edit this statistic or download as text // json
Identifier
Values
[1,0] => 0
[1,0,1,0] => 0
[1,1,0,0] => 1
[1,0,1,0,1,0] => 0
[1,0,1,1,0,0] => 1
[1,1,0,0,1,0] => 1
[1,1,0,1,0,0] => 2
[1,1,1,0,0,0] => 2
[1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,0] => 3
[1,1,1,0,0,0,1,0] => 2
[1,1,1,0,0,1,0,0] => 3
[1,1,1,0,1,0,0,0] => 4
[1,1,1,1,0,0,0,0] => 3
[1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,0,0] => 3
[1,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,0,0] => 4
[1,0,1,1,1,1,0,0,0,0] => 3
[1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,0,0] => 3
[1,1,0,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,0] => 3
[1,1,0,1,0,1,0,0,1,0] => 3
[1,1,0,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,1,1,0,0,0] => 4
[1,1,0,1,1,0,0,0,1,0] => 3
[1,1,0,1,1,0,0,1,0,0] => 4
[1,1,0,1,1,0,1,0,0,0] => 5
[1,1,0,1,1,1,0,0,0,0] => 4
[1,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,1,0,0] => 3
[1,1,1,0,0,1,0,0,1,0] => 3
[1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,0,0,1,1,0,0,0] => 4
[1,1,1,0,1,0,0,0,1,0] => 4
[1,1,1,0,1,0,0,1,0,0] => 5
[1,1,1,0,1,0,1,0,0,0] => 6
[1,1,1,0,1,1,0,0,0,0] => 5
[1,1,1,1,0,0,0,0,1,0] => 3
[1,1,1,1,0,0,0,1,0,0] => 4
[1,1,1,1,0,0,1,0,0,0] => 5
[1,1,1,1,0,1,0,0,0,0] => 6
[1,1,1,1,1,0,0,0,0,0] => 4
[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
[1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,0] => 1
[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] => 2
[1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,0,1,1,0,0,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,0] => 3
[1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,1,0,1,0,0,1,0] => 3
[1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,1,0,1,1,0,0,0] => 4
[1,0,1,1,0,1,1,0,0,0,1,0] => 3
[1,0,1,1,0,1,1,0,0,1,0,0] => 4
[1,0,1,1,0,1,1,0,1,0,0,0] => 5
[1,0,1,1,0,1,1,1,0,0,0,0] => 4
[1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,1,1,0,0,1,1,0,0,0] => 4
[1,0,1,1,1,0,1,0,0,0,1,0] => 4
[1,0,1,1,1,0,1,0,0,1,0,0] => 5
[1,0,1,1,1,0,1,0,1,0,0,0] => 6
[1,0,1,1,1,0,1,1,0,0,0,0] => 5
>>> Load all 2245 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,0,0,0,1,0,0] => 4
[1,0,1,1,1,1,0,0,1,0,0,0] => 5
[1,0,1,1,1,1,0,1,0,0,0,0] => 6
[1,0,1,1,1,1,1,0,0,0,0,0] => 4
[1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => 3
[1,1,0,0,1,0,1,1,1,0,0,0] => 3
[1,1,0,0,1,1,0,0,1,0,1,0] => 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] => 3
[1,1,0,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,0,1,1,0,1,1,0,0,0] => 4
[1,1,0,0,1,1,1,0,0,0,1,0] => 3
[1,1,0,0,1,1,1,0,0,1,0,0] => 4
[1,1,0,0,1,1,1,0,1,0,0,0] => 5
[1,1,0,0,1,1,1,1,0,0,0,0] => 4
[1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,1,0,0,1,1,0,1,0,0] => 4
[1,1,0,1,0,0,1,1,1,0,0,0] => 4
[1,1,0,1,0,1,0,0,1,0,1,0] => 3
[1,1,0,1,0,1,0,0,1,1,0,0] => 4
[1,1,0,1,0,1,0,1,0,0,1,0] => 4
[1,1,0,1,0,1,0,1,0,1,0,0] => 5
[1,1,0,1,0,1,0,1,1,0,0,0] => 5
[1,1,0,1,0,1,1,0,0,0,1,0] => 4
[1,1,0,1,0,1,1,0,0,1,0,0] => 5
[1,1,0,1,0,1,1,0,1,0,0,0] => 6
[1,1,0,1,0,1,1,1,0,0,0,0] => 5
[1,1,0,1,1,0,0,0,1,0,1,0] => 3
[1,1,0,1,1,0,0,0,1,1,0,0] => 4
[1,1,0,1,1,0,0,1,0,0,1,0] => 4
[1,1,0,1,1,0,0,1,0,1,0,0] => 5
[1,1,0,1,1,0,0,1,1,0,0,0] => 5
[1,1,0,1,1,0,1,0,0,0,1,0] => 5
[1,1,0,1,1,0,1,0,0,1,0,0] => 6
[1,1,0,1,1,0,1,0,1,0,0,0] => 7
[1,1,0,1,1,0,1,1,0,0,0,0] => 6
[1,1,0,1,1,1,0,0,0,0,1,0] => 4
[1,1,0,1,1,1,0,0,0,1,0,0] => 5
[1,1,0,1,1,1,0,0,1,0,0,0] => 6
[1,1,0,1,1,1,0,1,0,0,0,0] => 7
[1,1,0,1,1,1,1,0,0,0,0,0] => 5
[1,1,1,0,0,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,0,1,1,0,0] => 3
[1,1,1,0,0,0,1,1,0,0,1,0] => 3
[1,1,1,0,0,0,1,1,0,1,0,0] => 4
[1,1,1,0,0,0,1,1,1,0,0,0] => 4
[1,1,1,0,0,1,0,0,1,0,1,0] => 3
[1,1,1,0,0,1,0,0,1,1,0,0] => 4
[1,1,1,0,0,1,0,1,0,0,1,0] => 4
[1,1,1,0,0,1,0,1,0,1,0,0] => 5
[1,1,1,0,0,1,0,1,1,0,0,0] => 5
[1,1,1,0,0,1,1,0,0,0,1,0] => 4
[1,1,1,0,0,1,1,0,0,1,0,0] => 5
[1,1,1,0,0,1,1,0,1,0,0,0] => 6
[1,1,1,0,0,1,1,1,0,0,0,0] => 5
[1,1,1,0,1,0,0,0,1,0,1,0] => 4
[1,1,1,0,1,0,0,0,1,1,0,0] => 5
[1,1,1,0,1,0,0,1,0,0,1,0] => 5
[1,1,1,0,1,0,0,1,0,1,0,0] => 6
[1,1,1,0,1,0,0,1,1,0,0,0] => 6
[1,1,1,0,1,0,1,0,0,0,1,0] => 6
[1,1,1,0,1,0,1,0,0,1,0,0] => 7
[1,1,1,0,1,0,1,0,1,0,0,0] => 8
[1,1,1,0,1,0,1,1,0,0,0,0] => 7
[1,1,1,0,1,1,0,0,0,0,1,0] => 5
[1,1,1,0,1,1,0,0,0,1,0,0] => 6
[1,1,1,0,1,1,0,0,1,0,0,0] => 7
[1,1,1,0,1,1,0,1,0,0,0,0] => 8
[1,1,1,0,1,1,1,0,0,0,0,0] => 6
[1,1,1,1,0,0,0,0,1,0,1,0] => 3
[1,1,1,1,0,0,0,0,1,1,0,0] => 4
[1,1,1,1,0,0,0,1,0,0,1,0] => 4
[1,1,1,1,0,0,0,1,0,1,0,0] => 5
[1,1,1,1,0,0,0,1,1,0,0,0] => 5
[1,1,1,1,0,0,1,0,0,0,1,0] => 5
[1,1,1,1,0,0,1,0,0,1,0,0] => 6
[1,1,1,1,0,0,1,0,1,0,0,0] => 7
[1,1,1,1,0,0,1,1,0,0,0,0] => 6
[1,1,1,1,0,1,0,0,0,0,1,0] => 6
[1,1,1,1,0,1,0,0,0,1,0,0] => 7
[1,1,1,1,0,1,0,0,1,0,0,0] => 8
[1,1,1,1,0,1,0,1,0,0,0,0] => 9
[1,1,1,1,0,1,1,0,0,0,0,0] => 7
[1,1,1,1,1,0,0,0,0,0,1,0] => 4
[1,1,1,1,1,0,0,0,0,1,0,0] => 5
[1,1,1,1,1,0,0,0,1,0,0,0] => 6
[1,1,1,1,1,0,0,1,0,0,0,0] => 7
[1,1,1,1,1,0,1,0,0,0,0,0] => 8
[1,1,1,1,1,1,0,0,0,0,0,0] => 5
[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
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[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] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[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] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 3
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 4
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 3
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 4
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 5
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 4
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 4
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 4
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 5
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 6
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 5
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 3
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 4
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 5
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 6
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 4
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[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] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 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] => 3
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 4
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 4
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 5
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 4
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 4
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 3
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 4
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 5
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 5
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 4
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 5
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 6
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 5
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 4
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 4
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 5
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 5
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 5
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 6
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 7
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 6
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 4
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 5
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 6
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 7
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 5
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 4
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 4
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 3
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 4
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 5
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 5
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 4
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 5
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 6
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 5
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 5
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 5
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 6
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 6
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 6
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 7
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 8
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 7
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 5
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 6
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 7
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 8
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 6
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 4
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 5
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 5
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 5
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 6
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 7
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 6
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 6
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 7
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 8
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 9
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 7
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 4
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 5
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 6
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 7
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 8
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 5
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 3
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 3
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 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] => 3
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 4
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 3
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 5
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 4
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 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] => 3
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 4
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 3
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 4
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 5
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 5
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 4
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 5
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 6
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 5
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 4
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 4
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 5
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 5
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 5
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 6
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 7
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 6
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 6
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 7
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 5
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 4
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 4
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 5
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 5
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 5
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 6
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 5
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 3
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 4
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 4
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 5
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 5
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 5
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 6
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 6
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 5
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 6
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 7
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 6
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 4
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 5
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 5
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 6
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 6
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 6
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 7
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 8
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 7
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 5
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 6
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 7
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 8
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 6
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 3
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 4
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 4
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 5
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 5
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 5
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 5
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 6
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 6
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 5
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 6
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 7
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 6
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 5
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 6
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 6
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 7
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 7
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 7
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 8
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 9
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 8
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 6
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 7
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 8
