Identifier
Values
[1,1,1,1] => [1,1,1] => [1,1] => [1] => 0
[2,1,1,1] => [1,1,1] => [1,1] => [1] => 0
[1,1,1,1,1] => [1,1,1,1] => [1,1,1] => [1,1] => 0
[3,1,1,1] => [1,1,1] => [1,1] => [1] => 0
[2,2,1,1] => [2,1,1] => [1,1] => [1] => 0
[2,1,1,1,1] => [1,1,1,1] => [1,1,1] => [1,1] => 0
[1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => [1,1,1] => 0
[4,1,1,1] => [1,1,1] => [1,1] => [1] => 0
[3,2,1,1] => [2,1,1] => [1,1] => [1] => 0
[3,1,1,1,1] => [1,1,1,1] => [1,1,1] => [1,1] => 0
[2,2,2,1] => [2,2,1] => [2,1] => [1] => 0
[2,2,1,1,1] => [2,1,1,1] => [1,1,1] => [1,1] => 0
[2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => [1,1,1] => 0
[1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 0
[5,1,1,1] => [1,1,1] => [1,1] => [1] => 0
[4,2,1,1] => [2,1,1] => [1,1] => [1] => 0
[4,1,1,1,1] => [1,1,1,1] => [1,1,1] => [1,1] => 0
[3,3,1,1] => [3,1,1] => [1,1] => [1] => 0
[3,2,2,1] => [2,2,1] => [2,1] => [1] => 0
[3,2,1,1,1] => [2,1,1,1] => [1,1,1] => [1,1] => 0
[3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => [1,1,1] => 0
[2,2,2,2] => [2,2,2] => [2,2] => [2] => 1
[2,2,2,1,1] => [2,2,1,1] => [2,1,1] => [1,1] => 0
[2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1] => 0
[2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 0
[1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 0
[6,1,1,1] => [1,1,1] => [1,1] => [1] => 0
[5,2,1,1] => [2,1,1] => [1,1] => [1] => 0
[5,1,1,1,1] => [1,1,1,1] => [1,1,1] => [1,1] => 0
[4,3,1,1] => [3,1,1] => [1,1] => [1] => 0
[4,2,2,1] => [2,2,1] => [2,1] => [1] => 0
[4,2,1,1,1] => [2,1,1,1] => [1,1,1] => [1,1] => 0
[4,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => [1,1,1] => 0
[3,3,2,1] => [3,2,1] => [2,1] => [1] => 0
[3,3,1,1,1] => [3,1,1,1] => [1,1,1] => [1,1] => 0
[3,2,2,2] => [2,2,2] => [2,2] => [2] => 1
[3,2,2,1,1] => [2,2,1,1] => [2,1,1] => [1,1] => 0
[3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1] => 0
[3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 0
[2,2,2,2,1] => [2,2,2,1] => [2,2,1] => [2,1] => 1
[2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 0
[2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 0
[2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[7,1,1,1] => [1,1,1] => [1,1] => [1] => 0
[6,2,1,1] => [2,1,1] => [1,1] => [1] => 0
[6,1,1,1,1] => [1,1,1,1] => [1,1,1] => [1,1] => 0
[5,3,1,1] => [3,1,1] => [1,1] => [1] => 0
[5,2,2,1] => [2,2,1] => [2,1] => [1] => 0
[5,2,1,1,1] => [2,1,1,1] => [1,1,1] => [1,1] => 0
[5,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => [1,1,1] => 0
[4,4,1,1] => [4,1,1] => [1,1] => [1] => 0
[4,3,2,1] => [3,2,1] => [2,1] => [1] => 0
[4,3,1,1,1] => [3,1,1,1] => [1,1,1] => [1,1] => 0
[4,2,2,2] => [2,2,2] => [2,2] => [2] => 1
[4,2,2,1,1] => [2,2,1,1] => [2,1,1] => [1,1] => 0
[4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1] => 0
[4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 0
[3,3,3,1] => [3,3,1] => [3,1] => [1] => 0
[3,3,2,2] => [3,2,2] => [2,2] => [2] => 1
[3,3,2,1,1] => [3,2,1,1] => [2,1,1] => [1,1] => 0
[3,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1] => 0
[3,2,2,2,1] => [2,2,2,1] => [2,2,1] => [2,1] => 1
[3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 0
[3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 0
[3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 0
[2,2,2,2,2] => [2,2,2,2] => [2,2,2] => [2,2] => 1
[2,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 0
[2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[8,1,1,1] => [1,1,1] => [1,1] => [1] => 0
[7,2,1,1] => [2,1,1] => [1,1] => [1] => 0
[7,1,1,1,1] => [1,1,1,1] => [1,1,1] => [1,1] => 0
[6,3,1,1] => [3,1,1] => [1,1] => [1] => 0
[6,2,2,1] => [2,2,1] => [2,1] => [1] => 0
[6,2,1,1,1] => [2,1,1,1] => [1,1,1] => [1,1] => 0
[6,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => [1,1,1] => 0
[5,4,1,1] => [4,1,1] => [1,1] => [1] => 0
[5,3,2,1] => [3,2,1] => [2,1] => [1] => 0
[5,3,1,1,1] => [3,1,1,1] => [1,1,1] => [1,1] => 0
[5,2,2,2] => [2,2,2] => [2,2] => [2] => 1
[5,2,2,1,1] => [2,2,1,1] => [2,1,1] => [1,1] => 0
[5,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1] => 0
[5,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 0
[4,4,2,1] => [4,2,1] => [2,1] => [1] => 0
[4,4,1,1,1] => [4,1,1,1] => [1,1,1] => [1,1] => 0
[4,3,3,1] => [3,3,1] => [3,1] => [1] => 0
[4,3,2,2] => [3,2,2] => [2,2] => [2] => 1
[4,3,2,1,1] => [3,2,1,1] => [2,1,1] => [1,1] => 0
[4,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1] => 0
[4,2,2,2,1] => [2,2,2,1] => [2,2,1] => [2,1] => 1
[4,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 0
[4,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 0
[4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 0
[3,3,3,2] => [3,3,2] => [3,2] => [2] => 1
[3,3,3,1,1] => [3,3,1,1] => [3,1,1] => [1,1] => 0
[3,3,2,2,1] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[3,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 0
[3,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 0
>>> Load all 1194 entries. <<<
[3,2,2,2,2] => [2,2,2,2] => [2,2,2] => [2,2] => 1
[3,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 0
[3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[2,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[2,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 0
[2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[9,1,1,1] => [1,1,1] => [1,1] => [1] => 0
[8,2,1,1] => [2,1,1] => [1,1] => [1] => 0
[8,1,1,1,1] => [1,1,1,1] => [1,1,1] => [1,1] => 0
[7,3,1,1] => [3,1,1] => [1,1] => [1] => 0
[7,2,2,1] => [2,2,1] => [2,1] => [1] => 0
[7,2,1,1,1] => [2,1,1,1] => [1,1,1] => [1,1] => 0
[7,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => [1,1,1] => 0
[6,4,1,1] => [4,1,1] => [1,1] => [1] => 0
[6,3,2,1] => [3,2,1] => [2,1] => [1] => 0
[6,3,1,1,1] => [3,1,1,1] => [1,1,1] => [1,1] => 0
[6,2,2,2] => [2,2,2] => [2,2] => [2] => 1
[6,2,2,1,1] => [2,2,1,1] => [2,1,1] => [1,1] => 0
[6,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1] => 0
[6,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 0
[5,5,1,1] => [5,1,1] => [1,1] => [1] => 0
[5,4,2,1] => [4,2,1] => [2,1] => [1] => 0
[5,4,1,1,1] => [4,1,1,1] => [1,1,1] => [1,1] => 0
[5,3,3,1] => [3,3,1] => [3,1] => [1] => 0
[5,3,2,2] => [3,2,2] => [2,2] => [2] => 1
[5,3,2,1,1] => [3,2,1,1] => [2,1,1] => [1,1] => 0
[5,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1] => 0
[5,2,2,2,1] => [2,2,2,1] => [2,2,1] => [2,1] => 1
[5,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 0
[5,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 0
[5,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 0
[4,4,3,1] => [4,3,1] => [3,1] => [1] => 0
[4,4,2,2] => [4,2,2] => [2,2] => [2] => 1
[4,4,2,1,1] => [4,2,1,1] => [2,1,1] => [1,1] => 0
[4,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 0
[4,3,3,2] => [3,3,2] => [3,2] => [2] => 1
[4,3,3,1,1] => [3,3,1,1] => [3,1,1] => [1,1] => 0
[4,3,2,2,1] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[4,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 0
[4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 0
[4,2,2,2,2] => [2,2,2,2] => [2,2,2] => [2,2] => 1
[4,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[4,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 0
[4,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[3,3,3,3] => [3,3,3] => [3,3] => [3] => 2
[3,3,3,2,1] => [3,3,2,1] => [3,2,1] => [2,1] => 1
[3,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => [1,1,1] => 0
[3,3,2,2,2] => [3,2,2,2] => [2,2,2] => [2,2] => 1
[3,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 0
[3,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 0
[3,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[3,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[2,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => [2,2,2] => 1
[2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[2,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 0
[10,1,1,1] => [1,1,1] => [1,1] => [1] => 0
[9,2,1,1] => [2,1,1] => [1,1] => [1] => 0
[9,1,1,1,1] => [1,1,1,1] => [1,1,1] => [1,1] => 0
[8,3,1,1] => [3,1,1] => [1,1] => [1] => 0
[8,2,2,1] => [2,2,1] => [2,1] => [1] => 0
[8,2,1,1,1] => [2,1,1,1] => [1,1,1] => [1,1] => 0
[8,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => [1,1,1] => 0
[7,4,1,1] => [4,1,1] => [1,1] => [1] => 0
[7,3,2,1] => [3,2,1] => [2,1] => [1] => 0
[7,3,1,1,1] => [3,1,1,1] => [1,1,1] => [1,1] => 0
[7,2,2,2] => [2,2,2] => [2,2] => [2] => 1
[7,2,2,1,1] => [2,2,1,1] => [2,1,1] => [1,1] => 0
[7,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1] => 0
