Identifier
-
Mp00039:
Integer compositions
—complement⟶
Integer compositions
Mp00040: Integer compositions —to partition⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
St000676: Dyck paths ⟶ ℤ
Values
[1] => [1] => [1] => [1,0] => 1
[1,1] => [2] => [2] => [1,0,1,0] => 2
[2] => [1,1] => [1,1] => [1,1,0,0] => 1
[1,1,1] => [3] => [3] => [1,0,1,0,1,0] => 3
[1,2] => [2,1] => [2,1] => [1,0,1,1,0,0] => 2
[2,1] => [1,2] => [2,1] => [1,0,1,1,0,0] => 2
[3] => [1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1
[1,1,1,1] => [4] => [4] => [1,0,1,0,1,0,1,0] => 4
[1,1,2] => [3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 3
[1,2,1] => [2,2] => [2,2] => [1,1,1,0,0,0] => 2
[1,3] => [2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 2
[2,1,1] => [1,3] => [3,1] => [1,0,1,0,1,1,0,0] => 3
[2,2] => [1,2,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 2
[3,1] => [1,1,2] => [2,1,1] => [1,0,1,1,0,1,0,0] => 2
[4] => [1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1
[1,1,1,1,1] => [5] => [5] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,2] => [4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 4
[1,1,2,1] => [3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 3
[1,1,3] => [3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 3
[1,2,1,1] => [2,3] => [3,2] => [1,0,1,1,1,0,0,0] => 3
[1,2,2] => [2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 2
[1,3,1] => [2,1,2] => [2,2,1] => [1,1,1,0,0,1,0,0] => 2
[1,4] => [2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 2
[2,1,1,1] => [1,4] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 4
[2,1,2] => [1,3,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 3
[2,2,1] => [1,2,2] => [2,2,1] => [1,1,1,0,0,1,0,0] => 2
[2,3] => [1,2,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 2
[3,1,1] => [1,1,3] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 3
[3,2] => [1,1,2,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 2
[4,1] => [1,1,1,2] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 2
[5] => [1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1] => [6] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,1,1,1,2] => [5,1] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 5
[1,1,1,2,1] => [4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 4
[1,1,1,3] => [4,1,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,2,1,1] => [3,3] => [3,3] => [1,1,1,0,1,0,0,0] => 3
[1,1,2,2] => [3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[1,1,3,1] => [3,1,2] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[1,1,4] => [3,1,1,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,2,1,1,1] => [2,4] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 4
[1,2,1,2] => [2,3,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[1,2,2,1] => [2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => 2
[1,2,3] => [2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 2
[1,3,1,1] => [2,1,3] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[1,3,2] => [2,1,2,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 2
[1,4,1] => [2,1,1,2] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 2
[1,5] => [2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 2
[2,1,1,1,1] => [1,5] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 5
[2,1,1,2] => [1,4,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[2,1,2,1] => [1,3,2] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[2,1,3] => [1,3,1,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[2,2,1,1] => [1,2,3] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[2,2,2] => [1,2,2,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 2
[2,3,1] => [1,2,1,2] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 2
[2,4] => [1,2,1,1,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 2
[3,1,1,1] => [1,1,4] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[3,1,2] => [1,1,3,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[3,2,1] => [1,1,2,2] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 2
[3,3] => [1,1,2,1,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 2
[4,1,1] => [1,1,1,3] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[4,2] => [1,1,1,2,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 2
[5,1] => [1,1,1,1,2] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 2
[6] => [1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1] => [7] => [7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,1,1,1,1,2] => [6,1] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6
[1,1,1,1,2,1] => [5,2] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 5
[1,1,1,1,3] => [5,1,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,1,1,2,1,1] => [4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 4
[1,1,1,2,2] => [4,2,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,1,1,3,1] => [4,1,2] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,1,1,4] => [4,1,1,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,2,1,1,1] => [3,4] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 4
[1,1,2,1,2] => [3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 3
[1,1,2,2,1] => [3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 3
[1,1,2,3] => [3,2,1,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,3,1,1] => [3,1,3] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 3
[1,1,3,2] => [3,1,2,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,4,1] => [3,1,1,2] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,5] => [3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,2,1,1,1,1] => [2,5] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 5
[1,2,1,1,2] => [2,4,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,2,1,2,1] => [2,3,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 3
[1,2,1,3] => [2,3,1,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,2,2,1,1] => [2,2,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 3
[1,2,2,2] => [2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 2
[1,2,3,1] => [2,2,1,2] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 2
[1,2,4] => [2,2,1,1,1] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,3,1,1,1] => [2,1,4] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,3,1,2] => [2,1,3,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,3,2,1] => [2,1,2,2] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 2
[1,3,3] => [2,1,2,1,1] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,4,1,1] => [2,1,1,3] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,4,2] => [2,1,1,2,1] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,5,1] => [2,1,1,1,2] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,6] => [2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[2,1,1,1,1,1] => [1,6] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6
[2,1,1,1,2] => [1,5,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[2,1,1,2,1] => [1,4,2] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[2,1,1,3] => [1,4,1,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[2,1,2,1,1] => [1,3,3] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 3
[2,1,2,2] => [1,3,2,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
>>> Load all 880 entries. <<<[2,1,3,1] => [1,3,1,2] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[2,1,4] => [1,3,1,1,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[2,2,1,1,1] => [1,2,4] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[2,2,1,2] => [1,2,3,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[2,2,2,1] => [1,2,2,2] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 2
[2,2,3] => [1,2,2,1,1] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[2,3,1,1] => [1,2,1,3] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[2,3,2] => [1,2,1,2,1] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[2,4,1] => [1,2,1,1,2] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[2,5] => [1,2,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[3,1,1,1,1] => [1,1,5] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[3,1,1,2] => [1,1,4,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[3,1,2,1] => [1,1,3,2] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[3,1,3] => [1,1,3,1,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[3,2,1,1] => [1,1,2,3] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[3,2,2] => [1,1,2,2,1] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[3,3,1] => [1,1,2,1,2] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[3,4] => [1,1,2,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[4,1,1,1] => [1,1,1,4] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[4,1,2] => [1,1,1,3,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[4,2,1] => [1,1,1,2,2] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[4,3] => [1,1,1,2,1,1] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[5,1,1] => [1,1,1,1,3] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[5,2] => [1,1,1,1,2,1] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[6,1] => [1,1,1,1,1,2] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[7] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,1] => [8] => [8] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 8
[1,1,1,1,1,1,2] => [7,1] => [7,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 7
[1,1,1,1,1,2,1] => [6,2] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 6
[1,1,1,1,1,3] => [6,1,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,1,2,1,1] => [5,3] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 5