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 9
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 7
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 4
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 5
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 5
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 6
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 6
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 6
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 7
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 8
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 7
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 7
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 8
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 9
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 10
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 8
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 6
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 7
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 8
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 9
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 6
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 3
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 3
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 4
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 4
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 4
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 5
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 5
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 4
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 6
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 5
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 3
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 4
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 4
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 5
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 5
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 5
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 6
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 6
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 5
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 6
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 7
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 6
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 4
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 5
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 5
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 6
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 6
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 6
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 7
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 8
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 7
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 5
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 6
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 7
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 8
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 6
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 4
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 5
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 5
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 6
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 6
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 6
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 6
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 7
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 7
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 6
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 7
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 8
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 7
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 6
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 7
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 7
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 8
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 8
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 8
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 9
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 10
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 9
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 7
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 8
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 9
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 10
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 8
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 5
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 6
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 6
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 7
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 7
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 7
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 8
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 9
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 8
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 8
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 9
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 10
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 11
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 9
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 6
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 7
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 8
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 9
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 10
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 7
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 3
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 4
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 4
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 5
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 5
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 5
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 5
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 6
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 6
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 5
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 6
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 7
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 6
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 5
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 6
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 6
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 7
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 7
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 7
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 8
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 9
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 8
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 6
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 7
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 8
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 9
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 7
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 6
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 7
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 7
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 8
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 8
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 8
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 9
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 10
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 9
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 9
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 10
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 11
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 12
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 10
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 7
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 8
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 9
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 10
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 11
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 4
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 5
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 6
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 6
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 6
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 7
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 8
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 7
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 7
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 8
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 9
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 10
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 8
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 9
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 10
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 11
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 12
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 9
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 5
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 6
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 8
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 9
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 10
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 6
[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
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 3
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 4
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 3
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 5
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 4
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 4
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 4
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 5
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 6
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 5
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 3
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 5
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 6
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 4
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 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] => 3
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 4
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 4
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 5
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 4
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 4
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 3
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 4
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 4
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 5
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 5
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 4
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 5
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 6
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 5
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 4
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 4
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 5
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 5
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 5
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 6
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 7
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 6
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 4
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 5
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 6
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 7
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 5
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 4
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 4
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 3
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 4
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 5
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 5
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 4
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 5
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 6
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 5
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 5
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 5
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 6
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 6
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 6
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 7
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 8
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 7
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 5
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 6
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 7
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 8
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 6
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 4
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 5
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 5
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 5
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 6
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 7
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 6
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 6
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 7
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 8
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 9
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 7
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 4
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 5
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 6
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 7
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 8
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 5
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 3
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 4
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 5
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 4
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 4
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 4
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 5
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 5
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 4
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 5