[7,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 0
[6,5,1,1] => [5,1,1] => [1,1] => [1] => 0
[6,4,2,1] => [4,2,1] => [2,1] => [1] => 0
[6,4,1,1,1] => [4,1,1,1] => [1,1,1] => [1,1] => 0
[6,3,3,1] => [3,3,1] => [3,1] => [1] => 0
[6,3,2,2] => [3,2,2] => [2,2] => [2] => 1
[6,3,2,1,1] => [3,2,1,1] => [2,1,1] => [1,1] => 0
[6,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1] => 0
[6,2,2,2,1] => [2,2,2,1] => [2,2,1] => [2,1] => 1
[6,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 0
[6,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 0
[6,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 0
[5,5,2,1] => [5,2,1] => [2,1] => [1] => 0
[5,5,1,1,1] => [5,1,1,1] => [1,1,1] => [1,1] => 0
[5,4,3,1] => [4,3,1] => [3,1] => [1] => 0
[5,4,2,2] => [4,2,2] => [2,2] => [2] => 1
[5,4,2,1,1] => [4,2,1,1] => [2,1,1] => [1,1] => 0
[5,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 0
[5,3,3,2] => [3,3,2] => [3,2] => [2] => 1
[5,3,3,1,1] => [3,3,1,1] => [3,1,1] => [1,1] => 0
[5,3,2,2,1] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[5,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 0
[5,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 0
[5,2,2,2,2] => [2,2,2,2] => [2,2,2] => [2,2] => 1
[5,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[5,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 0
[5,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[4,4,4,1] => [4,4,1] => [4,1] => [1] => 0
[4,4,3,2] => [4,3,2] => [3,2] => [2] => 1
[4,4,3,1,1] => [4,3,1,1] => [3,1,1] => [1,1] => 0
[4,4,2,2,1] => [4,2,2,1] => [2,2,1] => [2,1] => 1
[4,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 0
[4,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 0
[4,3,3,3] => [3,3,3] => [3,3] => [3] => 2
[4,3,3,2,1] => [3,3,2,1] => [3,2,1] => [2,1] => 1
[4,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => [1,1,1] => 0
[4,3,2,2,2] => [3,2,2,2] => [2,2,2] => [2,2] => 1
[4,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[4,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 0
[4,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[4,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 0
[4,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[4,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[3,3,3,3,1] => [3,3,3,1] => [3,3,1] => [3,1] => 2
[3,3,3,2,2] => [3,3,2,2] => [3,2,2] => [2,2] => 1
[3,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[3,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 0
[3,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[3,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 0
[3,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[3,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => [2,2,2] => 1
[3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[3,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[3,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[3,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[3,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[2,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 1
[2,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[2,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[2,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[2,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[2,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 0
[11,1,1,1] => [1,1,1] => [1,1] => [1] => 0
[10,2,1,1] => [2,1,1] => [1,1] => [1] => 0
[10,1,1,1,1] => [1,1,1,1] => [1,1,1] => [1,1] => 0
[9,3,1,1] => [3,1,1] => [1,1] => [1] => 0
[9,2,2,1] => [2,2,1] => [2,1] => [1] => 0
[9,2,1,1,1] => [2,1,1,1] => [1,1,1] => [1,1] => 0
[9,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => [1,1,1] => 0
[8,4,1,1] => [4,1,1] => [1,1] => [1] => 0
[8,3,2,1] => [3,2,1] => [2,1] => [1] => 0
[8,3,1,1,1] => [3,1,1,1] => [1,1,1] => [1,1] => 0
[8,2,2,2] => [2,2,2] => [2,2] => [2] => 1
[8,2,2,1,1] => [2,2,1,1] => [2,1,1] => [1,1] => 0
[8,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1] => 0
[8,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 0
[7,5,1,1] => [5,1,1] => [1,1] => [1] => 0
[7,4,2,1] => [4,2,1] => [2,1] => [1] => 0
[7,4,1,1,1] => [4,1,1,1] => [1,1,1] => [1,1] => 0
[7,3,3,1] => [3,3,1] => [3,1] => [1] => 0
[7,3,2,2] => [3,2,2] => [2,2] => [2] => 1
[7,3,2,1,1] => [3,2,1,1] => [2,1,1] => [1,1] => 0
[7,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1] => 0
[7,2,2,2,1] => [2,2,2,1] => [2,2,1] => [2,1] => 1
[7,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 0
[7,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 0
[7,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 0
[6,6,1,1] => [6,1,1] => [1,1] => [1] => 0
[6,5,2,1] => [5,2,1] => [2,1] => [1] => 0
[6,5,1,1,1] => [5,1,1,1] => [1,1,1] => [1,1] => 0
[6,4,3,1] => [4,3,1] => [3,1] => [1] => 0
[6,4,2,2] => [4,2,2] => [2,2] => [2] => 1
[6,4,2,1,1] => [4,2,1,1] => [2,1,1] => [1,1] => 0
[6,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 0
[6,3,3,2] => [3,3,2] => [3,2] => [2] => 1
[6,3,3,1,1] => [3,3,1,1] => [3,1,1] => [1,1] => 0
[6,3,2,2,1] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[6,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 0
[6,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 0
[6,2,2,2,2] => [2,2,2,2] => [2,2,2] => [2,2] => 1
[6,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[6,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[6,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 0
[6,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[5,5,3,1] => [5,3,1] => [3,1] => [1] => 0
[5,5,2,2] => [5,2,2] => [2,2] => [2] => 1
[5,5,2,1,1] => [5,2,1,1] => [2,1,1] => [1,1] => 0
[5,5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => [1,1,1] => 0
[5,4,4,1] => [4,4,1] => [4,1] => [1] => 0
[5,4,3,2] => [4,3,2] => [3,2] => [2] => 1
[5,4,3,1,1] => [4,3,1,1] => [3,1,1] => [1,1] => 0
[5,4,2,2,1] => [4,2,2,1] => [2,2,1] => [2,1] => 1
[5,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 0
[5,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 0
[5,3,3,3] => [3,3,3] => [3,3] => [3] => 2
[5,3,3,2,1] => [3,3,2,1] => [3,2,1] => [2,1] => 1
[5,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => [1,1,1] => 0
[5,3,2,2,2] => [3,2,2,2] => [2,2,2] => [2,2] => 1
[5,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[5,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[5,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 0
[5,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[5,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[5,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 0
[5,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[5,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[4,4,4,2] => [4,4,2] => [4,2] => [2] => 1
[4,4,4,1,1] => [4,4,1,1] => [4,1,1] => [1,1] => 0
[4,4,3,3] => [4,3,3] => [3,3] => [3] => 2
[4,4,3,2,1] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[4,4,3,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => [1,1,1] => 0
[4,4,2,2,2] => [4,2,2,2] => [2,2,2] => [2,2] => 1
[4,4,2,2,1,1] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[4,4,2,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[4,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 0
[4,3,3,3,1] => [3,3,3,1] => [3,3,1] => [3,1] => 2
[4,3,3,2,2] => [3,3,2,2] => [3,2,2] => [2,2] => 1
[4,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[4,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 0
[4,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[4,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[4,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 0
[4,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[4,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => [2,2,2] => 1
[4,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[4,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[4,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[4,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[4,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[3,3,3,3,2] => [3,3,3,2] => [3,3,2] => [3,2] => 2
[3,3,3,3,1,1] => [3,3,3,1,1] => [3,3,1,1] => [3,1,1] => 2
[3,3,3,2,2,1] => [3,3,2,2,1] => [3,2,2,1] => [2,2,1] => 1
[3,3,3,2,1,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[3,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 0
[3,3,2,2,2,2] => [3,2,2,2,2] => [2,2,2,2] => [2,2,2] => 1
[3,3,2,2,2,1,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[3,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[3,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[3,3,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[3,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 1
