Processing math: 100%

Identifier
Values
[1,0,1,0] => [1] => [1,0,1,0] => 1
[1,0,1,0,1,0] => [2,1] => [1,0,1,0,1,0] => 1
[1,0,1,1,0,0] => [1,1] => [1,0,1,1,0,0] => 1
[1,1,0,0,1,0] => [2] => [1,1,0,0,1,0] => 1
[1,1,0,1,0,0] => [1] => [1,0,1,0] => 1
[1,0,1,0,1,0,1,0] => [3,2,1] => [1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,0] => [2,2,1] => [1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,0] => [3,1,1] => [1,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,0] => [1,1,1] => [1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,0] => [3,2] => [1,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,0] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,0] => [3,1] => [1,1,0,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,0] => [2,1] => [1,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,0] => [1,1] => [1,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,0] => [3] => [1,1,1,0,0,0,1,0] => 1
[1,1,1,0,0,1,0,0] => [2] => [1,1,0,0,1,0] => 1
[1,1,1,0,1,0,0,0] => [1] => [1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,0] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,0] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,0] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,0] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,0] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,0,1,0] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,1,0,0] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,0] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,0] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,0] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,0] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,0] => [3,2,1] => [1,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,0,0,0] => [2,2,1] => [1,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,0,0,0,1,0] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 2
[1,1,0,1,1,0,0,1,0,0] => [3,1,1] => [1,0,1,1,0,0,1,0] => 2
[1,1,0,1,1,0,1,0,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,0] => [1,1,1] => [1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,0] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,0] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,0,1,0] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,0,0] => [3,2] => [1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,1,0,0,0] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,0,1,0] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,0] => [3,1] => [1,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,0] => [2,1] => [1,0,1,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,0] => [1,1] => [1,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,0,1,0] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,0] => [3] => [1,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,0,0] => [2] => [1,1,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,0] => [1] => [1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0] => [5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,0] => [4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,0] => [5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,0] => [5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,0,1,1,0,1,0,0] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,0] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,0] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,0] => [5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,0] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,0] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,0] => [5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,0] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,0,1,0] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
>>> Load all 604 entries. <<<
[1,1,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,0] => [5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,0] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,0] => [5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,0] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,0] => [5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,0] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,0] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,0] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,0] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,0] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,0] => [5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,0] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,0,1,0,0,1,0] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,0] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,1,0,0,0,1,0] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,0] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,0] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,0] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 2
[1,1,0,1,1,1,0,0,0,1,0,0] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 2
[1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,0] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,0,1,1,0,1,0,0] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,0] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,0] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,0] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,1,0,0,0,0] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,0] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1] => [1,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1] => [1,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 2
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,1,1] => [1,0,1,1,0,0,1,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1] => [1,0,1,1,1,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,0] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,0] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,1,0,0,0] => [3,2] => [1,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,1,1,0,0,0,0] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,0] => [3,1] => [1,1,0,1,0,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => [1,0,1,0,1,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,1] => [1,0,1,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => [3] => [1,1,1,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => [2] => [1,1,0,0,1,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => [1] => [1,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 1
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => 2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => [1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,2,1] => [1,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [3,1,1] => [1,0,1,1,0,0,1,0] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1] => [1,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,2] => [1,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,1] => [1,1,0,1,0,0,1,0] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => [1,0,1,0,1,0] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1] => [1,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => [1,1,1,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => [1,1,0,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1] => [1,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => 1
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 1
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 1
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => 1
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 1
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 1
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 1
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 1
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 1
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 2
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 2
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => 1
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 1
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => [1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [2,2,1] => [1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 2
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 2
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [3,1,1] => [1,0,1,1,0,0,1,0] => 2
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1] => [1,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => [1,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => [1,1,0,1,0,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => [1,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1] => [1,0,1,1,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => [1,1,1,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => [1,1,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1] => [1,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0,0] => [5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 1
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 2
[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 1
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 1
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0] => [4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 1
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0] => [5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0] => [4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 2
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 2
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0] => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1] => [1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1] => [1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 2
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1] => [1,0,1,1,0,0,1,0] => 2
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1] => [1,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [3,2] => [1,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [3,1] => [1,1,0,1,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => [1,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1] => [1,0,1,1,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [3] => [1,1,1,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2] => [1,1,0,0,1,0] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1] => [1,0,1,0] => 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] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [1,1] => [1,0,1,1,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [2] => [1,1,0,0,1,0] => 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] => [1,0,1,1,0,0] => 1
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1] => [1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [3,2] => [1,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [2] => [1,1,0,0,1,0] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1] => [1,0,1,0] => 1
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1] => [1,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 1
[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] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [1] => [1,0,1,0] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [3] => [1,1,1,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1] => [1,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [3,1] => [1,1,0,1,0,0,1,0] => 1
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [2,1] => [1,0,1,0,1,0] => 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] => [1,0,1,0,1,0] => 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] => [1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1] => [1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0] => [3] => [1,1,1,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0] => [5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => 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] => [1,1,0,1,0,1,0,0,1,0,1,0] => 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] => [1,1,0,1,0,0,1,0,1,0,1,0] => 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] => [1,1,0,1,0,0,1,0] => 1
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 1
[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] => [1,0,1,0,1,0,1,1,0,1,0,0] => 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] => [1,0,1,0,1,1,0,1,0,1,0,0] => 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] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 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] => [1,0,1,1,1,0,1,0,0,0] => 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] => [1,0,1,1,1,1,0,1,0,0,0,0] => 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] => [1,0,1,1,0,1,0,0] => 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] => [1,0,1,0,1,1,0,1,0,0] => 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] => [1,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1] => [1,0,1,1,0,0,1,0] => 2
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 1
[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 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] => [1,1,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,0,0,0,1,0] => 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] => [1,0,1,1,0,0] => 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] => [1,1,1,1,0,1,0,0,0,0,1,0] => 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] => [1,1,1,0,1,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 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] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 1
search for individual values
searching the database for the individual values of this statistic
Description
Number of simple modules with projective dimension equal to the global dimension of the Nakayama algebra corresponding to the Dyck path.
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).
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.