Identifier
Values
[3] => [1,1,1] => [1,1] => 0
[4] => [1,1,1,1] => [1,1,1] => 0
[3,1] => [2,1,1] => [1,1] => 0
[2,1,1] => [2,2] => [2] => 1
[5] => [1,1,1,1,1] => [1,1,1,1] => 0
[4,1] => [2,1,1,1] => [1,1,1] => 0
[2,2,1] => [2,2,1] => [2,1] => 1
[2,1,1,1] => [3,1,1] => [1,1] => 0
[1,1,1,1,1] => [3,2] => [2] => 1
[6] => [1,1,1,1,1,1] => [1,1,1,1,1] => 0
[5,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[4,2] => [2,2,1,1] => [2,1,1] => 1
[4,1,1] => [3,1,1,1] => [1,1,1] => 0
[3,1,1,1] => [3,3] => [3] => 0
[2,2,2] => [2,2,2] => [2,2] => 1
[2,2,1,1] => [4,1,1] => [1,1] => 0
[2,1,1,1,1] => [4,2] => [2] => 1
[1,1,1,1,1,1] => [3,2,1] => [2,1] => 1
[7] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[6,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 0
[5,2] => [2,2,1,1,1] => [2,1,1,1] => 1
[5,1,1] => [3,1,1,1,1] => [1,1,1,1] => 0
[4,2,1] => [5,1,1] => [1,1] => 0
[4,1,1,1] => [3,2,1,1] => [2,1,1] => 1
[3,2,2] => [2,2,2,1] => [2,2,1] => 2
[3,2,1,1] => [5,2] => [2] => 1
[3,1,1,1,1] => [3,2,2] => [2,2] => 1
[2,2,2,1] => [4,1,1,1] => [1,1,1] => 0
[2,2,1,1,1] => [4,3] => [3] => 0
[2,1,1,1,1,1] => [3,3,1] => [3,1] => 1
[1,1,1,1,1,1,1] => [4,2,1] => [2,1] => 1
[8] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[7,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[6,2] => [2,2,1,1,1,1] => [2,1,1,1,1] => 1
[6,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 0
[5,3] => [2,2,2,1,1] => [2,2,1,1] => 3
[5,2,1] => [4,1,1,1,1] => [1,1,1,1] => 0
[5,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 1
[4,2,2] => [6,1,1] => [1,1] => 0
[4,2,1,1] => [4,4] => [4] => 1
[4,1,1,1,1] => [5,2,1] => [2,1] => 1
[3,3,2] => [2,2,2,2] => [2,2,2] => 2
[3,3,1,1] => [6,2] => [2] => 1
[3,2,2,1] => [3,2,2,1] => [2,2,1] => 2
[3,2,1,1,1] => [3,3,1,1] => [3,1,1] => 2
[3,1,1,1,1,1] => [4,2,1,1] => [2,1,1] => 1
[2,2,2,2] => [5,1,1,1] => [1,1,1] => 0
[2,2,2,1,1] => [5,3] => [3] => 0
[2,2,1,1,1,1] => [3,3,2] => [3,2] => 2
[2,1,1,1,1,1,1] => [4,2,2] => [2,2] => 1
[1,1,1,1,1,1,1,1] => [4,3,1] => [3,1] => 1
[9] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[8,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[7,2] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[7,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[6,3] => [2,2,2,1,1,1] => [2,2,1,1,1] => 4
[6,2,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 0
[6,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 1
[5,3,1] => [3,2,2,1,1] => [2,2,1,1] => 3
[5,2,2] => [6,1,1,1] => [1,1,1] => 0
[5,2,1,1] => [3,3,1,1,1] => [3,1,1,1] => 3
[5,1,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 1
[4,3,2] => [7,1,1] => [1,1] => 0
[4,3,1,1] => [7,2] => [2] => 1
[4,2,2,1] => [6,3] => [3] => 0
[4,2,1,1,1] => [6,2,1] => [2,1] => 1
[4,1,1,1,1,1] => [4,4,1] => [4,1] => 2
[3,3,3] => [2,2,2,2,1] => [2,2,2,1] => 5
[3,3,2,1] => [3,2,2,2] => [2,2,2] => 2
[3,3,1,1,1] => [5,2,1,1] => [2,1,1] => 1
[3,2,2,2] => [5,1,1,1,1] => [1,1,1,1] => 0
[3,2,2,1,1] => [3,3,3] => [3,3] => 2
[3,2,1,1,1,1] => [5,2,2] => [2,2] => 1
[3,1,1,1,1,1,1] => [5,3,1] => [3,1] => 1
[2,2,2,2,1] => [5,4] => [4] => 1
[2,2,2,1,1,1] => [3,3,2,1] => [3,2,1] => 6
[2,2,1,1,1,1,1] => [4,2,2,1] => [2,2,1] => 2
[2,1,1,1,1,1,1,1] => [4,3,1,1] => [3,1,1] => 2
[1,1,1,1,1,1,1,1,1] => [4,3,2] => [3,2] => 2
[10] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 0
[9,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[8,2] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[8,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[7,3] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 5
[7,2,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[7,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[6,4] => [2,2,2,2,1,1] => [2,2,2,1,1] => 9
[6,3,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 4
[6,2,2] => [5,1,1,1,1,1] => [1,1,1,1,1] => 0
[6,2,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 4
[6,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => 1
[5,3,2] => [7,1,1,1] => [1,1,1] => 0
[5,3,1,1] => [6,2,1,1] => [2,1,1] => 1
[5,2,2,1] => [3,3,2,1,1] => [3,2,1,1] => 12
[5,2,1,1,1] => [4,2,2,1,1] => [2,2,1,1] => 3
[5,1,1,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => 3
[4,4,2] => [8,1,1] => [1,1] => 0
[4,4,1,1] => [8,2] => [2] => 1
[4,3,3] => [2,2,2,2,2] => [2,2,2,2] => 5
[4,3,2,1] => [7,3] => [3] => 0
[4,3,1,1,1] => [7,2,1] => [2,1] => 1
>>> Load all 1069 entries. <<<
[4,2,2,2] => [5,5] => [5] => 0
[4,2,2,1,1] => [3,3,2,2] => [3,2,2] => 8
[4,2,1,1,1,1] => [6,3,1] => [3,1] => 1
[4,1,1,1,1,1,1] => [4,3,3] => [3,3] => 2
[3,3,3,1] => [3,2,2,2,1] => [2,2,2,1] => 5
[3,3,2,2] => [6,1,1,1,1] => [1,1,1,1] => 0
[3,3,2,1,1] => [6,2,2] => [2,2] => 1
[3,3,1,1,1,1] => [5,4,1] => [4,1] => 2
[3,2,2,2,1] => [5,2,1,1,1] => [2,1,1,1] => 1
[3,2,2,1,1,1] => [4,2,2,2] => [2,2,2] => 2
[3,2,1,1,1,1,1] => [4,4,1,1] => [4,1,1] => 4
[3,1,1,1,1,1,1,1] => [4,4,2] => [4,2] => 4
[2,2,2,2,2] => [6,4] => [4] => 1
[2,2,2,2,1,1] => [3,3,3,1] => [3,3,1] => 8
[2,2,2,1,1,1,1] => [5,2,2,1] => [2,2,1] => 2
[2,2,1,1,1,1,1,1] => [5,3,1,1] => [3,1,1] => 2
[2,1,1,1,1,1,1,1,1] => [5,3,2] => [3,2] => 2
[1,1,1,1,1,1,1,1,1,1] => [4,3,2,1] => [3,2,1] => 6
[11] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 0
[10,1] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 0
[9,2] => [2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 1
[9,1,1] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[8,3] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 6
[8,2,1] => [4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[8,1,1,1] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[7,4] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => 14
[7,3,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => 5
[7,2,2] => [5,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[7,2,1,1] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => 5
[7,1,1,1,1] => [4,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[6,4,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => 9
[6,3,2] => [7,1,1,1,1] => [1,1,1,1] => 0
[6,3,1,1] => [5,2,1,1,1,1] => [2,1,1,1,1] => 1
[6,2,2,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => 20
[6,2,1,1,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => 4
[6,1,1,1,1,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => 4
[5,4,2] => [9,1,1] => [1,1] => 0
[5,4,1,1] => [9,2] => [2] => 1
[5,3,3] => [8,1,1,1] => [1,1,1] => 0
[5,3,2,1] => [7,2,1,1] => [2,1,1] => 1
[5,3,1,1,1] => [5,5,1] => [5,1] => 2
[5,2,2,2] => [7,4] => [4] => 1
[5,2,2,1,1] => [6,2,2,1] => [2,2,1] => 2
[5,2,1,1,1,1] => [6,3,1,1] => [3,1,1] => 2
[5,1,1,1,1,1,1] => [4,3,2,1,1] => [3,2,1,1] => 12
[4,4,3] => [2,2,2,2,2,1] => [2,2,2,2,1] => 14
[4,4,2,1] => [8,3] => [3] => 0
[4,4,1,1,1] => [8,2,1] => [2,1] => 1
[4,3,3,1] => [3,2,2,2,2] => [2,2,2,2] => 5
[4,3,2,2] => [3,3,2,2,1] => [3,2,2,1] => 25
[4,3,2,1,1] => [7,2,2] => [2,2] => 1
[4,3,1,1,1,1] => [7,3,1] => [3,1] => 1
[4,2,2,2,1] => [3,3,3,1,1] => [3,3,1,1] => 20
[4,2,2,1,1,1] => [5,2,2,1,1] => [2,2,1,1] => 3
[4,2,1,1,1,1,1] => [6,3,2] => [3,2] => 2
[4,1,1,1,1,1,1,1] => [4,3,2,2] => [3,2,2] => 8
[3,3,3,2] => [6,1,1,1,1,1] => [1,1,1,1,1] => 0
[3,3,3,1,1] => [4,2,2,2,1] => [2,2,2,1] => 5
[3,3,2,2,1] => [6,2,1,1,1] => [2,1,1,1] => 1
