,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 7
[4,1,1,1,1,1,1,1,1,1,1,1] => [12,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 4
[3,3,3,3,3] => [5,5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 21
[3,3,3,3,2,1] => [6,5,4] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 20
[3,3,3,3,1,1,1] => [7,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 15
[3,3,3,2,2,2] => [6,6,3] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 22
[3,3,3,2,2,1,1] => [7,5,3] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 18
[3,3,3,2,1,1,1,1] => [8,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 14
[3,3,3,1,1,1,1,1,1] => [9,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 10
[3,3,2,2,2,2,1] => [7,6,2] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 18
[3,3,2,2,2,1,1,1] => [8,5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 15
[3,3,2,2,1,1,1,1,1] => [9,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 12
[3,3,2,1,1,1,1,1,1,1] => [10,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => 9
[3,3,1,1,1,1,1,1,1,1,1] => [11,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 6
[3,2,2,2,2,2,1,1] => [8,6,1] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 13
[3,2,2,2,2,1,1,1,1] => [9,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 11
[3,2,2,2,1,1,1,1,1,1] => [10,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 9
[3,2,2,1,1,1,1,1,1,1,1] => [11,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => 7
[3,2,1,1,1,1,1,1,1,1,1,1] => [12,2,1] => [2,1] => [1,0,1,0,1,0] => 5
[3,1,1,1,1,1,1,1,1,1,1,1,1] => [13,1,1] => [1,1] => [1,0,1,1,0,0] => 3
[2,2,2,2,2,2,1,1,1] => [9,6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[2,2,2,2,2,1,1,1,1,1] => [10,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[2,2,2,2,1,1,1,1,1,1,1] => [11,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => 5
[2,2,2,1,1,1,1,1,1,1,1,1] => [12,3] => [3] => [1,1,1,0,0,0,1,0] => 4
[2,2,1,1,1,1,1,1,1,1,1,1,1] => [13,2] => [2] => [1,1,0,0,1,0] => 3
[2,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14,1] => [1] => [1,0,1,0] => 2
[8,7,1] => [3,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 35
[8,6,2] => [3,3,2,2,2,2,1,1] => [3,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 58
[8,6,1,1] => [4,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 33
[8,5,3] => [3,3,3,2,2,1,1,1] => [3,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 67
[8,5,2,1] => [4,3,2,2,2,1,1,1] => [3,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 52
[8,5,1,1,1] => [5,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 30
[8,4,4] => [3,3,3,3,1,1,1,1] => [3,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 60
[8,4,3,1] => [4,3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 55
[8,4,2,2] => [4,4,2,2,1,1,1,1] => [4,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 62
[8,4,2,1,1] => [5,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 44
[8,4,1,1,1,1] => [6,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 26
[8,3,3,2] => [4,4,3,1,1,1,1,1] => [4,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 59
[8,3,3,1,1] => [5,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 40
[8,3,2,2,1] => [5,4,2,1,1,1,1,1] => [4,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 47
[8,3,2,1,1,1] => [6,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 34
[8,3,1,1,1,1,1] => [7,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 21
[8,2,2,2,2] => [5,5,1,1,1,1,1,1] => [5,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 36
[8,2,2,2,1,1] => [6,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 29
[8,2,2,1,1,1,1] => [7,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 22
[8,2,1,1,1,1,1,1] => [8,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 15
[8,1,1,1,1,1,1,1,1] => [9,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,7,2] => [3,3,2,2,2,2,2] => [3,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 49
[7,7,1,1] => [4,2,2,2,2,2,2] => [2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 28
[7,6,3] => [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] => 61
[7,6,2,1] => [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] => 47
[7,6,1,1,1] => [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] => 27
[7,5,4] => [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] => 62
[7,5,3,1] => [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] => 55
[7,5,2,2] => [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] => 61
[7,5,2,1,1] => [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] => 43
[7,5,1,1,1,1] => [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] => 25
[7,4,4,1] => [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] => 50
[7,4,3,2] => [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] => 70
[7,4,3,1,1] => [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] => 46
[7,4,2,2,1] => [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] => 52
[7,4,2,1,1,1] => [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] => 37
[7,4,1,1,1,1,1] => [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] => 22
[7,3,3,3] => [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] => 55
[7,3,3,2,1] => [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] => 50
[7,3,3,1,1,1] => [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] => 34
[7,3,2,2,2] => [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] => 51
[7,3,2,2,1,1] => [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] => 40
[7,3,2,1,1,1,1] => [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] => 29
[7,3,1,1,1,1,1,1] => [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] => 18
[7,2,2,2,2,1] => [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] => 31
[7,2,2,2,1,1,1] => [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] => 25
[7,2,2,1,1,1,1,1] => [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] => 19
[7,2,1,1,1,1,1,1,1] => [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] => 13
[7,1,1,1,1,1,1,1,1,1] => [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] => 7
[6,6,4] => [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] => 52
[6,6,3,1] => [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] => 46
[6,6,2,2] => [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] => 51
