Identifier
-
Mp00100:
Dyck paths
—touch composition⟶
Integer compositions
Mp00041: Integer compositions —conjugate⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
St001037: Dyck paths ⟶ ℤ
Values
[1,0] => [1] => [1] => [1,0] => 0
[1,0,1,0] => [1,1] => [2] => [1,1,0,0] => 0
[1,1,0,0] => [2] => [1,1] => [1,0,1,0] => 0
[1,0,1,0,1,0] => [1,1,1] => [3] => [1,1,1,0,0,0] => 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] => 0
[1,1,0,1,0,0] => [3] => [1,1,1] => [1,0,1,0,1,0] => 0
[1,1,1,0,0,0] => [3] => [1,1,1] => [1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0] => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,1,0,0] => [1,1,2] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,0] => [1,2,1] => [2,2] => [1,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,0] => [1,3] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,0] => [1,3] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,0] => [2,1,1] => [3,1] => [1,1,1,0,0,0,1,0] => 0
[1,1,0,0,1,1,0,0] => [2,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,0,1,0] => [3,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,0] => [4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,0] => [4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,0,1,0] => [3,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 0
[1,1,1,0,0,1,0,0] => [4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,0] => [4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,0] => [4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,0] => [1,1,1,2] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,0] => [1,1,2,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 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] => 1
[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] => 1
[1,0,1,1,0,0,1,0,1,0] => [1,2,1,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 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] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,0] => [1,4] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,0] => [1,4] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,0] => [1,3,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,0] => [1,4] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,0] => [1,4] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,0] => [1,4] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,0] => [2,1,1,1] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,0,1,0,1,1,0,0] => [2,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,0,1,0] => [2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,0] => [2,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,0] => [2,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,0] => [3,1,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,1,0,1,0,0,1,1,0,0] => [3,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,0,1,0] => [4,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,0] => [5] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,0] => [5] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,0,1,0] => [4,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,0] => [5] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,0] => [5] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,0,0,0] => [5] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,0,1,0,1,0] => [3,1,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,1,1,0,0,0,1,1,0,0] => [3,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,0,1,0] => [4,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,0] => [5] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,1,0,0,0] => [5] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,0,1,0] => [4,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,0] => [5] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,0] => [5] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,0] => [5] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,0,1,0] => [4,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,0] => [5] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,0] => [5] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,0] => [5] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,0] => [5] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,2] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,2,1] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,3] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,3] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,2,1,1] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,2,2] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,3,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,4] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,4] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,3,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,4] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,4] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,4] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,1,1,1] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,1,2] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,1] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,1,1] => [3,1,2] => [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] => [1,3,2] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,4,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,5] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,5] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,4,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,5] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,5] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,5] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,3,1,1] => [3,1,2] => [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] => [1,3,2] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,5] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,5] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,5] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,5] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,5] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
>>> Load all 1923 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [1,4,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,5] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,2,1] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,2,1,1] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,4] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,4] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,4] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,4] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,4] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,0] => [3,1,2] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [3,2,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [3,3] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,3] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => [4,1,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,0] => [4,2] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => [5,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,0] => [6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,0] => [6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,1,0,0] => [6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,0] => [6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,1,0,0,0,0] => [6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,0,1,0,1,0] => [4,1,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,0,1,1,0,0] => [4,2] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => [5,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,0] => [6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,0] => [6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,0,1,0] => [5,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,1,0,0] => [6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,0] => [6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,0] => [6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,0,0,0,1,0] => [5,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,0,0,1,0,0] => [6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,0,1,0,0,0] => [6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,1,0,0,0,0] => [6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,0] => [6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,3] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,3] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,0] => [4,1,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,0,0,1,1,0,0] => [4,2] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [5,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,0] => [6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,0,1,1,0,0,0] => [6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,1,0,0,0,1,0] => [5,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,1,0,0,1,0,0] => [6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,1,0,1,0,0,0] => [6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,1,1,0,0,0,0] => [6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,2] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [5,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,0] => [6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,1,1,0,0,0] => [6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,0] => [6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,0,1,0,0,0] => [6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,0] => [6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,1,0,0] => [6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,0,1,0,0,0] => [6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,1,0,0,0,0] => [6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,1,0,0,0,0,0] => [6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,1,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,2] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,0] => [5,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,1,0,0] => [6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,1,1,0,0,0] => [6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,1,0,0] => [6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,0] => [6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,1,0,0,0,0] => [6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,0] => [6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,0] => [6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,0] => [6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,0] => [6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,1,0,0] => [6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,0] => [6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,0] => [6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,0] => [6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,0] => [6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,2] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,2,1] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,3] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,3] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,2,1,1] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,2,2] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,3,1] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[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] => 1
[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] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,3,1] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[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] => 1
[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] => 1
[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] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,2,1,1,1] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,2,1,2] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,2,2,1] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 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] => 2
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,2,3] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,3,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,3,2] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,4,1] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,5] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,5] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,4,1] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,5] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,5] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,5] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,3,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,3,2] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,4,1] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,5] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,5] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,4,1] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,5] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,5] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,5] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,4,1] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,5] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,5] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,5] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,5] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,1,1,2] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,1,2,1] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,1,3] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,1,3] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,2,1,1] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 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] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,4] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,3,1] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,4] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,4] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,1,1,1] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,1,2] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,2,1] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,3] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,3] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,4,1,1] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,4,2] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,5,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,6] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,6] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,5,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,6] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,6] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,6] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,4,1,1] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,4,2] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,5,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,6] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,6] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,5,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,6] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,6] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,6] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,5,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,6] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,6] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,6] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,6] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,3,1,1,1] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,3,1,2] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,3,2,1] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,3,3] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,3,3] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,1,1] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,5,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,6] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,6] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,5,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,6] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,6] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,6] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,1,1] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,2] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,5,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,6] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,6] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,5,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,6] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,6] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,6] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,5,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,6] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,6] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,6] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,6] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,4,1,1] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,4,2] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,6] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,6] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,6] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,6] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,6] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,5,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,6] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,6] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,6] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,6] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,5,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,6] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,6] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,6] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,2] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,2,1] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,3] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,3] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,2,1,1] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,2,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,1] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,4] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,4] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,1] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,4] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,4] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,4] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,2,1,1,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,2,1,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2
