Identifier
Values
[1,0] => [] => 0
[1,0,1,0] => [1] => 1
[1,1,0,0] => [] => 0
[1,0,1,0,1,0] => [2,1] => 1
[1,0,1,1,0,0] => [1,1] => 1
[1,1,0,0,1,0] => [2] => 1
[1,1,0,1,0,0] => [1] => 1
[1,1,1,0,0,0] => [] => 0
[1,0,1,0,1,0,1,0] => [3,2,1] => 1
[1,0,1,0,1,1,0,0] => [2,2,1] => 2
[1,0,1,1,0,0,1,0] => [3,1,1] => 2
[1,0,1,1,0,1,0,0] => [2,1,1] => 2
[1,0,1,1,1,0,0,0] => [1,1,1] => 1
[1,1,0,0,1,0,1,0] => [3,2] => 1
[1,1,0,0,1,1,0,0] => [2,2] => 1
[1,1,0,1,0,0,1,0] => [3,1] => 1
[1,1,0,1,0,1,0,0] => [2,1] => 1
[1,1,0,1,1,0,0,0] => [1,1] => 1
[1,1,1,0,0,0,1,0] => [3] => 1
[1,1,1,0,0,1,0,0] => [2] => 1
[1,1,1,0,1,0,0,0] => [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
[1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => 2
[1,0,1,0,1,1,0,0,1,0] => [4,2,2,1] => 2
[1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => 2
[1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => 2
[1,0,1,1,0,0,1,0,1,0] => [4,3,1,1] => 2
[1,0,1,1,0,0,1,1,0,0] => [3,3,1,1] => 1
[1,0,1,1,0,1,0,0,1,0] => [4,2,1,1] => 2
[1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => 2
[1,0,1,1,0,1,1,0,0,0] => [2,2,1,1] => 1
[1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => 2
[1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => 2
[1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => 2
[1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0] => [4,3,2] => 1
[1,1,0,0,1,0,1,1,0,0] => [3,3,2] => 2
[1,1,0,0,1,1,0,0,1,0] => [4,2,2] => 2
[1,1,0,0,1,1,0,1,0,0] => [3,2,2] => 2
[1,1,0,0,1,1,1,0,0,0] => [2,2,2] => 1
[1,1,0,1,0,0,1,0,1,0] => [4,3,1] => 1
[1,1,0,1,0,0,1,1,0,0] => [3,3,1] => 2
[1,1,0,1,0,1,0,0,1,0] => [4,2,1] => 1
[1,1,0,1,0,1,0,1,0,0] => [3,2,1] => 1
[1,1,0,1,0,1,1,0,0,0] => [2,2,1] => 2
[1,1,0,1,1,0,0,0,1,0] => [4,1,1] => 2
[1,1,0,1,1,0,0,1,0,0] => [3,1,1] => 2
[1,1,0,1,1,0,1,0,0,0] => [2,1,1] => 2
[1,1,0,1,1,1,0,0,0,0] => [1,1,1] => 1
[1,1,1,0,0,0,1,0,1,0] => [4,3] => 1
[1,1,1,0,0,0,1,1,0,0] => [3,3] => 1
[1,1,1,0,0,1,0,0,1,0] => [4,2] => 1
[1,1,1,0,0,1,0,1,0,0] => [3,2] => 1
[1,1,1,0,0,1,1,0,0,0] => [2,2] => 1
[1,1,1,0,1,0,0,0,1,0] => [4,1] => 1
[1,1,1,0,1,0,0,1,0,0] => [3,1] => 1
[1,1,1,0,1,0,1,0,0,0] => [2,1] => 1
[1,1,1,0,1,1,0,0,0,0] => [1,1] => 1
[1,1,1,1,0,0,0,0,1,0] => [4] => 1
[1,1,1,1,0,0,0,1,0,0] => [3] => 1
[1,1,1,1,0,0,1,0,0,0] => [2] => 1
[1,1,1,1,0,1,0,0,0,0] => [1] => 1
[1,1,1,1,1,0,0,0,0,0] => [] => 0
[1,0,1,0,1,0,1,1,1,0,0,0] => [3,3,3,2,1] => 2
[1,0,1,0,1,1,0,1,0,1,0,0] => [4,3,2,2,1] => 2
[1,0,1,0,1,1,0,1,1,0,0,0] => [3,3,2,2,1] => 2
[1,0,1,0,1,1,1,0,0,0,1,0] => [5,2,2,2,1] => 2
[1,0,1,0,1,1,1,0,0,1,0,0] => [4,2,2,2,1] => 2
[1,0,1,0,1,1,1,0,1,0,0,0] => [3,2,2,2,1] => 2
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => [4,3,3,1,1] => 2
[1,0,1,1,0,0,1,1,1,0,0,0] => [3,3,3,1,1] => 2
[1,0,1,1,0,1,0,0,1,1,0,0] => [4,4,2,1,1] => 2
[1,0,1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,1] => 2
[1,0,1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,1] => 2
[1,0,1,1,0,1,0,1,1,0,0,0] => [3,3,2,1,1] => 2
[1,0,1,1,0,1,1,0,0,0,1,0] => [5,2,2,1,1] => 2
[1,0,1,1,0,1,1,0,0,1,0,0] => [4,2,2,1,1] => 2
[1,0,1,1,0,1,1,0,1,0,0,0] => [3,2,2,1,1] => 2
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,2,2,1,1] => 2
[1,0,1,1,1,0,0,0,1,0,1,0] => [5,4,1,1,1] => 2
[1,0,1,1,1,0,0,0,1,1,0,0] => [4,4,1,1,1] => 2
[1,0,1,1,1,0,0,1,0,0,1,0] => [5,3,1,1,1] => 2
[1,0,1,1,1,0,0,1,0,1,0,0] => [4,3,1,1,1] => 2
[1,0,1,1,1,0,0,1,1,0,0,0] => [3,3,1,1,1] => 2
[1,0,1,1,1,0,1,0,0,0,1,0] => [5,2,1,1,1] => 2
[1,0,1,1,1,0,1,0,0,1,0,0] => [4,2,1,1,1] => 2
[1,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => 2
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 2
[1,0,1,1,1,1,0,0,0,0,1,0] => [5,1,1,1,1] => 2
[1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => 2
[1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => 2
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => 2
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,0] => [4,3,3,2] => 2
[1,1,0,0,1,0,1,1,1,0,0,0] => [3,3,3,2] => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => 1
[1,1,0,0,1,1,0,1,0,0,1,0] => [5,3,2,2] => 2
[1,1,0,0,1,1,0,1,0,1,0,0] => [4,3,2,2] => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => [3,3,2,2] => 1
>>> Load all 875 entries. <<<
[1,1,0,0,1,1,1,0,0,0,1,0] => [5,2,2,2] => 2
[1,1,0,0,1,1,1,0,0,1,0,0] => [4,2,2,2] => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => [3,2,2,2] => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,2,2] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [4,4,3,1] => 2
[1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,3,1] => 2
[1,1,0,1,0,0,1,1,0,1,0,0] => [4,3,3,1] => 2
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,3,3,1] => 2
[1,1,0,1,0,1,0,0,1,0,1,0] => [5,4,2,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,0] => [4,4,2,1] => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => [5,3,2,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,0] => [3,3,2,1] => 2
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,2,2,1] => 2
[1,1,0,1,0,1,1,0,0,1,0,0] => [4,2,2,1] => 2
[1,1,0,1,0,1,1,0,1,0,0,0] => [3,2,2,1] => 2
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,2,2,1] => 2
[1,1,0,1,1,0,0,0,1,0,1,0] => [5,4,1,1] => 2
[1,1,0,1,1,0,0,0,1,1,0,0] => [4,4,1,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => [5,3,1,1] => 2
[1,1,0,1,1,0,0,1,0,1,0,0] => [4,3,1,1] => 2
[1,1,0,1,1,0,0,1,1,0,0,0] => [3,3,1,1] => 1
[1,1,0,1,1,0,1,0,0,0,1,0] => [5,2,1,1] => 2
[1,1,0,1,1,0,1,0,0,1,0,0] => [4,2,1,1] => 2
[1,1,0,1,1,0,1,0,1,0,0,0] => [3,2,1,1] => 2
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,1,1] => 1
[1,1,0,1,1,1,0,0,0,0,1,0] => [5,1,1,1] => 2
[1,1,0,1,1,1,0,0,0,1,0,0] => [4,1,1,1] => 2
[1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,1,1] => 2
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,1] => 2
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => [5,4,3] => 1
[1,1,1,0,0,0,1,0,1,1,0,0] => [4,4,3] => 2
[1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => 2
[1,1,1,0,0,0,1,1,0,1,0,0] => [4,3,3] => 2
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => 1
[1,1,1,0,0,1,0,0,1,0,1,0] => [5,4,2] => 1
[1,1,1,0,0,1,0,0,1,1,0,0] => [4,4,2] => 2
[1,1,1,0,0,1,0,1,0,0,1,0] => [5,3,2] => 1
[1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => 1
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,3,2] => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => [5,2,2] => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [4,2,2] => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,2] => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [2,2,2] => 1
[1,1,1,0,1,0,0,0,1,0,1,0] => [5,4,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,4,1] => 2
[1,1,1,0,1,0,0,1,0,0,1,0] => [5,3,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => 1
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,3,1] => 2
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1] => 1
[1,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1] => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,1,1] => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,1] => 2
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,1,1] => 2
[1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,1] => 2
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => 1
[1,1,1,1,0,0,0,1,0,0,1,0] => [5,3] => 1
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => 1
[1,1,1,1,0,0,0,1,1,0,0,0] => [3,3] => 1
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,2] => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,2] => 1
[1,1,1,1,0,0,1,0,1,0,0,0] => [3,2] => 1
[1,1,1,1,0,0,1,1,0,0,0,0] => [2,2] => 1
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,0] => [3,1] => 1
[1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => 1
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => [5] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [4] => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => [3] => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => [2] => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => [1] => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => [] => 0
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2,1] => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2,1] => 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1,1] => 3
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1,1] => 3
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1,1] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1,1] => 3
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1,1] => 3
