Identifier
Values
[2,2,1] => [2,1] => [1,0,1,1,0,0] => [1,1] => 0
[1,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [2,1] => 1
[3,3] => [3] => [1,0,1,0,1,0] => [2,1] => 1
[3,2,1] => [2,1] => [1,0,1,1,0,0] => [1,1] => 0
[2,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [2,1,1] => 1
[2,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [2,1] => 1
[1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [3,2,1] => 2
[4,3] => [3] => [1,0,1,0,1,0] => [2,1] => 1
[4,2,1] => [2,1] => [1,0,1,1,0,0] => [1,1] => 0
[3,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => [2,2,1] => 1
[3,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [2,1,1] => 1
[3,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [2,1] => 1
[2,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2] => 0
[2,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => 2
[2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [3,2,1] => 2
[1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => 3
[5,3] => [3] => [1,0,1,0,1,0] => [2,1] => 1
[5,2,1] => [2,1] => [1,0,1,1,0,0] => [1,1] => 0
[4,4] => [4] => [1,0,1,0,1,0,1,0] => [3,2,1] => 2
[4,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => [2,2,1] => 1
[4,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [2,1,1] => 1
[4,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [2,1] => 1
[3,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1] => 0
[3,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => 2
[3,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2] => 0
[3,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => 2
[3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [3,2,1] => 2
[2,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2] => 1
[2,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,1] => 3
[2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => 3
[1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1] => 4
[6,3] => [3] => [1,0,1,0,1,0] => [2,1] => 1
[6,2,1] => [2,1] => [1,0,1,1,0,0] => [1,1] => 0
[5,4] => [4] => [1,0,1,0,1,0,1,0] => [3,2,1] => 2
[5,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => [2,2,1] => 1
[5,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [2,1,1] => 1
[5,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [2,1] => 1
[4,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => 2
[4,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1] => 0
[4,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => 2
[4,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2] => 0
[4,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => 2
[4,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [3,2,1] => 2
[3,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => 1
[3,3,1,1,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [4,3,2,2,1] => 3
[3,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2] => 1
[3,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,1] => 3
[3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => 3
[2,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [3] => 0
[2,2,2,1,1,1] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => 2
[2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1] => 4
[7,3] => [3] => [1,0,1,0,1,0] => [2,1] => 1
[7,2,1] => [2,1] => [1,0,1,1,0,0] => [1,1] => 0
[6,4] => [4] => [1,0,1,0,1,0,1,0] => [3,2,1] => 2
[6,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => [2,2,1] => 1
[6,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [2,1,1] => 1
[6,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [2,1] => 1
[5,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => [4,3,2,1] => 3
[5,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => 2
[5,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1] => 0
[5,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => 2
[5,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2] => 0
[5,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => 2
[5,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [3,2,1] => 2
[4,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => 1
[4,4,1,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [4,3,3,2,1] => 3
[4,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => 1
[4,3,1,1,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [4,3,2,2,1] => 3
[4,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2] => 1
[4,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,1] => 3
[4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => 3
[3,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [3,1] => 1
[3,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 0
[3,3,2,1,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [4,3,1,1,1] => 2
[3,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [3] => 0
[3,2,2,1,1,1] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => 2
[3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1] => 4
[2,2,2,2,1,1] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => 1
[2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2] => 3
[8,3] => [3] => [1,0,1,0,1,0] => [2,1] => 1
[8,2,1] => [2,1] => [1,0,1,1,0,0] => [1,1] => 0
[7,4] => [4] => [1,0,1,0,1,0,1,0] => [3,2,1] => 2
[7,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => [2,2,1] => 1
[7,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [2,1,1] => 1
[7,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [2,1] => 1
[6,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => [4,3,2,1] => 3
[6,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => 2
[6,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1] => 0
[6,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => 2
[6,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2] => 0
[6,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => 2
[6,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [3,2,1] => 2
[5,5,1] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [4,4,3,2,1] => 3
[5,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => 1
[5,4,1,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [4,3,3,2,1] => 3
[5,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => 1
[5,3,1,1,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [4,3,2,2,1] => 3
[5,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2] => 1
[5,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,1] => 3
[5,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => 3
[4,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => 1
>>> Load all 548 entries. <<<
[4,4,2,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [4,2,2,2,1] => 2
[4,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [3,1] => 1