[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] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,2,3] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,2,3] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,1] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,3,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,4,1] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,5] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,5] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,4,1] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,5] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,5] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,5] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,1] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,4,1] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,5] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,5] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,4,1] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,5] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,5] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,5] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,4,1] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,5] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,5] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,5] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,5] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,1,1,2] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,2,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [3,1,3] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,1,3] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,2,1,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [3,3,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,4] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [3,4] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,3,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,4] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [3,4] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,4] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [4,1,1,1] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [4,1,2] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [4,2,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [4,3] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [4,3] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [5,1,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [5,2] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [6,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [6,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [5,1,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [5,2] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [6,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [6,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [6,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [4,1,1,1] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [4,1,2] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [4,2,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [4,3] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,3] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [5,1,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [5,2] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [6,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [6,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [5,1,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [5,2] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [6,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [6,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [6,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [5,1,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [5,2] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [6,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [6,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [6,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [6,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,1,2] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,1,2,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,3] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,3] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,3,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,4] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,4] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,3,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,4] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,4] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,4] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [4,1,1,1] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [4,1,2] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [4,2,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [4,3] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,3] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [5,1,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [5,2] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [6,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [6,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [5,1,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [5,2] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [6,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [6,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [6,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,1,1,1] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,1,2] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,2,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,3] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,3] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [5,1,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [5,2] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [6,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [6,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [5,1,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,2] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [6,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,1,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,2] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [6,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,1,1] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,1,2] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,2,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [5,1,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [5,2] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [6,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [6,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,1,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,2] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [6,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,1,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,2] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [6,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,1,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,2] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7] => [1,1,1,1,1,1,1] => [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] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,2,1] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,3] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,3] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,2,2] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,3,1] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,4] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,4] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,3,1] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,4] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,4] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,4] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,2,1,2] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,2,2,1] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,2,3] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,2,3] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,3,2] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,4,1] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,5] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,5] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,4,1] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,5] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,5] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,5] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,3,2] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,4,1] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,5] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,5] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,4,1] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,5] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,5] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,5] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,4,1] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,5] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,5] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,5] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,5] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,2,1,1,2] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,2,1,2,1] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,2,1,3] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,2,1,3] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,2,2,2] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 3
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,2,3,1] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,2,4] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,2,4] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,2,3,1] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,2,4] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,2,4] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,2,4] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,3,1,2] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,3,2,1] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,3,3] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,3,3] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,4,2] => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,5,1] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,6] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,6] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,5,1] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,6] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,6] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,6] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,4,2] => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,5,1] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,6] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,6] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,5,1] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,6] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,6] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,6] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,5,1] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,6] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,6] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,6] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,6] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,3,1,2] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,3,2,1] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,3,3] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,3,3] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,4,2] => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,5,1] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,6] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,6] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,5,1] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,6] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,6] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,6] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,4,2] => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,5,1] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,6] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,6] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,5,1] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,6] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,6] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,6] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,5,1] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,6] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,6] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,6] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,6] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,4,2] => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,5,1] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,6] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,6] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,5,1] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,6] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,6] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,6] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,5,1] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,6] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,6] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,6] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,6] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,5,1] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,6] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,6] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,6] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,6] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,6] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,2,1,1,1,2] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,2,1,1,2,1] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,2,1,1,3] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,2,1,1,3] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,2,1,2,2] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,2,1,3,1] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,2,1,4] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,2,1,4] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,2,1,3,1] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,2,1,4] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,2,1,4] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,2,1,4] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,2,2,1,2] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,2,1] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,2,2,3] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,2,2,3] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,2] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,1] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,2,5] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,2,5] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,1] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,2,5] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,2,5] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,2,5] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,2] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,2,4,1] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,2,4,1] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,2,5] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,2,5] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,2,4,1] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,2,5] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,2,5] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,2,5] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,5] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,1,1,2] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,3,1,2,1] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,1,3] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,3,1,3] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,2] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,3,1] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4] => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,3,4] => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,3,3,1] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,3,4] => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,3,4] => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4] => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,4,1,2] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,4,2,1] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,4,3] => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,4,3] => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,5,2] => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,6,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,6,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,5,2] => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,6,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,6,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,6,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,4,1,2] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,4,2,1] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3] => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3] => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,5,2] => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,6,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,6,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