Identifier
Values
[1,0] => [1] => 1
[1,0,1,0] => [1,1] => 1
[1,1,0,0] => [2] => 2
[1,0,1,0,1,0] => [1,1,1] => 1
[1,0,1,1,0,0] => [1,2] => 1
[1,1,0,0,1,0] => [2,1] => 1
[1,1,0,1,0,0] => [3] => 3
[1,1,1,0,0,0] => [3] => 3
[1,0,1,0,1,0,1,0] => [1,1,1,1] => 1
[1,0,1,0,1,1,0,0] => [1,1,2] => 1
[1,0,1,1,0,0,1,0] => [1,2,1] => 1
[1,0,1,1,0,1,0,0] => [1,3] => 1
[1,0,1,1,1,0,0,0] => [1,3] => 1
[1,1,0,0,1,0,1,0] => [2,1,1] => 1
[1,1,0,0,1,1,0,0] => [2,2] => 2
[1,1,0,1,0,0,1,0] => [3,1] => 1
[1,1,0,1,0,1,0,0] => [4] => 4
[1,1,0,1,1,0,0,0] => [4] => 4
[1,1,1,0,0,0,1,0] => [3,1] => 1
[1,1,1,0,0,1,0,0] => [4] => 4
[1,1,1,0,1,0,0,0] => [4] => 4
[1,1,1,1,0,0,0,0] => [4] => 4
[1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,0] => [1,1,1,2] => 1
[1,0,1,0,1,1,0,0,1,0] => [1,1,2,1] => 1
[1,0,1,0,1,1,0,1,0,0] => [1,1,3] => 1
[1,0,1,0,1,1,1,0,0,0] => [1,1,3] => 1
[1,0,1,1,0,0,1,0,1,0] => [1,2,1,1] => 1
[1,0,1,1,0,0,1,1,0,0] => [1,2,2] => 1
[1,0,1,1,0,1,0,0,1,0] => [1,3,1] => 1
[1,0,1,1,0,1,0,1,0,0] => [1,4] => 1
[1,0,1,1,0,1,1,0,0,0] => [1,4] => 1
[1,0,1,1,1,0,0,0,1,0] => [1,3,1] => 1
[1,0,1,1,1,0,0,1,0,0] => [1,4] => 1
[1,0,1,1,1,0,1,0,0,0] => [1,4] => 1
[1,0,1,1,1,1,0,0,0,0] => [1,4] => 1
[1,1,0,0,1,0,1,0,1,0] => [2,1,1,1] => 1
[1,1,0,0,1,0,1,1,0,0] => [2,1,2] => 1
[1,1,0,0,1,1,0,0,1,0] => [2,2,1] => 1
[1,1,0,0,1,1,0,1,0,0] => [2,3] => 2
[1,1,0,0,1,1,1,0,0,0] => [2,3] => 2
[1,1,0,1,0,0,1,0,1,0] => [3,1,1] => 1
[1,1,0,1,0,0,1,1,0,0] => [3,2] => 2
[1,1,0,1,0,1,0,0,1,0] => [4,1] => 1
[1,1,0,1,0,1,0,1,0,0] => [5] => 5
[1,1,0,1,0,1,1,0,0,0] => [5] => 5
[1,1,0,1,1,0,0,0,1,0] => [4,1] => 1
[1,1,0,1,1,0,0,1,0,0] => [5] => 5
[1,1,0,1,1,0,1,0,0,0] => [5] => 5
[1,1,0,1,1,1,0,0,0,0] => [5] => 5
[1,1,1,0,0,0,1,0,1,0] => [3,1,1] => 1
[1,1,1,0,0,0,1,1,0,0] => [3,2] => 2
[1,1,1,0,0,1,0,0,1,0] => [4,1] => 1
[1,1,1,0,0,1,0,1,0,0] => [5] => 5
[1,1,1,0,0,1,1,0,0,0] => [5] => 5
[1,1,1,0,1,0,0,0,1,0] => [4,1] => 1
[1,1,1,0,1,0,0,1,0,0] => [5] => 5
[1,1,1,0,1,0,1,0,0,0] => [5] => 5
[1,1,1,0,1,1,0,0,0,0] => [5] => 5
[1,1,1,1,0,0,0,0,1,0] => [4,1] => 1
[1,1,1,1,0,0,0,1,0,0] => [5] => 5
[1,1,1,1,0,0,1,0,0,0] => [5] => 5
[1,1,1,1,0,1,0,0,0,0] => [5] => 5
[1,1,1,1,1,0,0,0,0,0] => [5] => 5
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,2] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,2,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,3] => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,3] => 1
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,2,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,2,2] => 1
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,3,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,4] => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,4] => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,3,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,4] => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,4] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,4] => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,1,2] => 1
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3] => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3] => 1
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,2] => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,4,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,5] => 1
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,5] => 1
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,4,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,5] => 1
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,5] => 1
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,5] => 1
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,3,1,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2] => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,5] => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,5] => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,5] => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,5] => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,5] => 1
>>> Load all 3307 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,4,1] => 1
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5] => 1
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5] => 1
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5] => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,5] => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,2] => 1
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,2,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3] => 1
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,2,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2] => 2
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,4] => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,4] => 2
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1] => 1
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,4] => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,4] => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,4] => 2
[1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [3,1,2] => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [3,2,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [3,3] => 3
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,3] => 3
[1,1,0,1,0,1,0,0,1,0,1,0] => [4,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,0] => [4,2] => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => [5,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,0] => [6] => 6
[1,1,0,1,0,1,0,1,1,0,0,0] => [6] => 6
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => [6] => 6
[1,1,0,1,0,1,1,0,1,0,0,0] => [6] => 6
[1,1,0,1,0,1,1,1,0,0,0,0] => [6] => 6
[1,1,0,1,1,0,0,0,1,0,1,0] => [4,1,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,0] => [4,2] => 2
[1,1,0,1,1,0,0,1,0,0,1,0] => [5,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => [6] => 6
[1,1,0,1,1,0,0,1,1,0,0,0] => [6] => 6
[1,1,0,1,1,0,1,0,0,0,1,0] => [5,1] => 1
[1,1,0,1,1,0,1,0,0,1,0,0] => [6] => 6
[1,1,0,1,1,0,1,0,1,0,0,0] => [6] => 6
[1,1,0,1,1,0,1,1,0,0,0,0] => [6] => 6
[1,1,0,1,1,1,0,0,0,0,1,0] => [5,1] => 1
[1,1,0,1,1,1,0,0,0,1,0,0] => [6] => 6
[1,1,0,1,1,1,0,0,1,0,0,0] => [6] => 6
[1,1,0,1,1,1,0,1,0,0,0,0] => [6] => 6
[1,1,0,1,1,1,1,0,0,0,0,0] => [6] => 6
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2] => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1] => 1
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,3] => 3
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,3] => 3
[1,1,1,0,0,1,0,0,1,0,1,0] => [4,1,1] => 1
[1,1,1,0,0,1,0,0,1,1,0,0] => [4,2] => 2
[1,1,1,0,0,1,0,1,0,0,1,0] => [5,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,0] => [6] => 6
[1,1,1,0,0,1,0,1,1,0,0,0] => [6] => 6
[1,1,1,0,0,1,1,0,0,0,1,0] => [5,1] => 1
[1,1,1,0,0,1,1,0,0,1,0,0] => [6] => 6
[1,1,1,0,0,1,1,0,1,0,0,0] => [6] => 6
[1,1,1,0,0,1,1,1,0,0,0,0] => [6] => 6
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,2] => 2
[1,1,1,0,1,0,0,1,0,0,1,0] => [5,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [6] => 6
[1,1,1,0,1,0,0,1,1,0,0,0] => [6] => 6
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,0] => [6] => 6
[1,1,1,0,1,0,1,0,1,0,0,0] => [6] => 6
[1,1,1,0,1,0,1,1,0,0,0,0] => [6] => 6
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,1] => 1
[1,1,1,0,1,1,0,0,0,1,0,0] => [6] => 6
[1,1,1,0,1,1,0,0,1,0,0,0] => [6] => 6
[1,1,1,0,1,1,0,1,0,0,0,0] => [6] => 6
[1,1,1,0,1,1,1,0,0,0,0,0] => [6] => 6
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,1,1] => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,2] => 2
[1,1,1,1,0,0,0,1,0,0,1,0] => [5,1] => 1
[1,1,1,1,0,0,0,1,0,1,0,0] => [6] => 6
[1,1,1,1,0,0,0,1,1,0,0,0] => [6] => 6
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,1] => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [6] => 6
[1,1,1,1,0,0,1,0,1,0,0,0] => [6] => 6
[1,1,1,1,0,0,1,1,0,0,0,0] => [6] => 6
[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] => [6] => 6
[1,1,1,1,0,1,0,0,1,0,0,0] => [6] => 6
[1,1,1,1,0,1,0,1,0,0,0,0] => [6] => 6
[1,1,1,1,0,1,1,0,0,0,0,0] => [6] => 6
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,1] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [6] => 6
[1,1,1,1,1,0,0,0,1,0,0,0] => [6] => 6
[1,1,1,1,1,0,0,1,0,0,0,0] => [6] => 6
[1,1,1,1,1,0,1,0,0,0,0,0] => [6] => 6
[1,1,1,1,1,1,0,0,0,0,0,0] => [6] => 6
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,2] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,2,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,3] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,3] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,2,1,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,2,2] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,3,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,4] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,4] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,3,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,4] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,4] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,4] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,2,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,2,1,2] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,2,2,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,2,3] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,2,3] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,3,1,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,3,2] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,4,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,5] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,5] => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,4,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,5] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,5] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,5] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,3,1,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,3,2] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,4,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,5] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,5] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,4,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,5] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,5] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,5] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,4,1] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,5] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,5] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,5] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,5] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,1,1,2] => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,1,2,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,1,3] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,1,3] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,2,1,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,2,2] => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,3,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,4] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,3,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,4] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,4] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,1,2] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,2,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,3] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,3] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,4,1,1] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,4,2] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,5,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,6] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,6] => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,5,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,6] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,6] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,6] => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,4,1,1] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,4,2] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,5,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,6] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,6] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,5,1] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,6] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,6] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,6] => 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,5,1] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,6] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,6] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,6] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,6] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,3,1,1,1] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,3,1,2] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,3,2,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,3,3] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,3,3] => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,1,1] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,5,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,6] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,6] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,5,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,6] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,6] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,6] => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,1,1] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,2] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,5,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,6] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,6] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,5,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,6] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,6] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,6] => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,5,1] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,6] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,6] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,6] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,6] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,4,1,1] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,4,2] => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,1] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,6] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,6] => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,1] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,6] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,6] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,6] => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,5,1] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,6] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,6] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,6] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,6] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,5,1] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,6] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,6] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,6] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,2] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,2,1] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,3] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,3] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,2,1,1] => 1
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,2,2] => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,4] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,4] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,1] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,4] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,4] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,4] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,2,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,2,1,2] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,2,2,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,2,3] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,2,3] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,1] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,3,2] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,4,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,5] => 2
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,5] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,4,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,5] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,5] => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,5] => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,1] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,2] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,4,1] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,5] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,5] => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,4,1] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,5] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,5] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,5] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,4,1] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,5] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,5] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,5] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,5] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,1,1,2] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,2,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [3,1,3] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,1,3] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,2,1,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,2] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [3,3,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,4] => 3
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [3,4] => 3
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,3,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,4] => 3
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [3,4] => 3
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,4] => 3
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [4,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [4,1,2] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [4,2,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [4,3] => 3
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [4,3] => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [5,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [5,2] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [6,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7] => 7
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7] => 7
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [6,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [7] => 7
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [7] => 7
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [7] => 7
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [5,1,1] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [5,2] => 2
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [6,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7] => 7
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [7] => 7
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [6,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [7] => 7
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [7] => 7
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [7] => 7
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [6,1] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7] => 7
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [7] => 7
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [7] => 7
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [7] => 7
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [4,1,1,1] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [4,1,2] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [4,2,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [4,3] => 3
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,3] => 3
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [5,1,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [5,2] => 2
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [6,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7] => 7
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [7] => 7
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [6,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7] => 7
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [7] => 7
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [7] => 7
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [5,1,1] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [5,2] => 2
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [6,1] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7] => 7
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [7] => 7
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [6,1] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7] => 7
