Identifier
-
Mp00100:
Dyck paths
—touch composition⟶
Integer compositions
Mp00314: Integer compositions —Foata bijection⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
St000445: Dyck paths ⟶ ℤ
Values
[1,0] => [1] => [1] => [1,0] => 1
[1,0,1,0] => [1,1] => [1,1] => [1,0,1,0] => 2
[1,1,0,0] => [2] => [2] => [1,1,0,0] => 0
[1,0,1,0,1,0] => [1,1,1] => [1,1,1] => [1,0,1,0,1,0] => 3
[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] => 4
[1,0,1,0,1,1,0,0] => [1,1,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0] => [1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,0,0] => [1,3] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[1,0,1,1,1,0,0,0] => [1,3] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,0] => [2,1,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,0] => [2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,0] => [3,1] => [3,1] => [1,1,1,0,0,0,1,0] => 1
[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] => 1
[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] => 5
[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] => 3
[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] => 3
[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] => 2
[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] => 2
[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] => 3
[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] => 1
[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] => 2
[1,0,1,1,0,1,0,1,0,0] => [1,4] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,0] => [1,4] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[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] => 2
[1,0,1,1,1,0,0,1,0,0] => [1,4] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,0] => [1,4] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,0] => [1,4] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[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] => 3
[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] => 1
[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] => 1
[1,1,0,0,1,1,0,1,0,0] => [2,3] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 0
[1,1,0,0,1,1,1,0,0,0] => [2,3] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 0
[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] => 2
[1,1,0,1,0,0,1,1,0,0] => [3,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,0] => [4,1] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[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] => 1
[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] => 2
[1,1,1,0,0,0,1,1,0,0] => [3,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,0,0,1,0] => [4,1] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
[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] => 1
[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] => 1
[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] => 6
[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] => 4
[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] => 4
[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] => 3
[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] => 3
[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] => 4
[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] => 3
[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] => 2
[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] => 2
[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] => 3
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 3
[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] => 2
[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] => 1
[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] => 1
[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] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 3
[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] => 2
[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] => 1
[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] => 1
[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] => 2
[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] => 1
[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] => 1
[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] => 1
>>> Load all 3573 entries. <<<[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] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 4
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 3
[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] => 2
[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] => 0
[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] => 1
[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] => 1
[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] => 2
[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] => 0
[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] => 1
[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] => 1
[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] => 1
[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] => 3
[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] => 2
[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] => 0
[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] => 1
[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] => 1
[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] => 2
[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] => 0
[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] => 1
[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] => 1
[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] => 1
[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] => 2
[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] => 0
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 7
[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] => 5
[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] => 5
[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] => 4
[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] => 4
[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] => 5
[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] => 3
[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] => 4
[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] => 3
[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] => 3
[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] => 4
[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] => 3
[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] => 3
[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] => 3
[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] => 5
[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] => 3
[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] => 3
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 3
[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] => 2
[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] => 2
[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] => 3
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 3
[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] => 2
[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] => 2
[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] => 3
[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] => 2
[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] => 2
[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] => 2
[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] => 3
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 5
[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] => 3
[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] => 3
[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] => 2
[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] => 2
[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] => 3
[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] => 1
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 1
[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] => 1
[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] => 3
[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] => 2
[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] => 1
[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] => 1
[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] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 3
[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] => 2
[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] => 1
[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] => 1
[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] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 4
[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] => 2
[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] => 2
[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] => 1
[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] => 1
[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] => 3
[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] => 2
[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] => 1
[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] => 1
[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] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 3
[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] => 2
[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] => 1
[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] => 1
[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] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 3
[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] => 2
[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] => 1
[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] => 1
[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] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 5
[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] => 3
[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] => 3
[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] => 2
[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] => 2
[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] => 3
[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] => 1
[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] => 2
[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] => 2
[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] => 3
[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] => 1
[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] => 1
[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] => 0
[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] => 0
[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] => 2
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 2
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 4
[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] => 2
[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] => 2
[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] => 1
[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] => 1
[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] => 2
[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] => 0
[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] => 1
[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] => 1
[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] => 3
[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] => 2
[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] => 0
[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] => 1
[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] => 1
[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] => 2
[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] => 0
[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] => 1
[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] => 1
[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] => 1
[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] => 3
[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] => 2
[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] => 0
[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] => 1
