Identifier
Values
[1,0,1,0,1,0] => [2,1] => [1,1,1] => [1,1,0,1,0,0] => 0
[1,0,1,1,0,0] => [1,1] => [2] => [1,0,1,0] => 0
[1,1,0,0,1,0] => [2] => [1,1] => [1,1,0,0] => 0
[1,0,1,0,1,0,1,0] => [3,2,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,0,1,0,1,1,0,0] => [2,2,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,1,0,0,1,0] => [3,1,1] => [3,2] => [1,0,1,1,1,0,0,0] => 0
[1,0,1,1,0,1,0,0] => [2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 0
[1,0,1,1,1,0,0,0] => [1,1,1] => [2,1] => [1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,0] => [3,2] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,0,1,1,0,0] => [2,2] => [4] => [1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,0,1,0] => [3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,0] => [2,1] => [1,1,1] => [1,1,0,1,0,0] => 0
[1,1,0,1,1,0,0,0] => [1,1] => [2] => [1,0,1,0] => 0
[1,1,1,0,0,0,1,0] => [3] => [3] => [1,0,1,0,1,0] => 0
[1,1,1,0,0,1,0,0] => [2] => [1,1] => [1,1,0,0] => 0
[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] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,0,1,1,0,0,1,0,1,0] => [4,3,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 0
[1,0,1,1,0,0,1,1,0,0] => [3,3,1,1] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,0,1,1,0,1,0,0,1,0] => [4,2,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 0
[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] => 0
[1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 0
[1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 0
[1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => [2,2] => [1,1,1,0,0,0] => 0
[1,1,0,0,1,0,1,1,0,0] => [3,3,2] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,0,1,1,0,0,1,0] => [4,2,2] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,0,1,1,0,1,0,0] => [3,2,2] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,0] => [2,2,2] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,0] => [4,3,1] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,0] => [3,3,1] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,0] => [4,2,1] => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,0] => [3,2,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,1,1,0,0,0] => [2,2,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,0,1,0] => [4,1,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,1,1,0,0,1,0,0] => [3,1,1] => [3,2] => [1,0,1,1,1,0,0,0] => 0
[1,1,0,1,1,0,1,0,0,0] => [2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 0
[1,1,0,1,1,1,0,0,0,0] => [1,1,1] => [2,1] => [1,0,1,1,0,0] => 0
[1,1,1,0,0,0,1,0,1,0] => [4,3] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,0,0,1,1,0,0] => [3,3] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,0,0,1,0] => [4,2] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,0,1,0,1,0,0] => [3,2] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,0,0,1,1,0,0,0] => [2,2] => [4] => [1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,0,1,0] => [4,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,0,0,1,0,0] => [3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 0
[1,1,1,0,1,0,1,0,0,0] => [2,1] => [1,1,1] => [1,1,0,1,0,0] => 0
[1,1,1,0,1,1,0,0,0,0] => [1,1] => [2] => [1,0,1,0] => 0
[1,1,1,1,0,0,0,0,1,0] => [4] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,0,0,1,0,0] => [3] => [3] => [1,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,0] => [2] => [1,1] => [1,1,0,0] => 0
[1,0,1,0,1,1,0,1,0,0,1,0] => [5,3,2,2,1] => [5,4,3,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => [3,3,2,2,1] => [6,4,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,0] => [3,2,2,2,1] => [4,3,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => [5,3,3,1,1] => [6,5,2] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,0] => [3,3,3,1,1] => [6,3,2] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,0] => [5,2,2,1,1] => [5,4,2] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,0,1,1,0,1,1,0,1,0,0,0] => [3,2,2,1,1] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,2,2,1,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 0
[1,0,1,1,1,0,0,1,0,0,1,0] => [5,3,1,1,1] => [5,3,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => [3,3,1,1,1] => [6,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 0
[1,0,1,1,1,1,0,0,0,0,1,0] => [5,1,1,1,1] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 0
[1,1,0,0,1,1,0,1,0,0,1,0] => [5,3,2,2] => [5,4,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => [3,3,2,2] => [6,4] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 2
[1,1,0,0,1,1,1,0,0,0,1,0] => [5,2,2,2] => [5,4,1,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => [3,2,2,2] => [4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 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] => 2
[1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,3,1] => [6,5,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 3
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,3,3,1] => [6,3,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,2,2,1] => [5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 2
[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] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,0,1,1,0,0,1,0,0,1,0] => [5,3,1,1] => [5,3,2] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => [4,3,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,0] => [3,3,1,1] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,1,0,1,1,0,1,0,0,0,1,0] => [5,2,1,1] => [5,2,1,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 0
[1,1,0,1,1,0,1,0,0,1,0,0] => [4,2,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,0] => [3,2,1,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 0
[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] => 0
[1,1,0,1,1,1,0,0,0,0,1,0] => [5,1,1,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 0
[1,1,0,1,1,1,0,0,0,1,0,0] => [4,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,1,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 0
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1] => [2,2] => [1,1,1,0,0,0] => 0
[1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => [6,5] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => [6,3] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [5,3,2] => [5,3,1,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,3,2] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,0,0,1,1,0,0,0,1,0] => [5,2,2] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [4,2,2] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,2] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,0,0,1,1,1,0,0,0,0] => [2,2,2] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,0,1,0,0,1,0,0,1,0] => [5,3,1] => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0
>>> Load all 608 entries. <<<
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,3,1] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,1,1] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,1,1] => [3,2] => [1,0,1,1,1,0,0,0] => 0
[1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 0
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1] => [2,1] => [1,0,1,1,0,0] => 0
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => [8] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,0,1,0] => [5,3] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,0,0,1,1,0,0,0] => [3,3] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,2] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,2] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,0] => [3,2] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,0,0,1,1,0,0,0,0] => [2,2] => [4] => [1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,0] => [3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => [1,1,1] => [1,1,0,1,0,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,1] => [2] => [1,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,0] => [5] => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
[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] => 0
[1,1,1,1,1,0,0,0,1,0,0,0] => [3] => [3] => [1,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,0] => [2] => [1,1] => [1,1,0,0] => 0
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2,1] => [5,4,4,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 6
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2,1] => [4,4,3,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2,1,1] => [4,3,3,3,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 3
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1,1] => [5,4,3,2] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 4
[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] => [4,3,2,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1,1] => [4,3,3,2,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1,1] => [5,4,2,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => [4,2,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1,1,1] => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 5
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1,1] => [5,3,2,2] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 4
[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] => 0
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1,1] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1,1] => [3,3,2,2,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 4
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1,1] => [5,2,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => [2,2,2] => [1,1,1,1,0,0,0,0] => 0
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [5,3,3,2,2] => [6,5,4] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 7
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => [6,4,3] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => [4,4,3,3] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2] => [5,4,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 6
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2] => [4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => [4,4,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2,1] => [4,3,3,3,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1] => [5,4,3,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => [6,4,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 2