[6,6,2,1,1] => [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] => 36
[6,6,1,1,1,1] => [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] => 21
[6,5,5] => [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] => 50
[6,5,4,1] => [4,3,3,3,2,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 48
[6,5,3,2] => [4,4,3,2,2,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 66
[6,5,3,1,1] => [5,3,3,2,2,1] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => 43
[6,5,2,2,1] => [5,4,2,2,2,1] => [4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 48
[6,5,2,1,1,1] => [6,3,2,2,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 34
[6,5,1,1,1,1,1] => [7,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 20
[6,4,4,2] => [4,4,3,3,1,1] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => 62
[6,4,4,1,1] => [5,3,3,3,1,1] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => 40
[6,4,3,3] => [4,4,4,2,1,1] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => 63
[6,4,3,2,1] => [5,4,3,2,1,1] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 56
[6,4,3,1,1,1] => [6,3,3,2,1,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 37
[6,4,2,2,2] => [5,5,2,2,1,1] => [5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => 54
[6,4,2,2,1,1] => [6,4,2,2,1,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 42
[6,4,2,1,1,1,1] => [7,3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 30
[6,4,1,1,1,1,1,1] => [8,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 18
[6,3,3,3,1] => [5,4,4,1,1,1] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => 45
[6,3,3,2,2] => [5,5,3,1,1,1] => [5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => 54
[6,3,3,2,1,1] => [6,4,3,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 41
[6,3,3,1,1,1,1] => [7,3,3,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 28
[6,3,2,2,2,1] => [6,5,2,1,1,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 42
[6,3,2,2,1,1,1] => [7,4,2,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 33
[6,3,2,1,1,1,1,1] => [8,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 24
[6,3,1,1,1,1,1,1,1] => [9,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 15
[6,2,2,2,2,2] => [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] => 31
[6,2,2,2,2,1,1] => [7,5,1,1,1,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 26
[6,2,2,2,1,1,1,1] => [8,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 21
[6,2,2,1,1,1,1,1,1] => [9,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 16
[6,2,1,1,1,1,1,1,1,1] => [10,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 11
[6,1,1,1,1,1,1,1,1,1,1] => [11,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 6
[5,5,5,1] => [4,3,3,3,3] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 35
[5,5,4,2] => [4,4,3,3,2] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => 53
[5,5,4,1,1] => [5,3,3,3,2] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 34
[5,5,3,3] => [4,4,4,2,2] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 53
[5,5,3,2,1] => [5,4,3,2,2] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => 47
[5,5,3,1,1,1] => [6,3,3,2,2] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 31
[5,5,2,2,2] => [5,5,2,2,2] => [5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => 45
[5,5,2,2,1,1] => [6,4,2,2,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 35
[5,5,2,1,1,1,1] => [7,3,2,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 25
[5,5,1,1,1,1,1,1] => [8,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 15
[5,4,4,3] => [4,4,4,3,1] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => 53
[5,4,4,2,1] => [5,4,3,3,1] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => 46
[5,4,4,1,1,1] => [6,3,3,3,1] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 30
[5,4,3,3,1] => [5,4,4,2,1] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => 47
[5,4,3,2,2] => [5,5,3,2,1] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => 56
[5,4,3,2,1,1] => [6,4,3,2,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 42
[5,4,3,1,1,1,1] => [7,3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 28
[5,4,2,2,2,1] => [6,5,2,2,1] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => 41
[5,4,2,2,1,1,1] => [7,4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 32
[5,4,2,1,1,1,1,1] => [8,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 23
[5,4,1,1,1,1,1,1,1] => [9,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 14
[5,3,3,3,2] => [5,5,4,1,1] => [5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => 48
[5,3,3,3,1,1] => [6,4,4,1,1] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => 35
[5,3,3,2,2,1] => [6,5,3,1,1] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 42
[5,3,3,2,1,1,1] => [7,4,3,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 32
[5,3,3,1,1,1,1,1] => [8,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 22
[5,3,2,2,2,2] => [6,6,2,1,1] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 40
[5,3,2,2,2,1,1] => [7,5,2,1,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 33
[5,3,2,2,1,1,1,1] => [8,4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 26
[5,3,2,1,1,1,1,1,1] => [9,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 19
[5,3,1,1,1,1,1,1,1,1] => [10,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 12
[5,2,2,2,2,2,1] => [7,6,1,1,1] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 25
[5,2,2,2,2,1,1,1] => [8,5,1,1,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 21
[5,2,2,2,1,1,1,1,1] => [9,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 17
[5,2,2,1,1,1,1,1,1,1] => [10,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 13
[5,2,1,1,1,1,1,1,1,1,1] => [11,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 9
[5,1,1,1,1,1,1,1,1,1,1,1] => [12,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 5
[4,4,4,4] => [4,4,4,4] => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 35
[4,4,4,3,1] => [5,4,4,3] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 34
[4,4,4,2,2] => [5,5,3,3] => [5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => 40
[4,4,4,2,1,1] => [6,4,3,3] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 30
[4,4,4,1,1,1,1] => [7,3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 20
[4,4,3,3,2] => [5,5,4,2] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => 43