[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] => 1
[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] => 2
[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] => 0
[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] => 1
[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] => 1
[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] => 1
[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] => 2
[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] => 0
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 4
[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] => 2
[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] => 2
[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] => 1
[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] => 1
[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] => 2
[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] => 0
[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] => 1
[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] => 1
[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] => 3
[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] => 2
[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] => 0
[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] => 1
[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] => 1
[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] => 2
[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] => 0
[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] => 1
[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] => 1
[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] => 1
[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] => 3
[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] => 2
[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] => 0
[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] => 1
[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] => 1
[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] => 2
[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] => 0
[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] => 1
[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] => 1
[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] => 1
[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] => 2
[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] => 0
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 3
[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] => 2
[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] => 0
[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] => 1
[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] => 1
[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] => 2
[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] => 0
[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] => 1
[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] => 1
[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] => 1
[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] => 2
[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] => 0
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 2
[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] => 0
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 8
[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] => 6
[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] => 6
[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] => 5
[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] => 5
[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] => 6
[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] => 4
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,3,1] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 5
[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] => 4
[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] => 4
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,3,1] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 5
[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] => 4
[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] => 4
[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] => 4
[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] => 6
[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] => 4
[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] => 4
[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] => 3
[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] => 3
[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] => 5
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,3,2] => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 3
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,4,1] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 4
[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] => 3
[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] => 3
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,4,1] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 4
[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] => 3
[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] => 3
[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] => 3
[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] => 5
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,3,2] => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,4,1] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 4
[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] => 3
[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] => 3
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,4,1] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 4
[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] => 3
[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] => 3
[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] => 3
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,4,1] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 4
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 6
[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] => 4
[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] => 4
[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] => 3
[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] => 3
[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] => 4
[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] => 2
[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] => 3
[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] => 2
[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] => 2
[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] => 3
[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] => 2
[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] => 2
[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] => 2
[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] => 5
[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] => 3
[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] => 2
[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] => 2
[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] => 4
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,4,2] => [4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,5,1] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 3
[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] => 2
[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] => 2
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,5,1] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 3
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,4,2] => [4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,5,1] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 3
[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] => 2
[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] => 2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,5,1] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 3
[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] => 2
[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] => 2
[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] => 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,5,1] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 3
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 5
[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] => 3
[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] => 2
[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] => 2
[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] => 4
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,4,2] => [4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,5,1] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 3
[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] => 2
[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] => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,5,1] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 3
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,4,2] => [4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,5,1] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 3
[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] => 2
[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] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,5,1] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 3
[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] => 2
[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] => 2
[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] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,5,1] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 3
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,4,2] => [4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,5,1] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 3
[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] => 2
[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] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,5,1] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 3
[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] => 2
[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] => 2
[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] => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,5,1] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 3
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,5,1] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 3
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 6
[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] => 4
[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] => 4
[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] => 3
[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] => 3
[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] => 4
[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] => 2
[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] => 3
[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] => 2
[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] => 2
[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] => 3
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 1
[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] => 1
[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] => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,2] => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => 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] => 2
[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] => 2
[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] => 3
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,2] => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => 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] => 2
[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] => 2
[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] => 2
[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] => 5
[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] => 3
