Identifier
-
Mp00043:
Integer partitions
—to Dyck path⟶
Dyck paths
Mp00102: Dyck paths —rise composition⟶ Integer compositions
Mp00040: Integer compositions —to partition⟶ Integer partitions
St000228: Integer partitions ⟶ ℤ
Values
[1] => [1,0,1,0] => [1,1] => [1,1] => 2
[2] => [1,1,0,0,1,0] => [2,1] => [2,1] => 3
[1,1] => [1,0,1,1,0,0] => [1,2] => [2,1] => 3
[3] => [1,1,1,0,0,0,1,0] => [3,1] => [3,1] => 4
[2,1] => [1,0,1,0,1,0] => [1,1,1] => [1,1,1] => 3
[1,1,1] => [1,0,1,1,1,0,0,0] => [1,3] => [3,1] => 4
[4] => [1,1,1,1,0,0,0,0,1,0] => [4,1] => [4,1] => 5
[3,1] => [1,1,0,1,0,0,1,0] => [2,1,1] => [2,1,1] => 4
[2,2] => [1,1,0,0,1,1,0,0] => [2,2] => [2,2] => 4
[2,1,1] => [1,0,1,1,0,1,0,0] => [1,2,1] => [2,1,1] => 4
[1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,4] => [4,1] => 5
[5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,1] => [5,1] => 6
[4,1] => [1,1,1,0,1,0,0,0,1,0] => [3,1,1] => [3,1,1] => 5
[3,2] => [1,1,0,0,1,0,1,0] => [2,1,1] => [2,1,1] => 4
[3,1,1] => [1,0,1,1,0,0,1,0] => [1,2,1] => [2,1,1] => 4
[2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,2] => [2,1,1] => 4
[2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,3,1] => [3,1,1] => 5
[1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,5] => [5,1] => 6
[6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,1] => [6,1] => 7
[5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [4,1,1] => [4,1,1] => 6
[4,2] => [1,1,1,0,0,1,0,0,1,0] => [3,1,1] => [3,1,1] => 5
[4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [2,2,1] => [2,2,1] => 5
[3,3] => [1,1,1,0,0,0,1,1,0,0] => [3,2] => [3,2] => 5
[3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,1,1] => [1,1,1,1] => 4
[3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [1,3,1] => [3,1,1] => 5
[2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [2,3] => [3,2] => 5
[2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,2,2] => [2,2,1] => 5
[2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,4,1] => [4,1,1] => 6
[1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,6] => [6,1] => 7
[7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,1] => [7,1] => 8
[6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [5,1,1] => [5,1,1] => 7
[5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [4,1,1] => [4,1,1] => 6
[5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [3,2,1] => [3,2,1] => 6
[4,3] => [1,1,1,0,0,0,1,0,1,0] => [3,1,1] => [3,1,1] => 5
[4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [2,1,1,1] => [2,1,1,1] => 5
[4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [1,3,1] => [3,1,1] => 5
[3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [2,1,2] => [2,2,1] => 5
[3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [2,2,1] => [2,2,1] => 5
[3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,2,1,1] => [2,1,1,1] => 5
[3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,4,1] => [4,1,1] => 6
[2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,1,3] => [3,1,1] => 5
[2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2] => [3,2,1] => 6
[2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,5,1] => [5,1,1] => 7
[1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,7] => [7,1] => 8
[8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => 9
[7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [6,1,1] => [6,1,1] => 8
[6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,1,1] => [5,1,1] => 7
[6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [4,2,1] => [4,2,1] => 7
[5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [4,1,1] => [4,1,1] => 6
[5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [3,1,1,1] => [3,1,1,1] => 6
[5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [2,3,1] => [3,2,1] => 6
[4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,2] => [4,2] => 6
[4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [2,1,1,1] => [2,1,1,1] => 5
[4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [2,2,1] => [2,2,1] => 5
[4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [1,2,1,1] => [2,1,1,1] => 5
[4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,4,1] => [4,1,1] => 6
[3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [2,1,2] => [2,2,1] => 5
[3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [1,2,2] => [2,2,1] => 5
[3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,2,1] => [2,1,1,1] => 5
[3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,3,1,1] => [3,1,1,1] => 6
[3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,5,1] => [5,1,1] => 7
[2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,4] => [4,2] => 6
[2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3] => [3,2,1] => 6
[2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,4,2] => [4,2,1] => 7
[2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,6,1] => [6,1,1] => 8
[1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,8] => [8,1] => 9
[9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => 10
[8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [7,1,1] => [7,1,1] => 9
[7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [6,1,1] => [6,1,1] => 8
[7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [5,2,1] => [5,2,1] => 8
[6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [5,1,1] => [5,1,1] => 7
[6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [4,1,1,1] => [4,1,1,1] => 7
[6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,3,1] => [3,3,1] => 7
[5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [4,1,1] => [4,1,1] => 6
[5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [3,1,1,1] => [3,1,1,1] => 6
[5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,1] => [3,2,1] => 6
[5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [2,2,1,1] => [2,2,1,1] => 6
[5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,4,1] => [4,1,1] => 6
[4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [3,1,2] => [3,2,1] => 6
[4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [2,1,1,1] => [2,1,1,1] => 5
[4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,2,1,1] => [2,1,1,1] => 5
[4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,2,1] => [2,1,1,1] => 5
[4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,3,1,1] => [3,1,1,1] => 6
[4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,5,1] => [5,1,1] => 7
[3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,3] => [3,3] => 6
[3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,2] => [2,1,1,1] => 5
[3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2] => [3,2,1] => 6
[3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1] => [3,2,1] => 6
[3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,2,1] => [2,2,1,1] => 6
[3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,4,1,1] => [4,1,1,1] => 7
[3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,6,1] => [6,1,1] => 8
[2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,4] => [4,1,1] => 6
[2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,3,3] => [3,3,1] => 7
[2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,5,2] => [5,2,1] => 8
[2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,7,1] => [7,1,1] => 9
[1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,9] => [9,1] => 10
[9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [8,1,1] => [8,1,1] => 10
[8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [7,1,1] => [7,1,1] => 9
[8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [6,2,1] => [6,2,1] => 9
[7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [6,1,1] => [6,1,1] => 8
[7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [5,1,1,1] => [5,1,1,1] => 8
>>> Load all 1096 entries. <<<[7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [4,3,1] => [4,3,1] => 8
[6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,1,1] => [5,1,1] => 7
[6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [4,1,1,1] => [4,1,1,1] => 7
[6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [4,2,1] => [4,2,1] => 7
[6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,2,1,1] => [3,2,1,1] => 7
[6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,4,1] => [4,2,1] => 7
[5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,2] => [5,2] => 7
[5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [3,1,1,1] => [3,1,1,1] => 6
[5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [3,1,1,1] => [3,1,1,1] => 6
[5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [2,2,1,1] => [2,2,1,1] => 6
[5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [2,1,2,1] => [2,2,1,1] => 6
[5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,3,1,1] => [3,1,1,1] => 6
[5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,5,1] => [5,1,1] => 7
[4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,2] => [3,2,1] => 6
[4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [2,2,2] => [2,2,2] => 6
[4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1] => [3,2,1] => 6
[4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1] => [1,1,1,1,1] => 5
[4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,3,1,1] => [3,1,1,1] => 6
[4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1] => [3,2,1] => 6
[4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,2,1] => [2,2,1,1] => 6
[4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,4,1,1] => [4,1,1,1] => 7
[4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,6,1] => [6,1,1] => 8
[3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [2,1,3] => [3,2,1] => 6
[3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [2,2,2] => [2,2,2] => 6
[3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,1,2] => [2,2,1,1] => 6
[3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,4,2] => [4,2,1] => 7
[3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,3,1] => [3,1,1,1] => 6
[3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,3,2,1] => [3,2,1,1] => 7
[3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,5,1,1] => [5,1,1,1] => 8
[3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,7,1] => [7,1,1] => 9
[2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,5] => [5,2] => 7
[2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4] => [4,2,1] => 7
[2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,4,3] => [4,3,1] => 8
[2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,6,2] => [6,2,1] => 9
[2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,8,1] => [8,1,1] => 10
[9,2] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0] => [8,1,1] => [8,1,1] => 10
[9,1,1] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => [7,2,1] => [7,2,1] => 10
[8,3] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [7,1,1] => [7,1,1] => 9
[8,2,1] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [6,1,1,1] => [6,1,1,1] => 9
[8,1,1,1] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => [5,3,1] => [5,3,1] => 9
[7,4] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [6,1,1] => [6,1,1] => 8
[7,3,1] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [5,1,1,1] => [5,1,1,1] => 8
[7,2,2] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [5,2,1] => [5,2,1] => 8
[7,2,1,1] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [4,2,1,1] => [4,2,1,1] => 8
[7,1,1,1,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [3,4,1] => [4,3,1] => 8
[6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,1,1] => [5,1,1] => 7
[6,4,1] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [4,1,1,1] => [4,1,1,1] => 7