,5,2] => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,6,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,6,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,6,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,5,2] => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,6,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,6,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,6,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,6,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,3,1,1,2] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,3,1,2,1] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,3,1,3] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,3,1,3] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,3,2,2] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,3,3,1] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,3,4] => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,3,4] => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,3,3,1] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,3,4] => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,3,4] => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,3,4] => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,4,1,2] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,2,1] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,4,3] => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,4,3] => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,5,2] => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,6,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,6,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,5,2] => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,6,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,6,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,6,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,4,1,2] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,4,2,1] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,4,3] => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,4,3] => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,5,2] => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,6,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,6,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,5,2] => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,6,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,6,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,6,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,5,2] => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,6,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,6,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,6,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,6,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,4,1,2] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,4,2,1] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,4,3] => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,4,3] => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,5,2] => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,6,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,6,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,5,2] => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,6,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,6,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,6,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,5,2] => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,6,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,6,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,6,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,6,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,5,2] => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,6,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,6,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,6,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,6,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,2] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,2,1] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,3] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,1,3] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,1,2,2] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,1,3,1] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,1,4] => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,1,1,4] => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,1,3,1] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,1,4] => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,1,4] => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,1,4] => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,2,1,2] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,2,2,1] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,2,3] => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,2,3] => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,2] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,1] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,5] => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,1,5] => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,1] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,1,5] => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,1,5] => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,1,5] => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,2] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,4,1] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5] => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5] => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,4,1] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,1,5] => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,5] => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,1,5] => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,1] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,1,5] => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,5] => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,5] => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,5] => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,2,1,1,2] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,2,1,2,1] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,2,1,3] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,2,1,3] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,2,3,1] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,2,4] => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,2,4] => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,2,3,1] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,2,4] => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,2,4] => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,4] => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,2] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,2,1] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,3] => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,3] => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,4,2] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,5,1] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,6] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,6] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,5,1] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,6] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,6] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,6] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,2] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,5,1] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,6] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,6] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,5,1] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,6] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,6] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,6] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,1] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,6] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,6] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,6] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,6] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,1,2] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,2,1] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,3,3] => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,3] => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,4,2] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,5,1] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,6] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,6] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,5,1] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,6] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,6] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,6] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,4,2] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,5,1] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,6] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,6] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,5,1] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,6] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,6] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,6] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,5,1] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,6] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,6] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,6] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,6] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,4,2] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,5,1] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,6] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,6] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,5,1] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,6] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,6] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,6] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,5,1] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,6] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,6] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,6] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,6] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,5,1] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,6] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,6] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,6] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,6] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,6] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,1,1,2] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,1,2,1] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,1,3] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [3,1,1,3] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [3,1,2,2] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,3,1] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [3,1,4] => [1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [3,1,4] => [1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,3,1] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [3,1,4] => [1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [3,1,4] => [1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,1,4] => [1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [3,2,1,2] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,2,1] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [3,2,3] => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => [3,2,3] => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [3,3,2] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [3,4,1] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [3,5] => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [3,5] => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [3,4,1] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [3,5] => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [3,5] => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,5] => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [3,3,2] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [3,4,1] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [3,5] => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [3,5] => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [3,4,1] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [3,5] => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [3,5] => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,5] => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [3,4,1] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [3,5] => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [3,5] => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,5] => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,5] => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [4,1,1,2] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [4,1,3] => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [4,2,2] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [4,3,1] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [4,4] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [4,3,1] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [4,4] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [4,4] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [5,1,2] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [5,2,1] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [5,3] => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [5,3] => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [6,2] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8] => [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
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [8] => [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
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [8] => [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
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [8] => [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
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [8] => [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
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [6,2] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [8] => [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
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [8] => [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
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [8] => [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
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [8] => [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
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [8] => [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
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [8] => [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
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [8] => [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
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [8] => [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
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [8] => [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
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [5,1,2] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [5,2,1] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [5,3] => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [5,3] => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [6,2] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [8] => [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
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [8] => [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
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [8] => [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
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [8] => [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
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [8] => [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
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [6,2] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [8] => [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
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [8] => [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
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [8] => [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
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [8] => [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
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [8] => [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
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [8] => [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
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [8] => [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
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [8] => [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
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [8] => [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
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [6,2] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [8] => [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
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [8] => [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
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [8] => [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
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [8] => [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
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [8] => [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
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [8] => [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
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [8] => [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
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [8] => [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