[4,4,3,3,1,1] => [6,4,4,2] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 31
[4,4,3,2,2,1] => [6,5,3,2] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => 37
[4,4,3,2,1,1,1] => [7,4,3,2] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 28
[4,4,3,1,1,1,1,1] => [8,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 19
[4,4,2,2,2,2] => [6,6,2,2] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 34
[4,4,2,2,2,1,1] => [7,5,2,2] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 28
[4,4,2,2,1,1,1,1] => [8,4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 22
[4,4,2,1,1,1,1,1,1] => [9,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 16
[4,4,1,1,1,1,1,1,1,1] => [10,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 10
[4,3,3,3,3] => [5,5,5,1] => [5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 36
[4,3,3,3,2,1] => [6,5,4,1] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 34
[4,3,3,3,1,1,1] => [7,4,4,1] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 25
[4,3,3,2,2,2] => [6,6,3,1] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 37
[4,3,3,2,2,1,1] => [7,5,3,1] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 30
[4,3,3,2,1,1,1,1] => [8,4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 23
[4,3,3,1,1,1,1,1,1] => [9,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 16
[4,3,2,2,2,2,1] => [7,6,2,1] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 29
[4,3,2,2,2,1,1,1] => [8,5,2,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 24
[4,3,2,2,1,1,1,1,1] => [9,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 19
[4,3,2,1,1,1,1,1,1,1] => [10,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 14
[4,3,1,1,1,1,1,1,1,1,1] => [11,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => 9
[4,2,2,2,2,2,1,1] => [8,6,1,1] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 19
[4,2,2,2,2,1,1,1,1] => [9,5,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 16
[4,2,2,2,1,1,1,1,1,1] => [10,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 13
[4,2,2,1,1,1,1,1,1,1,1] => [11,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 10
[4,2,1,1,1,1,1,1,1,1,1,1] => [12,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 7
[4,1,1,1,1,1,1,1,1,1,1,1,1] => [13,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 4
[3,3,3,3,3,1] => [6,5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 21
[3,3,3,3,2,2] => [6,6,4] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 25
[3,3,3,3,2,1,1] => [7,5,4] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 20
[3,3,3,3,1,1,1,1] => [8,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 15
[3,3,3,2,2,2,1] => [7,6,3] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 22
[3,3,3,2,2,1,1,1] => [8,5,3] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 18
[3,3,3,2,1,1,1,1,1] => [9,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 14
[3,3,3,1,1,1,1,1,1,1] => [10,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 10
[3,3,2,2,2,2,1,1] => [8,6,2] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 18
[3,3,2,2,2,1,1,1,1] => [9,5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 15
[3,3,2,2,1,1,1,1,1,1] => [10,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 12
[3,3,2,1,1,1,1,1,1,1,1] => [11,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => 9
[3,3,1,1,1,1,1,1,1,1,1,1] => [12,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 6
[3,2,2,2,2,2,1,1,1] => [9,6,1] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 13
[3,2,2,2,2,1,1,1,1,1] => [10,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 11
[3,2,2,2,1,1,1,1,1,1,1] => [11,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 9
[3,2,2,1,1,1,1,1,1,1,1,1] => [12,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => 7
[3,2,1,1,1,1,1,1,1,1,1,1,1] => [13,2,1] => [2,1] => [1,0,1,0,1,0] => 5
[3,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14,1,1] => [1,1] => [1,0,1,1,0,0] => 3
[2,2,2,2,2,2,1,1,1,1] => [10,6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[2,2,2,2,2,1,1,1,1,1,1] => [11,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[2,2,2,2,1,1,1,1,1,1,1,1] => [12,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => 5
[2,2,2,1,1,1,1,1,1,1,1,1,1] => [13,3] => [3] => [1,1,1,0,0,0,1,0] => 4
[2,2,1,1,1,1,1,1,1,1,1,1,1,1] => [14,2] => [2] => [1,1,0,0,1,0] => 3
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [15,1] => [1] => [1,0,1,0] => 2
[8,7,2] => [3,3,2,2,2,2,2,1] => [3,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 62
[8,7,1,1] => [4,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 35
[8,6,3] => [3,3,3,2,2,2,1,1] => [3,3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 76
[8,6,2,1] => [4,3,2,2,2,2,1,1] => [3,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 58
[8,6,1,1,1] => [5,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 33
[8,5,4] => [3,3,3,3,2,1,1,1] => [3,3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 76
[8,5,3,1] => [4,3,3,2,2,1,1,1] => [3,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 67
[8,5,2,2] => [4,4,2,2,2,1,1,1] => [4,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 74
[8,5,2,1,1] => [5,3,2,2,2,1,1,1] => [3,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 52
[8,5,1,1,1,1] => [6,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 30
[8,4,4,1] => [4,3,3,3,1,1,1,1] => [3,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 60
[8,4,3,2] => [4,4,3,2,1,1,1,1] => [4,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 84
[8,4,3,1,1] => [5,3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 55
[8,4,2,2,1] => [5,4,2,2,1,1,1,1] => [4,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 62
[8,4,2,1,1,1] => [6,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 44
[8,4,1,1,1,1,1] => [7,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 26
[8,3,3,3] => [4,4,4,1,1,1,1,1] => [4,4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 65
[8,3,3,2,1] => [5,4,3,1,1,1,1,1] => [4,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 59
[8,3,3,1,1,1] => [6,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 40
[8,3,2,2,2] => [5,5,2,1,1,1,1,1] => [5,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 60
[8,3,2,2,1,1] => [6,4,2,1,1,1,1,1] => [4,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 47
