Identifier
Values
[1,0] => [1,0] => [] => 0
[1,0,1,0] => [1,1,0,0] => [] => 0
[1,1,0,0] => [1,0,1,0] => [1] => 1
[1,0,1,0,1,0] => [1,1,1,0,0,0] => [] => 0
[1,0,1,1,0,0] => [1,1,0,1,0,0] => [1] => 1
[1,1,0,0,1,0] => [1,0,1,1,0,0] => [1,1] => 2
[1,1,0,1,0,0] => [1,1,0,0,1,0] => [2] => 1
[1,1,1,0,0,0] => [1,0,1,0,1,0] => [2,1] => 1
[1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => [] => 0
[1,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,0] => [1] => 1
[1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => [1,1] => 2
[1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,0] => [2] => 1
[1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0] => [2,1] => 1
[1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0] => [1,1,1] => 3
[1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0] => [2,1,1] => 2
[1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => [2,2] => 2
[1,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0] => [3] => 1
[1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0] => [3,2] => 1
[1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0] => [2,2,1] => 1
[1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => [3,1] => 1
[1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,0] => [3,1,1] => 2
[1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => [3,2,1] => 1
[1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => [] => 0
[1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,0] => [1] => 1
[1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => [1,1] => 2
[1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => [2] => 1
[1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => [2,1] => 1
[1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => [1,1,1] => 3
[1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => [2,1,1] => 2
[1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0] => [2,2] => 2
[1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0] => [3] => 1
[1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => [3,2] => 1
[1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0] => [2,2,1] => 1
[1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0] => [3,1] => 1
[1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0] => [3,1,1] => 2
[1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0] => [3,2,1] => 1
[1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 4
[1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => 3
[1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => [2,2,1,1] => 2
[1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => 3
[1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => 2
[1,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0] => [2,2,2] => 3
[1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0] => [3,2,2] => 2
[1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0] => [3,3] => 2
[1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => [4] => 1
[1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => [4,3] => 1
[1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => [3,3,2] => 1
[1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0] => [4,1] => 1
[1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0] => [4,2,2] => 2
[1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0] => [4,3,2] => 1
[1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => 1
[1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => 1
[1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => [3,3,1] => 1
[1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => [4,1,1] => 2
[1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => [4,3,1] => 1
[1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => [3,3,1,1] => 2
[1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => [4,2] => 1
[1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => 3
[1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0] => [4,3,1,1] => 2
[1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => 1
[1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => [4,2,1] => 1
[1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0] => [4,2,1,1] => 2
[1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0] => [4,2,2,1] => 1
[1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => [4,3,2,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => [] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1] => 2
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => [2] => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1] => 3
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,1] => 2
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => [2,2] => 2
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => [3] => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => [3,2] => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => [3,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => [3,1,1] => 2
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1] => 4
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,1] => 3
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,1,1] => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,1,1] => 3
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => [3,2,1,1] => 2
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => [2,2,2] => 3
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,2] => 2
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => [3,3] => 2
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => [4] => 1
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => 1
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => [3,3,2] => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => 1
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => [4,2,2] => 2
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => 1
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => [2,2,2,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => [3,2,2,1] => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => [3,3,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,1] => 2
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => [3,3,1,1] => 2
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => [4,2] => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => [4,1,1,1] => 3
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => [4,3,1,1] => 2
>>> Load all 628 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => [3,3,2,1] => 1
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => 1
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => [4,2,1,1] => 2
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => [4,2,2,1] => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 5
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => 4
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 3
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => 4
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => 3
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => [2,2,2,1,1] => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => [3,2,2,1,1] => 2
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => [3,3,1,1,1] => 3
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => 4
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => [4,3,1,1,1] => 3
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => [3,3,2,1,1] => 2
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => [4,2,1,1,1] => 3
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => [4,2,2,1,1] => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,1] => 2
[1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,2,2] => 4
[1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => [3,2,2,2] => 3
[1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => [3,3,2,2] => 2
[1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => [4,2,2,2] => 3
[1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => [4,3,2,2] => 2
[1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => 3
[1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => [4,3,3] => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => 2
[1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5] => 1
[1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => 1
[1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => [4,4,3] => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => 2
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => [5,4,3] => 1
[1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => [3,3,3,2] => 1
[1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => [4,3,3,2] => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => [4,4,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => [5,1,1] => 2
[1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => [5,4,1] => 1
[1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => 2
[1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => [5,2] => 1
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => [5,2,2,2] => 3
[1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => [5,4,2,2] => 2
[1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => [4,4,3,2] => 1
[1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,1] => 1
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => [5,3,2,2] => 2
[1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => [5,3,3,2] => 1
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2] => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => 1
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => [3,2,2,2,1] => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => [3,3,2,2,1] => 1
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => [4,2,2,2,1] => 1
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => [4,3,2,2,1] => 1
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => [3,3,3,1] => 1
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => [4,3,3,1] => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => [4,4,1,1] => 2
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => [5,1,1,1] => 3
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => [5,4,1,1] => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => [4,4,3,1] => 1
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => [5,2,1,1] => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,3,1] => 1
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => [5,4,3,1] => 1
[1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [3,3,3,1,1] => 2
[1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => [4,3,3,1,1] => 2
[1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => [4,4,2] => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => [5,2,2] => 2
[1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => [5,4,2] => 1