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [8] => [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
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [8] => [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
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [8] => [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
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [8] => [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
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [8] => [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
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [8] => [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
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [4,1,1,2] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [4,1,3] => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [4,2,2] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [4,3,1] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [4,4] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [4,3,1] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [4,4] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,4] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [5,1,2] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [5,2,1] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [5,3] => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [5,3] => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [6,2] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [8] => [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
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [8] => [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
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [8] => [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
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [8] => [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
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [8] => [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
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [6,2] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [8] => [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
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [8] => [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
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [8] => [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
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [8] => [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
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [8] => [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
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [8] => [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
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [8] => [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
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [8] => [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
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [8] => [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
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [5,1,2] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [5,2,1] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [5,3] => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [5,3] => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [6,2] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [8] => [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
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [8] => [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
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [8] => [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
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [8] => [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
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [8] => [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
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [6,2] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [8] => [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
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [8] => [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
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [8] => [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
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [8] => [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
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [8] => [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
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [8] => [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
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [8] => [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
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [8] => [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
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [8] => [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
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [6,2] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [8] => [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
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [8] => [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
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [8] => [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
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [8] => [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
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [8] => [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
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [8] => [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
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [8] => [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
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [8] => [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
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [8] => [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
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [8] => [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
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [8] => [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
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [8] => [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
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [8] => [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
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [8] => [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
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,1,2] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [5,2,1] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,3] => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,3] => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [6,2] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [8] => [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
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [8] => [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
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [8] => [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
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [8] => [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
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [8] => [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
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [6,2] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [8] => [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
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [8] => [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
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [8] => [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
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [8] => [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
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [8] => [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
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [8] => [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
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [8] => [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
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [8] => [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
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [8] => [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
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,2] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [8] => [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
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [8] => [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
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [8] => [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
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [8] => [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
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [8] => [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
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [8] => [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
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [8] => [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
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [8] => [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
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [8] => [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
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [8] => [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
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [8] => [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
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [8] => [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
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [8] => [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
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [8] => [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
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,2] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [8] => [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
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [8] => [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
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [8] => [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
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [8] => [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
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [8] => [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
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [8] => [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
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [8] => [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
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [8] => [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
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [8] => [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
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [8] => [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
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [8] => [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
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [8] => [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
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [8] => [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
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [8] => [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
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [8] => [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
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [8] => [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
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [8] => [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
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [8] => [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
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [8] => [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
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [8] => [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
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,1,1,2] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,1,2,1] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,1,3] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,1,1,3] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [3,1,2,2] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,3,1] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,1,4] => [1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,1,4] => [1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,3,1] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [3,1,4] => [1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,1,4] => [1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,1,4] => [1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [3,2,1,2] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,2,1] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [3,2,3] => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [3,2,3] => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [3,3,2] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [3,4,1] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,5] => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,5] => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,4,1] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [3,5] => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,5] => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,5] => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,3,2] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [3,4,1] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,5] => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,5] => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [3,4,1] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,5] => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,5] => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,5] => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,4,1] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [3,5] => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,5] => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,5] => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,5] => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [4,1,1,2] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [4,1,3] => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [4,2,2] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [4,3,1] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [4,4] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [4,3,1] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [4,4] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [4,4] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [5,1,2] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [5,2,1] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [5,3] => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [5,3] => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [6,2] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8] => [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
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [8] => [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
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [8] => [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
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [8] => [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
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [8] => [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
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [6,2] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [8] => [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
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [8] => [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
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [8] => [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
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [8] => [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
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [8] => [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
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [8] => [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
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [8] => [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
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [8] => [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
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [8] => [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
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [5,1,2] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [5,2,1] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [5,3] => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [5,3] => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [6,2] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [8] => [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
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [8] => [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
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [8] => [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
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [8] => [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
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [8] => [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