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [7] => 7
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [7] => 7
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [6,1] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [7] => 7
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [7] => 7
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [7] => 7
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [7] => 7
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [5,1,1] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [5,2] => 2
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [6,1] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [7] => 7
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [7] => 7
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [6,1] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [7] => 7
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [7] => 7
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [7] => 7
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [6,1] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [7] => 7
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [7] => 7
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [7] => 7
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [7] => 7
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [6,1] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [7] => 7
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [7] => 7
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [7] => 7
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [7] => 7
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [7] => 7
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,1,2] => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,1,2,1] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,3] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,3] => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,1] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,2] => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,3,1] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,4] => 3
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,4] => 3
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,3,1] => 1
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,4] => 3
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,4] => 3
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,4] => 3
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [4,1,1,1] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [4,1,2] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [4,2,1] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [4,3] => 3
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,3] => 3
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [5,1,1] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [5,2] => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [6,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7] => 7
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [7] => 7
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [6,1] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [7] => 7
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [7] => 7
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [7] => 7
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [5,1,1] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [5,2] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [6,1] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [7] => 7
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [7] => 7
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [6,1] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [7] => 7
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [7] => 7
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [7] => 7
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [6,1] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [7] => 7
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [7] => 7
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [7] => 7
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [7] => 7
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,1,2] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,2,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,3] => 3
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,3] => 3
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [5,1,1] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [5,2] => 2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [6,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7] => 7
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [7] => 7
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [6,1] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [7] => 7
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [7] => 7
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [7] => 7
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [5,1,1] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,2] => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [6,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [7] => 7
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [7] => 7
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [7] => 7
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7] => 7
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [7] => 7
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,1] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [7] => 7
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [7] => 7
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [7] => 7
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [7] => 7
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,1,1] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,2] => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [6,1] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [7] => 7
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [7] => 7
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,1] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [7] => 7
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7] => 7
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7] => 7
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,1] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [7] => 7
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7] => 7
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7] => 7
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7] => 7
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [7] => 7
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [7] => 7
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [7] => 7
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [7] => 7
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [7] => 7
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,1,2] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,2,1] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3] => 3
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3] => 3
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [5,1,1] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [5,2] => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [6,1] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7] => 7
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [7] => 7
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [6,1] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7] => 7
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [7] => 7
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [7] => 7
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,1,1] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,2] => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [6,1] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [7] => 7
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [7] => 7
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,1] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [7] => 7
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [7] => 7
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [7] => 7
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,1] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [7] => 7
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [7] => 7
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [7] => 7
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [7] => 7
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,1,1] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,2] => 2
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [6,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7] => 7
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [7] => 7
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7] => 7
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7] => 7
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7] => 7
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,1] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [7] => 7
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7] => 7
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7] => 7
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7] => 7
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,1] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [7] => 7
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [7] => 7
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [7] => 7
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [7] => 7
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [7] => 7
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,1,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,2] => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,1] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7] => 7
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [7] => 7
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,1] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [7] => 7
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [7] => 7
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [7] => 7
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,1] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [7] => 7
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [7] => 7
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [7] => 7
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [7] => 7
[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] => [7] => 7
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [7] => 7
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [7] => 7
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [7] => 7
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7] => 7
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7] => 7
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [7] => 7
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [7] => 7
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [7] => 7
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7] => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,2] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,2,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,3] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,3] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,2,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,2,2] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,3,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,4] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,4] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,3,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,4] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,4] => 1
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,4] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,2,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,2,1,2] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,2,2,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,2,3] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,2,3] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,3,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,3,2] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,4,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,5] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,5] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,4,1] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,5] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,5] => 1
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,5] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,3,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,3,2] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,4,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,5] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,5] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,4,1] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,5] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,5] => 1
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,5] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,4,1] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,5] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,5] => 1
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,5] => 1
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,5] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,2,1,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,2,1,1,2] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,2,1,2,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,2,1,3] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,2,1,3] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,2,2,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,2,2,2] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,2,3,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,2,4] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,2,4] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,2,3,1] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,2,4] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,2,4] => 1
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,2,4] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,3,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,3,1,2] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,3,2,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,3,3] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,3,3] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,4,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,4,2] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,5,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,6] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,6] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,5,1] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,6] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,6] => 1
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,6] => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,4,1,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,4,2] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,5,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,6] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,6] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,5,1] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,6] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,6] => 1
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,6] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,5,1] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,6] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,6] => 1
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,6] => 1
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,6] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,3,1,1,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,3,1,2] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,3,2,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,3,3] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,3,3] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,4,1,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,4,2] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,5,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,6] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,6] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,5,1] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,6] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,6] => 1
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,6] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,4,1,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,4,2] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,5,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,6] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,6] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,5,1] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,6] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,6] => 1
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,6] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,5,1] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,6] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,6] => 1
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,6] => 1
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,6] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,4,1,1] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,4,2] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,5,1] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,6] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,6] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,5,1] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,6] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,6] => 1
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,6] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,5,1] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,6] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,6] => 1
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,6] => 1
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,6] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,5,1] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,6] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,6] => 1
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,6] => 1
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,6] => 1
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,6] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,2,1,1,1,2] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,2,1,1,2,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,2,1,1,3] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,2,1,1,3] => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,2,1,2,1,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,2,1,2,2] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,2,1,3,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,2,1,4] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,2,1,4] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,2,1,3,1] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,2,1,4] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,2,1,4] => 1
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,2,1,4] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,2,2,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,2,2,1,2] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,2,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,2,2,3] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,2,2,3] => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,1,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,2] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,2,5] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,2,5] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,1] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,2,5] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,2,5] => 1
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,2,5] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,1,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,2] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,2,4,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,2,4,1] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,2,5] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,2,5] => 1
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,2,4,1] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,2,5] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,2,5] => 1
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,2,5] => 1
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,5] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,1,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,1,1,2] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,3,1,2,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,1,3] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,3,1,3] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,2] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,3,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,3,4] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,3,3,1] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,3,4] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,3,4] => 1