[3,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[3,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[3,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[3,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[3,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 0
[2,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 1
[2,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[2,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[2,2,2,2,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[2,2,2,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[2,2,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 0
[2,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 0
[12,1,1,1] => [1,1,1] => [1,1] => [1] => 0
[11,2,1,1] => [2,1,1] => [1,1] => [1] => 0
[11,1,1,1,1] => [1,1,1,1] => [1,1,1] => [1,1] => 0
[10,3,1,1] => [3,1,1] => [1,1] => [1] => 0
[10,2,2,1] => [2,2,1] => [2,1] => [1] => 0
[10,2,1,1,1] => [2,1,1,1] => [1,1,1] => [1,1] => 0
[10,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => [1,1,1] => 0
[9,4,1,1] => [4,1,1] => [1,1] => [1] => 0
[9,3,2,1] => [3,2,1] => [2,1] => [1] => 0
[9,3,1,1,1] => [3,1,1,1] => [1,1,1] => [1,1] => 0
[9,2,2,2] => [2,2,2] => [2,2] => [2] => 1
[9,2,2,1,1] => [2,2,1,1] => [2,1,1] => [1,1] => 0
[9,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1] => 0
[9,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 0
[8,5,1,1] => [5,1,1] => [1,1] => [1] => 0
[8,4,2,1] => [4,2,1] => [2,1] => [1] => 0
[8,4,1,1,1] => [4,1,1,1] => [1,1,1] => [1,1] => 0
[8,3,3,1] => [3,3,1] => [3,1] => [1] => 0
[8,3,2,2] => [3,2,2] => [2,2] => [2] => 1
[8,3,2,1,1] => [3,2,1,1] => [2,1,1] => [1,1] => 0
[8,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1] => 0
[8,2,2,2,1] => [2,2,2,1] => [2,2,1] => [2,1] => 1
[8,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 0
[8,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 0
[8,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 0
[7,6,1,1] => [6,1,1] => [1,1] => [1] => 0
[7,5,2,1] => [5,2,1] => [2,1] => [1] => 0
[7,5,1,1,1] => [5,1,1,1] => [1,1,1] => [1,1] => 0
[7,4,3,1] => [4,3,1] => [3,1] => [1] => 0
[7,4,2,2] => [4,2,2] => [2,2] => [2] => 1
[7,4,2,1,1] => [4,2,1,1] => [2,1,1] => [1,1] => 0
[7,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 0
[7,3,3,2] => [3,3,2] => [3,2] => [2] => 1
[7,3,3,1,1] => [3,3,1,1] => [3,1,1] => [1,1] => 0
[7,3,2,2,1] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[7,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 0
[7,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 0
[7,2,2,2,2] => [2,2,2,2] => [2,2,2] => [2,2] => 1
[7,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[7,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[7,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 0
[7,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[6,6,2,1] => [6,2,1] => [2,1] => [1] => 0
[6,6,1,1,1] => [6,1,1,1] => [1,1,1] => [1,1] => 0
[6,5,3,1] => [5,3,1] => [3,1] => [1] => 0
[6,5,2,2] => [5,2,2] => [2,2] => [2] => 1
[6,5,2,1,1] => [5,2,1,1] => [2,1,1] => [1,1] => 0
[6,5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => [1,1,1] => 0
[6,4,4,1] => [4,4,1] => [4,1] => [1] => 0
[6,4,3,2] => [4,3,2] => [3,2] => [2] => 1
[6,4,3,1,1] => [4,3,1,1] => [3,1,1] => [1,1] => 0
[6,4,2,2,1] => [4,2,2,1] => [2,2,1] => [2,1] => 1
[6,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 0
[6,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 0
[6,3,3,3] => [3,3,3] => [3,3] => [3] => 2
[6,3,3,2,1] => [3,3,2,1] => [3,2,1] => [2,1] => 1
[6,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => [1,1,1] => 0
[6,3,2,2,2] => [3,2,2,2] => [2,2,2] => [2,2] => 1
[6,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[6,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[6,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 0
[6,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[6,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[6,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 0
[6,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[6,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[5,5,4,1] => [5,4,1] => [4,1] => [1] => 0
[5,5,3,2] => [5,3,2] => [3,2] => [2] => 1
[5,5,3,1,1] => [5,3,1,1] => [3,1,1] => [1,1] => 0
[5,5,2,2,1] => [5,2,2,1] => [2,2,1] => [2,1] => 1
[5,5,2,1,1,1] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 0
[5,5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 0
[5,4,4,2] => [4,4,2] => [4,2] => [2] => 1
[5,4,4,1,1] => [4,4,1,1] => [4,1,1] => [1,1] => 0
[5,4,3,3] => [4,3,3] => [3,3] => [3] => 2
[5,4,3,2,1] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[5,4,3,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => [1,1,1] => 0
[5,4,2,2,2] => [4,2,2,2] => [2,2,2] => [2,2] => 1
[5,4,2,2,1,1] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[5,4,2,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[5,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 0
[5,3,3,3,1] => [3,3,3,1] => [3,3,1] => [3,1] => 2
[5,3,3,2,2] => [3,3,2,2] => [3,2,2] => [2,2] => 1
[5,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[5,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 0
[5,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[5,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[5,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 0
[5,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[5,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => [2,2,2] => 1
[5,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[5,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[5,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[5,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[5,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[4,4,4,3] => [4,4,3] => [4,3] => [3] => 2
[4,4,4,2,1] => [4,4,2,1] => [4,2,1] => [2,1] => 1
[4,4,4,1,1,1] => [4,4,1,1,1] => [4,1,1,1] => [1,1,1] => 0
[4,4,3,3,1] => [4,3,3,1] => [3,3,1] => [3,1] => 2
[4,4,3,2,2] => [4,3,2,2] => [3,2,2] => [2,2] => 1
[4,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[4,4,3,1,1,1,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 0
[4,4,2,2,2,1] => [4,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[4,4,2,2,1,1,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[4,4,2,1,1,1,1,1] => [4,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 0
[4,4,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[4,3,3,3,2] => [3,3,3,2] => [3,3,2] => [3,2] => 2
[4,3,3,3,1,1] => [3,3,3,1,1] => [3,3,1,1] => [3,1,1] => 2
[4,3,3,2,2,1] => [3,3,2,2,1] => [3,2,2,1] => [2,2,1] => 1
[4,3,3,2,1,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[4,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 0
[4,3,2,2,2,2] => [3,2,2,2,2] => [2,2,2,2] => [2,2,2] => 1
[4,3,2,2,2,1,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[4,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[4,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[4,3,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[4,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 1
[4,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[4,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[4,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[4,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[4,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 0
[3,3,3,3,3] => [3,3,3,3] => [3,3,3] => [3,3] => 3
[3,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => [3,2,1] => 2
[3,3,3,3,1,1,1] => [3,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 2
[3,3,3,2,2,2] => [3,3,2,2,2] => [3,2,2,2] => [2,2,2] => 1
[3,3,3,2,2,1,1] => [3,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 1
[3,3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[3,3,3,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[3,3,2,2,2,2,1] => [3,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 1
[3,3,2,2,2,1,1,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[3,3,2,2,1,1,1,1,1] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[3,3,2,1,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[3,3,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[3,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 1
[3,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[3,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[3,2,2,2,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[3,2,2,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[3,2,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 0