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [6,2] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [8] => [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
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [8] => [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
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [8] => [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
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [8] => [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
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [8] => [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
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [8] => [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
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [8] => [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
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [8] => [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
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [8] => [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
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [6,2] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [8] => [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
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [8] => [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
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [8] => [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
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [8] => [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
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [8] => [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
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [8] => [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
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [8] => [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
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [8] => [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
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [8] => [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
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [8] => [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
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [8] => [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
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [8] => [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
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [8] => [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
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [8] => [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
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [4,1,1,2] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [4,1,3] => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [4,2,2] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [4,3,1] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [4,4] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [4,3,1] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [4,4] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [4,4] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [5,1,2] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [5,2,1] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [5,3] => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [5,3] => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [6,2] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [8] => [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
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [8] => [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
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [8] => [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
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [8] => [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
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [8] => [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
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [6,2] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [8] => [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
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [8] => [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
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [8] => [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
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [8] => [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
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [8] => [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
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [8] => [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
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [8] => [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
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [8] => [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
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [8] => [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
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [5,1,2] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [5,2,1] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [5,3] => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [5,3] => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [6,2] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [8] => [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
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [8] => [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
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [8] => [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
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [8] => [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
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [8] => [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
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [6,2] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [8] => [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
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [8] => [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
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [8] => [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
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8] => [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
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [8] => [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
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [8] => [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
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [8] => [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
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [8] => [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
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [8] => [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
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [6,2] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [8] => [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
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [8] => [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
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [8] => [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
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [8] => [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
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [8] => [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
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [8] => [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
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [8] => [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
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [8] => [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
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [8] => [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
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [8] => [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
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [8] => [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
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [8] => [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
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [8] => [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
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [8] => [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
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [5,1,2] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [5,2,1] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [5,3] => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,3] => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [6,2] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [8] => [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
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [8] => [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
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [8] => [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
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [8] => [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
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [8] => [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
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [6,2] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [8] => [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
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [8] => [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
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [8] => [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
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [8] => [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
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [8] => [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
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [8] => [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
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [8] => [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
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [8] => [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
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [8] => [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
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [6,2] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [8] => [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
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [8] => [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
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [8] => [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
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [8] => [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
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [8] => [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
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [8] => [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
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [8] => [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
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [8] => [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
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [8] => [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
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [8] => [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
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [8] => [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
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [8] => [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
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [8] => [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
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [8] => [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
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [6,2] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [8] => [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
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [8] => [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
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [8] => [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
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [8] => [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
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [8] => [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
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [8] => [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
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [8] => [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
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [8] => [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
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [8] => [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
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [8] => [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
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [8] => [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
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [8] => [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
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [8] => [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
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [8] => [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
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [8] => [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
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [8] => [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
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [8] => [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
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [8] => [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
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [8] => [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
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [8] => [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
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,1,1,2] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,1,3] => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,2,2] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,3,1] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,4] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,4] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,3,1] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,4] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,4] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [5,1,2] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [5,2,1] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [5,3] => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [5,3] => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [6,2] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [8] => [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
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [8] => [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
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [8] => [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
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [8] => [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
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [8] => [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
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [6,2] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [8] => [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
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [8] => [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
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [8] => [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
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [8] => [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
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [8] => [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
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [8] => [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
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [8] => [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
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [8] => [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
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [8] => [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
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [5,1,2] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [5,2,1] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [5,3] => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,3] => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [6,2] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [8] => [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
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [8] => [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
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [8] => [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
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [8] => [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
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [8] => [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
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [6,2] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [8] => [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
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [8] => [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