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 6
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 5
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 4
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 4
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 5
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 5
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 5
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 6
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 7
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 6
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 6
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 7
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 5
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 4
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 4
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 5
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 5
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 6
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 5
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 3
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 4
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 4
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 5
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 5
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 5
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 5
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 6
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 6
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 5
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 6
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 7
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 6
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 4
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 5
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 5
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 6
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 6
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 6
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 7
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 8
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 7
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 5
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 6
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 7
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 8
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 6
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 3
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 4
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 4
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 5
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 5
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 5
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 5
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 6
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 6
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 5
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 6
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 7
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 6
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 5
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 6
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 6
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 7
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 7
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 7
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 8
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 9
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 8
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 6
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 7
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 8
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 9
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 7
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 4
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 5
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 5
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 6
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 6
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 6
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 7
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 8
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 7
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 7
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 8
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 9
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 10
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 8
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 6
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 7
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 8
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 9
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 6
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 3
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 4
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 4
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 5
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 4
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 5
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 6
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 5
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 3
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 4
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 4
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 5
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 5
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 4
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 5
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 6
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 6
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 5
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 6
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 7
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 6
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 4
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 5
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 5
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 6
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 6
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 6
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 7
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 8
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 7
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 5
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 6
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 7
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 8
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 6
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 4
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 5
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 5
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 6
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 6
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 6
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 6
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 7
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 7
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 6
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 7
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 8
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 7
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 6
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 7
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 7
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 8
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 8
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 8
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 9
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 10
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 9
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 7
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 8
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 9
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 10
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 8
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 5
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 6
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 6
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 7
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 7
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 7
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 8
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 9
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 8
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 8
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 9
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 10
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 11
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 9
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 6
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 7
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 8
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 9
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 10
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 7
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 3
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 4
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 4
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 5
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 5
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 5
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 5
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 6
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 6
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 5
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 6
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 7
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 6
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 5
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 6
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 6
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 7
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 7
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 7
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 8
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 9
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 8
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 6
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 7
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 8
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 9
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 7
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 6
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 7
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 7
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 8
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 8
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 8
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 9
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 10
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 9
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 9
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 10
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 11
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 12
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 10
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 7
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 8
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 9
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 10
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 11
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 8
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 4
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 5
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 6
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 6
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 6
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 7
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 8
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 7
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 7
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 8
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 9
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 10
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 8
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 9
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 10
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 11
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 12
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 9
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 5
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 6
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 8
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 9
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 10
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 3
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 5
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 4
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 3
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 4
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 5
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => 5
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 4
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 5
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => 6
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => 5
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 4
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 4
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 5
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 5
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 5
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 6
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => 7
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => 6
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 6
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => 7
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 5
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 4
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 4