[1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [4,4,1,1,1] => 3
[1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => [5,3] => 1
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => [5,1,1,1,1] => 4
[1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => [5,4,1,1,1] => 3
[1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => [4,4,3,1,1] => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => [5,3,2] => 1
[1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => [5,2,1,1,1] => 3
[1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => [5,3,3,1,1] => 2
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,1] => 2
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => [3,3,3,2,1] => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => [4,3,3,2,1] => 1
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => [4,4,2,1] => 1
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => [5,2,2,1] => 1
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => [5,4,2,1] => 1
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => [4,4,2,1,1] => 2
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => [5,3,1] => 1
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => [5,2,2,1,1] => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,1] => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => [4,4,2,2,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => [5,3,1,1] => 2
[1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => [5,3,1,1,1] => 3
[1,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => [5,2,2,2,1] => 1
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => [5,4,2,2,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => [4,4,3,2,1] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => [5,3,2,1] => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,1] => 2
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => [5,3,2,2,1] => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => [5,3,3,2,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1] => 3
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,1,1] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,2] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,2] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,2,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,1] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [3,1,1] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1] => 4
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1] => 3
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1] => 3
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,2,2] => 3
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2] => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,3] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [4] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [4,3] => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,3,2] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [4,1] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,2] => 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,2] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [3,3,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,1,1] => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,3,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1] => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [4,2] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1] => 3
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1] => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,2,1] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1] => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => 5
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1] => 4
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1] => 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1] => 4
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => 3
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => 2
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => 3
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1] => 4
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1] => 3
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1] => 3
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => 4
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2] => 3
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2] => 3
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2] => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,3,3] => 3
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,3] => 2
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,4] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4] => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,4,3] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [5,3,3] => 2
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [5,4,3] => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,4,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,1] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,4,1] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2] => 2
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2] => 3
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2] => 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2] => 2
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1] => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1] => 3
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1] => 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1] => 2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1] => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1] => 2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,4,2] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [5,2,2] => 2
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,4,2] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1] => 3
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,3] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1] => 4
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1] => 3
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1] => 2
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [5,3,2] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1] => 3
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1] => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,1] => 2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1] => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1] => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1] => 2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,3,1] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,1] => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1] => 3
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2,1] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 6
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 5
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1,1] => 4
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1,1] => 5
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1] => 4
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => 3
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => 3
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1,1] => 4
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1,1] => 5
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1,1] => 4
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1,1] => 3
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1,1] => 4
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1,1] => 3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1,1] => 3
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1,1] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1,1] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => 3
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1,1] => 4
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1,1] => 5
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1,1] => 4
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1,1] => 3
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1,1] => 4
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => 5
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2] => 4
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => 3
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2] => 4
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => 4
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => 3
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,5,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,1,1] => 2
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [6,5,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,2] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,2,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1] => 2
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,5,2] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,2,2] => 2
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,3] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,1] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1] => 4
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1] => 3
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1] => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1,1] => 3
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2] => 3
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [6,3,3] => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,4] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1,1] => 5
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1,1] => 4
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [6,4,1] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [6,4,2] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1] => 3
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,1,1] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,2] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [2,2,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [3,1,1] => 2
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1] => 4
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1] => 3
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1] => 3
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [2,2,2] => 3
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [3,2,2] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [3,3] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [4,3] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [3,3,2] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,1] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [4,2,2] => 2