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1,1] => 3
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => 3
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1,1] => 2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1,1] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1,1] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1,1] => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1,1] => 2
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1,1] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1,1] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1] => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1,1] => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1,1] => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1,1] => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1,1] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1,1] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1] => 2
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1] => 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1] => 2
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1] => 2
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1] => 2
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => 2
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1] => 2
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1] => 2
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1] => 2
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1] => 2
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1] => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => 2
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => 2
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1] => 2
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1] => 2
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1,1] => 2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1] => 2
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1] => 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => 2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1] => 2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1] => 2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1] => 2
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => 2
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1] => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1] => 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1] => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2] => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => 1
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1] => 2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1] => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1] => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1] => 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1] => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1] => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1] => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1] => 2
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1] => 2
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1] => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1] => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1] => 2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1] => 2
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1] => 2
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1] => 1
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1] => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1] => 2
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1] => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [5,4,3] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,4,3] => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [6,3,3] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [5,3,3] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,3] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,3,3] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,5,2] => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [6,4,2] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,4,2] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,4,2] => 2
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [5,3,2] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,2] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,3,2] => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,2,2] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [5,2,2] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,2] => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,2,2] => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [6,5,1] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,5,1] => 2
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [6,4,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,4,1] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,4,1] => 2
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,3,1] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,3,1] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [3,3,1] => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,2,1] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,2,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,2,1] => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,1,1] => 2
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,1] => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,1,1] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [3,1,1] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,1,1] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,4] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,4] => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,3] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,3] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [4,3] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,3] => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,2] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [4,2] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,2] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,2] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [4,1] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,1] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [4] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [] => 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
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1,1] => 2
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1,1] => 2
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1,1] => 3
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1,1,1] => 3
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1,1] => 3
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => 2
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1,1,1] => 2
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1,1] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1,1,1] => 2
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1,1] => 2
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1,1] => 2
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1,1] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1,1] => 2
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1,1] => 2
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1,1] => 2
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => 2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => 1
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1] => 2
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1] => 2
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => 1
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1] => 3
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1] => 3
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1] => 2
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1] => 1
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1,1] => 2
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1] => 3
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1] => 3
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1,1] => 3
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1] => 3
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1] => 1
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1] => 2
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1,1] => 2
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1,1] => 2
