Identifier
Values
[1,1] => [1] => [1,0,1,0] => [2,1] => 1
[2,1] => [1] => [1,0,1,0] => [2,1] => 1
[1,1,1] => [1,1] => [1,0,1,1,0,0] => [2,3,1] => 2
[3,1] => [1] => [1,0,1,0] => [2,1] => 1
[2,2] => [2] => [1,1,0,0,1,0] => [3,1,2] => 1
[2,1,1] => [1,1] => [1,0,1,1,0,0] => [2,3,1] => 2
[1,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [2,3,4,1] => 3
[4,1] => [1] => [1,0,1,0] => [2,1] => 1
[3,2] => [2] => [1,1,0,0,1,0] => [3,1,2] => 1
[3,1,1] => [1,1] => [1,0,1,1,0,0] => [2,3,1] => 2
[2,2,1] => [2,1] => [1,0,1,0,1,0] => [3,2,1] => 2
[2,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [2,3,4,1] => 3
[1,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 4
[5,1] => [1] => [1,0,1,0] => [2,1] => 1
[4,2] => [2] => [1,1,0,0,1,0] => [3,1,2] => 1
[4,1,1] => [1,1] => [1,0,1,1,0,0] => [2,3,1] => 2
[3,3] => [3] => [1,1,1,0,0,0,1,0] => [4,1,2,3] => 1
[3,2,1] => [2,1] => [1,0,1,0,1,0] => [3,2,1] => 2
[3,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [2,3,4,1] => 3
[2,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [3,4,1,2] => 3
[2,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [3,2,4,1] => 3
[2,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 4
[1,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => 5
[6,1] => [1] => [1,0,1,0] => [2,1] => 1
[5,2] => [2] => [1,1,0,0,1,0] => [3,1,2] => 1
[5,1,1] => [1,1] => [1,0,1,1,0,0] => [2,3,1] => 2
[4,3] => [3] => [1,1,1,0,0,0,1,0] => [4,1,2,3] => 1
[4,2,1] => [2,1] => [1,0,1,0,1,0] => [3,2,1] => 2
[4,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [2,3,4,1] => 3
[3,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => [4,2,1,3] => 2
[3,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [3,4,1,2] => 3
[3,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [3,2,4,1] => 3
[3,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 4
[2,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => [3,4,2,1] => 4
[2,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => 4
[2,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => 5
[7,1] => [1] => [1,0,1,0] => [2,1] => 1
[6,2] => [2] => [1,1,0,0,1,0] => [3,1,2] => 1
[6,1,1] => [1,1] => [1,0,1,1,0,0] => [2,3,1] => 2
[5,3] => [3] => [1,1,1,0,0,0,1,0] => [4,1,2,3] => 1
[5,2,1] => [2,1] => [1,0,1,0,1,0] => [3,2,1] => 2
[5,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [2,3,4,1] => 3
[4,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => 1
[4,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => [4,2,1,3] => 2
[4,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [3,4,1,2] => 3
[4,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [3,2,4,1] => 3
[4,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 4
[3,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => [4,3,1,2] => 3
[3,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => [4,2,3,1] => 3
[3,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => [3,4,2,1] => 4
[3,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => 4
[3,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => 5
[2,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => 5
[2,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => 5
[2,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => 5
[8,1] => [1] => [1,0,1,0] => [2,1] => 1
[7,2] => [2] => [1,1,0,0,1,0] => [3,1,2] => 1
[7,1,1] => [1,1] => [1,0,1,1,0,0] => [2,3,1] => 2
[6,3] => [3] => [1,1,1,0,0,0,1,0] => [4,1,2,3] => 1
[6,2,1] => [2,1] => [1,0,1,0,1,0] => [3,2,1] => 2
[6,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [2,3,4,1] => 3
[5,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => 1
[5,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => [4,2,1,3] => 2
[5,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [3,4,1,2] => 3
[5,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [3,2,4,1] => 3
[5,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 4
[4,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => 2
[4,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => [4,3,1,2] => 3
[4,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => [4,2,3,1] => 3
[4,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => [3,4,2,1] => 4
[4,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => 4
[4,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => 5
[3,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => 3
[3,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => [4,3,2,1] => 4
[3,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => 4
[3,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => 5
[3,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => 5
[3,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => 5
[2,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => 6
[2,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => 6
[9,1] => [1] => [1,0,1,0] => [2,1] => 1
[8,2] => [2] => [1,1,0,0,1,0] => [3,1,2] => 1
[8,1,1] => [1,1] => [1,0,1,1,0,0] => [2,3,1] => 2
[7,3] => [3] => [1,1,1,0,0,0,1,0] => [4,1,2,3] => 1
[7,2,1] => [2,1] => [1,0,1,0,1,0] => [3,2,1] => 2
[7,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [2,3,4,1] => 3
[6,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => 1
[6,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => [4,2,1,3] => 2
[6,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [3,4,1,2] => 3
[6,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [3,2,4,1] => 3
[6,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 4
[5,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => 1
[5,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => 2
[5,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => [4,3,1,2] => 3
[5,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => [4,2,3,1] => 3
[5,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => [3,4,2,1] => 4
[5,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => 4
[5,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => 5
[4,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => 3
[4,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => 3
[4,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => 3
>>> Load all 742 entries. <<<
[4,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => [4,3,2,1] => 4
[4,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => 4
[4,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => 5
[4,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => 5