[3,3,2,1,1,1] => [4,4,1,1,1] => [4,1,1,1] => 7
[3,3,1,1,1,1,1] => [4,4,3] => [4,3] => 6
[3,2,2,2,2] => [6,5] => [5] => 0
[3,2,2,2,1,1] => [6,4,1] => [4,1] => 2
[3,2,2,1,1,1,1] => [5,3,1,1,1] => [3,1,1,1] => 3
[3,2,1,1,1,1,1,1] => [5,3,3] => [3,3] => 2
[3,1,1,1,1,1,1,1,1] => [4,3,3,1] => [3,3,1] => 8
[2,2,2,2,2,1] => [3,3,3,2] => [3,3,2] => 16
[2,2,2,2,1,1,1] => [5,2,2,2] => [2,2,2] => 2
[2,2,2,1,1,1,1,1] => [5,4,1,1] => [4,1,1] => 4
[2,2,1,1,1,1,1,1,1] => [5,4,2] => [4,2] => 4
[2,1,1,1,1,1,1,1,1,1] => [4,4,2,1] => [4,2,1] => 14
[1,1,1,1,1,1,1,1,1,1,1] => [5,3,2,1] => [3,2,1] => 6
[12] => [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] => [2,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 0
[10,2] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 1
[10,1,1] => [3,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 0
[9,3] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 7
[9,2,1] => [4,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[9,1,1,1] => [3,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 1
[8,4] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 20
[8,3,1] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 6
[8,2,2] => [5,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[8,2,1,1] => [3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 6
[8,1,1,1,1] => [4,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[7,5] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => 28
[7,4,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => 14
[7,3,2] => [6,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[7,3,1,1] => [5,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[7,2,2,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => 30
[7,2,1,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => 5
[7,1,1,1,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => 5
[6,4,2] => [3,3,2,2,1,1] => [3,2,2,1,1] => 54
[6,4,1,1] => [4,2,2,2,1,1] => [2,2,2,1,1] => 9
[6,3,3] => [8,1,1,1,1] => [1,1,1,1] => 0
[6,3,2,1] => [7,2,1,1,1] => [2,1,1,1] => 1
[6,3,1,1,1] => [4,4,1,1,1,1] => [4,1,1,1,1] => 11
[6,2,2,2] => [3,3,3,1,1,1] => [3,3,1,1,1] => 40
[6,2,2,1,1] => [5,2,2,1,1,1] => [2,2,1,1,1] => 4
[6,2,1,1,1,1] => [5,3,1,1,1,1] => [3,1,1,1,1] => 4
[6,1,1,1,1,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => 20
[5,5,2] => [10,1,1] => [1,1] => 0
[5,5,1,1] => [10,2] => [2] => 1
[5,4,3] => [9,1,1,1] => [1,1,1] => 0
[5,4,2,1] => [9,3] => [3] => 0
[5,4,1,1,1] => [9,2,1] => [2,1] => 1
[5,3,3,1] => [8,2,1,1] => [2,1,1] => 1
[5,3,2,2] => [6,6] => [6] => 1
[5,3,2,1,1] => [7,4,1] => [4,1] => 2
[5,3,1,1,1,1] => [4,4,4] => [4,4] => 6
[5,2,2,2,1] => [7,2,2,1] => [2,2,1] => 2
[5,2,2,1,1,1] => [5,5,1,1] => [5,1,1] => 6
[5,2,1,1,1,1,1] => [5,5,2] => [5,2] => 6
[5,1,1,1,1,1,1,1] => [6,3,2,1] => [3,2,1] => 6
[4,4,4] => [2,2,2,2,2,2] => [2,2,2,2,2] => 14
[4,4,3,1] => [3,2,2,2,2,1] => [2,2,2,2,1] => 14
[4,4,2,2] => [8,4] => [4] => 1
[4,4,2,1,1] => [8,2,2] => [2,2] => 1
[4,4,1,1,1,1] => [8,3,1] => [3,1] => 1
[4,3,3,2] => [3,3,2,2,2] => [3,2,2,2] => 30
[4,3,3,1,1] => [4,2,2,2,2] => [2,2,2,2] => 5
[4,3,2,2,1] => [6,2,2,1,1] => [2,2,1,1] => 3
[4,3,2,1,1,1] => [6,3,1,1,1] => [3,1,1,1] => 3
[4,3,1,1,1,1,1] => [7,3,2] => [3,2] => 2
[4,2,2,2,2] => [3,3,3,3] => [3,3,3] => 16
[4,2,2,2,1,1] => [6,2,2,2] => [2,2,2] => 2
[4,2,2,1,1,1,1] => [4,3,3,1,1] => [3,3,1,1] => 20
[4,2,1,1,1,1,1,1] => [4,4,2,1,1] => [4,2,1,1] => 33
[4,1,1,1,1,1,1,1,1] => [5,3,2,1,1] => [3,2,1,1] => 12
[3,3,3,3] => [7,1,1,1,1,1] => [1,1,1,1,1] => 0
[3,3,3,2,1] => [6,2,1,1,1,1] => [2,1,1,1,1] => 1
[3,3,3,1,1,1] => [4,3,2,2,1] => [3,2,2,1] => 25
[3,3,2,2,2] => [7,5] => [5] => 0
[3,3,2,2,1,1] => [7,3,1,1] => [3,1,1] => 2
[3,3,2,1,1,1,1] => [6,3,3] => [3,3] => 2
[3,3,1,1,1,1,1,1] => [4,3,3,2] => [3,3,2] => 16
[3,2,2,2,2,1] => [6,5,1] => [5,1] => 2
[3,2,2,2,1,1,1] => [6,4,1,1] => [4,1,1] => 4
[3,2,2,1,1,1,1,1] => [6,4,2] => [4,2] => 4
[3,2,1,1,1,1,1,1,1] => [4,4,2,2] => [4,2,2] => 22
[3,1,1,1,1,1,1,1,1,1] => [5,3,2,2] => [3,2,2] => 8
[2,2,2,2,2,2] => [3,3,3,2,1] => [3,3,2,1] => 61
[2,2,2,2,2,1,1] => [5,2,2,2,1] => [2,2,2,1] => 5
[2,2,2,2,1,1,1,1] => [5,4,1,1,1] => [4,1,1,1] => 7
[2,2,2,1,1,1,1,1,1] => [5,4,3] => [4,3] => 6
[2,2,1,1,1,1,1,1,1,1] => [4,4,3,1] => [4,3,1] => 28
[2,1,1,1,1,1,1,1,1,1,1] => [5,3,3,1] => [3,3,1] => 8
[1,1,1,1,1,1,1,1,1,1,1,1] => [5,4,2,1] => [4,2,1] => 14
[13] => [1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => 0
[12,1] => [2,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => 0
[11,2] => [2,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => 1
[11,1,1] => [3,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 0
[10,3] => [2,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => 8
[10,2,1] => [4,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 0
[10,1,1,1] => [3,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 1
[9,4] => [2,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => 27
[9,3,1] => [3,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 7
[9,2,2] => [5,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[9,2,1,1] => [3,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 7
[9,1,1,1,1] => [4,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 1
[8,5] => [2,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => 48
[8,4,1] => [3,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 20
[8,3,2] => [6,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[8,3,1,1] => [5,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[8,2,2,1] => [3,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => 42
[8,2,1,1,1] => [4,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 6
[8,1,1,1,1,1] => [4,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 6
[7,5,1] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => 28
[7,4,2] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => 98
[7,4,1,1] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => 14
[7,3,3] => [8,1,1,1,1,1] => [1,1,1,1,1] => 0
[7,3,2,1] => [6,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[7,3,1,1,1] => [4,4,1,1,1,1,1] => [4,1,1,1,1,1] => 16
[7,2,2,2] => [3,3,3,1,1,1,1] => [3,3,1,1,1,1] => 70
[7,2,2,1,1] => [5,2,2,1,1,1,1] => [2,2,1,1,1,1] => 5
[7,2,1,1,1,1] => [5,3,1,1,1,1,1] => [3,1,1,1,1,1] => 5
[7,1,1,1,1,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => 30
[6,5,2] => [11,1,1] => [1,1] => 0
[6,5,1,1] => [11,2] => [2] => 1
[6,4,3] => [9,1,1,1,1] => [1,1,1,1] => 0
[6,4,2,1] => [7,2,2,1,1] => [2,2,1,1] => 3
[6,4,1,1,1] => [4,3,2,2,1,1] => [3,2,2,1,1] => 54
[6,3,3,1] => [8,2,1,1,1] => [2,1,1,1] => 1
[6,3,2,2] => [3,3,3,2,1,1] => [3,3,2,1,1] => 155
[6,3,2,1,1] => [7,3,1,1,1] => [3,1,1,1] => 3
[6,3,1,1,1,1] => [4,3,3,1,1,1] => [3,3,1,1,1] => 40
[6,2,2,2,1] => [5,2,2,2,1,1] => [2,2,2,1,1] => 9
[6,2,2,1,1,1] => [5,4,1,1,1,1] => [4,1,1,1,1] => 11
[6,2,1,1,1,1,1] => [4,4,2,1,1,1] => [4,2,1,1,1] => 64
[6,1,1,1,1,1,1,1] => [5,3,2,1,1,1] => [3,2,1,1,1] => 20
[5,5,3] => [10,1,1,1] => [1,1,1] => 0
[5,5,2,1] => [10,3] => [3] => 0
[5,5,1,1,1] => [10,2,1] => [2,1] => 1
[5,4,4] => [2,2,2,2,2,2,1] => [2,2,2,2,2,1] => 42
[5,4,3,1] => [9,2,1,1] => [2,1,1] => 1
[5,4,2,2] => [9,4] => [4] => 1
[5,4,2,1,1] => [9,2,2] => [2,2] => 1
[5,4,1,1,1,1] => [9,3,1] => [3,1] => 1
[5,3,3,2] => [8,5] => [5] => 0
