Identifier
-
Mp00044:
Integer partitions
—conjugate⟶
Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
St000419: Dyck paths ⟶ ℤ (values match St000420The number of Dyck paths that are weakly above a Dyck path.)
Values
[2] => [1,1] => [1] => [1,0,1,0] => 1
[3] => [1,1,1] => [1,1] => [1,0,1,1,0,0] => 2
[2,1] => [2,1] => [1] => [1,0,1,0] => 1
[4] => [1,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[3,1] => [2,1,1] => [1,1] => [1,0,1,1,0,0] => 2
[2,2] => [2,2] => [2] => [1,1,0,0,1,0] => 2
[2,1,1] => [3,1] => [1] => [1,0,1,0] => 1
[5] => [1,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 4
[4,1] => [2,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[3,2] => [2,2,1] => [2,1] => [1,0,1,0,1,0] => 4
[3,1,1] => [3,1,1] => [1,1] => [1,0,1,1,0,0] => 2
[2,2,1] => [3,2] => [2] => [1,1,0,0,1,0] => 2
[2,1,1,1] => [4,1] => [1] => [1,0,1,0] => 1
[6] => [1,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 5
[5,1] => [2,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 4
[4,2] => [2,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 6
[4,1,1] => [3,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[3,3] => [2,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 5
[3,2,1] => [3,2,1] => [2,1] => [1,0,1,0,1,0] => 4
[3,1,1,1] => [4,1,1] => [1,1] => [1,0,1,1,0,0] => 2
[2,2,2] => [3,3] => [3] => [1,1,1,0,0,0,1,0] => 3
[2,2,1,1] => [4,2] => [2] => [1,1,0,0,1,0] => 2
[2,1,1,1,1] => [5,1] => [1] => [1,0,1,0] => 1
[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] => 6
[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] => 5
[5,2] => [2,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 8
[5,1,1] => [3,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 4
[4,3] => [2,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => 8
[4,2,1] => [3,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 6
[4,1,1,1] => [4,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[3,3,1] => [3,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 5
[3,2,2] => [3,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => 6
[3,2,1,1] => [4,2,1] => [2,1] => [1,0,1,0,1,0] => 4
[3,1,1,1,1] => [5,1,1] => [1,1] => [1,0,1,1,0,0] => 2
[2,2,2,1] => [4,3] => [3] => [1,1,1,0,0,0,1,0] => 3
[2,2,1,1,1] => [5,2] => [2] => [1,1,0,0,1,0] => 2
[2,1,1,1,1,1] => [6,1] => [1] => [1,0,1,0] => 1
[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] => 7
[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] => 6
[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] => 10
[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] => 5
[5,3] => [2,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 11
[5,2,1] => [3,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 8
[5,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 4
[4,4] => [2,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 9
[4,3,1] => [3,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => 8
[4,2,2] => [3,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 9
[4,2,1,1] => [4,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 6
[4,1,1,1,1] => [5,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[3,3,2] => [3,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => 8
[3,3,1,1] => [4,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 5
[3,2,2,1] => [4,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => 6
[3,2,1,1,1] => [5,2,1] => [2,1] => [1,0,1,0,1,0] => 4
[3,1,1,1,1,1] => [6,1,1] => [1,1] => [1,0,1,1,0,0] => 2
[2,2,2,2] => [4,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => 4
[2,2,2,1,1] => [5,3] => [3] => [1,1,1,0,0,0,1,0] => 3
[2,2,1,1,1,1] => [6,2] => [2] => [1,1,0,0,1,0] => 2
[2,1,1,1,1,1,1] => [7,1] => [1] => [1,0,1,0] => 1
[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] => 7
[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] => 12
[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] => 6
[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] => 14
[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] => 10
[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] => 5
[5,4] => [2,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 13
[5,3,1] => [3,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 11
[5,2,2] => [3,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 12
[5,2,1,1] => [4,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 8
[5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 4
[4,4,1] => [3,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 9
[4,3,2] => [3,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 13
[4,3,1,1] => [4,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => 8
[4,2,2,1] => [4,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 9
[4,2,1,1,1] => [5,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 6
[4,1,1,1,1,1] => [6,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[3,3,3] => [3,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 9
[3,3,2,1] => [4,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => 8
[3,3,1,1,1] => [5,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 5
[3,2,2,2] => [4,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 8
[3,2,2,1,1] => [5,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => 6
[3,2,1,1,1,1] => [6,2,1] => [2,1] => [1,0,1,0,1,0] => 4
[3,1,1,1,1,1,1] => [7,1,1] => [1,1] => [1,0,1,1,0,0] => 2
[2,2,2,2,1] => [5,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => 4
[2,2,2,1,1,1] => [6,3] => [3] => [1,1,1,0,0,0,1,0] => 3
[2,2,1,1,1,1,1] => [7,2] => [2] => [1,1,0,0,1,0] => 2
[2,1,1,1,1,1,1,1] => [8,1] => [1] => [1,0,1,0] => 1
[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] => 14
[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] => 7
[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] => 17
[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] => 12
[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] => 6
[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] => 17
[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] => 14
[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] => 15
[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] => 10
[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] => 5
[5,5] => [2,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 14
[5,4,1] => [3,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 13
[5,3,2] => [3,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 18
[5,3,1,1] => [4,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 11
[5,2,2,1] => [4,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 12
>>> 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] => 8
[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] => 4
[4,4,2] => [3,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 15
[4,4,1,1] => [4,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 9
[4,3,3] => [3,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 15
[4,3,2,1] => [4,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 13
[4,3,1,1,1] => [5,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => 8
[4,2,2,2] => [4,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 12
[4,2,2,1,1] => [5,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 9
[4,2,1,1,1,1] => [6,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 6
[4,1,1,1,1,1,1] => [7,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[3,3,3,1] => [4,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 9
[3,3,2,2] => [4,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 11
[3,3,2,1,1] => [5,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => 8
[3,3,1,1,1,1] => [6,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 5
[3,2,2,2,1] => [5,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 8
[3,2,2,1,1,1] => [6,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => 6
[3,2,1,1,1,1,1] => [7,2,1] => [2,1] => [1,0,1,0,1,0] => 4
[3,1,1,1,1,1,1,1] => [8,1,1] => [1,1] => [1,0,1,1,0,0] => 2
[2,2,2,2,2] => [5,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[2,2,2,2,1,1] => [6,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => 4
[2,2,2,1,1,1,1] => [7,3] => [3] => [1,1,1,0,0,0,1,0] => 3
[2,2,1,1,1,1,1,1] => [8,2] => [2] => [1,1,0,0,1,0] => 2
[2,1,1,1,1,1,1,1,1] => [9,1] => [1] => [1,0,1,0] => 1
[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] => 20
[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] => 14
[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] => 7
[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] => 21
[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] => 17
[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] => 18
[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] => 12
[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] => 6
[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] => 19
[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] => 17
[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] => 23
[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] => 14
[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] => 15
[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] => 10
[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] => 5
[5,5,1] => [3,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 14
[5,4,2] => [3,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 22
[5,4,1,1] => [4,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 13
[5,3,3] => [3,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 21
