Identifier
-
Mp00102:
Dyck paths
—rise composition⟶
Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00222: Dyck paths —peaks-to-valleys⟶ Dyck paths
St000052: Dyck paths ⟶ ℤ
Values
[1,0] => [1] => [1,0] => [1,0] => 0
[1,0,1,0] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[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] => [1,1,1,0,0,0] => 0
[1,0,1,1,0,0] => [1,2] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 0
[1,1,0,0,1,0] => [2,1] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 0
[1,1,0,1,0,0] => [2,1] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 0
[1,1,1,0,0,0] => [3] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,0] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,1,0,0] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 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] => 0
[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] => 0
[1,0,1,1,1,0,0,0] => [1,3] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 1
[1,1,0,0,1,0,1,0] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0] => 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] => 0
[1,1,0,1,0,0,1,0] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,1,0,0] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0] => 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] => 0
[1,1,1,0,0,0,1,0] => [3,1] => [1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,0] => [3,1] => [1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,0] => [3,1] => [1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[1,1,1,1,0,0,0,0] => [4] => [1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0] => 1
[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] => [1,1,1,1,1,0,0,0,0,0] => 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] => [1,1,1,1,0,0,0,0,1,0] => 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] => [1,1,1,0,0,0,1,1,0,0] => 0
[1,0,1,0,1,1,0,1,0,0] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0] => 0
[1,0,1,0,1,1,1,0,0,0] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,0] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0] => 0
[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] => 0
[1,0,1,1,0,1,0,0,1,0] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,0] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0] => 0
[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] => 0
[1,0,1,1,1,0,0,0,1,0] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,0] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,0] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,0] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 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] => [1,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,0,1,0,1,1,0,0] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 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] => 0
[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] => 0
[1,1,0,0,1,1,1,0,0,0] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0] => 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] => [1,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,0,1,1,0,0] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 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] => [1,0,1,1,1,1,0,0,0,0] => 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] => [1,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,0,0] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 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] => 0
[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] => 0
[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] => 0
[1,1,0,1,1,1,0,0,0,0] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,0] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,0] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 1
[1,1,1,0,0,1,0,0,1,0] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,0] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,0] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,0] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,0] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,0] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,0] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,0] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,0] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,0] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,0] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,0] => [5] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[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] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 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] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[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] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[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] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[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] => [1,1,1,0,0,0,1,1,1,0,0,0] => 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] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[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] => [1,1,1,0,0,0,1,1,1,0,0,0] => 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] => [1,1,1,0,0,0,1,1,1,0,0,0] => 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] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[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] => [1,1,1,1,0,0,0,1,1,0,0,0] => 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] => [1,1,1,1,0,0,0,1,1,0,0,0] => 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] => [1,1,1,1,0,0,0,1,1,0,0,0] => 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] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[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] => [1,1,0,0,1,1,1,1,0,0,0,0] => 0
[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] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[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] => 0
[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] => 0
[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] => [1,1,0,0,1,1,1,0,0,1,0,0] => 1
[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] => [1,1,0,0,1,1,1,1,0,0,0,0] => 0
[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] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[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] => [1,1,0,0,1,1,1,1,0,0,0,0] => 0
[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] => [1,1,0,0,1,1,1,1,0,0,0,0] => 0
[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] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => [1,1,0,0,1,1,1,0,0,1,0,0] => 1
[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] => [1,1,1,0,0,1,1,1,0,0,0,0] => 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] => [1,1,1,0,0,1,1,0,0,0,1,0] => 1
[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] => [1,1,1,0,0,1,1,1,0,0,0,0] => 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] => [1,1,1,0,0,1,1,1,0,0,0,0] => 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] => [1,1,1,0,0,1,1,0,0,0,1,0] => 1
[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] => [1,1,1,0,0,1,1,1,0,0,0,0] => 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] => [1,1,1,0,0,1,1,1,0,0,0,0] => 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] => [1,1,1,0,0,1,1,1,0,0,0,0] => 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] => [1,1,1,0,0,1,1,0,0,0,1,0] => 1
>>> Load all 1304 entries. <<<[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] => [1,1,1,1,0,0,1,1,0,0,0,0] => 1
[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] => [1,1,1,1,0,0,1,1,0,0,0,0] => 1
[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] => [1,1,1,1,0,0,1,1,0,0,0,0] => 1
[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] => [1,1,1,1,0,0,1,1,0,0,0,0] => 1
[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] => [1,1,1,1,1,0,0,1,0,0,0,0] => 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] => [1,0,1,1,1,1,1,0,0,0,0,0] => 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] => [1,0,1,1,1,1,0,0,0,0,1,0] => 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] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[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] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[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] => [1,0,1,1,1,1,0,0,0,1,0,0] => 1
[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] => [1,0,1,1,0,0,1,1,1,0,0,0] => 0
[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] => 0
[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] => [1,0,1,1,0,0,1,1,1,0,0,0] => 0
[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] => [1,0,1,1,0,0,1,1,1,0,0,0] => 0
[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] => 0
[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] => [1,0,1,1,1,0,0,1,1,0,0,0] => 1
[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] => [1,0,1,1,1,0,0,1,1,0,0,0] => 1
[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] => [1,0,1,1,1,0,0,1,1,0,0,0] => 1
[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] => [1,0,1,1,1,1,0,0,1,0,0,0] => 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] => [1,0,1,1,1,1,1,0,0,0,0,0] => 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] => [1,0,1,1,1,1,0,0,0,0,1,0] => 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] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[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] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[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] => [1,0,1,1,1,1,0,0,0,1,0,0] => 1
[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] => [1,0,1,1,1,1,1,0,0,0,0,0] => 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] => [1,0,1,1,1,1,0,0,0,0,1,0] => 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] => [1,0,1,1,1,1,1,0,0,0,0,0] => 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] => [1,0,1,1,1,1,1,0,0,0,0,0] => 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] => [1,0,1,1,1,1,0,0,0,0,1,0] => 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] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[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] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[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] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[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] => [1,0,1,1,1,1,0,0,0,1,0,0] => 1
[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] => [1,0,1,1,0,0,1,1,1,0,0,0] => 0
[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] => 0
[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] => [1,0,1,1,0,0,1,1,1,0,0,0] => 0
[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] => [1,0,1,1,0,0,1,1,1,0,0,0] => 0
[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] => 0
[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] => [1,0,1,1,0,0,1,1,1,0,0,0] => 0
[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] => [1,0,1,1,0,0,1,1,1,0,0,0] => 0
[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] => [1,0,1,1,0,0,1,1,1,0,0,0] => 0
[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] => 0
[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] => [1,0,1,1,1,0,0,1,1,0,0,0] => 1
[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] => [1,0,1,1,1,0,0,1,1,0,0,0] => 1
[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] => [1,0,1,1,1,0,0,1,1,0,0,0] => 1
[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] => [1,0,1,1,1,0,0,1,1,0,0,0] => 1
[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] => [1,0,1,1,1,1,0,0,1,0,0,0] => 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] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[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] => [1,1,0,1,1,1,0,0,0,0,1,0] => 1
[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] => [1,1,0,1,1,0,0,0,1,1,0,0] => 1
[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] => [1,1,0,1,1,0,0,0,1,1,0,0] => 1
[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] => [1,1,0,1,1,1,0,0,0,1,0,0] => 2
[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] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[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] => [1,1,0,1,1,1,0,0,0,0,1,0] => 1
[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] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[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] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[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] => [1,1,0,1,1,1,0,0,0,0,1,0] => 1
[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] => [1,1,0,1,1,0,0,0,1,1,0,0] => 1
[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] => [1,1,0,1,1,0,0,0,1,1,0,0] => 1
[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] => [1,1,0,1,1,0,0,0,1,1,0,0] => 1
[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] => [1,1,0,1,1,1,0,0,0,1,0,0] => 2
[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] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[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] => [1,1,0,1,1,1,0,0,0,0,1,0] => 1
[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] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[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] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[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] => [1,1,0,1,1,1,0,0,0,0,1,0] => 1
[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] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[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] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[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] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[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] => [1,1,0,1,1,1,0,0,0,0,1,0] => 1
[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] => [1,1,0,1,1,0,0,0,1,1,0,0] => 1
[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] => [1,1,0,1,1,0,0,0,1,1,0,0] => 1
[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] => [1,1,0,1,1,0,0,0,1,1,0,0] => 1
[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] => [1,1,0,1,1,0,0,0,1,1,0,0] => 1
[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] => [1,1,0,1,1,1,0,0,0,1,0,0] => 2
[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] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,0,0,0,0,1,0] => 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] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,0,0,0,0,1,0] => 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] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,0,0,0,0,1,0] => 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] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,0,0,0,0,1,0] => 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] => [1,1,1,1,0,1,1,0,0,0,0,0] => 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] => [1,1,1,1,0,1,1,0,0,0,0,0] => 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] => [1,1,1,1,0,1,1,0,0,0,0,0] => 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] => [1,1,1,1,0,1,1,0,0,0,0,0] => 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] => [1,1,1,1,0,1,1,0,0,0,0,0] => 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] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[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] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 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] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0
[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] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0
[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] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 1
[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] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 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] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[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] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 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] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 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] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[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] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 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] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 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] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 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] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 1
[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] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 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] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 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] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0
[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] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0
[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] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 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] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 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] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 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] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 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] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 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] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 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] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0
[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] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0
[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] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0
[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] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 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] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 1
[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] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 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] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 1
[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] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 1
[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] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 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] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 1
[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] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 1
[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] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 1
[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] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 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] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 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] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 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] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 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] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 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] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[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] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[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] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[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] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0
[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] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0
[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] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 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] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0