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,1,3] => [3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,3,1,3] => [3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => 2
[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] => 3
[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] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,3,1] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => 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] => 1
[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] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,3,3,1] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 4
[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] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,4,2,1] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => 2
[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] => 3
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,6,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 2
[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] => 1
[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] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,6,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 3
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,6,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 2
[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] => 1
[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] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,6,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 2
[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] => 1
[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] => 1
[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] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,6,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 4
[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] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,4,2,1] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => 2
[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] => 3
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,6,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 2
[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] => 1
[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] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,6,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 3
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,6,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 2
[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] => 1
[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] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,6,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 2
[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] => 1
[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] => 1
[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] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,6,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 3
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,6,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 2
[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] => 1
[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] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,6,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 2
[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] => 1
[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] => 1
[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] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,6,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,6,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,3,1,1,1,1] => [1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 5
[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] => 3
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,3,1,3] => [3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,3,1,3] => [3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => 2
[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] => 3
[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] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,3,3,1] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => 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] => 1
[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] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,3,3,1] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 4
[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] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,2,1] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => 2
[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] => 3
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,6,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 2
[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] => 1
[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] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,6,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 3
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,6,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 2
[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] => 1
[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] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,6,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 2
[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] => 1
[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] => 1
[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] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,6,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 4
[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] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,4,2,1] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => 2
[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] => 3
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,6,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 2
[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] => 1
[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] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,6,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 3
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,6,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 2
[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] => 1
[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] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,6,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 2
[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] => 1
[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] => 1
[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] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,6,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 3
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,6,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 2
[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] => 1
[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] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,6,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 2
[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] => 1
[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] => 1
[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] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,6,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,6,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 4
[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] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,4,2,1] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => 2
[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] => 3
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,6,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 2
[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] => 1
[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] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,6,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 3
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,6,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 2
[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] => 1
[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] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,6,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 2
[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] => 1
[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] => 1
[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] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,6,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 3
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,6,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 2
[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] => 1
[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] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,6,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 2
[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] => 1
[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] => 1
[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] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,6,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,6,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 3
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,6,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 2
[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] => 1
[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] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,6,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 2
[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] => 1
[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] => 1
[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] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,6,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,6,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 6
[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] => 4
[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] => 4
[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] => 3
[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] => 3
[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] => 4
[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] => 2
[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] => 3
[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] => 2
[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] => 2
[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] => 3
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 1
[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] => 1
[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] => 3
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,2] => [3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => 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] => 2
[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] => 2
[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] => 3
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,2] => [3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => 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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 1
[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] => 1
[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] => 2
[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] => 0
[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] => 1
[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] => 0
[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] => 0
[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] => 1
[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] => 0
[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] => 0
[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] => 0
[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] => 3
