Identifier
Values
[1] => [1,0,1,0] => [1,1] => [2] => 2
[2] => [1,1,0,0,1,0] => [2,1] => [1,2] => 2
[1,1] => [1,0,1,1,0,0] => [1,2] => [2,1] => 1
[3] => [1,1,1,0,0,0,1,0] => [3,1] => [1,1,2] => 2
[2,1] => [1,0,1,0,1,0] => [1,1,1] => [3] => 3
[1,1,1] => [1,0,1,1,1,0,0,0] => [1,3] => [2,1,1] => 1
[4] => [1,1,1,1,0,0,0,0,1,0] => [4,1] => [1,1,1,2] => 2
[3,1] => [1,1,0,1,0,0,1,0] => [2,1,1] => [1,3] => 3
[2,2] => [1,1,0,0,1,1,0,0] => [2,2] => [1,2,1] => 1
[2,1,1] => [1,0,1,1,0,1,0,0] => [1,2,1] => [2,2] => 2
[1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,4] => [2,1,1,1] => 1
[5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,1] => [1,1,1,1,2] => 2
[4,1] => [1,1,1,0,1,0,0,0,1,0] => [3,1,1] => [1,1,3] => 3
[3,2] => [1,1,0,0,1,0,1,0] => [2,1,1] => [1,3] => 3
[3,1,1] => [1,0,1,1,0,0,1,0] => [1,2,1] => [2,2] => 2
[2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,2] => [3,1] => 1
[2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,3,1] => [2,1,2] => 2
[1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,5] => [2,1,1,1,1] => 1
[6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,1] => [1,1,1,1,1,2] => 2
[5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [4,1,1] => [1,1,1,3] => 3
[4,2] => [1,1,1,0,0,1,0,0,1,0] => [3,1,1] => [1,1,3] => 3
[4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [2,2,1] => [1,2,2] => 2
[3,3] => [1,1,1,0,0,0,1,1,0,0] => [3,2] => [1,1,2,1] => 1
[3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,1,1] => [4] => 4
[3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [1,3,1] => [2,1,2] => 2
[2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [2,3] => [1,2,1,1] => 1
[2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,2,2] => [2,2,1] => 1
[2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,4,1] => [2,1,1,2] => 2
[1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,6] => [2,1,1,1,1,1] => 1
[6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [5,1,1] => [1,1,1,1,3] => 3
[5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [4,1,1] => [1,1,1,3] => 3
[5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [3,2,1] => [1,1,2,2] => 2
[4,3] => [1,1,1,0,0,0,1,0,1,0] => [3,1,1] => [1,1,3] => 3
[4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [2,1,1,1] => [1,4] => 4
[4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [1,3,1] => [2,1,2] => 2
[3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [2,1,2] => [1,3,1] => 1
[3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [2,2,1] => [1,2,2] => 2
[3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,2,1,1] => [2,3] => 3
[3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,4,1] => [2,1,1,2] => 2
[2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,1,3] => [3,1,1] => 1
[2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2] => [2,1,2,1] => 1
[2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,5,1] => [2,1,1,1,2] => 2
[6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,1,1] => [1,1,1,1,3] => 3
[6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [4,2,1] => [1,1,1,2,2] => 2
[5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [4,1,1] => [1,1,1,3] => 3
[5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [3,1,1,1] => [1,1,4] => 4
[5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [2,3,1] => [1,2,1,2] => 2
[4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,2] => [1,1,1,2,1] => 1
[4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [2,1,1,1] => [1,4] => 4
[4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [2,2,1] => [1,2,2] => 2
[4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [1,2,1,1] => [2,3] => 3
[4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,4,1] => [2,1,1,2] => 2
[3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [2,1,2] => [1,3,1] => 1
[3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [1,2,2] => [2,2,1] => 1
[3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,2,1] => [3,2] => 2
[3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,3,1,1] => [2,1,3] => 3
[3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,5,1] => [2,1,1,1,2] => 2
[2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,4] => [1,2,1,1,1] => 1
[2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3] => [2,2,1,1] => 1
[2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,4,2] => [2,1,1,2,1] => 1
[2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,6,1] => [2,1,1,1,1,2] => 2
[7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [5,2,1] => [1,1,1,1,2,2] => 2
[6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [5,1,1] => [1,1,1,1,3] => 3
[6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [4,1,1,1] => [1,1,1,4] => 4
[6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,3,1] => [1,1,2,1,2] => 2
[5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [4,1,1] => [1,1,1,3] => 3
[5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [3,1,1,1] => [1,1,4] => 4
[5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,1] => [1,1,2,2] => 2
[5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [2,2,1,1] => [1,2,3] => 3
[5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,4,1] => [2,1,1,2] => 2
[4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [3,1,2] => [1,1,3,1] => 1
[4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [2,1,1,1] => [1,4] => 4
[4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,2,1,1] => [2,3] => 3
[4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,2,1] => [3,2] => 2
[4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,3,1,1] => [2,1,3] => 3
[4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,5,1] => [2,1,1,1,2] => 2
[3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,3] => [1,1,2,1,1] => 1
[3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,2] => [4,1] => 1
[3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2] => [2,1,2,1] => 1
[3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1] => [1,2,1,2] => 2
[3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,2,1] => [2,2,2] => 2
[3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,4,1,1] => [2,1,1,3] => 3
[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] => [2,1,1,1,1,2] => 2
[2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,4] => [3,1,1,1] => 1
[2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,3,3] => [2,1,2,1,1] => 1
[2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,5,2] => [2,1,1,1,2,1] => 1
[7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [4,3,1] => [1,1,1,2,1,2] => 2
[6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,1,1] => [1,1,1,1,3] => 3