[5,3,3,1,1] => [8,4,1] => [4,1] => 2
[5,3,2,2,1] => [6,6,1] => [6,1] => 3
[5,3,2,1,1,1] => [7,3,3] => [3,3] => 2
[5,3,1,1,1,1,1] => [7,4,2] => [4,2] => 4
[5,2,2,2,2] => [8,2,2,1] => [2,2,1] => 2
[5,2,2,2,1,1] => [7,4,1,1] => [4,1,1] => 4
[5,2,2,1,1,1,1] => [5,4,4] => [4,4] => 6
[5,2,1,1,1,1,1,1] => [4,4,4,1] => [4,4,1] => 34
[5,1,1,1,1,1,1,1,1] => [5,5,2,1] => [5,2,1] => 26
[4,4,4,1] => [3,2,2,2,2,2] => [2,2,2,2,2] => 14
[4,4,3,2] => [3,3,2,2,2,1] => [3,2,2,2,1] => 98
[4,4,3,1,1] => [4,2,2,2,2,1] => [2,2,2,2,1] => 14
[4,4,2,2,1] => [6,2,2,1,1,1] => [2,2,1,1,1] => 4
[4,4,2,1,1,1] => [8,3,1,1] => [3,1,1] => 2
[4,4,1,1,1,1,1] => [8,3,2] => [3,2] => 2
[4,3,3,3] => [7,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[4,3,3,2,1] => [7,2,2,2] => [2,2,2] => 2
[4,3,3,1,1,1] => [4,3,2,2,2] => [3,2,2,2] => 30
[4,3,2,2,2] => [3,3,3,2,2] => [3,3,2,2] => 91
[4,3,2,2,1,1] => [6,5,1,1] => [5,1,1] => 6
[4,3,2,1,1,1,1] => [6,3,2,1,1] => [3,2,1,1] => 12
[4,3,1,1,1,1,1,1] => [6,3,2,2] => [3,2,2] => 8
[4,2,2,2,2,1] => [5,2,2,2,2] => [2,2,2,2] => 5
[4,2,2,2,1,1,1] => [5,5,1,1,1] => [5,1,1,1] => 13
[4,2,2,1,1,1,1,1] => [7,3,2,1] => [3,2,1] => 6
[4,2,1,1,1,1,1,1,1] => [6,3,3,1] => [3,3,1] => 8
[4,1,1,1,1,1,1,1,1,1] => [6,4,2,1] => [4,2,1] => 14
[3,3,3,3,1] => [7,2,1,1,1,1] => [2,1,1,1,1] => 1
[3,3,3,2,2] => [7,6] => [6] => 1
[3,3,3,2,1,1] => [6,3,1,1,1,1] => [3,1,1,1,1] => 4
[3,3,3,1,1,1,1] => [4,3,3,3] => [3,3,3] => 16
[3,3,2,2,2,1] => [7,5,1] => [5,1] => 2
[3,3,2,2,1,1,1] => [6,5,2] => [5,2] => 6
[3,3,2,1,1,1,1,1] => [4,4,2,2,1] => [4,2,2,1] => 80
[3,3,1,1,1,1,1,1,1] => [5,3,2,2,1] => [3,2,2,1] => 25
[3,2,2,2,2,2] => [3,3,3,3,1] => [3,3,3,1] => 77
[3,2,2,2,2,1,1] => [4,3,3,2,1] => [3,3,2,1] => 61
[3,2,2,2,1,1,1,1] => [5,5,3] => [5,3] => 12
[3,2,2,1,1,1,1,1,1] => [4,4,3,1,1] => [4,3,1,1] => 81
[3,2,1,1,1,1,1,1,1,1] => [5,3,3,1,1] => [3,3,1,1] => 20
[3,1,1,1,1,1,1,1,1,1,1] => [5,4,2,1,1] => [4,2,1,1] => 33
[2,2,2,2,2,2,1] => [6,2,2,2,1] => [2,2,2,1] => 5
[2,2,2,2,2,1,1,1] => [6,4,1,1,1] => [4,1,1,1] => 7
[2,2,2,2,1,1,1,1,1] => [6,4,3] => [4,3] => 6
[2,2,2,1,1,1,1,1,1,1] => [4,4,3,2] => [4,3,2] => 66
[2,2,1,1,1,1,1,1,1,1,1] => [5,3,3,2] => [3,3,2] => 16
[2,1,1,1,1,1,1,1,1,1,1,1] => [5,4,2,2] => [4,2,2] => 22
[1,1,1,1,1,1,1,1,1,1,1,1,1] => [5,4,3,1] => [4,3,1] => 28
[13,1] => [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] => 0
[12,2] => [2,2,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => 1
[12,1,1] => [3,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => 0
[11,3] => [2,2,2,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 9
[11,2,1] => [4,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 0
[11,1,1,1] => [3,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => 1
[10,4] => [2,2,2,2,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => 35
[10,3,1] => [3,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => 8
[10,2,2] => [5,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 0
[10,2,1,1] => [3,3,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => 8
[10,1,1,1,1] => [4,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 1
[9,5] => [2,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => 75
[9,4,1] => [3,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => 27
[9,3,2] => [6,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[9,3,1,1] => [5,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 1
[9,2,2,1] => [3,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => 56
[9,2,1,1,1] => [4,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 7
[9,1,1,1,1,1] => [4,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 7
[8,6] => [2,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => 90
[8,5,1] => [3,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => 48
[8,4,2] => [3,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => 160
[8,4,1,1] => [4,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 20
[8,3,3] => [7,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[8,3,2,1] => [6,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[8,3,1,1,1] => [4,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => 22
[8,2,2,2] => [3,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => 112
[8,2,2,1,1] => [5,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 6
[8,2,1,1,1,1] => [5,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 6
[8,1,1,1,1,1,1] => [4,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => 42
[7,5,2] => [3,3,2,2,2,1,1] => [3,2,2,2,1,1] => 224
[7,5,1,1] => [4,2,2,2,2,1,1] => [2,2,2,2,1,1] => 28
[7,4,3] => [9,1,1,1,1,1] => [1,1,1,1,1] => 0
[7,4,2,1] => [6,2,2,1,1,1,1] => [2,2,1,1,1,1] => 5
[7,4,1,1,1] => [4,3,2,2,1,1,1] => [3,2,2,1,1,1] => 98
[7,3,3,1] => [8,2,1,1,1,1] => [2,1,1,1,1] => 1
[7,3,2,2] => [3,3,3,2,1,1,1] => [3,3,2,1,1,1] => 323
[7,3,2,1,1] => [6,3,1,1,1,1,1] => [3,1,1,1,1,1] => 5
[7,3,1,1,1,1] => [4,3,3,1,1,1,1] => [3,3,1,1,1,1] => 70
[7,2,2,2,1] => [5,2,2,2,1,1,1] => [2,2,2,1,1,1] => 14
[7,2,2,1,1,1] => [5,4,1,1,1,1,1] => [4,1,1,1,1,1] => 16
[7,2,1,1,1,1,1] => [4,4,2,1,1,1,1] => [4,2,1,1,1,1] => 110
[7,1,1,1,1,1,1,1] => [5,3,2,1,1,1,1] => [3,2,1,1,1,1] => 30
[6,6,2] => [12,1,1] => [1,1] => 0
[6,6,1,1] => [12,2] => [2] => 1
[6,5,3] => [11,1,1,1] => [1,1,1] => 0
[6,5,2,1] => [11,3] => [3] => 0
[6,5,1,1,1] => [11,2,1] => [2,1] => 1
[6,4,4] => [10,1,1,1,1] => [1,1,1,1] => 0
[6,4,3,1] => [9,2,1,1,1] => [2,1,1,1] => 1
[6,4,2,2] => [8,2,2,1,1] => [2,2,1,1] => 3
[6,4,2,1,1] => [6,6,1,1] => [6,1,1] => 9
[6,4,1,1,1,1] => [7,3,2,1,1] => [3,2,1,1] => 12
[6,3,3,2] => [7,7] => [7] => 0
[6,3,3,1,1] => [8,3,1,1,1] => [3,1,1,1] => 3
[6,3,2,2,1] => [4,3,3,2,1,1] => [3,3,2,1,1] => 155
[6,3,2,1,1,1] => [4,4,2,2,1,1] => [4,2,2,1,1] => 198
[6,3,1,1,1,1,1] => [5,3,2,2,1,1] => [3,2,2,1,1] => 54
[6,2,2,2,2] => [7,2,2,2,1] => [2,2,2,1] => 5
[6,2,2,2,1,1] => [7,4,1,1,1] => [4,1,1,1] => 7
[6,2,2,1,1,1,1] => [4,4,3,1,1,1] => [4,3,1,1,1] => 185
[6,2,1,1,1,1,1,1] => [5,3,3,1,1,1] => [3,3,1,1,1] => 40
[6,1,1,1,1,1,1,1,1] => [5,4,2,1,1,1] => [4,2,1,1,1] => 64
[5,5,4] => [2,2,2,2,2,2,2] => [2,2,2,2,2,2] => 42
[5,5,3,1] => [10,2,1,1] => [2,1,1] => 1
[5,5,2,2] => [10,4] => [4] => 1
[5,5,2,1,1] => [10,2,2] => [2,2] => 1
[5,5,1,1,1,1] => [10,3,1] => [3,1] => 1
[5,4,4,1] => [3,2,2,2,2,2,1] => [2,2,2,2,2,1] => 42
[5,4,3,2] => [9,5] => [5] => 0
[5,4,3,1,1] => [9,4,1] => [4,1] => 2
[5,4,2,2,1] => [9,2,2,1] => [2,2,1] => 2
[5,4,2,1,1,1] => [9,3,1,1] => [3,1,1] => 2
[5,4,1,1,1,1,1] => [9,3,2] => [3,2] => 2
[5,3,3,3] => [3,3,3,2,2,1] => [3,3,2,2,1] => 344
[5,3,3,2,1] => [8,5,1] => [5,1] => 2
[5,3,3,1,1,1] => [8,3,3] => [3,3] => 2
[5,3,2,2,2] => [3,3,3,3,1,1] => [3,3,3,1,1] => 232
[5,3,2,2,1,1] => [8,4,1,1] => [4,1,1] => 4
[5,3,2,1,1,1,1] => [8,4,2] => [4,2] => 4
[5,3,1,1,1,1,1,1] => [7,3,3,1] => [3,3,1] => 8
[5,2,2,2,2,1] => [5,5,1,1,1,1] => [5,1,1,1,1] => 24
[5,2,2,2,1,1,1] => [7,4,3] => [4,3] => 6
[5,2,2,1,1,1,1,1] => [4,4,3,3] => [4,3,3] => 82
[5,2,1,1,1,1,1,1,1] => [7,4,2,1] => [4,2,1] => 14
[5,1,1,1,1,1,1,1,1,1] => [5,4,4,1] => [4,4,1] => 34
[4,4,4,2] => [3,3,2,2,2,2] => [3,2,2,2,2] => 112
[4,4,4,1,1] => [4,2,2,2,2,2] => [2,2,2,2,2] => 14
[4,4,3,3] => [8,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[4,4,3,2,1] => [5,2,2,2,2,1] => [2,2,2,2,1] => 14