[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] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,2,1] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[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] => 0
[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] => 0
[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] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,4,2] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,2] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 3
[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] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,2,1] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[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] => 0
[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] => 0
[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] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,4,2] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,4,2] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,4,2] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 5
[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] => 3
[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] => 2
[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] => 2
[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] => 3
[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] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,3,1] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,3,1] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => 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] => 3
[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] => 1
[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] => 1
[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] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [3,4,1] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [3,5] => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [3,5] => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [3,4,1] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [3,5] => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [3,5] => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,5] => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 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] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [3,4,1] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [3,5] => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [3,5] => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [3,4,1] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [3,5] => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [3,5] => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,5] => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [3,4,1] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [3,5] => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [3,5] => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,5] => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,5] => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 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] => 4
[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] => 2
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => 2
[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] => 1
[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] => 1
[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] => 2
[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] => 0
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[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] => 3
[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
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [5,3] => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [5,3] => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 0
[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] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [6,2] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 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] => 2
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [6,2] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 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] => 3
[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
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [5,3] => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [5,3] => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 0
[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] => 2
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [6,2] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 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] => 2
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [6,2] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 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] => 2
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [6,2] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 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] => 4
[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] => 2
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => 2
[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] => 1
[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] => 1
[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] => 2
[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] => 0
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[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] => 3
[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
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [5,3] => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [5,3] => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 0
[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] => 2
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [6,2] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 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] => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [6,2] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 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] => 3
[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
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [5,3] => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [5,3] => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 0
[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] => 2
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [6,2] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 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] => 2
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [6,2] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 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] => 2
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [6,2] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 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] => 3
[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
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,3] => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,3] => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 0
[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] => 2
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [6,2] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 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] => 2
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [6,2] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 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] => 2
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,2] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 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] => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,2] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 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] => 5
[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] => 3
[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] => 2
[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] => 2
[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] => 3
[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] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,3,1] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,3,1] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => 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] => 3
[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] => 1
[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] => 1
[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] => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [3,4,1] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,5] => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,5] => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,4,1] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [3,5] => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,5] => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,5] => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 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] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [3,4,1] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,5] => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,5] => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [3,4,1] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,5] => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,5] => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,5] => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,4,1] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [3,5] => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,5] => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,5] => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,5] => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 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] => 4
[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] => 2
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => 2
[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] => 1
[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] => 1
[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] => 2
[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] => 0
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[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] => 3
[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
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [5,3] => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [5,3] => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 0
[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] => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [6,2] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 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] => 2
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [6,2] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 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] => 3
[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
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [5,3] => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [5,3] => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 0
[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] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [6,2] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 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] => 2
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [6,2] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 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] => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [6,2] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 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] => 4
[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] => 2
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => 2
[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] => 1