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 5
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 5
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 5
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 6
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 5
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 3
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 4
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 4
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 5
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 5
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 5
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 5
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 6
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 6
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => 5
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 6
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 7
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 6
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 4
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 5
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 5
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 6
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 6
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => 6
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 7
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 8
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 7
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => 5
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 6
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 7
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 8
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 6
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 4
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 4
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 5
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 5
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 5
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 5
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 6
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 6
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 5
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 6
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 7
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 6
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 5
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 6
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 6
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 7
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 7
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => 7
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 8
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 9
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 8
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 6
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 7
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 8
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 9
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 7
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 4
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 5
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 5
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 6
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 6
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 6
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 7
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 8
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 7
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 7
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 8
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 9
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 10
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 8
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 6
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 7
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 8
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 9
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 3
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 3
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => 4
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 4
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 4
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 5
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => 4
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 5
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 6
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 5
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => 4
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 7
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => 4
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => 5
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => 6
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 7
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => 7
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => 8
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => 6
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 3
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => 5
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => 5
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => 5
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => 6
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => 5
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => 6
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => 5
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => 5
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => 6
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => 6
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 5
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 7
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 7
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => 6
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => 7
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 8
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => 7
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => 5
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => 7
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => 7
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => 7
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 9
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => 8
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => 6
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => 7
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => 8
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => 9
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => 7
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => 7
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => 7
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => 7
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => 7
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => 6
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => 8
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => 9
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => 10
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => 10
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => 5
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => 7
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => 7
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => 9
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => 10
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => 11
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => 9
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => 6
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => 7
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => 8
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => 10
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => 7
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => 3
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => 5
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => 5
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => 5
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => 6
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => 7
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => 7
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => 7
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => 7
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => 6
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => 6
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => 7
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => 7
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => 7
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => 8
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => 9
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => 7
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => 5
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 7
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => 8
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => 7
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => 9
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => 10
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => 11
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => 10
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 9
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => 12
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => 11
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => 8
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => 7
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => 7
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => 7
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => 7
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => 7
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => 10
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => 9
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 9
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => 11
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => 12
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => 13
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => 10
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => 12
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => 9
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => 6
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => 7
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => 7
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => 9
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => 9
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => 11
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => 12
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => 13
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => 10
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => 7
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => 8
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => 9
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => 10
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => 11
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 7
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 3
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => 6
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => 8
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => 7
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 5
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => 8
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 6
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => 3
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => 6
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => 5
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => 6
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 7
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => 7
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => 7
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => 7
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => 7
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => 7
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => 7
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => 7
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => 7
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => 7
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => 7
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => 7
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => 10
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => 7
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => 7
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => 6
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => 7
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => 8
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => 10
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => 7
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => 6
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => 6
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => 8
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => 7
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => 7
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => 7
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => 8
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => 8
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => 6
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => 7
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => 7
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => 8
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => 8
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => 9
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => 8
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => 9
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => 10
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 10
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 11
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 12
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => 11
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => 11
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => 12
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => 10
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => 8
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => 9
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => 11
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => 10