[8,3,2,1,1,1,1] => [7,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 34
[8,3,1,1,1,1,1,1] => [8,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 21
[8,2,2,2,2,1] => [6,5,1,1,1,1,1,1] => [5,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 36
[8,2,2,2,1,1,1] => [7,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 29
[8,2,2,1,1,1,1,1] => [8,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 22
[8,2,1,1,1,1,1,1,1] => [9,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 15
[8,1,1,1,1,1,1,1,1,1] => [10,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[7,7,3] => [3,3,3,2,2,2,2] => [3,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 64
[7,7,2,1] => [4,3,2,2,2,2,2] => [3,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 49
[7,7,1,1,1] => [5,2,2,2,2,2,2] => [2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 28
[7,6,4] => [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] => 70
[7,6,3,1] => [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] => 61
[7,6,2,2] => [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] => 67
[7,6,2,1,1] => [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] => 47
[7,6,1,1,1,1] => [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] => 27
[7,5,5] => [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] => 65
[7,5,4,1] => [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] => 62
[7,5,3,2] => [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] => 85
[7,5,3,1,1] => [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] => 55
[7,5,2,2,1] => [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] => 61
[7,5,2,1,1,1] => [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] => 43
[7,5,1,1,1,1,1] => [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] => 25
[7,4,4,2] => [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] => 78
[7,4,4,1,1] => [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] => 50
[7,4,3,3] => [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] => 79
[7,4,3,2,1] => [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] => 70
[7,4,3,1,1,1] => [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] => 46
[7,4,2,2,2] => [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] => 67
[7,4,2,2,1,1] => [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] => 52
[7,4,2,1,1,1,1] => [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] => 37
[7,4,1,1,1,1,1,1] => [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] => 22
[7,3,3,3,1] => [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] => 55
[7,3,3,2,2] => [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] => 66
[7,3,3,2,1,1] => [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] => 50
[7,3,3,1,1,1,1] => [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] => 34
[7,3,2,2,2,1] => [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] => 51
[7,3,2,2,1,1,1] => [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] => 40
[7,3,2,1,1,1,1,1] => [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] => 29
[7,3,1,1,1,1,1,1,1] => [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] => 18
[7,2,2,2,2,2] => [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] => 37
[7,2,2,2,2,1,1] => [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] => 31
[7,2,2,2,1,1,1,1] => [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] => 25
[7,2,2,1,1,1,1,1,1] => [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] => 19
[7,2,1,1,1,1,1,1,1,1] => [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] => 13
[7,1,1,1,1,1,1,1,1,1,1] => [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] => 7
[6,6,5] => [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] => 55
[6,6,4,1] => [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] => 52
[6,6,3,2] => [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] => 71
[6,6,3,1,1] => [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] => 46
[6,6,2,2,1] => [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] => 51
[6,6,2,1,1,1] => [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] => 36
[6,6,1,1,1,1,1] => [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] => 21
[6,5,5,1] => [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] => 50
[6,5,4,2] => [4,4,3,3,2,1] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 76
[6,5,4,1,1] => [5,3,3,3,2,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 48
[6,5,3,3] => [4,4,4,2,2,1] => [4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => 75
[6,5,3,2,1] => [5,4,3,2,2,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 66
[6,5,3,1,1,1] => [6,3,3,2,2,1] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => 43
[6,5,2,2,2] => [5,5,2,2,2,1] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 62
[6,5,2,2,1,1] => [6,4,2,2,2,1] => [4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 48
[6,5,2,1,1,1,1] => [7,3,2,2,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 34
[6,5,1,1,1,1,1,1] => [8,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 20
[6,4,4,3] => [4,4,4,3,1,1] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => 72
[6,4,4,2,1] => [5,4,3,3,1,1] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => 62
[6,4,4,1,1,1] => [6,3,3,3,1,1] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => 40
[6,4,3,3,1] => [5,4,4,2,1,1] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => 63
[6,4,3,2,2] => [5,5,3,2,1,1] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => 75
[6,4,3,2,1,1] => [6,4,3,2,1,1] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 56
[6,4,3,1,1,1,1] => [7,3,3,2,1,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 37
[6,4,2,2,2,1] => [6,5,2,2,1,1] => [5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => 54
[6,4,2,2,1,1,1] => [7,4,2,2,1,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 42
[6,4,2,1,1,1,1,1] => [8,3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 30
[6,4,1,1,1,1,1,1,1] => [9,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 18
[6,3,3,3,2] => [5,5,4,1,1,1] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 62
[6,3,3,3,1,1] => [6,4,4,1,1,1] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => 45
[6,3,3,2,2,1] => [6,5,3,1,1,1] => [5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => 54
[6,3,3,2,1,1,1] => [7,4,3,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 41