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,4,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,4,1,2] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,4,2,1] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,4,3] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,4,3] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,5,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,5,2] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,7] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,7] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,7] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,7] => 1
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,7] => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,5,1,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,5,2] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,7] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,7] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,7] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,7] => 1
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,7] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,7] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,7] => 1
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,7] => 1
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,7] => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,4,1,1,1] => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,4,1,2] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,4,2,1] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,5,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,5,2] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,7] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,7] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,7] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,7] => 1
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,7] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,5,1,1] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,5,2] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,7] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,7] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,7] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,7] => 1
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,7] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,7] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,7] => 1
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,7] => 1
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,7] => 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,5,1,1] => 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,5,2] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,7] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,7] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,7] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,7] => 1
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,7] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,7] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,7] => 1
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,7] => 1
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,7] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,7] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,7] => 1
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,7] => 1
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,7] => 1
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,7] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,3,1,1,1,1] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,3,1,1,2] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,3,1,2,1] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,3,1,3] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,3,1,3] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,3,2,1,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,3,2,2] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,3,3,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,3,4] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,3,4] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,3,3,1] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,3,4] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,3,4] => 1
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,3,4] => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,4,1,1,1] => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,4,1,2] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,2,1] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,4,3] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,4,3] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,5,1,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,5,2] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,7] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,7] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,7] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,7] => 1
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,7] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,5,1,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,5,2] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,7] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,7] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,7] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,7] => 1
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,7] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,7] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,7] => 1
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,7] => 1
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,7] => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,4,1,1,1] => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,4,1,2] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,4,2,1] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,4,3] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,4,3] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,5,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,5,2] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,7] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,7] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,7] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,7] => 1
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,7] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,5,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,5,2] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,7] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,7] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,7] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,7] => 1
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,7] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,7] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,7] => 1
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,7] => 1
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,7] => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,5,1,1] => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,5,2] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,7] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,7] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,7] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,7] => 1
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,7] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,7] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,7] => 1
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,7] => 1
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,7] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,7] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,7] => 1
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,7] => 1
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,7] => 1
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,7] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,4,1,1,1] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,4,1,2] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,4,2,1] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,4,3] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,4,3] => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,5,1,1] => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,5,2] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,7] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,7] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,7] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,7] => 1
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,7] => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,5,1,1] => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,5,2] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,7] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,7] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,7] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,7] => 1
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,7] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,7] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,7] => 1
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,7] => 1
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,7] => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,5,1,1] => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,5,2] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,7] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,7] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,7] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,7] => 1
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,7] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,7] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,7] => 1
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,7] => 1
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,7] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,7] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,7] => 1
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,7] => 1
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,7] => 1
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,7] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,5,1,1] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,5,2] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,7] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,7] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,7] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,7] => 1
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,7] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,7] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,7] => 1
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,7] => 1
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,7] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,7] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,7] => 1
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,7] => 1
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,7] => 1
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,7] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,7] => 1
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,7] => 1
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7] => 1
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,7] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,7] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,2] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,2,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,3] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,1,3] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,1,2,1,1] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,1,2,2] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,1,3,1] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,1,4] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,1,1,4] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,1,3,1] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,1,4] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,1,4] => 1
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,1,4] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,2,1,1,1] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,2,1,2] => 1
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,2,2,1] => 1
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,2,3] => 1
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,2,3] => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,3,1,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,2] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,5] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,1,5] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,1] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,1,5] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,1,5] => 1
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,1,5] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,1,1] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,2] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,4,1] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,4,1] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,1,5] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,5] => 1
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,1,5] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,1] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,1,5] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,5] => 1
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,5] => 1
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,5] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,2,1,1,2] => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,2,1,2,1] => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,2,1,3] => 1
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,2,1,3] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,2,2,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,2,3,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,2,4] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,2,4] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,2,3,1] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,2,4] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,2,4] => 2
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,4] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,1,1] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,2] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,2,1] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,3] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,3] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,4,1,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,4,2] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,5,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,6] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,6] => 2
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,5,1] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,6] => 2
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,6] => 2
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,6] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,1,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,2] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,5,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,6] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,6] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,5,1] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,6] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,6] => 2
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,6] => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,1] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,6] => 2
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,6] => 2
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,6] => 2
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,6] => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,1,1,1] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,1,2] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,2,1] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,3,3] => 2
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,3] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,4,1,1] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,4,2] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,5,1] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,6] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,6] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,5,1] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,6] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,6] => 2
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,6] => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,4,1,1] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,4,2] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,5,1] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,6] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,6] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,5,1] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,6] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,6] => 2
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,6] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,5,1] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,6] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,6] => 2
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,6] => 2
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,6] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,4,1,1] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,4,2] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,5,1] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,6] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,6] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,5,1] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,6] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,6] => 2
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,6] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,5,1] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,6] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,6] => 2
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,6] => 2
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,6] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,5,1] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,6] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,6] => 2
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,6] => 2
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,6] => 2
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,6] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,1,1,2] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,1,2,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,1,3] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [3,1,1,3] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,2,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [3,1,2,2] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,3,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [3,1,4] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [3,1,4] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,3,1] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [3,1,4] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [3,1,4] => 1
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,1,4] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [3,2,1,2] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,2,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [3,2,3] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => [3,2,3] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [3,3,1,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [3,3,2] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [3,4,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [3,5] => 3
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [3,5] => 3
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [3,4,1] => 1
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [3,5] => 3
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [3,5] => 3
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,5] => 3
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [3,3,1,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [3,3,2] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [3,4,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [3,5] => 3
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [3,5] => 3
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [3,4,1] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [3,5] => 3
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [3,5] => 3
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,5] => 3
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [3,4,1] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [3,5] => 3