[5,3,2,1] => [4,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 18
[5,3,1,1,1] => [5,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 11
[5,2,2,2] => [4,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 16
[5,2,2,1,1] => [5,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 12
[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] => 8
[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] => 4
[4,4,3] => [3,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 18
[4,4,2,1] => [4,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 15
[4,4,1,1,1] => [5,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 9
[4,3,3,1] => [4,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 15
[4,3,2,2] => [4,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 18
[4,3,2,1,1] => [5,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 13
[4,3,1,1,1,1] => [6,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => 8
[4,2,2,2,1] => [5,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 12
[4,2,2,1,1,1] => [6,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 9
[4,2,1,1,1,1,1] => [7,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 6
[4,1,1,1,1,1,1,1] => [8,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[3,3,3,2] => [4,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 13
[3,3,3,1,1] => [5,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 9
[3,3,2,2,1] => [5,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 11
[3,3,2,1,1,1] => [6,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => 8
[3,3,1,1,1,1,1] => [7,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 5
[3,2,2,2,2] => [5,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 10
[3,2,2,2,1,1] => [6,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 8
[3,2,2,1,1,1,1] => [7,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => 6
[3,2,1,1,1,1,1,1] => [8,2,1] => [2,1] => [1,0,1,0,1,0] => 4
[3,1,1,1,1,1,1,1,1] => [9,1,1] => [1,1] => [1,0,1,1,0,0] => 2
[2,2,2,2,2,1] => [6,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[2,2,2,2,1,1,1] => [7,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => 4
[2,2,2,1,1,1,1,1] => [8,3] => [3] => [1,1,1,0,0,0,1,0] => 3
[2,2,1,1,1,1,1,1,1] => [9,2] => [2] => [1,1,0,0,1,0] => 2
[2,1,1,1,1,1,1,1,1,1] => [10,1] => [1] => [1,0,1,0] => 1
[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] => 25
[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] => 20
[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] => 21
[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] => 14
[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] => 7
[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] => 24
[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] => 21
[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] => 28
[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] => 17
[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] => 18
[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] => 12
[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] => 6
[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] => 20
[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] => 19
[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] => 29
[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] => 17
[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] => 27
[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] => 23
[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] => 14
[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] => 20
[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] => 15
[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] => 10
[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] => 5
[5,5,2] => [3,3,2,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 24
[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] => 14
[5,4,3] => [3,3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 27
[5,4,2,1] => [4,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 22
[5,4,1,1,1] => [5,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 13
[5,3,3,1] => [4,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 21
[5,3,2,2] => [4,4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 25
[5,3,2,1,1] => [5,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 18
[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] => 11
[5,2,2,2,1] => [5,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 16
[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] => 12
[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] => 8
[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] => 4
[4,4,4] => [3,3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 19
[4,4,3,1] => [4,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 18
[4,4,2,2] => [4,4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 21
[4,4,2,1,1] => [5,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 15
[4,4,1,1,1,1] => [6,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 9
[4,3,3,2] => [4,4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 22
[4,3,3,1,1] => [5,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 15
[4,3,2,2,1] => [5,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 18
[4,3,2,1,1,1] => [6,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 13
[4,3,1,1,1,1,1] => [7,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => 8
[4,2,2,2,2] => [5,5,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 15
[4,2,2,2,1,1] => [6,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 12
[4,2,2,1,1,1,1] => [7,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 9
[4,2,1,1,1,1,1,1] => [8,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 6
[4,1,1,1,1,1,1,1,1] => [9,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 3
[3,3,3,3] => [4,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 14
[3,3,3,2,1] => [5,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 13
[3,3,3,1,1,1] => [6,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 9
[3,3,2,2,2] => [5,5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 14
[3,3,2,2,1,1] => [6,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 11
[3,3,2,1,1,1,1] => [7,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => 8
[3,3,1,1,1,1,1,1] => [8,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 5
[3,2,2,2,2,1] => [6,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 10
[3,2,2,2,1,1,1] => [7,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 8
[3,2,2,1,1,1,1,1] => [8,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => 6
[3,2,1,1,1,1,1,1,1] => [9,2,1] => [2,1] => [1,0,1,0,1,0] => 4
[3,1,1,1,1,1,1,1,1,1] => [10,1,1] => [1,1] => [1,0,1,1,0,0] => 2
[2,2,2,2,2,2] => [6,6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,2,2,2,2,1,1] => [7,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[2,2,2,2,1,1,1,1] => [8,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => 4
[2,2,2,1,1,1,1,1,1] => [9,3] => [3] => [1,1,1,0,0,0,1,0] => 3
[2,2,1,1,1,1,1,1,1,1] => [10,2] => [2] => [1,1,0,0,1,0] => 2
[2,1,1,1,1,1,1,1,1,1,1] => [11,1] => [1] => [1,0,1,0] => 1
[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] => 29
[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] => 25
[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] => 33
[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] => 20
[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] => 21
[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] => 14
[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] => 7
[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] => 26
[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] => 24
[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] => 36
[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] => 21
[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] => 33
[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] => 28
[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] => 17
[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] => 24
[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] => 18
[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] => 12
[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] => 6
[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] => 20
[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] => 33
[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] => 19
[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] => 36
[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] => 29
[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] => 17
[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] => 27
[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] => 32
[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] => 23
[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] => 14
[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] => 20
[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] => 15
[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] => 10
[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] => 5
[5,5,3] => [3,3,3,2,2] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 30
[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] => 24
[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] => 14
[5,4,4] => [3,3,3,3,1] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 29
[5,4,3,1] => [4,3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 27