[4,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => 5
[3,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => 4
[3,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => 5
[3,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => 5
[3,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => 5
[3,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => 6
[3,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => 6
[2,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => 7
[2,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => 7
[10,1] => [1] => [1,0,1,0] => [2,1] => 1
[9,2] => [2] => [1,1,0,0,1,0] => [3,1,2] => 1
[9,1,1] => [1,1] => [1,0,1,1,0,0] => [2,3,1] => 2
[8,3] => [3] => [1,1,1,0,0,0,1,0] => [4,1,2,3] => 1
[8,2,1] => [2,1] => [1,0,1,0,1,0] => [3,2,1] => 2
[8,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [2,3,4,1] => 3
[7,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => 1
[7,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => [4,2,1,3] => 2
[7,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [3,4,1,2] => 3
[7,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [3,2,4,1] => 3
[7,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 4
[6,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => 1
[6,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => 2
[6,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => [4,3,1,2] => 3
[6,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => [4,2,3,1] => 3
[6,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => [3,4,2,1] => 4
[6,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => 4
[6,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => 5
[5,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => 2
[5,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => 3
[5,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => 3
[5,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => 3
[5,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => [4,3,2,1] => 4
[5,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => 4
[5,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => 5
[5,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => 5
[5,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => 5
[4,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => 3
[4,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,4] => 4
[4,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => 4
[4,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => 4
[4,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => 5
[4,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => 5
[4,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => 5
[4,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => 6
[4,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => 6
[3,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => 5
[3,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => 5
[3,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => 6
[3,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => 6
[3,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => 7
[3,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => 7
[2,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => 8
[11,1] => [1] => [1,0,1,0] => [2,1] => 1
[10,2] => [2] => [1,1,0,0,1,0] => [3,1,2] => 1
[10,1,1] => [1,1] => [1,0,1,1,0,0] => [2,3,1] => 2
[9,3] => [3] => [1,1,1,0,0,0,1,0] => [4,1,2,3] => 1
[9,2,1] => [2,1] => [1,0,1,0,1,0] => [3,2,1] => 2
[9,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [2,3,4,1] => 3
[8,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => 1
[8,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => [4,2,1,3] => 2
[8,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [3,4,1,2] => 3
[8,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [3,2,4,1] => 3
[8,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 4
[7,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => 1
[7,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => 2
[7,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => [4,3,1,2] => 3
[7,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => [4,2,3,1] => 3
[7,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => [3,4,2,1] => 4
[7,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => 4
[7,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => 5
[6,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => 2
[6,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => 3
[6,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => 3
[6,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => 3
[6,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => [4,3,2,1] => 4
[6,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => 4
[6,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => 5
[6,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => 5
[6,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => 5
[5,5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,2,4,5] => 3
[5,5,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,3,1,4,5] => 3
[5,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => 3
[5,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,4] => 4
[5,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => 4
[5,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => 4
[5,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => 5
[5,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => 5
[5,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => 5
[5,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => 6
[5,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => 6
[4,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => 3
[4,4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,3] => 4
[4,4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => 5
[4,4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [5,3,2,4,1] => 5
[4,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => 5
[4,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => 5
[4,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => 5
[4,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => 6
[4,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => 6
[4,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => 7
[4,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => 7
[3,3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => 6