[3,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 0
[2,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => 1
[2,2,2,2,2,2,1,1,1] => [2,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => 1
[2,2,2,2,2,1,1,1,1,1] => [2,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 1
[2,2,2,2,1,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 1
[2,2,2,1,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 0
[2,2,1,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 0
[13,1,1,1] => [1,1,1] => [1,1] => [1] => 0
[12,2,1,1] => [2,1,1] => [1,1] => [1] => 0
[12,1,1,1,1] => [1,1,1,1] => [1,1,1] => [1,1] => 0
[11,3,1,1] => [3,1,1] => [1,1] => [1] => 0
[11,2,2,1] => [2,2,1] => [2,1] => [1] => 0
[11,2,1,1,1] => [2,1,1,1] => [1,1,1] => [1,1] => 0
[11,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => [1,1,1] => 0
[10,4,1,1] => [4,1,1] => [1,1] => [1] => 0
[10,3,2,1] => [3,2,1] => [2,1] => [1] => 0
[10,3,1,1,1] => [3,1,1,1] => [1,1,1] => [1,1] => 0
[10,2,2,2] => [2,2,2] => [2,2] => [2] => 1
[10,2,2,1,1] => [2,2,1,1] => [2,1,1] => [1,1] => 0
[10,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1] => 0
[10,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 0
[9,5,1,1] => [5,1,1] => [1,1] => [1] => 0
[9,4,2,1] => [4,2,1] => [2,1] => [1] => 0
[9,4,1,1,1] => [4,1,1,1] => [1,1,1] => [1,1] => 0
[9,3,3,1] => [3,3,1] => [3,1] => [1] => 0
[9,3,2,2] => [3,2,2] => [2,2] => [2] => 1
[9,3,2,1,1] => [3,2,1,1] => [2,1,1] => [1,1] => 0
[9,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1] => 0
[9,2,2,2,1] => [2,2,2,1] => [2,2,1] => [2,1] => 1
[9,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 0
[9,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 0
[9,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 0
[8,6,1,1] => [6,1,1] => [1,1] => [1] => 0
[8,5,2,1] => [5,2,1] => [2,1] => [1] => 0
[8,5,1,1,1] => [5,1,1,1] => [1,1,1] => [1,1] => 0
[8,4,3,1] => [4,3,1] => [3,1] => [1] => 0
[8,4,2,2] => [4,2,2] => [2,2] => [2] => 1
[8,4,2,1,1] => [4,2,1,1] => [2,1,1] => [1,1] => 0
[8,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 0
[8,3,3,2] => [3,3,2] => [3,2] => [2] => 1
[8,3,3,1,1] => [3,3,1,1] => [3,1,1] => [1,1] => 0
[8,3,2,2,1] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[8,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 0
[8,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 0
[8,2,2,2,2] => [2,2,2,2] => [2,2,2] => [2,2] => 1
[8,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[8,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[8,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 0
[8,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[7,7,1,1] => [7,1,1] => [1,1] => [1] => 0
[7,6,2,1] => [6,2,1] => [2,1] => [1] => 0
[7,6,1,1,1] => [6,1,1,1] => [1,1,1] => [1,1] => 0
[7,5,3,1] => [5,3,1] => [3,1] => [1] => 0
[7,5,2,2] => [5,2,2] => [2,2] => [2] => 1
[7,5,2,1,1] => [5,2,1,1] => [2,1,1] => [1,1] => 0
[7,5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => [1,1,1] => 0
[7,4,4,1] => [4,4,1] => [4,1] => [1] => 0
[7,4,3,2] => [4,3,2] => [3,2] => [2] => 1
[7,4,3,1,1] => [4,3,1,1] => [3,1,1] => [1,1] => 0
[7,4,2,2,1] => [4,2,2,1] => [2,2,1] => [2,1] => 1
[7,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 0
[7,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 0
[7,3,3,3] => [3,3,3] => [3,3] => [3] => 2
[7,3,3,2,1] => [3,3,2,1] => [3,2,1] => [2,1] => 1
[7,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => [1,1,1] => 0
[7,3,2,2,2] => [3,2,2,2] => [2,2,2] => [2,2] => 1
[7,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[7,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[7,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 0
[7,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[7,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[7,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 0
[7,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[7,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[6,6,3,1] => [6,3,1] => [3,1] => [1] => 0
[6,6,2,2] => [6,2,2] => [2,2] => [2] => 1
[6,6,2,1,1] => [6,2,1,1] => [2,1,1] => [1,1] => 0
[6,6,1,1,1,1] => [6,1,1,1,1] => [1,1,1,1] => [1,1,1] => 0
[6,5,4,1] => [5,4,1] => [4,1] => [1] => 0
[6,5,3,2] => [5,3,2] => [3,2] => [2] => 1
[6,5,3,1,1] => [5,3,1,1] => [3,1,1] => [1,1] => 0
[6,5,2,2,1] => [5,2,2,1] => [2,2,1] => [2,1] => 1
[6,5,2,1,1,1] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 0
[6,5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 0
[6,4,4,2] => [4,4,2] => [4,2] => [2] => 1
[6,4,4,1,1] => [4,4,1,1] => [4,1,1] => [1,1] => 0
[6,4,3,3] => [4,3,3] => [3,3] => [3] => 2
[6,4,3,2,1] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[6,4,3,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => [1,1,1] => 0
[6,4,2,2,2] => [4,2,2,2] => [2,2,2] => [2,2] => 1
[6,4,2,2,1,1] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[6,4,2,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[6,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 0
[6,3,3,3,1] => [3,3,3,1] => [3,3,1] => [3,1] => 2
[6,3,3,2,2] => [3,3,2,2] => [3,2,2] => [2,2] => 1
[6,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[6,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 0
[6,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[6,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[6,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 0
[6,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[6,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => [2,2,2] => 1
[6,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[6,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[6,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[6,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[6,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[5,5,5,1] => [5,5,1] => [5,1] => [1] => 0
[5,5,4,2] => [5,4,2] => [4,2] => [2] => 1
[5,5,4,1,1] => [5,4,1,1] => [4,1,1] => [1,1] => 0
[5,5,3,3] => [5,3,3] => [3,3] => [3] => 2
[5,5,3,2,1] => [5,3,2,1] => [3,2,1] => [2,1] => 1
[5,5,3,1,1,1] => [5,3,1,1,1] => [3,1,1,1] => [1,1,1] => 0
[5,5,2,2,2] => [5,2,2,2] => [2,2,2] => [2,2] => 1
[5,5,2,2,1,1] => [5,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[5,5,2,1,1,1,1] => [5,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[5,5,1,1,1,1,1,1] => [5,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 0
[5,4,4,3] => [4,4,3] => [4,3] => [3] => 2
[5,4,4,2,1] => [4,4,2,1] => [4,2,1] => [2,1] => 1
[5,4,4,1,1,1] => [4,4,1,1,1] => [4,1,1,1] => [1,1,1] => 0
[5,4,3,3,1] => [4,3,3,1] => [3,3,1] => [3,1] => 2
[5,4,3,2,2] => [4,3,2,2] => [3,2,2] => [2,2] => 1
[5,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[5,4,3,1,1,1,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 0
[5,4,2,2,2,1] => [4,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[5,4,2,2,1,1,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[5,4,2,1,1,1,1,1] => [4,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 0
[5,4,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[5,3,3,3,2] => [3,3,3,2] => [3,3,2] => [3,2] => 2
[5,3,3,3,1,1] => [3,3,3,1,1] => [3,3,1,1] => [3,1,1] => 2
[5,3,3,2,2,1] => [3,3,2,2,1] => [3,2,2,1] => [2,2,1] => 1
[5,3,3,2,1,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[5,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 0
[5,3,2,2,2,2] => [3,2,2,2,2] => [2,2,2,2] => [2,2,2] => 1
[5,3,2,2,2,1,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[5,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[5,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[5,3,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[5,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 1
[5,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[5,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[5,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[5,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[5,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 0
[4,4,4,4] => [4,4,4] => [4,4] => [4] => 3
[4,4,4,3,1] => [4,4,3,1] => [4,3,1] => [3,1] => 2
[4,4,4,2,2] => [4,4,2,2] => [4,2,2] => [2,2] => 1
[4,4,4,2,1,1] => [4,4,2,1,1] => [4,2,1,1] => [2,1,1] => 1
[4,4,4,1,1,1,1] => [4,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 0
[4,4,3,3,2] => [4,3,3,2] => [3,3,2] => [3,2] => 2
[4,4,3,3,1,1] => [4,3,3,1,1] => [3,3,1,1] => [3,1,1] => 2
[4,4,3,2,2,1] => [4,3,2,2,1] => [3,2,2,1] => [2,2,1] => 1
[4,4,3,2,1,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[4,4,3,1,1,1,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 0
[4,4,2,2,2,2] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 1