[4,4,3,1,1,1] => [4,3,2,2,2,1] => [3,2,2,2,1] => 98
[4,4,2,2,2] => [8,2,2,2] => [2,2,2] => 2
[4,4,2,2,1,1] => [7,5,1,1] => [5,1,1] => 6
[4,4,2,1,1,1,1] => [6,3,2,1,1,1] => [3,2,1,1,1] => 20
[4,4,1,1,1,1,1,1] => [8,3,2,1] => [3,2,1] => 6
[4,3,3,3,1] => [7,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[4,3,3,2,2] => [7,2,2,1,1,1] => [2,2,1,1,1] => 4
[4,3,3,2,1,1] => [6,6,2] => [6,2] => 9
[4,3,3,1,1,1,1] => [7,3,2,2] => [3,2,2] => 8
[4,3,2,2,2,1] => [4,3,3,2,2] => [3,3,2,2] => 91
[4,3,2,2,1,1,1] => [5,5,4] => [5,4] => 18
[4,3,2,1,1,1,1,1] => [6,5,2,1] => [5,2,1] => 26
[4,3,1,1,1,1,1,1,1] => [5,5,2,1,1] => [5,2,1,1] => 72
[4,2,2,2,2,2] => [6,2,2,2,1,1] => [2,2,2,1,1] => 9
[4,2,2,2,2,1,1] => [6,4,1,1,1,1] => [4,1,1,1,1] => 11
[4,2,2,2,1,1,1,1] => [4,4,4,1,1] => [4,4,1,1] => 115
[4,2,2,1,1,1,1,1,1] => [4,4,4,2] => [4,4,2] => 100
[4,2,1,1,1,1,1,1,1,1] => [5,5,2,2] => [5,2,2] => 48
[4,1,1,1,1,1,1,1,1,1,1] => [5,5,3,1] => [5,3,1] => 66
[3,3,3,3,2] => [8,6] => [6] => 1
[3,3,3,3,1,1] => [7,3,1,1,1,1] => [3,1,1,1,1] => 4
[3,3,3,2,2,1] => [7,6,1] => [6,1] => 3
[3,3,3,2,1,1,1] => [4,4,2,2,2] => [4,2,2,2] => 110
[3,3,3,1,1,1,1,1] => [6,3,2,2,1] => [3,2,2,1] => 25
[3,3,2,2,2,2] => [3,3,3,3,2] => [3,3,3,2] => 168
[3,3,2,2,2,1,1] => [7,5,2] => [5,2] => 6
[3,3,2,2,1,1,1,1] => [5,3,2,2,2] => [3,2,2,2] => 30
[3,3,2,1,1,1,1,1,1] => [6,3,3,1,1] => [3,3,1,1] => 20
[3,3,1,1,1,1,1,1,1,1] => [6,4,2,1,1] => [4,2,1,1] => 33
[3,2,2,2,2,2,1] => [4,3,3,3,1] => [3,3,3,1] => 77
[3,2,2,2,2,1,1,1] => [6,4,4] => [4,4] => 6
[3,2,2,2,1,1,1,1,1] => [5,3,3,3] => [3,3,3] => 16
[3,2,2,1,1,1,1,1,1,1] => [6,3,3,2] => [3,3,2] => 16
[3,2,1,1,1,1,1,1,1,1,1] => [6,4,2,2] => [4,2,2] => 22
[3,1,1,1,1,1,1,1,1,1,1,1] => [6,4,3,1] => [4,3,1] => 28
[2,2,2,2,2,2,2] => [6,2,2,2,2] => [2,2,2,2] => 5
[2,2,2,2,2,2,1,1] => [6,5,1,1,1] => [5,1,1,1] => 13
[2,2,2,2,2,1,1,1,1] => [6,5,3] => [5,3] => 12
[2,2,2,2,1,1,1,1,1,1] => [4,4,3,2,1] => [4,3,2,1] => 288
[2,2,2,1,1,1,1,1,1,1,1] => [5,3,3,2,1] => [3,3,2,1] => 61
[2,2,1,1,1,1,1,1,1,1,1,1] => [5,4,2,2,1] => [4,2,2,1] => 80
[2,1,1,1,1,1,1,1,1,1,1,1,1] => [5,4,3,1,1] => [4,3,1,1] => 81
[1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [5,4,3,2] => [4,3,2] => 66
[13,1,1] => [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] => 0
[12,2,1] => [4,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => 0
[12,1,1,1] => [3,2,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => 1
[11,3,1] => [3,2,2,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 9
[11,2,2] => [5,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 0
[11,2,1,1] => [3,3,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1] => 9
[11,1,1,1,1] => [4,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => 1
[10,4,1] => [3,2,2,2,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => 35
[10,3,2] => [6,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 0
[10,3,1,1] => [5,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 1
[10,2,2,1] => [3,3,2,1,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1] => 72
[10,2,1,1,1] => [4,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => 8
[10,1,1,1,1,1] => [4,3,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => 8
[9,5,1] => [3,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => 75
[9,4,2] => [3,3,2,2,1,1,1,1,1] => [3,2,2,1,1,1,1,1] => 243
[9,4,1,1] => [4,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => 27
[9,3,3] => [7,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[9,3,2,1] => [6,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 1
[9,3,1,1,1] => [4,4,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1] => 29
[9,2,2,2] => [3,3,3,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1] => 168
[9,2,2,1,1] => [5,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 7
[9,2,1,1,1,1] => [5,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 7
[9,1,1,1,1,1,1] => [4,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => 56
[8,6,1] => [3,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => 90
[8,5,2] => [3,3,2,2,2,1,1,1] => [3,2,2,2,1,1,1] => 432
[8,5,1,1] => [4,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => 48
[8,4,3] => [9,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[8,4,2,1] => [6,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 6
[8,4,1,1,1] => [4,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => 160
[8,3,3,1] => [7,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[8,3,2,2] => [3,3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => 595
[8,3,2,1,1] => [6,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 6
[8,3,1,1,1,1] => [4,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => 112
[8,2,2,2,1] => [5,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 20
[8,2,2,1,1,1] => [5,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => 22
[8,2,1,1,1,1,1] => [4,4,2,1,1,1,1,1] => [4,2,1,1,1,1,1] => 174
[8,1,1,1,1,1,1,1] => [5,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => 42
[7,6,2] => [13,1,1] => [1,1] => 0
[7,6,1,1] => [13,2] => [2] => 1
[7,5,3] => [3,3,3,2,2,1,1] => [3,3,2,2,1,1] => 891
[7,5,2,1] => [5,2,2,2,2,1,1] => [2,2,2,2,1,1] => 28
[7,5,1,1,1] => [4,3,2,2,2,1,1] => [3,2,2,2,1,1] => 224
[7,4,4] => [10,1,1,1,1,1] => [1,1,1,1,1] => 0
[7,4,3,1] => [9,2,1,1,1,1] => [2,1,1,1,1] => 1
[7,4,2,2] => [8,2,2,1,1,1] => [2,2,1,1,1] => 4
[7,4,2,1,1] => [5,5,1,1,1,1,1] => [5,1,1,1,1,1] => 40
[7,4,1,1,1,1] => [6,3,2,1,1,1,1] => [3,2,1,1,1,1] => 30
[7,3,3,2] => [3,3,3,3,1,1,1] => [3,3,3,1,1,1] => 555
[7,3,3,1,1] => [8,3,1,1,1,1] => [3,1,1,1,1] => 4
[7,3,2,2,1] => [4,3,3,2,1,1,1] => [3,3,2,1,1,1] => 323
[7,3,2,1,1,1] => [4,4,2,2,1,1,1] => [4,2,2,1,1,1] => 406
[7,3,1,1,1,1,1] => [5,3,2,2,1,1,1] => [3,2,2,1,1,1] => 98
[7,2,2,2,2] => [6,2,2,2,1,1,1] => [2,2,2,1,1,1] => 14
[7,2,2,2,1,1] => [6,4,1,1,1,1,1] => [4,1,1,1,1,1] => 16
[7,2,2,1,1,1,1] => [4,4,3,1,1,1,1] => [4,3,1,1,1,1] => 365
[7,2,1,1,1,1,1,1] => [5,3,3,1,1,1,1] => [3,3,1,1,1,1] => 70
[7,1,1,1,1,1,1,1,1] => [5,4,2,1,1,1,1] => [4,2,1,1,1,1] => 110
[6,6,3] => [12,1,1,1] => [1,1,1] => 0
[6,6,2,1] => [12,3] => [3] => 0
[6,6,1,1,1] => [12,2,1] => [2,1] => 1
[6,5,4] => [11,1,1,1,1] => [1,1,1,1] => 0
[6,5,3,1] => [11,2,1,1] => [2,1,1] => 1
[6,5,2,2] => [11,4] => [4] => 1
[6,5,2,1,1] => [11,2,2] => [2,2] => 1
[6,5,1,1,1,1] => [11,3,1] => [3,1] => 1
[6,4,4,1] => [10,2,1,1,1] => [2,1,1,1] => 1
[6,4,3,2] => [9,2,2,1,1] => [2,2,1,1] => 3
[6,4,3,1,1] => [9,3,1,1,1] => [3,1,1,1] => 3
[6,4,2,2,1] => [8,5,1,1] => [5,1,1] => 6
[6,4,2,1,1,1] => [8,3,2,1,1] => [3,2,1,1] => 12
[6,4,1,1,1,1,1] => [6,6,2,1] => [6,2,1] => 44
[6,3,3,3] => [9,6] => [6] => 1
[6,3,3,2,1] => [7,7,1] => [7,1] => 3
[6,3,3,1,1,1] => [7,3,2,2,1] => [3,2,2,1] => 25
[6,3,2,2,2] => [8,2,2,2,1] => [2,2,2,1] => 5
[6,3,2,2,1,1] => [5,5,5] => [5,5] => 18
[6,3,2,1,1,1,1] => [7,3,3,1,1] => [3,3,1,1] => 20
[6,3,1,1,1,1,1,1] => [7,4,2,1,1] => [4,2,1,1] => 33
[6,2,2,2,2,1] => [6,6,1,1,1] => [6,1,1,1] => 22
[6,2,2,2,1,1,1] => [4,4,3,2,1,1] => [4,3,2,1,1] => 826
[6,2,2,1,1,1,1,1] => [5,3,3,2,1,1] => [3,3,2,1,1] => 155
[6,2,1,1,1,1,1,1,1] => [5,4,2,2,1,1] => [4,2,2,1,1] => 198
[6,1,1,1,1,1,1,1,1,1] => [5,4,3,1,1,1] => [4,3,1,1,1] => 185
[5,5,4,1] => [3,2,2,2,2,2,2] => [2,2,2,2,2,2] => 42