[6,3,3,1,1,1,1,1] => [8,3,3,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 28
[6,3,2,2,2,2] => [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] => 51
[6,3,2,2,2,1,1] => [7,5,2,1,1,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 42
[6,3,2,2,1,1,1,1] => [8,4,2,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 33
[6,3,2,1,1,1,1,1,1] => [9,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 24
[6,3,1,1,1,1,1,1,1,1] => [10,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 15
[6,2,2,2,2,2,1] => [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] => 31
[6,2,2,2,2,1,1,1] => [8,5,1,1,1,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 26
[6,2,2,2,1,1,1,1,1] => [9,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 21
[6,2,2,1,1,1,1,1,1,1] => [10,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 16
[6,2,1,1,1,1,1,1,1,1,1] => [11,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 11
[6,1,1,1,1,1,1,1,1,1,1,1] => [12,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 6
[5,5,5,2] => [4,4,3,3,3] => [4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 55
[5,5,5,1,1] => [5,3,3,3,3] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 35
[5,5,4,3] => [4,4,4,3,2] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 62
[5,5,4,2,1] => [5,4,3,3,2] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => 53
[5,5,4,1,1,1] => [6,3,3,3,2] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 34
[5,5,3,3,1] => [5,4,4,2,2] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 53
[5,5,3,2,2] => [5,5,3,2,2] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => 63
[5,5,3,2,1,1] => [6,4,3,2,2] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => 47
[5,5,3,1,1,1,1] => [7,3,3,2,2] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 31
[5,5,2,2,2,1] => [6,5,2,2,2] => [5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => 45
[5,5,2,2,1,1,1] => [7,4,2,2,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 35
[5,5,2,1,1,1,1,1] => [8,3,2,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 25
[5,5,1,1,1,1,1,1,1] => [9,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 15
[5,4,4,4] => [4,4,4,4,1] => [4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 55
[5,4,4,3,1] => [5,4,4,3,1] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => 53
[5,4,4,2,2] => [5,5,3,3,1] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => 62
[5,4,4,2,1,1] => [6,4,3,3,1] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => 46
[5,4,4,1,1,1,1] => [7,3,3,3,1] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 30
[5,4,3,3,2] => [5,5,4,2,1] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 66
[5,4,3,3,1,1] => [6,4,4,2,1] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => 47
[5,4,3,2,2,1] => [6,5,3,2,1] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => 56
[5,4,3,2,1,1,1] => [7,4,3,2,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 42
[5,4,3,1,1,1,1,1] => [8,3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 28
[5,4,2,2,2,2] => [6,6,2,2,1] => [6,2,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 50
[5,4,2,2,2,1,1] => [7,5,2,2,1] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => 41
[5,4,2,2,1,1,1,1] => [8,4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 32
[5,4,2,1,1,1,1,1,1] => [9,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 23
[5,4,1,1,1,1,1,1,1,1] => [10,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 14
[5,3,3,3,3] => [5,5,5,1,1] => [5,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 51
[5,3,3,3,2,1] => [6,5,4,1,1] => [5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => 48
[5,3,3,3,1,1,1] => [7,4,4,1,1] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => 35
[5,3,3,2,2,2] => [6,6,3,1,1] => [6,3,1,1] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 52
[5,3,3,2,2,1,1] => [7,5,3,1,1] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 42
[5,3,3,2,1,1,1,1] => [8,4,3,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 32
[5,3,3,1,1,1,1,1,1] => [9,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 22
[5,3,2,2,2,2,1] => [7,6,2,1,1] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 40
[5,3,2,2,2,1,1,1] => [8,5,2,1,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 33
[5,3,2,2,1,1,1,1,1] => [9,4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 26
[5,3,2,1,1,1,1,1,1,1] => [10,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 19
[5,3,1,1,1,1,1,1,1,1,1] => [11,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 12
[5,2,2,2,2,2,1,1] => [8,6,1,1,1] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 25
[5,2,2,2,2,1,1,1,1] => [9,5,1,1,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 21
[5,2,2,2,1,1,1,1,1,1] => [10,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 17
[5,2,2,1,1,1,1,1,1,1,1] => [11,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 13
[5,2,1,1,1,1,1,1,1,1,1,1] => [12,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 9
[5,1,1,1,1,1,1,1,1,1,1,1,1] => [13,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 5
[4,4,4,4,1] => [5,4,4,4] => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 35
[4,4,4,3,2] => [5,5,4,3] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => 48
[4,4,4,3,1,1] => [6,4,4,3] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 34
[4,4,4,2,2,1] => [6,5,3,3] => [5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => 40
[4,4,4,2,1,1,1] => [7,4,3,3] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 30
[4,4,4,1,1,1,1,1] => [8,3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 20
[4,4,3,3,3] => [5,5,5,2] => [5,5,2] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 46
[4,4,3,3,2,1] => [6,5,4,2] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => 43
[4,4,3,3,1,1,1] => [7,4,4,2] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 31
[4,4,3,2,2,2] => [6,6,3,2] => [6,3,2] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 46
[4,4,3,2,2,1,1] => [7,5,3,2] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => 37
[4,4,3,2,1,1,1,1] => [8,4,3,2] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 28
[4,4,3,1,1,1,1,1,1] => [9,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 19
[4,4,2,2,2,2,1] => [7,6,2,2] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 34
[4,4,2,2,2,1,1,1] => [8,5,2,2] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 28