[3,3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => 6
[3,3,3,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => 6
[3,3,2,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,5,6,1,2] => 7
[3,3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,5,2,6,1] => 7
[3,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => 8
[12,1] => [1] => [1,0,1,0] => [2,1] => 1
[11,2] => [2] => [1,1,0,0,1,0] => [3,1,2] => 1
[11,1,1] => [1,1] => [1,0,1,1,0,0] => [2,3,1] => 2
[10,3] => [3] => [1,1,1,0,0,0,1,0] => [4,1,2,3] => 1
[10,2,1] => [2,1] => [1,0,1,0,1,0] => [3,2,1] => 2
[10,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [2,3,4,1] => 3
[9,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => 1
[9,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => [4,2,1,3] => 2
[9,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [3,4,1,2] => 3
[9,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [3,2,4,1] => 3
[9,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 4
[8,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => 1
[8,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => 2
[8,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => [4,3,1,2] => 3
[8,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => [4,2,3,1] => 3
[8,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => [3,4,2,1] => 4
[8,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => 4
[8,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => 5
[7,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => 2
[7,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => 3
[7,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => 3
[7,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => 3
[7,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => [4,3,2,1] => 4
[7,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => 4
[7,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => 5
[7,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => 5
[7,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => 5
[6,5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,2,4,5] => 3
[6,5,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,3,1,4,5] => 3
[6,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => 3
[6,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,4] => 4
[6,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => 4
[6,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => 4
[6,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => 5
[6,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => 5
[6,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => 5
[6,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => 6
[6,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => 6
[5,5,3] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,2,3,5] => 3
[5,5,2,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,4,5] => 4
[5,5,1,1,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,3,4,1,5] => 4
[5,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => 3
[5,4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,3] => 4
[5,4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => 5
[5,4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [5,3,2,4,1] => 5
[5,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => 5
[5,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => 5
[5,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => 5
[5,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => 6
[5,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => 6
[5,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => 7
[5,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => 7
[4,4,4,1] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [5,6,2,1,3,4] => 4
[4,4,3,2] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => 5
[4,4,3,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => 5
[4,4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => 6
[4,4,2,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => 6
[4,3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => 6
[4,3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => 6
[4,3,3,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => 6
[4,3,2,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,5,6,1,2] => 7
[4,3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,5,2,6,1] => 7
[4,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => 8
[3,3,3,3,1] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [4,5,6,2,1,3] => 7
[3,3,3,2,2] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [4,5,3,6,1,2] => 7
[3,3,3,2,1,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [4,5,3,2,6,1] => 7
[3,3,2,2,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => 8
[13,1] => [1] => [1,0,1,0] => [2,1] => 1
[12,2] => [2] => [1,1,0,0,1,0] => [3,1,2] => 1
[12,1,1] => [1,1] => [1,0,1,1,0,0] => [2,3,1] => 2
[11,3] => [3] => [1,1,1,0,0,0,1,0] => [4,1,2,3] => 1
[11,2,1] => [2,1] => [1,0,1,0,1,0] => [3,2,1] => 2
[11,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [2,3,4,1] => 3
[10,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => 1
[10,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => [4,2,1,3] => 2
[10,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [3,4,1,2] => 3
[10,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [3,2,4,1] => 3
[10,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 4
[9,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => 1
[9,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => 2
[9,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => [4,3,1,2] => 3
[9,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => [4,2,3,1] => 3
[9,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => [3,4,2,1] => 4
[9,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => 4
[9,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => 5
[8,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => 2
[8,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => 3
[8,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => 3
[8,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => 3
[8,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => [4,3,2,1] => 4
[8,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => 4
[8,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => 5
[8,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => 5