[6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [4,1,1,1] => [1,1,1,4] => 4
[6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [4,2,1] => [1,1,1,2,2] => 2
[6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,2,1,1] => [1,1,2,3] => 3
[6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,4,1] => [1,2,1,1,2] => 2
[5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,2] => [1,1,1,1,2,1] => 1
[5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [3,1,1,1] => [1,1,4] => 4
[5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [3,1,1,1] => [1,1,4] => 4
[5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [2,2,1,1] => [1,2,3] => 3
[5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [2,1,2,1] => [1,3,2] => 2
[5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,3,1,1] => [2,1,3] => 3
[5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,5,1] => [2,1,1,1,2] => 2
[4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,2] => [1,1,3,1] => 1
[4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [2,2,2] => [1,2,2,1] => 1
>>> Load all 676 entries. <<<
[4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1] => [1,1,2,2] => 2
[4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1] => [5] => 5
[4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,3,1,1] => [2,1,3] => 3
[4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1] => [1,2,1,2] => 2
[4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,2,1] => [2,2,2] => 2
[4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,4,1,1] => [2,1,1,3] => 3
[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] => [2,1,1,1,1,2] => 2
[3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [2,1,3] => [1,3,1,1] => 1
[3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [2,2,2] => [1,2,2,1] => 1
[3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,1,2] => [2,3,1] => 1
[3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,4,2] => [2,1,1,2,1] => 1
[3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,3,1] => [3,1,2] => 2
[3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,3,2,1] => [2,1,2,2] => 2
[2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,5] => [1,2,1,1,1,1] => 1
[2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4] => [2,2,1,1,1] => 1
[2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,4,3] => [2,1,1,2,1,1] => 1
[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] => [2,1,1,1,1,1,1,2] => 2
[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] => [1,1,1,1,1,1,2,2] => 2
[7,2,2] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [5,2,1] => [1,1,1,1,2,2] => 2
[7,1,1,1,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [3,4,1] => [1,1,2,1,1,2] => 2
[6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,1,1] => [1,1,1,1,3] => 3
[6,4,1] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [4,1,1,1] => [1,1,1,4] => 4
[6,3,2] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [4,1,1,1] => [1,1,1,4] => 4
[6,3,1,1] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,2,1,1] => [1,1,2,3] => 3
[6,2,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,1,2,1] => [1,1,3,2] => 2
[6,2,1,1,1] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,3,1,1] => [1,2,1,3] => 3
[6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,5,1] => [2,1,1,1,2] => 2
[5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [4,1,2] => [1,1,1,3,1] => 1
[5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => [3,1,1,1] => [1,1,4] => 4
[5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => [2,2,1,1] => [1,2,3] => 3
[5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1] => [1,1,2,2] => 2
[5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,1,1,1] => [1,5] => 5
[5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,3,1,1] => [2,1,3] => 3
[5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1] => [1,2,1,2] => 2
[5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,2,1] => [2,2,2] => 2
[5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,4,1,1] => [2,1,1,3] => 3
[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] => [2,1,1,1,1,2] => 2
[4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2] => [1,1,3,1] => 1
[4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,1,2] => [1,4,1] => 1
[4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2] => [2,1,2,1] => 1
[4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => [2,1,2,1] => [1,3,2] => 2
[4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => [2,2,1,1] => [1,2,3] => 3
[4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,1,1,1] => [2,4] => 4
[4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,4,1,1] => [2,1,1,3] => 3
[4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,3,1] => [3,1,2] => 2
[4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,3,2,1] => [2,1,2,2] => 2
[3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3] => [1,3,1,1] => 1
[3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3] => [2,2,1,1] => 1
[3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,2,2] => [3,2,1] => 1
[3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,3,1,2] => [2,1,3,1] => 1
[3,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,5,2] => [2,1,1,1,2,1] => 1
[3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,4,1] => [1,2,1,1,2] => 2
[3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,2,3,1] => [2,2,1,2] => 2
[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] => [2,1,1,2,2] => 2
[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] => [2,1,1,1,1,1,1,2] => 2
[2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,5] => [3,1,1,1,1] => 1
[2,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,3,4] => [2,1,2,1,1,1] => 1
[7,2,2,1] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [4,1,2,1] => [1,1,1,3,2] => 2
[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] => [1,2,1,1,1,2] => 2
[6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,2] => [1,1,1,1,1,2,1] => 1
[6,5,1] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [4,1,1,1] => [1,1,1,4] => 4
[6,4,2] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,1,1] => [1,1,1,4] => 4
[6,4,1,1] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,2,1,1] => [1,1,2,3] => 3
[6,3,3] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,2,1] => [1,1,1,2,2] => 2
[6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,1,1,1,1] => [1,1,5] => 5
[6,3,1,1,1] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,3,1,1] => [1,2,1,3] => 3
[6,2,2,2] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,3,1] => [1,1,2,1,2] => 2
[6,2,2,1,1] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,2,2,1] => [1,2,2,2] => 2