[1,1,1,1,2,2] => [5,2,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,1,3,1] => [5,1,2] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,1,4] => [5,1,1,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,2,1,1,1] => [4,4] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,2,1,2] => [4,3,1] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,1,1,2,2,1] => [4,2,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[1,1,1,2,3] => [4,2,1,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,3,1,1] => [4,1,3] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,1,1,3,2] => [4,1,2,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,4,1] => [4,1,1,2] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,5] => [4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,2,1,1,1,1] => [3,5] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 5
[1,1,2,1,1,2] => [3,4,1] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,1,2,1,2,1] => [3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 3
[1,1,2,1,3] => [3,3,1,1] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,2,2,1,1] => [3,2,3] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 3
[1,1,2,2,2] => [3,2,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,2,3,1] => [3,2,1,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,2,4] => [3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,3,1,1,1] => [3,1,4] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,1,3,1,2] => [3,1,3,1] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,3,2,1] => [3,1,2,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,1,3,3] => [3,1,2,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,4,1,1] => [3,1,1,3] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,4,2] => [3,1,1,2,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,5,1] => [3,1,1,1,2] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,6] => [3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,2,1,1,1,1,1] => [2,6] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 6
[1,2,1,1,1,2] => [2,5,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,2,1,1,2,1] => [2,4,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[1,2,1,1,3] => [2,4,1,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,2,1,2,1,1] => [2,3,3] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 3
[1,2,1,2,2] => [2,3,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,2,1,3,1] => [2,3,1,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,2,1,4] => [2,3,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,2,2,1,1,1] => [2,2,4] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[1,2,2,1,2] => [2,2,3,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,2,2,2,1] => [2,2,2,2] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 2
[1,2,2,3] => [2,2,2,1,1] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,2,3,1,1] => [2,2,1,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,2,3,2] => [2,2,1,2,1] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,2,4,1] => [2,2,1,1,2] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,2,5] => [2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,3,1,1,1,1] => [2,1,5] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,3,1,1,2] => [2,1,4,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,3,1,2,1] => [2,1,3,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,3,1,3] => [2,1,3,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,3,2,1,1] => [2,1,2,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,3,2,2] => [2,1,2,2,1] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,3,3,1] => [2,1,2,1,2] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,3,4] => [2,1,2,1,1,1] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,4,1,1,1] => [2,1,1,4] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,4,1,2] => [2,1,1,3,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,4,2,1] => [2,1,1,2,2] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,4,3] => [2,1,1,2,1,1] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,5,1,1] => [2,1,1,1,3] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,5,2] => [2,1,1,1,2,1] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,6,1] => [2,1,1,1,1,2] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,7] => [2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[2,1,1,1,1,1,1] => [1,7] => [7,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 7
[2,1,1,1,1,2] => [1,6,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[2,1,1,1,2,1] => [1,5,2] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[2,1,1,1,3] => [1,5,1,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[2,1,1,2,1,1] => [1,4,3] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 4
[2,1,1,2,2] => [1,4,2,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[2,1,1,3,1] => [1,4,1,2] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[2,1,1,4] => [1,4,1,1,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[2,1,2,1,1,1] => [1,3,4] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 4
[2,1,2,1,2] => [1,3,3,1] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[2,1,2,2,1] => [1,3,2,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[2,1,2,3] => [1,3,2,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[2,1,3,1,1] => [1,3,1,3] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[2,1,3,2] => [1,3,1,2,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[2,1,4,1] => [1,3,1,1,2] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[2,1,5] => [1,3,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[2,2,1,1,1,1] => [1,2,5] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[2,2,1,1,2] => [1,2,4,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[2,2,1,2,1] => [1,2,3,2] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[2,2,1,3] => [1,2,3,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[2,2,2,1,1] => [1,2,2,3] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[2,2,2,2] => [1,2,2,2,1] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[2,2,3,1] => [1,2,2,1,2] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[2,2,4] => [1,2,2,1,1,1] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[2,3,1,1,1] => [1,2,1,4] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[2,3,1,2] => [1,2,1,3,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[2,3,2,1] => [1,2,1,2,2] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[2,3,3] => [1,2,1,2,1,1] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[2,4,1,1] => [1,2,1,1,3] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[2,4,2] => [1,2,1,1,2,1] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[2,5,1] => [1,2,1,1,1,2] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[2,6] => [1,2,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[3,1,1,1,1,1] => [1,1,6] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[3,1,1,1,2] => [1,1,5,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[3,1,1,2,1] => [1,1,4,2] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[3,1,1,3] => [1,1,4,1,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[3,1,2,1,1] => [1,1,3,3] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[3,1,2,2] => [1,1,3,2,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[3,1,3,1] => [1,1,3,1,2] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[3,1,4] => [1,1,3,1,1,1] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[3,2,1,1,1] => [1,1,2,4] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[3,2,1,2] => [1,1,2,3,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[3,2,2,1] => [1,1,2,2,2] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[3,2,3] => [1,1,2,2,1,1] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[3,3,1,1] => [1,1,2,1,3] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[3,3,2] => [1,1,2,1,2,1] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[3,4,1] => [1,1,2,1,1,2] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[3,5] => [1,1,2,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[4,1,1,1,1] => [1,1,1,5] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[4,1,1,2] => [1,1,1,4,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[4,1,2,1] => [1,1,1,3,2] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[4,1,3] => [1,1,1,3,1,1] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[4,2,1,1] => [1,1,1,2,3] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[4,2,2] => [1,1,1,2,2,1] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[4,3,1] => [1,1,1,2,1,2] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[4,4] => [1,1,1,2,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[5,1,1,1] => [1,1,1,1,4] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[5,1,2] => [1,1,1,1,3,1] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[5,2,1] => [1,1,1,1,2,2] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[5,3] => [1,1,1,1,2,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[6,1,1] => [1,1,1,1,1,3] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[6,2] => [1,1,1,1,1,2,1] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[7,1] => [1,1,1,1,1,1,2] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,1,1,1,1,2,1] => [7,2] => [7,2] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 7
[1,1,1,1,1,2,1,1] => [6,3] => [6,3] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 6
[1,1,1,1,1,2,2] => [6,2,1] => [6,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 6
[1,1,1,1,1,3,1] => [6,1,2] => [6,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 6