[8,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => 5
[7,5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,2,4,5] => 3
[7,5,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,3,1,4,5] => 3
[7,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => 3
[7,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,4] => 4
[7,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => 4
[7,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => 4
[7,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => 5
[7,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => 5
[7,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => 5
[7,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => 6
[7,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => 6
[6,5,3] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,2,3,5] => 3
[6,5,2,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,4,5] => 4
[6,5,1,1,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,3,4,1,5] => 4
[6,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => 3
[6,4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,3] => 4
[6,4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => 5
[6,4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [5,3,2,4,1] => 5
[6,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => 5
[6,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => 5
[6,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => 5
[6,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => 6
[6,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => 6
[6,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => 7
[6,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => 7
[5,5,4] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => 3
[5,5,3,1] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,3,5] => 4
[5,5,2,2] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,4,1,2,5] => 5
[5,5,2,1,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,4,1,5] => 5
[5,5,1,1,1,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => 5
[5,4,4,1] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [5,6,2,1,3,4] => 4
[5,4,3,2] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => 5
[5,4,3,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => 5
[5,4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => 6
[5,4,2,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => 6
[5,3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => 6
[5,3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => 6
[5,3,3,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => 6
[5,3,2,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,5,6,1,2] => 7
[5,3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,5,2,6,1] => 7
[5,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => 8
[4,4,4,2] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [5,6,3,1,2,4] => 5
[4,4,4,1,1] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [5,6,2,3,1,4] => 5
[4,4,3,3] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,6,1,2,3] => 6
[4,4,3,2,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => 6
[4,4,3,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,3,6,1] => 6
[4,4,2,2,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,4,6,1,2] => 7
[4,4,2,2,1,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,4,2,6,1] => 7
[4,3,3,3,1] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [4,5,6,2,1,3] => 7
[4,3,3,2,2] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [4,5,3,6,1,2] => 7
[4,3,3,2,1,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [4,5,3,2,6,1] => 7
[4,3,2,2,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => 8
[3,3,3,3,2] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => [4,5,6,3,1,2] => 8
[3,3,3,3,1,1] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => 8
[3,3,3,2,2,1] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => [4,5,3,6,2,1] => 8
[14,1] => [1] => [1,0,1,0] => [2,1] => 1
[13,2] => [2] => [1,1,0,0,1,0] => [3,1,2] => 1
[13,1,1] => [1,1] => [1,0,1,1,0,0] => [2,3,1] => 2
[12,3] => [3] => [1,1,1,0,0,0,1,0] => [4,1,2,3] => 1
[12,2,1] => [2,1] => [1,0,1,0,1,0] => [3,2,1] => 2
[12,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [2,3,4,1] => 3
[11,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => 1
[11,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => [4,2,1,3] => 2
[11,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [3,4,1,2] => 3
[11,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [3,2,4,1] => 3
[11,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 4
[10,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => 1
[10,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => 2
[10,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => [4,3,1,2] => 3
[10,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => [4,2,3,1] => 3
[10,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => [3,4,2,1] => 4
[10,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => 4
[10,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => 5
[9,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => 2
[9,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => 3
[9,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => 3
[9,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => 3
[9,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => [4,3,2,1] => 4
[9,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => 4
[9,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => 5
[9,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => 5
[9,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => 5
[8,5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,2,4,5] => 3
[8,5,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,3,1,4,5] => 3
[8,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => 3
[8,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,4] => 4
[8,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => 4
[8,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => 4
[8,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => 5
[8,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => 5
[8,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => 5
[8,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => 6
[8,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => 6
[7,5,3] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,2,3,5] => 3
