Identifier
-
Mp00100:
Dyck paths
—touch composition⟶
Integer compositions
Mp00041: Integer compositions —conjugate⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
St000340: Dyck paths ⟶ ℤ
Values
[1,0] => [1] => [1] => [1,0] => 0
[1,0,1,0] => [1,1] => [2] => [1,1,0,0] => 1
[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] => 1
[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] => 2
[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] => 1
[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] => 3
[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] => 2
[1,1,0,0,1,1,0,0] => [2,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,0,1,0] => [3,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
[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] => 2
[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] => 1
[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] => 3
[1,0,1,0,1,1,0,1,0,0] => [1,1,3] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 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] => 3
[1,0,1,1,0,0,1,1,0,0] => [1,2,2] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 3
[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] => 3
[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] => 3
[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] => 2
[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] => 2
[1,1,0,0,1,1,0,0,1,0] => [2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 1
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 5
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 4
[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] => 4
[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] => 4
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 1
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 5
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 5
[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] => 3
[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] => 3
[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] => 5
[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] => 5
[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] => 5
[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] => 3
[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] => 3
[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] => 5
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 5
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 5
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 4
[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] => 4
[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] => 4
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 4
[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] => 6
[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] => 4
[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] => 4
[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] => 4
[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] => 4
[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] => 4
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 4
[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] => 4
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 4
[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] => 4
[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] => 4
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 4
[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] => 4
[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] => 4
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 5
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 5
[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] => 3
[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] => 3
[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] => 5
[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] => 5
[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] => 3
[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] => 3
[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] => 5
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 5
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 5
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 5
[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] => 3
[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] => 3
[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] => 5
[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] => 5
[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] => 3
[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] => 3
[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] => 5
[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] => 3
[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] => 3
[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] => 3
[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] => 5
[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] => 7
[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] => 5
[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] => 5
[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] => 5
[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] => 5
[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] => 3
[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] => 3
[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] => 5
[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] => 3
[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] => 3
[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] => 3
[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] => 5
[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] => 5
[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] => 3
[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] => 3
[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] => 5
[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] => 3
[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] => 3
[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] => 3
[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] => 5
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 5
[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] => 3
[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] => 3
[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] => 5
[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] => 5
[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] => 3
[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] => 3
[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] => 5
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 5
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 5
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 5
[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] => 3
[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] => 3
[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] => 5
[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] => 5
[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] => 3
[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] => 3
[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] => 5
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 5
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 5
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 5
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 4
[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] => 4
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 6
[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] => 4
[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] => 4
[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] => 4
[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] => 4
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 4
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 6
[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] => 4
[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] => 4
[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] => 6
[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] => 6
[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] => 4
[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] => 4
[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] => 6
[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] => 4
[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] => 4
[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] => 4
[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] => 4
[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] => 6
[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] => 4
[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] => 4
[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] => 4
[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] => 4
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 4
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 6
[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] => 4
[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] => 4
[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] => 4
[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] => 4
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 4
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 4
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 4
[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] => 4
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 6
[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] => 4
[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] => 4
[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] => 4
[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] => 4
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 4
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 4
[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] => 4
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 4
[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] => 4
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 4
[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] => 4
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 6
[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] => 4
[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] => 4
[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] => 4
[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] => 4
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 4
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 4
[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] => 4
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 4
[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] => 4
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 4
[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] => 4
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 4
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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:
1,1 2,2,1 5,4,4,1 14,9,13,5,1 42,23,41,18,7,1 132,65,131,59,33,8,1
$F_{1} = 1$
$F_{2} = 1 + q$
$F_{3} = 2 + 2\ q + q^{2}$
$F_{4} = 5 + 4\ q + 4\ q^{2} + q^{3}$
$F_{5} = 14 + 9\ q + 13\ q^{2} + 5\ q^{3} + q^{4}$
$F_{6} = 42 + 23\ q + 41\ q^{2} + 18\ q^{3} + 7\ q^{4} + q^{5}$
$F_{7} = 132 + 65\ q + 131\ q^{2} + 59\ q^{3} + 33\ q^{4} + 8\ q^{5} + q^{6}$
Description
The number of non-final maximal constant sub-paths of length greater than one.
This is the total number of occurrences of the patterns $110$ and $001$.
This is the total number of occurrences of the patterns $110$ and $001$.
Map
bounce path
Description
The bounce path determined by an integer composition.
Map
conjugate
Description
Map
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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