[5,4,2,2] => [4,4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 31
[5,4,2,1,1] => [5,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 22
[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] => 13
[5,3,3,2] => [4,4,3,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 31
[5,3,3,1,1] => [5,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 21
[5,3,2,2,1] => [5,4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 25
[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] => 18
[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] => 11
[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] => 20
[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] => 16
[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] => 12
[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] => 8
[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] => 4
[4,4,4,1] => [4,3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 19
[4,4,3,2] => [4,4,3,2] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 27
[4,4,3,1,1] => [5,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 18
[4,4,2,2,1] => [5,4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 21
[4,4,2,1,1,1] => [6,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 15
[4,4,1,1,1,1,1] => [7,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 9
[4,3,3,3] => [4,4,4,1] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 24
[4,3,3,2,1] => [5,4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 22
[4,3,3,1,1,1] => [6,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 15
[4,3,2,2,2] => [5,5,2,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 23
[4,3,2,2,1,1] => [6,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 18
[4,3,2,1,1,1,1] => [7,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 13
[4,3,1,1,1,1,1,1] => [8,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => 8
[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] => 15
[4,2,2,2,1,1,1] => [7,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 12
[4,2,2,1,1,1,1,1] => [8,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 9
[4,2,1,1,1,1,1,1,1] => [9,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 6
[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] => 3
[3,3,3,3,1] => [5,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 14
[3,3,3,2,2] => [5,5,3] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 17
[3,3,3,2,1,1] => [6,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 13
[3,3,3,1,1,1,1] => [7,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 9
[3,3,2,2,2,1] => [6,5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 14
[3,3,2,2,1,1,1] => [7,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 11
[3,3,2,1,1,1,1,1] => [8,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => 8
[3,3,1,1,1,1,1,1,1] => [9,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 5
[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] => 12
[3,2,2,2,2,1,1] => [7,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 10
[3,2,2,2,1,1,1,1] => [8,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 8
[3,2,2,1,1,1,1,1,1] => [9,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => 6
[3,2,1,1,1,1,1,1,1,1] => [10,2,1] => [2,1] => [1,0,1,0,1,0] => 4
[3,1,1,1,1,1,1,1,1,1,1] => [11,1,1] => [1,1] => [1,0,1,1,0,0] => 2
[2,2,2,2,2,2,1] => [7,6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[2,2,2,2,2,1,1,1] => [8,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[2,2,2,2,1,1,1,1,1] => [9,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => 4
[2,2,2,1,1,1,1,1,1,1] => [10,3] => [3] => [1,1,1,0,0,0,1,0] => 3
[2,2,1,1,1,1,1,1,1,1,1] => [11,2] => [2] => [1,1,0,0,1,0] => 2
[2,1,1,1,1,1,1,1,1,1,1,1] => [12,1] => [1] => [1,0,1,0] => 1
[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] => 32
[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] => 29
[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] => 43
[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] => 25
[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] => 39
[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] => 33
[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] => 20
[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] => 28
[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] => 21
[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] => 14
[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] => 7
[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] => 27
[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] => 26
[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] => 42
[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] => 24
[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] => 45
[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] => 36
[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] => 21
[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] => 33
[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] => 39
[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] => 28
[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] => 17
[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] => 24
[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] => 18
[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] => 12
[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] => 6
[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] => 35
[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] => 20
[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] => 42
[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] => 33
[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] => 19
[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] => 39
[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] => 36
[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] => 41
[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] => 29
[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] => 17
[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] => 40
[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] => 27
[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] => 32
[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] => 23
[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] => 14
[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] => 25
[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] => 20
[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] => 15
[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] => 10
[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] => 5
[5,5,4] => [3,3,3,3,2] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 33
[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] => 30
[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] => 34
[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] => 24
[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] => 14
[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] => 29
[5,4,3,2] => [4,4,3,2,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 41
[5,4,3,1,1] => [5,3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 27
[5,4,2,2,1] => [5,4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 31
[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] => 22
[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] => 13
[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] => 34
[5,3,3,2,1] => [5,4,3,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 31
[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] => 21
[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] => 32
[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] => 25
[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] => 18
[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] => 11
[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] => 20
[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] => 16
[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] => 12
[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] => 8
[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] => 4
[4,4,4,2] => [4,4,3,3] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 29
[4,4,4,1,1] => [5,3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 19
[4,4,3,3] => [4,4,4,2] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 30
[4,4,3,2,1] => [5,4,3,2] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 27
[4,4,3,1,1,1] => [6,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 18
[4,4,2,2,2] => [5,5,2,2] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 27
[4,4,2,2,1,1] => [6,4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 21
[4,4,2,1,1,1,1] => [7,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 15
[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] => 9
[4,3,3,3,1] => [5,4,4,1] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 24
[4,3,3,2,2] => [5,5,3,1] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 29
[4,3,3,2,1,1] => [6,4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 22
[4,3,3,1,1,1,1] => [7,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 15
[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] => 23
[4,3,2,2,1,1,1] => [7,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 18
[4,3,2,1,1,1,1,1] => [8,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 13
[4,3,1,1,1,1,1,1,1] => [9,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => 8