[6,3,2] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [4,1,1,1] => [4,1,1,1] => 7
[6,3,1,1] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,2,1,1] => [3,2,1,1] => 7
[6,2,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,1,2,1] => [3,2,1,1] => 7
[6,2,1,1,1] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,3,1,1] => [3,2,1,1] => 7
[6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,5,1] => [5,1,1] => 7
[5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [4,1,2] => [4,2,1] => 7
[5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => [3,1,1,1] => [3,1,1,1] => 6
[5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => [2,2,1,1] => [2,2,1,1] => 6
[5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1] => [3,2,1] => 6
[5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,1,1,1] => [2,1,1,1,1] => 6
[5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,3,1,1] => [3,1,1,1] => 6
[5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1] => [3,2,1] => 6
[5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,2,1] => [2,2,1,1] => 6
[5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,4,1,1] => [4,1,1,1] => 7
[5,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,6,1] => [6,1,1] => 8
[4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2] => [3,2,1] => 6
[4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,1,2] => [2,2,1,1] => 6
[4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2] => [3,2,1] => 6
[4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => [2,1,2,1] => [2,2,1,1] => 6
[4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => [2,2,1,1] => [2,2,1,1] => 6
[4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,1,1,1] => [2,1,1,1,1] => 6
[4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,4,1,1] => [4,1,1,1] => 7
[4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,3,1] => [3,1,1,1] => 6
[4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,3,2,1] => [3,2,1,1] => 7
[4,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,5,1,1] => [5,1,1,1] => 8
[4,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,7,1] => [7,1,1] => 9
[3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3] => [3,2,1] => 6
[3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3] => [3,2,1] => 6
[3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,2,2] => [2,2,1,1] => 6
[3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,3,1,2] => [3,2,1,1] => 7
[3,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,5,2] => [5,2,1] => 8
[3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,4,1] => [4,2,1] => 7
[3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,2,3,1] => [3,2,1,1] => 7
[3,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,4,2,1] => [4,2,1,1] => 8
[3,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,6,1,1] => [6,1,1,1] => 9
[3,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,8,1] => [8,1,1] => 10
[2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,5] => [5,1,1] => 7
[2,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,3,4] => [4,3,1] => 8
[2,2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,5,3] => [5,3,1] => 9
[2,2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,7,2] => [7,2,1] => 10
[9,3] => [1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0] => [8,1,1] => [8,1,1] => 10
[9,2,1] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0] => [7,1,1,1] => [7,1,1,1] => 10
[9,1,1,1] => [1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0] => [6,3,1] => [6,3,1] => 10
[8,4] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0] => [7,1,1] => [7,1,1] => 9
[8,3,1] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => [6,1,1,1] => [6,1,1,1] => 9
[8,2,2] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => [6,2,1] => [6,2,1] => 9
[8,2,1,1] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => [5,2,1,1] => [5,2,1,1] => 9
[8,1,1,1,1] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [4,4,1] => [4,4,1] => 9
[7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,1,1] => [6,1,1] => 8
[7,4,1] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [5,1,1,1] => [5,1,1,1] => 8
[7,3,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [5,1,1,1] => [5,1,1,1] => 8
[7,3,1,1] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [4,2,1,1] => [4,2,1,1] => 8
[7,2,2,1] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [4,1,2,1] => [4,2,1,1] => 8
[7,2,1,1,1] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [3,3,1,1] => [3,3,1,1] => 8
[7,1,1,1,1,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,5,1] => [5,2,1] => 8
[6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,2] => [6,2] => 8
[6,5,1] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [4,1,1,1] => [4,1,1,1] => 7
[6,4,2] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,1,1] => [4,1,1,1] => 7
[6,4,1,1] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,2,1,1] => [3,2,1,1] => 7
[6,3,3] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,2,1] => [4,2,1] => 7
[6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,1,1,1,1] => [3,1,1,1,1] => 7
[6,3,1,1,1] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,3,1,1] => [3,2,1,1] => 7
[6,2,2,2] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,3,1] => [3,3,1] => 7
[6,2,2,1,1] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,2,2,1] => [2,2,2,1] => 7
[6,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,4,1,1] => [4,1,1,1] => 7
[6,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,6,1] => [6,1,1] => 8
[5,5,2] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [4,1,2] => [4,2,1] => 7
[5,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,2,2] => [3,2,2] => 7
[5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1] => [3,1,1,1] => 6
[5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [2,1,1,1,1] => [2,1,1,1,1] => 6
[5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,3,1,1] => [3,1,1,1] => 6
[5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => [2,1,2,1] => [2,2,1,1] => 6
[5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [2,2,1,1] => [2,2,1,1] => 6
[5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,1,1,1] => [2,1,1,1,1] => 6
[5,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,4,1,1] => [4,1,1,1] => 7
[5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,3,1] => [3,1,1,1] => 6
[5,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,3,2,1] => [3,2,1,1] => 7
[5,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,5,1,1] => [5,1,1,1] => 8
[5,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,7,1] => [7,1,1] => 9
[4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3] => [4,3] => 7
[4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [2,1,1,2] => [2,2,1,1] => 6
[4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2] => [2,2,2] => 6
[4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,1,2] => [2,2,1,1] => 6
[4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,4,2] => [4,2,1] => 7
[4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,2,1] => [2,2,1,1] => 6
[4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,2,1] => [2,2,1,1] => 6
[4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,2,1,1] => [2,1,1,1,1] => 6
[4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,3,1,1,1] => [3,1,1,1,1] => 7
[4,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,5,1,1] => [5,1,1,1] => 8
[4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,4,1] => [4,2,1] => 7
[4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,2,3,1] => [3,2,1,1] => 7
[4,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,4,2,1] => [4,2,1,1] => 8
[4,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [1,6,1,1] => [6,1,1,1] => 9
[4,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [1,8,1] => [8,1,1] => 10
[3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,4] => [4,3] => 7
[3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,3] => [3,1,1,1] => 6
[3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,3,3] => [3,3,1] => 7
[3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,3,2] => [3,2,2] => 7
[3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,2,2,2] => [2,2,2,1] => 7
[3,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,4,1,2] => [4,2,1,1] => 8
[3,3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,6,2] => [6,2,1] => 9
[3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,4,1] => [4,1,1,1] => 7
[3,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,3,3,1] => [3,3,1,1] => 8
[3,2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,5,2,1] => [5,2,1,1] => 9
[3,2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,7,1,1] => [7,1,1,1] => 10
[2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,6] => [6,2] => 8
[2,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,2,5] => [5,2,1] => 8
[2,2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,4,4] => [4,4,1] => 9
[2,2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,6,3] => [6,3,1] => 10
[9,4] => [1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0] => [8,1,1] => [8,1,1] => 10
[9,3,1] => [1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,1,0] => [7,1,1,1] => [7,1,1,1] => 10
[9,2,1,1] => [1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,1,0] => [6,2,1,1] => [6,2,1,1] => 10
[9,1,1,1,1] => [1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [5,4,1] => [5,4,1] => 10
[8,5] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [7,1,1] => [7,1,1] => 9
[8,4,1] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0] => [6,1,1,1] => [6,1,1,1] => 9
[8,3,2] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0] => [6,1,1,1] => [6,1,1,1] => 9
[8,3,1,1] => [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0] => [5,2,1,1] => [5,2,1,1] => 9
[8,2,2,1] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0] => [5,1,2,1] => [5,2,1,1] => 9
[8,2,1,1,1] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0] => [4,3,1,1] => [4,3,1,1] => 9
[8,1,1,1,1,1] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [3,5,1] => [5,3,1] => 9
[7,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => 8
[7,5,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [5,1,1,1] => [5,1,1,1] => 8
[7,4,2] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [5,1,1,1] => [5,1,1,1] => 8
[7,4,1,1] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [4,2,1,1] => [4,2,1,1] => 8
[7,3,3] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [5,2,1] => [5,2,1] => 8
[7,3,2,1] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [4,1,1,1,1] => [4,1,1,1,1] => 8
[7,3,1,1,1] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [3,3,1,1] => [3,3,1,1] => 8
[7,2,2,2] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [4,3,1] => [4,3,1] => 8
[7,2,2,1,1] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [3,2,2,1] => [3,2,2,1] => 8
[7,2,1,1,1,1] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,4,1,1] => [4,2,1,1] => 8
[7,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,6,1] => [6,1,1] => 8
[6,6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [5,1,2] => [5,2,1] => 8
[6,5,2] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [4,1,1,1] => [4,1,1,1] => 7
[6,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,2,1,1] => [3,2,1,1] => 7
[6,4,3] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,1,1,1] => [4,1,1,1] => 7
[6,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,1,1,1,1] => [3,1,1,1,1] => 7
[6,4,1,1,1] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,3,1,1] => [3,2,1,1] => 7