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [3,5] => 3
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,5] => 3
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,5] => 3
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [4,1,1,2] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [4,1,3] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [4,2,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [4,2,2] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [4,3,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [4,4] => 4
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4] => 4
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [4,3,1] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [4,4] => 4
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [4,4] => 4
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4] => 4
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [5,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [5,1,2] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [5,2,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [5,3] => 3
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [5,3] => 3
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [6,2] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [7,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [8] => 8
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [8] => 8
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [8] => 8
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [8] => 8
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [6,2] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [8] => 8
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [8] => 8
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [8] => 8
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [8] => 8
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [8] => 8
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [8] => 8
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [8] => 8
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [8] => 8
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [8] => 8
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [5,1,2] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [5,2,1] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [5,3] => 3
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [5,3] => 3
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [6,2] => 2
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [7,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [8] => 8
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [8] => 8
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [8] => 8
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [8] => 8
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [8] => 8
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [6,2] => 2
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [8] => 8
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [8] => 8
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [8] => 8
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [8] => 8
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [8] => 8
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [8] => 8
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [8] => 8
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [8] => 8
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [8] => 8
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [6,2] => 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [8] => 8
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [8] => 8
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [8] => 8
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [8] => 8
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [8] => 8
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [8] => 8
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [8] => 8
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [8] => 8
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [8] => 8
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [8] => 8
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [8] => 8
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [8] => 8
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [8] => 8
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [8] => 8
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1] => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [4,1,1,2] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [4,1,3] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [4,2,1,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [4,2,2] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [4,3,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [4,4] => 4
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4] => 4
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [4,3,1] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [4,4] => 4
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,4] => 4
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4] => 4
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [5,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [5,1,2] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [5,2,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [5,3] => 3
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [5,3] => 3
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [6,2] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [8] => 8
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [8] => 8
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [8] => 8
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [8] => 8
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [8] => 8
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [6,2] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [8] => 8
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [8] => 8
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [8] => 8
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [8] => 8
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [8] => 8
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [8] => 8
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [8] => 8
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [8] => 8
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [8] => 8
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [5,1,2] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [5,2,1] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [5,3] => 3
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [5,3] => 3
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [6,2] => 2
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [8] => 8
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [8] => 8
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [8] => 8
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [8] => 8
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [8] => 8
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [6,2] => 2
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [8] => 8
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [8] => 8
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [8] => 8
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [8] => 8
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [8] => 8
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [8] => 8
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [8] => 8
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [8] => 8
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [8] => 8
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [6,2] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [8] => 8
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [8] => 8
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [8] => 8
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [8] => 8
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [8] => 8
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [8] => 8
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [8] => 8
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [8] => 8
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [8] => 8
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [8] => 8
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [8] => 8
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [8] => 8
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [8] => 8
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [8] => 8
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => 1
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,1,2] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [5,2,1] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,3] => 3
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,3] => 3
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [6,2] => 2
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [8] => 8
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [8] => 8
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [8] => 8
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [8] => 8
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [8] => 8
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [6,2] => 2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [8] => 8
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [8] => 8
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [8] => 8
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [8] => 8
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [8] => 8
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [8] => 8
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [8] => 8
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [8] => 8
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [8] => 8
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,2] => 2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [8] => 8
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [8] => 8
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [8] => 8
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [8] => 8
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [8] => 8
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [8] => 8
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [8] => 8
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [8] => 8
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [8] => 8
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [8] => 8
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [8] => 8
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [8] => 8
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [8] => 8
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [8] => 8
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,2] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [8] => 8
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [8] => 8
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [8] => 8
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [8] => 8
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [8] => 8
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [8] => 8
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [8] => 8
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [8] => 8
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [8] => 8
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [8] => 8
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [8] => 8
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [8] => 8
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [8] => 8
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [8] => 8
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [8] => 8
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [8] => 8
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [8] => 8
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [8] => 8
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [8] => 8
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [8] => 8
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,1,1,2] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,1,2,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,1,3] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,1,1,3] => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,2,1,1] => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [3,1,2,2] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,3,1] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,1,4] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,1,4] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,3,1] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [3,1,4] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,1,4] => 1
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,1,4] => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,1,1] => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [3,2,1,2] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,2,1] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [3,2,3] => 2
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [3,2,3] => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,3,1,1] => 1
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [3,3,2] => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [3,4,1] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,5] => 3
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,5] => 3
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,4,1] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [3,5] => 3
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,5] => 3
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,5] => 3
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [3,3,1,1] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,3,2] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [3,4,1] => 1
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,5] => 3
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,5] => 3
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [3,4,1] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,5] => 3
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,5] => 3
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,5] => 3
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,4,1] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [3,5] => 3
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,5] => 3
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,5] => 3
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,5] => 3
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [4,1,1,2] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [4,1,3] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [4,2,1,1] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [4,2,2] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [4,3,1] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [4,4] => 4
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4] => 4
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [4,3,1] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [4,4] => 4
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [4,4] => 4
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4] => 4
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [5,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [5,1,2] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [5,2,1] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [5,3] => 3
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [5,3] => 3
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [6,2] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8] => 8
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [8] => 8
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [8] => 8
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [8] => 8
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [8] => 8
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [6,2] => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [8] => 8
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [8] => 8
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [8] => 8
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [8] => 8
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [8] => 8
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [8] => 8
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [8] => 8
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [8] => 8
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [8] => 8
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => 1
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [5,1,2] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [5,2,1] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [5,3] => 3
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [5,3] => 3
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [6,2] => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [8] => 8
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [8] => 8
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [8] => 8
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [8] => 8
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [8] => 8
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [6,2] => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [8] => 8
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [8] => 8
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [8] => 8
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [8] => 8
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [8] => 8
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [8] => 8
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [8] => 8
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [8] => 8
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [8] => 8
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [6,2] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [8] => 8
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [8] => 8
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [8] => 8
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [8] => 8
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [8] => 8
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [8] => 8
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [8] => 8
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [8] => 8
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [8] => 8
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [8] => 8
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [8] => 8
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [8] => 8
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [8] => 8
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [8] => 8
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [4,1,1,2] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [4,1,3] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [4,2,1,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [4,2,2] => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [4,3,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [4,4] => 4
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4] => 4
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [4,3,1] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [4,4] => 4
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [4,4] => 4
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4] => 4
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [5,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [5,1,2] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [5,2,1] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [5,3] => 3
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [5,3] => 3
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [6,2] => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [8] => 8
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [8] => 8
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [8] => 8
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [8] => 8
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [8] => 8
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [6,2] => 2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [8] => 8
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [8] => 8
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [8] => 8
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [8] => 8
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [8] => 8
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [8] => 8
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [8] => 8
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [8] => 8
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [8] => 8
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [5,1,2] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [5,2,1] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [5,3] => 3
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [5,3] => 3
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [6,2] => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [8] => 8
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [8] => 8
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [8] => 8
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [8] => 8
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [8] => 8