[5,5,3,2] => [10,5] => [5] => 0
[5,5,3,1,1] => [10,4,1] => [4,1] => 2
[5,5,2,2,1] => [10,2,2,1] => [2,2,1] => 2
[5,5,2,1,1,1] => [10,3,1,1] => [3,1,1] => 2
[5,5,1,1,1,1,1] => [10,3,2] => [3,2] => 2
[5,4,4,2] => [3,3,2,2,2,2,1] => [3,2,2,2,2,1] => 378
[5,4,4,1,1] => [4,2,2,2,2,2,1] => [2,2,2,2,2,1] => 42
[5,4,3,3] => [3,3,3,2,2,2] => [3,3,2,2,2] => 456
[5,4,3,2,1] => [9,5,1] => [5,1] => 2
[5,4,3,1,1,1] => [9,3,3] => [3,3] => 2
[5,4,2,2,2] => [9,2,2,2] => [2,2,2] => 2
[5,4,2,2,1,1] => [9,4,1,1] => [4,1,1] => 4
[5,4,2,1,1,1,1] => [9,4,2] => [4,2] => 4
[5,4,1,1,1,1,1,1] => [9,3,2,1] => [3,2,1] => 6
[5,3,3,3,1] => [4,3,3,2,2,1] => [3,3,2,2,1] => 344
[5,3,3,2,2] => [3,3,3,3,3] => [3,3,3,3] => 168
[5,3,3,2,1,1] => [8,5,2] => [5,2] => 6
[5,3,3,1,1,1,1] => [6,3,2,2,1,1] => [3,2,2,1,1] => 54
[5,3,2,2,2,1] => [4,3,3,3,1,1] => [3,3,3,1,1] => 232
[5,3,2,2,1,1,1] => [8,4,3] => [4,3] => 6
[5,3,2,1,1,1,1,1] => [8,3,3,1] => [3,3,1] => 8
[5,3,1,1,1,1,1,1,1] => [8,4,2,1] => [4,2,1] => 14
[5,2,2,2,2,2] => [7,2,2,2,2] => [2,2,2,2] => 5
[5,2,2,2,2,1,1] => [6,6,3] => [6,3] => 21
[5,2,2,2,1,1,1,1] => [4,4,3,2,2] => [4,3,2,2] => 489
[5,2,2,1,1,1,1,1,1] => [5,3,3,2,2] => [3,3,2,2] => 91
[5,2,1,1,1,1,1,1,1,1] => [7,4,3,1] => [4,3,1] => 28
[5,1,1,1,1,1,1,1,1,1,1] => [5,4,3,3] => [4,3,3] => 82
[4,4,4,3] => [8,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[4,4,4,2,1] => [5,2,2,2,2,2] => [2,2,2,2,2] => 14
[4,4,4,1,1,1] => [4,3,2,2,2,2] => [3,2,2,2,2] => 112
[4,4,3,3,1] => [8,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[4,4,3,2,2] => [7,2,2,2,1,1] => [2,2,2,1,1] => 9
[4,4,3,2,1,1] => [4,4,2,2,2,1] => [4,2,2,2,1] => 406
[4,4,3,1,1,1,1] => [5,3,2,2,2,1] => [3,2,2,2,1] => 98
[4,4,2,2,2,1] => [8,4,1,1,1] => [4,1,1,1] => 7
[4,4,2,2,1,1,1] => [4,4,4,1,1,1] => [4,4,1,1,1] => 300
[4,4,2,1,1,1,1,1] => [7,5,2,1] => [5,2,1] => 26
[4,4,1,1,1,1,1,1,1] => [5,5,4,1] => [5,4,1] => 118
[4,3,3,3,2] => [7,2,2,1,1,1,1] => [2,2,1,1,1,1] => 5
[4,3,3,3,1,1] => [7,3,1,1,1,1,1] => [3,1,1,1,1,1] => 5
[4,3,3,2,2,1] => [7,4,1,1,1,1] => [4,1,1,1,1] => 11
[4,3,3,2,1,1,1] => [8,3,2,2] => [3,2,2] => 8
[4,3,3,1,1,1,1,1] => [5,5,2,1,1,1] => [5,2,1,1,1] => 160
[4,3,2,2,2,2] => [7,6,1,1] => [6,1,1] => 9
[4,3,2,2,2,1,1] => [7,4,4] => [4,4] => 6
[4,3,2,2,1,1,1,1] => [4,4,4,3] => [4,4,3] => 182
[4,3,2,1,1,1,1,1,1] => [7,4,2,2] => [4,2,2] => 22
[4,3,1,1,1,1,1,1,1,1] => [6,4,4,1] => [4,4,1] => 34
[4,2,2,2,2,2,1] => [7,5,1,1,1] => [5,1,1,1] => 13
[4,2,2,2,2,1,1,1] => [7,5,3] => [5,3] => 12
[4,2,2,2,1,1,1,1,1] => [6,4,2,1,1,1] => [4,2,1,1,1] => 64
[4,2,2,1,1,1,1,1,1,1] => [5,4,2,2,2] => [4,2,2,2] => 110
[4,2,1,1,1,1,1,1,1,1,1] => [5,4,4,1,1] => [4,4,1,1] => 115
[4,1,1,1,1,1,1,1,1,1,1,1] => [5,4,4,2] => [4,4,2] => 100
[3,3,3,3,3] => [8,7] => [7] => 0
[3,3,3,3,2,1] => [8,6,1] => [6,1] => 3
[3,3,3,3,1,1,1] => [7,3,2,1,1,1] => [3,2,1,1,1] => 20
[3,3,3,2,2,2] => [3,3,3,3,2,1] => [3,3,3,2,1] => 744
[3,3,3,2,2,1,1] => [7,6,2] => [6,2] => 9
[3,3,3,2,1,1,1,1] => [7,3,3,2] => [3,3,2] => 16
[3,3,3,1,1,1,1,1,1] => [6,5,2,1,1] => [5,2,1,1] => 72
[3,3,2,2,2,2,1] => [4,3,3,3,2] => [3,3,3,2] => 168
[3,3,2,2,2,1,1,1] => [6,3,3,1,1,1] => [3,3,1,1,1] => 40
[3,3,2,2,1,1,1,1,1] => [6,3,3,3] => [3,3,3] => 16
[3,3,2,1,1,1,1,1,1,1] => [6,5,2,2] => [5,2,2] => 48
[3,3,1,1,1,1,1,1,1,1,1] => [6,5,3,1] => [5,3,1] => 66
[3,2,2,2,2,2,2] => [6,2,2,2,2,1] => [2,2,2,2,1] => 14
[3,2,2,2,2,2,1,1] => [6,3,2,2,2] => [3,2,2,2] => 30
[3,2,2,2,2,1,1,1,1] => [4,4,3,3,1] => [4,3,3,1] => 447
[3,2,2,2,1,1,1,1,1,1] => [4,4,4,2,1] => [4,4,2,1] => 503
[3,2,2,1,1,1,1,1,1,1,1] => [5,5,2,2,1] => [5,2,2,1] => 200
[3,2,1,1,1,1,1,1,1,1,1,1] => [5,5,3,1,1] => [5,3,1,1] => 219
[3,1,1,1,1,1,1,1,1,1,1,1,1] => [5,5,3,2] => [5,3,2] => 180
[2,2,2,2,2,2,2,1] => [6,5,1,1,1,1] => [5,1,1,1,1] => 24
[2,2,2,2,2,2,1,1,1] => [6,5,4] => [5,4] => 18
[2,2,2,2,2,1,1,1,1,1] => [5,3,3,3,1] => [3,3,3,1] => 77
[2,2,2,2,1,1,1,1,1,1,1] => [6,3,3,2,1] => [3,3,2,1] => 61
[2,2,2,1,1,1,1,1,1,1,1,1] => [6,4,2,2,1] => [4,2,2,1] => 80
[2,2,1,1,1,1,1,1,1,1,1,1,1] => [6,4,3,1,1] => [4,3,1,1] => 81
[2,1,1,1,1,1,1,1,1,1,1,1,1,1] => [6,4,3,2] => [4,3,2] => 66
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [5,4,3,2,1] => [4,3,2,1] => 288
[13,2,1] => [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] => 0
[12,2,2] => [5,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => 0
[12,1,1,1,1] => [4,2,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => 1
[11,3,2] => [6,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 0
[11,3,1,1] => [5,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => 1
[11,2,1,1,1] => [4,2,2,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 9
[11,1,1,1,1,1] => [4,3,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1] => 9
[10,4,1,1] => [4,2,2,2,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => 35
[10,3,3] => [7,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 0
[10,3,2,1] => [6,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 1
[10,3,1,1,1] => [4,4,1,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1,1] => 37
[10,2,2,1,1] => [5,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => 8
[10,2,1,1,1,1] => [5,3,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => 8
[10,1,1,1,1,1,1] => [4,3,2,1,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1] => 72
[9,5,1,1] => [4,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => 75
[9,4,3] => [8,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[9,4,2,1] => [6,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 7
[9,4,1,1,1] => [4,3,2,2,1,1,1,1,1] => [3,2,2,1,1,1,1,1] => 243
[9,3,3,1] => [7,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 1
[9,3,2,1,1] => [6,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 7
[9,3,1,1,1,1] => [4,3,3,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1] => 168
[9,2,2,2,1] => [5,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => 27
[9,2,2,1,1,1] => [5,4,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1] => 29
[9,2,1,1,1,1,1] => [4,4,2,1,1,1,1,1,1] => [4,2,1,1,1,1,1,1] => 259
[9,1,1,1,1,1,1,1] => [5,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => 56
[8,6,1,1] => [4,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => 90
[8,5,2,1] => [5,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => 48
[8,5,1,1,1] => [4,3,2,2,2,1,1,1] => [3,2,2,2,1,1,1] => 432
[8,4,4] => [10,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[8,4,3,1] => [9,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[8,4,2,2] => [7,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 6
[8,4,2,1,1] => [5,5,1,1,1,1,1,1] => [5,1,1,1,1,1,1] => 62
[8,4,1,1,1,1] => [6,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => 42
[8,3,3,1,1] => [7,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 6
[8,3,2,2,1] => [4,3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => 595
[8,3,2,1,1,1] => [4,4,2,2,1,1,1,1] => [4,2,2,1,1,1,1] => 740
[8,3,1,1,1,1,1] => [5,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => 160
[8,2,2,2,2] => [6,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 20
[8,2,2,2,1,1] => [6,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => 22
[8,2,2,1,1,1,1] => [4,4,3,1,1,1,1,1] => [4,3,1,1,1,1,1] => 651