[6,3,3,1] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,1,2,1] => [3,2,1,1] => 7
[6,3,2,2] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,1,1] => [3,2,1,1] => 7
[6,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,2,1,1,1] => [2,2,1,1,1] => 7
[6,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,4,1,1] => [4,1,1,1] => 7
[6,2,2,2,1] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,1,3,1] => [3,2,1,1] => 7
[6,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,3,2,1] => [3,2,1,1] => 7
[6,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,5,1,1] => [5,1,1,1] => 8
[6,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,7,1] => [7,1,1] => 9
[5,5,3] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,1,2] => [4,2,1] => 7
[5,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,1,1,2] => [3,2,1,1] => 7
[5,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,2] => [3,2,2] => 7
[5,4,4] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,2,1] => [4,2,1] => 7
[5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,1,1,1] => [2,1,1,1,1] => 6
[5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => [2,2,1,1] => [2,2,1,1] => 6
[5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,1,1,1] => [2,1,1,1,1] => 6
[5,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,4,1,1] => [4,1,1,1] => 7
[5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,2,1] => [2,2,1,1] => 6
[5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,1] => [2,2,1,1] => 6
[5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,2,1,1] => [2,1,1,1,1] => 6
[5,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,3,1,1,1] => [3,1,1,1,1] => 7
[5,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,5,1,1] => [5,1,1,1] => 8
[5,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,4,1] => [4,2,1] => 7
[5,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,2,3,1] => [3,2,1,1] => 7
[5,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,4,2,1] => [4,2,1,1] => 8
[5,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [1,6,1,1] => [6,1,1,1] => 9
[5,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [1,8,1] => [8,1,1] => 10
[4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,1,3] => [3,3,1] => 7
[4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,2] => [2,2,1,1] => 6
[4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,1,2] => [2,2,1,1] => 6
[4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,2,2] => [2,2,1,1] => 6
[4,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,3,1,2] => [3,2,1,1] => 7
[4,4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,5,2] => [5,2,1] => 8
[4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,3,1] => [3,3,1] => 7
[4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,2,1] => [2,1,1,1,1] => 6
[4,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,3,2,1] => [3,2,1,1] => 7
[4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,1] => [3,2,1,1] => 7
[4,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,2,2,1,1] => [2,2,1,1,1] => 7
[4,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,4,1,1,1] => [4,1,1,1,1] => 8
[4,3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,6,1,1] => [6,1,1,1] => 9
[4,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,4,1] => [4,1,1,1] => 7
[4,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,3,3,1] => [3,3,1,1] => 8
[4,2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [1,5,2,1] => [5,2,1,1] => 9
[4,2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [1,7,1,1] => [7,1,1,1] => 10
[3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4] => [4,2,1] => 7
[3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,2,3] => [3,2,2] => 7
[3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,1,3] => [3,2,1,1] => 7
[3,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,4,3] => [4,3,1] => 8
[3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,3,2] => [3,2,1,1] => 7
[3,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,3,2,2] => [3,2,2,1] => 8
[3,3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,5,1,2] => [5,2,1,1] => 9
[3,3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [1,7,2] => [7,2,1] => 10
[3,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,5,1] => [5,2,1] => 8
[3,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,2,4,1] => [4,2,1,1] => 8
[3,2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [1,4,3,1] => [4,3,1,1] => 9
[3,2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [1,6,2,1] => [6,2,1,1] => 10
[2,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,6] => [6,1,1] => 8
[2,2,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,5] => [5,3,1] => 9
[2,2,2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,5,4] => [5,4,1] => 10
[9,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0] => [8,1,1] => [8,1,1] => 10
[9,3,2] => [1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,1,0] => [7,1,1,1] => [7,1,1,1] => 10
[9,2,2,1] => [1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,1,0] => [6,1,2,1] => [6,2,1,1] => 10
[9,1,1,1,1,1] => [1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [4,5,1] => [5,4,1] => 10
[8,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [7,1,1] => [7,1,1] => 9
[8,4,2] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0] => [6,1,1,1] => [6,1,1,1] => 9
[8,3,3] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,1,0] => [6,2,1] => [6,2,1] => 9
[8,3,2,1] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => 9
[8,2,2,1,1] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0] => [4,2,2,1] => [4,2,2,1] => 9
[8,1,1,1,1,1,1] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,6,1] => [6,2,1] => 9
[7,7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,2] => [7,2] => 9
[7,6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [5,1,1,1] => [5,1,1,1] => 8
[7,5,2] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [5,1,1,1] => [5,1,1,1] => 8
[7,5,1,1] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [4,2,1,1] => [4,2,1,1] => 8
[7,4,3] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [5,1,1,1] => [5,1,1,1] => 8
[7,4,2,1] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [4,1,1,1,1] => [4,1,1,1,1] => 8
[7,4,1,1,1] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [3,3,1,1] => [3,3,1,1] => 8
[7,3,3,1] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [4,1,2,1] => [4,2,1,1] => 8
[7,3,2,2] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [4,2,1,1] => [4,2,1,1] => 8
[7,3,2,1,1] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [3,2,1,1,1] => [3,2,1,1,1] => 8
[7,3,1,1,1,1] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [2,4,1,1] => [4,2,1,1] => 8
[7,2,2,2,1] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [3,1,3,1] => [3,3,1,1] => 8
[7,2,2,1,1,1] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [2,3,2,1] => [3,2,2,1] => 8
[7,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,5,1,1] => [5,1,1,1] => 8
[7,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,7,1] => [7,1,1] => 9
[6,6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [5,1,2] => [5,2,1] => 8
[6,6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [4,2,2] => [4,2,2] => 8
[6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,1,1,1] => [4,1,1,1] => 7
[6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,1,1,1,1] => [3,1,1,1,1] => 7
[6,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,3,1,1] => [3,2,1,1] => 7
[6,4,4] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,2,1] => [4,2,1] => 7
[6,4,3,1] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,1,1,1,1] => [3,1,1,1,1] => 7
[6,4,2,2] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,1,1] => [3,2,1,1] => 7
[6,4,2,1,1] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,2,1,1,1] => [2,2,1,1,1] => 7
[6,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,4,1,1] => [4,1,1,1] => 7
[6,3,3,2] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,1,2,1] => [3,2,1,1] => 7
[6,3,3,1,1] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,2,2,1] => [2,2,2,1] => 7
[6,3,2,2,1] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,1,2,1,1] => [2,2,1,1,1] => 7
[6,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,3,1,1,1] => [3,1,1,1,1] => 7
[6,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,5,1,1] => [5,1,1,1] => 8
[6,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,4,1] => [4,2,1] => 7
[6,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,2,3,1] => [3,2,1,1] => 7
[6,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,4,2,1] => [4,2,1,1] => 8
[6,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [1,8,1] => [8,1,1] => 10
[5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,1,2] => [4,2,1] => 7
[5,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,1,1,2] => [3,2,1,1] => 7
[5,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,2] => [3,2,2] => 7
[5,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,2,1,2] => [2,2,2,1] => 7
[5,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,4,2] => [4,2,1] => 7
[5,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,1,2,1] => [3,2,1,1] => 7
[5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1] => [2,1,1,1,1] => 6
[5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,1,1,1] => [2,1,1,1,1] => 6
[5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,2,1,1] => [2,1,1,1,1] => 6
[5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,3,1,1,1] => [3,1,1,1,1] => 7
[5,4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,5,1,1] => [5,1,1,1] => 8
[5,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,3,1] => [3,3,1] => 7
[5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,2,1] => [2,1,1,1,1] => 6
[5,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,3,2,1] => [3,2,1,1] => 7
[5,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,3,1,1] => [3,2,1,1] => 7
[5,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,2,2,1,1] => [2,2,1,1,1] => 7
[5,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,4,1,1,1] => [4,1,1,1,1] => 8
[5,3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,6,1,1] => [6,1,1,1] => 9
[5,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,4,1] => [4,1,1,1] => 7
[5,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,3,3,1] => [3,3,1,1] => 8
[4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,1,3] => [3,3,1] => 7
[4,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,2,3] => [3,2,2] => 7
[4,4,3,3] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,2] => [3,2,2] => 7
[4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,2] => [2,1,1,1,1] => 6
[4,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,3,1,2] => [3,2,1,1] => 7
[4,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,2] => [3,2,2] => 7
[4,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,2,2,2] => [2,2,2,1] => 7
[4,4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,4,1,2] => [4,2,1,1] => 8
[4,4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,6,2] => [6,2,1] => 9
[4,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,1,3,1] => [3,2,1,1] => 7
[4,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,2,2,1] => [2,2,2,1] => 7
[4,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,1,2,1] => [2,2,1,1,1] => 7
[4,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,4,2,1] => [4,2,1,1] => 8
[4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,3,1,1] => [3,1,1,1,1] => 7
[4,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,3,2,1,1] => [3,2,1,1,1] => 8
[4,3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,5,1,1,1] => [5,1,1,1,1] => 9