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [6,2] => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [8] => 8
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [8] => 8
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [8] => 8
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8] => 8
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [8] => 8
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [8] => 8
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [8] => 8
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [8] => 8
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [8] => 8
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [6,2] => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [8] => 8
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [8] => 8
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [8] => 8
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [8] => 8
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [8] => 8
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [8] => 8
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [8] => 8
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [8] => 8
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [8] => 8
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [8] => 8
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [8] => 8
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [8] => 8
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [8] => 8
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [8] => 8
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [5,1,2] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [5,2,1] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [5,3] => 3
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,3] => 3
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [6,2] => 2
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [8] => 8
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [8] => 8
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [8] => 8
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [8] => 8
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [8] => 8
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [6,2] => 2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [8] => 8
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [8] => 8
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [8] => 8
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [8] => 8
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [8] => 8
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [8] => 8
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [8] => 8
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [8] => 8
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [8] => 8
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [6,2] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [8] => 8
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [8] => 8
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [8] => 8
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [8] => 8
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [8] => 8
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [8] => 8
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [8] => 8
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [8] => 8
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [8] => 8
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [8] => 8
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [8] => 8
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [8] => 8
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [8] => 8
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [8] => 8
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [6,2] => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [8] => 8
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [8] => 8
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [8] => 8
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [8] => 8
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [8] => 8
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [8] => 8
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [8] => 8
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [8] => 8
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [8] => 8
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [8] => 8
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [8] => 8
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [8] => 8
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [8] => 8
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [8] => 8
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [8] => 8
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [8] => 8
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [8] => 8
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [8] => 8
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [8] => 8
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [8] => 8
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,1,1,2] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,1,3] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,2,1,1] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,2,2] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,3,1] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,4] => 4
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,4] => 4
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,3,1] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,4] => 4
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,4] => 4
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4] => 4
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [5,1,1,1] => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [5,1,2] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [5,2,1] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [5,3] => 3
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [5,3] => 3
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [6,2] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [8] => 8
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [8] => 8
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [8] => 8
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [8] => 8
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [8] => 8
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [6,2] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [8] => 8
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [8] => 8
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [8] => 8
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [8] => 8
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [8] => 8
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [8] => 8
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [8] => 8
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [8] => 8
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [8] => 8
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => 1
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [5,1,2] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [5,2,1] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [5,3] => 3
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,3] => 3
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [6,2] => 2
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [8] => 8
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [8] => 8
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [8] => 8
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [8] => 8
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [8] => 8
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [6,2] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [8] => 8
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [8] => 8
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [8] => 8
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [8] => 8
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [8] => 8
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [8] => 8
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [8] => 8
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [8] => 8
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [8] => 8
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,2] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [8] => 8
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [8] => 8
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [8] => 8
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [8] => 8
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [8] => 8
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [8] => 8
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [8] => 8
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [8] => 8
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [8] => 8
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [8] => 8
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [8] => 8
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [8] => 8
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [8] => 8
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [8] => 8
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [5,1,2] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [5,2,1] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [5,3] => 3
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,3] => 3
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [6,2] => 2
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [8] => 8
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [8] => 8
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [8] => 8
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [8] => 8
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [8] => 8
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [6,2] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [8] => 8
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [8] => 8
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [8] => 8
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [8] => 8
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [8] => 8
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [8] => 8
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [8] => 8
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [8] => 8
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [8] => 8
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [6,2] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [8] => 8
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [8] => 8
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [8] => 8
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [8] => 8
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [8] => 8
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [8] => 8
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [8] => 8
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [8] => 8
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [8] => 8
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [8] => 8
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [8] => 8
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [8] => 8
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [8] => 8
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [8] => 8
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,2] => 2
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [8] => 8
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [8] => 8
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [8] => 8
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [8] => 8
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [8] => 8
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [8] => 8
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [8] => 8
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [8] => 8
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [8] => 8
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [8] => 8
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [8] => 8
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [8] => 8
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [8] => 8
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [8] => 8
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [8] => 8
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [8] => 8
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [8] => 8
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [8] => 8
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [8] => 8
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [8] => 8
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,1,2] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,2,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,3] => 3
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,3] => 3
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [6,2] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [8] => 8
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [8] => 8
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [8] => 8
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [8] => 8
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [8] => 8
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,2] => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [8] => 8
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [8] => 8
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [8] => 8
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [8] => 8
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [8] => 8
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [8] => 8
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [8] => 8
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [8] => 8
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [8] => 8
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,2] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [8] => 8
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [8] => 8
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [8] => 8
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [8] => 8
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [8] => 8
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [8] => 8
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [8] => 8
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [8] => 8
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [8] => 8
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [8] => 8
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [8] => 8
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [8] => 8
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [8] => 8
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [8] => 8
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,2] => 2
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [8] => 8
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [8] => 8
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [8] => 8
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [8] => 8
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [8] => 8
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [8] => 8
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [8] => 8
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [8] => 8
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [8] => 8
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [8] => 8
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [8] => 8
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [8] => 8
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [8] => 8
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [8] => 8
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [8] => 8
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [8] => 8
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [8] => 8
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [8] => 8
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [8] => 8
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [8] => 8
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,2] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [8] => 8
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [8] => 8
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [8] => 8
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [8] => 8
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [8] => 8
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [8] => 8
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [8] => 8
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [8] => 8
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [8] => 8
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [8] => 8
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [8] => 8
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [8] => 8
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [8] => 8
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [8] => 8
[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] => [8] => 8
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [8] => 8
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [8] => 8
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [8] => 8
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [8] => 8
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [8] => 8
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [8] => 8
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [8] => 8
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [8] => 8
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [8] => 8
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [8] => 8
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [8] => 8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8] => 8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,1] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,8] => 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] => [1,8] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [8,1] => 1
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,8] => 1
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,8] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,8] => 1
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,8] => 1
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,8] => 1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,8] => 1
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [1,8] => 1
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,8] => 1
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,8] => 1
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,8] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,8] => 1
[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [1,8] => 1
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,8] => 1
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [1,8] => 1
[1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,8] => 1
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [1,8] => 1
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [8,1] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0] => [8,1] => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,2] => 2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,8] => 1
[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,8] => 1
[1,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,8] => 1
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,8] => 1
[1,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,8] => 1
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,7] => 2
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0] => [8,1] => 1
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,1,0] => [8,1] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,7,1] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [7,2] => 2
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,8] => 1
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,8] => 1
[1,0,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,8] => 1
[1,0,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [1,8] => 1
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [1,8] => 1
[1,0,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,8] => 1
[1,0,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [1,8] => 1
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,7] => 2
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,8] => 1
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,7] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0] => [8,1] => 1
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [8,1] => 1
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,7,1] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0] => [7,2] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => [7,2] => 2
[1,0,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [1,8] => 1
[1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [1,8] => 1
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,7] => 2
[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,8] => 1
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,7] => 2
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,7] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,0] => [8,1] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0] => [8,1] => 1