[1,1,1,1,2,1,1,1] => [5,4] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => 5
[1,1,1,1,2,1,2] => [5,3,1] => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 5
[1,1,1,1,2,2,1] => [5,2,2] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 5
[1,1,1,1,2,3] => [5,2,1,1] => [5,2,1,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 5
[1,1,1,1,3,1,1] => [5,1,3] => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 5
[1,1,1,1,3,2] => [5,1,2,1] => [5,2,1,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 5
[1,1,1,1,4,1] => [5,1,1,2] => [5,2,1,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 5
[1,1,1,2,1,1,1,1] => [4,5] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => 5
[1,1,1,2,1,1,2] => [4,4,1] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 4
[1,1,1,2,1,2,1] => [4,3,2] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 4
[1,1,1,2,1,3] => [4,3,1,1] => [4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4
[1,1,1,2,2,1,1] => [4,2,3] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 4
[1,1,1,2,2,2] => [4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 4
[1,1,1,2,3,1] => [4,2,1,2] => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 4
[1,1,1,2,4] => [4,2,1,1,1] => [4,2,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4
[1,1,1,3,1,1,1] => [4,1,4] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 4
[1,1,1,3,1,2] => [4,1,3,1] => [4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4
[1,1,1,3,2,1] => [4,1,2,2] => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 4
[1,1,1,3,3] => [4,1,2,1,1] => [4,2,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4
[1,1,1,4,1,1] => [4,1,1,3] => [4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4
[1,1,1,4,2] => [4,1,1,2,1] => [4,2,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4
[1,1,1,5,1] => [4,1,1,1,2] => [4,2,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4
[1,1,2,1,1,1,1,1] => [3,6] => [6,3] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 6
[1,1,2,1,1,1,2] => [3,5,1] => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 5
[1,1,2,1,1,2,1] => [3,4,2] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 4
[1,1,2,1,1,3] => [3,4,1,1] => [4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4
[1,1,2,1,2,1,1] => [3,3,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 3
[1,1,2,1,2,2] => [3,3,2,1] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 3
[1,1,2,1,3,1] => [3,3,1,2] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 3
[1,1,2,1,4] => [3,3,1,1,1] => [3,3,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,2,2,1,1,1] => [3,2,4] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 4
[1,1,2,2,1,2] => [3,2,3,1] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 3
[1,1,2,2,2,1] => [3,2,2,2] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,1,2,2,3] => [3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,1,2,3,1,1] => [3,2,1,3] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 3
[1,1,2,3,2] => [3,2,1,2,1] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,1,2,4,1] => [3,2,1,1,2] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,1,2,5] => [3,2,1,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,3,1,1,1,1] => [3,1,5] => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 5
[1,1,3,1,1,2] => [3,1,4,1] => [4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4
[1,1,3,1,2,1] => [3,1,3,2] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 3
[1,1,3,1,3] => [3,1,3,1,1] => [3,3,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,3,2,1,1] => [3,1,2,3] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 3
[1,1,3,2,2] => [3,1,2,2,1] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,1,3,3,1] => [3,1,2,1,2] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,1,3,4] => [3,1,2,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,4,1,1,1] => [3,1,1,4] => [4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4
[1,1,4,1,2] => [3,1,1,3,1] => [3,3,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,4,2,1] => [3,1,1,2,2] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,1,4,3] => [3,1,1,2,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,5,1,1] => [3,1,1,1,3] => [3,3,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,5,2] => [3,1,1,1,2,1] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,6,1] => [3,1,1,1,1,2] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[1,2,1,1,1,1,1,1] => [2,7] => [7,2] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 7
[1,2,1,1,1,1,2] => [2,6,1] => [6,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 6
[1,2,1,1,1,2,1] => [2,5,2] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 5
[1,2,1,1,1,3] => [2,5,1,1] => [5,2,1,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 5
[1,2,1,1,2,1,1] => [2,4,3] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 4
[1,2,1,1,2,2] => [2,4,2,1] => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 4
[1,2,1,1,3,1] => [2,4,1,2] => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 4
[1,2,1,1,4] => [2,4,1,1,1] => [4,2,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4
[1,2,1,2,1,1,1] => [2,3,4] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 4
[1,2,1,2,1,2] => [2,3,3,1] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 3
[1,2,1,2,2,1] => [2,3,2,2] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,2,1,2,3] => [2,3,2,1,1] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,2,1,3,1,1] => [2,3,1,3] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 3
[1,2,1,3,2] => [2,3,1,2,1] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,2,1,4,1] => [2,3,1,1,2] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,2,1,5] => [2,3,1,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[1,2,2,1,1,1,1] => [2,2,5] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 5
[1,2,2,1,1,2] => [2,2,4,1] => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 4
[1,2,2,1,2,1] => [2,2,3,2] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,2,2,1,3] => [2,2,3,1,1] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,2,2,2,1,1] => [2,2,2,3] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,2,2,2,2] => [2,2,2,2,1] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 2
[1,2,2,3,1] => [2,2,2,1,2] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 2
[1,2,2,4] => [2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[1,2,3,1,1,1] => [2,2,1,4] => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 4
[1,2,3,1,2] => [2,2,1,3,1] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,2,3,2,1] => [2,2,1,2,2] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 2
[1,2,3,3] => [2,2,1,2,1,1] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[1,2,4,1,1] => [2,2,1,1,3] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,2,4,2] => [2,2,1,1,2,1] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[1,2,5,1] => [2,2,1,1,1,2] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[1,3,1,1,1,1,1] => [2,1,6] => [6,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 6
[1,3,1,1,1,2] => [2,1,5,1] => [5,2,1,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 5
[1,3,1,1,2,1] => [2,1,4,2] => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 4
[1,3,1,1,3] => [2,1,4,1,1] => [4,2,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4
[1,3,1,2,1,1] => [2,1,3,3] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 3
[1,3,1,2,2] => [2,1,3,2,1] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,3,1,3,1] => [2,1,3,1,2] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,3,1,4] => [2,1,3,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[1,3,2,1,1,1] => [2,1,2,4] => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 4
[1,3,2,1,2] => [2,1,2,3,1] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,3,2,2,1] => [2,1,2,2,2] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 2
[1,3,2,3] => [2,1,2,2,1,1] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[1,3,3,1,1] => [2,1,2,1,3] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,3,3,2] => [2,1,2,1,2,1] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[1,3,4,1] => [2,1,2,1,1,2] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[1,4,1,1,1,1] => [2,1,1,5] => [5,2,1,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 5
[1,4,1,1,2] => [2,1,1,4,1] => [4,2,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4
[1,4,1,2,1] => [2,1,1,3,2] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,4,1,3] => [2,1,1,3,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[1,4,2,1,1] => [2,1,1,2,3] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,4,2,2] => [2,1,1,2,2,1] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[1,4,3,1] => [2,1,1,2,1,2] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[1,5,1,1,1] => [2,1,1,1,4] => [4,2,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4
[1,5,1,2] => [2,1,1,1,3,1] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[1,5,2,1] => [2,1,1,1,2,2] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[1,6,1,1] => [2,1,1,1,1,3] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[2,1,1,1,1,2,1] => [1,6,2] => [6,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 6
[2,1,1,1,2,1,1] => [1,5,3] => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 5
[2,1,1,1,2,2] => [1,5,2,1] => [5,2,1,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 5
[2,1,1,1,3,1] => [1,5,1,2] => [5,2,1,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 5
[2,1,1,2,1,1,1] => [1,4,4] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 4
