Identifier
Values
[1] => [1,0,1,0] => 1
[2] => [1,1,0,0,1,0] => 2
[1,1] => [1,0,1,1,0,0] => 1
[3] => [1,1,1,0,0,0,1,0] => 3
[2,1] => [1,0,1,0,1,0] => 2
[1,1,1] => [1,0,1,1,1,0,0,0] => 1
[4] => [1,1,1,1,0,0,0,0,1,0] => 4
[3,1] => [1,1,0,1,0,0,1,0] => 4
[2,2] => [1,1,0,0,1,1,0,0] => 2
[2,1,1] => [1,0,1,1,0,1,0,0] => 2
[1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 1
[5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[4,1] => [1,1,1,0,1,0,0,0,1,0] => 5
[3,2] => [1,1,0,0,1,0,1,0] => 3
[3,1,1] => [1,0,1,1,0,0,1,0] => 3
[2,2,1] => [1,0,1,0,1,1,0,0] => 2
[2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 6
[4,2] => [1,1,1,0,0,1,0,0,1,0] => 6
[4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 5
[3,3] => [1,1,1,0,0,0,1,1,0,0] => 3
[3,2,1] => [1,0,1,0,1,0,1,0] => 3
[3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 2
[2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 2
[2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 7
[5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 7
[5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 6
[4,3] => [1,1,1,0,0,0,1,0,1,0] => 4
[4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 6
[4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 4
[3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 4
[3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 3
[3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 3
[3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 3
[2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 2
[2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 8
[6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 7
[5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 8
[5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 7
[5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
[4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
[4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 5
[4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 4
[4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
[4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 4
[3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 3
[3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 3
[3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 3
[3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 3
[3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 3
[2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
[2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 2
[2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 2
[2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 9
[6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 8
[6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 7
[5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 5
[5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 9
[5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 7
[5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 7
[5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 5
[4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 5
[4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 4
[4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 4
[4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 4
[4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 5
[4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 4
[3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 3
[3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 3
[3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 3
[3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 3
[3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 3
[3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 3
[2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
[2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 2
[6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 10
[6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 10
[6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 8
[6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 8
[6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 7
[5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 6
[5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => 8
[5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 8
[5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => 7
[5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 6
[5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 5
[4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 6
[4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => 5
[4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 4
>>> Load all 632 entries. <<<
[4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 4
[4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 4
[4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 4
[4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 4
[4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 5
[4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 4
[3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 4
[3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 3
[3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 3
[3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 3
[3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 3
[3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 3
[2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2
[2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 2
[6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 6
[6,4,1] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 11
[6,3,2] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 9
[6,3,1,1] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 9
[6,2,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 8
[6,2,1,1,1] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 8
[6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 6
[5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 6
[5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => 7
[5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => 6
[5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => 5
[5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => 8
[5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => 7
[5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => 5
[5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => 6
[5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 6
[5,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 5
[4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 4
[4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => 6
[4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => 4
[4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => 5
[4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => 4
[4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 4
[4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 4
[4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 4
[4,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 5
[3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 3
[3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => 3
[3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => 3
[3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 3
[3,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 3
[3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 3
[3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 3
[3,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 3
[2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[2,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 2
[6,5,1] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 7
[6,4,2] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 12
[6,4,1,1] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 11
[6,3,3] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 9
[6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 9
[6,3,1,1,1] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 9
[6,2,2,2] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 8
[6,2,2,1,1] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 8
[6,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 7
[6,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 6
[5,5,2] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 7
[5,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 6
[5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => 5
[5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 7
[5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 5
[5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => 6
[5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => 6
[5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => 7
[5,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 7
[5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 5
[5,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 6
[5,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 6
[4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
[4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => 5
[4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
[4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => 5
[4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 4
[4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => 4
[4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => 4
[4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 4
[4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 4
[4,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 4
[4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 4
[4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 4
[4,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 4
[3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 3
[3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 3
[3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 3
[3,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 3
[3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3
[3,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 3
[2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[2,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 2
[7,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[6,5,2] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 8
[6,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 7
[6,4,3] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 10
[6,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 12
[6,4,1,1,1] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 10
[6,3,3,1] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 10
[6,3,2,2] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 9
[6,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 9
[6,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 8
[6,2,2,2,1] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 8
[6,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 7
[6,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 7
[5,5,3] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 8
[5,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 7
[5,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 6
[5,4,4] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 5
[5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => 6
[5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => 5
[5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => 6
[5,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 5
[5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => 5
[5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 5
[5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => 6
[5,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 7
[5,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 7
[5,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 5
[5,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 5
[5,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 6
[4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 5
[4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 4
[4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => 4
