Processing math: 100%

Identifier
Values
[1,0,1,0,1,0] => [2,1] => [2,1] => [1,0,1,1,0,0] => 1
[1,0,1,1,0,0] => [1,1] => [2] => [1,0,1,0] => 2
[1,1,0,0,1,0] => [2] => [1,1] => [1,1,0,0] => 1
[1,0,1,0,1,0,1,0] => [3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 1
[1,0,1,0,1,1,0,0] => [2,2,1] => [3,2] => [1,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,0,1,0] => [3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,1,0,0] => [2,1,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,0] => [1,1,1] => [3] => [1,0,1,0,1,0] => 3
[1,1,0,0,1,0,1,0] => [3,2] => [2,2,1] => [1,1,1,0,0,1,0,0] => 1
[1,1,0,0,1,1,0,0] => [2,2] => [2,2] => [1,1,1,0,0,0] => 2
[1,1,0,1,0,0,1,0] => [3,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1
[1,1,0,1,0,1,0,0] => [2,1] => [2,1] => [1,0,1,1,0,0] => 1
[1,1,0,1,1,0,0,0] => [1,1] => [2] => [1,0,1,0] => 2
[1,1,1,0,0,0,1,0] => [3] => [1,1,1] => [1,1,0,1,0,0] => 1
[1,1,1,0,0,1,0,0] => [2] => [1,1] => [1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0] => [4,3,2,1] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[1,0,1,0,1,1,0,0,1,0] => [4,2,2,1] => [4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 3
[1,0,1,1,0,0,1,0,1,0] => [4,3,1,1] => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 1
[1,0,1,1,0,0,1,1,0,0] => [3,3,1,1] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,0,1,1,0,1,0,0,1,0] => [4,2,1,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,0] => [2,2,1,1] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => [4] => [1,0,1,0,1,0,1,0] => 4
[1,1,0,0,1,0,1,0,1,0] => [4,3,2] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,0,0,1,0,1,1,0,0] => [3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,0] => [4,2,2] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,1,0,0] => [3,2,2] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,0] => [2,2,2] => [3,3] => [1,1,1,0,1,0,0,0] => 3
[1,1,0,1,0,0,1,0,1,0] => [4,3,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 1
[1,1,0,1,0,0,1,1,0,0] => [3,3,1] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,0,1,0,1,0,0,1,0] => [4,2,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,0] => [3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,0,0] => [2,2,1] => [3,2] => [1,0,1,1,1,0,0,0] => 2
[1,1,0,1,1,0,0,0,1,0] => [4,1,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,1,0,0] => [3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,0,0] => [2,1,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,0] => [1,1,1] => [3] => [1,0,1,0,1,0] => 3
[1,1,1,0,0,0,1,0,1,0] => [4,3] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 1
[1,1,1,0,0,0,1,1,0,0] => [3,3] => [2,2,2] => [1,1,1,1,0,0,0,0] => 2
[1,1,1,0,0,1,0,0,1,0] => [4,2] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,0] => [3,2] => [2,2,1] => [1,1,1,0,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,0,0] => [2,2] => [2,2] => [1,1,1,0,0,0] => 2
[1,1,1,0,1,0,0,0,1,0] => [4,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,0] => [3,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,0] => [2,1] => [2,1] => [1,0,1,1,0,0] => 1
[1,1,1,0,1,1,0,0,0,0] => [1,1] => [2] => [1,0,1,0] => 2
[1,1,1,1,0,0,0,0,1,0] => [4] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,0] => [3] => [1,1,1] => [1,1,0,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,0] => [2] => [1,1] => [1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0] => [4,4,3,2,1] => [5,4,3,2] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,0] => [4,3,3,2,1] => [5,4,3,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [3,3,3,2,1] => [5,4,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 3
[1,0,1,0,1,1,0,0,1,1,0,0] => [4,4,2,2,1] => [5,4,2,2] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,0] => [4,3,2,2,1] => [5,4,2,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => [3,3,2,2,1] => [5,4,2] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,0,0] => [4,2,2,2,1] => [5,4,1,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => [3,2,2,2,1] => [5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,1,0,0,1,0,1,1,0,0] => [4,4,3,1,1] => [5,3,3,2] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => [4,3,3,1,1] => [5,3,3,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [3,3,3,1,1] => [5,3,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,0,1,1,0,1,0,0,1,1,0,0] => [4,4,2,1,1] => [5,3,2,2] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,1] => [5,3,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,0] => [3,3,2,1,1] => [5,3,2] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2
[1,0,1,1,0,1,1,0,0,1,0,0] => [4,2,2,1,1] => [5,3,1,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,0] => [3,2,2,1,1] => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,2,2,1,1] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,0,1,1,1,0,0,0,1,1,0,0] => [4,4,1,1,1] => [5,2,2,2] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,0,1,1,1,0,0,1,0,1,0,0] => [4,3,1,1,1] => [5,2,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => [3,3,1,1,1] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,0,0] => [4,2,1,1,1] => [5,2,1,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => [5] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,0,1,0,1,0,1,1,0,0] => [4,4,3,2] => [4,4,3,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => [4,3,3,2] => [4,4,3,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [3,3,3,2] => [4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => [4,4,2,2] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,0] => [4,3,2,2] => [4,4,2,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => [3,3,2,2] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,0] => [4,2,2,2] => [4,4,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,0] => [3,2,2,2] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,2,2] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 4
[1,1,0,1,0,0,1,0,1,0,1,0] => [5,4,3,1] => [4,3,3,2,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [4,4,3,1] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,3,1] => [4,3,3,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [4,3,3,1] => [4,3,3,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,3,3,1] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,0,1,0,1,0,0,1,0,1,0] => [5,4,2,1] => [4,3,2,2,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,0] => [4,4,2,1] => [4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => [5,3,2,1] => [4,3,2,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 1
>>> Load all 726 entries. <<<
[1,1,0,1,0,1,0,1,1,0,0,0] => [3,3,2,1] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,2,2,1] => [4,3,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => [4,2,2,1] => [4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,0] => [3,2,2,1] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,2,2,1] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 3
[1,1,0,1,1,0,0,0,1,0,1,0] => [5,4,1,1] => [4,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,0] => [4,4,1,1] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,0,1,1,0,0,1,0,0,1,0] => [5,3,1,1] => [4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => [4,3,1,1] => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,0] => [3,3,1,1] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,0,1,1,0,1,0,0,0,1,0] => [5,2,1,1] => [4,2,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,0] => [4,2,1,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,0] => [3,2,1,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,1,1] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,1,1,1,0,0,0,0,1,0] => [5,1,1,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,0] => [4,1,1,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,1,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1] => [4] => [1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,0,1,0,1,0] => [5,4,3] => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,0] => [4,4,3] => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => [3,3,3,1,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,0] => [4,3,3] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,0,0,1,0,0,1,0,1,0] => [5,4,2] => [3,3,2,2,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,0] => [4,4,2] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,1,0,0,1,0,1,0,0,1,0] => [5,3,2] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => [5,2,2] => [3,3,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,0] => [4,2,2] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,2] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 1