[2,1,1,2,1,2] => [1,4,3,1] => [4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4
[2,1,1,2,2,1] => [1,4,2,2] => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 4
[2,1,1,2,3] => [1,4,2,1,1] => [4,2,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4
[2,1,1,3,1,1] => [1,4,1,3] => [4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4
[2,1,1,3,2] => [1,4,1,2,1] => [4,2,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4
[2,1,1,4,1] => [1,4,1,1,2] => [4,2,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4
[2,1,2,1,1,1,1] => [1,3,5] => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 5
[2,1,2,1,1,2] => [1,3,4,1] => [4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4
[2,1,2,1,2,1] => [1,3,3,2] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 3
[2,1,2,1,3] => [1,3,3,1,1] => [3,3,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 3
[2,1,2,2,1,1] => [1,3,2,3] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 3
[2,1,2,2,2] => [1,3,2,2,1] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[2,1,2,3,1] => [1,3,2,1,2] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[2,1,2,4] => [1,3,2,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[2,1,3,1,1,1] => [1,3,1,4] => [4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4
[2,1,3,1,2] => [1,3,1,3,1] => [3,3,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 3
[2,1,3,2,1] => [1,3,1,2,2] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[2,1,3,3] => [1,3,1,2,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[2,1,4,1,1] => [1,3,1,1,3] => [3,3,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 3
[2,1,4,2] => [1,3,1,1,2,1] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[2,1,5,1] => [1,3,1,1,1,2] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[2,2,1,1,1,1,1] => [1,2,6] => [6,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 6
[2,2,1,1,1,2] => [1,2,5,1] => [5,2,1,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 5
[2,2,1,1,2,1] => [1,2,4,2] => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 4
[2,2,1,1,3] => [1,2,4,1,1] => [4,2,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4
[2,2,1,2,1,1] => [1,2,3,3] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 3
[2,2,1,2,2] => [1,2,3,2,1] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[2,2,1,3,1] => [1,2,3,1,2] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[2,2,1,4] => [1,2,3,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[2,2,2,1,1,1] => [1,2,2,4] => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 4
[2,2,2,1,2] => [1,2,2,3,1] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[2,2,2,2,1] => [1,2,2,2,2] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 2
[2,2,2,3] => [1,2,2,2,1,1] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[2,2,3,1,1] => [1,2,2,1,3] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[2,2,3,2] => [1,2,2,1,2,1] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[2,2,4,1] => [1,2,2,1,1,2] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[2,3,1,1,1,1] => [1,2,1,5] => [5,2,1,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 5
[2,3,1,1,2] => [1,2,1,4,1] => [4,2,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4
[2,3,1,2,1] => [1,2,1,3,2] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[2,3,1,3] => [1,2,1,3,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[2,3,2,1,1] => [1,2,1,2,3] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[2,3,2,2] => [1,2,1,2,2,1] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[2,3,3,1] => [1,2,1,2,1,2] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[2,4,1,1,1] => [1,2,1,1,4] => [4,2,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4
[2,4,1,2] => [1,2,1,1,3,1] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[2,4,2,1] => [1,2,1,1,2,2] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[2,5,1,1] => [1,2,1,1,1,3] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[3,1,1,1,2,1] => [1,1,5,2] => [5,2,1,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 5
[3,1,1,2,1,1] => [1,1,4,3] => [4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4
[3,1,1,2,2] => [1,1,4,2,1] => [4,2,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4
[3,1,1,3,1] => [1,1,4,1,2] => [4,2,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4
[3,1,2,1,1,1] => [1,1,3,4] => [4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4
[3,1,2,1,2] => [1,1,3,3,1] => [3,3,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 3
[3,1,2,2,1] => [1,1,3,2,2] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[3,1,2,3] => [1,1,3,2,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[3,1,3,1,1] => [1,1,3,1,3] => [3,3,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 3
[3,1,3,2] => [1,1,3,1,2,1] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[3,1,4,1] => [1,1,3,1,1,2] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[3,2,1,1,1,1] => [1,1,2,5] => [5,2,1,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 5
[3,2,1,1,2] => [1,1,2,4,1] => [4,2,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4
[3,2,1,2,1] => [1,1,2,3,2] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[3,2,1,3] => [1,1,2,3,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[3,2,2,1,1] => [1,1,2,2,3] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[3,2,2,2] => [1,1,2,2,2,1] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[3,2,3,1] => [1,1,2,2,1,2] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[3,3,1,1,1] => [1,1,2,1,4] => [4,2,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4
[3,3,1,2] => [1,1,2,1,3,1] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[3,3,2,1] => [1,1,2,1,2,2] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[3,4,1,1] => [1,1,2,1,1,3] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[4,1,1,2,1] => [1,1,1,4,2] => [4,2,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4
[4,1,2,1,1] => [1,1,1,3,3] => [3,3,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 3
[4,1,2,2] => [1,1,1,3,2,1] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[4,1,3,1] => [1,1,1,3,1,2] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[4,2,1,1,1] => [1,1,1,2,4] => [4,2,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4
[4,2,1,2] => [1,1,1,2,3,1] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[4,2,2,1] => [1,1,1,2,2,2] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[4,3,1,1] => [1,1,1,2,1,3] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[5,1,2,1] => [1,1,1,1,3,2] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[5,2,1,1] => [1,1,1,1,2,3] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,1,1,1,2,1,1] => [7,3] => [7,3] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 7
[1,1,1,1,1,2,1,1,1] => [6,4] => [6,4] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 6
[1,1,1,1,1,2,1,2] => [6,3,1] => [6,3,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 6
[1,1,1,1,1,2,2,1] => [6,2,2] => [6,2,2] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,1,1,1,1,3,1,1] => [6,1,3] => [6,3,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 6
[1,1,1,1,2,1,1,1,1] => [5,5] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 5
[1,1,1,1,2,1,1,2] => [5,4,1] => [5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 5
[1,1,1,1,2,1,2,1] => [5,3,2] => [5,3,2] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 5
[1,1,1,1,2,1,3] => [5,3,1,1] => [5,3,1,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 5
[1,1,1,1,2,2,1,1] => [5,2,3] => [5,3,2] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 5
[1,1,1,1,2,2,2] => [5,2,2,1] => [5,2,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,1,1,1,2,3,1] => [5,2,1,2] => [5,2,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,1,1,1,3,1,1,1] => [5,1,4] => [5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 5
[1,1,1,1,3,1,2] => [5,1,3,1] => [5,3,1,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 5
[1,1,1,1,3,2,1] => [5,1,2,2] => [5,2,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,1,1,1,4,1,1] => [5,1,1,3] => [5,3,1,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 5
[1,1,1,2,1,1,1,1,1] => [4,6] => [6,4] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 6
[1,1,1,2,1,1,1,2] => [4,5,1] => [5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 5
[1,1,1,2,1,1,2,1] => [4,4,2] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 4
[1,1,1,2,1,1,3] => [4,4,1,1] => [4,4,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 4
[1,1,1,2,1,2,1,1] => [4,3,3] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 4
[1,1,1,2,1,2,2] => [4,3,2,1] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 4
[1,1,1,2,1,3,1] => [4,3,1,2] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 4
[1,1,1,2,1,4] => [4,3,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 4
[1,1,1,2,2,1,1,1] => [4,2,4] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 4
[1,1,1,2,2,1,2] => [4,2,3,1] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 4
[1,1,1,2,2,2,1] => [4,2,2,2] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[1,1,1,2,2,3] => [4,2,2,1,1] => [4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 4
[1,1,1,2,3,1,1] => [4,2,1,3] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 4
[1,1,1,2,3,2] => [4,2,1,2,1] => [4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 4
[1,1,1,2,4,1] => [4,2,1,1,2] => [4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 4
[1,1,1,3,1,1,1,1] => [4,1,5] => [5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 5