[4,4,2,2,2,1,1] => [4,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[4,4,2,2,1,1,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[4,4,2,1,1,1,1,1,1] => [4,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[4,4,1,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[4,3,3,3,3] => [3,3,3,3] => [3,3,3] => [3,3] => 3
[4,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => [3,2,1] => 2
[4,3,3,3,1,1,1] => [3,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 2
[4,3,3,2,2,2] => [3,3,2,2,2] => [3,2,2,2] => [2,2,2] => 1
[4,3,3,2,2,1,1] => [3,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 1
[4,3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[4,3,3,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[4,3,2,2,2,2,1] => [3,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 1
[4,3,2,2,2,1,1,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[4,3,2,2,1,1,1,1,1] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[4,3,2,1,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[4,3,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[4,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 1
[4,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[4,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[4,2,2,2,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[4,2,2,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[4,2,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 0
[4,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 0
[3,3,3,3,3,1] => [3,3,3,3,1] => [3,3,3,1] => [3,3,1] => 3
[3,3,3,3,2,2] => [3,3,3,2,2] => [3,3,2,2] => [3,2,2] => 2
[3,3,3,3,2,1,1] => [3,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => 2
[3,3,3,3,1,1,1,1] => [3,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 2
[3,3,3,2,2,2,1] => [3,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 1
[3,3,3,2,2,1,1,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[3,3,3,2,1,1,1,1,1] => [3,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[3,3,3,1,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[3,3,2,2,2,2,2] => [3,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 1
[3,3,2,2,2,2,1,1] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[3,3,2,2,2,1,1,1,1] => [3,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[3,3,2,2,1,1,1,1,1,1] => [3,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[3,3,2,1,1,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[3,3,1,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 0
[3,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => 1
[3,2,2,2,2,2,1,1,1] => [2,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => 1
[3,2,2,2,2,1,1,1,1,1] => [2,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 1
[3,2,2,2,1,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 1
[3,2,2,1,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 0
[3,2,1,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 0
[2,2,2,2,2,2,2,2] => [2,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => 1
[2,2,2,2,2,2,2,1,1] => [2,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => 1
[2,2,2,2,2,2,1,1,1,1] => [2,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 1
[2,2,2,2,2,1,1,1,1,1,1] => [2,2,2,2,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 1
[2,2,2,2,1,1,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 1
[2,2,2,1,1,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 0
[14,1,1,1] => [1,1,1] => [1,1] => [1] => 0
[13,2,1,1] => [2,1,1] => [1,1] => [1] => 0
[13,1,1,1,1] => [1,1,1,1] => [1,1,1] => [1,1] => 0
[12,3,1,1] => [3,1,1] => [1,1] => [1] => 0
[12,2,2,1] => [2,2,1] => [2,1] => [1] => 0
[12,2,1,1,1] => [2,1,1,1] => [1,1,1] => [1,1] => 0
[12,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => [1,1,1] => 0
[11,4,1,1] => [4,1,1] => [1,1] => [1] => 0
[11,3,2,1] => [3,2,1] => [2,1] => [1] => 0
[11,3,1,1,1] => [3,1,1,1] => [1,1,1] => [1,1] => 0
[11,2,2,2] => [2,2,2] => [2,2] => [2] => 1
[11,2,2,1,1] => [2,2,1,1] => [2,1,1] => [1,1] => 0
[11,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1] => 0
[11,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 0
[10,5,1,1] => [5,1,1] => [1,1] => [1] => 0
[10,4,2,1] => [4,2,1] => [2,1] => [1] => 0
[10,4,1,1,1] => [4,1,1,1] => [1,1,1] => [1,1] => 0
[10,3,3,1] => [3,3,1] => [3,1] => [1] => 0
[10,3,2,2] => [3,2,2] => [2,2] => [2] => 1
[10,3,2,1,1] => [3,2,1,1] => [2,1,1] => [1,1] => 0
[10,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1] => 0
[10,2,2,2,1] => [2,2,2,1] => [2,2,1] => [2,1] => 1
[10,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 0
[10,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 0
[10,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 0
[9,6,1,1] => [6,1,1] => [1,1] => [1] => 0
[9,5,2,1] => [5,2,1] => [2,1] => [1] => 0
[9,5,1,1,1] => [5,1,1,1] => [1,1,1] => [1,1] => 0
[9,4,3,1] => [4,3,1] => [3,1] => [1] => 0
[9,4,2,2] => [4,2,2] => [2,2] => [2] => 1
[9,4,2,1,1] => [4,2,1,1] => [2,1,1] => [1,1] => 0
[9,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 0
[9,3,3,2] => [3,3,2] => [3,2] => [2] => 1
[9,3,3,1,1] => [3,3,1,1] => [3,1,1] => [1,1] => 0
[9,3,2,2,1] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[9,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 0
[9,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 0
[9,2,2,2,2] => [2,2,2,2] => [2,2,2] => [2,2] => 1
[9,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[9,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[9,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 0
[9,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[8,7,1,1] => [7,1,1] => [1,1] => [1] => 0
[8,6,2,1] => [6,2,1] => [2,1] => [1] => 0
[8,6,1,1,1] => [6,1,1,1] => [1,1,1] => [1,1] => 0
[8,5,3,1] => [5,3,1] => [3,1] => [1] => 0
[8,5,2,2] => [5,2,2] => [2,2] => [2] => 1
[8,5,2,1,1] => [5,2,1,1] => [2,1,1] => [1,1] => 0
[8,5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => [1,1,1] => 0
[8,4,4,1] => [4,4,1] => [4,1] => [1] => 0
[8,4,3,2] => [4,3,2] => [3,2] => [2] => 1
[8,4,3,1,1] => [4,3,1,1] => [3,1,1] => [1,1] => 0
[8,4,2,2,1] => [4,2,2,1] => [2,2,1] => [2,1] => 1
[8,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 0
[8,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 0
[8,3,3,3] => [3,3,3] => [3,3] => [3] => 2
[8,3,3,2,1] => [3,3,2,1] => [3,2,1] => [2,1] => 1
[8,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => [1,1,1] => 0
[8,3,2,2,2] => [3,2,2,2] => [2,2,2] => [2,2] => 1
[8,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[8,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[8,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 0
[8,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[8,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[8,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 0
[8,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[8,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[7,7,2,1] => [7,2,1] => [2,1] => [1] => 0
[7,7,1,1,1] => [7,1,1,1] => [1,1,1] => [1,1] => 0
[7,6,3,1] => [6,3,1] => [3,1] => [1] => 0
[7,6,2,2] => [6,2,2] => [2,2] => [2] => 1
[7,6,2,1,1] => [6,2,1,1] => [2,1,1] => [1,1] => 0
[7,6,1,1,1,1] => [6,1,1,1,1] => [1,1,1,1] => [1,1,1] => 0
[7,5,4,1] => [5,4,1] => [4,1] => [1] => 0
[7,5,3,2] => [5,3,2] => [3,2] => [2] => 1
[7,5,3,1,1] => [5,3,1,1] => [3,1,1] => [1,1] => 0
[7,5,2,2,1] => [5,2,2,1] => [2,2,1] => [2,1] => 1
[7,5,2,1,1,1] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 0
[7,5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 0
[7,4,4,2] => [4,4,2] => [4,2] => [2] => 1
[7,4,4,1,1] => [4,4,1,1] => [4,1,1] => [1,1] => 0
[7,4,3,3] => [4,3,3] => [3,3] => [3] => 2
[7,4,3,2,1] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[7,4,3,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => [1,1,1] => 0
[7,4,2,2,2] => [4,2,2,2] => [2,2,2] => [2,2] => 1
[7,4,2,2,1,1] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[7,4,2,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[7,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 0
[7,3,3,3,1] => [3,3,3,1] => [3,3,1] => [3,1] => 2
[7,3,3,2,2] => [3,3,2,2] => [3,2,2] => [2,2] => 1
[7,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[7,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 0
[7,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[7,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[7,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 0
[7,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[7,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => [2,2,2] => 1
