Identifier
-
Mp00100:
Dyck paths
—touch composition⟶
Integer compositions
Mp00314: Integer compositions —Foata bijection⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
St000658: Dyck paths ⟶ ℤ
Values
[1,0,1,0] => [1,1] => [1,1] => [1,0,1,0] => 0
[1,1,0,0] => [2] => [2] => [1,1,0,0] => 1
[1,0,1,0,1,0] => [1,1,1] => [1,1,1] => [1,0,1,0,1,0] => 0
[1,0,1,1,0,0] => [1,2] => [1,2] => [1,0,1,1,0,0] => 1
[1,1,0,0,1,0] => [2,1] => [2,1] => [1,1,0,0,1,0] => 1
[1,1,0,1,0,0] => [3] => [3] => [1,1,1,0,0,0] => 0
[1,1,1,0,0,0] => [3] => [3] => [1,1,1,0,0,0] => 0
[1,0,1,0,1,0,1,0] => [1,1,1,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,0] => [1,1,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,0] => [1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,0,0] => [1,3] => [1,3] => [1,0,1,1,1,0,0,0] => 0
[1,0,1,1,1,0,0,0] => [1,3] => [1,3] => [1,0,1,1,1,0,0,0] => 0
[1,1,0,0,1,0,1,0] => [2,1,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,0] => [2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,0] => [3,1] => [3,1] => [1,1,1,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,0] => [4] => [4] => [1,1,1,1,0,0,0,0] => 0
[1,1,0,1,1,0,0,0] => [4] => [4] => [1,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,0,1,0] => [3,1] => [3,1] => [1,1,1,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,0] => [4] => [4] => [1,1,1,1,0,0,0,0] => 0
[1,1,1,0,1,0,0,0] => [4] => [4] => [1,1,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,0,0] => [4] => [4] => [1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,0] => [1,1,1,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,0] => [1,1,2,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,1,0,0] => [1,1,3] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,1,1,0,0,0] => [1,1,3] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 0
[1,0,1,1,0,0,1,0,1,0] => [1,2,1,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,0] => [1,2,2] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,0] => [1,3,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,0] => [1,4] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,0] => [1,4] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,1,0,0,0,1,0] => [1,3,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,0,1,0,0] => [1,4] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,0] => [1,4] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,0] => [1,4] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0] => [2,1,1,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,0] => [2,1,2] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,0] => [2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,1,0,0] => [2,3] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,0] => [2,3] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,0] => [3,1,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,0,0,1,1,0,0] => [3,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,0] => [4,1] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,0] => [5] => [5] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,0,0] => [5] => [5] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,0,1,0] => [4,1] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,0] => [5] => [5] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,0,0] => [5] => [5] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,0,0] => [5] => [5] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,0] => [3,1,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,0,0,0,1,1,0,0] => [3,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,0,1,0] => [4,1] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,0] => [5] => [5] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,0,0] => [5] => [5] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,0] => [4,1] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,0] => [5] => [5] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,0,0] => [5] => [5] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,0,0] => [5] => [5] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,0] => [4,1] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,0] => [5] => [5] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,0,0] => [5] => [5] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,0] => [5] => [5] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,0] => [5] => [5] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,2] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,2,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,3] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,3] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,2,1,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,2,2] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,3,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,4] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,4] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,3,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,4] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,4] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,4] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,1,1,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,1,2] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,1] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,1,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,2] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,4,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,5] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,5] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,4,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,5] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,5] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,5] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,3,1,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,5] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,5] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,5] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,5] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,5] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,4,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
>>> Load all 1185 entries. <<<[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,5] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,2] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,2,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,2,1,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,4] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,4] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,4] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,4] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,4] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,0] => [3,1,2] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [3,2,1] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [3,3] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,3] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,0] => [4,1,1] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,0] => [4,2] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => [5,1] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,1] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,1,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,1,0,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,0,1,0,1,0] => [4,1,1] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,0,1,1,0,0] => [4,2] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => [5,1] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,0,0,1,0] => [5,1] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,1,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,0,0,1,0] => [5,1] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,1,0,0,0,1,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,1,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,0,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,3] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,3] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,0,1,0] => [4,1,1] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,0,1,1,0,0] => [4,2] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [5,1] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,1,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,0,0,1,0] => [5,1] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,1,0,0,1,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,1,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,1] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,2] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [5,1] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,1,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,1] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,1] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,1,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,1,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,0,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,1,1] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,2] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,0] => [5,1] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,1,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,1] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,1,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,1] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,1,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,2] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,2,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,3] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,3] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,2,1,1] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,2,2] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,3,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,4] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,4] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,3,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,4] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,4] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,4] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,2,1,1,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,2,1,2] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,2,2,1] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,2,3] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,2,3] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,3,1,1] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,3,2] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,4,1] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,5] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,5] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,4,1] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,5] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,5] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,5] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,3,1,1] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,3,2] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,4,1] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,5] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,5] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,4,1] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,5] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,5] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,5] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,4,1] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,5] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,5] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,5] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,5] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,1,1,2] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,1,2,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,1,3] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,1,3] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,2,1,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,2,2] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,3,1] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,4] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,3,1] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,4] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,4] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,1,1,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,1,2] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,2,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,3] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,3] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,4,1,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,4,2] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,5,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