[1,1,1,0,0,1,1,1,0,0,0,0] => [2,2,2] => [3,3] => [1,1,1,0,1,0,0,0] => 3
[1,1,1,0,1,0,0,0,1,0,1,0] => [5,4,1] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,4,1] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,0,0,1,0,0,1,0] => [5,3,1] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,3,1] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1] => [3,2] => [1,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,1,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1] => [3] => [1,0,1,0,1,0] => 3
[1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,0,0,1,0] => [5,3] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,0] => [3,3] => [2,2,2] => [1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,2] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,2] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,0,0] => [3,2] => [2,2,1] => [1,1,1,0,0,1,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,0,0] => [2,2] => [2,2] => [1,1,1,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,0] => [3,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => [2,1] => [1,0,1,1,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,1] => [2] => [1,0,1,0] => 2
[1,1,1,1,1,0,0,0,0,0,1,0] => [5] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [4] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => [3] => [1,1,1] => [1,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => [2] => [1,1] => [1,1,0,0] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2,1] => [6,5,4] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 4
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2,1] => [6,5,3] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 3
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2,1] => [6,5,2] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2,1] => [6,5,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2,1] => [6,5] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 5
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => [6,4,4] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 4
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1,1] => [6,4,3] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 3
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => [6,4,2] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1,1] => [6,4,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => [6,4] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => [6,3,3] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1,1] => [6,3,2] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => [6,3,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => [6,3] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1,1] => [6,2,2] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1] => [6,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1,1] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2] => [5,5,4] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 4
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => [5,5,3] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 3
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => [5,5,2] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2] => [5,5,1] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 5
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1] => [5,4,4,3] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 3
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3,1] => [5,4,4,2] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3,1] => [5,4,4,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1] => [5,4,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 4
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2,1] => [5,4,3,3] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 3
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1] => [5,4,3,2] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 2
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1] => [5,4,3,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1] => [5,4,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 3
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1] => [5,4,2,2] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1] => [5,4,2,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => [5,4,2] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1] => [5,4,1,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1] => [5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1] => [5,3,3,3] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1] => [5,3,3,2] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1] => [5,3,3,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => [5,3,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1] => [5,3,2,2] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1] => [5,3,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1] => [5,3,2] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1] => [5,3,1,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 1
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1] => [5,2,2,2] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1] => [5,2,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1] => [5,2,1,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => [5] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3] => [4,4,4,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 3
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => [4,4,4,2] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3] => [4,4,4,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => [4,4,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 4
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2] => [4,4,3,3] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 3
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2] => [4,4,3,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2] => [4,4,3,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2] => [4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2] => [4,4,2,2] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2] => [4,4,2,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2] => [4,4,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1] => [4,3,3,3,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [5,4,4,1] => [4,3,3,3,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1] => [4,3,3,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [5,5,3,1] => [4,3,3,2,2] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1] => [4,3,3,2,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1] => [4,3,3,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1] => [4,3,3,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,5,2,1] => [4,3,2,2,2] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1] => [4,3,2,2,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1] => [4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1] => [4,3,2,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1] => [4,3,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1] => [4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1] => [4,2,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1] => [4,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1] => [4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1] => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1] => [4,2,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1] => [4] => [1,0,1,0,1,0,1,0] => 4
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,5,4] => [3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,4,4] => [3,3,3,3,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [5,5,3] => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [5,4,3] => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,4,3] => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [5,3,3] => [3,3,3,1,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,3] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,3,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,5,2] => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,4,2] => [3,3,2,2,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,4,2] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [5,3,2] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,2] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [5,2,2] => [3,3,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,2] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,2,2] => [3,3] => [1,1,1,0,1,0,0,0] => 3