[7,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[7,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[7,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[7,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[7,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[6,6,4,1] => [6,4,1] => [4,1] => [1] => 0
[6,6,3,2] => [6,3,2] => [3,2] => [2] => 1
[6,6,3,1,1] => [6,3,1,1] => [3,1,1] => [1,1] => 0
[6,6,2,2,1] => [6,2,2,1] => [2,2,1] => [2,1] => 1
[6,6,2,1,1,1] => [6,2,1,1,1] => [2,1,1,1] => [1,1,1] => 0
[6,6,1,1,1,1,1] => [6,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 0
[6,5,5,1] => [5,5,1] => [5,1] => [1] => 0
[6,5,4,2] => [5,4,2] => [4,2] => [2] => 1
[6,5,4,1,1] => [5,4,1,1] => [4,1,1] => [1,1] => 0
[6,5,3,3] => [5,3,3] => [3,3] => [3] => 2
[6,5,3,2,1] => [5,3,2,1] => [3,2,1] => [2,1] => 1
[6,5,3,1,1,1] => [5,3,1,1,1] => [3,1,1,1] => [1,1,1] => 0
[6,5,2,2,2] => [5,2,2,2] => [2,2,2] => [2,2] => 1
[6,5,2,2,1,1] => [5,2,2,1,1] => [2,2,1,1] => [2,1,1] => 1
[6,5,2,1,1,1,1] => [5,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[6,5,1,1,1,1,1,1] => [5,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 0
[6,4,4,3] => [4,4,3] => [4,3] => [3] => 2
[6,4,4,2,1] => [4,4,2,1] => [4,2,1] => [2,1] => 1
[6,4,4,1,1,1] => [4,4,1,1,1] => [4,1,1,1] => [1,1,1] => 0
[6,4,3,3,1] => [4,3,3,1] => [3,3,1] => [3,1] => 2
[6,4,3,2,2] => [4,3,2,2] => [3,2,2] => [2,2] => 1
[6,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[6,4,3,1,1,1,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 0
[6,4,2,2,2,1] => [4,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[6,4,2,2,1,1,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[6,4,2,1,1,1,1,1] => [4,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 0
[6,4,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[6,3,3,3,2] => [3,3,3,2] => [3,3,2] => [3,2] => 2
[6,3,3,3,1,1] => [3,3,3,1,1] => [3,3,1,1] => [3,1,1] => 2
[6,3,3,2,2,1] => [3,3,2,2,1] => [3,2,2,1] => [2,2,1] => 1
[6,3,3,2,1,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[6,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 0
[6,3,2,2,2,2] => [3,2,2,2,2] => [2,2,2,2] => [2,2,2] => 1
[6,3,2,2,2,1,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[6,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[6,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[6,3,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[6,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 1
[6,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[6,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[6,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[6,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[6,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 0
[5,5,5,2] => [5,5,2] => [5,2] => [2] => 1
[5,5,5,1,1] => [5,5,1,1] => [5,1,1] => [1,1] => 0
[5,5,4,3] => [5,4,3] => [4,3] => [3] => 2
[5,5,4,2,1] => [5,4,2,1] => [4,2,1] => [2,1] => 1
[5,5,4,1,1,1] => [5,4,1,1,1] => [4,1,1,1] => [1,1,1] => 0
[5,5,3,3,1] => [5,3,3,1] => [3,3,1] => [3,1] => 2
[5,5,3,2,2] => [5,3,2,2] => [3,2,2] => [2,2] => 1
[5,5,3,2,1,1] => [5,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[5,5,3,1,1,1,1] => [5,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 0
[5,5,2,2,2,1] => [5,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[5,5,2,2,1,1,1] => [5,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 1
[5,5,2,1,1,1,1,1] => [5,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 0
[5,5,1,1,1,1,1,1,1] => [5,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[5,4,4,4] => [4,4,4] => [4,4] => [4] => 3
[5,4,4,3,1] => [4,4,3,1] => [4,3,1] => [3,1] => 2
[5,4,4,2,2] => [4,4,2,2] => [4,2,2] => [2,2] => 1
[5,4,4,2,1,1] => [4,4,2,1,1] => [4,2,1,1] => [2,1,1] => 1
[5,4,4,1,1,1,1] => [4,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 0
[5,4,3,3,2] => [4,3,3,2] => [3,3,2] => [3,2] => 2
[5,4,3,3,1,1] => [4,3,3,1,1] => [3,3,1,1] => [3,1,1] => 2
[5,4,3,2,2,1] => [4,3,2,2,1] => [3,2,2,1] => [2,2,1] => 1
[5,4,3,2,1,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[5,4,3,1,1,1,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 0
[5,4,2,2,2,2] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 1
[5,4,2,2,2,1,1] => [4,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 1
[5,4,2,2,1,1,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[5,4,2,1,1,1,1,1,1] => [4,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[5,4,1,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[5,3,3,3,3] => [3,3,3,3] => [3,3,3] => [3,3] => 3
[5,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => [3,2,1] => 2
[5,3,3,3,1,1,1] => [3,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 2
[5,3,3,2,2,2] => [3,3,2,2,2] => [3,2,2,2] => [2,2,2] => 1
[5,3,3,2,2,1,1] => [3,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 1
[5,3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[5,3,3,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[5,3,2,2,2,2,1] => [3,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 1
[5,3,2,2,2,1,1,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[5,3,2,2,1,1,1,1,1] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[5,3,2,1,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[5,3,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[5,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 1
[5,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[5,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[5,2,2,2,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[5,2,2,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[5,2,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 0
[5,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 0
[4,4,4,4,1] => [4,4,4,1] => [4,4,1] => [4,1] => 3
[4,4,4,3,2] => [4,4,3,2] => [4,3,2] => [3,2] => 2
[4,4,4,3,1,1] => [4,4,3,1,1] => [4,3,1,1] => [3,1,1] => 2
[4,4,4,2,2,1] => [4,4,2,2,1] => [4,2,2,1] => [2,2,1] => 1
[4,4,4,2,1,1,1] => [4,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 1
[4,4,4,1,1,1,1,1] => [4,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 0
[4,4,3,3,3] => [4,3,3,3] => [3,3,3] => [3,3] => 3
[4,4,3,3,2,1] => [4,3,3,2,1] => [3,3,2,1] => [3,2,1] => 2
[4,4,3,3,1,1,1] => [4,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 2
[4,4,3,2,2,2] => [4,3,2,2,2] => [3,2,2,2] => [2,2,2] => 1
[4,4,3,2,2,1,1] => [4,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 1
[4,4,3,2,1,1,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[4,4,3,1,1,1,1,1,1] => [4,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[4,4,2,2,2,2,1] => [4,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 1
[4,4,2,2,2,1,1,1] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 1
[4,4,2,2,1,1,1,1,1] => [4,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[4,4,2,1,1,1,1,1,1,1] => [4,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[4,4,1,1,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[4,3,3,3,3,1] => [3,3,3,3,1] => [3,3,3,1] => [3,3,1] => 3
[4,3,3,3,2,2] => [3,3,3,2,2] => [3,3,2,2] => [3,2,2] => 2
[4,3,3,3,2,1,1] => [3,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => 2
[4,3,3,3,1,1,1,1] => [3,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 2
[4,3,3,2,2,2,1] => [3,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 1
[4,3,3,2,2,1,1,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 1
[4,3,3,2,1,1,1,1,1] => [3,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[4,3,3,1,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[4,3,2,2,2,2,2] => [3,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 1
[4,3,2,2,2,2,1,1] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 1
[4,3,2,2,2,1,1,1,1] => [3,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[4,3,2,2,1,1,1,1,1,1] => [3,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[4,3,2,1,1,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[4,3,1,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 0
[4,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => 1
[4,2,2,2,2,2,1,1,1] => [2,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => 1
[4,2,2,2,2,1,1,1,1,1] => [2,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 1
[4,2,2,2,1,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 1
[4,2,2,1,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 0
[4,2,1,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 0
[3,3,3,3,3,2] => [3,3,3,3,2] => [3,3,3,2] => [3,3,2] => 3
[3,3,3,3,3,1,1] => [3,3,3,3,1,1] => [3,3,3,1,1] => [3,3,1,1] => 3
[3,3,3,3,2,2,1] => [3,3,3,2,2,1] => [3,3,2,2,1] => [3,2,2,1] => 2