[4,3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [1,7,1,1] => [7,1,1,1] => 10
[4,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,5,1] => [5,2,1] => 8
[4,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,2,4,1] => [4,2,1,1] => 8
[4,2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [1,6,2,1] => [6,2,1,1] => 10
[3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,4] => [4,2,1] => 7
[3,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4] => [4,2,1] => 7
[3,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,2,3] => [3,2,1,1] => 7
[3,3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,3,1,3] => [3,3,1,1] => 8
[3,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,4,2] => [4,2,2] => 8
[3,3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,2,3,2] => [3,2,2,1] => 8
[3,3,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,4,2,2] => [4,2,2,1] => 9
[3,3,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [1,6,1,2] => [6,2,1,1] => 10
[3,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,5,1] => [5,1,1,1] => 8
[3,2,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [1,3,4,1] => [4,3,1,1] => 9
[2,2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,7] => [7,2] => 9
[2,2,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,6] => [6,2,1] => 9
[2,2,2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,4,5] => [5,4,1] => 10
[9,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0] => [8,1,1] => [8,1,1] => 10
[9,3,3] => [1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,1,0] => [7,2,1] => [7,2,1] => 10
[9,3,2,1] => [1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0] => [6,1,1,1,1] => [6,1,1,1,1] => 10
[9,2,2,2] => [1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,1,0] => [6,3,1] => [6,3,1] => 10
[9,1,1,1,1,1,1] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [3,6,1] => [6,3,1] => 10
[8,7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => 9
[8,6,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0] => [6,1,1,1] => [6,1,1,1] => 9
[8,4,2,1] => [1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => 9
[8,4,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,1,0] => [4,3,1,1] => [4,3,1,1] => 9
[8,3,3,1] => [1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,0] => [5,1,2,1] => [5,2,1,1] => 9
[8,3,2,2] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,1,0] => [5,2,1,1] => [5,2,1,1] => 9
[8,3,2,1,1] => [1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,1,0] => [4,2,1,1,1] => [4,2,1,1,1] => 9
[8,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,7,1] => [7,1,1] => 9
[7,7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [6,1,2] => [6,2,1] => 9
[7,6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [5,1,1,1] => [5,1,1,1] => 8
[7,6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [4,2,1,1] => [4,2,1,1] => 8
[7,5,3] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [5,1,1,1] => [5,1,1,1] => 8
[7,5,2,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [4,1,1,1,1] => [4,1,1,1,1] => 8
[7,5,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [3,3,1,1] => [3,3,1,1] => 8
[7,4,4] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [5,2,1] => [5,2,1] => 8
[7,4,3,1] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [4,1,1,1,1] => [4,1,1,1,1] => 8
[7,4,2,2] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [4,2,1,1] => [4,2,1,1] => 8
[7,4,2,1,1] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [3,2,1,1,1] => [3,2,1,1,1] => 8
[7,4,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [2,4,1,1] => [4,2,1,1] => 8
[7,3,3,2] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [4,1,2,1] => [4,2,1,1] => 8
[7,3,3,1,1] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [3,2,2,1] => [3,2,2,1] => 8
[7,3,2,2,1] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [3,1,2,1,1] => [3,2,1,1,1] => 8
[7,3,2,1,1,1] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,3,1,1,1] => [3,2,1,1,1] => 8
[7,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,5,1,1] => [5,1,1,1] => 8
[7,2,2,2,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,4,1] => [4,3,1] => 8
[7,2,2,2,1,1] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [2,2,3,1] => [3,2,2,1] => 8
[7,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,4,2,1] => [4,2,1,1] => 8
[7,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,6,1,1] => [6,1,1,1] => 9
[7,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [1,8,1] => [8,1,1] => 10
[6,6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [5,1,2] => [5,2,1] => 8
[6,6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [4,1,1,2] => [4,2,1,1] => 8
[6,6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [3,3,2] => [3,3,2] => 8
[6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,1,1] => [4,1,1,1] => 7
[6,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,1,1,1,1] => [3,1,1,1,1] => 7
[6,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,1,1] => [3,2,1,1] => 7
[6,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,2,1,1,1] => [2,2,1,1,1] => 7
[6,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,4,1,1] => [4,1,1,1] => 7
[6,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,1,2,1] => [3,2,1,1] => 7
[6,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,1,1,1] => [3,1,1,1,1] => 7
[6,4,3,1,1] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,2,1,1,1] => [2,2,1,1,1] => 7
[6,4,2,2,1] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,1,2,1,1] => [2,2,1,1,1] => 7
[6,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,3,1,1,1] => [3,1,1,1,1] => 7
[6,4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,5,1,1] => [5,1,1,1] => 8
[6,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,3,1] => [3,3,1] => 7
[6,3,3,2,1] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,1,1,2,1] => [2,2,1,1,1] => 7
[6,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,3,2,1] => [3,2,1,1] => 7
[6,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,3,1,1] => [3,2,1,1] => 7
[6,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,2,2,1,1] => [2,2,1,1,1] => 7
[6,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,4,1,1,1] => [4,1,1,1,1] => 8
[6,3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,6,1,1] => [6,1,1,1] => 9
[6,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,4,1] => [4,1,1,1] => 7
[6,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,3,3,1] => [3,3,1,1] => 8
[5,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,3] => [5,3] => 8
[5,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,1,1,2] => [3,2,1,1] => 7
[5,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,1,1,2] => [3,2,1,1] => 7
[5,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,2,1,2] => [2,2,2,1] => 7
[5,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,1,2,2] => [2,2,2,1] => 7
[5,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,3,1,2] => [3,2,1,1] => 7
[5,5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,5,2] => [5,2,1] => 8
[5,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,1,2,1] => [3,2,1,1] => 7
[5,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,2,2,1] => [2,2,2,1] => 7
[5,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => [3,2,1,1] => 7
[5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1] => [1,1,1,1,1,1] => 6
[5,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,3,1,1,1] => [3,1,1,1,1] => 7
[5,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,1] => [3,2,1,1] => 7
[5,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,2,2,1,1] => [2,2,1,1,1] => 7
[5,4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,4,1,1,1] => [4,1,1,1,1] => 8
[5,4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,6,1,1] => [6,1,1,1] => 9
[5,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,1,3,1] => [3,2,1,1] => 7
[5,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,2,2,1] => [2,2,2,1] => 7
[5,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,2,1,2,1] => [2,2,1,1,1] => 7
[5,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,4,2,1] => [4,2,1,1] => 8
[5,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,3,1,1] => [3,1,1,1,1] => 7
[5,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,3,2,1,1] => [3,2,1,1,1] => 8
[5,3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [1,5,1,1,1] => [5,1,1,1,1] => 9
[5,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,5,1] => [5,2,1] => 8
[5,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,2,4,1] => [4,2,1,1] => 8
[5,2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [1,4,3,1] => [4,3,1,1] => 9
[4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,3] => [3,3,1] => 7
[4,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,1,1,3] => [3,2,1,1] => 7
[4,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,3,3] => [3,3,1] => 7
[4,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,1,2,2] => [2,2,2,1] => 7
[4,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,2,1,2] => [2,2,2,1] => 7
[4,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,1,1,2] => [2,2,1,1,1] => 7
[4,4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,4,1,2] => [4,2,1,1] => 8
[4,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,3,2] => [3,2,1,1] => 7
[4,4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,3,2,2] => [3,2,2,1] => 8
[4,4,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [1,5,1,2] => [5,2,1,1] => 9
[4,4,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [1,7,2] => [7,2,1] => 10
[4,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,1] => [3,2,1,1] => 7
[4,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,3,1] => [3,2,1,1] => 7
[4,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,2,2,1] => [2,2,1,1,1] => 7
[4,3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,3,1,2,1] => [3,2,1,1,1] => 8
[4,3,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,5,2,1] => [5,2,1,1] => 9
[4,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,4,1,1] => [4,2,1,1] => 8
[4,3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,2,3,1,1] => [3,2,1,1,1] => 8
[4,3,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [1,4,2,1,1] => [4,2,1,1,1] => 9
[4,3,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [1,6,1,1,1] => [6,1,1,1,1] => 10
[4,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,5,1] => [5,1,1,1] => 8
[3,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,5] => [5,3] => 8
[3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,4] => [4,1,1,1] => 7
[3,3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,3,4] => [4,3,1] => 8
[3,3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,3] => [3,3,2] => 8
[3,3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,2,2,3] => [3,2,2,1] => 8
[3,3,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [1,4,1,3] => [4,3,1,1] => 9
[3,3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,4,2] => [4,2,1,1] => 8
[3,3,2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [1,5,2,2] => [5,2,2,1] => 10
[3,2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,6,1] => [6,2,1] => 9
[3,2,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,2,5,1] => [5,2,1,1] => 9
[2,2,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,7] => [7,1,1] => 9
[2,2,2,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,3,6] => [6,3,1] => 10
[9,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => [8,1,1] => [8,1,1] => 10
[9,1,1,1,1,1,1,1] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [2,7,1] => [7,2,1] => 10
[8,8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,2] => [8,2] => 10