[4,4,2,2,1,1,1,1,1] => [9,4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 22
[4,4,2,1,1,1,1,1,1,1] => [10,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 16
[4,4,1,1,1,1,1,1,1,1,1] => [11,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 10
[4,3,3,3,3,1] => [6,5,5,1] => [5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 36
[4,3,3,3,2,2] => [6,6,4,1] => [6,4,1] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 43
[4,3,3,3,2,1,1] => [7,5,4,1] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 34
[4,3,3,3,1,1,1,1] => [8,4,4,1] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 25
[4,3,3,2,2,2,1] => [7,6,3,1] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 37
[4,3,3,2,2,1,1,1] => [8,5,3,1] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 30
[4,3,3,2,1,1,1,1,1] => [9,4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 23
[4,3,3,1,1,1,1,1,1,1] => [10,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 16
[4,3,2,2,2,2,1,1] => [8,6,2,1] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 29
[4,3,2,2,2,1,1,1,1] => [9,5,2,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 24
[4,3,2,2,1,1,1,1,1,1] => [10,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 19
[4,3,2,1,1,1,1,1,1,1,1] => [11,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 14
[4,3,1,1,1,1,1,1,1,1,1,1] => [12,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => 9
[4,2,2,2,2,2,1,1,1] => [9,6,1,1] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 19
[4,2,2,2,2,1,1,1,1,1] => [10,5,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 16
[4,2,2,2,1,1,1,1,1,1,1] => [11,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 13
[4,2,2,1,1,1,1,1,1,1,1,1] => [12,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 10
[4,2,1,1,1,1,1,1,1,1,1,1,1] => [13,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 7
[4,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 4
[3,3,3,3,3,2] => [6,6,5] => [6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 27
[3,3,3,3,3,1,1] => [7,5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 21
[3,3,3,3,2,2,1] => [7,6,4] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 25
[3,3,3,3,2,1,1,1] => [8,5,4] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 20
[3,3,3,3,1,1,1,1,1] => [9,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 15
[3,3,3,2,2,2,1,1] => [8,6,3] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 22
[3,3,3,2,2,1,1,1,1] => [9,5,3] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 18
[3,3,3,2,1,1,1,1,1,1] => [10,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 14
[3,3,3,1,1,1,1,1,1,1,1] => [11,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 10
[3,3,2,2,2,2,1,1,1] => [9,6,2] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 18
[3,3,2,2,2,1,1,1,1,1] => [10,5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 15
[3,3,2,2,1,1,1,1,1,1,1] => [11,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 12
[3,3,2,1,1,1,1,1,1,1,1,1] => [12,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => 9
[3,3,1,1,1,1,1,1,1,1,1,1,1] => [13,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 6
[3,2,2,2,2,2,1,1,1,1] => [10,6,1] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 13
[3,2,2,2,2,1,1,1,1,1,1] => [11,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 11
[3,2,2,2,1,1,1,1,1,1,1,1] => [12,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 9
[3,2,2,1,1,1,1,1,1,1,1,1,1] => [13,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => 7
[3,2,1,1,1,1,1,1,1,1,1,1,1,1] => [14,2,1] => [2,1] => [1,0,1,0,1,0] => 5
[3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [15,1,1] => [1,1] => [1,0,1,1,0,0] => 3
[2,2,2,2,2,2,1,1,1,1,1] => [11,6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[2,2,2,2,2,1,1,1,1,1,1,1] => [12,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[2,2,2,2,1,1,1,1,1,1,1,1,1] => [13,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => 5
[2,2,2,1,1,1,1,1,1,1,1,1,1,1] => [14,3] => [3] => [1,1,1,0,0,0,1,0] => 4
[2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] => [15,2] => [2] => [1,1,0,0,1,0] => 3
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [16,1] => [1] => [1,0,1,0] => 2
[6,5,4,3,2,1] => [6,5,4,3,2,1] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 132
[5,5,4,3,2,1] => [6,5,4,3,2] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => 90
[6,4,4,3,2,1] => [6,5,4,3,1,1] => [5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 104
[5,4,4,3,2,1] => [6,5,4,3,1] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => 76
[4,4,4,3,2,1] => [6,5,4,3] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => 48
[6,5,3,3,2,1] => [6,5,4,2,2,1] => [5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 107
[5,5,3,3,2,1] => [6,5,4,2,2] => [5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => 75
[6,4,3,3,2,1] => [6,5,4,2,1,1] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => 89
[5,4,3,3,2,1] => [6,5,4,2,1] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 66
[6,3,3,3,2,1] => [6,5,4,1,1,1] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 62
[6,5,4,2,2,1] => [6,5,3,3,2,1] => [5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 104
[5,5,4,2,2,1] => [6,5,3,3,2] => [5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => 72
[6,4,4,2,2,1] => [6,5,3,3,1,1] => [5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 84
[5,4,4,2,2,1] => [6,5,3,3,1] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => 62
[6,5,3,2,2,1] => [6,5,3,2,2,1] => [5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => 89
[5,5,3,2,2,1] => [6,5,3,2,2] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => 63
[6,4,3,2,2,1] => [6,5,3,2,1,1] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => 75
[6,5,2,2,2,1] => [6,5,2,2,2,1] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 62
[6,5,4,3,1,1] => [6,4,4,3,2,1] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 90
[5,5,4,3,1,1] => [6,4,4,3,2] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 62
[6,4,4,3,1,1] => [6,4,4,3,1,1] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => 72
[5,4,4,3,1,1] => [6,4,4,3,1] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => 53
[6,5,3,3,1,1] => [6,4,4,2,2,1] => [4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => 75
[5,5,3,3,1,1] => [6,4,4,2,2] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 53