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => 11
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => 12
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => 13
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => 11
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => 10
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => 11
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => 12
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => 9
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => 8
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => 11
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => 10
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => 10
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => 11
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => 9
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => 9
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => 9
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => 10
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => 12
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => 11
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => 12
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => 13
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => 14
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => 12
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => 11
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => 12
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => 13
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => 10
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 7
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => 8
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => 10
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => 9
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => 10
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => 11
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => 12
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => 10
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => 11
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => 12
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => 13
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => 14
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => 11
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => 8
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => 9
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => 10
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => 11
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => 12
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 3
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => 5
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 5
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => 7
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 6
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => 6
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => 5
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => 6
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => 7
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => 7
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => 7
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => 7
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => 7
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => 7
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => 7
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => 9
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => 7
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => 5
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => 7
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => 10
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 11
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => 10
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => 10
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => 11
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => 9
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => 10
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => 9
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => 11
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => 12
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => 10
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => 8
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => 9
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => 10
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => 11
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => 8
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => 8
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => 9
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => 9
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => 12
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => 11
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => 11
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => 12
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => 10
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => 10
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => 11
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => 13
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => 12
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => 13
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => 14
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => 15
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => 13
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => 10
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => 12
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => 13
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => 14
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => 11
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => 8
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => 9
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => 11
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => 10
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => 12
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => 13
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => 11
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => 12
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => 13
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => 14
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => 15
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => 12
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 8
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => 9
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => 10
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => 11
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => 12
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => 13
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 9
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 4
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => 6
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 6
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => 5
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => 6
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => 7
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => 7
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => 7
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => 8
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => 7
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => 6
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => 7
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => 10
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => 9
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => 7
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => 9
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => 10
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 8
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => 7
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => 8
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => 8
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => 11
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => 10
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => 12
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => 13
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => 11
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => 8
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => 9
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => 10
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => 11
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => 12
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => 9
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => 9
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => 10
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => 11
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => 12
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => 11
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => 12
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => 13
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => 14
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => 12
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => 12
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => 13
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => 14
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => 15
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => 16
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => 13
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 9
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => 10
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => 11
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => 12
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => 13
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => 14
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 10
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 5
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 6
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => 6
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => 7
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => 7
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => 7
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => 8
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => 9
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => 8
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 8
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => 9
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => 10
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => 11
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 9
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 9
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => 10
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => 11
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => 12
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => 13
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 10
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 10
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => 11
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => 12
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => 13
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => 14
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 15
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 11
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 6
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 8
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 9
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 10
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 11
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 12
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 7
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 7
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 7
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => 12
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 12
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => 11
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => 11
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 11
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 11
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => 10
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => 10
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 15
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => 10
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0] => 13
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => 13
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => 7
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 7
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => 16
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 6
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 6
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => 11
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 11
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 6
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0] => 10
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => 10
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 10
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 10
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0] => 9
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0] => 13
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => 13
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 9
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => 8
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => 8
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => 9
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 10
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => 9
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => 8
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => 9
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => 10
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => 8
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => 8
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => 11
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => 10
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => 11
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => 12
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => 9
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => 10
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => 12
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => 11
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => 12
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => 14
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => 10
