Identifier
Values
[1,0,1,0] => [1,1] => [1,1] => [1,0,1,0] => 0
[1,1,0,0] => [2] => [2] => [1,1,0,0] => 1
[1,0,1,0,1,0] => [1,1,1] => [1,1,1] => [1,0,1,0,1,0] => 0
[1,0,1,1,0,0] => [1,2] => [1,2] => [1,0,1,1,0,0] => 1
[1,1,0,0,1,0] => [2,1] => [2,1] => [1,1,0,0,1,0] => 1
[1,1,0,1,0,0] => [3] => [3] => [1,1,1,0,0,0] => 0
[1,1,1,0,0,0] => [3] => [3] => [1,1,1,0,0,0] => 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] => 0
[1,0,1,0,1,1,0,0] => [1,1,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,0] => [1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,0,0] => [1,3] => [1,3] => [1,0,1,1,1,0,0,0] => 0
[1,0,1,1,1,0,0,0] => [1,3] => [1,3] => [1,0,1,1,1,0,0,0] => 0
[1,1,0,0,1,0,1,0] => [2,1,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,0] => [2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,0] => [3,1] => [3,1] => [1,1,1,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,0] => [4] => [4] => [1,1,1,1,0,0,0,0] => 0
[1,1,0,1,1,0,0,0] => [4] => [4] => [1,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,0,1,0] => [3,1] => [3,1] => [1,1,1,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,0] => [4] => [4] => [1,1,1,1,0,0,0,0] => 0
[1,1,1,0,1,0,0,0] => [4] => [4] => [1,1,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,0,0] => [4] => [4] => [1,1,1,1,0,0,0,0] => 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] => 0
[1,0,1,0,1,0,1,1,0,0] => [1,1,1,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,0] => [1,1,2,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,1,0,0] => [1,1,3] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,1,1,0,0,0] => [1,1,3] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 0
[1,0,1,1,0,0,1,0,1,0] => [1,2,1,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,0] => [1,2,2] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,0] => [1,3,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,0] => [1,4] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,0] => [1,4] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,1,0,0,0,1,0] => [1,3,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,0,1,0,0] => [1,4] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,0] => [1,4] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,0] => [1,4] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0] => [2,1,1,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,0] => [2,1,2] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,0] => [2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,1,0,0] => [2,3] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,0] => [2,3] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,0] => [3,1,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,0,0,1,1,0,0] => [3,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,0] => [4,1] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,0] => [5] => [5] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,0,0] => [5] => [5] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,0,1,0] => [4,1] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,0] => [5] => [5] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,0,0] => [5] => [5] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,0,0] => [5] => [5] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,0] => [3,1,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,0,0,0,1,1,0,0] => [3,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,0,1,0] => [4,1] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,0] => [5] => [5] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,0,0] => [5] => [5] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,0] => [4,1] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,0] => [5] => [5] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,0,0] => [5] => [5] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,0,0] => [5] => [5] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,0] => [4,1] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,0] => [5] => [5] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,0,0] => [5] => [5] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,0] => [5] => [5] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,0] => [5] => [5] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,2] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,2,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,3] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,3] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,2,1,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,2,2] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,3,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,4] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,4] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,3,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,4] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,4] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,4] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,1,1,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,1,2] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,1] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,1,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,2] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,4,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,5] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,5] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,4,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,5] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,5] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,5] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,3,1,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,5] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,5] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,5] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,5] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,5] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,4,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
>>> Load all 1185 entries. <<<
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,5] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,2] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,2,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,2,1,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,4] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,4] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,4] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,4] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,4] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,0] => [3,1,2] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [3,2,1] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [3,3] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,3] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,0] => [4,1,1] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,0] => [4,2] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => [5,1] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,1] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,1,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,1,0,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,0,1,0,1,0] => [4,1,1] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,0,1,1,0,0] => [4,2] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => [5,1] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,0,0,1,0] => [5,1] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,1,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,0,0,1,0] => [5,1] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,1,0,0,0,1,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,1,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,0,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,3] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,3] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,0,1,0] => [4,1,1] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,0,1,1,0,0] => [4,2] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [5,1] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,1,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,0,0,1,0] => [5,1] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,1,0,0,1,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,1,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,1] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,2] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [5,1] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,1,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,1] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,1] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,1,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,1,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,0,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,1,1] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,2] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,0] => [5,1] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,1,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,1] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,1,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,1] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,1,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[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] => 0
[1,1,1,1,1,1,0,0,0,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,2] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,2,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,3] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,3] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,2,1,1] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,2,2] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,3,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,4] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,4] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,3,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,4] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,4] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,4] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,2,1,1,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,2,1,2] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,2,2,1] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,2,3] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,2,3] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,3,1,1] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,3,2] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,4,1] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,5] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,5] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,4,1] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,5] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,5] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,5] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,3,1,1] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,3,2] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,4,1] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,5] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,5] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,4,1] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,5] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,5] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,5] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,4,1] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,5] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,5] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,5] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,5] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,1,1,2] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,1,2,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,1,3] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,1,3] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,2,1,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,2,2] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,3,1] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,4] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,3,1] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,4] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,4] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,1,1,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,1,2] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,2,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,3] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,3] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,4,1,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,4,2] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,5,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,