[6,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,4,1,1] => [2,1,1,3] => 3
[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] => [2,1,1,1,1,2] => 2
[5,5,2] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [4,1,2] => [1,1,1,3,1] => 1
[5,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,2,2] => [1,1,2,2,1] => 1
[5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1] => [1,1,4] => 4
[5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [2,1,1,1,1] => [1,5] => 5
[5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,3,1,1] => [2,1,3] => 3
[5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => [2,1,2,1] => [1,3,2] => 2
[5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [2,2,1,1] => [1,2,3] => 3
[5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,1,1,1] => [2,4] => 4
[5,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,4,1,1] => [2,1,1,3] => 3
[5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,3,1] => [3,1,2] => 2
[5,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,3,2,1] => [2,1,2,2] => 2
[4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3] => [1,1,1,2,1,1] => 1
[4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [2,1,1,2] => [1,4,1] => 1
[4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2] => [1,2,2,1] => 1
[4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,1,2] => [2,3,1] => 1
[4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,4,2] => [2,1,1,2,1] => 1
[4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,2,1] => [1,3,2] => 2
[4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,2,1] => [2,2,2] => 2
[4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,2,1,1] => [3,3] => 3
[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] => [2,1,4] => 4
[4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,4,1] => [1,2,1,1,2] => 2
[4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,2,3,1] => [2,2,1,2] => 2
[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] => [2,1,1,2,2] => 2
[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] => [2,1,1,1,1,1,1,2] => 2
[3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,4] => [1,1,2,1,1,1] => 1
[3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,3] => [4,1,1] => 1
[3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,3,3] => [2,1,2,1,1] => 1
[3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,3,2] => [1,2,1,2,1] => 1
[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] => 1
[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] => [2,1,1,3,1] => 1
[3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,4,1] => [3,1,1,2] => 2
[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] => [2,1,2,1,2] => 2
[2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,6] => [1,2,1,1,1,1,1] => 1
[2,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,2,5] => [2,2,1,1,1,1] => 1
[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] => [2,1,1,1,1,2,1,1] => 1
[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] => [1,1,1,1,2,1,1,2] => 2
[7,3,3] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [5,2,1] => [1,1,1,1,2,2] => 2
[7,2,2,2] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [4,3,1] => [1,1,1,2,1,2] => 2
[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] => [1,1,2,2,2] => 2
[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] => [2,1,1,1,1,2] => 2
[6,6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [5,1,2] => [1,1,1,1,3,1] => 1
[6,5,2] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [4,1,1,1] => [1,1,1,4] => 4
[6,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,2,1,1] => [1,1,2,3] => 3
[6,4,3] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,1,1,1] => [1,1,1,4] => 4
[6,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,1,1,1,1] => [1,1,5] => 5
[6,4,1,1,1] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,3,1,1] => [1,2,1,3] => 3
[6,3,3,1] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,1,2,1] => [1,1,3,2] => 2
[6,3,2,2] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,1,1] => [1,1,2,3] => 3
[6,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,2,1,1,1] => [1,2,4] => 4
[6,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,4,1,1] => [2,1,1,3] => 3
[6,2,2,2,1] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,1,3,1] => [1,3,1,2] => 2
[6,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,3,2,1] => [2,1,2,2] => 2
[5,5,3] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,1,2] => [1,1,1,3,1] => 1
[5,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,1,1,2] => [1,1,4,1] => 1
[5,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,2] => [1,2,1,2,1] => 1
[5,4,4] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,2,1] => [1,1,1,2,2] => 2
[5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,1,1,1] => [1,5] => 5
[5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => [2,2,1,1] => [1,2,3] => 3
[5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,1,1,1] => [2,4] => 4
[5,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,4,1,1] => [2,1,1,3] => 3
[5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,2,1] => [1,3,2] => 2
[5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,1] => [2,2,2] => 2
[5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,2,1,1] => [3,3] => 3
[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] => [2,1,4] => 4
[5,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,4,1] => [1,2,1,1,2] => 2
[5,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,2,3,1] => [2,2,1,2] => 2
[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] => [2,1,1,2,2] => 2
[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] => [2,1,1,1,1,1,1,2] => 2
[4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,1,3] => [1,1,3,1,1] => 1
[4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,2] => [1,4,1] => 1
[4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,1,2] => [2,3,1] => 1
[4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,2,2] => [3,2,1] => 1
[4,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,3,1,2] => [2,1,3,1] => 1
[4,4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,5,2] => [2,1,1,1,2,1] => 1
[4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,3,1] => [1,1,2,1,2] => 2
[4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,2,1] => [4,2] => 2
[4,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,3,2,1] => [2,1,2,2] => 2
[4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,1] => [1,2,1,3] => 3
[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] => [2,2,3] => 3
[4,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,4,1] => [3,1,1,2] => 2