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 8
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => 8
[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => 8
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 12
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 13
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 12
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => 13
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => 16
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => 11
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 11
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 16
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 12
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => 8
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 11
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 12
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 13
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 8
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 8
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => 8
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 9
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 13
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 14
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => 15
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 10
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => 13
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0] => 15
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0] => 10
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0] => 14
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => 15
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => 15
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => 18
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => 16
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => 12
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => 10
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0] => 12
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => 15
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => 16
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0] => 12
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => 17
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => 15
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => 11
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => 14
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => 16
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => 11
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => 17
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => 14
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => 15
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0] => 12
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => 15
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0] => 16
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => 16
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => 12
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => 16
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => 17
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => 12
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => 8
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => 8
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0] => 11
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => 12
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => 15
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => 16
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => 13
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => 18
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => 13
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => 8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => 9
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => 10
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => 11
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => 12
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 13
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 14
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 5
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 6
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 5
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 6
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 7
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 7
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 5
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 8
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => 9
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 7
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 7
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => 9
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 6
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 9
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 11
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => 8
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => 11
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 8
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 12
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 5
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => 10
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => 15
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 5
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 5
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 4
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 5
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 7
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => 3
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 7
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => 7
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => 5
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => 7
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 7
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 3
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => 5
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => 6
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => 7
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 3
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 3
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 12
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => 10
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => 8
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => 6
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => 6
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => 5
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => 11
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 11
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 11
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 7
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 8
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => 9
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => 10
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 3
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => 5
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 3
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 11
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 7
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 7
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 7
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 7
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => 7
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => 7
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => 9
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 11
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 13
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 7
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 8
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 8
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => 9
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => 9
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => 7
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => 8
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 10
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 8
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => 6
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => 5
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 3
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => 5
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => 6
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => 7
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => 7
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => 6
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 5
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => 7
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => 8
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => 6
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => 7
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 6
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => 5
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 6
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 8
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => 8
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => 7
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => 7
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 7
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 7
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 8
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 8
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => 14
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 14
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => 13
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 13
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => 18
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => 20
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 8
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 7
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 7
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0] => 13
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 13
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 5
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 6
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 7
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 9
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 9
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 5
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 9
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => 12
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 14
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 15
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => 18
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 6
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 4
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 5
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 3
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 8
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => 8
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => 6
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => 8
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 9
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 7
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 8
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => 21
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => 21
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => 19
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => 19
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 9
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => 15
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => 15
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => 19
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => 19
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 3
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 9
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => 9
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => 15
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 16
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => 14
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => 13
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 12
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 11
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 15
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 3
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => 11
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => 10
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => 9
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => 20
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => 9
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => 11
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => 13
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => 15
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => 17
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => 19
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => 21
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => 10
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => 11
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => 12
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => 13
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => 14
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => 12
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0] => 19
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => 19
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 6
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => 7
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => 8
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => 9
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => 8
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => 7
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => 6
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 10
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 11
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => 13
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 14
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 16
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => 10
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => 11
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => 12
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 13
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => 14
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 15
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => 14