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [8] => [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
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [8] => [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
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [8] => [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
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [8] => [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
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [8] => [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
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [8] => [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
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [8] => [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
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,2] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [8] => [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
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [8] => [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
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [8] => [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
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [8] => [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
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [8] => [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
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [8] => [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
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [8] => [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
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [8] => [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
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [8] => [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
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [8] => [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
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [8] => [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
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [8] => [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
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [8] => [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
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [8] => [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
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [5,1,2] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [5,2,1] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [5,3] => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,3] => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [6,2] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [8] => [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
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [8] => [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
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [8] => [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
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [8] => [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
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [8] => [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
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [6,2] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [8] => [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
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [8] => [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
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [8] => [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
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [8] => [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
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [8] => [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
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [8] => [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
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [8] => [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
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [8] => [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
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [8] => [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
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [6,2] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [8] => [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
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [8] => [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
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [8] => [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
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [8] => [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
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [8] => [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
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [8] => [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
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [8] => [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
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [8] => [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
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [8] => [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
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [8] => [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
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [8] => [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
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [8] => [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
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [8] => [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
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [8] => [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
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,2] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [8] => [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
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [8] => [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
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [8] => [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
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [8] => [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
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [8] => [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
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [8] => [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
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [8] => [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
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [8] => [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
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [8] => [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
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [8] => [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
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [8] => [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
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [8] => [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
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [8] => [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
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [8] => [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
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [8] => [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
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [8] => [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
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [8] => [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
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [8] => [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
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [8] => [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
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [8] => [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
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,1,2] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,2,1] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,3] => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,3] => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [6,2] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [8] => [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
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [8] => [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
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [8] => [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
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [8] => [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
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [8] => [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
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,2] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [8] => [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
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [8] => [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
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [8] => [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
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [8] => [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
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [8] => [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
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [8] => [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
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [8] => [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
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [8] => [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
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [8] => [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
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,2] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [8] => [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
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [8] => [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
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [8] => [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
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [8] => [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
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [8] => [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
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [8] => [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
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [8] => [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
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [8] => [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
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [8] => [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
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [8] => [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
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [8] => [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
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [8] => [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
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [8] => [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
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [8] => [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
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,2] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [8] => [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
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [8] => [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
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [8] => [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
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [8] => [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
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [8] => [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
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [8] => [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
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [8] => [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
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [8] => [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
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [8] => [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
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [8] => [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
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [8] => [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
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [8] => [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
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [8] => [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
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [8] => [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
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [8] => [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
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [8] => [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
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [8] => [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
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [8] => [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
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [8] => [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
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [8] => [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
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,2] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [8] => [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
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [8] => [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
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [8] => [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
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [8] => [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
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [8] => [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
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [8] => [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
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [8] => [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
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [8] => [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
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [8] => [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
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [8] => [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
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [8] => [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
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [8] => [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
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [8] => [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
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [8] => [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
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [8] => [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
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [8] => [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
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [8] => [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
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [8] => [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
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [8] => [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
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [8] => [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
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [8] => [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
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [8] => [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
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [8] => [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
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [8] => [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
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [8] => [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
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [8] => [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
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8] => [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
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
4,1 9,5 23,18,1 65,59,8 197,190,41,1
F1=1
F2=2
F3=4+q
F4=9+5 q
F5=23+18 q+q2
F6=65+59 q+8 q2
F7=197+190 q+41 q2+q3
Description
The number of inner corners of the upper path of the parallelogram polyomino associated with the Dyck path.
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bounce path
Description
The bounce path determined by an integer composition.
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conjugate
Description
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touch composition
Description
Sends a Dyck path to its touch composition given by the composition of lengths of its touch points.
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