[6,4,3,3,1,1] => [6,4,4,2,1,1] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => 63
[6,5,4,2,1,1] => [6,4,3,3,2,1] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 76
[5,5,4,2,1,1] => [6,4,3,3,2] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => 53
[6,4,4,2,1,1] => [6,4,3,3,1,1] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => 62
[6,5,3,2,1,1] => [6,4,3,2,2,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 66
[6,5,4,1,1,1] => [6,3,3,3,2,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 48
[6,5,4,3,2] => [5,5,4,3,2,1] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 132
[5,5,4,3,2] => [5,5,4,3,2] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => 90
[6,4,4,3,2] => [5,5,4,3,1,1] => [5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 104
[5,4,4,3,2] => [5,5,4,3,1] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => 76
[6,5,3,3,2] => [5,5,4,2,2,1] => [5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 107
[5,5,3,3,2] => [5,5,4,2,2] => [5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => 75
[6,4,3,3,2] => [5,5,4,2,1,1] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => 89
[6,5,4,2,2] => [5,5,3,3,2,1] => [5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 104
[5,5,4,2,2] => [5,5,3,3,2] => [5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => 72
[6,4,4,2,2] => [5,5,3,3,1,1] => [5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 84
[6,5,3,2,2] => [5,5,3,2,2,1] => [5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => 89
[6,5,4,3,1] => [5,4,4,3,2,1] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 90
[5,5,4,3,1] => [5,4,4,3,2] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 62
[6,4,4,3,1] => [5,4,4,3,1,1] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => 72
[6,5,3,3,1] => [5,4,4,2,2,1] => [4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => 75
[6,5,4,2,1] => [5,4,3,3,2,1] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 76
[6,5,4,3] => [4,4,4,3,2,1] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 90
[7,6,5,4,3,2,1] => [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] => 429
[6,6,5,4,3,2,1] => [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] => 297
[7,5,5,4,3,2,1] => [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] => 345
[6,5,5,4,3,2,1] => [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] => 255
[5,5,5,4,3,2,1] => [7,6,5,4,3] => [6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 165
[6,5,4,4,3,2,1] => [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] => 227
[5,5,4,4,3,2,1] => [7,6,5,4,2] => [6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 151
[7,4,4,4,3,2,1] => [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] => 219
[6,4,4,4,3,2,1] => [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] => 171
[5,4,4,4,3,2,1] => [7,6,5,4,1] => [6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 123
[4,4,4,4,3,2,1] => [7,6,5,4] => [6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 75
[6,5,4,3,3,2,1] => [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] => 202
[7,6,3,3,3,2,1] => [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] => 233
[6,6,3,3,3,2,1] => [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] => 171
[6,5,3,3,3,2,1] => [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] => 157
[6,4,3,3,3,2,1] => [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] => 129
[6,3,3,3,3,2,1] => [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] => 87
[3,3,3,3,3,2,1] => [7,6,5] => [6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 27
[7,6,5,4,2,2,1] => [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] => 345
[6,6,5,4,2,2,1] => [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] => 241
[6,5,4,3,2,2,1] => [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] => 174
[6,5,4,2,2,2,1] => [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] => 132
[6,5,3,2,2,2,1] => [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] => 112
[6,4,3,2,2,2,1] => [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] => 94
[6,5,2,2,2,2,1] => [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] => 76
[7,2,2,2,2,2,1] => [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] => 37
[7,6,5,4,3,1,1] => [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] => 297
[6,6,5,4,3,1,1] => [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] => 207
[6,5,4,3,2,1,1] => [7,5,4,3,2,1] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 132
[5,5,4,3,2,1,1] => [7,5,4,3,2] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => 90
[7,6,5,4,1,1,1] => [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] => 165
[6,5,4,3,1,1,1] => [7,4,4,3,2,1] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 90
[6,5,4,2,1,1,1] => [7,4,3,3,2,1] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 76
[7,4,3,2,1,1,1] => [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] => 70
[6,4,3,2,1,1,1] => [7,4,3,2,1,1] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 56
[5,5,5,1,1,1,1] => [7,3,3,3,3] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 35
[6,5,4,1,1,1,1] => [7,3,3,3,2,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 48
[7,6,1,1,1,1,1] => [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] => 27
[7,6,5,4,3,2] => [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] => 429
[6,6,5,4,3,2] => [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] => 297
[7,5,5,4,3,2] => [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] => 345
[6,5,5,4,3,2] => [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] => 255
[5,5,5,4,3,2] => [6,6,5,4,3] => [6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 165
[7,6,4,4,3,2] => [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] => 359
[7,6,5,4,2,2] => [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] => 345
[6,6,2,2,2,2] => [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] => 81
[7,6,5,4,3,1] => [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] => 297
[6,6,5,4,3,1] => [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] => 207
[6,5,5,4,3,1] => [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] => 179
[4,4,4,4,3,1] => [6,5,5,4] => [5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 55