[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] => 1
[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] => 2
[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] => 0
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[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] => 3
[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
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [5,3] => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [5,3] => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 0
[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] => 2
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [6,2] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 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] => 2
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [6,2] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 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] => 3
[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
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [5,3] => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [5,3] => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 0
[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] => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [6,2] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 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] => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [6,2] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 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] => 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [6,2] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 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] => 3
[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
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [5,3] => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,3] => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 0
[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] => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [6,2] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 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] => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [6,2] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 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] => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [6,2] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 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] => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [6,2] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 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] => 4
[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] => 2
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => 2
[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] => 1
[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] => 1
[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] => 2
[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] => 0
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[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] => 3
[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
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [5,3] => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [5,3] => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 0
[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] => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [6,2] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 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] => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [6,2] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 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] => 3
[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
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [5,3] => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,3] => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 0
[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] => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [6,2] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 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] => 2
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [6,2] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 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] => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,2] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 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] => 3
[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
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [5,3] => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,3] => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 0
[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] => 2
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [6,2] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 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] => 2
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [6,2] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 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] => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [6,2] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 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] => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,2] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 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] => 3
[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
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,3] => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,3] => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 0
[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] => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [6,2] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 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] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,2] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 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] => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,2] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 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] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,2] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 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] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,2] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,2] => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,7] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [7,1,1] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,7,1] => [7,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [7,2] => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,7] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,7] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,2] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [7,1,1] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,7,1] => [7,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0] => [7,2] => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => [7,2] => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,7] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,7] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,7] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,8] => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [8,1,1] => [1,8,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,8,1] => [8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0] => [8,2] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0] => [7,1,1] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0] => [7,1,1] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,1] => [7,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,7,1] => [7,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,1,0,0] => [7,2] => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0] => [7,2] => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,2] => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,7] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,7] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,7] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,7] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,8] => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,8] => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 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] => [1,1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,2] => [1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,3] => [1,1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 6
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,4] => [1,1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 5
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,6] => [1,1,1,6] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,7] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 10
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,1,2] => [1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,3] => [1,1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 6
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,4] => [1,1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 5
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,6] => [1,1,1,6] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,7] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,8] => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,4] => [1,1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 5
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,4] => [1,1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 5
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,6] => [1,1,1,6] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,7] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,6] => [1,1,1,6] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,6] => [1,1,1,6] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,7] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,7] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,8] => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 2
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,6] => [1,1,1,6] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,7] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,6] => [1,1,1,6] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,6] => [1,1,1,6] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,7] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,7] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,7] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,7] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,7] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,6] => [1,1,1,6] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,7] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,6] => [1,1,1,6] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,7] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,6] => [1,1,1,6] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,8] => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,8] => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,8] => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 2
[1,0,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,7] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,7] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,1,2,1,1] => [1,2,1,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,1,2,2] => [1,1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 5
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,1,3,1] => [3,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,2,1,1,1] => [1,1,2,1,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,1,2,1,2] => [2,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 5
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,1,2,2,1] => [2,1,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 5