[1,1,1,3,1,1,2] => [4,1,4,1] => [4,4,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 4
[1,1,1,3,1,2,1] => [4,1,3,2] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 4
[1,1,1,3,1,3] => [4,1,3,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 4
[1,1,1,3,2,1,1] => [4,1,2,3] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 4
[1,1,1,3,2,2] => [4,1,2,2,1] => [4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 4
[1,1,1,3,3,1] => [4,1,2,1,2] => [4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 4
[1,1,1,4,1,1,1] => [4,1,1,4] => [4,4,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 4
[1,1,1,4,1,2] => [4,1,1,3,1] => [4,3,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 4
[1,1,1,4,2,1] => [4,1,1,2,2] => [4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 4
[1,1,1,5,1,1] => [4,1,1,1,3] => [4,3,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 4
[1,1,2,1,1,1,1,1,1] => [3,7] => [7,3] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 7
[1,1,2,1,1,1,1,2] => [3,6,1] => [6,3,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 6
[1,1,2,1,1,1,2,1] => [3,5,2] => [5,3,2] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 5
[1,1,2,1,1,1,3] => [3,5,1,1] => [5,3,1,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 5
[1,1,2,1,1,2,1,1] => [3,4,3] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 4
[1,1,2,1,1,2,2] => [3,4,2,1] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 4
[1,1,2,1,1,3,1] => [3,4,1,2] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 4
[1,1,2,1,1,4] => [3,4,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 4
[1,1,2,1,2,1,1,1] => [3,3,4] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 4
[1,1,2,1,2,1,2] => [3,3,3,1] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 3
[1,1,2,1,2,2,1] => [3,3,2,2] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 3
[1,1,2,1,2,3] => [3,3,2,1,1] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[1,1,2,1,3,1,1] => [3,3,1,3] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 3
[1,1,2,1,3,2] => [3,3,1,2,1] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[1,1,2,1,4,1] => [3,3,1,1,2] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[1,1,2,2,1,1,1,1] => [3,2,5] => [5,3,2] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 5
[1,1,2,2,1,1,2] => [3,2,4,1] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 4
[1,1,2,2,1,2,1] => [3,2,3,2] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 3
[1,1,2,2,1,3] => [3,2,3,1,1] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[1,1,2,2,2,1,1] => [3,2,2,3] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 3
[1,1,2,2,2,2] => [3,2,2,2,1] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,1,2,2,3,1] => [3,2,2,1,2] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,1,2,2,4] => [3,2,2,1,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[1,1,2,3,1,1,1] => [3,2,1,4] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 4
[1,1,2,3,1,2] => [3,2,1,3,1] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[1,1,2,3,2,1] => [3,2,1,2,2] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,1,2,3,3] => [3,2,1,2,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[1,1,2,4,1,1] => [3,2,1,1,3] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[1,1,2,4,2] => [3,2,1,1,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[1,1,2,5,1] => [3,2,1,1,1,2] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[1,1,3,1,1,1,1,1] => [3,1,6] => [6,3,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 6
[1,1,3,1,1,1,2] => [3,1,5,1] => [5,3,1,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 5
[1,1,3,1,1,2,1] => [3,1,4,2] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 4
[1,1,3,1,1,3] => [3,1,4,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 4
[1,1,3,1,2,1,1] => [3,1,3,3] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 3
[1,1,3,1,2,2] => [3,1,3,2,1] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[1,1,3,1,3,1] => [3,1,3,1,2] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[1,1,3,2,1,1,1] => [3,1,2,4] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 4
[1,1,3,2,1,2] => [3,1,2,3,1] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[1,1,3,2,2,1] => [3,1,2,2,2] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,1,3,2,3] => [3,1,2,2,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[1,1,3,3,1,1] => [3,1,2,1,3] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[1,1,3,3,2] => [3,1,2,1,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[1,1,3,4,1] => [3,1,2,1,1,2] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[1,1,4,1,1,1,1] => [3,1,1,5] => [5,3,1,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 5
[1,1,4,1,1,2] => [3,1,1,4,1] => [4,3,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 4
[1,1,4,1,2,1] => [3,1,1,3,2] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[1,1,4,2,1,1] => [3,1,1,2,3] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[1,1,4,2,2] => [3,1,1,2,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[1,1,4,3,1] => [3,1,1,2,1,2] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[1,1,5,1,1,1] => [3,1,1,1,4] => [4,3,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 4
[1,1,5,2,1] => [3,1,1,1,2,2] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[1,2,1,1,1,1,2,1] => [2,6,2] => [6,2,2] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,2,1,1,1,2,1,1] => [2,5,3] => [5,3,2] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 5
[1,2,1,1,1,2,2] => [2,5,2,1] => [5,2,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,2,1,1,1,3,1] => [2,5,1,2] => [5,2,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,2,1,1,2,1,1,1] => [2,4,4] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 4
[1,2,1,1,2,1,2] => [2,4,3,1] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 4
[1,2,1,1,2,2,1] => [2,4,2,2] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[1,2,1,1,2,3] => [2,4,2,1,1] => [4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 4
[1,2,1,1,3,1,1] => [2,4,1,3] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 4
[1,2,1,1,3,2] => [2,4,1,2,1] => [4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 4
[1,2,1,1,4,1] => [2,4,1,1,2] => [4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 4
[1,2,1,2,1,1,1,1] => [2,3,5] => [5,3,2] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 5
[1,2,1,2,1,1,2] => [2,3,4,1] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 4
[1,2,1,2,1,2,1] => [2,3,3,2] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 3
[1,2,1,2,1,3] => [2,3,3,1,1] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[1,2,1,2,2,1,1] => [2,3,2,3] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 3
[1,2,1,2,2,2] => [2,3,2,2,1] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,2,1,2,3,1] => [2,3,2,1,2] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,2,1,2,4] => [2,3,2,1,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[1,2,1,3,1,1,1] => [2,3,1,4] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 4
[1,2,1,3,1,2] => [2,3,1,3,1] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[1,2,1,3,2,1] => [2,3,1,2,2] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,2,1,3,3] => [2,3,1,2,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[1,2,1,4,1,1] => [2,3,1,1,3] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[1,2,1,4,2] => [2,3,1,1,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[1,2,1,5,1] => [2,3,1,1,1,2] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[1,2,2,1,1,1,1,1] => [2,2,6] => [6,2,2] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,2,2,1,1,1,2] => [2,2,5,1] => [5,2,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,2,2,1,1,2,1] => [2,2,4,2] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[1,2,2,1,1,3] => [2,2,4,1,1] => [4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 4
[1,2,2,1,2,1,1] => [2,2,3,3] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 3
[1,2,2,1,2,2] => [2,2,3,2,1] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,2,2,1,3,1] => [2,2,3,1,2] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,2,2,1,4] => [2,2,3,1,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[1,2,2,2,1,1,1] => [2,2,2,4] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[1,2,2,2,1,2] => [2,2,2,3,1] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,2,2,2,2,1] => [2,2,2,2,2] => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,2,2,2,3] => [2,2,2,2,1,1] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 2
[1,2,2,3,1,1] => [2,2,2,1,3] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,2,2,3,2] => [2,2,2,1,2,1] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 2
[1,2,2,4,1] => [2,2,2,1,1,2] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 2
[1,2,3,1,1,1,1] => [2,2,1,5] => [5,2,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,2,3,1,1,2] => [2,2,1,4,1] => [4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 4
[1,2,3,1,2,1] => [2,2,1,3,2] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,2,3,1,3] => [2,2,1,3,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[1,2,3,2,1,1] => [2,2,1,2,3] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,2,3,2,2] => [2,2,1,2,2,1] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 2
[1,2,3,3,1] => [2,2,1,2,1,2] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 2
[1,2,4,1,1,1] => [2,2,1,1,4] => [4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 4
[1,2,4,1,2] => [2,2,1,1,3,1] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[1,2,4,2,1] => [2,2,1,1,2,2] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 2