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [4,3,2] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [3,3,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [4,1,1] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [4,3,1] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [4,2] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1] => 3
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [4,2,1] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1] => 2
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1] => 1
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1] => 5
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1] => 4
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => 3
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1] => 4
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1] => 3
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1] => 3
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1] => 4
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1] => 3
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1] => 2
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1] => 3
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1] => 2
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1] => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2] => 4
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2] => 3
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => 2
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2] => 3
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2] => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => 3
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [4,3,3] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [4,4] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [5,4] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [4,4,3] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [5,1] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,3,3] => 2
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3] => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2] => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [4,4,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,1,1] => 2
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,4,1] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2] => 2
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [5,2] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2] => 3
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2] => 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,2,1] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2] => 2
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2] => 1
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1] => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1] => 3
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1] => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1] => 2
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1] => 1
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1] => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1] => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [4,4,2] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,2,2] => 2
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [5,4,2] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [5,3] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1] => 4
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1] => 3
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,3,2] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1] => 3
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1] => 2
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1] => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,3,1] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1] => 2
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1] => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1] => 2
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1] => 3
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1] => 1
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1] => 2
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1] => 1
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1] => 1
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 6
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1] => 5
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1] => 4
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1] => 5
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1] => 4
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1] => 3
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1] => 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1] => 4
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1] => 5
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1,1] => 4
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1] => 3
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1] => 4
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1,1] => 3
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1,1] => 3
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1] => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1] => 2
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1] => 3
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1] => 4
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1] => 5
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1,1] => 4
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1] => 3
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1,1] => 4
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2] => 5
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2] => 4
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2] => 3
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2] => 4
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3] => 4
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [4,4,4] => 3
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [5,5] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [5,5,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [6,1,1] => 2
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [6,5,1] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,2] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [6,2,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1] => 2
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1] => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1] => 2
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,5,2] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [6,2,2] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,3] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [6,3,2] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [6,3,1] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1] => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1] => 4
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1] => 3
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1] => 2
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1] => 3
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2] => 3
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [6,3,3] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,4] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1] => 5
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1,1] => 4
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [6,4,1] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [6,4,2] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 7
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => 6
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => 5
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1,1] => 6
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1,1] => 5
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => 4
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1,1] => 4
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1,1] => 5
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1,1] => 6
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1,1,1] => 5
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1,1] => 4
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1,1] => 5
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1,1,1] => 4
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1,1] => 3
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1,1] => 3
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1,1] => 6
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1,1,1] => 5
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1,1] => 6
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,1,1] => 2
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,2] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,2,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1] => 3
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1] => 2
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [7,2,2] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,3] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [7,3,2] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [7,3,1] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,1] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1] => 4
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1,1] => 3
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,4] => 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [7,4,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1,1] => 5
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [7,5] => 1
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Description
The multiplicity of the smallest part of a partition.
This counts the number of occurrences of the smallest part $spt(\lambda)$ of a partition $\lambda$.
The sum $spt(n) = \sum_{\lambda \vdash n} spt(\lambda)$ satisfies the congruences
\begin{align*}
spt(5n+4) &\equiv 0\quad \pmod{5}\\
spt(7n+5) &\equiv 0\quad \pmod{7}\\
spt(13n+6) &\equiv 0\quad \pmod{13},
\end{align*}
analogous to those of the counting function of partitions, see [1] and [2].
Map
inverse Kreweras complement
Description
Return the inverse of the Kreweras complement of a Dyck path, regarded as a noncrossing set partition.
To identify Dyck paths and noncrossing set partitions, this maps uses the following classical bijection. The number of down steps after the $i$-th up step of the Dyck path is the size of the block of the set partition whose maximal element is $i$. If $i$ is not a maximal element of a block, the $(i+1)$-st step is also an up step.
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 $(n-1,\ldots,2,1)$.