[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] => [2,1,2,1,2] => 2
[3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4] => [1,3,1,1,1] => 1
[3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,2,3] => [1,2,2,1,1] => 1
[3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,1,3] => [2,3,1,1] => 1
[3,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,4,3] => [2,1,1,2,1,1] => 1
[3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,3,2] => [3,1,2,1] => 1
[3,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,3,2,2] => [2,1,2,2,1] => 1
[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] => [1,2,1,1,1,2] => 2
[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] => [2,2,1,1,2] => 2
[7,3,3,1] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [4,1,2,1] => [1,1,1,3,2] => 2
[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] => [1,1,3,1,2] => 2
[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] => [1,2,1,2,2] => 2
[6,6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [5,1,2] => [1,1,1,1,3,1] => 1
[6,6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [4,2,2] => [1,1,1,2,2,1] => 1
[6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,1,1,1] => [1,1,1,4] => 4
[6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,1,1,1,1] => [1,1,5] => 5
[6,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,3,1,1] => [1,2,1,3] => 3
[6,4,4] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,2,1] => [1,1,1,2,2] => 2
[6,4,3,1] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,1,1,1,1] => [1,1,5] => 5
[6,4,2,2] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,1,1] => [1,1,2,3] => 3
[6,4,2,1,1] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,2,1,1,1] => [1,2,4] => 4
[6,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,4,1,1] => [2,1,1,3] => 3
[6,3,3,2] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,1,2,1] => [1,1,3,2] => 2
[6,3,3,1,1] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,2,2,1] => [1,2,2,2] => 2
[6,3,2,2,1] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,1,2,1,1] => [1,3,3] => 3
[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] => [2,1,4] => 4
[6,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,4,1] => [1,2,1,1,2] => 2
[6,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,2,3,1] => [2,2,1,2] => 2
[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] => [2,1,1,2,2] => 2
[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] => [2,1,1,1,1,1,1,2] => 2
[5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,1,2] => [1,1,1,3,1] => 1
[5,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,1,1,2] => [1,1,4,1] => 1
[5,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,2] => [1,1,2,2,1] => 1
[5,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,2,1,2] => [1,2,3,1] => 1
[5,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,4,2] => [2,1,1,2,1] => 1
[5,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,1,2,1] => [1,1,3,2] => 2
[5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1] => [1,5] => 5
[5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,1,1,1] => [2,4] => 4
[5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,2,1,1] => [3,3] => 3
[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] => [2,1,4] => 4
[5,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,3,1] => [1,1,2,1,2] => 2
[5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,2,1] => [4,2] => 2
[5,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,3,2,1] => [2,1,2,2] => 2
[5,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,3,1,1] => [1,2,1,3] => 3
[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] => [2,2,3] => 3
[5,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,4,1] => [3,1,1,2] => 2
[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] => [2,1,2,1,2] => 2
[4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,1,3] => [1,1,3,1,1] => 1
[4,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,2,3] => [1,2,2,1,1] => 1
[4,4,3,3] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,2] => [1,1,2,2,1] => 1
[4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,2] => [5,1] => 1
[4,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,3,1,2] => [2,1,3,1] => 1
[4,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,2] => [1,2,1,2,1] => 1
[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] => 1
[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] => [2,1,1,3,1] => 1
[4,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,1,3,1] => [1,3,1,2] => 2
[4,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,2,2,1] => [1,2,2,2] => 2
[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] => [2,3,2] => 2
[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] => [2,1,1,2,2] => 2
[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] => [3,1,3] => 3
[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] => [2,1,2,3] => 3
[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] => [1,2,1,1,1,2] => 2
[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] => [2,2,1,1,2] => 2
[3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,4] => [1,3,1,1,1] => 1
[3,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4] => [2,2,1,1,1] => 1
[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] => 1
[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] => [2,1,3,1,1] => 1
[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] => [1,2,1,1,2,1] => 1
[3,3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,2,3,2] => [2,2,1,2,1] => 1
[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] => [2,1,1,2,1,1,1,1] => 1
[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] => [1,1,1,1,1,1,2,2] => 2
[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] => [1,1,2,1,1,1,1,2] => 2
[7,4,4] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [5,2,1] => [1,1,1,1,2,2] => 2
[7,3,3,2] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [4,1,2,1] => [1,1,1,3,2] => 2
[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] => [1,1,2,2,2] => 2
[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] => [1,1,3,3] => 3
[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] => [1,2,1,4] => 4
[7,2,2,2,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,4,1] => [1,1,2,1,1,2] => 2
[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] => [1,2,2,1,2] => 2
[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] => [2,1,1,2,2] => 2
[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] => [2,1,1,1,1,1,1,2] => 2
[6,6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [5,1,2] => [1,1,1,1,3,1] => 1
[6,6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [3,3,2] => [1,1,2,1,2,1] => 1