[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] => 18
[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] => 15
[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] => 12
[4,2,2,1,1,1,1,1,1] => [9,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 9
[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] => 6
[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] => 3
[3,3,3,3,2] => [5,5,4] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 19
[3,3,3,3,1,1] => [6,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 14
[3,3,3,2,2,1] => [6,5,3] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 17
[3,3,3,2,1,1,1] => [7,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 13
[3,3,3,1,1,1,1,1] => [8,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 9
[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] => 17
[3,3,2,2,2,1,1] => [7,5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 14
[3,3,2,2,1,1,1,1] => [8,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 11
[3,3,2,1,1,1,1,1,1] => [9,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => 8
[3,3,1,1,1,1,1,1,1,1] => [10,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 5
[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] => 12
[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] => 10
[3,2,2,2,1,1,1,1,1] => [9,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 8
[3,2,2,1,1,1,1,1,1,1] => [10,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => 6
[3,2,1,1,1,1,1,1,1,1,1] => [11,2,1] => [2,1] => [1,0,1,0,1,0] => 4
[3,1,1,1,1,1,1,1,1,1,1,1] => [12,1,1] => [1,1] => [1,0,1,1,0,0] => 2
[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] => 6
[2,2,2,2,2,1,1,1,1] => [9,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[2,2,2,2,1,1,1,1,1,1] => [10,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => 4
[2,2,2,1,1,1,1,1,1,1,1] => [11,3] => [3] => [1,1,1,0,0,0,1,0] => 3
[2,2,1,1,1,1,1,1,1,1,1,1] => [12,2] => [2] => [1,1,0,0,1,0] => 2
[2,1,1,1,1,1,1,1,1,1,1,1,1] => [13,1] => [1] => [1,0,1,0] => 1
[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] => 34
[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] => 32
[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] => 51
[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] => 29
[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] => 54
[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] => 43
[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] => 25
[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] => 39
[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] => 46
[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] => 33
[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] => 20
[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] => 28
[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] => 21
[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] => 14
[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] => 7
[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] => 27
[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] => 46
[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] => 26
[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] => 54
[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] => 42
[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] => 24
[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] => 49
[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] => 45
[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] => 51
[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] => 36
[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] => 21
[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] => 49
[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] => 33
[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] => 39
[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] => 28
[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] => 17
[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] => 30
[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] => 24
[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] => 18
[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] => 12
[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] => 6
[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] => 45
[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] => 35
[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] => 20
[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] => 47
[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] => 42
[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] => 47
[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] => 33
[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] => 19
[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] => 39
[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] => 55
[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] => 36
[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] => 41
[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] => 29
[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] => 17
[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] => 44
[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] => 40
[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] => 27
[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] => 41
[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] => 32
[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] => 23
[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] => 14
[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] => 25
[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] => 20
[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] => 15
[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] => 10
[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] => 5
[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] => 34
[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] => 33
[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] => 46
[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] => 30
[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] => 34
[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] => 24
[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] => 14
[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] => 45
[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] => 29
[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] => 46
[5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 41
[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] => 27
[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] => 40
[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] => 31
[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] => 22
[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] => 13
[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] => 34
[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] => 41
[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] => 31
[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] => 21
[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] => 32
[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] => 25
[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] => 18
[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] => 11
[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] => 24
[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] => 20
[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] => 16
[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] => 12
[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] => 8
[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] => 4
[4,4,4,3] => [4,4,4,3] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 33
[4,4,4,2,1] => [5,4,3,3] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 29
[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] => 19
[4,4,3,3,1] => [5,4,4,2] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 30
[4,4,3,2,2] => [5,5,3,2] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => 36
[4,4,3,2,1,1] => [6,4,3,2] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 27
[4,4,3,1,1,1,1] => [7,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 18
[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] => 27
[4,4,2,2,1,1,1] => [7,4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 21
[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] => 15
[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] => 9
[4,3,3,3,2] => [5,5,4,1] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 33
[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] => 24
[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] => 29
[4,3,3,2,1,1,1] => [7,4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 22
[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] => 15
[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] => 28
[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] => 23
[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] => 18
[4,3,2,1,1,1,1,1,1] => [9,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 13
[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] => 8
[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] => 18
[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] => 15
[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] => 12