[4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => 4
[4,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 5
[4,4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 4
[4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 4
[4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[4,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 4
[4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 4
[4,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 4
[4,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 4
[4,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 4
[4,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 4
[3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 4
[3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 3
[3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 3
[3,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 3
[3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3
[3,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 3
[3,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 3
[3,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 3
[2,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[7,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 8
[6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 9
[6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 8
[6,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 7
[6,4,4] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 6
[6,4,3,1] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 11
[6,4,2,2] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 10
[6,4,2,1,1] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 11
[6,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 9
[6,3,3,2] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 9
[6,3,3,1,1] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 9
[6,3,2,2,1] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 9
[6,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 8
[6,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 8
[6,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 6
[6,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 7
[6,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 7
[5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 5
[5,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 9
[5,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 7
[5,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 7
[5,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 5
[5,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 6
[5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => 5
[5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 5
[5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 5
[5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 6
[5,4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 5
[5,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 5
[5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 5
[5,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 5
[5,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 6
[5,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 6
[5,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 7
[5,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 5
[5,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 5
[4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 6
[4,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 5
[4,4,3,3] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 4
[4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 4
[4,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 4
[4,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 4
[4,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 4
[4,4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 5
[4,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 5
[4,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 4
[4,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 4
[4,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 4
[4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 4
[4,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 4
[4,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 4
[4,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 4
[3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 3
[3,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 3
[3,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3
[3,3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 3
[3,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 3
[3,3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 3
[3,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 3
[7,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 9
[7,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 8
[6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 6
[6,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 10
[6,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 8
[6,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 8
[6,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 6
[6,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 7
[6,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 10
[6,4,3,1,1] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 10
[6,4,2,2,1] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 10
[6,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 10
[6,4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 9
[6,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 6
[6,3,3,2,1] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 9
[6,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 8
[6,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 7
[6,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 8
[6,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 8
[6,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 6
[6,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 7
[5,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 6
[5,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 8
[5,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 8
[5,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 7
[5,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 6
[5,5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 5
[5,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 7
[5,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 6
[5,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 5
[5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[5,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 5
[5,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 5
[5,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 5
[5,4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 6
[5,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 6
[5,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 5
[5,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 5
[5,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 5
[5,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 6
[5,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 6
[5,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 5
[5,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 5
[4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 4
[4,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 6
[4,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 4
[4,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 5
[4,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 4
[4,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 4
[4,4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 4
[4,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 4
[4,4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 4
[4,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 4
[4,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 4
[4,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 4
[4,3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 4
[4,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 4
[4,3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 4
[4,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 4
[3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[3,3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 3
[3,3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 3
[3,3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 3
[3,3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 3
[7,4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 10
[7,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 9
[7,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 8
[6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 7
[6,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 9
[6,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 9
[6,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 8
[6,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 7
[6,5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 6
[6,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 8
[6,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 7
[6,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 7
[6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 10
[6,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 9
[6,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 8
[6,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 9
[6,4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 10
[6,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 7
[6,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 7
[6,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 8
[6,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 8
[6,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 7
[6,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 8
[6,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 6
[6,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 6
[5,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 7
[5,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 6
[5,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 5
[5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 8
[5,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 7
[5,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 5
[5,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 6
[5,5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 6
[5,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 5
[5,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 7
[5,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 5
[5,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 6
[5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 5
[5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 5
[5,4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 5
[5,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 5
[5,4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 5
[5,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 5
[5,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 5
[5,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 5
[5,3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 5
[5,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 6
[5,3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 6
[5,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 5
[4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 5
[4,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 4
[4,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 5
[4,4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 4
[4,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 4
[4,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 4
[4,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 4
[4,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 4
[4,4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 4
[4,4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 4
[4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4
[4,3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 4