[1,2,5,1,1] => [2,2,1,1,1,3] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[1,3,1,1,1,2,1] => [2,1,5,2] => [5,2,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,3,1,1,2,1,1] => [2,1,4,3] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 4
[1,3,1,1,2,2] => [2,1,4,2,1] => [4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 4
[1,3,1,1,3,1] => [2,1,4,1,2] => [4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 4
[1,3,1,2,1,1,1] => [2,1,3,4] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 4
[1,3,1,2,1,2] => [2,1,3,3,1] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[1,3,1,2,2,1] => [2,1,3,2,2] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,3,1,2,3] => [2,1,3,2,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[1,3,1,3,1,1] => [2,1,3,1,3] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[1,3,1,3,2] => [2,1,3,1,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[1,3,1,4,1] => [2,1,3,1,1,2] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[1,3,2,1,1,1,1] => [2,1,2,5] => [5,2,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,3,2,1,1,2] => [2,1,2,4,1] => [4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 4
[1,3,2,1,2,1] => [2,1,2,3,2] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,3,2,1,3] => [2,1,2,3,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[1,3,2,2,1,1] => [2,1,2,2,3] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,3,2,2,2] => [2,1,2,2,2,1] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 2
[1,3,2,3,1] => [2,1,2,2,1,2] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 2
[1,3,3,1,1,1] => [2,1,2,1,4] => [4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 4
[1,3,3,1,2] => [2,1,2,1,3,1] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[1,3,3,2,1] => [2,1,2,1,2,2] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 2
[1,3,4,1,1] => [2,1,2,1,1,3] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[1,4,1,1,2,1] => [2,1,1,4,2] => [4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 4
[1,4,1,2,1,1] => [2,1,1,3,3] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[1,4,1,2,2] => [2,1,1,3,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[1,4,1,3,1] => [2,1,1,3,1,2] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[1,4,2,1,1,1] => [2,1,1,2,4] => [4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 4
[1,4,2,1,2] => [2,1,1,2,3,1] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[1,4,2,2,1] => [2,1,1,2,2,2] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 2
[1,4,3,1,1] => [2,1,1,2,1,3] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[1,5,1,2,1] => [2,1,1,1,3,2] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[1,5,2,1,1] => [2,1,1,1,2,3] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[2,1,1,1,1,2,1,1] => [1,6,3] => [6,3,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 6
[2,1,1,1,2,1,1,1] => [1,5,4] => [5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 5
[2,1,1,1,2,1,2] => [1,5,3,1] => [5,3,1,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 5
[2,1,1,1,2,2,1] => [1,5,2,2] => [5,2,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 5
[2,1,1,1,3,1,1] => [1,5,1,3] => [5,3,1,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 5
[2,1,1,2,1,1,1,1] => [1,4,5] => [5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 5
[2,1,1,2,1,1,2] => [1,4,4,1] => [4,4,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 4
[2,1,1,2,1,2,1] => [1,4,3,2] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 4
[2,1,1,2,1,3] => [1,4,3,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 4
[2,1,1,2,2,1,1] => [1,4,2,3] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 4
[2,1,1,2,2,2] => [1,4,2,2,1] => [4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 4
[2,1,1,2,3,1] => [1,4,2,1,2] => [4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 4
[2,1,1,3,1,1,1] => [1,4,1,4] => [4,4,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 4
[2,1,1,3,1,2] => [1,4,1,3,1] => [4,3,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 4
[2,1,1,3,2,1] => [1,4,1,2,2] => [4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 4
[2,1,1,4,1,1] => [1,4,1,1,3] => [4,3,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 4
[2,1,2,1,1,1,1,1] => [1,3,6] => [6,3,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 6
[2,1,2,1,1,1,2] => [1,3,5,1] => [5,3,1,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 5
[2,1,2,1,1,2,1] => [1,3,4,2] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 4
[2,1,2,1,1,3] => [1,3,4,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 4
[2,1,2,1,2,1,1] => [1,3,3,3] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 3
[2,1,2,1,2,2] => [1,3,3,2,1] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[2,1,2,1,3,1] => [1,3,3,1,2] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[2,1,2,2,1,1,1] => [1,3,2,4] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 4
[2,1,2,2,1,2] => [1,3,2,3,1] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[2,1,2,2,2,1] => [1,3,2,2,2] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[2,1,2,2,3] => [1,3,2,2,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[2,1,2,3,1,1] => [1,3,2,1,3] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[2,1,2,3,2] => [1,3,2,1,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[2,1,2,4,1] => [1,3,2,1,1,2] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[2,1,3,1,1,1,1] => [1,3,1,5] => [5,3,1,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 5
[2,1,3,1,1,2] => [1,3,1,4,1] => [4,3,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 4
[2,1,3,1,2,1] => [1,3,1,3,2] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[2,1,3,2,1,1] => [1,3,1,2,3] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[2,1,3,2,2] => [1,3,1,2,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[2,1,3,3,1] => [1,3,1,2,1,2] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[2,1,4,1,1,1] => [1,3,1,1,4] => [4,3,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 4
[2,1,4,2,1] => [1,3,1,1,2,2] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[2,2,1,1,1,2,1] => [1,2,5,2] => [5,2,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 5
[2,2,1,1,2,1,1] => [1,2,4,3] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 4
[2,2,1,1,2,2] => [1,2,4,2,1] => [4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 4
[2,2,1,1,3,1] => [1,2,4,1,2] => [4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 4
[2,2,1,2,1,1,1] => [1,2,3,4] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 4
[2,2,1,2,1,2] => [1,2,3,3,1] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[2,2,1,2,2,1] => [1,2,3,2,2] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[2,2,1,2,3] => [1,2,3,2,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[2,2,1,3,1,1] => [1,2,3,1,3] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[2,2,1,3,2] => [1,2,3,1,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[2,2,1,4,1] => [1,2,3,1,1,2] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[2,2,2,1,1,1,1] => [1,2,2,5] => [5,2,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 5
[2,2,2,1,1,2] => [1,2,2,4,1] => [4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 4
[2,2,2,1,2,1] => [1,2,2,3,2] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[2,2,2,1,3] => [1,2,2,3,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[2,2,2,2,1,1] => [1,2,2,2,3] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[2,2,2,2,2] => [1,2,2,2,2,1] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 2
[2,2,2,3,1] => [1,2,2,2,1,2] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 2
[2,2,3,1,1,1] => [1,2,2,1,4] => [4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 4
[2,2,3,1,2] => [1,2,2,1,3,1] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[2,2,3,2,1] => [1,2,2,1,2,2] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 2
[2,2,4,1,1] => [1,2,2,1,1,3] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[2,3,1,1,2,1] => [1,2,1,4,2] => [4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 4
[2,3,1,2,1,1] => [1,2,1,3,3] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[2,3,1,2,2] => [1,2,1,3,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[2,3,1,3,1] => [1,2,1,3,1,2] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[2,3,2,1,1,1] => [1,2,1,2,4] => [4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 4
[2,3,2,1,2] => [1,2,1,2,3,1] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[2,3,2,2,1] => [1,2,1,2,2,2] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 2
[2,3,3,1,1] => [1,2,1,2,1,3] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[2,4,1,2,1] => [1,2,1,1,3,2] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[2,4,2,1,1] => [1,2,1,1,2,3] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[3,1,1,1,2,1,1] => [1,1,5,3] => [5,3,1,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 5
[3,1,1,2,1,1,1] => [1,1,4,4] => [4,4,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 4
[3,1,1,2,1,2] => [1,1,4,3,1] => [4,3,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 4
[3,1,1,2,2,1] => [1,1,4,2,2] => [4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 4
[3,1,1,3,1,1] => [1,1,4,1,3] => [4,3,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 4
[3,1,2,1,1,1,1] => [1,1,3,5] => [5,3,1,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 5
[3,1,2,1,1,2] => [1,1,3,4,1] => [4,3,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 4