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,3,1,1] => [1,3,1,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,4,1] => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,2,1,1,1,1] => [1,1,1,2,1,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 7
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,2,1,2,1] => [2,2,1,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,2,2,2] => [1,1,1,2,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,5,1] => [5,1,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => 4
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,4,3] => [4,1,1,3] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,6,1] => [6,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,2,2,2] => [1,2,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,2,4] => [1,2,2,4] => [1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,3,3] => [1,2,3,3] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,6] => [1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,3,2] => [3,1,3,2] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,4,1,3] => [1,4,1,3] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,6,1,1] => [1,6,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 3
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,3,3] => [2,1,3,3] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,2,1,4] => [2,2,1,4] => [1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,2,2,2,1] => [2,2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,2,3,2] => [3,2,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,3,3,1] => [2,3,3,1] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,6,1] => [2,6,1] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,1,1,1,1,2] => [1,1,1,1,3,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 4
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,1] => [3,4,1,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,6] => [3,6] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,0,0,0] => [4,1,1,3] => [1,1,4,3] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,0] => [4,1,3,1] => [4,1,3,1] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,0] => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [4,2,2,1] => [2,4,2,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0] => [4,3,1,1] => [1,4,3,1] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => 2
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5] => [4,5] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,4] => [5,4] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => [1,1,6,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0] => [6,1,2] => [1,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,3] => [6,3] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,1,1,2,2] => [1,1,1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 6
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,1,1,3,1] => [3,1,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,4,1] => [4,1,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,2,2,2] => [1,1,1,1,2,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,5,1] => [5,1,1,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,6,1] => [6,1,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => 4
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,2,1,1,1,1,1,1] => [1,1,1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 8
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,2,2,2,2] => [1,1,2,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,1,7,1] => [7,1,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,2,3,4] => [1,2,3,4] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [1,7,1,1] => [1,7,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,2,2,2,1,1] => [1,2,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2,2] => [2,2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [2,4,3,1] => [4,2,3,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,7] => [3,7] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,6] => [4,6] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,4] => [6,4] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [7,1,1,1] => [1,1,7,1] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 3
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [7,3] => [7,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [6,1,1,1] => [1,1,6,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [7,1,1] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => [1,1,6,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 3
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [7,1,1] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [7,1,1,1] => [1,1,7,1] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [8,1,1] => [1,8,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,1,1,1,1,2] => [1,1,1,1,3,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 4
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [7,1,1] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => [1,1,6,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 3
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [7,1,1] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [6,1,1,1] => [1,1,6,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 3
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [7,2] => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,7] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,6] => [3,6] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5] => [4,5] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,4] => [5,4] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => [6,3] => [6,3] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,4,1] => [4,1,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,2] => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,7] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [6,3] => [6,3] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,4] => [5,4] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,5] => [4,5] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,6] => [3,6] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,7] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,2] => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,6] => [3,6] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,3] => [6,3] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,5] => [4,5] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [6,3] => [6,3] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4] => [5,4] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,6] => [3,6] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0] => [7,2] => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,7] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,1,0,0,0] => [6,3] => [6,3] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,6] => [3,6] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,4,1] => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,3,1,1] => [1,3,1,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [4,2,2,1] => [2,4,2,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [7,2] => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [8,2] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [7,1,1] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [5,4] => [5,4] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,4,2,2] => [1,4,2,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,7] => [3,7] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [3,7] => [3,7] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,7] => [3,7] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,7] => [3,7] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [3,7] => [3,7] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [7,3] => [7,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [7,3] => [7,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [7,3] => [7,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => [7,3] => [7,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => [7,3] => [7,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,7] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,6] => [1,1,1,6] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,4] => [1,1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 5
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [3,6] => [3,6] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0] => [4,5] => [4,5] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,1,0,0] => [5,4] => [5,4] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [7,1,1] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,6] => [3,6] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,7] => [3,7] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [3,6] => [3,6] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [4,6] => [4,6] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,8] => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => [1,1,6,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 3
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0] => [6,3] => [6,3] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,1,0,0] => [6,1,2] => [1,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,4,1] => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,7] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,8] => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [3,6] => [3,6] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,7] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,6] => [1,1,1,6] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [5,4] => [5,4] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [6,4] => [6,4] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,3,1] => [3,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,6] => [1,1,1,6] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,1,3,1] => [3,1,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [6,1,2] => [1,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,7] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,7,1,1] => [1,7,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 3
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,7,1] => [7,1,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => 3
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,7] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,6,1] => [2,6,1] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,1,1] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,2,4,1] => [2,2,4,1] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,6] => [3,6] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,6,1] => [2,6,1] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,7] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,7,1] => [7,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,3,4] => [1,1,3,4] => [1,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [6,3] => [6,3] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5] => [4,5] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,3,4] => [1,1,3,4] => [1,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 2
[1,0,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,7] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,6,1] => [6,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => 3
[1,1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [1,7,1] => [7,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [8,2] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [6,3] => [6,3] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,1,0,0] => [6,1,2] => [1,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,1,0,0] => [4,1,1,3] => [1,1,4,3] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0] => [7,1,1] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0,1,0] => [7,1,1] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,1,0] => [7,1,1] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0] => [7,1,1,1] => [1,1,7,1] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 3