[7,5,2,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,4,5] => 4
[7,5,1,1,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,3,4,1,5] => 4
[7,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => 3
[7,4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,3] => 4
[7,4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => 5
[7,4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [5,3,2,4,1] => 5
[7,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => 5
[7,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => 5
[7,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => 5
[7,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => 6
[7,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => 6
[7,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => 7
[7,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => 7
[6,5,4] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => 3
[6,5,3,1] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,3,5] => 4
[6,5,2,2] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,4,1,2,5] => 5
[6,5,2,1,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,4,1,5] => 5
[6,5,1,1,1,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => 5
[6,4,4,1] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [5,6,2,1,3,4] => 4
[6,4,3,2] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => 5
[6,4,3,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => 5
[6,4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => 6
[6,4,2,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => 6
[6,3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => 6
[6,3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => 6
[6,3,3,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => 6
[6,3,2,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,5,6,1,2] => 7
[6,3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,5,2,6,1] => 7
[6,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => 8
[5,5,4,1] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,3,4] => 4
[5,5,3,2] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,2,5] => 5
[5,5,3,1,1] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,3,1,5] => 5
[5,5,2,2,1] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,4,2,1,5] => 6
[5,5,2,1,1,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1] => 6
[5,4,4,2] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [5,6,3,1,2,4] => 5
[5,4,4,1,1] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [5,6,2,3,1,4] => 5
[5,4,3,3] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,6,1,2,3] => 6
[5,4,3,2,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => 6
[5,4,3,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,3,6,1] => 6
[5,4,2,2,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,4,6,1,2] => 7
[5,4,2,2,1,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,4,2,6,1] => 7
[5,3,3,3,1] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [4,5,6,2,1,3] => 7
[5,3,3,2,2] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [4,5,3,6,1,2] => 7
[5,3,3,2,1,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [4,5,3,2,6,1] => 7
[5,3,2,2,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => 8
[4,4,4,3] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [5,6,4,1,2,3] => 6
[4,4,4,2,1] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => [5,6,3,2,1,4] => 6
[4,4,4,1,1,1] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => [5,6,2,3,4,1] => 6
[4,4,3,3,1] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,6,2,1,3] => 7
[4,4,3,2,2] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,6,1,2] => 7
[4,4,3,2,1,1] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,1] => 7
[4,4,2,2,2,1] => [4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,4,6,2,1] => 8
[4,3,3,3,2] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => [4,5,6,3,1,2] => 8
[4,3,3,3,1,1] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => 8
[4,3,3,2,2,1] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => [4,5,3,6,2,1] => 8
[3,3,3,3,2,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => 9
[15,1] => [1] => [1,0,1,0] => [2,1] => 1
[14,2] => [2] => [1,1,0,0,1,0] => [3,1,2] => 1
[14,1,1] => [1,1] => [1,0,1,1,0,0] => [2,3,1] => 2
[13,3] => [3] => [1,1,1,0,0,0,1,0] => [4,1,2,3] => 1
[13,2,1] => [2,1] => [1,0,1,0,1,0] => [3,2,1] => 2
[13,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [2,3,4,1] => 3
[12,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => 1
[12,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => [4,2,1,3] => 2
[12,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [3,4,1,2] => 3
[12,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [3,2,4,1] => 3
[12,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 4
[11,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => 1
[11,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => 2
[11,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => [4,3,1,2] => 3
[11,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => [4,2,3,1] => 3
[11,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => [3,4,2,1] => 4
[11,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => 4
[11,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => 5
[10,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => 2
[10,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => 3
[10,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => 3
[10,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => 3
[10,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => [4,3,2,1] => 4
[10,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => 4
[10,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => 5
[10,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => 5
[10,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => 5
[9,5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,2,4,5] => 3
[9,5,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,3,1,4,5] => 3
[9,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => 3
[9,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,4] => 4
[9,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => 4
[9,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => 4
[9,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => 5
[9,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => 5