5,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,4,1,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,4,2] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,5,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,5,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,5,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,3,1,1,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,3,1,2] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,3,2,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,3,3] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,3,3] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,1,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,5,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,5,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,1,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,2] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,5,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,5,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,5,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,4,1,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,4,2] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,5,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,5,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,2] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,2,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,3] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,3] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,2,1,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,2,2] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,4] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,4] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,4] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,4] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,4] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,2,1,1,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,2,1,2] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,2,2,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,2,3] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,2,3] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,3,2] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,4,1] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,5] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,5] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,4,1] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,5] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,5] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,5] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,2] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,4,1] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,5] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,5] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,4,1] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,5] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,5] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,5] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,4,1] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,5] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,5] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,5] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,5] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,1,1,2] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,2,1] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [3,1,3] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,1,3] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,2,1,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,2] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [3,3,1] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,4] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [3,4] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,3,1] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,4] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [3,4] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,4] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [4,1,1,1] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [4,1,2] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [4,2,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [4,3] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [4,3] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [5,1,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [5,2] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [5,1,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [5,2] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [4,1,1,1] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [4,1,2] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [4,2,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [4,3] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,3] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [5,1,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [5,2] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [5,1,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [5,2] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [5,1,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [5,2] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,1,2] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,1,2,1] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,3] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,3] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,2] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,3,1] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,4] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,4] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,3,1] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,4] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,4] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,4] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [4,1,1,1] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [4,1,2] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [4,2,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [4,3] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,3] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [5,1,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [5,2] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [5,1,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [5,2] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,1,1,1] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,1,2] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,2,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,3] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,3] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [5,1,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [5,2] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [5,1,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,2] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,1,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,2] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,1,1] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,1,2] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,2,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [5,1,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [5,2] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,1,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,2] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,1,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,2] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,1,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,2] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[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] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,2] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,2,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,3] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,3] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,2,1,1] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,2,2] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,4] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,4] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,4] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,4] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,4] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,2,1,1,1] => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,2,1,2] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,2,2,1] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,2,3] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,2,3] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,3,1,1] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,5] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,5] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,5] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,5] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,5] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,3,1,1] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,5] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,5] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,5] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,5] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,5] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,5] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,5] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,5] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,5] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,2,1,1,1,1] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,2,1,1,2] => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,2,1,2,1] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,2,1,3] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,2,1,3] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,2,2,1,1] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,2,2,2] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,2,3,1] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,2,4] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,2,4] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,2,3,1] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,2,4] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,2,4] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,2,4] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,3,1,1,1] => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,3,1,2] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,3,3] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,3,3] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,4,1,1] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,4,1,1] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,3,1,1,1] => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,3,1,2] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,3,3] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,3,3] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,4,1,1] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,4,1,1] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,4,1,1] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1] => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,2,1,1,1,2] => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,2,1,1,2,1] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,2,1,1,3] => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,2,1,1,3] => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,2,1,2,1,1] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,2,1,2,2] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,2,1,3,1] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,2,1,4] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,2,1,4] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,2,1,3,1] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,2,1,4] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,2,1,4] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,2,1,4] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,2,2,1,1,1] => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,2,2,1,2] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,2,1] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,2,2,3] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,2,2,3] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,1,1] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,1] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,2,5] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,2,5] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,1] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,2,5] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,2,5] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,2,5] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,1,1] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,2,4,1] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,2,4,1] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,2,5] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,2,5] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,2,4,1] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,2,5] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,2,5] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,2,5] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,5] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,1,1,1,1] => [1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,1,1,2] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,1,1] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,2] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,3,4] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,3,4] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,3,4] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,4,1,1,1] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,4,1,2] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,5,1,1] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,5,1,1] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,4,1,1,1] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,4,1,2] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,5,1,1] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,5,1,1] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,5,1,1] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,3,1,1,1,1] => [1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,3,1,1,2] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,3,2,1,1] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,3,2,2] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,3,4] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,3,4] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,3,4] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,3,4] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,3,4] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,4,1,1,1] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,4,1,2] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,5,1,1] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,5,1,1] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,4,1,1,1] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,4,1,2] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,5,1,1] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,5,1,1] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,5,1,1] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,4,1,1,1] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,4,1,2] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,5,1,1] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,5,1,1] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,5,1,1] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,5,1,1] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,2] => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,2,1] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,3] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,1,3] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,1,2,1,1] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,1,2,2] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,1,3,1] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,1,4] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,1,1,4] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,1,3,1] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,1,4] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,1,4] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,1,4] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,2,1,1,1] => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,2,1,2] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,2,2,1] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,2,3] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,2,3] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,3,1,1] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,1] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,5] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,1,5] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,1] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,1,5] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,1,5] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,1,5] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,1,1] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,4,1] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,4,1] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,1,5] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,5] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,1,5] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,1] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,1,5] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,5] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,5] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,5] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,2,1,1,2] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,2,1,2,1] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,2,1,3] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,2,1,3] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,2,2,1,1] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,2,3,1] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,2,4] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,2,4] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,2,3,1] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,2,4] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,2,4] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,4] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,1,1] => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,2] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,3] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,3] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,4,1,1] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,5,1] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,5,1] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,1,1] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,5,1] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,5,1] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,1] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,1,1,1] => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,1,2] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,3,3] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,3] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,4,1,1] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,5,1] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,5,1] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,4,1,1] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,5,1] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,5,1] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,5,1] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,4,1,1] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,5,1] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,5,1] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,5,1] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,5,1] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,1,1,2] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,1,3] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [3,1,1,3] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,2,1,1] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [3,1,2,2] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,1,1] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [3,2,1,2] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,2,1] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [3,3,1,1] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [3,3,1,1] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1] => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [4,1,1,2] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [4,1,3] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [4,2,1,1] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [4,2,2] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [5,1,1,1] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [5,1,2] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [5,1,2] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1] => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [4,1,1,2] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [4,1,3] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [4,2,1,1] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [4,2,2] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [5,1,1,1] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [5,1,2] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [5,1,2] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,1,2] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,1,1,2] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,1,3] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,1,1,3] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,2,1,1] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [3,1,2,2] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,1,1] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [3,2,1,2] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,2,1] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,3,1,1] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [3,3,1,1] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1] => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [4,1,1,2] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [4,1,3] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [4,2,1,1] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [4,2,2] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [5,1,1,1] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [5,1,2] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [5,1,2] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1] => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [4,1,1,2] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [4,1,3] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [4,2,1,1] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [4,2,2] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [5,1,1,1] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [5,1,2] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [5,1,2] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [5,1,2] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1] => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,1,1,2] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,1,3] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,2,1,1] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,2,2] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [5,1,1,1] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [5,1,2] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [5,1,2] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [5,1,2] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,1,2] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
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Description
The number of rises of length 2 of a Dyck path.
This is also the number of $(1,1)$ steps of the associated Łukasiewicz path, see [1].
A related statistic is the number of double rises in a Dyck path, St000024The number of double up and double down steps of a Dyck path..
Map
bounce path
Description
The bounce path determined by 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.
Map
Foata bijection
Description
The Foata bijection for compositions.
The Foata bijection $\phi$ is a bijection on the set of words whose letters are positive integers. It can be defined by induction on the size of the word:
Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$.
At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.
  • If $w_{i+1} \geq v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} \geq v_k$.
  • If $w_{i+1} < v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} < v_k$.
In either case, place a vertical line at the start of the word as well. Now, within each block between vertical lines, cyclically shift the entries one place to the right.
To compute $\phi([1,4,2,5,3])$, the sequence of words is
  • $1$
  • $|1|4 \to 14$
  • $|14|2 \to 412$
  • $|4|1|2|5 \to 4125$
  • $|4|125|3 \to 45123.$
In total, this gives $\phi([1,4,2,5,3]) = [4,5,1,2,3]$.
This bijection sends the major index St000769The major index of a composition regarded as a word. to the number of inversions St000766The number of inversions of an integer composition..