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,6] => [1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [4,2,2,1] => [2,4,2,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,4] => [5,4] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [3,6] => [3,6] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,6] => [1,1,1,6] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,7] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,0,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [6,3] => [6,3] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [7,2] => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,0,1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,1,0] => [7,1,1] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,1,4,1] => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,4] => [6,4] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,1,0,0,0] => [6,3] => [6,3] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,8,1] => [8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [6,1,1,1] => [1,1,6,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 3
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [7,1,1] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [4,5] => [4,5] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,7] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,6] => [1,1,1,6] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => [1,1,6,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 3
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,2,4,1] => [2,2,4,1] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [7,1,1] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
[1,1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,6,1] => [6,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => 3
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,5,1] => [5,1,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => 4
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,1,6,1] => [6,1,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => 4
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [1,6,1,1] => [1,6,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 3
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [1,7,1] => [7,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,1] => [3,1,4,1] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,7,1] => [7,1,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => 3
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,1,0,0,0] => [6,3] => [6,3] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [7,3] => [7,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,7] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,8] => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 2
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [3,6] => [3,6] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,1,0,0] => [8,2] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [4,2,2,1] => [2,4,2,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [8,2] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,2] => [1,4,2,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [7,1,1] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [7,1,1] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => [1,1,6,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 3
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,1,1] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [7,1,1] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => [1,1,6,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 3
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [7,1,1] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,5,1] => [5,1,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => 4
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,1] => [7,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,7,1] => [7,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [4,1,3,1] => [4,1,3,1] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [3,1,4,1] => [3,4,1,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,6,1] => [6,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => 3
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [4,1,1,3] => [1,1,4,3] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [3,1,1,4] => [1,3,1,4] => [1,0,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [7,1,1] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0] => [8,1,1] => [1,8,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => [1,1,6,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 3
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,4,1] => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,5,1] => [5,1,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => 4
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,1,4,1] => [4,1,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,8] => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,3] => [6,3] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,0] => [5,4] => [5,4] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,1,0,0] => [5,4] => [5,4] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,7] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,4] => [5,4] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,6] => [4,6] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,1,0,0,0] => [5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,1,0,0,0,0] => [5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,7] => [3,7] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,6,1] => [2,6,1] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,2,4] => [1,2,2,4] => [1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,2,6] => [1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,7] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,2,6] => [1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,8] => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,7] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [4,5] => [4,5] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0,1,0] => [7,1,1] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,6] => [1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,5,1] => [5,1,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,6,1,1] => [1,6,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 3
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [5,4] => [5,4] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,6] => [3,6] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,8] => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [4,6] => [4,6] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [6,4] => [6,4] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => [1,1,6,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [8,1,1] => [1,8,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [3,6] => [3,6] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,4] => [5,4] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5] => [4,5] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [2,7] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,6,1] => [6,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => 3
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [1,6,1,1] => [1,6,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 3
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [7,2] => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,7] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,2,4,2] => [4,1,2,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [7,1,1] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => [1,1,6,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 3
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,7,1] => [7,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,6,1] => [6,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,8,1] => [8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,7,1] => [7,1,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => 3
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [3,6] => [3,6] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,4,3] => [4,1,1,3] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [4,5] => [4,5] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [8,2] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [8,2] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [8,2] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [8,2] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [4,6] => [4,6] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [2,8] => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [2,8] => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [2,8] => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [6,4] => [6,4] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [6,4] => [6,4] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [2,8] => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [4,6] => [4,6] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,6,1] => [2,6,1] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,7,1] => [7,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,6,1] => [2,6,1] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [1,7,1] => [7,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,6,1] => [2,6,1] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [1,7,1] => [7,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,8,1] => [8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [7,2] => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,7] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,1,0,0] => [8,2] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [1,7,1] => [7,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,1,0,0] => [4,5] => [4,5] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [7,1,1] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,4,1] => [3,1,4,1] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,1] => [4,3,1,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [8,2] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [5,4] => [5,4] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [1,8,1] => [8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => [1,8,1] => [8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,8,1] => [8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [1,8,1] => [8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => [1,8,1] => [8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [1,8,1] => [8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0] => [1,8,1] => [8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [1,8,1] => [8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,1,0] => [1,8,1] => [8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [1,8,1] => [8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0] => [1,8,1] => [8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,8,1] => [8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [1,8,1] => [8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [1,8,1] => [8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0] => [7,3] => [7,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,1,0,0] => [6,4] => [6,4] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,1,0,0] => [5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [4,6] => [4,6] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,7] => [3,7] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,2,1] => [4,2,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,6,1] => [2,6,1] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,7] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0,1,0] => [7,1,1] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [1,7,1,1] => [1,7,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 3
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,1,7,1] => [7,1,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => 3