[4,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 0
[4,3,2,1,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [4,3,1,1,1] => 2
[4,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [3] => 0
[4,2,2,1,1,1] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => 2
[4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1] => 4
[3,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [1,1] => 0
[3,3,3,1,1] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => 2
[3,3,2,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => 1
[3,2,2,2,1,1] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => 1
[3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2] => 3
[2,2,2,2,2,1] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => 1
[2,2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [5,4,3] => 2
[9,3] => [3] => [1,0,1,0,1,0] => [2,1] => 1
[9,2,1] => [2,1] => [1,0,1,1,0,0] => [1,1] => 0
[8,4] => [4] => [1,0,1,0,1,0,1,0] => [3,2,1] => 2
[8,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => [2,2,1] => 1
[8,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [2,1,1] => 1
[8,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [2,1] => 1
[7,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => [4,3,2,1] => 3
[7,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => 2
[7,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1] => 0
[7,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => 2
[7,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2] => 0
[7,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => 2
[7,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [3,2,1] => 2
[6,6] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => 4
[6,5,1] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [4,4,3,2,1] => 3
[6,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => 1
[6,4,1,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [4,3,3,2,1] => 3
[6,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => 1
[6,3,1,1,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [4,3,2,2,1] => 3
[6,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2] => 1
[6,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,1] => 3
[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] => [4,3,2,1] => 3
[5,5,2] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [3,3,3,2,1] => 2
[5,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => 1
[5,4,2,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [4,2,2,2,1] => 2
[5,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [3,1] => 1
[5,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 0
[5,3,2,1,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [4,3,1,1,1] => 2
[5,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [3] => 0
[5,2,2,1,1,1] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => 2
[5,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1] => 4
[4,4,4] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [2,1] => 1
[4,4,3,1] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [4,2,1,1,1] => 2
[4,4,2,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => 1
[4,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [1,1] => 0
[4,3,3,1,1] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => 2
[4,3,2,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => 1
[4,2,2,2,1,1] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => 1
[4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2] => 3
[3,3,3,2,1] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,1] => 1
[3,3,3,1,1,1] => [3,3,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1] => 3
[3,3,2,2,2] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => 1
[3,2,2,2,2,1] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => 1
[3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [5,4,3] => 2
[2,2,2,2,2,2] => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => 1
[2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,4,1] => 2
[10,3] => [3] => [1,0,1,0,1,0] => [2,1] => 1
[10,2,1] => [2,1] => [1,0,1,1,0,0] => [1,1] => 0
[9,4] => [4] => [1,0,1,0,1,0,1,0] => [3,2,1] => 2
[9,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => [2,2,1] => 1
[9,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [2,1,1] => 1
[9,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [2,1] => 1
[8,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => [4,3,2,1] => 3
[8,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => 2
[8,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1] => 0
[8,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => 2
[8,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2] => 0
[8,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => 2
[8,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [3,2,1] => 2
[7,6] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => 4
[7,5,1] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [4,4,3,2,1] => 3
[7,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => 1
[7,4,1,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [4,3,3,2,1] => 3
[7,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => 1
[7,3,1,1,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [4,3,2,2,1] => 3
[7,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2] => 1
[7,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,1] => 3
[7,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => 3
[6,5,2] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [3,3,3,2,1] => 2
[6,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => 1
[6,4,2,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [4,2,2,2,1] => 2
[6,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [3,1] => 1
[6,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 0
[6,3,2,1,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [4,3,1,1,1] => 2
[6,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [3] => 0
[6,2,2,1,1,1] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => 2
[6,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1] => 4
[5,5,3] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [3,2,2,2,1] => 2
[5,4,4] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [2,1] => 1
[5,4,3,1] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [4,2,1,1,1] => 2
[5,4,2,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => 1
[5,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [1,1] => 0
[5,3,3,1,1] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => 2
[5,3,2,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => 1
[5,2,2,2,1,1] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => 1
[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] => [5,4,3,2] => 3