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1,1] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1,1] => 2
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1] => 2
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1] => 2
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1,1] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1] => 2
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1] => 2
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1] => 2
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1] => 2
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2] => 2
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2] => 2
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2] => 2
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2] => 1
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1] => 2
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1] => 2
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1] => 2
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1] => 2
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1] => 2
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1] => 2
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1] => 2
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1] => 2
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1] => 2
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1] => 2
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1] => 2
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1] => 2
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1] => 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1] => 2
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1] => 2
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1] => 2
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => 2
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1] => 2
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1] => 2
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1] => 2
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1,1] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1] => 2
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1] => 2
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1] => 2
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1] => 2
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1] => 2
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1] => 2
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1] => 2
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1] => 1
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3] => 1
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2] => 2
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2] => 2
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2] => 2
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2] => 2
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2] => 2
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2] => 2
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2] => 2
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2] => 1
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1] => 2
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1] => 2
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1] => 2
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1] => 2
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1] => 1
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1] => 2
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1] => 1
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1] => 2
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1] => 2
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1] => 2
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1] => 2
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1] => 2
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => 2
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1] => 2
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1] => 2
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1] => 2
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,1] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1] => 2
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1] => 2
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1] => 2
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1] => 2
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1] => 2
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1] => 2
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1] => 2
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1] => 2
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1] => 2
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [4,4,4] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3] => 1
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [4,4,3] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [6,3,3] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,3,3] => 2
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [4,3,3] => 2
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,5,2] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [6,4,2] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [5,4,2] => 1
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [4,4,2] => 2
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [7,3,2] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [6,3,2] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,3,2] => 1
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [4,3,2] => 1
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [3,3,2] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [7,2,2] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [6,2,2] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,2,2] => 2
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [4,2,2] => 2
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [3,2,2] => 2
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [2,2,2] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [6,5,1] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [5,5,1] => 2
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [7,4,1] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [6,4,1] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,4,1] => 1
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [4,4,1] => 2
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [7,3,1] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [6,3,1] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,3,1] => 1
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [4,3,1] => 1
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [3,3,1] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,2,1] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [6,2,1] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,2,1] => 1
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [4,2,1] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => 1
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [2,2,1] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,1,1] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [6,1,1] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,1,1] => 2
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [4,1,1] => 2
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [3,1,1] => 2
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,1,1] => 2
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [7,5] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [5,5] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,4] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,4] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [5,4] => 1
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [4,4] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,3] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,3] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [5,3] => 1
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [4,3] => 1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [3,3] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,2] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,2] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [5,2] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [4,2] => 1
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,2] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [5,1] => 1
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,1] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => 1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1] => 1