[9,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => 5
[9,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => 6
[9,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => 6
[8,5,3] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,2,3,5] => 3
[8,5,2,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,4,5] => 4
[8,5,1,1,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,3,4,1,5] => 4
[8,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => 3
[8,4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,3] => 4
[8,4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => 5
[8,4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [5,3,2,4,1] => 5
[8,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => 5
[8,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => 5
[8,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => 5
[8,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => 6
[8,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => 6
[8,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => 7
[8,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => 7
[7,5,4] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => 3
[7,5,3,1] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,3,5] => 4
[7,5,2,2] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,4,1,2,5] => 5
[7,5,2,1,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,4,1,5] => 5
[7,5,1,1,1,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => 5
[7,4,4,1] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [5,6,2,1,3,4] => 4
[7,4,3,2] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => 5
[7,4,3,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => 5
[7,4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => 6
[7,4,2,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => 6
[7,3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => 6
[7,3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => 6
[7,3,3,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => 6
[7,3,2,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,5,6,1,2] => 7
[7,3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,5,2,6,1] => 7
[7,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => 8
[6,5,4,1] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,3,4] => 4
[6,5,3,2] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,2,5] => 5
[6,5,3,1,1] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,3,1,5] => 5
[6,5,2,2,1] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,4,2,1,5] => 6
[6,5,2,1,1,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1] => 6
[6,4,4,2] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [5,6,3,1,2,4] => 5
[6,4,4,1,1] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [5,6,2,3,1,4] => 5
[6,4,3,3] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,6,1,2,3] => 6
[6,4,3,2,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => 6
[6,4,3,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,3,6,1] => 6
[6,4,2,2,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,4,6,1,2] => 7
[6,4,2,2,1,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,4,2,6,1] => 7
[6,3,3,3,1] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [4,5,6,2,1,3] => 7
[6,3,3,2,2] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [4,5,3,6,1,2] => 7
[6,3,3,2,1,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [4,5,3,2,6,1] => 7
[6,3,2,2,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => 8
[5,5,4,2] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,2,4] => 5
[5,5,4,1,1] => [5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,3,1,4] => 5
[5,5,3,3] => [5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,5,1,2,3] => 6
[5,5,3,2,1] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,5] => 6
[5,5,3,1,1,1] => [5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,3,5,1] => 6
[5,5,2,2,2] => [5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,4,5,1,2] => 7
[5,5,2,2,1,1] => [5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,4,2,5,1] => 7
[5,4,4,3] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [5,6,4,1,2,3] => 6
[5,4,4,2,1] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => [5,6,3,2,1,4] => 6
[5,4,4,1,1,1] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => [5,6,2,3,4,1] => 6
[5,4,3,3,1] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,6,2,1,3] => 7
[5,4,3,2,2] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,6,1,2] => 7
[5,4,3,2,1,1] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,1] => 7
[5,4,2,2,2,1] => [4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,4,6,2,1] => 8
[5,3,3,3,2] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => [4,5,6,3,1,2] => 8
[5,3,3,3,1,1] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => 8
[5,3,3,2,2,1] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => [4,5,3,6,2,1] => 8
[4,4,4,3,1] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [5,6,4,2,1,3] => 7
[4,4,4,2,2] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [5,6,3,4,1,2] => 7
[4,4,4,2,1,1] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => [5,6,3,2,4,1] => 7
[4,4,3,3,2] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [5,4,6,3,1,2] => 8
[4,4,3,3,1,1] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,6,2,3,1] => 8
[4,4,3,2,2,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,6,2,1] => 8
[4,3,3,3,2,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => 9
[16,1] => [1] => [1,0,1,0] => [2,1] => 1
[15,2] => [2] => [1,1,0,0,1,0] => [3,1,2] => 1
[15,1,1] => [1,1] => [1,0,1,1,0,0] => [2,3,1] => 2
[14,3] => [3] => [1,1,1,0,0,0,1,0] => [4,1,2,3] => 1
[14,2,1] => [2,1] => [1,0,1,0,1,0] => [3,2,1] => 2
[14,1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [2,3,4,1] => 3
[13,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => 1
[13,3,1] => [3,1] => [1,1,0,1,0,0,1,0] => [4,2,1,3] => 2
[13,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [3,4,1,2] => 3
[13,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [3,2,4,1] => 3
[13,1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 4
[12,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => 1
[12,4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => 2
[12,3,2] => [3,2] => [1,1,0,0,1,0,1,0] => [4,3,1,2] => 3
[12,3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => [4,2,3,1] => 3
[12,2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => [3,4,2,1] => 4