[4,4,4,1] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => 2
[4,4,3,2] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 1
[4,3,3,2,1] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,1] => 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] => [5,4,3,1] => 3
[4,3,2,2,2] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => 1
[4,2,2,2,2,1] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => 1
[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] => [5,4,3] => 2
[3,3,3,3,1] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [4] => 0
[3,3,3,2,2] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,1] => 1
[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] => [5,4,1,1] => 2
[3,2,2,2,2,2] => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => 1
[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] => [5,4,1] => 2
[2,2,2,2,2,2,1] => [2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => 2
[11,3] => [3] => [1,0,1,0,1,0] => [2,1] => 1
[11,2,1] => [2,1] => [1,0,1,1,0,0] => [1,1] => 0
[10,4] => [4] => [1,0,1,0,1,0,1,0] => [3,2,1] => 2
[10,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => [2,2,1] => 1
[10,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [2,1,1] => 1
[10,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [2,1] => 1
[9,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => [4,3,2,1] => 3
[9,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => 2
[9,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1] => 0
[9,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => 2
[9,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2] => 0
[9,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => 2
[9,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [3,2,1] => 2
[8,6] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => 4
[8,5,1] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [4,4,3,2,1] => 3
[8,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => 1
[8,4,1,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [4,3,3,2,1] => 3
[8,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => 1
[8,3,1,1,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [4,3,2,2,1] => 3
[8,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2] => 1
[8,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,1] => 3
[8,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => 3
[7,5,2] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [3,3,3,2,1] => 2
[7,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => 1
[7,4,2,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [4,2,2,2,1] => 2
[7,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [3,1] => 1
[7,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 0
[7,3,2,1,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [4,3,1,1,1] => 2
[7,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [3] => 0
[7,2,2,1,1,1] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => 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] => [5,4,3,2,1] => 4
[6,5,3] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [3,2,2,2,1] => 2
[6,4,4] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [2,1] => 1
[6,4,3,1] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [4,2,1,1,1] => 2
[6,4,2,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => 1
[6,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [1,1] => 0
[6,3,3,1,1] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => 2
[6,3,2,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => 1
[6,2,2,2,1,1] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => 1
[6,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2] => 3
[5,5,4] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => 2
[5,4,4,1] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => 2
[5,4,3,2] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 1
[5,3,3,2,1] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,1] => 1
[5,3,3,1,1,1] => [3,3,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1] => 3
[5,3,2,2,2] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => 1
[5,2,2,2,2,1] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => 1
[5,2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [5,4,3] => 2
[4,4,4,2] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1] => 1
[4,4,4,1,1] => [4,4,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1] => 3
[4,4,3,3] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 0
[4,3,3,3,1] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [4] => 0
[4,3,3,2,2] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,1] => 1
[4,3,3,2,1,1] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1] => 2
[4,2,2,2,2,2] => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => 1
[4,2,2,2,2,1,1] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,4,1] => 2
[3,3,3,3,2] => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [2] => 0
[3,3,3,3,1,1] => [3,3,3,1,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4] => 1
[3,3,3,2,2,1] => [3,3,2,2,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1] => 2
[3,3,2,2,2,2] => [3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1] => 2
[3,2,2,2,2,2,1] => [2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => 2
[2,2,2,2,2,2,2] => [2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => 2
[12,3] => [3] => [1,0,1,0,1,0] => [2,1] => 1
[12,2,1] => [2,1] => [1,0,1,1,0,0] => [1,1] => 0
[11,4] => [4] => [1,0,1,0,1,0,1,0] => [3,2,1] => 2
[11,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => [2,2,1] => 1
[11,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [2,1,1] => 1
[11,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [2,1] => 1
[10,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => [4,3,2,1] => 3
[10,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => 2
[10,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1] => 0
[10,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => 2
[10,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2] => 0
[10,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => 2
[10,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [3,2,1] => 2
[9,6] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => 4
[9,5,1] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [4,4,3,2,1] => 3
[9,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => 1
[9,4,1,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [4,3,3,2,1] => 3
[9,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => 1
[9,3,1,1,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [4,3,2,2,1] => 3
[9,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2] => 1
[9,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,1] => 3
