Identifier
-
Mp00102:
Dyck paths
—rise composition⟶
Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00229: Dyck paths —Delest-Viennot⟶ Dyck paths
St001139: Dyck paths ⟶ ℤ
Values
[1,0,1,0] => [1,1] => [1,0,1,0] => [1,1,0,0] => 1
[1,1,0,0] => [2] => [1,1,0,0] => [1,0,1,0] => 0
[1,0,1,0,1,0] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[1,0,1,1,0,0] => [1,2] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 1
[1,1,0,0,1,0] => [2,1] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
[1,1,0,1,0,0] => [2,1] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
[1,1,1,0,0,0] => [3] => [1,1,1,0,0,0] => [1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,0,1,0,1,1,0,0] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,0] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,0] => [1,3] => [1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0] => 0
[1,1,0,0,1,1,0,0] => [2,2] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,0,1,0] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,1,0,0] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0] => 0
[1,1,0,1,1,0,0,0] => [2,2] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,0] => [3,1] => [1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,0] => [3,1] => [1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,0] => [3,1] => [1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,0] => [4] => [1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,0,1,0,1,0,1,1,0,0] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,1,0,0,1,0] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,0] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,0] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,0,0,1,0,1,0] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,1,0,0] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,0,1,0] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,0] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,0] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,0,0,0,1,0] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,0] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,0] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,1,0,0,0,0] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 0
[1,1,0,0,1,0,1,1,0,0] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0] => 0
[1,1,0,0,1,1,0,0,1,0] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,0] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,0,0,0] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,0] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,0] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,0,1,0] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,0] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,1,1,0,0,0] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0] => 0
[1,1,0,1,1,0,0,0,1,0] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,0,1,0,0] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,1,0,0,0] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,1,1,1,0,0,0,0] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,0] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,0,0,0,1,1,0,0] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,1,0,0,1,0] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,0,0,1,0,1,0,0] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,0,0,1,1,0,0,0] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,0] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,0,1,0,0,1,0,0] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,0,1,0,1,0,0,0] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,0,1,1,0,0,0,0] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,0] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,0] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,0] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,0] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,0] => [5] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
>>> Load all 1972 entries. <<<[1,0,1,1,1,1,0,0,0,1,0,0] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,1,4] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [3,2,3] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,2,3] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,3,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,3,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,1,4] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,1,4] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,2,3] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [3,2,3] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,2,3] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [3,3,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,3,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,4] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,1,4] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,1,4] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [3,2,3] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [3,2,3] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,2,3] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [3,2,3] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [3,3,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [3,3,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [3,3,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,1,3] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,1,3] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [4,1,3] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,1,3] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [4,1,3] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [4,1,3] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,1,3] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,1,3] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [4,1,3] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [5,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [5,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [5,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [5,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [5,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [5,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [5,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [5,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [5,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [5,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Generating function
click to show known generating functions
Search the OEIS for these generating functions
Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 2,3 6,6,2 17,15,10 46,51,30,5 128,175,91,35
$F_{2} = 1 + q$
$F_{3} = 2 + 3\ q$
$F_{4} = 6 + 6\ q + 2\ q^{2}$
$F_{5} = 17 + 15\ q + 10\ q^{2}$
$F_{6} = 46 + 51\ q + 30\ q^{2} + 5\ q^{3}$
$F_{7} = 128 + 175\ q + 91\ q^{2} + 35\ q^{3}$
Description
The number of occurrences of hills of size 2 in a Dyck path.
A hill of size two is a subpath beginning at height zero, consisting of two up steps followed by two down steps.
A hill of size two is a subpath beginning at height zero, consisting of two up steps followed by two down steps.
Map
bounce path
Description
The bounce path determined by an integer composition.
Map
rise composition
Description
Send a Dyck path to the composition of sizes of its rises.
Map
Delest-Viennot
Description
Return the Dyck path corresponding to the parallelogram polyomino obtained by applying Delest-Viennot's bijection.
Let $D$ be a Dyck path of semilength $n$. The parallelogram polyomino $\gamma(D)$ is defined as follows: let $\tilde D = d_0 d_1 \dots d_{2n+1}$ be the Dyck path obtained by prepending an up step and appending a down step to $D$. Then, the upper path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with even indices, and the lower path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with odd indices.
The Delest-Viennot bijection $\beta$ returns the parallelogram polyomino, whose column heights are the heights of the peaks of the Dyck path, and the intersection heights between columns are the heights of the valleys of the Dyck path.
This map returns the Dyck path $(\gamma^{(-1)}\circ\beta)(D)$.
Let $D$ be a Dyck path of semilength $n$. The parallelogram polyomino $\gamma(D)$ is defined as follows: let $\tilde D = d_0 d_1 \dots d_{2n+1}$ be the Dyck path obtained by prepending an up step and appending a down step to $D$. Then, the upper path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with even indices, and the lower path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with odd indices.
The Delest-Viennot bijection $\beta$ returns the parallelogram polyomino, whose column heights are the heights of the peaks of the Dyck path, and the intersection heights between columns are the heights of the valleys of the Dyck path.
This map returns the Dyck path $(\gamma^{(-1)}\circ\beta)(D)$.
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!