[8,2,1,1,1,1,1,1] => [5,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => 112
[8,1,1,1,1,1,1,1,1] => [5,4,2,1,1,1,1,1] => [4,2,1,1,1,1,1] => 174
[7,7,2] => [14,1,1] => [1,1] => 0
[7,7,1,1] => [14,2] => [2] => 1
[7,6,3] => [13,1,1,1] => [1,1,1] => 0
[7,6,2,1] => [13,3] => [3] => 0
[7,6,1,1,1] => [13,2,1] => [2,1] => 1
[7,5,4] => [11,1,1,1,1,1] => [1,1,1,1,1] => 0
[7,5,3,1] => [4,3,3,2,2,1,1] => [3,3,2,2,1,1] => 891
[7,5,2,2] => [8,2,2,2,1,1] => [2,2,2,1,1] => 9
[7,5,2,1,1] => [4,4,2,2,2,1,1] => [4,2,2,2,1,1] => 1036
[7,5,1,1,1,1] => [5,3,2,2,2,1,1] => [3,2,2,2,1,1] => 224
[7,4,4,1] => [10,2,1,1,1,1] => [2,1,1,1,1] => 1
[7,4,3,2] => [9,2,2,1,1,1] => [2,2,1,1,1] => 4
[7,4,3,1,1] => [9,3,1,1,1,1] => [3,1,1,1,1] => 4
[7,4,2,2,1] => [8,4,1,1,1,1] => [4,1,1,1,1] => 11
[7,4,2,1,1,1] => [8,3,2,1,1,1] => [3,2,1,1,1] => 20
[7,4,1,1,1,1,1] => [5,5,2,1,1,1,1] => [5,2,1,1,1,1] => 310
[7,3,3,2,1] => [4,3,3,3,1,1,1] => [3,3,3,1,1,1] => 555
[7,3,3,1,1,1] => [6,3,2,2,1,1,1] => [3,2,2,1,1,1] => 98
[7,3,2,2,2] => [6,2,2,2,2,1,1] => [2,2,2,2,1,1] => 28
[7,3,2,2,1,1] => [4,4,4,1,1,1,1] => [4,4,1,1,1,1] => 665
[7,3,2,1,1,1,1] => [6,3,3,1,1,1,1] => [3,3,1,1,1,1] => 70
[7,3,1,1,1,1,1,1] => [6,4,2,1,1,1,1] => [4,2,1,1,1,1] => 110
[7,2,2,2,2,1] => [6,5,1,1,1,1,1] => [5,1,1,1,1,1] => 40
[7,2,2,2,1,1,1] => [4,4,3,2,1,1,1] => [4,3,2,1,1,1] => 1920
[7,2,2,1,1,1,1,1] => [5,3,3,2,1,1,1] => [3,3,2,1,1,1] => 323
[7,2,1,1,1,1,1,1,1] => [5,4,2,2,1,1,1] => [4,2,2,1,1,1] => 406
[7,1,1,1,1,1,1,1,1,1] => [5,4,3,1,1,1,1] => [4,3,1,1,1,1] => 365
[6,6,4] => [12,1,1,1,1] => [1,1,1,1] => 0
[6,6,3,1] => [12,2,1,1] => [2,1,1] => 1
[6,6,2,2] => [12,4] => [4] => 1
[6,6,2,1,1] => [12,2,2] => [2,2] => 1
[6,6,1,1,1,1] => [12,3,1] => [3,1] => 1
[6,5,4,1] => [11,2,1,1,1] => [2,1,1,1] => 1
[6,5,3,2] => [11,5] => [5] => 0
[6,5,3,1,1] => [11,4,1] => [4,1] => 2
[6,5,2,2,1] => [11,2,2,1] => [2,2,1] => 2
[6,5,2,1,1,1] => [11,3,1,1] => [3,1,1] => 2
[6,5,1,1,1,1,1] => [11,3,2] => [3,2] => 2
[6,4,4,2] => [10,2,2,1,1] => [2,2,1,1] => 3
[6,4,4,1,1] => [10,3,1,1,1] => [3,1,1,1] => 3
[6,4,3,3] => [8,8] => [8] => 1
[6,4,3,2,1] => [9,5,1,1] => [5,1,1] => 6
[6,4,3,1,1,1] => [9,3,2,1,1] => [3,2,1,1] => 12
[6,4,2,2,2] => [7,7,1,1] => [7,1,1] => 12
[6,4,2,2,1,1] => [8,4,4] => [4,4] => 6
[6,4,2,1,1,1,1] => [8,5,2,1] => [5,2,1] => 26
[6,4,1,1,1,1,1,1] => [5,5,5,1] => [5,5,1] => 136
[6,3,3,3,1] => [9,6,1] => [6,1] => 3
[6,3,3,2,2] => [9,2,2,2,1] => [2,2,2,1] => 5
[6,3,3,2,1,1] => [7,7,2] => [7,2] => 12
[6,3,3,1,1,1,1] => [6,6,2,1,1] => [6,2,1,1] => 138
[6,3,2,2,2,1] => [8,3,2,2,1] => [3,2,2,1] => 25
[6,3,2,2,1,1,1] => [8,3,3,1,1] => [3,3,1,1] => 20
[6,3,2,1,1,1,1,1] => [6,6,2,2] => [6,2,2] => 92
[6,3,1,1,1,1,1,1,1] => [6,6,3,1] => [6,3,1] => 131
[6,2,2,2,2,2] => [8,5,1,1,1] => [5,1,1,1] => 13
[6,2,2,2,2,1,1] => [6,5,5] => [5,5] => 18
[6,2,2,2,1,1,1,1] => [7,3,3,2,1] => [3,3,2,1] => 61
[6,2,2,1,1,1,1,1,1] => [7,4,2,2,1] => [4,2,2,1] => 80
[6,2,1,1,1,1,1,1,1,1] => [7,4,3,1,1] => [4,3,1,1] => 81
[6,1,1,1,1,1,1,1,1,1,1] => [5,4,3,2,1,1] => [4,3,2,1,1] => 826
[5,5,4,1,1] => [4,2,2,2,2,2,2] => [2,2,2,2,2,2] => 42
[5,5,3,3] => [10,6] => [6] => 1
[5,5,3,2,1] => [10,5,1] => [5,1] => 2
[5,5,3,1,1,1] => [10,3,3] => [3,3] => 2
[5,5,2,2,2] => [10,2,2,2] => [2,2,2] => 2
[5,5,2,2,1,1] => [10,4,1,1] => [4,1,1] => 4
[5,5,2,1,1,1,1] => [10,4,2] => [4,2] => 4
[5,5,1,1,1,1,1,1] => [10,3,2,1] => [3,2,1] => 6
[5,4,4,2,1] => [5,2,2,2,2,2,1] => [2,2,2,2,2,1] => 42
[5,4,4,1,1,1] => [4,3,2,2,2,2,1] => [3,2,2,2,2,1] => 378
[5,4,3,3,1] => [4,3,3,2,2,2] => [3,3,2,2,2] => 456
[5,4,3,2,2] => [7,2,2,2,1,1,1] => [2,2,2,1,1,1] => 14
[5,4,3,2,1,1] => [9,5,2] => [5,2] => 6
[5,4,3,1,1,1,1] => [9,3,2,2] => [3,2,2] => 8
[5,4,2,2,2,1] => [9,4,1,1,1] => [4,1,1,1] => 7
[5,4,2,2,1,1,1] => [9,4,3] => [4,3] => 6
[5,4,2,1,1,1,1,1] => [9,3,3,1] => [3,3,1] => 8
[5,4,1,1,1,1,1,1,1] => [9,4,2,1] => [4,2,1] => 14
[5,3,3,3,1,1] => [7,3,2,2,1,1] => [3,2,2,1,1] => 54
[5,3,3,2,2,1] => [4,3,3,3,3] => [3,3,3,3] => 168
[5,3,3,2,1,1,1] => [7,3,3,1,1,1] => [3,3,1,1,1] => 40
[5,3,3,1,1,1,1,1] => [7,5,2,1,1] => [5,2,1,1] => 72
[5,3,2,2,2,2] => [6,2,2,2,2,2] => [2,2,2,2,2] => 14
[5,3,2,2,2,1,1] => [7,3,2,2,2] => [3,2,2,2] => 30
[5,3,2,2,1,1,1,1] => [4,4,4,2,1,1] => [4,4,2,1,1] => 1629
[5,3,2,1,1,1,1,1,1] => [5,5,2,2,1,1] => [5,2,2,1,1] => 558
[5,3,1,1,1,1,1,1,1,1] => [8,4,3,1] => [4,3,1] => 28
[5,2,2,2,2,2,1] => [4,4,3,3,1,1] => [4,3,3,1,1] => 1505
[5,2,2,2,2,1,1,1] => [8,3,3,2] => [3,3,2] => 16
[5,2,2,2,1,1,1,1,1] => [6,3,3,2,1,1] => [3,3,2,1,1] => 155
[5,2,2,1,1,1,1,1,1,1] => [5,5,3,1,1,1] => [5,3,1,1,1] => 564
[5,2,1,1,1,1,1,1,1,1,1] => [7,4,3,2] => [4,3,2] => 66
[5,1,1,1,1,1,1,1,1,1,1,1] => [5,4,3,2,2] => [4,3,2,2] => 489
[4,4,4,4] => [9,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[4,4,4,3,1] => [8,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[4,4,4,2,2] => [8,2,2,2,2] => [2,2,2,2] => 5
[4,4,4,2,1,1] => [4,4,2,2,2,2] => [4,2,2,2,2] => 518
[4,4,4,1,1,1,1] => [5,3,2,2,2,2] => [3,2,2,2,2] => 112
[4,4,3,3,2] => [8,2,2,1,1,1,1] => [2,2,1,1,1,1] => 5
[4,4,3,3,1,1] => [8,3,1,1,1,1,1] => [3,1,1,1,1,1] => 5
[4,4,3,2,2,1] => [4,4,3,2,2,1] => [4,3,2,2,1] => 2065
[4,4,3,2,1,1,1] => [5,3,3,2,2,1] => [3,3,2,2,1] => 344
[4,4,3,1,1,1,1,1] => [5,4,2,2,2,1] => [4,2,2,2,1] => 406
[4,4,2,2,2,2] => [7,6,1,1,1] => [6,1,1,1] => 22
[4,4,2,2,2,1,1] => [7,6,3] => [6,3] => 21
[4,4,2,2,1,1,1,1] => [8,4,2,1,1] => [4,2,1,1] => 33
[4,4,2,1,1,1,1,1,1] => [5,4,4,1,1,1] => [4,4,1,1,1] => 300
[4,4,1,1,1,1,1,1,1,1] => [5,4,4,3] => [4,4,3] => 182
[4,3,3,3,3] => [9,7] => [7] => 0
[4,3,3,3,2,1] => [7,4,1,1,1,1,1] => [4,1,1,1,1,1] => 16
[4,3,3,3,1,1,1] => [7,3,2,1,1,1,1] => [3,2,1,1,1,1] => 30
[4,3,3,2,2,2] => [8,6,1,1] => [6,1,1] => 9
[4,3,3,2,2,1,1] => [8,5,3] => [5,3] => 12
[4,3,3,2,1,1,1,1] => [5,3,3,3,1,1] => [3,3,3,1,1] => 232
[4,3,3,1,1,1,1,1,1] => [8,4,2,2] => [4,2,2] => 22
[4,3,2,2,2,2,1] => [4,4,4,4] => [4,4,4] => 182
[4,3,2,2,2,1,1,1] => [4,4,3,3,2] => [4,3,3,2] => 1104
[4,3,2,2,1,1,1,1,1] => [7,4,4,1] => [4,4,1] => 34
[4,3,2,1,1,1,1,1,1,1] => [7,5,3,1] => [5,3,1] => 66
[4,3,1,1,1,1,1,1,1,1,1] => [5,5,3,3] => [5,3,3] => 262
[4,2,2,2,2,2,2] => [6,6,1,1,1,1] => [6,1,1,1,1] => 46
[4,2,2,2,2,2,1,1] => [6,6,4] => [6,4] => 39
[4,2,2,2,2,1,1,1,1] => [5,3,3,3,2] => [3,3,3,2] => 168
[4,2,2,2,1,1,1,1,1,1] => [6,4,2,2,1,1] => [4,2,2,1,1] => 198
[4,2,2,1,1,1,1,1,1,1,1] => [6,4,3,1,1,1] => [4,3,1,1,1] => 185
[4,2,1,1,1,1,1,1,1,1,1,1] => [6,4,3,3] => [4,3,3] => 82
[4,1,1,1,1,1,1,1,1,1,1,1,1] => [5,4,3,3,1] => [4,3,3,1] => 447
[3,3,3,3,3,1] => [8,7,1] => [7,1] => 3
[3,3,3,3,2,1,1] => [8,6,2] => [6,2] => 9
[3,3,3,3,1,1,1,1] => [7,4,2,1,1,1] => [4,2,1,1,1] => 64
[3,3,3,2,2,2,1] => [4,3,3,3,2,1] => [3,3,3,2,1] => 744
[3,3,3,2,2,1,1,1] => [7,6,2,1] => [6,2,1] => 44
[3,3,3,2,1,1,1,1,1] => [7,5,2,2] => [5,2,2] => 48
[3,3,3,1,1,1,1,1,1,1] => [6,5,4,1] => [5,4,1] => 118
[3,3,2,2,2,2,2] => [7,2,2,2,2,1] => [2,2,2,2,1] => 14
[3,3,2,2,2,2,1,1] => [7,3,3,3] => [3,3,3] => 16
[3,3,2,2,2,1,1,1,1] => [4,4,4,2,2] => [4,4,2,2] => 992
[3,3,2,2,1,1,1,1,1,1] => [5,5,2,2,2] => [5,2,2,2] => 310
[3,3,2,1,1,1,1,1,1,1,1] => [5,5,4,1,1] => [5,4,1,1] => 452
[3,3,1,1,1,1,1,1,1,1,1,1] => [5,5,4,2] => [5,4,2] => 398
[3,2,2,2,2,2,2,1] => [6,3,2,2,2,1] => [3,2,2,2,1] => 98