[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] => 9
[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] => 6
[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] => 3
[3,3,3,3,3] => [5,5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 20
[3,3,3,3,2,1] => [6,5,4] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 19
[3,3,3,3,1,1,1] => [7,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 14
[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] => 21
[3,3,3,2,2,1,1] => [7,5,3] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 17
[3,3,3,2,1,1,1,1] => [8,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 13
[3,3,3,1,1,1,1,1,1] => [9,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 9
[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] => 17
[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] => 14
[3,3,2,2,1,1,1,1,1] => [9,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 11
[3,3,2,1,1,1,1,1,1,1] => [10,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => 8
[3,3,1,1,1,1,1,1,1,1,1] => [11,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 5
[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] => 12
[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] => 10
[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] => 8
[3,2,2,1,1,1,1,1,1,1,1] => [11,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => 6
[3,2,1,1,1,1,1,1,1,1,1,1] => [12,2,1] => [2,1] => [1,0,1,0,1,0] => 4
[3,1,1,1,1,1,1,1,1,1,1,1,1] => [13,1,1] => [1,1] => [1,0,1,1,0,0] => 2
[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] => 6
[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] => 5
[2,2,2,2,1,1,1,1,1,1,1] => [11,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => 4
[2,2,2,1,1,1,1,1,1,1,1,1] => [12,3] => [3] => [1,1,1,0,0,0,1,0] => 3
[2,2,1,1,1,1,1,1,1,1,1,1,1] => [13,2] => [2] => [1,1,0,0,1,0] => 2
[2,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14,1] => [1] => [1,0,1,0] => 1
[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] => 34
[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] => 57
[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] => 32
[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] => 66
[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] => 51
[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] => 29
[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] => 59
[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] => 54
[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] => 61
[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] => 43
[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] => 25
[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] => 58
[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] => 39
[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] => 46
[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] => 33
[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] => 20
[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] => 35
[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] => 28
[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] => 21
[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] => 14
[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] => 7
[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] => 48
[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] => 27
[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] => 60
[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] => 46
[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] => 26
[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] => 61
[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] => 54
[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] => 60
[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] => 42
[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] => 24
[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] => 49
[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] => 69
[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] => 45
[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] => 51
[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] => 36
[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] => 21
[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] => 54
[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] => 49
[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] => 33
[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] => 50
[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] => 39
[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] => 28
[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] => 17
[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] => 30
[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] => 24
[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] => 18
[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] => 12
[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] => 6
[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] => 51
[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] => 45
[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] => 50
[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] => 35
[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] => 20
[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] => 49
[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] => 47
[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] => 65
[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] => 42
[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] => 47
[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] => 33
[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] => 19
[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] => 61
[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] => 39
[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] => 62
[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] => 55
[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] => 36
[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] => 53
[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] => 41
[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] => 29
[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] => 17
[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] => 44
[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] => 53
[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] => 40
[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] => 27
[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] => 41
[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] => 32
[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] => 23
[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] => 14
[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] => 30
[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] => 25
[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] => 20
[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] => 15
[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] => 10
[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] => 5
[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] => 34
[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] => 52
[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] => 33
[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] => 52
[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] => 46
[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] => 30
[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] => 44
[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] => 34
[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] => 24
[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] => 14
[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] => 52
[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] => 45
[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] => 29
[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] => 46
[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] => 55
[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] => 41
[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] => 27
[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] => 40
[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] => 31
[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] => 22
[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] => 13
[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] => 47
[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] => 34
[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] => 41
[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] => 31
[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] => 21
[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] => 39
[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] => 32
[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] => 25
[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] => 18
[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] => 11
[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] => 24
[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] => 20
[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] => 16
[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] => 12
[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] => 8