[8,7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [6,1,1,1] => [6,1,1,1] => 9
[8,5,3] => [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,1,0] => [6,1,1,1] => [6,1,1,1] => 9
[8,5,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => 9
[8,3,2,1,1,1] => [1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [3,3,1,1,1] => [3,3,1,1,1] => 9
[8,2,2,1,1,1,1] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [2,4,2,1] => [4,2,2,1] => 9
[8,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,6,1,1] => [6,1,1,1] => 9
[8,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,8,1] => [8,1,1] => 10
[7,7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0] => [6,1,2] => [6,2,1] => 9
[7,7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => [5,2,2] => [5,2,2] => 9
[7,6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [5,1,1,1] => [5,1,1,1] => 8
[7,6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [4,1,1,1,1] => [4,1,1,1,1] => 8
[7,6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [3,3,1,1] => [3,3,1,1] => 8
[7,5,4] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [5,1,1,1] => [5,1,1,1] => 8
[7,5,3,1] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [4,1,1,1,1] => [4,1,1,1,1] => 8
[7,5,2,2] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [4,2,1,1] => [4,2,1,1] => 8
[7,5,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [3,2,1,1,1] => [3,2,1,1,1] => 8
[7,5,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,4,1,1] => [4,2,1,1] => 8
[7,4,4,1] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [4,1,2,1] => [4,2,1,1] => 8
[7,4,3,2] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [4,1,1,1,1] => [4,1,1,1,1] => 8
[7,4,3,1,1] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [3,2,1,1,1] => [3,2,1,1,1] => 8
[7,4,2,2,1] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [3,1,2,1,1] => [3,2,1,1,1] => 8
[7,4,2,1,1,1] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [2,3,1,1,1] => [3,2,1,1,1] => 8
[7,4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,5,1,1] => [5,1,1,1] => 8
[7,3,3,3] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [4,3,1] => [4,3,1] => 8
[7,3,3,2,1] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [3,1,1,2,1] => [3,2,1,1,1] => 8
[7,3,3,1,1,1] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,3,2,1] => [3,2,2,1] => 8
[7,3,2,2,2] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,3,1,1] => [3,3,1,1] => 8
[7,3,2,2,1,1] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [2,2,2,1,1] => [2,2,2,1,1] => 8
[7,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,4,1,1,1] => [4,1,1,1,1] => 8
[7,2,2,2,2,1] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,1,4,1] => [4,2,1,1] => 8
[7,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,3,3,1] => [3,3,1,1] => 8
[6,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,1,2] => [5,2,1] => 8
[6,6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [4,1,1,2] => [4,2,1,1] => 8
[6,6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [4,2,2] => [4,2,2] => 8
[6,6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [3,2,1,2] => [3,2,2,1] => 8
[6,6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,4,2] => [4,2,2] => 8
[6,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,2,1] => [5,2,1] => 8
[6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1,1] => [3,1,1,1,1] => 7
[6,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,1,1,1,1] => [3,1,1,1,1] => 7
[6,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,2,1,1,1] => [2,2,1,1,1] => 7
[6,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,1,2,1,1] => [2,2,1,1,1] => 7
[6,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,3,1,1,1] => [3,1,1,1,1] => 7
[6,5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,5,1,1] => [5,1,1,1] => 8
[6,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,2,1] => [3,2,1,1] => 7
[6,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,2,2,1] => [2,2,2,1] => 7
[6,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,1] => [3,2,1,1] => 7
[6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,1,1,1,1] => [2,1,1,1,1,1] => 7
[6,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,3,1,1,1] => [3,1,1,1,1] => 7
[6,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,1] => [3,2,1,1] => 7
[6,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,2,2,1,1] => [2,2,1,1,1] => 7
[6,4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,4,1,1,1] => [4,1,1,1,1] => 8
[6,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,1,3,1] => [3,2,1,1] => 7
[6,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,2,2,1] => [2,2,2,1] => 7
[6,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,2,1,2,1] => [2,2,1,1,1] => 7
[6,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,4,2,1] => [4,2,1,1] => 8
[6,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,3,1,1] => [3,1,1,1,1] => 7
[6,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,3,2,1,1] => [3,2,1,1,1] => 8
[6,3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [1,5,1,1,1] => [5,1,1,1,1] => 9
[6,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,5,1] => [5,2,1] => 8
[6,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,2,4,1] => [4,2,1,1] => 8
[5,5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [4,1,3] => [4,3,1] => 8
[5,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,1,1,2] => [3,2,1,1] => 7
[5,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,2,1,2] => [2,2,2,1] => 7
[5,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,2] => [3,2,2] => 7
[5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,1,1,1,2] => [2,2,1,1,1] => 7
[5,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,3,1,2] => [3,2,1,1] => 7
[5,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,2] => [3,2,2] => 7
[5,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,2,2,2] => [2,2,2,1] => 7
[5,5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,4,1,2] => [4,2,1,1] => 8
[5,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,2,1] => [3,2,1,1] => 7
[5,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,1,1,2,1] => [2,2,1,1,1] => 7
[5,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,3,2,1] => [3,2,1,1] => 7
[5,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,1,2,1,1] => [2,2,1,1,1] => 7
[5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,2,1,1,1] => [2,2,1,1,1] => 7
[5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,1,1,1,1] => [2,1,1,1,1,1] => 7
[5,4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,4,1,1,1] => [4,1,1,1,1] => 8
[5,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,3,1,1] => [3,1,1,1,1] => 7
[5,4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,3,2,1,1] => [3,2,1,1,1] => 8
[5,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,1] => [3,2,1,1] => 7
[5,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,3,1] => [3,2,1,1] => 7
[5,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,2,2,1] => [2,2,1,1,1] => 7
[5,3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,3,1,2,1] => [3,2,1,1,1] => 8
[5,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,4,1,1] => [4,2,1,1] => 8
[5,3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,2,3,1,1] => [3,2,1,1,1] => 8
[5,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,5,1] => [5,1,1,1] => 8
[5,2,2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [1,5,3,1] => [5,3,1,1] => 10
[4,4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4] => [4,4] => 8
[4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,1,1,3] => [3,2,1,1] => 7
[4,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,2,3] => [3,2,2] => 7
[4,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,1,3] => [3,2,1,1] => 7
[4,4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,4,3] => [4,3,1] => 8
[4,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,2,2] => [2,2,2,1] => 7
[4,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,2,2] => [2,2,2,1] => 7
[4,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,2,1,2] => [2,2,1,1,1] => 7
[4,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,3,1,1,2] => [3,2,1,1,1] => 8
[4,4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,4,2] => [4,2,2] => 8
[4,4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,2,3,2] => [3,2,2,1] => 8
[4,4,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [1,4,2,2] => [4,2,2,1] => 9
[4,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,4,1] => [4,3,1] => 8
[4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,3,1] => [3,1,1,1,1] => 7
[4,3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,3,3,1] => [3,3,1,1] => 8
[4,3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,3,2,1] => [3,2,2,1] => 8
[4,3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,2,2,2,1] => [2,2,2,1,1] => 8
[4,3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,4,1,1] => [4,1,1,1,1] => 8
[4,3,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [1,3,3,1,1] => [3,3,1,1,1] => 9
[4,2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,6,1] => [6,2,1] => 9
[4,2,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,2,5,1] => [5,2,1,1] => 9
[3,3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,5] => [5,2,1] => 8
[3,3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,4] => [4,2,2] => 8
[3,3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,2,1,4] => [4,2,1,1] => 8
[3,3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,3,3] => [3,3,1,1] => 8
[3,3,3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [1,5,1,3] => [5,3,1,1] => 10
[3,3,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,5,2] => [5,2,2] => 9
[3,2,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,6,1] => [6,1,1,1] => 9
[2,2,2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,8] => [8,2] => 10
[2,2,2,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,7] => [7,2,1] => 10
[9,8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [8,1,1] => [8,1,1] => 10
[9,7,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,1,0] => [7,1,1,1] => [7,1,1,1] => 10
[9,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,8,1] => [8,1,1] => 10
[8,8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0] => [7,1,2] => [7,2,1] => 10
[8,7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0] => [6,1,1,1] => [6,1,1,1] => 9
[8,7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0] => [5,2,1,1] => [5,2,1,1] => 9
[8,6,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => 9
[8,5,4] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,0] => [6,1,1,1] => [6,1,1,1] => 9
[8,5,1,1,1,1] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [3,4,1,1] => [4,3,1,1] => 9
[8,4,3,2] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => 9
[8,3,3,3] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,1,0] => [5,3,1] => [5,3,1] => 9
[8,3,3,2,1] => [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0] => [4,1,1,2,1] => [4,2,1,1,1] => 9
[8,3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,6,1,1] => [6,1,1,1] => 9
[8,2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,5,2,1] => [5,2,1,1] => 9
[7,7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,1,0,0] => [6,1,2] => [6,2,1] => 9
[7,7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0] => [5,1,1,2] => [5,2,1,1] => 9
[7,7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,1,0,0] => [4,3,2] => [4,3,2] => 9
[7,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [5,1,1,1] => [5,1,1,1] => 8
[7,6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [4,1,1,1,1] => [4,1,1,1,1] => 8