[3,2,2,2,2,2,1,1,1] => [6,5,2,1,1,1] => [5,2,1,1,1] => 160
[3,2,2,2,2,1,1,1,1,1] => [6,3,3,2,2] => [3,3,2,2] => 91
[3,2,2,2,1,1,1,1,1,1,1] => [6,4,2,2,2] => [4,2,2,2] => 110
[3,2,2,1,1,1,1,1,1,1,1,1] => [6,4,4,1,1] => [4,4,1,1] => 115
[3,2,1,1,1,1,1,1,1,1,1,1,1] => [6,4,4,2] => [4,4,2] => 100
[3,1,1,1,1,1,1,1,1,1,1,1,1,1] => [5,4,4,2,1] => [4,4,2,1] => 503
[2,2,2,2,2,2,2,2] => [7,5,1,1,1,1] => [5,1,1,1,1] => 24
[2,2,2,2,2,2,2,1,1] => [7,5,4] => [5,4] => 18
[2,2,2,2,2,2,1,1,1,1] => [4,4,4,3,1] => [4,4,3,1] => 1132
[2,2,2,2,2,1,1,1,1,1,1] => [6,3,3,3,1] => [3,3,3,1] => 77
[2,2,2,2,1,1,1,1,1,1,1,1] => [6,5,2,2,1] => [5,2,2,1] => 200
[2,2,2,1,1,1,1,1,1,1,1,1,1] => [6,5,3,1,1] => [5,3,1,1] => 219
[2,2,1,1,1,1,1,1,1,1,1,1,1,1] => [6,5,3,2] => [5,3,2] => 180
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [5,5,3,2,1] => [5,3,2,1] => 887
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [6,4,3,2,1] => [4,3,2,1] => 288
[13,2,2] => [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] => 0
[12,3,2] => [6,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => 0
[12,3,1,1] => [5,2,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => 1
[11,3,3] => [7,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 0
[11,3,2,1] => [6,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => 1
[11,2,2,1,1] => [5,2,2,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 9
[11,2,1,1,1,1] => [5,3,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1] => 9
[10,4,3] => [8,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 0
[10,4,2,1] => [6,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => 8
[10,3,3,1] => [7,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 1
[10,3,2,1,1] => [6,3,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => 8
[10,2,2,2,1] => [5,2,2,2,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => 35
[10,2,2,1,1,1] => [5,4,1,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1,1] => 37
[10,1,1,1,1,1,1,1] => [5,3,2,1,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1] => 72
[9,5,2,1] => [5,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => 75
[9,4,4] => [10,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[9,4,3,1] => [8,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 1
[9,4,2,2] => [7,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 7
[9,4,2,1,1] => [5,5,1,1,1,1,1,1,1] => [5,1,1,1,1,1,1,1] => 91
[9,4,1,1,1,1] => [6,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => 56
[9,3,3,1,1] => [7,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 7
[9,3,1,1,1,1,1] => [5,3,2,2,1,1,1,1,1] => [3,2,2,1,1,1,1,1] => 243
[9,2,2,2,2] => [6,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => 27
[9,2,2,2,1,1] => [6,4,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1] => 29
[9,2,1,1,1,1,1,1] => [5,3,3,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1] => 168
[9,1,1,1,1,1,1,1,1] => [5,4,2,1,1,1,1,1,1] => [4,2,1,1,1,1,1,1] => 259
[8,7,2] => [15,1,1] => [1,1] => 0
[8,7,1,1] => [15,2] => [2] => 1
[8,6,2,1] => [5,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => 90
[8,5,4] => [11,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[8,5,2,2] => [7,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 20
[8,5,1,1,1,1] => [5,3,2,2,2,1,1,1] => [3,2,2,2,1,1,1] => 432
[8,4,4,1] => [10,2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[8,4,3,2] => [9,2,2,1,1,1,1] => [2,2,1,1,1,1] => 5
[8,4,3,1,1] => [9,3,1,1,1,1,1] => [3,1,1,1,1,1] => 5
[8,4,2,2,1] => [7,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => 22
[8,4,2,1,1,1] => [7,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => 42
[8,4,1,1,1,1,1] => [5,5,2,1,1,1,1,1] => [5,2,1,1,1,1,1] => 546
[8,3,3,1,1,1] => [6,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => 160
[8,3,2,2,2] => [6,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => 48
[8,3,2,1,1,1,1] => [6,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => 112
[8,3,1,1,1,1,1,1] => [6,4,2,1,1,1,1,1] => [4,2,1,1,1,1,1] => 174
[8,2,2,2,2,1] => [6,5,1,1,1,1,1,1] => [5,1,1,1,1,1,1] => 62
[8,2,2,1,1,1,1,1] => [5,3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => 595
[8,2,1,1,1,1,1,1,1] => [5,4,2,2,1,1,1,1] => [4,2,2,1,1,1,1] => 740
[8,1,1,1,1,1,1,1,1,1] => [5,4,3,1,1,1,1,1] => [4,3,1,1,1,1,1] => 651
[7,7,3] => [14,1,1,1] => [1,1,1] => 0
[7,7,2,1] => [14,3] => [3] => 0
[7,7,1,1,1] => [14,2,1] => [2,1] => 1
[7,6,4] => [13,1,1,1,1] => [1,1,1,1] => 0
[7,6,3,1] => [13,2,1,1] => [2,1,1] => 1
[7,6,2,2] => [13,4] => [4] => 1
[7,6,2,1,1] => [13,2,2] => [2,2] => 1
[7,6,1,1,1,1] => [13,3,1] => [3,1] => 1
[7,5,5] => [12,1,1,1,1,1] => [1,1,1,1,1] => 0
[7,5,4,1] => [11,2,1,1,1,1] => [2,1,1,1,1] => 1
[7,5,3,2] => [9,2,2,2,1,1] => [2,2,2,1,1] => 9
[7,5,3,1,1] => [8,3,2,2,1,1] => [3,2,2,1,1] => 54
[7,5,2,1,1,1] => [5,3,3,2,2,1,1] => [3,3,2,2,1,1] => 891
[7,5,1,1,1,1,1] => [5,4,2,2,2,1,1] => [4,2,2,2,1,1] => 1036
[7,4,4,2] => [10,2,2,1,1,1] => [2,2,1,1,1] => 4
[7,4,4,1,1] => [10,3,1,1,1,1] => [3,1,1,1,1] => 4
[7,4,3,3] => [10,7] => [7] => 0
[7,4,3,2,1] => [9,4,1,1,1,1] => [4,1,1,1,1] => 11
[7,4,3,1,1,1] => [9,3,2,1,1,1] => [3,2,1,1,1] => 20
[7,4,2,2,2] => [7,7,1,1,1] => [7,1,1,1] => 34
[7,4,2,1,1,1,1] => [8,4,2,1,1,1] => [4,2,1,1,1] => 64
[7,4,1,1,1,1,1,1] => [5,4,4,1,1,1,1] => [4,4,1,1,1,1] => 665
[7,3,3,2,2] => [8,2,2,2,2,1] => [2,2,2,2,1] => 14
[7,3,3,2,1,1] => [8,3,3,1,1,1] => [3,3,1,1,1] => 40
[7,3,3,1,1,1,1] => [6,5,2,1,1,1,1] => [5,2,1,1,1,1] => 310
[7,3,2,2,2,1] => [6,3,2,2,2,1,1] => [3,2,2,2,1,1] => 224
[7,3,2,2,1,1,1] => [5,3,3,3,1,1,1] => [3,3,3,1,1,1] => 555
[7,3,2,1,1,1,1,1] => [5,5,2,2,1,1,1] => [5,2,2,1,1,1] => 1274
[7,3,1,1,1,1,1,1,1] => [5,5,3,1,1,1,1] => [5,3,1,1,1,1] => 1239
[7,2,2,2,2,2] => [8,5,1,1,1,1] => [5,1,1,1,1] => 24
[7,2,2,2,1,1,1,1] => [6,3,3,2,1,1,1] => [3,3,2,1,1,1] => 323
[7,2,2,1,1,1,1,1,1] => [6,4,2,2,1,1,1] => [4,2,2,1,1,1] => 406
[7,2,1,1,1,1,1,1,1,1] => [6,4,3,1,1,1,1] => [4,3,1,1,1,1] => 365
[7,1,1,1,1,1,1,1,1,1,1] => [5,4,3,2,1,1,1] => [4,3,2,1,1,1] => 1920
[6,6,4,1] => [12,2,1,1,1] => [2,1,1,1] => 1
[6,6,3,2] => [12,5] => [5] => 0
[6,6,3,1,1] => [12,4,1] => [4,1] => 2
[6,6,2,2,1] => [12,2,2,1] => [2,2,1] => 2
[6,6,2,1,1,1] => [12,3,1,1] => [3,1,1] => 2
[6,6,1,1,1,1,1] => [12,3,2] => [3,2] => 2
[6,5,4,2] => [11,2,2,1,1] => [2,2,1,1] => 3
[6,5,4,1,1] => [11,3,1,1,1] => [3,1,1,1] => 3
[6,5,3,3] => [11,6] => [6] => 1
[6,5,3,2,1] => [11,5,1] => [5,1] => 2
[6,5,3,1,1,1] => [11,3,3] => [3,3] => 2
[6,5,2,2,2] => [11,2,2,2] => [2,2,2] => 2
[6,5,2,2,1,1] => [11,4,1,1] => [4,1,1] => 4
[6,5,2,1,1,1,1] => [11,4,2] => [4,2] => 4
[6,5,1,1,1,1,1,1] => [11,3,2,1] => [3,2,1] => 6
[6,4,4,2,1] => [10,5,1,1] => [5,1,1] => 6
[6,4,4,1,1,1] => [10,3,2,1,1] => [3,2,1,1] => 12
[6,4,3,3,1] => [8,8,1] => [8,1] => 4
[6,4,3,2,2] => [9,6,1,1] => [6,1,1] => 9
[6,4,3,2,1,1] => [9,4,4] => [4,4] => 6
[6,4,3,1,1,1,1] => [9,5,2,1] => [5,2,1] => 26
[6,4,2,2,2,1] => [9,5,1,1,1] => [5,1,1,1] => 13
[6,4,2,1,1,1,1,1] => [8,4,4,1] => [4,4,1] => 34
[6,4,1,1,1,1,1,1,1] => [8,5,3,1] => [5,3,1] => 66
[6,3,3,3,2] => [10,2,2,2,1] => [2,2,2,1] => 5
[6,3,3,3,1,1] => [9,6,2] => [6,2] => 9
[6,3,3,2,2,1] => [9,3,2,2,1] => [3,2,2,1] => 25
[6,3,3,2,1,1,1] => [7,7,2,1] => [7,2,1] => 68
[6,3,3,1,1,1,1,1] => [6,5,5,1] => [5,5,1] => 136