[7,6,5,4,2,1] => [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] => 255
[7,6,5,3,2,1] => [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] => 227
[7,6,4,3,2,1] => [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] => 202
[6,6,4,3,2,1] => [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] => 146
[7,5,4,3,2,1] => [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] => 174
[7,4,4,3,2,1] => [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] => 132
[7,6,3,3,2,1] => [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] => 157
[7,3,3,3,2,1] => [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] => 76
[7,6,5,2,2,1] => [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] => 171
[7,6,2,2,2,1] => [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] => 87
[7,6,5,4,1,1] => [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] => 165
[7,6,5,1,1,1] => [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] => 75
[7,6,5,4,3] => [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] => 297
[6,6,5,4,3] => [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] => 207
[7,5,4,3,2] => [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] => 174
[7,6,5,4,1] => [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] => 165
[7,5,4,3,1] => [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] => 118
[7,6,5,2,1] => [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] => 123
[7,6,3,2,1] => [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] => 95
[6,6,3,2,1] => [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] => 71
[7,6,5,4] => [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] => 165
[6,5,4,4] => [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] => 95
[5,5,4,4] => [4,4,4,4,2] => [4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 65
[7,6,5] => [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] => 75
[8,2,2,2,2,2,2] => [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] => 50
[8,7,6,5,4,3,2,1] => [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] => 1430
[7,7,6,5,4,3,2,1] => [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] => 1001
[7,6,6,5,4,3,2,1] => [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] => 869
[7,6,5,4,3,2,1,1] => [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] => 429
[7,6,5,4,3,1,1,1] => [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] => 297
[8,7,6,5,4,3,2,1,1] => [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] => 1430
[8,7,6,5,4,3,2] => [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] => 1430
[8,7,6,5,4,3,1] => [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] => 1001
[8,7,6,5,4,2,1] => [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] => 869
[8,7,6,5,3,2,1] => [7,6,5,4,4,3,2,1] => [6,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 785
[8,7,6,4,3,2,1] => [7,6,5,4,3,3,2,1] => [6,5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 715
[8,7,5,4,3,2,1] => [7,6,5,4,3,2,2,1] => [6,5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 645
[8,6,5,4,3,2,1] => [7,6,5,4,3,2,1,1] => [6,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 561
[8,7,6,5,4,3] => [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] => 1001
[8,7,6,5,4,1,1] => [7,5,5,5,4,3,2,1] => [5,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 572
[8,7,6,5,2,2,1] => [7,6,4,4,4,3,2,1] => [6,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 605
[8,7,6,3,3,2,1] => [7,6,5,3,3,3,2,1] => [6,5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 575
[8,7,4,4,3,2,1] => [7,6,5,4,2,2,2,1] => [6,5,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 519
[8,5,5,4,3,2,1] => [7,6,5,4,3,1,1,1] => [6,5,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 435
[7,7,1,1,1,1] => [6,2,2,2,2,2,2] => [2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 28
[8,5,4,3,2,1] => [6,5,4,3,2,1,1,1] => [5,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 216
[8,7,4,3,2,1] => [6,5,4,3,2,2,2,1] => [5,4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 286
[6,5,4,3,2,1,1,1] => [8,5,4,3,2,1] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 132
[8,6,5,4,3,2] => [6,6,5,4,3,2,1,1] => [6,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 561
[7,5,4,3,2,1,1,1] => [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] => 174
[7,7,6,5,4,3,2] => [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] => 1001
[8,7,6,3,2,1] => [6,5,4,3,3,3,2,1] => [5,4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 356
[8,7,6,5,2,1] => [6,5,4,4,4,3,2,1] => [5,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 440
[8,7,6,5,4,1] => [6,5,5,5,4,3,2,1] => [5,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 572
[7,6,6,5,4,3,2] => [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] => 869
[7,6,6,5,4,3,1] => [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] => 614
[7,7,6,5,4,3,1] => [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] => 704
[7,7,6,5,4,3,1,1] => [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] => 704
[8,6,6,5,4,3,2] => [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] => 1166
[8,7,6,5,4,2,2] => [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] => 1166
[3,3,3,3,2,2,1,1,1,1] => [10,6,4] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 25
[4,4,3,3,2,2,1,1] => [8,6,4,2] => [6,4,2] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 55
[8,5,5,5,4,3,2,1] => [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] => 770
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Description
The number of Dyck paths that are weakly above a Dyck path.
Map
first row removal
Description
Removes the first entry of an integer partition
Map
conjugate
Description
Return the conjugate partition of the partition.
The conjugate partition of the partition λ of n is the partition λ∗ whose Ferrers diagram is obtained from the diagram of λ by interchanging rows with columns.
This is also called the associated partition or the transpose in the literature.
The conjugate partition of the partition λ of n is the partition λ∗ whose Ferrers diagram is obtained from the diagram of λ by interchanging rows with columns.
This is also called the associated partition or the transpose in the literature.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.
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