[7,6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [4,2,1,1] => [4,2,1,1] => 8
[7,6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [3,2,1,1,1] => [3,2,1,1,1] => 8
[7,6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,4,1,1] => [4,2,1,1] => 8
[7,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,2,1] => [5,2,1] => 8
[7,5,4,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [4,1,1,1,1] => [4,1,1,1,1] => 8
[7,5,3,2] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [4,1,1,1,1] => [4,1,1,1,1] => 8
[7,5,3,1,1] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [3,2,1,1,1] => [3,2,1,1,1] => 8
[7,5,2,2,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [3,1,2,1,1] => [3,2,1,1,1] => 8
[7,5,2,1,1,1] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [2,3,1,1,1] => [3,2,1,1,1] => 8
[7,5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,5,1,1] => [5,1,1,1] => 8
[7,4,4,2] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [4,1,2,1] => [4,2,1,1] => 8
[7,4,4,1,1] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [3,2,2,1] => [3,2,2,1] => 8
[7,4,3,3] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [4,2,1,1] => [4,2,1,1] => 8
[7,4,3,2,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,1,1,1,1,1] => [3,1,1,1,1,1] => 8
[7,4,3,1,1,1] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,3,1,1,1] => [3,2,1,1,1] => 8
[7,4,2,2,2] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [3,3,1,1] => [3,3,1,1] => 8
[7,4,2,2,1,1] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [2,2,2,1,1] => [2,2,2,1,1] => 8
[7,4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,4,1,1,1] => [4,1,1,1,1] => 8
[7,3,3,3,1] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [3,1,3,1] => [3,3,1,1] => 8
[7,3,3,2,2] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [3,2,2,1] => [3,2,2,1] => 8
[7,3,3,2,1,1] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [2,2,1,2,1] => [2,2,2,1,1] => 8
[7,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,4,2,1] => [4,2,1,1] => 8
[7,3,2,2,2,1] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,1,3,1,1] => [3,2,1,1,1] => 8
[7,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,3,2,1,1] => [3,2,1,1,1] => 8
[7,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,5,1] => [5,2,1] => 8
[7,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,2,4,1] => [4,2,1,1] => 8
[6,6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,1,2] => [5,2,1] => 8
[6,6,4,1] => [1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [4,1,1,2] => [4,2,1,1] => 8
[6,6,3,2] => [1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [4,1,1,2] => [4,2,1,1] => 8
[6,6,3,1,1] => [1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [3,2,1,2] => [3,2,2,1] => 8
[6,6,2,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [3,1,2,2] => [3,2,2,1] => 8
[6,6,2,1,1,1] => [1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [2,3,1,2] => [3,2,2,1] => 8
[6,6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,5,2] => [5,2,1] => 8
[6,5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [4,1,2,1] => [4,2,1,1] => 8
[6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1,1] => [3,1,1,1,1] => 7
[6,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,2,1,1,1] => [2,2,1,1,1] => 7
[6,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,1] => [3,2,1,1] => 7
[6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,1,1,1,1,1] => [2,1,1,1,1,1] => 7
[6,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,3,1,1,1] => [3,1,1,1,1] => 7
[6,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,1] => [3,2,1,1] => 7
[6,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,2,2,1,1] => [2,2,1,1,1] => 7
[6,5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,4,1,1,1] => [4,1,1,1,1] => 8
[6,5,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,6,1,1] => [6,1,1,1] => 9
[6,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,1,2,1] => [3,2,1,1] => 7
[6,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,1,1,2,1] => [2,2,1,1,1] => 7
[6,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,3,2,1] => [3,2,1,1] => 7
[6,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,1,2,1,1] => [2,2,1,1,1] => 7
[6,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,2,1,1,1] => [2,2,1,1,1] => 7
[6,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,2,1,1,1,1] => [2,1,1,1,1,1] => 7
[6,4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,4,1,1,1] => [4,1,1,1,1] => 8
[6,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,3,1,1] => [3,1,1,1,1] => 7
[6,4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,3,2,1,1] => [3,2,1,1,1] => 8
[6,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,1] => [3,2,1,1] => 7
[6,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,3,1] => [3,2,1,1] => 7
[6,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,2,2,1] => [2,2,1,1,1] => 7
[6,3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,3,1,2,1] => [3,2,1,1,1] => 8
[6,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,4,1,1] => [4,2,1,1] => 8
[6,3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,2,3,1,1] => [3,2,1,1,1] => 8
[6,3,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [1,4,2,1,1] => [4,2,1,1,1] => 9
[6,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,5,1] => [5,1,1,1] => 8
[6,2,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [1,3,4,1] => [4,3,1,1] => 9
[5,5,5,2] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [4,1,3] => [4,3,1] => 8
[5,5,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [3,2,3] => [3,3,2] => 8
[5,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,1,2] => [3,2,1,1] => 7
[5,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,1,1,1,2] => [2,2,1,1,1] => 7
[5,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,3,1,2] => [3,2,1,1] => 7
[5,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,1,2,2] => [2,2,2,1] => 7
[5,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,2,1,2] => [2,2,2,1] => 7
[5,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,2,1,1,2] => [2,2,1,1,1] => 7
[5,5,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,4,1,2] => [4,2,1,1] => 8
[5,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,3,2] => [3,2,1,1] => 7
[5,5,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,3,2,2] => [3,2,2,1] => 8
[5,4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,1] => [4,3,1] => 8
[5,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,1,1,2,1] => [2,2,1,1,1] => 7
[5,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,2,2,1] => [2,2,2,1] => 7
[5,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,1,2,1] => [2,2,1,1,1] => 7
[5,4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,4,2,1] => [4,2,1,1] => 8
[5,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,2,1,1] => [2,2,1,1,1] => 7
[5,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,2,1,1] => [2,2,1,1,1] => 7
[5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,2,1,1,1] => [2,1,1,1,1,1] => 7
[5,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,3,1,1,1,1] => [3,1,1,1,1,1] => 8
[5,4,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,5,1,1,1] => [5,1,1,1,1] => 9
[5,4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,4,1,1] => [4,2,1,1] => 8
[5,4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,2,3,1,1] => [3,2,1,1,1] => 8
[5,4,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [1,4,2,1,1] => [4,2,1,1,1] => 9
[5,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,4,1] => [4,3,1] => 8
[5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,3,1] => [3,1,1,1,1] => 7
[5,3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,3,3,1] => [3,3,1,1] => 8
[5,3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,3,2,1] => [3,2,2,1] => 8
[5,3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,2,2,2,1] => [2,2,2,1,1] => 8
[5,3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,4,1,1] => [4,1,1,1,1] => 8
[4,4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,4] => [4,3,1] => 8
[4,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,3] => [3,2,1,1] => 7
[4,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,1,3] => [3,2,1,1] => 7
[4,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,2,3] => [3,2,1,1] => 7
[4,4,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,3,1,3] => [3,3,1,1] => 8
[4,4,4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,5,3] => [5,3,1] => 9
[4,4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2] => [3,3,2] => 8
[4,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,2,2] => [2,2,1,1,1] => 7
[4,4,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,3,2,2] => [3,2,2,1] => 8
[4,4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,3,1,2] => [3,2,2,1] => 8
[4,4,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,2,2,1,2] => [2,2,2,1,1] => 8
[4,4,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,4,1,1,2] => [4,2,1,1,1] => 9
[4,4,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,4,2] => [4,2,1,1] => 8
[4,3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,4,1] => [4,2,1,1] => 8
[4,3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,2,3,1] => [3,2,2,1] => 8
[4,3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,2,1,3,1] => [3,2,1,1,1] => 8
[4,3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,3,2,1] => [3,2,1,1,1] => 8
[4,3,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,5,1,1] => [5,2,1,1] => 9
[4,3,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,2,4,1,1] => [4,2,1,1,1] => 9
[4,2,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,6,1] => [6,1,1,1] => 9
[3,3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,5] => [5,2,1] => 8
[3,3,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,5] => [5,2,1] => 8
[3,3,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,2,4] => [4,2,1,1] => 8
[3,3,3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [1,3,1,4] => [4,3,1,1] => 9
[3,3,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,4,3] => [4,3,2] => 9
[3,3,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,5,2] => [5,2,1,1] => 9
[3,2,2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,7,1] => [7,2,1] => 10
[3,2,2,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,2,6,1] => [6,2,1,1] => 10
[2,2,2,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,8] => [8,1,1] => 10
[6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 7
[5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,2] => [2,1,1,1,1,1] => 7
[6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,2,1] => [2,1,1,1,1,1] => 7
[5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,2,1] => [2,1,1,1,1,1] => 7
[4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,3] => [3,1,1,1,1] => 7
[6,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,2,1,1] => [2,1,1,1,1,1] => 7
[5,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,2,2] => [2,2,1,1,1] => 7
[6,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,2,1,1] => [2,1,1,1,1,1] => 7
[5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,2,1,1] => [2,1,1,1,1,1] => 7
[6,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,3,1] => [3,1,1,1,1] => 7
[6,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,2,1,1,1] => [2,1,1,1,1,1] => 7
[5,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,2,1,2] => [2,2,1,1,1] => 7
[6,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,2,2,1] => [2,2,1,1,1] => 7
[5,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,2,2,1] => [2,2,1,1,1] => 7
[6,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,2,1,1,1] => [2,1,1,1,1,1] => 7