[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] => 4
[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] => 34
[4,4,4,3,1] => [5,4,4,3] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 33
[4,4,4,2,2] => [5,5,3,3] => [5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => 39
[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] => 29
[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] => 19
[4,4,3,3,2] => [5,5,4,2] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => 42
[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] => 30
[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] => 36
[4,4,3,2,1,1,1] => [7,4,3,2] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 27
[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] => 18
[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] => 33
[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] => 27
[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] => 21
[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] => 15
[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] => 9
[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] => 35
[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] => 33
[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] => 24
[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] => 36
[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] => 29
[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] => 22
[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] => 15
[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] => 28
[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] => 23
[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] => 18
[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] => 13
[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] => 8
[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] => 18
[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] => 15
[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] => 12
[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] => 9
[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] => 6
[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] => 3
[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] => 20
[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] => 24
[3,3,3,3,2,1,1] => [7,5,4] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 19
[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] => 14
[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] => 21
[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] => 17
[3,3,3,2,1,1,1,1,1] => [9,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 13
[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] => 9
[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] => 17
[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] => 14
[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] => 11
[3,3,2,1,1,1,1,1,1,1,1] => [11,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => 8
[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] => 5
[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] => 12
[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] => 10
[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] => 8
[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] => 6
[3,2,1,1,1,1,1,1,1,1,1,1,1] => [13,2,1] => [2,1] => [1,0,1,0,1,0] => 4
[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] => 2
[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] => 6
[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] => 5
[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] => 4
[2,2,2,1,1,1,1,1,1,1,1,1,1] => [13,3] => [3] => [1,1,1,0,0,0,1,0] => 3
[2,2,1,1,1,1,1,1,1,1,1,1,1,1] => [14,2] => [2] => [1,1,0,0,1,0] => 2
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [15,1] => [1] => [1,0,1,0] => 1
[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] => 61
[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] => 34
[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] => 75
[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] => 57
[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] => 32
[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] => 75
[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] => 66
[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] => 73
[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] => 51
[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] => 29
[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] => 59
[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] => 83
[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] => 54
[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] => 61
[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] => 43
[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] => 25
[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] => 64
[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] => 58
[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] => 39
[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] => 59
[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] => 46
[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] => 33
[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] => 20
[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] => 35
[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] => 28
[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] => 21
[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] => 14
[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] => 7
[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] => 63
[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] => 48
[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] => 27
[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] => 69
[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] => 60
[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] => 66
[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] => 46
[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] => 26
[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] => 64
[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] => 61
[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] => 84
[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] => 54
[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] => 60
[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] => 42
[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] => 24
[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] => 77
[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] => 49
[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] => 78
[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] => 69
[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] => 45
[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] => 66
[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] => 51
[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] => 36
[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] => 21
[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] => 54
[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] => 65
[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] => 49
[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] => 33
[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] => 50
[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] => 39
[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] => 28
[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] => 17
[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] => 36
[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] => 30
[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] => 24
[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] => 18
[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] => 12
[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] => 6
[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] => 54
[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] => 51
[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] => 70
[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] => 45
[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] => 50
[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] => 35
[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] => 20
[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] => 49
[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] => 75
[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] => 47
[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] => 74
[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] => 65
[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] => 42
[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] => 61
[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] => 47
[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] => 33
[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] => 19
[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] => 71
[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] => 61
[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] => 39
[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] => 62
[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] => 74
[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] => 55
[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] => 36