[9,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => 3
[8,5,2] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [3,3,3,2,1] => 2
[8,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => 1
[8,4,2,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [4,2,2,2,1] => 2
[8,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [3,1] => 1
[8,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 0
[8,3,2,1,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [4,3,1,1,1] => 2
[8,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [3] => 0
[8,2,2,1,1,1] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => 2
[8,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1] => 4
[7,5,3] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [3,2,2,2,1] => 2
[7,4,4] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [2,1] => 1
[7,4,3,1] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [4,2,1,1,1] => 2
[7,4,2,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => 1
[7,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [1,1] => 0
[7,3,3,1,1] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => 2
[7,3,2,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => 1
[7,2,2,2,1,1] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => 1
[7,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2] => 3
[6,5,4] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => 2
[6,4,4,1] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => 2
[6,4,3,2] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 1
[6,3,3,2,1] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,1] => 1
[6,3,3,1,1,1] => [3,3,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1] => 3
[6,3,2,2,2] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => 1
[6,2,2,2,2,1] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => 1
[6,2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [5,4,3] => 2
[5,5,5] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1] => 2
[5,4,4,2] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1] => 1
[5,4,4,1,1] => [4,4,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1] => 3
[5,4,3,3] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 0
[5,3,3,3,1] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [4] => 0
[5,3,3,2,2] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,1] => 1
[5,3,3,2,1,1] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1] => 2
[5,2,2,2,2,2] => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => 1
[5,2,2,2,2,1,1] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,4,1] => 2
[4,4,4,3] => [4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1] => 0
[4,4,4,2,1] => [4,4,2,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1] => 2
[4,4,3,3,1] => [4,3,3,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1,1] => 1
[4,4,3,2,2] => [4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => 2
[4,3,3,3,2] => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [2] => 0
[4,3,3,3,1,1] => [3,3,3,1,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4] => 1
[4,3,3,2,2,1] => [3,3,2,2,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1] => 2
[4,3,2,2,2,2] => [3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1] => 2
[4,2,2,2,2,2,1] => [2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => 2
[3,3,3,3,2,1] => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => 1
[3,3,3,2,2,2] => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => 2
[3,2,2,2,2,2,2] => [2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => 2
[13,3] => [3] => [1,0,1,0,1,0] => [2,1] => 1
[13,2,1] => [2,1] => [1,0,1,1,0,0] => [1,1] => 0
[12,4] => [4] => [1,0,1,0,1,0,1,0] => [3,2,1] => 2
[12,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => [2,2,1] => 1
[12,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [2,1,1] => 1
[12,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [2,1] => 1
[11,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => [4,3,2,1] => 3
[11,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => 2
[11,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1] => 0
[11,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => 2
[11,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2] => 0
[11,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => 2
[11,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [3,2,1] => 2
[10,6] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => 4
[10,5,1] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [4,4,3,2,1] => 3
[10,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => 1
[10,4,1,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [4,3,3,2,1] => 3
[10,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => 1
[10,3,1,1,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [4,3,2,2,1] => 3
[10,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2] => 1
[10,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,1] => 3
[10,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => 3
[9,5,2] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [3,3,3,2,1] => 2
[9,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => 1
[9,4,2,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [4,2,2,2,1] => 2
[9,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [3,1] => 1
[9,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 0
[9,3,2,1,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [4,3,1,1,1] => 2
[9,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [3] => 0
[9,2,2,1,1,1] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => 2
[9,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1] => 4
[8,5,3] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [3,2,2,2,1] => 2
[8,4,4] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [2,1] => 1
[8,4,3,1] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [4,2,1,1,1] => 2
[8,4,2,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => 1
[8,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [1,1] => 0
[8,3,3,1,1] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => 2
[8,3,2,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => 1
[8,2,2,2,1,1] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => 1
[8,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2] => 3
[7,5,4] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => 2
[7,4,4,1] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => 2
[7,4,3,2] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 1
[7,3,3,2,1] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,1] => 1
[7,3,3,1,1,1] => [3,3,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1] => 3
[7,3,2,2,2] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => 1