[5,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,2,1,2] => [2,2,1,1,1] => 7
[6,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,2,1,1,1] => [2,1,1,1,1,1] => 7
[6,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,3,1,1] => [3,1,1,1,1] => 7
[6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1] => [2,1,1,1,1,1] => 7
[5,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,1,1,2] => [2,2,1,1,1] => 7
[6,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,1,2,1] => [2,2,1,1,1] => 7
[5,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,1,2,1] => [2,2,1,1,1] => 7
[6,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,2,1,1] => [2,2,1,1,1] => 7
[5,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,2,2] => [2,2,2,1] => 7
[6,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,2,1,1] => [2,2,1,1,1] => 7
[6,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,2,1,1,1,1] => [2,1,1,1,1,1] => 7
[5,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,2,1,1,2] => [2,2,1,1,1] => 7
[6,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,2,1,2,1] => [2,2,1,1,1] => 7
[6,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,1,1,1,1] => [2,1,1,1,1,1] => 7
[6,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,3,1,1,1] => [3,1,1,1,1] => 7
[6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1] => [2,1,1,1,1,1] => 7
[5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,2] => [2,2,1,1,1] => 7
[6,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,2,1] => [2,2,1,1,1] => 7
[5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,2,1] => [2,2,1,1,1] => 7
[6,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,2,1,1] => [2,2,1,1,1] => 7
[5,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,2,2] => [2,2,2,1] => 7
[6,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,2,1,1] => [2,2,1,1,1] => 7
[6,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,2,1,1,1] => [2,2,1,1,1] => 7
[5,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,2,1,2] => [2,2,2,1] => 7
[6,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,2,2,1] => [2,2,2,1] => 7
[6,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,2,1,1,1] => [2,2,1,1,1] => 7
[6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1] => [2,1,1,1,1,1] => 7
[5,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,1,2] => [2,2,1,1,1] => 7
[6,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,1,1,2,1] => [2,2,1,1,1] => 7
[6,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,1,2,1,1] => [2,2,1,1,1] => 7
[6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,1,1,1,1,1] => [2,1,1,1,1,1] => 7
[6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1] => [3,1,1,1,1] => 7
[7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 8
[6,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,2] => [2,1,1,1,1,1,1] => 8
[7,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,2,1] => [2,1,1,1,1,1,1] => 8
[6,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,2,1] => [2,1,1,1,1,1,1] => 8
[5,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,3] => [3,1,1,1,1,1] => 8
[7,6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,2,1,1] => [2,1,1,1,1,1,1] => 8
[6,6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,2,2] => [2,2,1,1,1,1] => 8
[7,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,2,1,1] => [2,1,1,1,1,1,1] => 8
[6,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,2,1,1] => [2,1,1,1,1,1,1] => 8
[5,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,2,2] => [2,2,1,1,1,1] => 8
[7,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,3,1] => [3,1,1,1,1,1] => 8
[6,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,3,1] => [3,1,1,1,1,1] => 8
[5,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,3,1] => [3,1,1,1,1,1] => 8
[4,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,4] => [4,1,1,1,1] => 8
[6,6,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,2,1,2] => [2,2,1,1,1,1] => 8
[6,5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,2,1,1,1] => [2,1,1,1,1,1,1] => 8
[6,5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,3,1,1] => [3,1,1,1,1,1] => 8
[6,4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,3,1,1] => [3,1,1,1,1,1] => 8
[5,4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,3,1,1] => [3,1,1,1,1,1] => 8
[6,3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,4,1] => [4,1,1,1,1] => 8
[3,3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,5] => [5,1,1,1] => 8
[6,6,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,2,1,1,2] => [2,2,1,1,1,1] => 8
[6,5,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,2,1,2,1] => [2,2,1,1,1,1] => 8
[6,5,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,2,2,1,1] => [2,2,1,1,1,1] => 8
[6,5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,2,1,1,1,1] => [2,1,1,1,1,1,1] => 8
[5,5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,2,1,1,2] => [2,2,1,1,1,1] => 8
[7,6,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,3,1,1,1] => [3,1,1,1,1,1] => 8
[6,5,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,3,1,1,1] => [3,1,1,1,1,1] => 8
[6,5,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,3,1,1,1] => [3,1,1,1,1,1] => 8
[6,4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,3,1,1,1] => [3,1,1,1,1,1] => 8
[5,4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,3,1,1,1] => [3,1,1,1,1,1] => 8
[6,5,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,4,1,1] => [4,1,1,1,1] => 8
[7,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,5,1] => [5,1,1,1] => 8
[7,6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1] => [2,1,1,1,1,1,1] => 8
[6,6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,2,1,1,1,2] => [2,2,1,1,1,1] => 8
[6,5,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,2,1,1,2,1] => [2,2,1,1,1,1] => 8
[6,6,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,2,1,1,1,2] => [2,2,1,1,1,1] => 8
[6,5,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,2,1,1,2,1] => [2,2,1,1,1,1] => 8
[4,4,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,2,1,4] => [4,2,1,1] => 8
[6,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,1,1,1,1,1] => [2,1,1,1,1,1,1] => 8
[5,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,2,1,1,1,2] => [2,2,1,1,1,1] => 8
[7,6,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,3,1,1,1,1] => [3,1,1,1,1,1] => 8
[6,5,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,3,1,2,1] => [3,2,1,1,1] => 8
[6,5,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,3,1,1,1,1] => [3,1,1,1,1,1] => 8
[7,6,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,3,1,1,1,1] => [3,1,1,1,1,1] => 8
[5,5,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,3,1,3] => [3,3,1,1] => 8
[7,5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,3,1,1,1,1] => [3,1,1,1,1,1] => 8
[6,5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,3,1,1,1,1] => [3,1,1,1,1,1] => 8
[7,6,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,3,1,1,1,1] => [3,1,1,1,1,1] => 8
[7,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,3,1,1,1,1] => [3,1,1,1,1,1] => 8
[6,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,3,1,1,1,1] => [3,1,1,1,1,1] => 8
[6,5,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,4,1,1,1] => [4,1,1,1,1] => 8
[6,6,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,4,1,2] => [4,2,1,1] => 8
[7,6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,5,1,1] => [5,1,1,1] => 8
[7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 8
[6,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,2] => [2,2,1,1,1,1] => 8
[7,5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,2,1] => [2,2,1,1,1,1] => 8
[6,5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,2,1] => [2,2,1,1,1,1] => 8
[5,5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,1,3] => [3,2,1,1,1] => 8
[7,6,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,1,2,1,1] => [2,2,1,1,1,1] => 8
[6,5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,1,2,1,1] => [2,2,1,1,1,1] => 8
[6,5,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,2,1,1,1] => [2,2,1,1,1,1] => 8
[5,4,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,1,1] => [3,2,1,1,1] => 8
[4,3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,4,1] => [4,2,1,1] => 8
[6,5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,2,1,1,1,1] => [2,2,1,1,1,1] => 8
[4,4,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,2,1,3] => [3,2,2,1] => 8
[7,6,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,1,1,1] => [3,2,1,1,1] => 8
[6,5,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,3,1,1,1] => [3,2,1,1,1] => 8
[5,4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,3,1,1,1] => [3,2,1,1,1] => 8
[6,6,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,4,2] => [4,2,2] => 8
[7,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 8
[6,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,2] => [2,2,1,1,1,1] => 8
[6,5,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,2,1] => [2,2,1,1,1,1] => 8
[4,4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,1,4] => [4,2,1,1] => 8
[7,6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 8
[5,5,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,1,1,1,3] => [3,2,1,1,1] => 8
[4,4,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,1,1,4] => [4,2,1,1] => 8
[7,6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 8
[6,6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,1,1,1,1,2] => [2,2,1,1,1,1] => 8
[5,5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,1,1,1,3] => [3,2,1,1,1] => 8
[7,6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 8
[6,6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,1,1,1,1,2] => [2,2,1,1,1,1] => 8
[7,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 8
[7,6,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,1,2,1,1,1] => [2,2,1,1,1,1] => 8
[7,6,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => [2,2,1,1,1,1] => 8
[7,6,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,2,1,1,1,1] => [2,2,1,1,1,1] => 8
[7,4,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,2,1,1,1,1] => [2,2,1,1,1,1] => 8
[7,6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => [3,1,1,1,1,1] => 8
[6,6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,1,1,2] => [3,2,1,1,1] => 8
[6,5,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,1,2,1] => [3,2,1,1,1] => 8
[5,4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,1,3,1] => [3,3,1,1] => 8
[5,4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,3,1,1] => [3,3,1,1] => 8
[7,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,4,1] => [4,3,1] => 8
[7,6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => [3,1,1,1,1,1] => 8
[4,4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,1,4] => [4,3,1] => 8
[7,6,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => [3,1,1,1,1,1] => 8
[7,6,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [3,1,1,1,1,1] => [3,1,1,1,1,1] => 8
[7,5,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,1,1,1,1] => [3,1,1,1,1,1] => 8
[7,6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => [3,1,1,1,1,1] => 8
[7,5,4,3,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,1,1,1,1] => [3,1,1,1,1,1] => 8
[7,6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => [3,1,1,1,1,1] => 8
[6,6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [3,1,1,1,2] => [3,2,1,1,1] => 8
[7,6,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [3,1,1,1,1,1] => [3,1,1,1,1,1] => 8