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,1] => 1
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,7,1] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,1,0,0] => [7,2] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0] => [7,2] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,2] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,8] => 1
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [1,8] => 1
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [1,8] => 1
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,8] => 1
[1,0,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [1,8] => 1
[1,0,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,8] => 1
[1,0,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,8] => 1
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,7] => 2
[1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,7] => 1
[1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [1,8] => 1
[1,1,0,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,7] => 2
[1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,7] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9] => 9
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [9] => 9
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [9] => 9
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [9] => 9
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [9] => 9
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [9] => 9
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [9] => 9
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [9] => 9
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [9] => 9
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [9] => 9
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [9] => 9
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [9] => 9
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [9] => 9
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [9] => 9
[1,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [9] => 9
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [9] => 9
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [9] => 9
[1,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [9] => 9
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [9] => 9
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [9] => 9
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [9] => 9
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [9] => 9
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [9] => 9
[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [9] => 9
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [9] => 9
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [9] => 9
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [9] => 9
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [9] => 9
[1,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [9] => 9
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [9] => 9
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [9] => 9
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [9] => 9
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [9] => 9
[1,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [9] => 9
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [9] => 9
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [9] => 9
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [9] => 9
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [9] => 9
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [9] => 9
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [9] => 9
[1,1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [9] => 9
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [9] => 9
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [9] => 9
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [9] => 9
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [9] => 9
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [9] => 9
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [9] => 9
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [9] => 9
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [9] => 9
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [9] => 9
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [9] => 9
[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [9] => 9
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [9] => 9
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [9] => 9
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [9] => 9
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [9] => 9
[1,1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [9] => 9
[1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [9] => 9
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [9] => 9
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [9] => 9
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [9] => 9
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [9] => 9
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [9] => 9
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9] => 9
[1,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [9] => 9
[1,1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [9] => 9
[1,1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [9] => 9
[1,1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [9] => 9
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [9] => 9
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [9] => 9
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [9] => 9
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [9] => 9
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [9] => 9
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [9] => 9
[1,1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [9] => 9
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [9] => 9
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [9] => 9
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [9] => 9
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [9] => 9
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [9] => 9
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [9] => 9
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [9] => 9
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [9] => 9
[1,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [9] => 9
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [9] => 9
[1,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [9] => 9
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [9] => 9
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [9] => 9
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [9] => 9
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [9] => 9
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [9] => 9
[1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [9] => 9
[1,1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [9] => 9
[1,1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [9] => 9
[1,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [9] => 9
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [9] => 9
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [9] => 9
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [9] => 9
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [9] => 9
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [9] => 9
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [9] => 9
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [9] => 9
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [9] => 9
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [9] => 9
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9] => 9
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [9] => 9
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [9] => 9
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [9] => 9
[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [9] => 9
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [9] => 9
[1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [9] => 9
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [9] => 9
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [9] => 9
[1,1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [9] => 9
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [9] => 9
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [9] => 9
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [9] => 9
[1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [9] => 9
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [9] => 9
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [9] => 9
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [9] => 9
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [9] => 9
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [9] => 9
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [9] => 9
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [9] => 9
[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [9] => 9
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [9] => 9
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [9] => 9
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [9] => 9
[1,1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [9] => 9
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [9] => 9
[1,1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [9] => 9
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [9] => 9
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [9] => 9
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [9] => 9
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9] => 9
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [9] => 9
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [9] => 9
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [9] => 9
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [9] => 9
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [9] => 9
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [9] => 9
[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [9] => 9
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [9] => 9
[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [9] => 9
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [9] => 9
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [9] => 9
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [9] => 9
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [9] => 9
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [9] => 9
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [9] => 9
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [9] => 9
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [9] => 9
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [9] => 9
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [9] => 9
[1,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [9] => 9
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [9] => 9
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [9] => 9
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [9] => 9
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [9] => 9
[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [9] => 9
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [9] => 9
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [9] => 9
[1,1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [9] => 9
[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [9] => 9
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [9] => 9
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [9] => 9
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [9] => 9
[1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [9] => 9
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [9] => 9
[1,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [9] => 9
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [9] => 9
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [9] => 9
[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [9] => 9
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [9] => 9
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [9] => 9
[1,1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [9] => 9
[1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [9] => 9
[1,1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [9] => 9
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [9] => 9
[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [9] => 9
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [9] => 9
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [9] => 9
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [9] => 9
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [9] => 9
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [9] => 9
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [9] => 9
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [9] => 9
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [9] => 9
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [9] => 9
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0] => [9] => 9
[1,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,0] => [9] => 9
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,0] => [9] => 9
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0] => [9] => 9
[1,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,0] => [9] => 9
[1,1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0,0] => [9] => 9
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,0] => [9] => 9
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,0] => [9] => 9
[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0] => [9] => 9
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [9] => 9
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0] => [9] => 9
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0,0] => [9] => 9
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,0] => [9] => 9
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9] => 9
[1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0] => [9] => 9
[1,1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0,0] => [9] => 9
[1,1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0,0] => [9] => 9
[1,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0,0] => [9] => 9
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0,0] => [9] => 9
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0] => [9] => 9
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0,0] => [9] => 9
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0] => [9] => 9
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0] => [9] => 9
[1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0] => [9] => 9
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0] => [9] => 9
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0] => [9] => 9
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [9] => 9
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,0] => [9] => 9
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0] => [9] => 9
[1,1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0,0] => [9] => 9
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0] => [9] => 9
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [9] => 9
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0] => [9] => 9
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0] => [9] => 9
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => [9] => 9
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0] => [9] => 9
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => [9] => 9
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [9] => 9
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [9] => 9
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,0] => [9] => 9
[1,1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0,0] => [9] => 9
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => [9] => 9
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [9] => 9
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,0] => [9] => 9
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0,0] => [9] => 9
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0] => [9] => 9
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [9] => 9
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,0] => [9] => 9
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [9] => 9
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0] => [9] => 9
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0] => [9] => 9
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [9] => 9
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0] => [9] => 9
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0,0] => [9] => 9
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0,0] => [9] => 9
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0,0] => [9] => 9
[1,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0] => [9] => 9
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0] => [9] => 9
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0] => [9] => 9
[1,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0] => [9] => 9
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0] => [9] => 9
[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0] => [9] => 9
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [9] => 9
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0] => [9] => 9
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0] => [9] => 9
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0] => [9] => 9
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [9] => 9
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0] => [9] => 9
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0] => [9] => 9
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0,0] => [9] => 9
[1,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,0] => [9] => 9
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,0] => [9] => 9
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,0] => [9] => 9
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0] => [9] => 9
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0] => [9] => 9
[1,1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0] => [9] => 9
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0,0] => [9] => 9
[1,1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0] => [9] => 9
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0,0] => [9] => 9
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => [9] => 9
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [9] => 9
[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0] => [9] => 9
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0] => [9] => 9
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,0] => [9] => 9
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [9] => 9
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,0] => [9] => 9
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0] => [9] => 9
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0] => [9] => 9
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0] => [9] => 9
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0] => [9] => 9
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0] => [9] => 9
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0] => [9] => 9
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [9] => 9
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0] => [9] => 9
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0,0] => [9] => 9
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => [9] => 9
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0] => [9] => 9
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0] => [9] => 9
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0] => [9] => 9
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0] => [9] => 9
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0] => [9] => 9
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0] => [9] => 9
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => [9] => 9
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,0] => [9] => 9
[1,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0,0] => [9] => 9
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => [9] => 9
[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0] => [9] => 9
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [9] => 9
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0] => [9] => 9
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0] => [9] => 9
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0] => [9] => 9
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0] => [9] => 9
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0] => [9] => 9
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0] => [9] => 9
[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0] => [9] => 9
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => [9] => 9
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => [9] => 9
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [9] => 9
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [9] => 9
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0] => [9] => 9
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [9] => 9
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [9] => 9
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [9] => 9
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [9] => 9