[4,3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 4
[4,3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 4
[4,3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 4
[3,3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 3
[3,3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 3
[3,3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 3
[7,5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11
[7,4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 11
[7,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 9
[7,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 9
[7,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[7,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 8
[6,6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 6
[6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 8
[6,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 7
[6,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 6
[6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 9
[6,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 8
[6,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 6
[6,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 7
[6,5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 7
[6,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 6
[6,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 8
[6,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 6
[6,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 8
[6,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 8
[6,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 9
[6,4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 9
[6,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 8
[6,4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 9
[6,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 6
[6,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 6
[6,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 7
[6,3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 8
[6,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 7
[6,3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 7
[6,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 6
[5,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 5
[5,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 7
[5,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 5
[5,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 6
[5,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 6
[5,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 7
[5,5,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 7
[5,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 5
[5,5,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 6
[5,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 6
[5,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 5
[5,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 6
[5,4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 5
[5,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 5
[5,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 5
[5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 5
[5,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 5
[5,4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 5
[5,4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 5
[5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[5,3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 5
[5,3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 5
[5,3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 5
[5,3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 6
[4,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 4
[4,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 4
[4,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 4
[4,4,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 5
[4,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4
[4,4,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 4
[4,4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 4
[4,4,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 4
[4,4,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 4
[4,3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 4
[4,3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 4
[4,3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 4
[3,3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[3,3,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
[3,3,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 3
[6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 6
[5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 5
[6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 6
[5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4
[6,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 6
[5,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 5
[6,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 7
[5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[6,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 6
[6,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 6
[5,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 5
[6,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 6
[5,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 5
[6,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 7
[5,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 6
[6,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 8
[6,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 6
[6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 6
[5,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 5
[6,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 6
[5,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 5
[6,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 6
[5,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 5
[6,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 7
[6,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 7
[5,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 6
[6,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 7
[6,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 8
[6,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 6
[6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6
[5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 5
[6,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 6
[5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 5
[6,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 6
[5,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 5
[6,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 7
[6,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 6
[5,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 5
[6,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 6
[6,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 7
[6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 7
[5,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 6
[6,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 7
[6,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 7
[6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 8
[6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 6
[7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[6,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6
[7,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 7
[6,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[5,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 5
[7,6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 7
[6,6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 6
[7,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 8
[6,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 6
[5,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 5
[7,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 7
[6,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 6
[5,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 5
[4,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
[6,6,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 6
[6,5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 6
[6,5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 6
[6,4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 7
[5,4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 5
[6,3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 6
[3,3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[6,6,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 6
[6,5,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 6
[6,5,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 6
[6,5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 6
[5,5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 5
[7,6,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 7
[6,5,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 6
[6,5,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 7
[6,4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 8
[5,4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 5
[6,5,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 6
[7,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 7
[7,6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 7
[6,6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 6
[6,5,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 6
[6,6,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 7
[6,5,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 7
[4,4,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 5
[6,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 6
[5,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 5
[7,6,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 7
[6,5,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 6
[6,5,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 6
[7,6,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 8
[5,5,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 6
[7,5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 12
[6,5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 7
[7,6,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 9
[7,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 10
[6,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 9
[6,5,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 6
[6,6,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 7
[7,6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 7
[7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[6,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6
[7,5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 7
[6,5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[5,5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 5
[7,6,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 7
[6,5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 6
[6,5,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 6
[5,4,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => 5
[4,3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[6,5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 6
[4,4,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 4
[7,6,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 7
[6,5,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 6
[5,4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 5
[6,6,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 6
[7,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 8
[6,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 7
[6,5,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 7
[4,4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 5
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
click to show known generating functions       
Description
The sum of the semi-lengths of tunnels before a valley of a Dyck path.
For each valley $v$ in a Dyck path $D$ there is a corresponding tunnel, which
is the factor $T_v = s_i\dots s_j$ of $D$ where $s_i$ is the step after the first intersection of $D$ with the line $y = ht(v)$ to the left of $s_j$. This statistic is
$$ \sum_v (j_v-i_v)/2. $$
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.