[6,3,2,2,2,2] => [6,6,1,1,1,1,1] => [6,1,1,1,1,1] => 86
[6,3,2,2,2,1,1] => [8,5,2,1,1] => [5,2,1,1] => 72
[6,3,2,2,1,1,1,1] => [8,5,2,2] => [5,2,2] => 48
[6,3,2,1,1,1,1,1,1] => [5,5,5,1,1] => [5,5,1,1] => 588
[6,3,1,1,1,1,1,1,1,1] => [5,5,5,2] => [5,5,2] => 534
[6,2,2,2,2,2,1] => [8,5,4] => [5,4] => 18
[6,2,2,2,2,1,1,1] => [8,3,3,2,1] => [3,3,2,1] => 61
[6,2,2,2,1,1,1,1,1] => [6,6,2,2,1] => [6,2,2,1] => 430
[6,2,2,1,1,1,1,1,1,1] => [6,6,3,1,1] => [6,3,1,1] => 488
[6,2,1,1,1,1,1,1,1,1,1] => [6,6,3,2] => [6,3,2] => 403
[6,1,1,1,1,1,1,1,1,1,1,1] => [7,4,3,2,1] => [4,3,2,1] => 288
[5,5,4,2,1] => [5,2,2,2,2,2,2] => [2,2,2,2,2,2] => 42
[5,5,3,3,1] => [10,6,1] => [6,1] => 3
[5,5,3,2,2] => [8,2,2,2,1,1,1] => [2,2,2,1,1,1] => 14
[5,5,3,2,1,1] => [10,5,2] => [5,2] => 6
[5,5,3,1,1,1,1] => [10,3,2,2] => [3,2,2] => 8
[5,5,2,2,2,1] => [10,4,1,1,1] => [4,1,1,1] => 7
[5,5,2,2,1,1,1] => [10,4,3] => [4,3] => 6
[5,5,2,1,1,1,1,1] => [10,3,3,1] => [3,3,1] => 8
[5,5,1,1,1,1,1,1,1] => [10,4,2,1] => [4,2,1] => 14
[5,4,4,4] => [9,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[5,4,4,2,2] => [6,2,2,2,2,2,1] => [2,2,2,2,2,1] => 42
[5,4,4,1,1,1,1] => [5,3,2,2,2,2,1] => [3,2,2,2,2,1] => 378
[5,4,3,3,2] => [9,2,2,2,2] => [2,2,2,2] => 5
[5,4,3,3,1,1] => [8,3,2,2,2] => [3,2,2,2] => 30
[5,4,3,2,2,1] => [7,3,2,2,1,1,1] => [3,2,2,1,1,1] => 98
[5,4,3,2,1,1,1] => [9,3,3,1,1] => [3,3,1,1] => 20
[5,4,3,1,1,1,1,1] => [9,4,2,1,1] => [4,2,1,1] => 33
[5,4,2,2,2,2] => [8,6,1,1,1] => [6,1,1,1] => 22
[5,4,2,2,2,1,1] => [9,5,3] => [5,3] => 12
[5,4,2,2,1,1,1,1] => [9,3,3,2] => [3,3,2] => 16
[5,4,2,1,1,1,1,1,1] => [9,4,2,2] => [4,2,2] => 22
[5,4,1,1,1,1,1,1,1,1] => [9,4,3,1] => [4,3,1] => 28
[5,3,3,3,1,1,1] => [7,6,2,1,1] => [6,2,1,1] => 138
[5,3,3,2,2,2] => [7,2,2,2,2,1,1] => [2,2,2,2,1,1] => 28
[5,3,3,2,2,1,1] => [8,3,3,3] => [3,3,3] => 16
[5,3,3,2,1,1,1,1] => [7,6,2,2] => [6,2,2] => 92
[5,3,3,1,1,1,1,1,1] => [6,6,4,1] => [6,4,1] => 288
[5,3,2,2,2,2,1] => [6,3,2,2,2,2] => [3,2,2,2,2] => 112
[5,3,2,2,2,1,1,1] => [7,3,3,2,2] => [3,3,2,2] => 91
[5,3,2,2,1,1,1,1,1] => [8,4,2,2,1] => [4,2,2,1] => 80
[5,3,2,1,1,1,1,1,1,1] => [7,4,4,1,1] => [4,4,1,1] => 115
[5,3,1,1,1,1,1,1,1,1,1] => [5,4,4,2,1,1] => [4,4,2,1,1] => 1629
[5,2,2,2,2,2,2] => [6,6,5] => [6,5] => 57
[5,2,2,2,2,1,1,1,1] => [7,3,3,3,1] => [3,3,3,1] => 77
[5,2,2,2,1,1,1,1,1,1] => [7,5,2,2,1] => [5,2,2,1] => 200
[5,2,2,1,1,1,1,1,1,1,1] => [8,4,3,2] => [4,3,2] => 66
[5,2,1,1,1,1,1,1,1,1,1,1] => [5,5,3,2,1,1] => [5,3,2,1,1] => 2835
[5,1,1,1,1,1,1,1,1,1,1,1,1] => [6,4,3,2,1,1] => [4,3,2,1,1] => 826
[4,4,4,4,1] => [9,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[4,4,4,3,2] => [8,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 6
[4,4,4,3,1,1] => [8,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 6
[4,4,4,2,1,1,1] => [5,3,3,2,2,2] => [3,3,2,2,2] => 456
[4,4,4,1,1,1,1,1] => [5,4,2,2,2,2] => [4,2,2,2,2] => 518
[4,4,3,3,3] => [9,8] => [8] => 1
[4,4,3,3,2,1] => [8,4,1,1,1,1,1] => [4,1,1,1,1,1] => 16
[4,4,3,3,1,1,1] => [8,3,2,1,1,1,1] => [3,2,1,1,1,1] => 30
[4,4,3,2,2,2] => [7,7,3] => [7,3] => 33
[4,4,3,2,2,1,1] => [7,3,3,2,1,1] => [3,3,2,1,1] => 155
[4,4,3,2,1,1,1,1] => [7,4,2,2,1,1] => [4,2,2,1,1] => 198
[4,4,3,1,1,1,1,1,1] => [5,4,3,2,2,1] => [4,3,2,2,1] => 2065
[4,4,2,2,2,1,1,1] => [5,3,3,3,3] => [3,3,3,3] => 168
[4,4,2,2,1,1,1,1,1] => [7,6,3,1] => [6,3,1] => 131
[4,4,2,1,1,1,1,1,1,1] => [8,4,3,1,1] => [4,3,1,1] => 81
[4,4,1,1,1,1,1,1,1,1,1] => [5,4,3,3,2] => [4,3,3,2] => 1104
[4,3,3,3,3,1] => [9,7,1] => [7,1] => 3
[4,3,3,3,2,2] => [8,7,1,1] => [7,1,1] => 12
[4,3,3,3,2,1,1] => [7,3,3,1,1,1,1] => [3,3,1,1,1,1] => 70
[4,3,3,3,1,1,1,1] => [7,4,2,1,1,1,1] => [4,2,1,1,1,1] => 110
[4,3,3,2,2,2,1] => [8,6,3] => [6,3] => 21
[4,3,3,2,1,1,1,1,1] => [7,4,3,1,1,1] => [4,3,1,1,1] => 185
[4,3,3,1,1,1,1,1,1,1] => [5,4,3,3,1,1] => [4,3,3,1,1] => 1505
[4,3,2,2,2,2,2] => [7,5,1,1,1,1,1] => [5,1,1,1,1,1] => 40
[4,3,2,2,2,2,1,1] => [6,6,2,1,1,1] => [6,2,1,1,1] => 344
[4,3,2,2,2,1,1,1,1] => [6,3,3,2,2,1] => [3,3,2,2,1] => 344
[4,3,2,2,1,1,1,1,1,1] => [7,4,3,3] => [4,3,3] => 82
[4,3,2,1,1,1,1,1,1,1,1] => [7,4,4,2] => [4,4,2] => 100
[4,3,1,1,1,1,1,1,1,1,1,1] => [5,4,4,2,2] => [4,4,2,2] => 992
[4,2,2,2,2,2,2,1] => [7,5,5] => [5,5] => 18
[4,2,2,2,2,1,1,1,1,1] => [5,5,4,1,1,1] => [5,4,1,1,1] => 1316
[4,2,2,2,1,1,1,1,1,1,1] => [7,5,3,1,1] => [5,3,1,1] => 219
[4,2,2,1,1,1,1,1,1,1,1,1] => [7,5,3,2] => [5,3,2] => 180
[4,2,1,1,1,1,1,1,1,1,1,1,1] => [5,5,3,2,2] => [5,3,2,2] => 1686
[4,1,1,1,1,1,1,1,1,1,1,1,1,1] => [6,4,3,2,2] => [4,3,2,2] => 489
[3,3,3,3,3,1,1] => [8,7,2] => [7,2] => 12
[3,3,3,3,2,1,1,1] => [8,6,2,1] => [6,2,1] => 44
[3,3,3,3,1,1,1,1,1] => [7,4,2,2,2] => [4,2,2,2] => 110
[3,3,3,2,2,2,2] => [7,2,2,2,2,2] => [2,2,2,2,2] => 14
[3,3,3,2,2,2,1,1] => [5,3,3,3,2,1] => [3,3,3,2,1] => 744
[3,3,3,2,2,1,1,1,1] => [5,4,4,4] => [4,4,4] => 182
[3,3,3,2,1,1,1,1,1,1] => [7,5,4,1] => [5,4,1] => 118
[3,3,3,1,1,1,1,1,1,1,1] => [5,5,4,3] => [5,4,3] => 842
[3,3,2,2,2,2,2,1] => [7,3,2,2,2,1] => [3,2,2,2,1] => 98
[3,3,2,2,2,2,1,1,1] => [5,5,2,2,2,1] => [5,2,2,2,1] => 1274
[3,3,2,2,2,1,1,1,1,1] => [6,4,2,2,2,1] => [4,2,2,2,1] => 406
[3,3,2,2,1,1,1,1,1,1,1] => [6,4,4,1,1,1] => [4,4,1,1,1] => 300
[3,3,2,1,1,1,1,1,1,1,1,1] => [6,4,4,3] => [4,4,3] => 182
[3,3,1,1,1,1,1,1,1,1,1,1,1] => [5,4,4,3,1] => [4,4,3,1] => 1132
[3,2,2,2,2,2,2,2] => [7,6,1,1,1,1] => [6,1,1,1,1] => 46
[3,2,2,2,2,2,2,1,1] => [7,5,2,1,1,1] => [5,2,1,1,1] => 160
[3,2,2,2,2,2,1,1,1,1] => [6,3,3,3,1,1] => [3,3,3,1,1] => 232
[3,2,2,2,2,1,1,1,1,1,1] => [6,5,2,2,1,1] => [5,2,2,1,1] => 558
[3,2,2,2,1,1,1,1,1,1,1,1] => [6,5,3,1,1,1] => [5,3,1,1,1] => 564
[3,2,2,1,1,1,1,1,1,1,1,1,1] => [6,5,3,3] => [5,3,3] => 262
[3,2,1,1,1,1,1,1,1,1,1,1,1,1] => [5,5,3,3,1] => [5,3,3,1] => 1596
[3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [6,4,3,3,1] => [4,3,3,1] => 447
[2,2,2,2,2,2,2,2,1] => [7,6,4] => [6,4] => 39
[2,2,2,2,2,2,1,1,1,1,1] => [6,3,3,3,2] => [3,3,3,2] => 168
[2,2,2,2,2,1,1,1,1,1,1,1] => [6,5,2,2,2] => [5,2,2,2] => 310
[2,2,2,2,1,1,1,1,1,1,1,1,1] => [6,5,4,1,1] => [5,4,1,1] => 452
[2,2,2,1,1,1,1,1,1,1,1,1,1,1] => [6,5,4,2] => [5,4,2] => 398
[2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] => [5,5,4,2,1] => [5,4,2,1] => 2240
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [6,4,4,2,1] => [4,4,2,1] => 503
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [6,5,3,2,1] => [5,3,2,1] => 887
[6,5,4,3,2,1] => [11,7,3] => [7,3] => 33
[2,2,2,2,2,2,2,2,2] => [7,6,5] => [6,5] => 57
search for individual values
searching the database for the individual values of this statistic
Description
The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is even.
To be precise, this is given for a partition $\lambda \vdash n$ by the number of standard tableaux $T$ of shape $\lambda$ such that $\min\big( \operatorname{Des}(T) \cup \{n\} \big)$ is even.
This notion was used in [1, Proposition 2.3], see also [2, Theorem 1.1].
The case of an odd minimum is St000620The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is odd..
Map
first row removal
Description
Removes the first entry of an integer partition
Map
Loehr-Warrington
Description
Return a partition whose diagonal inversion number is the length of the preimage.