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1] => [4,3,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1] => [6,5,2] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 3
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => [6,3,2] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 3
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1] => [5,4,2] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 0
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1,1] => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1] => [5,3,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => [6,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 4
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 0
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3] => [6,5,3] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [6,5,2,2] => [5,4,3,3] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [6,3,2,2] => [4,3,3,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2] => [5,4,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => [6,4] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2] => [4,3,3,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 0
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2] => [5,4,1,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2] => [4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 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] => 2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1] => [6,5,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1] => [6,3,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1] => [4,3,3,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1] => [5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 2
[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] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1] => [5,3,3,2] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 3
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1] => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 3
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1] => [5,3,2] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1] => [5,2,1,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 0
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 0
[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] => 0
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 0
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1] => [2,2] => [1,1,1,0,0,0] => 0
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [6,5,3] => [5,3,3,3] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [6,3,3] => [6,3,3] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [5,3,3] => [6,5] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,3,3] => [6,3] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2] => [3,3,3,1,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [5,3,2] => [5,3,1,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,3,2] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,2,2] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [5,2,2] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,2] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,2,2] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [6,5,1] => [5,3,3,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,1] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,3,1] => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,3,1] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [3,3,1] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,2,1] => [3,3,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,2,1] => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,2,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,1,1] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,1] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,1,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [3,1,1] => [3,2] => [1,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1] => [2,1] => [1,0,1,1,0,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => [5,3,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,4] => [8] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,3] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [4,3] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,3] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,2] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [4,2] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,2] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,2] => [4] => [1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [4,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => [1,1,1] => [1,1,0,1,0,0] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1] => [2] => [1,0,1,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => [3,3] => [1,1,1,0,1,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
[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] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => [3] => [1,0,1,0,1,0] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => [1,1] => [1,1,0,0] => 0
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => [4,4,4,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 6
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1,1] => [5,4,4,2] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 8
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1,1] => [4,4,3,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 4
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1,1] => [4,4,2,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1,1,1] => [4,3,3,2,2] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 5
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1,1] => [5,4,2,2] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 5
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1,1] => [4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 4
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => [4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 0
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 0
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1,1] => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 6
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1,1] => [5,2,2,2] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1,1] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 0
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 0
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,2] => [5,4,4,3] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 6
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2] => [6,4,4] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 6
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => [4,4,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 6
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1] => [5,4,4,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 6
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1] => [4,4,3,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1,1] => [4,3,3,3,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 3
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1] => [5,4,3,2] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 4
[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] => [4,3,2,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1,1] => [4,3,3,2,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1] => [5,4,2,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 2
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1] => [4,2,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 0
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1,1] => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 5
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1,1] => [5,3,2,2] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 4
[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] => 0
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 0
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1] => [3,3,2,2,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 4
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1] => [5,2,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 0
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 0
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 0
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => [2,2,2] => [1,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2] => [6,5,4] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 7
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2] => [6,4,3] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2] => [4,4,3,3] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2] => [5,4,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 6
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2] => [4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2] => [4,4,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1] => [4,3,3,3,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 0
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1] => [5,4,3,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1] => [6,4,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1] => [4,3,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1] => [6,5,2] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1] => [6,3,2] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 3
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1] => [5,4,2] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 0
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1] => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1] => [5,3,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1] => [6,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 0
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 4
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 0