[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
[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] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [8,2] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1] => 2
[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] => 2
[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] => 2
[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
[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] => 1
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0] => [11] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1] => 1
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0] => [9,2] => 1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,1] => 2
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [8,3] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1,1] => 2
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1,1,1,1,1] => 2
[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] => 2
[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] => 2
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1,1,1,1] => 2
[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] => 2
[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0] => [11,1] => 1
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0] => [10,2] => 1
[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] => 2
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0] => [9,3] => 1
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0] => [9,2,1] => 1
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,1,1] => 2
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0] => [8,4] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => [8,2,2] => 2
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1,1] => 2
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1,1,1] => 2
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1,1,1,1] => 2
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,1,1,1,1,1] => 2
[1,0,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [4,1,1,1,1,1,1,1,1] => 2
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1,1,1,1,1] => 2
[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] => 3
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1,1,1,1,1,1] => 2
[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] => 2
[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] => 1
[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,1,1,1,1,1,1] => 2
[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] => 2
[1,0,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1,1,1,1] => 2
[] => [] => 0
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => 2
[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] => 3
[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] => 2
[1,1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1,1,1,1] => 2
[1,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1,1,1,1] => 2
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,1,1,1,1] => 2
[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] => 2
[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] => 2
[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] => 2
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1,1,1,1] => 2
[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] => 2
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => 2
[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] => 1
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2] => 1
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,1] => 2
[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1,1] => 2
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,1,1] => 2
[1,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2,1,1,1] => 3
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,2,2,1,1,1] => 3
[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1,1] => 1
[1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1,1,1,1] => 2
[1,1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1,1,1] => 2
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1,1,1,1] => 2
[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1,1] => 2
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1,1] => 2
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1,1,1] => 2
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1,1,1] => 2
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1,1] => 2
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1,1,1] => 2
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1,1,1] => 2
[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
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,2,2,2] => 2
[1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,2] => 2
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2] => 1
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [3,3,3,2,1] => 2
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,2,1] => 2
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,1] => 2
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1] => 2
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,1] => 2
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1,1] => 2
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1] => 2
[1,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,1,1] => 2
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1,1,1] => 2
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1,1,1] => 2
[1,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1,1] => 2
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1,1] => 2
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1,1,1] => 2
[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,1,1] => 2
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1] => 2
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1] => 2
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1,1] => 2
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1,1] => 2
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1] => 2
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1] => 2
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1] => 1
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [4,4,2,2] => 1
[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2,2] => 1
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0] => [5,2,2,2] => 2
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3,1] => 2
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3,1] => 2
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1] => 1
[1,1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0] => [4,4,2,1] => 2
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0] => [6,3,2,1] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1] => 1
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2,1] => 2
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2,1] => 2
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1] => 2
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1] => 2
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1] => 2
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1] => 1
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,1] => 2
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1] => 2
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1] => 2
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1] => 2
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1] => 2
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1] => 2
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1] => 2
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1] => 2
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0] => [4,4,4] => 1
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3] => 1
[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0] => [4,4,3] => 2
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0] => [6,3,3] => 2
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3] => 2
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [6,4,2] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0] => [4,4,2] => 2
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2] => 1
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2] => 1
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2] => 2
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0] => [7,2,2] => 2
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2] => 2
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2] => 2
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1] => 1
[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1] => 1