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [6,5,1] => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,5,1] => [3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [6,4,1] => [3,2,2,2,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,4,1] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,4,1] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,1] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,3,1] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,3,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [3,3,1] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,2,1] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,2,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,2,1] => [3,2] => [1,0,1,1,1,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,1,1] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,1,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,1,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1] => [3] => [1,0,1,0,1,0] => 3
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => [2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,4] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,4] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,3] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,3] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [4,3] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,3] => [2,2,2] => [1,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,2] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [4,2] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,2] => [2,2,1] => [1,1,1,0,0,1,0,0] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,2] => [2,2] => [1,1,1,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [4,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => [2,1] => [1,0,1,1,0,0] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1] => [2] => [1,0,1,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [4] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => [1,1,1] => [1,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => [1,1] => [1,1,0,0] => 1
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => [7,6] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 6
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => [7,5] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 5
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1,1] => [7,4] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => [7,3] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => [7,2] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => [7,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => [7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 6
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1] => [6,5,5] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 5
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1] => [6,5,4] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 4
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1] => [6,5,3] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 3
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1] => [6,5,2] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 2
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1] => [6,5,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1] => [6,5] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 5
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1] => [6,4,4] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 4
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1] => [6,4,3] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 3
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => [6,4,2] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1] => [6,4,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1] => [6,4] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1] => [6,3,3] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1] => [6,3,2] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1] => [6,3,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 1
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1] => [6,3] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1] => [6,2,2] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1] => [6,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => [5,5,5] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 5
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2] => [5,5,4] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 4
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2] => [5,5,3] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 3
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2] => [5,5,2] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 2
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2] => [5,5,1] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 5
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,1] => [5,4,4,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 4
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1] => [5,4,4,3] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 3
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1] => [5,4,4,2] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 2
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1] => [5,4,4,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 1
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1] => [5,4,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 4
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1] => [5,4,3,3] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1] => [5,4,3,2] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 2
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1] => [5,4,3,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1] => [5,4,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 3
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1] => [5,4,2,2] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1] => [5,4,2,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1] => [5,4,2] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1] => [5,4,1,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1] => [5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1] => [5,3,3,3] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1] => [5,3,3,2] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1] => [5,3,3,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1] => [5,3,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1] => [5,3,2,2] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1] => [5,3,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1] => [5,3,2] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1] => [5,3,1,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 1
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1] => [5,2,2,2] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1] => [5,2,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1] => [5,2,1,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1] => [5] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => [4,4,4,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 4
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3] => [4,4,4,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 3
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3] => [4,4,4,2] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3] => [4,4,4,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 1
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3] => [4,4,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 4
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2] => [4,4,3,3] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 3
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2] => [4,4,3,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2] => [4,4,3,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2] => [4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2] => [4,4,2,2] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2] => [4,4,2,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2] => [4,4,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1] => [4,3,3,3,3] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 3