[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] => 0
[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] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0
[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] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0
[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] => 0
[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] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1
[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] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1
[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] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1
[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] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 1
[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] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[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] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[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] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0
[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] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0
[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] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 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] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[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] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[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] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[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] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[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] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[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] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0
[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] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0
[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] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0
[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] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 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] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0
[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] => 0
[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] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0
[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] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0
[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] => 0
[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] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0
[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] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0
[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] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0
[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] => 0
[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] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1
[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] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1
[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] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1
[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] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1
[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] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 1
[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] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 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] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 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] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 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] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 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] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 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] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 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] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 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] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 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] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 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] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 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] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 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] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 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] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 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] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 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] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 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] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 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] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 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] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 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] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 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] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 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] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 1
[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] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 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] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 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] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 1
[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] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 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] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 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] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 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] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 1
[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] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 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] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 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] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 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] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 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] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 1
[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] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[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] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[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] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[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] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[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] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[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] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 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] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[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] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[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] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 1
[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] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 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] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
[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] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 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] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 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] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
[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] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 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] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 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] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 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] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[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] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 0
[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] => 0
[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] => 0
[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] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1
[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] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[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] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 0
[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] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[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] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[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] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1
[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] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 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] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 1
[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] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 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] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 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] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 1
[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] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 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] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 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] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 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] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 1
[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] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1
[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] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1
[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] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1
[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] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1
[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] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 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] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 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] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 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] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[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] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[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] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 1
[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] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 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] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
[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] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 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] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 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] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
[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] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 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] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 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] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 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] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 1
[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] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 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] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 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] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[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] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[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] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 1
[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] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 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] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 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] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 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] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 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] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 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] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[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] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[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] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[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] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 1
[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] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 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] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
[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] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 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] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 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] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
[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] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 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] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 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] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 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] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
[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] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 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] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 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] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 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] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 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] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 1
[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] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[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] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 0
[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] => 0
[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] => 0
[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] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1
[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] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[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] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 0
[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] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[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] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[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] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1
[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] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[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] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 0
[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] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[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] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[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] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 0
[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] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[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] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[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] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[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] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1
[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] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 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] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 1
[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] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 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] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 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] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 1
[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] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 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] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 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] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 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] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 1
[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] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 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] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 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] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 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] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 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] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 1
[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] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1
[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] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1
[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] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1
[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] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1
[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] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1
[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] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 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] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 1