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0] => [9] => 9
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [9] => 9
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [9] => 9
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0] => [9] => 9
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0] => [9] => 9
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [9] => 9
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [9] => 9
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [9] => 9
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [9] => 9
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [9] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,2] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,3] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,4] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,5] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,6] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,7] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,8] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,3] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,4] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,5] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,6] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,7] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,8] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,4] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,5] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,4] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,6] => 1
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,5] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,7] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,6] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,8] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,5] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,6] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,5] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,7] => 1
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,5] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,8] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,7] => 1
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,6] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,7] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [1,8] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,6] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,6] => 1
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,5] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [1,8] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,7] => 1
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,7] => 1
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,7] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,7] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,8] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,7] => 1
[1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,6] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [1,8] => 1
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [1,8] => 1
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,7] => 1
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,8] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,8] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,8] => 1
[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,6] => 1
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,7] => 1
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,6] => 1
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [1,8] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,8] => 1
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,8] => 1
[1,0,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,7] => 1
[1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,7] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,1,2,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,1,2,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,1,2,2] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,1,3,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,2,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,1,2,1,2] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,1,2,2,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,1,2,3] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,3,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,3,2] => 1
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,4,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,2,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,2,1,2,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,2,2,1,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,2,2,2] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,2,4] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,3,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,3,2,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,3,3] => 1
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,5,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,2,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,2,1,1,1,2] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,2,1,1,2,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,2,1,1,3] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,2,1,2,2] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,2,2,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,2,2,2,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,2,2,3] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,2,3,2] => 1
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,2,4,1] => 1
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,2,5] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,3,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,3,2,2] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,4,1,1,1] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,4,3] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,5,1,1] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,5,2] => 1
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,6,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,1,1,1,1,2] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,1,1,1,2,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,1,1,1,3] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,1,1,2,1,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,1,2,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,1,5] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,2,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,2,1,1,2] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,2,2,1,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,2,2,2] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,2,3,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,2,4] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,3,1,1,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,3,3] => 1
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,5,1] => 1
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,6] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,1,1,1,1,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,2,1] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,3,1,1] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,3,2] => 1
[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,5] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,4,1,1,1,1] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,4,1,3] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,4,2,1,1] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,4,4] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,5,1,1,1] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,5,3] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,6,1,1] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,6,2] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,1,2] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,1,2,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,1,1,3] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,1,1,2,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,1,1,2,2] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,1,1,3,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,1,1,4] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,1,2,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,1,2,3] => 1
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,1,4,1] => 1
[1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,1,5] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,2,1,1,1,1] => 1
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,2,2,2] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,3,3] => 1
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,5,1] => 1
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,6] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,2,1,1,1,2] => 1
[1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,2,1,4] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,2,2,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,2,2,1,2] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,2,2,2,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,2,2,3] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,2,3,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,2,3,2] => 2
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,5] => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,3,1,1,1,1] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,3,3,1] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,4,1,1,1] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,4,3] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,5,1,1] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,5,2] => 2
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,6,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,1,1,1,1,2] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [3,1,1,1,2,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [3,1,1,1,3] => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [3,1,2,1,2] => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,2,1] => 1
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,1] => 1
[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,5] => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,2,1,1,1,1] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,2,2,2] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [3,3,1,1,1] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => 3
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [3,4,2] => 2
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [3,5,1] => 1
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,6] => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,1,0,0] => [4,1,1,1,2] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,0,0,0] => [4,1,1,3] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,0] => [4,1,3,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0] => [4,1,4] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0] => [4,2,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [4,2,2,1] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0] => [4,2,3] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0] => [4,3,1,1] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0] => [4,3,2] => 2
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [4,4,1] => 1
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5] => 4
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,1,0,0] => [5,1,1,2] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,1,0] => [5,1,2,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0] => [5,1,3] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [5,2,1,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [5,3,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,4] => 4
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0] => [6,1,2] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [6,2,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,3] => 3
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [6,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,1] => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [8,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,1,3] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [3,1,1,1,3] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,1,1,1,3] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,1,1,1,1,2] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [6,1,1,1] => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [7,2] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,7] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,1] => 1
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,6] => 3
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5] => 4
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,4] => 4
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => [6,3] => 3
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,4,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,3,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [5,1,1,2] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,1,1,1] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,8] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,8] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,2] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,7] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [6,3] => 3
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,4] => 4
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,5] => 4
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,6] => 3
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,7] => 2
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,2] => 2
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,6] => 3
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,3] => 3
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,5] => 4
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [6,3] => 3
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4] => 4
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,6] => 3
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,2,1,4] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0] => [7,2] => 2
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,7] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,1,0,0,0] => [6,3] => 3
[1,1,1,0,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,6] => 3
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,4,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,3,1,1] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,1,5] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,3,2] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [6,2,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [5,2,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [4,2,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,2,1,1,1,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [4,2,2,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [6,2,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [8,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [7,2] => 2
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [5,2,2] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,2,2,2] => 2
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [6,2,1] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [8,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [5,4] => 4
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [3,4,2] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,4,2,2] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [4,1,4] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [8,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [3,1,1,1,2,1] => 1
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,7] => 1
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,6] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,5] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,4] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [3,6] => 3
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0] => [4,5] => 4
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,1,0,0] => [5,4] => 4
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [4,1,2,1,1] => 1
[1,1,1,0,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,6] => 3
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [3,6] => 3
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0,1,0] => [4,4,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,5] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0] => [6,3] => 3
[1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,8] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [4,1,1,1,2] => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,1,0,0] => [5,1,1,2] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,1,0,0] => [6,1,2] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,4,1] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,8] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,5,1,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,7] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [3,6] => 3
[1,0,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [1,8] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,7] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,6] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [1,5,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,4,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [5,4] => 4
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,3,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,6] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [6,1,2] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,6,2] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,7] => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,7] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,2] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,6,1] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,2,4,1] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [5,2,2] => 2
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,6] => 3
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,6,1] => 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,7] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,7,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,3,4] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,5,3] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [6,3] => 3
[1,1,0,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5] => 4
[1,0,1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,3,4] => 1
[1,0,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,7] => 1
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,6,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [8,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [8,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [5,3,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [8,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [1,7,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,6] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,1,1,3,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [3,1,1,3,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,1,1,3,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,5] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [6,3] => 3
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,1,0,0] => [6,1,2] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,1,0,0] => [4,1,1,3] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [8,1] => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,4,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [4,1,1,2,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,5,1,1] => 1
[1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,6] => 1
[1,0,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,1,5] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,1,1,4] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,2,2,3] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,2,3,1,1] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [5,2,2] => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [4,2,2,1] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,4] => 4
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [3,6] => 3
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,5] => 1
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,6] => 1
[1,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,7] => 1
[1,0,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,8] => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [6,3] => 3
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [7,2] => 2
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,1,0] => [7,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,1,4,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,3,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,1,1,4] => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,4,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,4,1,1] => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,1,0,0,0] => [6,3] => 3