[3,1,2,1,2,1] => [1,1,3,3,2] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[3,1,2,2,1,1] => [1,1,3,2,3] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[3,1,2,2,2] => [1,1,3,2,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[3,1,2,3,1] => [1,1,3,2,1,2] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[3,1,3,1,1,1] => [1,1,3,1,4] => [4,3,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 4
[3,1,3,2,1] => [1,1,3,1,2,2] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[3,2,1,1,2,1] => [1,1,2,4,2] => [4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 4
[3,2,1,2,1,1] => [1,1,2,3,3] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[3,2,1,2,2] => [1,1,2,3,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[3,2,1,3,1] => [1,1,2,3,1,2] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[3,2,2,1,1,1] => [1,1,2,2,4] => [4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 4
[3,2,2,1,2] => [1,1,2,2,3,1] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[3,2,2,2,1] => [1,1,2,2,2,2] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 2
[3,2,3,1,1] => [1,1,2,2,1,3] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[3,3,1,2,1] => [1,1,2,1,3,2] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[3,3,2,1,1] => [1,1,2,1,2,3] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[4,1,1,2,1,1] => [1,1,1,4,3] => [4,3,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 4
[4,1,2,1,1,1] => [1,1,1,3,4] => [4,3,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 4
[4,1,2,2,1] => [1,1,1,3,2,2] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[4,2,1,2,1] => [1,1,1,2,3,2] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[4,2,2,1,1] => [1,1,1,2,2,3] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,1,2,2,1,1,1,1] => [5,2,5] => [5,5,2] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 5
[1,1,1,1,2,1,1,2,1,1] => [5,4,3] => [5,4,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 5
[1,1,1,1,2,1,1,1,1,2] => [5,6,1] => [6,5,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 6
[1,1,2,2,1,1,2,2] => [3,2,4,2,1] => [4,3,2,2,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 4
[1,1,2,2,2,2,1,1] => [3,2,2,2,3] => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 3
[1,1,2,2,2,1,1,2] => [3,2,2,4,1] => [4,3,2,2,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 4
[1,1,2,1,1,2,1,1,1,1] => [3,4,5] => [5,4,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 5
[1,1,2,1,1,2,2,2] => [3,4,2,2,1] => [4,3,2,2,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 4
[1,1,2,1,1,1,1,2,1,1] => [3,6,3] => [6,3,3] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 6
[1,1,2,1,2,3,1,1] => [3,3,2,1,3] => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3
[1,1,2,1,2,2,1,2] => [3,3,2,3,1] => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3
[1,1,2,1,2,1,1,3] => [3,3,4,1,1] => [4,3,3,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 4
[1,1,3,2,1,2,1,1] => [3,1,2,3,3] => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3
[1,1,3,1,1,3,1,1] => [3,1,4,1,3] => [4,3,3,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 4
[1,1,3,1,1,2,1,2] => [3,1,4,3,1] => [4,3,3,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 4
[2,2,1,1,2,2,1,1] => [1,2,4,2,3] => [4,3,2,2,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 4
[2,2,2,1,1,2,1,1] => [1,2,2,4,3] => [4,3,2,2,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 4
[2,1,1,2,2,2,1,1] => [1,4,2,2,3] => [4,3,2,2,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 4
[2,1,1,1,1,2,1,1,1,1] => [1,6,5] => [6,5,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 6
[2,1,2,2,1,2,1,1] => [1,3,2,3,3] => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3
[2,1,2,1,1,3,1,1] => [1,3,4,1,3] => [4,3,3,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 4
[2,1,2,1,1,2,1,2] => [1,3,4,3,1] => [4,3,3,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 4
[3,1,1,2,1,2,1,1] => [1,1,4,3,3] => [4,3,3,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 4
[1,2,2,2,2,2,1] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2
[1,2,2,2,1,3] => [2,2,2,3,1,1] => [3,2,2,2,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 3
[1,2,1,2,3,2] => [2,3,2,1,2,1] => [3,2,2,2,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 3
[1,1,2,3,2,2] => [3,2,1,2,2,1] => [3,2,2,2,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 3
[1,1,2,3,2,2,1] => [3,2,1,2,2,2] => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3
[1,3,2,1,2,2,1] => [2,1,2,3,2,2] => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3
[1,1,1,2,1,1,2,2,1] => [4,4,2,2] => [4,4,2,2] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 4
[1,2,2,1,2,3,1] => [2,2,3,2,1,2] => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3
[1,1,2,2,2,3,1] => [3,2,2,2,1,2] => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3
[1,1,1,1,2,1,1,3,1] => [5,4,1,2] => [5,4,2,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 5
[1,1,2,1,2,1,2,1,1] => [3,3,3,3] => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,2,2,3,2,1,1] => [2,2,2,1,2,3] => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3
[1,3,2,2,2,1,1] => [2,1,2,2,2,3] => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3
[1,1,1,2,1,2,2,1,1] => [4,3,2,3] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 4
[1,2,2,1,1,2,1,1,1] => [2,2,4,4] => [4,4,2,2] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 4
[1,1,2,2,1,2,1,1,1] => [3,2,3,4] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 4
[1,1,1,2,2,2,1,1,1] => [4,2,2,4] => [4,4,2,2] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 4
[1,1,1,1,2,3,1,1,1] => [5,2,1,4] => [5,4,2,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 5
[1,3,1,1,2,1,1,1,1] => [2,1,4,5] => [5,4,2,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 5
[1,1,1,3,2,1,1,1,1] => [4,1,2,5] => [5,4,2,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 5
[1,1,1,1,1,2,1,1,1,1,1] => [6,6] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 6
[2,2,2,2,1,2,1] => [1,2,2,2,3,2] => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3
[2,2,2,1,2,2,1] => [1,2,2,3,2,2] => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3
[2,2,1,2,1,1,2,1] => [1,2,3,4,2] => [4,3,2,2,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 4
[2,2,1,2,2,2,1] => [1,2,3,2,2,2] => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3
[2,2,1,1,2,1,2,1] => [1,2,4,3,2] => [4,3,2,2,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 4
[2,1,2,1,2,1,2,1] => [1,3,3,3,2] => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3
[2,1,2,1,1,2,2,1] => [1,3,4,2,2] => [4,3,2,2,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 4
[2,1,2,2,1,1,2,1] => [1,3,2,4,2] => [4,3,2,2,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 4
[2,1,2,2,2,2,1] => [1,3,2,2,2,2] => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3
[2,1,1,2,2,1,2,1] => [1,4,2,3,2] => [4,3,2,2,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 4
[2,1,1,2,1,2,1,2] => [1,4,3,3,1] => [4,3,3,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 4
[2,1,1,2,1,2,2,1] => [1,4,3,2,2] => [4,3,2,2,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 4
[1,2,1,2,2,2,2] => [2,3,2,2,2,1] => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3
[1,2,1,2,2,1,2,1] => [2,3,2,3,2] => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 3
[1,2,1,2,1,2,1,2] => [2,3,3,3,1] => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3
[1,2,1,2,1,2,2,1] => [2,3,3,2,2] => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 3
[1,2,1,2,1,1,2,2] => [2,3,4,2,1] => [4,3,2,2,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 4
[1,2,1,1,2,1,2,2] => [2,4,3,2,1] => [4,3,2,2,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 4
[1,2,1,1,2,1,1,2,1] => [2,4,4,2] => [4,4,2,2] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 4
[1,2,1,1,2,2,1,2] => [2,4,2,3,1] => [4,3,2,2,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 4
[1,2,1,1,2,2,2,1] => [2,4,2,2,2] => [4,2,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 4
[1,2,1,1,1,2,1,2,1] => [2,5,3,2] => [5,3,2,2] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 5
[1,2,2,1,2,2,2] => [2,2,3,2,2,1] => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3
[1,2,2,1,2,1,2,1] => [2,2,3,3,2] => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 3
[1,2,2,1,1,2,1,2] => [2,2,4,3,1] => [4,3,2,2,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 4
[1,2,2,1,1,2,2,1] => [2,2,4,2,2] => [4,2,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 4
[1,2,2,2,1,2,2] => [2,2,2,3,2,1] => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3
[1,2,2,2,1,1,2,1] => [2,2,2,4,2] => [4,2,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 4
[1,2,2,2,2,1,2] => [2,2,2,2,3,1] => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3
[1,1,2,2,2,2,2] => [3,2,2,2,2,1] => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3
[1,1,2,2,2,1,2,1] => [3,2,2,3,2] => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 3
[1,1,2,2,1,2,1,2] => [3,2,3,3,1] => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3
[1,1,2,2,1,2,2,1] => [3,2,3,2,2] => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 3
[1,1,2,1,2,1,2,2] => [3,3,3,2,1] => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3
[1,1,2,1,2,1,1,2,1] => [3,3,4,2] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 4
[1,1,2,1,2,2,2,1] => [3,3,2,2,2] => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 3
[1,1,2,1,1,2,1,2,1] => [3,4,3,2] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 4
[1,1,2,1,1,1,2,2,1] => [3,5,2,2] => [5,3,2,2] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 5