[6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,1,1] => [1,1,1,4] => 4
[6,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,1,1,1,1] => [1,1,5] => 5
[6,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,1,1] => [1,1,2,3] => 3
[6,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,2,1,1,1] => [1,2,4] => 4
[6,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,4,1,1] => [2,1,1,3] => 3
[6,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,1,2,1] => [1,1,3,2] => 2
[6,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,1,1,1] => [1,1,5] => 5
[6,4,3,1,1] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,2,1,1,1] => [1,2,4] => 4
[6,4,2,2,1] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,1,2,1,1] => [1,3,3] => 3
[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] => [2,1,4] => 4
[6,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,3,1] => [1,1,2,1,2] => 2
[6,3,3,2,1] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,1,1,2,1] => [1,4,2] => 2
[6,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,3,2,1] => [2,1,2,2] => 2
[6,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,3,1,1] => [1,2,1,3] => 3
[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] => [2,2,3] => 3
[6,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,4,1] => [3,1,1,2] => 2
[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] => [2,1,2,1,2] => 2
[5,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,3] => [1,1,1,1,2,1,1] => 1
[5,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,1,1,2] => [1,1,4,1] => 1
[5,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,1,1,2] => [1,1,4,1] => 1
[5,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,2,1,2] => [1,2,3,1] => 1
[5,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,1,2,2] => [1,3,2,1] => 1
[5,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,3,1,2] => [2,1,3,1] => 1
[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] => [2,1,1,1,2,1] => 1
[5,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,1,2,1] => [1,1,3,2] => 2
[5,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,2,2,1] => [1,2,2,2] => 2
[5,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => [1,1,2,3] => 3
[5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1] => [6] => 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] => [2,1,4] => 4
[5,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,1] => [1,2,1,3] => 3
[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] => [2,2,3] => 3
[5,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,1,3,1] => [1,3,1,2] => 2
[5,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,2,2,1] => [1,2,2,2] => 2
[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] => [2,3,2] => 2
[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] => [2,1,1,2,2] => 2
[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] => [3,1,3] => 3
[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] => [2,1,2,3] => 3
[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] => [1,2,1,1,1,2] => 2
[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] => [2,2,1,1,2] => 2
[4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,3] => [1,1,3,1,1] => 1
[4,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,1,1,3] => [1,4,1,1] => 1
[4,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,3,3] => [2,1,2,1,1] => 1
[4,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,1,2,2] => [1,3,2,1] => 1
[4,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,2,1,2] => [1,2,3,1] => 1
[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] => [2,4,1] => 1
[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] => [2,1,1,3,1] => 1
[4,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,3,2] => [3,1,2,1] => 1
[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] => [2,1,2,2,1] => 1
[4,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,1] => [1,3,1,2] => 2
[4,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,3,1] => [2,2,1,2] => 2
[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] => [3,2,2] => 2
[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] => [2,1,3,2] => 2
[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] => [2,2,1,3] => 3
[3,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,5] => [1,1,2,1,1,1,1] => 1
[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] => 1
[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] => [2,1,2,1,1,1] => 1
[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] => [1,2,1,2,1,1] => 1
[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] => [2,2,2,1,1] => 1
[8,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,8,1] => [2,1,1,1,1,1,1,2] => 2
[7,4,4,1] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [4,1,2,1] => [1,1,1,3,2] => 2
[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] => [1,1,3,3] => 3
[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] => [1,2,1,4] => 4
[7,3,3,3] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [4,3,1] => [1,1,1,2,1,2] => 2
[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] => [1,2,1,2,2] => 2
[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] => [1,2,2,3] => 3
[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] => [1,3,1,1,2] => 2
[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] => [2,1,2,1,2] => 2
[6,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,1,2] => [1,1,1,1,3,1] => 1
[6,6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [4,2,2] => [1,1,1,2,2,1] => 1
[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] => [1,1,2,3,1] => 1
[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] => [1,2,1,1,2,1] => 1
[6,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,2,1] => [1,1,1,1,2,2] => 2
[6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1,1] => [1,1,5] => 5
[6,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,1,1,1,1] => [1,1,5] => 5
[6,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,2,1,1,1] => [1,2,4] => 4
[6,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,1,2,1,1] => [1,3,3] => 3
[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] => [2,1,4] => 4
[6,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,2,1] => [1,1,3,2] => 2
[6,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,2,2,1] => [1,2,2,2] => 2
[6,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,1] => [1,1,2,3] => 3
[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] => [1,6] => 6
[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] => [2,1,4] => 4
[6,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,1] => [1,2,1,3] => 3