[12,2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => 4
[12,1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => 5
[11,5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => 2
[11,4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => 3
[11,4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => 3
[11,3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => 3
[11,3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => [4,3,2,1] => 4
[11,3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => 4
[11,2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => 5
[11,2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => 5
[11,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => 5
[10,5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,2,4,5] => 3
[10,5,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,3,1,4,5] => 3
[10,4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => 3
[10,4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,4] => 4
[10,4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => 4
[10,3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => 4
[10,3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => 5
[10,3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => 5
[10,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => 5
[10,2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => 6
[10,2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => 6
[9,5,3] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,2,3,5] => 3
[9,5,2,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,4,5] => 4
[9,5,1,1,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,3,4,1,5] => 4
[9,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => 3
[9,4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,3] => 4
[9,4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => 5
[9,4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [5,3,2,4,1] => 5
[9,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => 5
[9,3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => 5
[9,3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => 5
[9,3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => 6
[9,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => 6
[9,2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => 7
[9,2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => 7
[8,5,4] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => 3
[8,5,3,1] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,3,5] => 4
[8,5,2,2] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,4,1,2,5] => 5
[8,5,2,1,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,4,1,5] => 5
[8,5,1,1,1,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => 5
[8,4,4,1] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [5,6,2,1,3,4] => 4
[8,4,3,2] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => 5
[8,4,3,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => 5
[8,4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => 6
[8,4,2,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => 6
[8,3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => 6
[8,3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => 6
[8,3,3,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => 6
[8,3,2,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,5,6,1,2] => 7
[8,3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,5,2,6,1] => 7
[8,2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => 8
[7,5,4,1] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,3,4] => 4
[7,5,3,2] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,2,5] => 5
[7,5,3,1,1] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,3,1,5] => 5
[7,5,2,2,1] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,4,2,1,5] => 6
[7,5,2,1,1,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1] => 6
[7,4,4,2] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [5,6,3,1,2,4] => 5
[7,4,4,1,1] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [5,6,2,3,1,4] => 5
[7,4,3,3] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,6,1,2,3] => 6
[7,4,3,2,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => 6
[7,4,3,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,3,6,1] => 6
[7,4,2,2,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,4,6,1,2] => 7
[7,4,2,2,1,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,4,2,6,1] => 7
[7,3,3,3,1] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [4,5,6,2,1,3] => 7
[7,3,3,2,2] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [4,5,3,6,1,2] => 7
[7,3,3,2,1,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [4,5,3,2,6,1] => 7
[7,3,2,2,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => 8
[6,5,4,2] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,2,4] => 5
[6,5,4,1,1] => [5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,3,1,4] => 5
[6,5,3,3] => [5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,5,1,2,3] => 6
[6,5,3,2,1] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,5] => 6
[6,5,3,1,1,1] => [5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,3,5,1] => 6
[6,5,2,2,2] => [5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,4,5,1,2] => 7
[6,5,2,2,1,1] => [5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,4,2,5,1] => 7
[6,4,4,3] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [5,6,4,1,2,3] => 6
[6,4,4,2,1] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => [5,6,3,2,1,4] => 6
[6,4,4,1,1,1] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => [5,6,2,3,4,1] => 6
[6,4,3,3,1] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,6,2,1,3] => 7
[6,4,3,2,2] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,6,1,2] => 7
[6,4,3,2,1,1] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,1] => 7
[6,4,2,2,2,1] => [4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,4,6,2,1] => 8
[6,3,3,3,2] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => [4,5,6,3,1,2] => 8
[6,3,3,3,1,1] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => 8
[6,3,3,2,2,1] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => [4,5,3,6,2,1] => 8
[5,5,4,3] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,2,3] => 6
[5,5,4,2,1] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1,4] => 6
[5,5,4,1,1,1] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,3,4,1] => 6