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1] => [4,3,3,3,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1] => [4,3,3,3,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1] => [4,3,3,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1] => [4,3,3,2,2] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1] => [4,3,3,2,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1] => [4,3,3,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1] => [4,3,3,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1] => [4,3,2,2,2] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1] => [4,3,2,2,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1] => [4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1] => [4,3,2,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1] => [4,3,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1] => [4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1] => [4,2,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1] => [4,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1] => [4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1] => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1] => [4,2,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1] => [4] => [1,0,1,0,1,0,1,0] => 4
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => [3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,5,4] => [3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,4] => [3,3,3,3,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [4,4,4] => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,5,3] => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3] => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [4,4,3] => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,3,3] => [3,3,3,1,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [4,3,3] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,5,2] => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [5,4,2] => [3,3,2,2,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [4,4,2] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,3,2] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [4,3,2] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,2,2] => [3,3,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [4,2,2] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [3,2,2] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 1
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [2,2,2] => [3,3] => [1,1,1,0,1,0,0,0] => 3
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,6,1] => [3,2,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [6,5,1] => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [5,5,1] => [3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [6,4,1] => [3,2,2,2,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,4,1] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [4,4,1] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [6,3,1] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,3,1] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [4,3,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [3,3,1] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [6,2,1] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,2,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [4,2,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [2,2,1] => [3,2] => [1,0,1,1,1,0,0,0] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [6,1,1] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,1,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [4,1,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,1,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1] => [3] => [1,0,1,0,1,0] => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => [2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5] => [2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [5,5] => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,4] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [5,4] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [4,4] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,3] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [5,3] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [4,3] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [3,3] => [2,2,2] => [1,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,2] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [5,2] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [4,2] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => [2,2,1] => [1,1,1,0,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,2] => [2,2] => [1,1,1,0,0,0] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [5,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => [2,1] => [1,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1] => [2] => [1,0,1,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => [1,1,1] => [1,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => [1,1] => [1,1,0,0] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => [8] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 8
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => [7,6] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 6
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => [7,5] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 5
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => [7,3] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => [7,2] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => [7,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => [7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 6
[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,1] => [6,5,5] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 5
[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,2,1] => [6,5,4] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 4
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,1] => [6,5] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 5
[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1,1] => [6,4] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2,1,1,1] => [6,3,2] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2
[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1,1] => [6,3] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1,1] => [6,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1,1] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1,1,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3] => [5,5,5] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 5
[1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,2] => [5,5,1] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 5
[1,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,4,4,4,1] => [5,4,4,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 4
[1,1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,1] => [5,4,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 4
[1,1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,4,4,2,1] => [5,4,3,3] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 3
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,4,3,2,1] => [5,4,3,2] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,3,3,2,1] => [5,4,3,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [3,3,3,2,1] => [5,4,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,2,1] => [5,4,2,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,1] => [5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0] => [4,4,3,1,1] => [5,3,3,2] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,1] => [5,3,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1,1] => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1,1,1] => [5,2,2,2] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1,1] => [5,2,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 1
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1,1] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1] => [5] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [4,4,4,4] => [4,4,4,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 4
[1,1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0,0] => [4,4,4,3] => [4,4,4,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,3,3] => [4,4,4,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0] => [4,4,3,2] => [4,4,3,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 2
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [4,4,2,2] => [4,4,2,2] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2,2] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,0] => [5,5,5,1] => [4,3,3,3,3] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 3
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3,1] => [4,3,3,2,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3,1] => [4,3,3,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3,1] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1] => [4,3,2,2,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0] => [4,4,2,1] => [4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1] => [4,3,2,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2,1] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2,1] => [4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1] => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 1