,5,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,4,1,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,4,2] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,5,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,5,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,5,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,3,1,1,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,3,1,2] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,3,2,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,3,3] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,3,3] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,1,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,5,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,5,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,1,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,2] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,5,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,5,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,5,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,4,1,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,4,2] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,5,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,5,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,2] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,2,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,3] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,3] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,2,1,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,2,2] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,4] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,4] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,4] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,4] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,4] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,2,1,1,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,2,1,2] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,2,2,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,2,3] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,2,3] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,3,2] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,4,1] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,5] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,5] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,4,1] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,5] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,5] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,5] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,2] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,4,1] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,5] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,5] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,4,1] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,5] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,5] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,5] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,4,1] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,5] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,5] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,5] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,5] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,1,1,2] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,2,1] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [3,1,3] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,1,3] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,2,1,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,2] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [3,3,1] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,4] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [3,4] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,3,1] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,4] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [3,4] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,4] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [4,1,1,1] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [4,1,2] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [4,2,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [4,3] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [4,3] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [5,1,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [5,2] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [5,1,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [5,2] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [4,1,1,1] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [4,1,2] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [4,2,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [4,3] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,3] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [5,1,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [5,2] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [5,1,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [5,2] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [5,1,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [5,2] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,1,2] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,1,2,1] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,3] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,3] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,2] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,3,1] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,4] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,4] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,3,1] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,4] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,4] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,4] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [4,1,1,1] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [4,1,2] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [4,2,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [4,3] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,3] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [5,1,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [5,2] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [5,1,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [5,2] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,1,1,1] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,1,2] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,2,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,3] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,3] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [5,1,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [5,2] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [5,1,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,2] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,1,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,2] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,1,1] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,1,2] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,2,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [5,1,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [5,2] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,1,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,2] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,1,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,2] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,1,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,2] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,2] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,2,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,3] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,3] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,2,1,1] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,2,2] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,4] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,4] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,4] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,4] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,4] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,2,1,1,1] => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,2,1,2] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,2,2,1] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,2,3] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,2,3] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,3,1,1] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,5] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,5] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,5] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,5] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,5] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,3,1,1] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,5] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,5] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,5] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,5] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,5] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,5] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,5] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,5] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,5] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,2,1,1,1,1] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,2,1,1,2] => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,2,1,2,1] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,2,1,3] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,2,1,3] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,2,2,1,1] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,2,2,2] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,2,3,1] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,2,4] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,2,4] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,2,3,1] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,2,4] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,2,4] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,2,4] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,3,1,1,1] => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,3,1,2] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,3,3] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,3,3] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,4,1,1] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,4,1,1] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,3,1,1,1] => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,3,1,2] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,3,3] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,3,3] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,4,1,1] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,4,1,1] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,4,1,1] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1] => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,2,1,1,1,2] => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,2,1,1,2,1] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,2,1,1,3] => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,2,1,1,3] => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,2,1,2,1,1] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,2,1,2,2] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,2,1,3,1] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,2,1,4] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,2,1,4] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,2,1,3,1] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,2,1,4] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,2,1,4] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,2,1,4] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,2,2,1,1,1] => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,2,2,1,2] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,2,1] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,2,2,3] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,2,2,3] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,1,1] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,1] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,2,5] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,2,5] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,1] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,2,5] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,2,5] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,2,5] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