[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] => [2,2,3] => 3
[6,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,1,3,1] => [1,3,1,2] => 2
[6,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,2,2,1] => [1,2,2,2] => 2
[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] => [2,3,2] => 2
[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] => [2,1,1,2,2] => 2
[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] => [3,1,3] => 3
[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] => [2,1,2,3] => 3
[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] => [1,2,1,1,1,2] => 2
[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] => [2,2,1,1,2] => 2
[5,5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [4,1,3] => [1,1,1,3,1,1] => 1
[5,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,1,1,2] => [1,1,4,1] => 1
[5,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,2,1,2] => [1,2,3,1] => 1
[5,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,2] => [1,1,2,2,1] => 1
[5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,1,1,1,2] => [1,5,1] => 1
[5,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,3,1,2] => [2,1,3,1] => 1
[5,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,2] => [1,2,1,2,1] => 1
[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] => 1
[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] => [2,1,1,3,1] => 1
[5,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,2,1] => [1,1,3,2] => 2
[5,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,1,1,2,1] => [1,4,2] => 2
[5,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,3,2,1] => [2,1,2,2] => 2
[5,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,1,2,1,1] => [1,3,3] => 3
[5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,2,1,1,1] => [1,2,4] => 4
[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] => [2,5] => 5
[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] => [3,1,3] => 3
[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] => [2,1,2,3] => 3
[5,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,1] => [1,3,1,2] => 2
[5,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,3,1] => [2,2,1,2] => 2
[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] => [3,2,2] => 2
[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] => [2,1,3,2] => 2
[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] => [2,2,1,3] => 3
[4,4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4] => [1,1,1,2,1,1,1] => 1
[4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,1,1,3] => [1,4,1,1] => 1
[4,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,2,3] => [1,2,2,1,1] => 1
[4,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,1,3] => [2,3,1,1] => 1
[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] => [2,1,1,2,1,1] => 1
[4,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,2,2] => [1,3,2,1] => 1
[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] => 1
[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] => [3,3,1] => 1
[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] => [2,1,4,1] => 1
[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] => [1,2,1,1,2,1] => 1
[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] => [2,2,1,2,1] => 1
[4,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,4,1] => [1,1,2,1,1,2] => 2
[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] => [4,1,2] => 2
[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] => [2,1,2,1,2] => 2
[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] => [1,2,1,2,2] => 2
[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] => [2,2,2,2] => 2
[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] => [3,1,1,3] => 3
[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] => [1,3,1,1,1,1] => 1
[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] => [1,2,2,1,1,1] => 1
[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] => [2,3,1,1,1] => 1
[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] => [2,2,1,1,1,1,1,1] => 1
[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] => [2,1,1,1,1,1,1,2] => 2
[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] => [1,1,1,1,4,1] => 1
[7,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,2,1] => [1,1,1,1,2,2] => 2
[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] => [1,1,3,3] => 3
[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] => [1,2,1,4] => 4
[7,4,4,2] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [4,1,2,1] => [1,1,1,3,2] => 2
[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] => [1,1,2,2,2] => 2
[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] => [1,2,1,4] => 4
[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] => [1,2,2,3] => 3
[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] => [1,1,3,1,2] => 2
[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] => [1,1,2,2,2] => 2
[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] => [1,2,3,2] => 2
[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] => [2,1,1,2,2] => 2
[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] => [1,3,1,3] => 3
[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] => [2,1,2,3] => 3
[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] => [1,2,1,1,1,2] => 2
[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] => [2,2,1,1,2] => 2
[6,6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,1,2] => [1,1,1,1,3,1] => 1
[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] => [1,1,2,3,1] => 1
[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] => [1,1,3,2,1] => 1
[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] => [1,2,1,3,1] => 1
[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] => [2,1,1,1,2,1] => 1
[6,5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [4,1,2,1] => [1,1,1,3,2] => 2
[6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1,1] => [1,1,5] => 5
[6,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,2,1,1,1] => [1,2,4] => 4
[6,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,1] => [1,1,2,3] => 3
[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] => [1,6] => 6
[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] => [2,1,4] => 4
[6,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,1] => [1,2,1,3] => 3
[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] => [2,2,3] => 3
[6,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,1,2,1] => [1,1,3,2] => 2
[6,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,1,1,2,1] => [1,4,2] => 2
[6,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,3,2,1] => [2,1,2,2] => 2
[6,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,1,2,1,1] => [1,3,3] => 3