[3,3,3,3,2,1,1,1] => [3,3,3,2,1,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => 2
[3,3,3,3,1,1,1,1,1] => [3,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => 2
[3,3,3,2,2,2,2] => [3,3,2,2,2,2] => [3,2,2,2,2] => [2,2,2,2] => 1
[3,3,3,2,2,2,1,1] => [3,3,2,2,2,1,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => 1
[3,3,3,2,2,1,1,1,1] => [3,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[3,3,3,2,1,1,1,1,1,1] => [3,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[3,3,3,1,1,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[3,3,2,2,2,2,2,1] => [3,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => 1
[3,3,2,2,2,2,1,1,1] => [3,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => 1
[3,3,2,2,2,1,1,1,1,1] => [3,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 1
[3,3,2,2,1,1,1,1,1,1,1] => [3,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 1
[3,3,2,1,1,1,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 0
[3,3,1,1,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 0
[3,2,2,2,2,2,2,2] => [2,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => 1
[3,2,2,2,2,2,2,1,1] => [2,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => 1
[3,2,2,2,2,2,1,1,1,1] => [2,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 1
[3,2,2,2,2,1,1,1,1,1,1] => [2,2,2,2,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 1
[3,2,2,2,1,1,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 1
[3,2,2,1,1,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 0
[6,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => [3,2,1] => 2
[5,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => [3,2,1] => 2
[6,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => [3,2,1] => 2
[5,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => [3,2,1] => 2
[4,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => [3,2,1] => 2
[6,5,3,3,2,1] => [5,3,3,2,1] => [3,3,2,1] => [3,2,1] => 2
[5,5,3,3,2,1] => [5,3,3,2,1] => [3,3,2,1] => [3,2,1] => 2
[6,4,3,3,2,1] => [4,3,3,2,1] => [3,3,2,1] => [3,2,1] => 2
[5,4,3,3,2,1] => [4,3,3,2,1] => [3,3,2,1] => [3,2,1] => 2
[6,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => [3,2,1] => 2
[6,5,4,2,2,1] => [5,4,2,2,1] => [4,2,2,1] => [2,2,1] => 1
[5,5,4,2,2,1] => [5,4,2,2,1] => [4,2,2,1] => [2,2,1] => 1
[6,4,4,2,2,1] => [4,4,2,2,1] => [4,2,2,1] => [2,2,1] => 1
[5,4,4,2,2,1] => [4,4,2,2,1] => [4,2,2,1] => [2,2,1] => 1
[6,5,3,2,2,1] => [5,3,2,2,1] => [3,2,2,1] => [2,2,1] => 1
[5,5,3,2,2,1] => [5,3,2,2,1] => [3,2,2,1] => [2,2,1] => 1
[6,4,3,2,2,1] => [4,3,2,2,1] => [3,2,2,1] => [2,2,1] => 1
[6,5,2,2,2,1] => [5,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[6,5,4,3,1,1] => [5,4,3,1,1] => [4,3,1,1] => [3,1,1] => 2
[5,5,4,3,1,1] => [5,4,3,1,1] => [4,3,1,1] => [3,1,1] => 2
[6,4,4,3,1,1] => [4,4,3,1,1] => [4,3,1,1] => [3,1,1] => 2
[5,4,4,3,1,1] => [4,4,3,1,1] => [4,3,1,1] => [3,1,1] => 2
[6,5,3,3,1,1] => [5,3,3,1,1] => [3,3,1,1] => [3,1,1] => 2
[5,5,3,3,1,1] => [5,3,3,1,1] => [3,3,1,1] => [3,1,1] => 2
[6,4,3,3,1,1] => [4,3,3,1,1] => [3,3,1,1] => [3,1,1] => 2
[6,5,4,2,1,1] => [5,4,2,1,1] => [4,2,1,1] => [2,1,1] => 1
[5,5,4,2,1,1] => [5,4,2,1,1] => [4,2,1,1] => [2,1,1] => 1
[6,4,4,2,1,1] => [4,4,2,1,1] => [4,2,1,1] => [2,1,1] => 1
[6,5,3,2,1,1] => [5,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[6,5,4,1,1,1] => [5,4,1,1,1] => [4,1,1,1] => [1,1,1] => 0
[6,5,4,3,2] => [5,4,3,2] => [4,3,2] => [3,2] => 2
[5,5,4,3,2] => [5,4,3,2] => [4,3,2] => [3,2] => 2
[6,4,4,3,2] => [4,4,3,2] => [4,3,2] => [3,2] => 2
[5,4,4,3,2] => [4,4,3,2] => [4,3,2] => [3,2] => 2
[6,5,3,3,2] => [5,3,3,2] => [3,3,2] => [3,2] => 2
[5,5,3,3,2] => [5,3,3,2] => [3,3,2] => [3,2] => 2
[6,4,3,3,2] => [4,3,3,2] => [3,3,2] => [3,2] => 2
[6,5,4,2,2] => [5,4,2,2] => [4,2,2] => [2,2] => 1
[5,5,4,2,2] => [5,4,2,2] => [4,2,2] => [2,2] => 1
[6,4,4,2,2] => [4,4,2,2] => [4,2,2] => [2,2] => 1
[6,5,3,2,2] => [5,3,2,2] => [3,2,2] => [2,2] => 1
[6,5,4,3,1] => [5,4,3,1] => [4,3,1] => [3,1] => 2
[5,5,4,3,1] => [5,4,3,1] => [4,3,1] => [3,1] => 2
[6,4,4,3,1] => [4,4,3,1] => [4,3,1] => [3,1] => 2
[6,5,3,3,1] => [5,3,3,1] => [3,3,1] => [3,1] => 2
[6,5,4,2,1] => [5,4,2,1] => [4,2,1] => [2,1] => 1
[6,5,4,3] => [5,4,3] => [4,3] => [3] => 2
[7,6,5,4,3,2,1] => [6,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => 4
[6,6,5,4,3,2,1] => [6,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => 4
[7,5,5,4,3,2,1] => [5,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => 4
[6,5,5,4,3,2,1] => [5,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => 4
[5,5,5,4,3,2,1] => [5,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => 4
[7,6,4,4,3,2,1] => [6,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => 4
[6,6,4,4,3,2,1] => [6,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => 4
[7,5,4,4,3,2,1] => [5,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => 4
[6,5,4,4,3,2,1] => [5,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => 4
[5,5,4,4,3,2,1] => [5,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => 4
[7,4,4,4,3,2,1] => [4,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => 4
[6,4,4,4,3,2,1] => [4,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => 4
[5,4,4,4,3,2,1] => [4,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => 4
[4,4,4,4,3,2,1] => [4,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => 4
[6,6,5,3,3,2,1] => [6,5,3,3,2,1] => [5,3,3,2,1] => [3,3,2,1] => 3
[6,5,4,3,3,2,1] => [5,4,3,3,2,1] => [4,3,3,2,1] => [3,3,2,1] => 3
[6,5,3,3,3,2,1] => [5,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => 3
[6,4,3,3,3,2,1] => [4,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => 3
[5,4,3,3,3,2,1] => [4,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => 3
[6,3,3,3,3,2,1] => [3,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => 3
[3,3,3,3,3,2,1] => [3,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => 3
[6,6,5,4,2,2,1] => [6,5,4,2,2,1] => [5,4,2,2,1] => [4,2,2,1] => 3
[6,5,5,4,2,2,1] => [5,5,4,2,2,1] => [5,4,2,2,1] => [4,2,2,1] => 3
[6,5,4,4,2,2,1] => [5,4,4,2,2,1] => [4,4,2,2,1] => [4,2,2,1] => 3
[6,5,4,3,2,2,1] => [5,4,3,2,2,1] => [4,3,2,2,1] => [3,2,2,1] => 2
[5,5,4,3,2,2,1] => [5,4,3,2,2,1] => [4,3,2,2,1] => [3,2,2,1] => 2
[7,6,5,2,2,2,1] => [6,5,2,2,2,1] => [5,2,2,2,1] => [2,2,2,1] => 1
[6,5,4,2,2,2,1] => [5,4,2,2,2,1] => [4,2,2,2,1] => [2,2,2,1] => 1
[6,5,3,2,2,2,1] => [5,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 1
[6,4,3,2,2,2,1] => [4,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 1
[5,4,3,2,2,2,1] => [4,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 1
[6,5,2,2,2,2,1] => [5,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 1
[7,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 1
[7,6,5,4,3,1,1] => [6,5,4,3,1,1] => [5,4,3,1,1] => [4,3,1,1] => 4
[6,6,5,4,3,1,1] => [6,5,4,3,1,1] => [5,4,3,1,1] => [4,3,1,1] => 4
[6,5,5,4,3,1,1] => [5,5,4,3,1,1] => [5,4,3,1,1] => [4,3,1,1] => 4
[6,6,5,4,2,1,1] => [6,5,4,2,1,1] => [5,4,2,1,1] => [4,2,1,1] => 3
[6,5,5,4,2,1,1] => [5,5,4,2,1,1] => [5,4,2,1,1] => [4,2,1,1] => 3
[4,4,4,4,2,1,1] => [4,4,4,2,1,1] => [4,4,2,1,1] => [4,2,1,1] => 3
[6,5,4,3,2,1,1] => [5,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => 2
[5,5,4,3,2,1,1] => [5,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => 2
[5,4,4,3,2,1,1] => [4,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => 2
[7,6,5,4,1,1,1] => [6,5,4,1,1,1] => [5,4,1,1,1] => [4,1,1,1] => 3
[6,5,5,4,1,1,1] => [5,5,4,1,1,1] => [5,4,1,1,1] => [4,1,1,1] => 3
[6,5,4,3,1,1,1] => [5,4,3,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => 2
[7,6,5,2,1,1,1] => [6,5,2,1,1,1] => [5,2,1,1,1] => [2,1,1,1] => 1
[5,5,5,2,1,1,1] => [5,5,2,1,1,1] => [5,2,1,1,1] => [2,1,1,1] => 1
[7,5,4,2,1,1,1] => [5,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 1
[6,5,4,2,1,1,1] => [5,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 1
[7,6,3,2,1,1,1] => [6,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[7,4,3,2,1,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[6,4,3,2,1,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[6,5,4,1,1,1,1] => [5,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 0
[6,6,2,1,1,1,1] => [6,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[7,6,1,1,1,1,1] => [6,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 0
[7,6,5,4,3,2] => [6,5,4,3,2] => [5,4,3,2] => [4,3,2] => 4
[6,6,5,4,3,2] => [6,5,4,3,2] => [5,4,3,2] => [4,3,2] => 4
[7,5,5,4,3,2] => [5,5,4,3,2] => [5,4,3,2] => [4,3,2] => 4
[6,5,5,4,3,2] => [5,5,4,3,2] => [5,4,3,2] => [4,3,2] => 4
[5,5,5,4,3,2] => [5,5,4,3,2] => [5,4,3,2] => [4,3,2] => 4