,1,1] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,2,4,1] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,2,4,1] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,2,5] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,2,5] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,2,4,1] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,2,5] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,2,5] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,2,5] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,5] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,1,1,1,1] => [1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,1,1,2] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,1,1] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,2] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,3,4] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,3,4] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,3,4] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,4,1,1,1] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,4,1,2] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,5,1,1] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,5,1,1] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,4,1,1,1] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,4,1,2] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,5,1,1] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,5,1,1] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,5,1,1] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,3,1,1,1,1] => [1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,3,1,1,2] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,3,2,1,1] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,3,2,2] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,3,4] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,3,4] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,3,4] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,3,4] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,3,4] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,4,1,1,1] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,4,1,2] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,5,1,1] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,5,1,1] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,4,1,1,1] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,4,1,2] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,5,1,1] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,5,1,1] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,5,1,1] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,4,1,1,1] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,4,1,2] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,5,1,1] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,5,1,1] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,5,1,1] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,5,1,1] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,2] => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,2,1] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,3] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,1,3] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,1,2,1,1] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,1,2,2] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,1,3,1] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,1,4] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,1,1,4] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,1,3,1] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,1,4] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,1,4] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,1,4] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,2,1,1,1] => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,2,1,2] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,2,2,1] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,2,3] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,2,3] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,3,1,1] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,1] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,5] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,1,5] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,1] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,1,5] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,1,5] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,1,5] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,1,1] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,4,1] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,4,1] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,1,5] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,5] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,1,5] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,1] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,1,5] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,5] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,5] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,5] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,2,1,1,2] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,2,1,2,1] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,2,1,3] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,2,1,3] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,2,2,1,1] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,2,3,1] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,2,4] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,2,4] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,2,3,1] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,2,4] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,2,4] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,4] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,1,1] => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,2] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,3] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,3] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,4,1,1] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,5,1] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,5,1] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,1,1] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,5,1] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,5,1] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,1] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,1,1,1] => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,1,2] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,3,3] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,3] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,4,1,1] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,5,1] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,5,1] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,4,1,1] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,5,1] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,5,1] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,5,1] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,4,1,1] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,5,1] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,5,1] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,5,1] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,5,1] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,1,1,2] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,1,3] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [3,1,1,3] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,2,1,1] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [3,1,2,2] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,1,1] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [3,2,1,2] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,2,1] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [3,3,1,1] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [3,3,1,1] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1] => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [4,1,1,2] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [4,1,3] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [4,2,1,1] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [4,2,2] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [5,1,1,1] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [5,1,2] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [5,1,2] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1] => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [4,1,1,2] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [4,1,3] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [4,2,1,1] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [4,2,2] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [5,1,1,1] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [5,1,2] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [5,1,2] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,1,2] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,1,1,2] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,1,3] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,1,1,3] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,2,1,1] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [3,1,2,2] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,1,1] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [3,2,1,2] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,2,1] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,3,1,1] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [3,3,1,1] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1] => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [4,1,1,2] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [4,1,3] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [4,2,1,1] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [4,2,2] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [5,1,1,1] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [5,1,2] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [5,1,2] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1] => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [4,1,1,2] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [4,1,3] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [4,2,1,1] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [4,2,2] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [5,1,1,1] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [5,1,2] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [5,1,2] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [5,1,2] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1] => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,1,1,2] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,1,3] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,2,1,1] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,2,2] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [5,1,1,1] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [5,1,2] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [5,1,2] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [5,1,2] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,1,2] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,1,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Generating function
click to show known generating functions
Search the OEIS for these generating functions
Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 3,2 10,3,1 31,8,3 98,27,6,1 321,88,16,4
$F_{2} = 1 + q$
$F_{3} = 3 + 2\ q$
$F_{4} = 10 + 3\ q + q^{2}$
$F_{5} = 31 + 8\ q + 3\ q^{2}$
$F_{6} = 98 + 27\ q + 6\ q^{2} + q^{3}$
$F_{7} = 321 + 88\ q + 16\ q^{2} + 4\ q^{3}$
Description
The number of rises of length 2 of a Dyck path.
This is also the number of $(1,1)$ steps of the associated Łukasiewicz path, see [1].
A related statistic is the number of double rises in a Dyck path, St000024The number of double up and double down steps of a Dyck path..
This is also the number of $(1,1)$ steps of the associated Łukasiewicz path, see [1].
A related statistic is the number of double rises in a Dyck path, St000024The number of double up and double down steps of a Dyck path..
Map
bounce path
Description
The bounce path determined by an integer composition.
Map
touch composition
Description
Sends a Dyck path to its touch composition given by the composition of lengths of its touch points.
Map
Foata bijection
Description
The Foata bijection for compositions.
The Foata bijection $\phi$ is a bijection on the set of words whose letters are positive integers. It can be defined by induction on the size of the word:
Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$.
At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.
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..
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!