[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] => 53
[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] => 41
[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] => 29
[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] => 17
[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] => 61
[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] => 44
[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] => 53
[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] => 40
[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] => 27
[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] => 50
[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] => 41
[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] => 32
[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] => 23
[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] => 14
[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] => 30
[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] => 25
[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] => 20
[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] => 15
[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] => 10
[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] => 5
[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] => 54
[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] => 34
[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] => 61
[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] => 52
[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] => 33
[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] => 52
[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] => 62
[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] => 46
[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] => 30
[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] => 44
[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] => 34
[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] => 24
[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] => 14
[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] => 54
[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] => 52
[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] => 61
[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] => 45
[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] => 29
[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] => 65
[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] => 46
[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] => 55
[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] => 41
[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] => 27
[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] => 49
[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] => 40
[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] => 31
[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] => 22
[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] => 13
[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] => 50
[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] => 47
[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] => 34
[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] => 51
[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] => 41
[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] => 31
[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] => 21
[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] => 39
[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] => 32
[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] => 25
[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] => 18
[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] => 11
[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] => 24
[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] => 20
[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] => 16
[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] => 12
[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] => 8
[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] => 4
[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] => 34
[4,4,4,3,2] => [5,5,4,3] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => 47
[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] => 33
[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] => 39
[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] => 29
[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] => 19
[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] => 45
[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] => 42
[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] => 30
[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] => 45
[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] => 36
[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] => 27
[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] => 18
[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] => 33
[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] => 27
[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] => 21
[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] => 15
[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] => 9
[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] => 35
[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] => 42
[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] => 33
[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] => 24
[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] => 36
[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] => 29
[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] => 22
[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] => 15
[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] => 28
[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] => 23
[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] => 18
[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] => 13
[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] => 8
[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] => 18
[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] => 15
[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] => 12
[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] => 9
[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] => 6
[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] => 3
[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] => 26
[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] => 20
[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] => 24
[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] => 19
[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] => 14
[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] => 21
[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] => 17
[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] => 13
[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] => 9
[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] => 17
[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] => 14
[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] => 11
[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] => 8
[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] => 5
[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] => 12
[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] => 10
[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] => 8
[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] => 6
[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] => 4
[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] => 2
[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] => 6
[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] => 5
[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] => 4
[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] => 3
[2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] => [15,2] => [2] => [1,1,0,0,1,0] => 2
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [16,1] => [1] => [1,0,1,0] => 1
[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] => 131
[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] => 89
[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] => 103
[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] => 75
[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] => 47
[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] => 106
[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] => 74
[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] => 88
[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] => 65
[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] => 61
[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] => 103
[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] => 71
[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] => 83
[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] => 61
[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] => 88
[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] => 62
[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] => 74
[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] => 61
[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] => 89
[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] => 61
[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] => 71
[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] => 52