[6,6,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [3,1,1,1,2] => [3,2,1,1,1] => 8
[7,5,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [3,1,1,1,1,1] => [3,1,1,1,1,1] => 8
[7,6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [3,1,1,1,1,1] => [3,1,1,1,1,1] => 8
[6,6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [3,1,1,1,2] => [3,2,1,1,1] => 8
[7,6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1] => [4,1,1,1,1] => 8
[6,5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,1,2,1] => [4,2,1,1] => 8
[7,6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,1,1,1,1] => [4,1,1,1,1] => 8
[7,6,4,3] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [4,1,1,1,1] => [4,1,1,1,1] => 8
[7,5,4,3] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,1,1,1,1] => [4,1,1,1,1] => 8
[7,6,5,2] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [4,1,1,1,1] => [4,1,1,1,1] => 8
[7,6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => [5,1,1,1] => 8
[3,3,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,6] => [6,3] => 9
[3,3,3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,6] => [6,2,1] => 9
[3,3,3,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,7] => [7,3] => 10
[3,3,3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,5] => [5,2,2] => 9
[4,3,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,5,1] => [5,3,1] => 9
[4,4,4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5] => [5,4] => 9
[4,4,4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3] => [3,3,3] => 9
[4,4,4,4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,6] => [6,4] => 10
[5,5,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,4] => [5,4] => 9
[6,6,6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,4] => [6,4] => 10
[6,2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,6,1] => [6,2,1] => 9
[6,6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,3] => [6,3] => 9
[7,6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [6,2,1] => [6,2,1] => 9
[8,2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,6,1] => [6,2,1] => 9
[8,6,4,2] => [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => 9
[8,7,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => [6,1,1,1] => 9
[9,8,7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [7,1,1,1] => [7,1,1,1] => 10
[7,7,7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [7,3] => [7,3] => 10
[9,7,5,3,1] => [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [5,1,1,1,1,1] => [5,1,1,1,1,1] => 10
[8,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 9
[7,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1] => 9
[7,6,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1] => 9
[7,6,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,2,1,1] => [2,1,1,1,1,1,1,1] => 9
[7,6,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1] => 9
[7,6,5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,2,1,1,1,1] => [2,1,1,1,1,1,1,1] => 9
[7,6,5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 9
[7,6,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 9
[9,8,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 10
[8,8,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1,1] => 10
[6,6,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,3] => [3,1,1,1,1,1,1] => 9
[8,7,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1,1] => 10
[7,5,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,3,1] => [3,1,1,1,1,1,1] => 9
[8,7,6,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,2,1,1] => [2,1,1,1,1,1,1,1,1] => 10
[7,6,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,3,1,1] => [3,1,1,1,1,1,1] => 9
[8,7,6,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1,1] => 10
[7,6,5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,3,1,1,1] => [3,1,1,1,1,1,1] => 9
[8,7,6,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,2,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 10
[7,6,5,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,3,1,1,1,1] => [3,1,1,1,1,1,1] => 9
[8,7,6,5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 10
[7,6,5,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,1,1,1,1,1] => [3,1,1,1,1,1,1] => 9
[8,7,6,5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 10
[8,7,6,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 10
[8,7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 9
[8,7,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 9
[8,7,6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 9
[8,7,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 9
[8,6,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 9
[9,8,7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 10
[8,7,6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 9
[8,7,6,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 9
[9,7,6,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 10
[5,5,5,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,5] => [5,5] => 10
[7,7,1,1,1,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [3,4,2] => [4,3,2] => 9
[8,5,4,3,2,1] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 9
[8,7,4,3,2,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 9
[7,7,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,6,2] => [6,2,1] => 9
[5,4,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,4,1,1,1,1] => [4,1,1,1,1,1] => 9
[6,5,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,3,1,1,1,1,1] => [3,1,1,1,1,1,1] => 9
[5,4,3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,5,1,1,1,1] => [5,1,1,1,1,1] => 10
[6,5,4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,4,1,1,1,1] => [4,1,1,1,1,1] => 9
[6,5,4,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,4,1,1,1,1,1] => [4,1,1,1,1,1,1] => 10
[7,6,5,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 10
[8,6,5,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 9
[7,5,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,3,1,1,1,1,1] => [3,1,1,1,1,1,1] => 9
[7,6,4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,3,1,1,1,1] => [3,1,1,1,1,1,1] => 9
[7,6,5,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,2,1,2,1,1] => [2,2,1,1,1,1,1] => 9
[7,6,6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,1,1,1,2,1] => [2,2,1,1,1,1,1] => 9
[7,7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,1,2] => [2,2,1,1,1,1,1] => 9
[6,6,6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,1,1,1,1,3] => [3,2,1,1,1,1] => 9
[5,5,5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,1,1,1,4] => [4,2,1,1,1] => 9
[6,5,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,3,1] => [3,1,1,1,1,1,1] => 9
[5,4,4,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,4,1] => [4,2,1,1,1] => 9
[6,5,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,3,1,1] => [3,1,1,1,1,1,1] => 9
[5,4,3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,4,1,1] => [4,2,1,1,1] => 9
[6,5,4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,3,1,1,1] => [3,1,1,1,1,1,1] => 9
[5,4,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,4,1,1,1] => [4,2,1,1,1] => 9
[6,5,4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,3,1,1,1,1] => [3,1,1,1,1,1,1] => 9
[6,5,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [5,3,1] => [5,3,1] => 9
[5,4,4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,4,1] => [4,4,1] => 9
[8,7,6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 9
[8,7,6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 9
[8,7,6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 9
[7,6,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,1,2,1] => [2,2,1,1,1,1,1] => 9
[8,7,7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1] => 10
[7,6,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,1,2,1] => [2,2,1,1,1,1,1] => 9
[7,7,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,1,2] => [2,2,1,1,1,1,1] => 9
[7,7,6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,1,1,1,1,2] => [2,2,1,1,1,1,1] => 9
[8,8,7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => 10
[8,7,6,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 9
[8,7,6,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 9
[8,7,6,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,2,1,1,1,1] => [2,1,1,1,1,1,1,1] => 9
[9,8,7,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1,1] => 10
[9,8,6,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1,1] => 10
[9,7,6,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1,1] => 10
[7,7,6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,1,2] => [2,2,1,1,1,1,1] => 9
[8,7,6,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 9
[8,7,6,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,2,1,1,1,1] => [2,2,1,1,1,1,1] => 9
[8,7,6,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 9
[8,7,6,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,1,1,1,1,1] => [3,1,1,1,1,1,1] => 9
[9,8,7,6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 10
[8,6,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,1,2,1] => [2,2,1,1,1,1,1] => 9
[8,7,6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => 9
[8,7,6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => 9
[8,7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [6,1,1,1] => [6,1,1,1] => 9
[9,8,7,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,1,1,1,1] => [6,1,1,1,1] => 10
[8,7,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => 9
[9,8,7,6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1,1] => [5,1,1,1,1,1] => 10
[8,7,6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => 9
[9,8,7,6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => 10
[8,7,6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 9
[4,4,4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,5] => [5,3,1] => 9
[5,5,5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,4] => [4,4,1] => 9
[6,6,6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => [5,1,3] => [5,3,1] => 9
[7,7,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,1,2,2] => [2,2,1,1,1,1,1] => 9
[7,7,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,1,1,1,1,1,2] => [2,2,1,1,1,1,1] => 9
[6,6,6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => [4,2,3] => [4,3,2] => 9
[7,7,4,3,2,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [3,1,1,1,1,2] => [3,2,1,1,1,1] => 9
[6,5,4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,1,1,1,1] => [3,2,1,1,1,1] => 9
[8,5,4,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 9
[6,6,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,2,1,1,1,1,2] => [2,2,1,1,1,1,1] => 9
[7,6,5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 9
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,2 3,2 3,2,2 1,6,2,2 7,4,2,2 6,8,4,2,2 4,12,6,4,2,2
$F_{1} = q^{2}$
$F_{2} = 2\ q^{3}$
$F_{3} = q^{3} + 2\ q^{4}$
$F_{4} = 3\ q^{4} + 2\ q^{5}$
$F_{5} = 3\ q^{4} + 2\ q^{5} + 2\ q^{6}$
$F_{6} = q^{4} + 6\ q^{5} + 2\ q^{6} + 2\ q^{7}$
$F_{7} = 7\ q^{5} + 4\ q^{6} + 2\ q^{7} + 2\ q^{8}$
$F_{8} = 6\ q^{5} + 8\ q^{6} + 4\ q^{7} + 2\ q^{8} + 2\ q^{9}$
$F_{9} = 4\ q^{5} + 12\ q^{6} + 6\ q^{7} + 4\ q^{8} + 2\ q^{9} + 2\ q^{10}$
Description
The size of a partition.
This statistic is the constant statistic of the level sets.
This statistic is the constant statistic of the level sets.
Map
to partition
Description
Sends a composition to the partition obtained by sorting the entries.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.
Map
rise composition
Description
Send a Dyck path to the composition of sizes of its rises.
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