Identifier
-
Mp00028:
Dyck paths
—reverse⟶
Dyck paths
Mp00143: Dyck paths —inverse promotion⟶ Dyck paths
St001037: Dyck paths ⟶ ℤ
Values
[1,0] => [1,0] => [1,0] => 0
[1,0,1,0] => [1,0,1,0] => [1,1,0,0] => 0
[1,1,0,0] => [1,1,0,0] => [1,0,1,0] => 0
[1,0,1,0,1,0] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[1,0,1,1,0,0] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
[1,1,0,0,1,0] => [1,0,1,1,0,0] => [1,1,1,0,0,0] => 0
[1,1,0,1,0,0] => [1,1,0,1,0,0] => [1,0,1,0,1,0] => 0
[1,1,1,0,0,0] => [1,1,1,0,0,0] => [1,1,0,0,1,0] => 0
[1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 1
[1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 0
[1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0] => 1
[1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0] => [1,1,1,0,1,0,0,0] => 0
[1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,0] => 0
[1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0] => [1,1,0,1,0,0,1,0] => 0
[1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => 1
[1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 0
[1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 0
[1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => 0
[1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
>>> Load all 1200 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,0] => [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
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => 0
[1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 0
[1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 0
[1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => [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] => [1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => 0
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 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] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2
[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] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 0
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 0
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 0
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 0
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 2
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 0
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 0
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 0
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 2
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 0
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 3
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 3
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 3
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 3
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 3
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 3
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 3
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 3
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 2
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 2
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 2
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 2
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 2
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 2
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 2
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 2
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 2
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 3
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 3
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 3
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 2
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 3
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 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 8,6 16,24,2 32,80,20 64,240,120,5
$F_{1} = 1$
$F_{2} = 2$
$F_{3} = 4 + q$
$F_{4} = 8 + 6\ q$
$F_{5} = 16 + 24\ q + 2\ q^{2}$
$F_{6} = 32 + 80\ q + 20\ q^{2}$
$F_{7} = 64 + 240\ q + 120\ q^{2} + 5\ q^{3}$
Description
The number of inner corners of the upper path of the parallelogram polyomino associated with the Dyck path.
Map
inverse promotion
Description
The inverse promotion of a Dyck path.
This is the bijection obtained by applying the inverse of Schützenberger's promotion to the corresponding two rowed standard Young tableau.
This is the bijection obtained by applying the inverse of Schützenberger's promotion to the corresponding two rowed standard Young tableau.
Map
reverse
Description
The reversal of a Dyck path.
This is the Dyck path obtained by reading the path backwards.
This is the Dyck path obtained by reading the path backwards.
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