[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] => 74
[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] => 52
[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] => 62
[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] => 75
[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] => 52
[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] => 61
[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] => 65
[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] => 47
[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] => 131
[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] => 89
[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] => 103
[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] => 75
[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] => 106
[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] => 74
[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] => 88
[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] => 103
[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] => 71
[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] => 83
[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] => 88
[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] => 89
[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] => 61
[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] => 71
[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] => 74
[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] => 75
[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] => 89
[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] => 428
[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] => 296
[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] => 344
[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] => 254
[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] => 164
[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] => 226
[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] => 150
[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] => 218
[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] => 170
[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] => 122
[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] => 74
[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] => 201
[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] => 232
[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] => 170
[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] => 156
[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] => 128
[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] => 86
[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] => 26
[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] => 344
[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] => 240
[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] => 173
[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] => 131
[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] => 111
[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] => 93
[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] => 75
[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] => 36
[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] => 296
[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] => 206
[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] => 131
[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] => 89
[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] => 164
[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] => 89
[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] => 75
[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] => 69
[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] => 55
[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] => 34
[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] => 47
[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] => 26
[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] => 428
[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] => 296
[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] => 344
[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] => 254
[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] => 164
[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] => 358
[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] => 344
[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] => 80
[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] => 296
[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] => 206
[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] => 178
[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] => 54
[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] => 254
[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] => 226
[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] => 201
[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] => 145
[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] => 173
[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] => 131
[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] => 156
[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] => 75
[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] => 170
[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] => 86
[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] => 164
[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] => 74
[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] => 296
[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] => 206
[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] => 173
[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] => 164
[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] => 117
[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] => 122
[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] => 94
[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] => 70
[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] => 164
[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] => 94
[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] => 64
[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] => 74
[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] => 49
[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] => 1429
[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] => 1000
[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] => 868
[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] => 428
[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] => 296
[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] => 1429
[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] => 1429
[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] => 1000
[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] => 868
[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] => 784
[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] => 714
[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] => 644
[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] => 560
[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] => 1000
[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] => 571
[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] => 604
[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] => 574
[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] => 518
[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] => 434
[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] => 27
[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] => 215
[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] => 285
[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] => 131
[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] => 560
[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] => 173
[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] => 1000
[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] => 355
[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] => 439
[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] => 571
[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] => 868
[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] => 613
[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] => 703
[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] => 703
[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] => 1165
[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] => 1165
[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] => 24
[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] => 54
[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] => 769
search for individual values
searching the database for the individual values of this statistic
Description
The number of Dyck paths that are weakly above the Dyck path, except for the path itself.
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 $\lambda$ of $n$ is the partition $\lambda^*$ whose Ferrers diagram is obtained from the diagram of $\lambda$ by interchanging rows with columns.
This is also called the associated partition or the transpose in the literature.
The conjugate partition of the partition $\lambda$ of $n$ is the partition $\lambda^*$ whose Ferrers diagram is obtained from the diagram of $\lambda$ 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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