[7,2,2,2,2,1] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => 1
[7,2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [5,4,3] => 2
[6,5,5] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1] => 2
[6,4,4,2] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1] => 1
[6,4,4,1,1] => [4,4,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1] => 3
[6,4,3,3] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 0
[6,3,3,3,1] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [4] => 0
[6,3,3,2,2] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,1] => 1
[6,3,3,2,1,1] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1] => 2
[6,2,2,2,2,2] => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => 1
[6,2,2,2,2,1,1] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,4,1] => 2
[5,5,5,1] => [5,5,1] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1] => 3
[5,4,4,3] => [4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1] => 0
[5,4,4,2,1] => [4,4,2,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1] => 2
[5,4,3,3,1] => [4,3,3,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1,1] => 1
[5,4,3,2,2] => [4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => 2
[5,3,3,3,2] => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [2] => 0
[5,3,3,3,1,1] => [3,3,3,1,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4] => 1
[5,3,3,2,2,1] => [3,3,2,2,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1] => 2
[5,3,2,2,2,2] => [3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1] => 2
[5,2,2,2,2,2,1] => [2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => 2
[4,4,4,3,1] => [4,4,3,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1] => 1
[4,4,4,2,2] => [4,4,2,2] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => 2
[4,4,3,3,2] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1,1] => 1
[4,3,3,3,2,1] => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => 1
[4,3,3,2,2,2] => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => 2
[4,2,2,2,2,2,2] => [2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => 2
[3,3,3,3,3,1] => [3,3,3,3,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => 0
[3,3,3,3,2,2] => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,2] => 1
[2,2,2,2,2,2,2,2] => [2,2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1] => 3
[14,3] => [3] => [1,0,1,0,1,0] => [2,1] => 1
[14,2,1] => [2,1] => [1,0,1,1,0,0] => [1,1] => 0
[13,4] => [4] => [1,0,1,0,1,0,1,0] => [3,2,1] => 2
[13,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => [2,2,1] => 1
[13,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [2,1,1] => 1
[13,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [2,1] => 1
[12,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => [4,3,2,1] => 3
[12,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => 2
[12,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1] => 0
[12,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => 2
[12,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => [2] => 0
[12,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => 2
[12,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [3,2,1] => 2
[11,6] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => 4
[11,5,1] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [4,4,3,2,1] => 3
[11,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => 1
[11,4,1,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [4,3,3,2,1] => 3
[11,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => 1
[11,3,1,1,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [4,3,2,2,1] => 3
[11,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2] => 1
[11,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,1] => 3
[11,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => 3
[10,5,2] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [3,3,3,2,1] => 2
[10,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => 1
[10,4,2,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [4,2,2,2,1] => 2
[10,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [3,1] => 1
[10,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 0
[10,3,2,1,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [4,3,1,1,1] => 2
[10,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [3] => 0
[10,2,2,1,1,1] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => 2
[10,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1] => 4
[9,5,3] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [3,2,2,2,1] => 2
[9,4,4] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [2,1] => 1
[9,4,3,1] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [4,2,1,1,1] => 2
[9,4,2,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => 1
[9,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [1,1] => 0
[9,3,3,1,1] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => 2
[9,3,2,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => 1
[9,2,2,2,1,1] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => 1
[9,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2] => 3
[8,5,4] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => 2
[8,4,4,1] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => 2
[8,4,3,2] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 1
[8,3,3,2,1] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,1] => 1
[8,3,3,1,1,1] => [3,3,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1] => 3
[8,3,2,2,2] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => 1
[8,2,2,2,2,1] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => 1
[8,2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [5,4,3] => 2
[7,5,5] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1] => 2
[7,4,4,2] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1] => 1
[7,4,4,1,1] => [4,4,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1] => 3
[7,4,3,3] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 0
[7,3,3,3,1] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [4] => 0
[7,3,3,2,2] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,1] => 1
[7,3,3,2,1,1] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1] => 2
[7,2,2,2,2,2] => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => 1
[7,2,2,2,2,1,1] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,4,1] => 2
[6,5,5,1] => [5,5,1] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1] => 3
[6,4,4,3] => [4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1] => 0
[6,4,4,2,1] => [4,4,2,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1] => 2
[6,4,3,3,1] => [4,3,3,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1,1] => 1