[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] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 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] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 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] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 2
[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] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 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] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 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] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 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] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 1
[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] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 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] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 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] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 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] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2
[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] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 1
[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] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 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] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 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] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 2
[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] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 1
[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] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 1
[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] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 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] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 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] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 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] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 2
[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] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 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] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 1
[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] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 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] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 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] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 1
[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] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 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] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 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] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 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] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 1
[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] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 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] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 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] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 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] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 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] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2
[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] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 1
[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] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 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] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 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] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 2
[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] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 1
[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] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 1
[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] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 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] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 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] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 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] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 2
[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] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 1
[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] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 1
[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] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 1
[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] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 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] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 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] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 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] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 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] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 2
[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] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 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] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 1
[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] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 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] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 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] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 1
[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] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 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] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 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] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 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] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 1
[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] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 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] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 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] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 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] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 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] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 1
[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] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 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] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 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] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 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] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 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] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 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] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2
[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] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 1
[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] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 2
[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] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 1
[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] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 1
[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] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 2
[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] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 1
[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] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 1
[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] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 1
[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] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 2
[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] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 1
[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] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 1
[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] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 1
[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] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 1
[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] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 2
[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] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 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] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 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] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 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] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 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] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 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] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 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] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 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] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 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] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 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] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 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] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 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] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[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] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => 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] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 1
[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] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 1
[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] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => 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] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 1
[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] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 1
[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] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 1
[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] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => 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] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 1
[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] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 1
[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] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 1
[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] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 1
[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] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => 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] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 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] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 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] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 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] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 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] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 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] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 1
[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] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[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] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[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] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[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] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[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] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 1
[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] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[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] => 0
[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] => 0
[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] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[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] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[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] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 1
[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] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[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] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[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] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[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] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[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] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 1
[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] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 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] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[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] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[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] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[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] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[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] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 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] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[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] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[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] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[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] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[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] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[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] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[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] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[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] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[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] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 1
[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] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 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] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[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] => 0
[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] => 0
[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] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[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] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[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] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[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] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[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] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[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] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[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] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[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] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => 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] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => 1
[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] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => 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] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => 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] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => 1
[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] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => 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] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => 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] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => 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] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => 1
[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] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => 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] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => 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] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => 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] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => 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] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => 1
[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] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => 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] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => 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] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => 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] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => 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] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => 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] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => 1
[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] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0
[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] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 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] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[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] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 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] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 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] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[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] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[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] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[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] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[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] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[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] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[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] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 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] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 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] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 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] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0