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => 14
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => 13
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => 14
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => 14
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => 12
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => 12
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => 12
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => 12
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => 14
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => 14
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => 13
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => 14
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => 14
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 11
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 11
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 10
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 11
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 11
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => 10
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => 10
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 10
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 10
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => 11
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => 11
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 10
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => 11
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => 11
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => 14
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => 14
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => 13
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => 14
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0] => 14
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 12
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 12
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => 12
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => 12
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => 14
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0] => 14
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => 13
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => 14
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => 14
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 14
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => 20
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 15
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0] => 14
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0] => 14
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 14
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => 14
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => 25
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => 9
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,1,0,0] => 12
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => 10
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 10
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => 9
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 9
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0] => 16
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0] => 15
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,1,0] => 11
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 10
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 10
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => 25
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => 25
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => 17
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => 17
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => 10
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => 18
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0] => 17
[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 17
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 10
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 11
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 12
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => 13
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => 14
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 15
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 16
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 17
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 18
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => 10
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 9
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 10
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => 9
[1,1,1,0,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 9
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => 20
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 9
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 7
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 7
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0] => 12
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0] => 10
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => 20
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0] => 20
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => 19
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0] => 20
[1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => 20
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0] => 18
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0] => 18
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0] => 18
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0] => 18
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0] => 20
[1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => 20
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0] => 19
[1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0] => 20
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0] => 20
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => 17
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => 17
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => 16
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => 17
[1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => 17
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => 16
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0] => 16
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => 16
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => 16
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0] => 17
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0] => 17
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => 16
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0] => 17
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => 17
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0] => 20
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0] => 20
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0] => 19
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0] => 20
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0] => 20
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => 18
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => 18
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0] => 18
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => 18
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0] => 20
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0] => 20
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => 19
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => 20
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => 20
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => 16
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => 16
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => 15
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => 16
[1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => 16
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => 14
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => 14
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => 14
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => 14
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => 16
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => 16
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => 15
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => 16
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => 16
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 14
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 14
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 13
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 14
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 14
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 14
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 14
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 13
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 14
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 14
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0] => 14
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0] => 14
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => 14
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => 14
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => 13
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => 13
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 14
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 14
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 14
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 14
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0] => 16
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0] => 16
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => 15
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0] => 16
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => 16
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => 14
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => 14
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 14
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 14
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0] => 16
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => 16
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => 15
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => 16
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => 16
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => 20
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => 20
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0,1,0] => 19
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,1,0] => 20
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0] => 20
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => 18
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => 18
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0] => 18
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => 18
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0] => 20
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0] => 20
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => 19
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0] => 20
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0] => 20
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => 17
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => 17
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => 16
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => 17
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0] => 17
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 16
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 16
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 16
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 16
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0] => 17
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => 17
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => 16
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => 17
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => 17
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0] => 20
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,1,0] => 20
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => 19
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0] => 20
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0] => 20
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => 18
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0] => 18
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => 18
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => 18
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0] => 20
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0] => 20
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => 19
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0] => 20
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => 20
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0] => 11
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => 11
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0] => 10
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => 15
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 8
[1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0] => 11
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0] => 17
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 6
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => 42
[1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0] => 12
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => 12
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0] => 13
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0] => 14
[1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0] => 63
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 28
[1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => 21
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => 42
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 12
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0] => 15
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0] => 15
[1,1,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] => 16
[1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0] => 171
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] => 27
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Description
The sum of the heights of the peaks of a Dyck path minus the number of peaks.
References
[1] Feinberg, G., Lee, K.-H. Homogeneous representations of Type A KLR-algebras and Dyck paths arXiv:1505.04075
[2] Cheng, S.-E., Elizalde, S., Kasraoui, A., Sagan, B. Inversion polynomials for 321-avoiding permutations arXiv:1112.6014
Code
def statistic(D):
    heights = D.heights()
    return sum(heights[i+1]-1 for i in D.peaks())

Created
Feb 17, 2016 at 20:41 by Christian Stump
Updated
Dec 30, 2023 at 12:12 by Martin Rubey