[6,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,2,1,1,1] => [1,2,4] => 4
[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] => [2,5] => 5
[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] => [3,1,3] => 3
[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] => [2,1,2,3] => 3
[6,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,1] => [1,3,1,2] => 2
[6,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,3,1] => [2,2,1,2] => 2
[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] => [3,2,2] => 2
[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] => [2,1,3,2] => 2
[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] => [2,2,1,3] => 3
[5,5,5,2] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [4,1,3] => [1,1,1,3,1,1] => 1
[5,5,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [3,2,3] => [1,1,2,2,1,1] => 1
[5,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,1,2] => [1,1,4,1] => 1
[5,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,1,1,1,2] => [1,5,1] => 1
[5,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,3,1,2] => [2,1,3,1] => 1
[5,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,1,2,2] => [1,3,2,1] => 1
[5,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,2,1,2] => [1,2,3,1] => 1
[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] => [2,4,1] => 1
[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] => [2,1,1,3,1] => 1
[5,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,3,2] => [3,1,2,1] => 1
[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] => [2,1,2,2,1] => 1
[5,4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,1] => [1,1,1,2,1,2] => 2
[5,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,1,1,2,1] => [1,4,2] => 2
[5,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,2,2,1] => [1,2,2,2] => 2
[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] => [2,3,2] => 2
[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] => [2,1,1,2,2] => 2
[5,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,2,1,1] => [1,3,3] => 3
[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] => [2,2,3] => 3
[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] => [3,4] => 4
[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] => [2,2,1,3] => 3
[5,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,4,1] => [1,1,2,1,1,2] => 2
[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] => [4,1,2] => 2
[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] => [2,1,2,1,2] => 2
[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] => [1,2,1,2,2] => 2
[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] => [2,2,2,2] => 2
[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] => [3,1,1,3] => 3
[4,4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,4] => [1,1,3,1,1,1] => 1
[4,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,3] => [1,4,1,1] => 1
[4,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,1,3] => [2,3,1,1] => 1
[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] => 1
[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] => [2,1,3,1,1] => 1
[4,4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2] => [1,1,2,1,2,1] => 1
[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] => [4,2,1] => 1
[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] => [2,1,2,2,1] => 1
[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] => [1,2,1,3,1] => 1
[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] => [2,2,3,1] => 1
[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] => [1,3,1,1,2] => 2
[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] => [1,2,2,1,2] => 2
[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] => [2,3,1,2] => 2
[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] => [3,1,2,2] => 2
[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] => [1,3,1,1,1,1] => 1
[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] => [2,2,1,1,1,1] => 1
[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] => [7] => 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] => [6,1] => 1
[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] => [5,2] => 2
[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] => [5,2] => 2
[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] => [5,1,1] => 1
[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] => [4,3] => 3
[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] => [4,2,1] => 1
[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] => [4,3] => 3
[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] => [4,3] => 3
[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] => [4,1,2] => 2
[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] => [3,4] => 4
[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] => [3,3,1] => 1
[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] => [3,2,2] => 2
[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] => [3,2,2] => 2
[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] => [3,4] => 4
[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] => [3,3,1] => 1
[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] => [3,4] => 4
[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] => [3,1,3] => 3
[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] => [2,5] => 5
[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] => [2,4,1] => 1
[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] => [2,3,2] => 2
[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] => [2,3,2] => 2
[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] => [2,2,3] => 3
[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] => 1
[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] => [2,2,3] => 3
[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] => [2,5] => 5
[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] => [2,4,1] => 1
[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] => [2,3,2] => 2
[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] => [2,5] => 5
[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] => [2,1,4] => 4
[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] => [1,6] => 6
[5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,2] => [1,5,1] => 1
[6,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,2,1] => [1,4,2] => 2
[5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,2,1] => [1,4,2] => 2
[6,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,2,1,1] => [1,3,3] => 3
[5,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,2,2] => [1,3,2,1] => 1
[6,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,2,1,1] => [1,3,3] => 3