[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] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 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] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[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] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 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] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 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] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[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] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[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] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 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] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 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] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0
[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] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 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] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 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] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 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] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 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] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0
[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] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0
[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] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 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] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[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] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 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] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 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] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[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] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 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] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 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] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 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] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[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] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[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] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[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] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[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] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[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] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[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] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[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] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[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] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[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] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[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] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[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] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[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] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[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] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[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] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[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] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[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] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[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] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 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] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => 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] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => 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] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => 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] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => 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] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => 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] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => 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] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => 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] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => 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] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[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] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => 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] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => 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] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => 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] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => 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] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[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] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => 2
[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] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[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] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[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] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 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] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 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] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => 2
[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] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[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] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[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] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 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] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 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] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[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] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[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] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 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] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 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] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 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] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => 2
[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] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[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] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[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] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 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] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 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] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[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] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[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] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 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] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 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] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 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] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[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] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[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] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 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] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 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] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 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] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 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] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => 2
[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] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1
[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] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => 2
[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] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1
[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] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => 2
[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] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1
[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] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1
[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] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => 2
[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] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1
[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] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1
[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] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1
[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] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => 2
[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] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1
[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] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1
[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] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1
[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] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1
[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] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => 2
[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] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 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] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 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] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 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] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 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] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 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] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 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] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 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] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 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] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 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] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 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] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 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] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [6,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,10] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => [6,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,1,0] => [6,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [6,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0] => [6,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,1,0,0] => [6,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,1,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,1,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [2,2,1,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [2,2,1,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [2,2,1,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [2,2,1,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,2,1,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [3,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0] => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0] => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0] => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,0] => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,0] => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0] => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0] => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0,0] => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0,0] => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0] => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0] => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0] => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0] => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0] => [6,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0] => [6,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0] => [6,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0,0] => [6,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0] => [6,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0] => [6,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0] => [6,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,0] => [6,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0] => [6,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0] => [6,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0] => [6,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => [6,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [6,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0] => [6,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0] => [6,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [6,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [6,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [6,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0] => [6,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0] => [6,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [6,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [6,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0] => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,1,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,1,1,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [3,1,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,1,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,1,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0] => [6,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [6,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,1,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,1,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,1,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [3,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [2,2,1,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 0
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,2,1,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 0
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,2,1,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [6,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0] => [6,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,1,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,1,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,1,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,2,1,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,2,1,1,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,2,1,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [3,1,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,1,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,1,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0,1,0] => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0,1,0] => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,1,0] => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,2,1,1,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,2,1,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,1,0] => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [2,2,1,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,1,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [3,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [3,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0] => [6,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,2,1,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0,1,0] => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,2,1,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,1,0] => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0,1,0] => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [3,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,2,1,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [2,2,1,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,1,0] => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,1,0] => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,1,0] => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0] => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,1,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0,1,0] => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [3,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [3,1,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0] => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
4,1 9,5 21,21 51,78,3 127,274,28
$F_{1} = 1$
$F_{2} = 2$
$F_{3} = 4 + q$
$F_{4} = 9 + 5\ q$
$F_{5} = 21 + 21\ q$
$F_{6} = 51 + 78\ q + 3\ q^{2}$
$F_{7} = 127 + 274\ q + 28\ q^{2}$
Description
The number of valleys of a Dyck path not on the x-axis.
That is, the number of valleys of nonminimal height. This corresponds to the number of -1's in an inclusion of Dyck paths into alternating sign matrices.
That is, the number of valleys of nonminimal height. This corresponds to the number of -1's in an inclusion of Dyck paths into alternating sign matrices.
Map
peaks-to-valleys
Description
Return the path that has a valley wherever the original path has a peak of height at least one.
More precisely, the height of a valley in the image is the height of the corresponding peak minus $2$.
This is also (the inverse of) rowmotion on Dyck paths regarded as order ideals in the triangular poset.
More precisely, the height of a valley in the image is the height of the corresponding peak minus $2$.
This is also (the inverse of) rowmotion on Dyck paths regarded as order ideals in the triangular poset.
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.
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