[1,1,1,2,2,1,2,2] => [4,2,3,2,1] => [4,3,2,2,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 4
[1,1,1,2,2,1,1,2,1] => [4,2,4,2] => [4,4,2,2] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 4
[1,1,1,2,2,2,1,2] => [4,2,2,3,1] => [4,3,2,2,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 4
[1,1,1,2,2,2,2,1] => [4,2,2,2,2] => [4,2,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 4
[1,1,1,2,1,2,2,2] => [4,3,2,2,1] => [4,3,2,2,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 4
[1,1,1,2,1,2,1,2,1] => [4,3,3,2] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 4
[1,1,1,1,2,2,1,2,1] => [5,2,3,2] => [5,3,2,2] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 5
[1,1,1,1,2,1,2,2,1] => [5,3,2,2] => [5,3,2,2] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 5
[3,1,2,2,2,1] => [1,1,3,2,2,2] => [3,2,2,2,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 3
[3,2,1,2,2,1] => [1,1,2,3,2,2] => [3,2,2,2,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 3
[2,2,1,2,1,2,1,1] => [1,2,3,3,3] => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3
[2,2,1,1,1,2,1,1,1] => [1,2,5,4] => [5,4,2,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 5
[2,1,2,1,1,1,2,1,1] => [1,3,5,3] => [5,3,3,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 5
[2,1,2,1,2,1,1,2] => [1,3,3,4,1] => [4,3,3,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 4
[2,1,2,1,2,2,1,1] => [1,3,3,2,3] => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3
[2,1,2,1,1,2,1,1,1] => [1,3,4,4] => [4,4,3,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 4
[2,1,1,2,1,1,1,2,1] => [1,4,5,2] => [5,4,2,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 5
[2,1,1,2,1,1,2,1,1] => [1,4,4,3] => [4,4,3,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 4
[2,1,1,2,1,2,1,1,1] => [1,4,3,4] => [4,4,3,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 4
[2,1,1,1,2,1,1,2,1] => [1,5,4,2] => [5,4,2,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 5
[2,1,1,1,2,1,2,1,1] => [1,5,3,3] => [5,3,3,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 5
[2,1,1,1,2,2,1,1,1] => [1,5,2,4] => [5,4,2,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 5
[1,2,1,2,1,1,2,1,1] => [2,3,4,3] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 4
[1,2,1,1,2,1,2,1,1] => [2,4,3,3] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 4
[1,2,1,1,1,2,1,1,2] => [2,5,4,1] => [5,4,2,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 5
[1,2,1,1,1,2,2,1,1] => [2,5,2,3] => [5,3,2,2] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 5
[1,2,1,1,1,1,2,1,1,1] => [2,6,4] => [6,4,2] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 6
[1,2,2,1,1,1,2,1,1] => [2,2,5,3] => [5,3,2,2] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 5
[1,2,2,2,1,2,1,1] => [2,2,2,3,3] => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 3
[1,2,2,1,2,1,1,2] => [2,2,3,4,1] => [4,3,2,2,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 4
[1,2,2,1,2,2,1,1] => [2,2,3,2,3] => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 3
[1,2,1,2,1,1,1,2,1] => [2,3,5,2] => [5,3,2,2] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 5
[1,2,1,2,2,1,1,2] => [2,3,2,4,1] => [4,3,2,2,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 4
[1,2,1,2,2,2,1,1] => [2,3,2,2,3] => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 3
[1,2,1,2,1,2,1,1,1] => [2,3,3,4] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 4
[1,2,1,1,2,1,1,1,2] => [2,4,5,1] => [5,4,2,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 5
[1,2,1,1,2,2,1,1,1] => [2,4,2,4] => [4,4,2,2] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 4
[1,2,1,1,1,2,1,1,1,1] => [2,5,5] => [5,5,2] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 5
[1,1,2,1,1,1,2,1,2] => [3,5,3,1] => [5,3,3,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 5
[1,1,2,1,1,2,1,1,2] => [3,4,4,1] => [4,4,3,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 4
[1,1,2,1,1,2,2,1,1] => [3,4,2,3] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 4
[1,1,2,1,1,1,2,1,1,1] => [3,5,4] => [5,4,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 5
[1,1,2,2,1,1,1,2,1] => [3,2,5,2] => [5,3,2,2] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 5
[1,1,2,2,1,1,2,1,1] => [3,2,4,3] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 4
[1,1,2,1,2,1,1,1,2] => [3,3,5,1] => [5,3,3,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 5
[1,1,2,1,2,2,1,1,1] => [3,3,2,4] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 4
[1,1,1,2,1,1,1,2,2] => [4,5,2,1] => [5,4,2,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 5
[1,1,1,2,1,1,1,1,2,1] => [4,6,2] => [6,4,2] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 6
[1,1,1,2,1,1,2,1,2] => [4,4,3,1] => [4,4,3,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 4
[1,1,1,2,1,1,1,2,1,1] => [4,5,3] => [5,4,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 5
[1,1,1,2,1,2,1,1,2] => [4,3,4,1] => [4,4,3,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 4
[1,1,1,2,1,1,2,1,1,1] => [4,4,4] => [4,4,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 4
[1,1,1,2,2,1,1,1,2] => [4,2,5,1] => [5,4,2,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 5
[1,1,1,2,2,1,2,1,1] => [4,2,3,3] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 4
[1,1,1,2,1,2,1,1,1,1] => [4,3,5] => [5,4,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 5
[1,1,1,1,2,1,1,1,2,1] => [5,5,2] => [5,5,2] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 5
[1,1,1,1,2,1,2,1,1,1] => [5,3,4] => [5,4,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 5
[2,2,2,2,2,1,1] => [1,2,2,2,2,3] => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3
[1,1,1,1,1,2,2,1,1,1] => [6,2,4] => [6,4,2] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 6
[1,1,1,1,1,2,1,1,2,1] => [6,4,2] => [6,4,2] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 6
[1,1,1,1,2,1,1,2,2] => [5,4,2,1] => [5,4,2,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 5
[1,1,1,1,2,2,2,1,1] => [5,2,2,3] => [5,3,2,2] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 5
[1,1,1,1,2,2,1,1,2] => [5,2,4,1] => [5,4,2,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 5
[1,1,1,1,1,1,2,1,1,1,1] => [7,5] => [7,5] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 7
[2,1,1,2,1,1,1,1,1] => [1,4,6] => [6,4,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 6
[2,1,1,1,1,2,1,1,1] => [1,6,4] => [6,4,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 6
[2,1,1,1,2,1,1,1,1] => [1,5,5] => [5,5,1] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 5
[1,1,1,1,1,2,1,2,1,1] => [6,3,3] => [6,3,3] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 6
[1,1,1,1,2,1,2,1,2] => [5,3,3,1] => [5,3,3,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 5
[1,1,1,1,1,2,1,1,1,2] => [6,5,1] => [6,5,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 6
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,2,1 1,4,2,1 1,7,5,2,1 1,12,11,5,2,1 1,20,23,12,5,2,1
$F_{1} = q$
$F_{2} = q + q^{2}$
$F_{3} = q + 2\ q^{2} + q^{3}$
$F_{4} = q + 4\ q^{2} + 2\ q^{3} + q^{4}$
$F_{5} = q + 7\ q^{2} + 5\ q^{3} + 2\ q^{4} + q^{5}$
$F_{6} = q + 12\ q^{2} + 11\ q^{3} + 5\ q^{4} + 2\ q^{5} + q^{6}$
$F_{7} = q + 20\ q^{2} + 23\ q^{3} + 12\ q^{4} + 5\ q^{5} + 2\ q^{6} + q^{7}$
Description
The number of odd rises of a Dyck path.
This is the number of ones at an odd position, with the initial position equal to 1.
The number of Dyck paths of semilength $n$ with $k$ up steps in odd positions and $k$ returns to the main diagonal are counted by the binomial coefficient $\binom{n-1}{k-1}$ [3,4].
This is the number of ones at an odd position, with the initial position equal to 1.
The number of Dyck paths of semilength $n$ with $k$ up steps in odd positions and $k$ returns to the main diagonal are counted by the binomial coefficient $\binom{n-1}{k-1}$ [3,4].
Map
to partition
Description
Sends a composition to the partition obtained by sorting the entries.
Map
parallelogram polyomino
Description
Return the Dyck path corresponding to the partition interpreted as a parallogram polyomino.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
Map
complement
Description
The complement of a composition.
The complement of a composition $I$ is defined as follows:
If $I$ is the empty composition, then the complement is also the empty composition. Otherwise, let $S$ be the descent set corresponding to $I=(i_1,\dots,i_k)$, that is, the subset
$$\{ i_1, i_1 + i_2, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$$
of $\{ 1, 2, \ldots, |I|-1 \}$. Then, the complement of $I$ is the composition of the same size as $I$, whose descent set is $\{ 1, 2, \ldots, |I|-1 \} \setminus S$.
The complement of a composition $I$ coincides with the reversal (Mp00038reverse) of the composition conjugate (Mp00041conjugate) to $I$.
The complement of a composition $I$ is defined as follows:
If $I$ is the empty composition, then the complement is also the empty composition. Otherwise, let $S$ be the descent set corresponding to $I=(i_1,\dots,i_k)$, that is, the subset
$$\{ i_1, i_1 + i_2, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$$
of $\{ 1, 2, \ldots, |I|-1 \}$. Then, the complement of $I$ is the composition of the same size as $I$, whose descent set is $\{ 1, 2, \ldots, |I|-1 \} \setminus S$.
The complement of a composition $I$ coincides with the reversal (Mp00038reverse) of the composition conjugate (Mp00041conjugate) to $I$.
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