[5,5,3,3,1] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => [6,4,5,2,1,3] => 7
[5,5,3,2,2] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,5,1,2] => 7
[5,5,3,2,1,1] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,5,1] => 7
[5,5,2,2,2,1] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,4,5,2,1] => 8
[5,4,4,3,1] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [5,6,4,2,1,3] => 7
[5,4,4,2,2] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [5,6,3,4,1,2] => 7
[5,4,4,2,1,1] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => [5,6,3,2,4,1] => 7
[5,4,3,3,2] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [5,4,6,3,1,2] => 8
[5,4,3,3,1,1] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,6,2,3,1] => 8
[5,4,3,2,2,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,6,2,1] => 8
[5,3,3,3,2,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => 9
[4,4,4,3,2] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [5,6,4,3,1,2] => 8
[4,4,4,3,1,1] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => [5,6,4,2,3,1] => 8
[4,4,4,2,2,1] => [4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => [5,6,3,4,2,1] => 8
[4,4,3,3,2,1] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,6,3,2,1] => 9
[6,5,4,3,2,1] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => 9
[5,5,4,3,2,1] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => 9
[6,4,4,3,2,1] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [5,6,4,3,2,1] => 9
[5,4,4,3,2,1] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [5,6,4,3,2,1] => 9
[4,4,4,3,2,1] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [5,6,4,3,2,1] => 9
[6,5,3,3,2,1] => [5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,5,3,2,1] => 9
[5,5,3,3,2,1] => [5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,5,3,2,1] => 9
[6,4,3,3,2,1] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,6,3,2,1] => 9
[5,4,3,3,2,1] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,6,3,2,1] => 9
[6,3,3,3,2,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => 9
[6,5,4,2,2,1] => [5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,4,2,1] => 8
[5,5,4,2,2,1] => [5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,4,2,1] => 8
[6,4,4,2,2,1] => [4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => [5,6,3,4,2,1] => 8
[5,4,4,2,2,1] => [4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => [5,6,3,4,2,1] => 8
[6,5,3,2,2,1] => [5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,5,2,1] => 8
[5,5,3,2,2,1] => [5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,5,2,1] => 8
[6,4,3,2,2,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,6,2,1] => 8
[6,5,2,2,2,1] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,4,5,2,1] => 8
[6,5,4,3,1,1] => [5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,3,1] => 8
[5,5,4,3,1,1] => [5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,3,1] => 8
[6,4,4,3,1,1] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => [5,6,4,2,3,1] => 8
[5,4,4,3,1,1] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => [5,6,4,2,3,1] => 8
[6,5,3,3,1,1] => [5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,5,2,3,1] => 8
[5,5,3,3,1,1] => [5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,5,2,3,1] => 8
[6,4,3,3,1,1] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,6,2,3,1] => 8
[6,5,4,2,1,1] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,4,1] => 7
[5,5,4,2,1,1] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,4,1] => 7
[6,4,4,2,1,1] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => [5,6,3,2,4,1] => 7
[6,5,3,2,1,1] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,5,1] => 7
[6,5,4,1,1,1] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,3,4,1] => 6
[6,5,4,3,2] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,2] => 8
[5,5,4,3,2] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,2] => 8
[6,4,4,3,2] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [5,6,4,3,1,2] => 8
[5,4,4,3,2] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [5,6,4,3,1,2] => 8
[6,5,3,3,2] => [5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,5,3,1,2] => 8
[5,5,3,3,2] => [5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,5,3,1,2] => 8
[6,4,3,3,2] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [5,4,6,3,1,2] => 8
[6,5,4,2,2] => [5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,4,1,2] => 7
[5,5,4,2,2] => [5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,4,1,2] => 7
[6,4,4,2,2] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [5,6,3,4,1,2] => 7
[6,5,3,2,2] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,5,1,2] => 7
[6,5,4,3,1] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1,3] => 7
[5,5,4,3,1] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1,3] => 7
[6,4,4,3,1] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [5,6,4,2,1,3] => 7
[6,5,3,3,1] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => [6,4,5,2,1,3] => 7
[6,5,4,2,1] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1,4] => 6
[6,5,4,3] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,2,3] => 6
[7,5,4,3,2,1] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => 9
[7,4,4,3,2,1] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [5,6,4,3,2,1] => 9
[7,4,3,3,2,1] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,6,3,2,1] => 9
[7,3,3,3,2,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => 9
[7,4,3,2,1,1] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,1] => 7
[7,5,4,3,2] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,2] => 8
[7,5,4,3,1] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1,3] => 7
[7,5,4,2,1] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1,4] => 6
[7,5,4,3] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,2,3] => 6
[10,4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => 3
[8,5,4,2] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,2,4] => 5
[8,5,4,3,2,1] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => 9
search for individual values
searching the database for the individual values of this statistic
Description
The number of visible inversions of a permutation.
A visible inversion of a permutation $\pi$ is a pair $i < j$ such that $\pi(j) \leq \min(i, \pi(i))$.
Map
first row removal
Description
Removes the first entry of an integer partition
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.