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1] => [4] => [1,0,1,0,1,0,1,0] => 4
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => [5,5,5] => [3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 3
[1,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0,0] => [5,4,4] => [3,3,3,3,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0] => [4,4,4] => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3] => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0] => [4,4,3] => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2] => [3,3,2,2,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0] => [4,4,2] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2] => [3,3] => [1,1,1,0,1,0,0,0] => 3
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0] => [6,6,1] => [3,2,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1] => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 1
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1] => [3,2] => [1,0,1,1,1,0,0,0] => 2
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1] => [3] => [1,0,1,0,1,0] => 3
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [6,6] => [2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [5,5] => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0] => [4,4] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [4,3] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [3,3] => [2,2,2] => [1,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [4,2] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [3,2] => [2,2,1] => [1,1,1,0,0,1,0,0] => 1
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [2,2] => [2,2] => [1,1,1,0,0,0] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [7,1] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0] => [6,1] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0] => [5,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0] => [4,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [3,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => [2,1] => [1,0,1,1,0,0] => 1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1] => [2] => [1,0,1,0] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [6] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [5] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [4] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [3] => [1,1,1] => [1,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2] => [1,1] => [1,1,0,0] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [4,4,3,2,1] => [5,4,3,2] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [1,1] => [2] => [1,0,1,0] => 2
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [2] => [1,1] => [1,1,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1] => [2] => [1,0,1,0] => 2
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1] => [3,2] => [1,0,1,1,1,0,0,0] => 2
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [3,2] => [2,2,1] => [1,1,1,0,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [2] => [1,1] => [1,1,0,0] => 1
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => [8] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 8
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1] => [3] => [1,0,1,0,1,0] => 3
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1] => [4] => [1,0,1,0,1,0,1,0] => 4
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1] => [5] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => [7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [6] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [5] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [4] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [3] => [1,1,1] => [1,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [2,2] => [2,2] => [1,1,1,0,0,0] => 2
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0] => [3,3] => [2,2,2] => [1,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [3,3,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0] => [4,4,4] => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [4,4,4,4] => [4,4,4,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 4
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [3,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0] => [6,6] => [2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1,1,1,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [2,1] => [2,1] => [1,0,1,1,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1] => [2,1] => [1,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0] => [3] => [1,1,1] => [1,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [3,3,3,3,2,1] => [6,5,4] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 4
[1,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => [7,6] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 6
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0] => [5,3,2,1] => [4,3,2,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0] => [5,4,2,1] => [4,3,2,2,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,1] => [4,3,3,2,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0] => [3,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0] => [4,2] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,1] => [6,5] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 5
[1,1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [4,3,3,2,1] => [5,4,3,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,2,1] => [5,4,2,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1,1] => [5,3,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0,0] => [6,5,1] => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0] => [5,4,1] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0] => [4,3,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2] => [3,3] => [1,1,1,0,1,0,0,0] => 3
[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 6
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0] => [7,1] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0] => [6,1] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0] => [5,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0] => [4,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => [7,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,1] => [3,1] => [1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0] => [3,2,2,1] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1] => [3] => [1,0,1,0,1,0] => 3
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1,1] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0] => [2,2] => [2,2] => [1,1,1,0,0,0] => 2
[1,1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0] => [3,3] => [2,2,2] => [1,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0] => [3] => [1,1,1] => [1,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,1] => [2] => [1,0,1,0] => 2
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0,0] => [7,1] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0,0] => [6,1] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0,0] => [5,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0] => [4,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0] => [5,5] => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0] => [4,4] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0] => [5,3,1] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,1] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0] => [3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 2
search for individual values
searching the database for the individual values of this statistic
Description
The minimal height of a column in the parallelogram polyomino associated with the Dyck path.
Map
parallelogram polyomino
Description
Return the Dyck path corresponding to the partition interpreted as a parallogram polyomino.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
Map
conjugate
Description
Return the conjugate partition of the partition.
The conjugate partition of the partition λ of n is the partition λ∗ whose Ferrers diagram is obtained from the diagram of λ by interchanging rows with columns.
This is also called the associated partition or the transpose in the literature.
Map
to partition
Description
The cut-out partition of a Dyck path.
The partition λ associated to a Dyck path is defined to be the complementary partition inside the staircase partition (n−1,…,2,1) when cutting out D considered as a path from (0,0) to (n,n).
In other words, λi is the number of down-steps before the (n+1−i)-th up-step of D.
This map is a bijection between Dyck paths of size n and partitions inside the staircase partition (n−1,…,2,1).