[7,6,4,4,3,2] => [6,4,4,3,2] => [4,4,3,2] => [4,3,2] => 4
[6,5,4,4,3,2] => [5,4,4,3,2] => [4,4,3,2] => [4,3,2] => 4
[6,5,4,3,3,2] => [5,4,3,3,2] => [4,3,3,2] => [3,3,2] => 3
[5,4,3,3,3,2] => [4,3,3,3,2] => [3,3,3,2] => [3,3,2] => 3
[4,3,3,3,3,2] => [3,3,3,3,2] => [3,3,3,2] => [3,3,2] => 3
[6,5,4,3,2,2] => [5,4,3,2,2] => [4,3,2,2] => [3,2,2] => 2
[4,4,4,3,2,2] => [4,4,3,2,2] => [4,3,2,2] => [3,2,2] => 2
[7,6,5,2,2,2] => [6,5,2,2,2] => [5,2,2,2] => [2,2,2] => 1
[6,5,4,2,2,2] => [5,4,2,2,2] => [4,2,2,2] => [2,2,2] => 1
[5,4,3,2,2,2] => [4,3,2,2,2] => [3,2,2,2] => [2,2,2] => 1
[6,6,2,2,2,2] => [6,2,2,2,2] => [2,2,2,2] => [2,2,2] => 1
[7,6,5,4,3,1] => [6,5,4,3,1] => [5,4,3,1] => [4,3,1] => 4
[6,6,5,4,3,1] => [6,5,4,3,1] => [5,4,3,1] => [4,3,1] => 4
[6,5,5,4,3,1] => [5,5,4,3,1] => [5,4,3,1] => [4,3,1] => 4
[4,4,4,4,3,1] => [4,4,4,3,1] => [4,4,3,1] => [4,3,1] => 4
[7,6,5,4,2,1] => [6,5,4,2,1] => [5,4,2,1] => [4,2,1] => 3
[5,5,5,4,2,1] => [5,5,4,2,1] => [5,4,2,1] => [4,2,1] => 3
[4,4,4,4,2,1] => [4,4,4,2,1] => [4,4,2,1] => [4,2,1] => 3
[7,6,5,3,2,1] => [6,5,3,2,1] => [5,3,2,1] => [3,2,1] => 2
[6,6,5,3,2,1] => [6,5,3,2,1] => [5,3,2,1] => [3,2,1] => 2
[5,5,5,3,2,1] => [5,5,3,2,1] => [5,3,2,1] => [3,2,1] => 2
[7,6,4,3,2,1] => [6,4,3,2,1] => [4,3,2,1] => [3,2,1] => 2
[6,6,4,3,2,1] => [6,4,3,2,1] => [4,3,2,1] => [3,2,1] => 2
[7,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => [3,2,1] => 2
[7,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => [3,2,1] => 2
[7,6,3,3,2,1] => [6,3,3,2,1] => [3,3,2,1] => [3,2,1] => 2
[7,4,3,3,2,1] => [4,3,3,2,1] => [3,3,2,1] => [3,2,1] => 2
[7,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => [3,2,1] => 2
[7,6,5,2,2,1] => [6,5,2,2,1] => [5,2,2,1] => [2,2,1] => 1
[7,6,3,2,2,1] => [6,3,2,2,1] => [3,2,2,1] => [2,2,1] => 1
[7,6,2,2,2,1] => [6,2,2,2,1] => [2,2,2,1] => [2,2,1] => 1
[7,6,5,4,1,1] => [6,5,4,1,1] => [5,4,1,1] => [4,1,1] => 3
[7,6,5,2,1,1] => [6,5,2,1,1] => [5,2,1,1] => [2,1,1] => 1
[7,6,3,2,1,1] => [6,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[7,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => [2,1,1] => 1
[7,6,5,1,1,1] => [6,5,1,1,1] => [5,1,1,1] => [1,1,1] => 0
[7,6,5,4,3] => [6,5,4,3] => [5,4,3] => [4,3] => 4
[6,6,5,4,3] => [6,5,4,3] => [5,4,3] => [4,3] => 4
[6,5,5,4,3] => [5,5,4,3] => [5,4,3] => [4,3] => 4
[5,4,4,4,3] => [4,4,4,3] => [4,4,3] => [4,3] => 4
[5,4,3,3,3] => [4,3,3,3] => [3,3,3] => [3,3] => 3
[7,3,3,3,3] => [3,3,3,3] => [3,3,3] => [3,3] => 3
[7,6,5,4,2] => [6,5,4,2] => [5,4,2] => [4,2] => 3
[4,4,4,4,2] => [4,4,4,2] => [4,4,2] => [4,2] => 3
[7,6,5,3,2] => [6,5,3,2] => [5,3,2] => [3,2] => 2
[7,6,4,3,2] => [6,4,3,2] => [4,3,2] => [3,2] => 2
[7,5,4,3,2] => [5,4,3,2] => [4,3,2] => [3,2] => 2
[7,6,5,4,1] => [6,5,4,1] => [5,4,1] => [4,1] => 3
[7,5,4,3,1] => [5,4,3,1] => [4,3,1] => [3,1] => 2
[7,6,5,2,1] => [6,5,2,1] => [5,2,1] => [2,1] => 1
[6,6,5,2,1] => [6,5,2,1] => [5,2,1] => [2,1] => 1
[7,6,4,2,1] => [6,4,2,1] => [4,2,1] => [2,1] => 1
[6,6,4,2,1] => [6,4,2,1] => [4,2,1] => [2,1] => 1
[7,5,4,2,1] => [5,4,2,1] => [4,2,1] => [2,1] => 1
[7,6,3,2,1] => [6,3,2,1] => [3,2,1] => [2,1] => 1
[6,6,3,2,1] => [6,3,2,1] => [3,2,1] => [2,1] => 1
[7,6,5,4] => [6,5,4] => [5,4] => [4] => 3
[6,5,5,4] => [5,5,4] => [5,4] => [4] => 3
[7,6,5,3] => [6,5,3] => [5,3] => [3] => 2
[7,6,4,3] => [6,4,3] => [4,3] => [3] => 2
[7,5,4,3] => [5,4,3] => [4,3] => [3] => 2
[7,6,5,2] => [6,5,2] => [5,2] => [2] => 1
[3,3,3,3,3,3] => [3,3,3,3,3] => [3,3,3,3] => [3,3,3] => 3
[3,3,3,3,3,3,1] => [3,3,3,3,3,1] => [3,3,3,3,1] => [3,3,3,1] => 3
[3,3,3,3,3,2,2] => [3,3,3,3,2,2] => [3,3,3,2,2] => [3,3,2,2] => 3
[4,3,3,3,3,3] => [3,3,3,3,3] => [3,3,3,3] => [3,3,3] => 3
[4,4,4,4,4] => [4,4,4,4] => [4,4,4] => [4,4] => 5
[4,4,4,3,3,3] => [4,4,3,3,3] => [4,3,3,3] => [3,3,3] => 3
[5,5,5,5] => [5,5,5] => [5,5] => [5] => 4
[6,6,6,6] => [6,6,6] => [6,6] => [6] => 5
[6,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 1
[8,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 1
[8,6,4,2] => [6,4,2] => [4,2] => [2] => 1
[7,7,7,7] => [7,7,7] => [7,7] => [7] => 6
[11,7,5,1] => [7,5,1] => [5,1] => [1] => 0
[9,7,5,3,1] => [7,5,3,1] => [5,3,1] => [3,1] => 2
[11,9,7,5,3,1] => [9,7,5,3,1] => [7,5,3,1] => [5,3,1] => 5
[7,6,5,4,3,1,1,1] => [6,5,4,3,1,1,1] => [5,4,3,1,1,1] => [4,3,1,1,1] => 4
[8,7,6,4,3,2,1] => [7,6,4,3,2,1] => [6,4,3,2,1] => [4,3,2,1] => 4
[8,7,5,4,3,2,1] => [7,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => 4
[8,6,5,4,3,2,1] => [6,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => 4
[8,7,6,5,2,2,1] => [7,6,5,2,2,1] => [6,5,2,2,1] => [5,2,2,1] => 4
[8,7,6,3,3,2,1] => [7,6,3,3,2,1] => [6,3,3,2,1] => [3,3,2,1] => 3
[8,7,4,4,3,2,1] => [7,4,4,3,2,1] => [4,4,3,2,1] => [4,3,2,1] => 4
[8,5,5,4,3,2,1] => [5,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => 4
[8,5,4,2] => [5,4,2] => [4,2] => [2] => 1
[9,6,5,3] => [6,5,3] => [5,3] => [3] => 2
[10,7,5,3] => [7,5,3] => [5,3] => [3] => 2
[9,6,4,3] => [6,4,3] => [4,3] => [3] => 2
[9,7,5,4,1] => [7,5,4,1] => [5,4,1] => [4,1] => 3
[8,6,5,3,1] => [6,5,3,1] => [5,3,1] => [3,1] => 2
[10,8,6,4,2] => [8,6,4,2] => [6,4,2] => [4,2] => 3
[8,5,5,1] => [5,5,1] => [5,1] => [1] => 0
[9,5,5,1] => [5,5,1] => [5,1] => [1] => 0
[9,7,5,3] => [7,5,3] => [5,3] => [3] => 2
[3,3,3,3,1,1,1,1,1,1] => [3,3,3,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 2
[5,5,5,5,5] => [5,5,5,5] => [5,5,5] => [5,5] => 7
[7,7,1,1,1,1] => [7,1,1,1,1] => [1,1,1,1] => [1,1,1] => 0
[8,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => [3,2,1] => 2
[8,7,4,3,2,1] => [7,4,3,2,1] => [4,3,2,1] => [3,2,1] => 2
[7,7,1,1,1,1,1,1] => [7,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 0
[5,4,3,2,1,1,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[6,5,4,3,2,1,1,1] => [5,4,3,2,1,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => 2
[5,4,3,2,1,1,1,1,1] => [4,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[6,5,4,3,1,1,1,1] => [5,4,3,1,1,1,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => 2
[6,5,4,3,2,1,1,1,1] => [5,4,3,2,1,1,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => 2
[8,6,5,4,3,2] => [6,5,4,3,2] => [5,4,3,2] => [4,3,2] => 4
[7,5,4,3,2,1,1,1] => [5,4,3,2,1,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => 2
[7,6,4,3,2,2,2,1] => [6,4,3,2,2,2,1] => [4,3,2,2,2,1] => [3,2,2,2,1] => 2
[6,6,6,4,3,2,1] => [6,6,4,3,2,1] => [6,4,3,2,1] => [4,3,2,1] => 4
[5,4,3,3,3,3,1] => [4,3,3,3,3,1] => [3,3,3,3,1] => [3,3,3,1] => 3
[5,4,3,2,2,2,2] => [4,3,2,2,2,2] => [3,2,2,2,2] => [2,2,2,2] => 1
[6,5,4,3,2,2,2,1] => [5,4,3,2,2,2,1] => [4,3,2,2,2,1] => [3,2,2,2,1] => 2
[6,5,5,5] => [5,5,5] => [5,5] => [5] => 4
[5,4,4,4,4] => [4,4,4,4] => [4,4,4] => [4,4] => 5
[8,7,6,3,2,1] => [7,6,3,2,1] => [6,3,2,1] => [3,2,1] => 2
[8,7,6,5,2,1] => [7,6,5,2,1] => [6,5,2,1] => [5,2,1] => 4
[8,7,6,5,4,1] => [7,6,5,4,1] => [6,5,4,1] => [5,4,1] => 6
[8,7,6,5] => [7,6,5] => [6,5] => [5] => 4
[8,7,6,5,4] => [7,6,5,4] => [6,5,4] => [5,4] => 6
[9,8,7,6] => [8,7,6] => [7,6] => [6] => 5
[8,7,6,4] => [7,6,4] => [6,4] => [4] => 3
[8,7,6,5,3] => [7,6,5,3] => [6,5,3] => [5,3] => 5
[4,4,4,4,4,1] => [4,4,4,4,1] => [4,4,4,1] => [4,4,1] => 5
[5,5,5,5,1] => [5,5,5,1] => [5,5,1] => [5,1] => 4
[6,6,6,1] => [6,6,1] => [6,1] => [1] => 0
[7,7,5,4,3,2,1] => [7,5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => 4
[6,6,6,1,1] => [6,6,1,1] => [6,1,1] => [1,1] => 0
[7,7,4,3,2,1] => [7,4,3,2,1] => [4,3,2,1] => [3,2,1] => 2
[6,5,4,3,2,2,2] => [5,4,3,2,2,2] => [4,3,2,2,2] => [3,2,2,2] => 2
[8,5,4,3,2,1,1] => [5,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => 2
search for individual values
searching the database for the individual values of this statistic
Description
The spin of an integer partition.
The Ferrers shape of an integer partition $\lambda$ can be decomposed into border strips. The spin is then defined to be the total number of crossings of border strips of $\lambda$ with the vertical lines in the Ferrers shape.
The following example is taken from Appendix B in [1]: Let $\lambda = (5,5,4,4,2,1)$. Removing the border strips successively yields the sequence of partitions
$$(5,5,4,4,2,1), (4,3,3,1), (2,2), (1), ().$$
The first strip $(5,5,4,4,2,1) \setminus (4,3,3,1)$ crosses $4$ times, the second strip $(4,3,3,1) \setminus (2,2)$ crosses $3$ times, the strip $(2,2) \setminus (1)$ crosses $1$ time, and the remaining strip $(1) \setminus ()$ does not cross.
This yields the spin of $(5,5,4,4,2,1)$ to be $4+3+1 = 8$.
Map
first row removal
Description
Removes the first entry of an integer partition