[6,4,3,2,2] => [4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => 2
[6,3,3,3,2] => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [2] => 0
[6,3,3,3,1,1] => [3,3,3,1,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4] => 1
[6,3,3,2,2,1] => [3,3,2,2,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1] => 2
[6,3,2,2,2,2] => [3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1] => 2
[6,2,2,2,2,2,1] => [2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => 2
[5,5,5,2] => [5,5,2] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1] => 2
[5,5,4,3] => [5,4,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => 1
[5,4,4,3,1] => [4,4,3,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1] => 1
[5,4,4,2,2] => [4,4,2,2] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => 2
[5,4,3,3,2] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1,1] => 1
[5,3,3,3,2,1] => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => 1
[5,3,3,2,2,2] => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => 2
[5,2,2,2,2,2,2] => [2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => 2
[4,4,4,4,1] => [4,4,4,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1] => 1
[4,4,4,3,2] => [4,4,3,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1] => 1
[4,4,3,3,3] => [4,3,3,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0
[4,3,3,3,3,1] => [3,3,3,3,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => 0
[4,3,3,3,2,2] => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,2] => 1
[3,3,3,3,3,2] => [3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => 0
[3,3,3,2,2,2,2] => [3,3,2,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1] => 3
[3,2,2,2,2,2,2,2] => [2,2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1] => 3
[6,3,3,3,2,1] => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => 1
[6,4,4,3,2] => [4,4,3,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1] => 1
[5,4,4,3,2] => [4,4,3,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1] => 1
[6,4,3,3,2] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1,1] => 1
[6,4,4,2,2] => [4,4,2,2] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => 2
[6,4,4,3,1] => [4,4,3,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1] => 1
[6,5,4,3] => [5,4,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => 1
[6,3,3,3,3,2,1] => [3,3,3,3,2,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,3] => 1
[3,3,3,3,3,2,1] => [3,3,3,3,2,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,3] => 1
[7,2,2,2,2,2,1] => [2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => 2
[5,4,3,3,3,2] => [4,3,3,3,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1,1] => 1
[4,3,3,3,3,2] => [3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => 0
[4,4,4,3,2,2] => [4,4,3,2,2] => [1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1] => 2
[4,4,4,4,3,1] => [4,4,4,3,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [6,1,1] => 1
[4,4,4,4,2,1] => [4,4,4,2,1] => [1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [6,3,1] => 2
[7,3,3,3,2,1] => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => 1
[6,5,5,4,3] => [5,5,4,3] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => 1
[5,4,4,4,3] => [4,4,4,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1] => 0
[5,4,3,3,3] => [4,3,3,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0
[4,4,4,4,2] => [4,4,4,2] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,1] => 1
[6,5,5,4] => [5,5,4] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1] => 1
[7,5,4,3] => [5,4,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => 1
[2,2,2,2,2,2,2,2,2] => [2,2,2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1] => 4
[3,3,3,3,3,3,3,3] => [3,3,3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1] => 2
[3,3,3,3,3,3,1] => [3,3,3,3,3,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1] => 1
[3,3,3,3,3,3,3] => [3,3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 1
[3,3,3,3,3,2,2] => [3,3,3,3,2,2] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [4,3] => 1
[4,4,4,3,3,3] => [4,4,3,3,3] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1] => 1
[5,5,5,5] => [5,5,5] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => 1
[6,6,6,6] => [6,6,6] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => 2
[6,2,2,2,2,2,2] => [2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => 2
[6,6,6] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1] => 3
[7,6,6] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1] => 3
[10,4,4] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [2,1] => 1
[6,6,6,6,6] => [6,6,6,6] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => 1
[8,2,2,2,2,2,2] => [2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => 2
[15,5,5] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1] => 2
[7,7,7,7] => [7,7,7] => [1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1] => 3
[7,7,7] => [7,7] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1] => 4
[8,5,5,1] => [5,5,1] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1] => 3
[9,5,5,1] => [5,5,1] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1] => 3
[6,5,5,5] => [5,5,5] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => 1
[4,4,4,4,4,1] => [4,4,4,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 0
[5,5,5,5,1] => [5,5,5,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [6,2,1] => 2
search for individual values
searching the database for the individual values of this statistic
Description
The multiplicity of the standard representation in the Kronecker square corresponding to a partition.
The Kronecker coefficient is the multiplicity $g_{\mu,\nu}^\lambda$ of the Specht module $S^\lambda$ in $S^\mu\otimes S^\nu$:
$$ S^\mu\otimes S^\nu = \bigoplus_\lambda g_{\mu,\nu}^\lambda S^\lambda $$
This statistic records the Kronecker coefficient $g_{\lambda,\lambda}^{(n-1)1}$, for $\lambda\vdash n > 1$. For $n\leq1$ the statistic is undefined.
It follows from [3, Prop.4.1] (or, slightly easier from [3, Thm.4.2]) that this is one less than St000159The number of distinct parts of the integer partition., the number of distinct parts of the partition.
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.
Map
to partition
Description
The cut-out partition of a Dyck path.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ is the number of down-steps before the $(n+1-i)$-th up-step of $D$.
This map is a bijection between Dyck paths of size $n$ and partitions inside the staircase partition $(n-1,\ldots,2,1)$.
Map
first row removal
Description
Removes the first entry of an integer partition