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 0
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3] => [6,5,3] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 4
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2] => [5,4,3,3] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2] => [4,3,3,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2] => [5,4,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => [6,4] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2] => [4,3,3,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 0
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2] => [5,4,1,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2] => [4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 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] => 2
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1] => [6,5,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 3
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1] => [6,3,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1] => [4,3,3,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1] => [5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 2
[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] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1] => [5,3,3,2] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 3
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1] => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 3
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1] => [5,3,2] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1] => [5,2,1,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 0
[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] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 0
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 0
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1] => [2,2] => [1,1,1,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [6,5,3] => [5,3,3,3] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [7,3,3] => [7,6] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 4
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [6,3,3] => [6,3,3] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,3,3] => [6,5] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => [6,3] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [6,3,2] => [3,3,3,1,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,3,2] => [5,3,1,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [3,3,2] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [7,2,2] => [7,4] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [6,2,2] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,2,2] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [4,2,2] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [3,2,2] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [2,2,2] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [6,5,1] => [5,3,3,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [6,3,1] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,3,1] => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [4,3,1] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [3,3,1] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [6,2,1] => [3,3,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,2,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [4,2,1] => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [2,2,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,1,1] => [7,2] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [6,1,1] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,1,1] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [4,1,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [3,1,1] => [3,2] => [1,0,1,1,1,0,0,0] => 0
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1] => [2,1] => [1,0,1,1,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [7,5] => [7,5] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5] => [5,3,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [4,4] => [8] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,3] => [7,3] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [5,3] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [4,3] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [3,3] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,2] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [5,2] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [4,2] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,2] => [4] => [1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => [7,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [5,1] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 0
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => [1,1,1] => [1,1,0,1,0,0] => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1] => [2] => [1,0,1,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => [7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => [3,3] => [1,1,1,0,1,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
[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] => 0
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => [3] => [1,0,1,0,1,0] => 0
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => [1,1] => [1,1,0,0] => 0
[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] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 3
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 0
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1,1,1,1,1] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1,1,1,1] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1,1] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 3
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1] => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 5
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1] => [5,5,1] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 3
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1,1,1,1] => [3,2,2,2,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 3
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1,1,1,1,1,1,1] => [3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 5
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1,1,1,1,1,1,1] => [4,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1,1] => [5,5,2] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 3
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1,1,1,1,1] => [4,3,2,2,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 4
[1,0,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [3,1,1,1,1,1,1,1,1,1] => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 5
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1,1,1,1] => [4,4,2,2] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 5
[1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [2,2,1,1,1,1,1,1,1,1] => [4,2,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 5
[1,0,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [3,2,2,1,1,1,1,1,1] => [4,3,2,2,2] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 6
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,1,1] => [4,4,4,2] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 8
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,2,2,2] => [4,4,4,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 6
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2,2] => [4,4,4,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[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] => [4,4,4,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 6
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1,1,1,1] => [4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 4
[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] => [4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 0
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 0
[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] => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 0
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1,1,1,1] => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 6
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1,1,1,1] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[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] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 0
[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] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 0
[1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2,2,2,2] => [6,4,4] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 6
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2] => [4,4,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 6
[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1,1] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,2,2,1,1,1] => [5,4,2,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 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] => [4,2,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1,1] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 0
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1,1] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1,1,1] => [3,3,2,2,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 4
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1,1] => [5,2,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 0
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1,1,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 0
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => [2,2,2] => [1,1,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,2,2,2] => [4,4,3,3] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,2] => [4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2] => [4,4,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,2,1] => [5,4,3,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,1] => [4,3,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 2