[6,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,2,1,1,1] => [1,2,4] => 4
[5,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,2,1,2] => [1,2,3,1] => 1
[6,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,2,2,1] => [1,2,2,2] => 2
[6,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,2,1,1,1] => [1,2,4] => 4
[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] => [1,6] => 6
[5,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,1,2] => [1,5,1] => 1
[6,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,1,1,2,1] => [1,4,2] => 2
[6,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,1,2,1,1] => [1,3,3] => 3
[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] => [1,6] => 6
[6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1] => [1,1,5] => 5
[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] => [7,1] => 1
[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] => [6,1,1] => 1
[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] => [5,2,1] => 1
[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] => [5,2,1] => 1
[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] => [5,1,1,1] => 1
[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] => [4,3,1] => 1
[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] => [4,4] => 4
[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] => [3,4,1] => 1
[6,5,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,2,1,2,1] => [3,3,2] => 2
[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] => [3,2,3] => 3
[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] => [3,4,1] => 1
[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] => [3,1,1,3] => 3
[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] => [2,4,2] => 2
[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] => [2,4,2] => 2
[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] => [2,3,1,1,1] => 1
[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] => [2,1,3,2] => 2
[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] => [2,1,3,1,1] => 1
[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] => [2,1,1,3,1] => 1
[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] => [1,7] => 7
[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] => [1,6,1] => 1
[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] => [1,5,2] => 2
[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] => [1,5,2] => 2
[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] => [1,5,1,1] => 1
[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] => [1,4,3] => 3
[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] => [1,4,3] => 3
[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] => [1,3,1,3] => 3
[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] => [1,3,1,1,2] => 2
[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] => [1,2,3,1,1] => 1
[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] => [1,2,1,4] => 4
[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] => [1,2,1,4] => 4
[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] => [1,2,1,4] => 4
[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] => [1,2,1,1,2,1] => 1
[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] => [1,7] => 7
[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] => [1,6,1] => 1
[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] => [1,5,2] => 2
[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] => [1,7] => 7
[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] => [1,5,1,1] => 1
[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] => [1,7] => 7
[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] => [1,6,1] => 1
[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] => [1,5,1,1] => 1
[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] => [1,7] => 7
[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] => [1,6,1] => 1
[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] => [1,7] => 7
[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] => [1,1,5,1] => 1
[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] => [1,1,3,1,2] => 2
[7,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,4,1] => [1,1,2,1,1,2] => 2
[4,4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,1,4] => [1,1,3,1,1,1] => 1
[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] => [1,1,5,1] => 1
[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] => [1,1,5,1] => 1
[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] => [1,1,5,1] => 1
[6,5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,1,2,1] => [1,1,1,3,2] => 2
[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] => [8,1] => 1
[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] => [9,1] => 1
[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] => [7,1,1] => 1
[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] => [5,5] => 5
[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] => [1,8] => 8
[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] => [1,8] => 8
[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] => [1,8] => 8
[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] => [1,8] => 8
[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] => [1,8] => 8
[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] => [1,9] => 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] => [1,9] => 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] => [1,7,1] => 1
[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] => [1,6,1,1] => 1
[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] => [1,6,2] => 2
[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] => [1,6,2] => 2
[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] => [1,7,1] => 1
[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] => [1,8,1] => 1
[9,9,8,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,1,1,2] => [10,1] => 1
[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] => [1,7,1] => 1
[10,9,8,7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1,1,1] => [1,10] => 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] => [1,6,2] => 2
[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] => [6,2,1] => 1
[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] => [1,7,1] => 1
[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] => [1,1,6,1] => 1
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Description
The last part of an integer composition.
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 $I$.
Map
rise composition
Description
Send a Dyck path to the composition of sizes of its rises.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.