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1] => 2
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1] => 1
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1] => 2
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1] => 1
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1] => 1
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1] => 2
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1] => 2
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1] => 2
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1] => 2
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1] => 2
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1] => 2
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [6,6] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [7,5] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [5,5] => 1
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0] => [4,4] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0] => [7,3] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [4,3] => 1
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [3,3] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [7,2] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [4,2] => 1
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [3,2] => 1
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [2,2] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [7,1] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0] => [6,1] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0] => [5,1] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0] => [4,1] => 1
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [3,1] => 1
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => 1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [6] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [5] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [4] => 1
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [3] => 1
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [] => 0
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [] => 0
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [1,1] => 1
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [2] => 1
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1] => 1
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1] => 2
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [3,2] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [2] => 1
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [8] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [9] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [8,1] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1] => 1
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1] => 1
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1] => 1
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1] => 1
[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] => 1
[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] => 1
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [1] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [7] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [6] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [5] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [4] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [3] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0] => [9,1] => 1
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0] => [8,2,1] => 1
[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] => 2
[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
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [2,2] => 1
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0] => [3,3] => 1
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [3,3,3] => 1
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0] => [4,4,4] => 1
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [] => 0
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1] => 2
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1] => 2
[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] => 1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,1] => 2
[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] => 2
[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] => 2
[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] => 1
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [3,1] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0] => [6,6] => 1
[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
[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] => 2
[1,1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [4,1,1,1,1,1] => 2
[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] => 2
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [2,1] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1] => 1
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1] => 1
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0] => [3] => 1
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0] => [7,2,1] => 1
[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] => 2
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0,0] => [8,2,1] => 1
[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] => 2
[1,1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [4,1,1,1,1,1,1,1] => 2
[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] => 2
[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] => 2
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [7,1,1,1,1] => 2
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,1,1] => 2
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0] => [5,3,2,1] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0] => [5,4,2,1] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0] => [3,1] => 1
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0] => [4,2] => 1
[1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,1] => 2
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0] => [6,3,2,1] => 1
[1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1,1,1] => 2
[1,1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,2,1] => 2
[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1,1] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0,0] => [6,5,1] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0] => [5,4,1] => 1
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0] => [4,3,1] => 1
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2] => 1
[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0] => [7,1] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0] => [6,1] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0] => [5,1] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0] => [4,1] => 1
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1] => 2
[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
[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
[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
[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0] => [3,2,2,1] => 2
[1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1] => 1
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1] => 2
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1,1] => 1
[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1] => 2
[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0] => [2,2] => 1
[1,1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [3,2,2,2,1,1,1] => 2
[1,1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0] => [3,3] => 1
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0] => [3] => 1
[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,1] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0,0] => [8,1] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0,0] => [7,1] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0,0] => [6,1] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0,0] => [5,1] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0] => [4,1] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0] => [5,5] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0] => [4,4] => 1
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0] => [5,3,1] => 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] => 2
[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0] => [3,3,2] => 2
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Description
The number of different multiplicities of parts of an integer partition.
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 $(n-1,\ldots,2,1)$.