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [3,1,2,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [6,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,1,6] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [3,1,5] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,1,0,0] => [4,1,4] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [4,5] => 4
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,1,5] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,7] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,6] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,5,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,2,4,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [7,1,1] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,8] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [3,3,1,1,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,3,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,0] => [8,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,8] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,5,1,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,6,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,4,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,5,1] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [1,6,1,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,4,1,1] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [1,7,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,1] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,1,0,0,0] => [6,3] => 3
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,8] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,1,0,0] => [5,2,2] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,8] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,7] => 1
[1,1,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,1,5] => 1
[1,1,0,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,5] => 1
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [3,6] => 3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,5,1,2] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [4,2,2,1] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [6,2,1] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,2,2] => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [6,2,1] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [8,1] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,2] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [8,1] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [8,1] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [8,1] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [8,1] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,1,1,5] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [8,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [8,1] => 1
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,5,1] => 1
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,7,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [4,1,1,1,2] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [5,1,2,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [4,1,3,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [3,1,4,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,5,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,6,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [4,1,1,3] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [3,1,1,4] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,5] => 1
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0] => [8,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,4,1] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,4,1,1] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,5,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,3] => 3
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,0] => [5,4] => 4
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,1,0,0] => [5,4] => 4
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,8] => 1
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,1] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [1,8] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,7] => 2
[1,1,0,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,4] => 4
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [3,3,3] => 3
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,6,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,2,4] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,2,6] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,8] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,7] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,2,5] => 2
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,2,6] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [1,8] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,7] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [4,5] => 4
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3] => 2
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,5] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,1,0,0] => [5,1,3] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [3,1,1,1,3] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,8] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,2,5] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,1,1,4] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [3,1,5] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,6] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,2,5] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,2,4] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,1,2,3] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,5,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,4,2,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,2,4,1,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [1,5,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,1,5] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,6,1,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [5,4] => 4
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,6] => 3
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,8] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [3,6] => 3
[1,0,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,8] => 1
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,8] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,4,1,2] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,4] => 4
[1,1,0,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5] => 4
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,5] => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [8,1] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,8] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [1,8] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [1,6,2] => 1
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [2,7] => 2
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,6,1] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [1,6,1,1] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [7,2] => 2
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,7] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,1,5] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,2,4,2] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => 1
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,4,2] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,4,2] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,5,2] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,5,2] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,5,2] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,5,2] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,7,1] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,6,1] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [8,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,3,1,3,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,2,1,3,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,1,1,2,1] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [3,6] => 3
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [3,3,3] => 3
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,5,2] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,4,3] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4] => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,4,3] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [1,6,2] => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [1,5,3] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,4] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [4,5] => 4
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [4,4,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [3,5,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [5,3,1] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [4,4,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [3,5,1] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,6,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,7,1] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [4,4,1] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [3,5,1] => 1
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [4,4,1] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,6,1] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [3,5,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [1,7,1] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,6,1] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [1,7,1] => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [6,2,1] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [8,1] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [8,1] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,8] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [1,8] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [7,2] => 2
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,7] => 2
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [1,7,1] => 1
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,1,0,0] => [4,5] => 4
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,1,1,1,1] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,0] => [6,2,1] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,0] => [6,2,1] => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [6,2,1] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0] => [6,2,1] => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [6,2,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [8,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [8,1] => 1
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [3,5,1] => 1
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [4,4,1] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,1,0] => [5,3,1] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0] => [6,2,1] => 1
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [4,4,1] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0] => [5,3,1] => 1
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,4,1] => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,1,0] => [6,2,1] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,1] => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [1,5,2,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [5,4] => 4
[1,0,1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [1,8] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [3,1,5] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,1,1,4] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,8] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,8] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,5,2] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,2,1] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [8,1] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [8,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,6,1] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [4,4,1] => 1
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [6,2,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,7] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,3] => 3
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,2] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [7,1,1] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,2,6] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,8] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,2,5] => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,8] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [6,1,1,1] => 1
[1,0,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [1,8] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,6] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [1,8] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,8] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [1,8] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [1,8] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [2,6,1] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,1,0,0] => [5,2,2] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,2] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,6,2] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,1,0] => [8,1] => 1
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0,1,0] => [8,1] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [1,8] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0] => [8,1] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,1,5] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [2,6,1] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,6,2] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,7,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,5,2,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,2,1] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,6,2] => 1
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,8] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,5,3] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,4,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,4,2,1] => 1
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,8] => 1
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,8] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [8,1] => 1
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,1,0] => [8,1] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [8,1] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,2,4,2] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,5,1,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,3,1,1,2] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [8,1] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0,1,0] => [8,1] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0,1,0] => [6,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [8,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [7,2] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,7] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,7] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [8,1] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [8,1] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [1,6,2] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,4,4] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,1,4] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,1,1,4] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [8,1] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => [6,3] => 3
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [4,5] => 4
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [2,7] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,8] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [3,6] => 3
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [5,4] => 4
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [7,2] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [4,5] => 4
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,7] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [1,8] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [3,6] => 3
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [7,2] => 2
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [5,2,2] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [8,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [4,4,1] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [1,8] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,8] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [4,2,2,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,1,1,4] => 1
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,8] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,6,2] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,4,2,2] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0] => [7,2] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0] => [7,2] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [5,2,2] => 2
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,2,1] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [3,6] => 3
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [5,4] => 4
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [3,1,1,4] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,1,0,0,0] => [4,1,4] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [7,2] => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [6,3] => 3
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,8] => 1
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,8] => 1
[1,1,0,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,7] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,7] => 2
[1,0,1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,7] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [3,4,1,1] => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [6,3] => 3
[1,1,0,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [4,5] => 4
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [7,2] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [7,2] => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,7] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,7] => 2
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,7] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,7] => 2
[1,1,0,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,7] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [4,5] => 4
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,2,1,3] => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0,1,0] => [6,2,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0,1,0] => [6,2,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0] => [7,1,1] => 1
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,8] => 1
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,8] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,6,1] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [8,1] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,2,2] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0] => [5,2,2] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [1,6,1,1] => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [1,5,1,1,1] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [5,3,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3] => 2
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [3,2,4] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,6,1] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [4,3,2] => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [3,1,1,3,1] => 1
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,7] => 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,5,3] => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,5,3] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,5,1] => 1
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5] => 4
[1,1,1,1,0,0,0,1,0,0,1,1,1,1,0,0,0,0] => [5,4] => 4
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,1,0,0,0] => [6,3] => 3
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0] => [8,1] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [8,1] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [1,7,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [5,2,1,1] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,5] => 4
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [6,3] => 3
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,1,0,0] => [7,2] => 2
[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,7] => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,2,1,1,3] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [5,4] => 4
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,5,3] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,4,1,3] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [1,8] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,1,1,3] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [1,4,4] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,1,4] => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [5,1,2,1] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [1,8] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [1,8] => 1
[1,0,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,8] => 1
[1,0,1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,8] => 1
[1,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,8] => 1
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
click to show known generating functions       
Description
The smallest part of an integer composition.
Map
touch composition
Description
Sends a Dyck path to its touch composition given by the composition of lengths of its touch points.