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [1,8,1] => [8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1,8] => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,3] => [6,3] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,2] => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [7,1,1] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,2,6] => [1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,8] => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [2,8] => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [8,2] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [7,1,1] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [6,1,1,1] => [1,1,6,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,6] => [3,6] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [2,6,1] => [2,6,1] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,1,0] => [7,1,1] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0,1,0] => [8,1,1] => [1,8,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 2
[1,1,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,1,0] => [8,1,1] => [1,8,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0] => [1,8,1] => [8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,1,0,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [8,1,1] => [1,8,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 2
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [1,8,1] => [8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [1,8,1] => [8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,1,8] => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => [1,8,1] => [8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [1,8,1] => [8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [8,1,1] => [1,8,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 2
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [1,8,1] => [8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [1,8,1] => [8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [1,1,8] => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [1,8,1] => [8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,8] => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 2
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [2,6,1] => [2,6,1] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,8] => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,8] => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,8] => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,6] => [4,6] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [6,4] => [6,4] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [8,2] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [8,2] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [8,2] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [8,2] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,7,1] => [7,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [1,8,1] => [8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,4,1] => [3,1,4,1] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,2,4,2] => [4,1,2,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [7,3] => [7,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [8,1,1] => [1,8,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [7,1,1] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [7,1,1] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0,1,0] => [7,1,1] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0] => [7,1,1] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0,1,0] => [6,1,1,1] => [1,1,6,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 3
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,8] => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,8] => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [2,8] => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [2,8] => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,8] => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,7,1] => [7,1,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => 3
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [1,1,7,1] => [7,1,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => 3
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,8,1] => [8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [1,7,1,1] => [1,7,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 3
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [1,7,1,1] => [1,7,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 3
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [8,1,1] => [1,8,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 2
[1,0,1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [8,2] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,1,0,0] => [8,2] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0] => [8,2] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [8,2] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [7,2] => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,7] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,7] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,1,0,0] => [8,2] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,8] => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,1,4] => [3,1,1,4] => [1,1,1,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => [6,3] => [6,3] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [4,5] => [4,5] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [2,7] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [3,6] => [3,6] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [5,4] => [5,4] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [7,2] => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [4,5] => [4,5] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,7] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [3,6] => [3,6] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [7,2] => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [2,8] => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [4,2,2,1] => [2,4,2,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,4,2,2] => [1,4,2,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0] => [7,2] => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [1,8,1] => [8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [1,8,1] => [8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0] => [7,2] => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [3,6] => [3,6] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [5,4] => [5,4] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [3,1,1,4] => [1,3,1,4] => [1,0,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2,8] => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [7,2] => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [6,3] => [6,3] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,1,8] => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 2
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,8] => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,7] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,8] => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,7] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,7] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [3,4,1,1] => [1,3,4,1] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [6,3] => [6,3] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [4,5] => [4,5] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [7,2] => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [7,2] => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,7] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,7] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,7] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,7] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,7] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [8,2] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [8,2] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [4,6] => [4,6] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [7,3] => [7,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0,1,1,0,0] => [8,2] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => [7,3] => [7,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,7] => [3,7] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [3,7] => [3,7] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [4,5] => [4,5] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0] => [7,1,1] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,6,1] => [6,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => 3
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [8,1,1] => [1,8,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [1,6,1,1] => [1,6,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 3
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [7,1,1,1] => [1,1,7,1] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 3
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,0,1,0] => [8,1,1] => [1,8,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 2
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [7,1,1] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,6,1] => [2,6,1] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,8] => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,7] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[1,0,1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,8] => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 2
[1,0,1,0,1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,8] => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 2
[1,0,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,8] => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [3,1,2,4] => [1,3,2,4] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [1,8,1] => [8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,7,1] => [7,1,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => 3
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,8,1] => [8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,4,2,1] => [3,4,2,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,5,1] => [5,1,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => 4
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,1,4,1] => [4,1,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,5,1] => [5,1,1,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,6,1] => [6,1,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5] => [4,5] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,0,0,1,1,1,1,0,0,0,0] => [5,4] => [5,4] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,1,0,0,0] => [6,3] => [6,3] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [8,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [1,7,1] => [7,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [9,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,5] => [4,5] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [6,3] => [6,3] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,1,0,0] => [7,2] => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,7] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [5,4] => [5,4] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,4,1,3] => [1,4,1,3] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,1,4] => [3,1,1,4] => [1,1,1,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,2,4,3] => [4,1,2,3] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,4,2,3] => [1,4,2,3] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [1,9] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,8] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,0,1 2,2,0,1 6,4,3,0,1 18,13,6,4,0,1 57,40,21,8,5,0,1 186,130,66,30,10,6,0,1
$F_{1} = q$
$F_{2} = 1 + q^{2}$
$F_{3} = 2 + 2\ q + q^{3}$
$F_{4} = 6 + 4\ q + 3\ q^{2} + q^{4}$
$F_{5} = 18 + 13\ q + 6\ q^{2} + 4\ q^{3} + q^{5}$
$F_{6} = 57 + 40\ q + 21\ q^{2} + 8\ q^{3} + 5\ q^{4} + q^{6}$
$F_{7} = 186 + 130\ q + 66\ q^{2} + 30\ q^{3} + 10\ q^{4} + 6\ q^{5} + q^{7}$
Description
The number of rises of length 1 of a Dyck path.
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.
To compute $\phi([1,4,2,5,3])$, the sequence of words is
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..
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 $w_{i+1} < v_k$.
To compute $\phi([1,4,2,5,3])$, the sequence of words is
- $1$
- $|1|4 \to 14$
- $|14|2 \to 412$
- $|4|1|2|5 \to 4125$
- $|4|125|3 \to 45123.$
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..
Map
bounce path
Description
The bounce path determined by an integer composition.
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