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1,1] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1,1,1] => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1,1] => [6,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 0
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 0
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1,1] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 4
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 0
[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2,2] => [6,4] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0] => [5,2,2,2] => [5,4,1,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3,1] => [6,3,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 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] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1,1] => [5,3,3,2] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 3
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 0
[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] => 0
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 0
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 0
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1] => [2,2] => [1,1,1,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0] => [6,3,3] => [6,3,3] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3] => [6,3] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2] => [5,3,1,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0] => [7,2,2] => [7,4] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1] => [5,3,3,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 0
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 0
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1] => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1] => [3,3,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1] => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1] => [7,2] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1] => [3,2] => [1,0,1,1,1,0,0,0] => 0
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1] => [2,1] => [1,0,1,1,0,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [7,5] => [7,5] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0] => [4,4] => [8] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0] => [7,3] => [7,3] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [4,3] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [3,3] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [4,2] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [3,2] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [2,2] => [4] => [1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [7,1] => [7,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0] => [6,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0] => [5,1] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0] => [4,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 0
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => [1,1,1] => [1,1,0,1,0,0] => 0
[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] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => [7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [6] => [3,3] => [1,1,1,0,1,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [5] => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [4] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [3] => [3] => [1,0,1,0,1,0] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [3,2] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 0
[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] => 0
[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] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 3
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1] => [2,1] => [1,0,1,1,0,0] => 0
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1] => [2,2] => [1,1,1,0,0,0] => 0
[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] => [2,2,1] => [1,1,1,0,0,1,0,0] => 0
[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] => [2,2,2] => [1,1,1,1,0,0,0,0] => 0
[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] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [7] => [7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [6] => [3,3] => [1,1,1,0,1,0,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [5] => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [4] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [3] => [3] => [1,0,1,0,1,0] => 0
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1,1,1,1,1] => [3,2,2,2,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 3
[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1,1] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 3
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [2,2] => [4] => [1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0] => [3,3] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [3,3,3] => [6,3] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 0
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 0
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1,1,1,1,1,1] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1,1,1,1,1,1] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1] => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 5
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 0
[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] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 0
[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] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 0
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [5,1,1,1,1,1] => [5,2,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 0
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [2,1] => [1,1,1] => [1,1,0,1,0,0] => 0
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1] => [1,1,1] => [1,1,0,1,0,0] => 0
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0] => [3] => [3] => [1,0,1,0,1,0] => 0
[1,1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1,1,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [3,2,1,1,1,1,1,1] => [3,2,2,2,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 3
[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] => [4,4,4,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 6
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [5,1,1,1,1,1,1] => [5,2,2,2] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [6,1,1,1,1,1] => [3,3,2,2,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 4
[1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0] => [3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 0
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0] => [4,2] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0,0] => [6,5,1] => [5,3,3,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 0
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0] => [4,3,1] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 0
[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] => [4,4,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 6
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0] => [7,1] => [7,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0] => [6,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0] => [5,1] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0] => [4,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 0
[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] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 0
[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] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 0
[1,1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 0
[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
[1,1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,2,2,2,2,2,2] => [4,4,4,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 6
[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] => [2,1] => [1,0,1,1,0,0] => 0
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1] => [3,2] => [1,0,1,1,1,0,0,0] => 0
[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] => 0
[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 0
[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0] => [2,2] => [4] => [1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0] => [3,3] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0] => [3] => [3] => [1,0,1,0,1,0] => 0
[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,1] => [2] => [1,0,1,0] => 0
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0,0] => [7,1] => [7,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0,0] => [6,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 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] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0] => [4,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0] => [4,4] => [8] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0] => [5,3,1] => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 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] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0] => [3,3,2] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
search for individual values
searching the database for the individual values of this statistic
Description
The number of boxes weakly below the path and above the diagonal that lie below at least two peaks.
For example, the path $111011010000$ has three peaks in positions $03, 15, 26$. The boxes below $03$ are $01,02,\textbf{12}$, the boxes below $15$ are $\textbf{12},13,14,\textbf{23},\textbf{24},\textbf{34}$, and the boxes below $26$ are $\textbf{23},\textbf{24},25,\textbf{34},35,45$.
We thus obtain the four boxes in positions $12,23,24,34$ that are below at least two peaks.
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
to partition
Description
The cut-out partition of a Dyck path.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ 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 $(n-1,\ldots,2,1)$.
Map
Glaisher-Franklin inverse
Description
The Glaisher-Franklin bijection on integer partitions.
This map sends the number of distinct repeated part sizes to the number of distinct even part sizes, see [1, 3.3.1].