Identifier
-
Mp00222:
Dyck paths
—peaks-to-valleys⟶
Dyck paths
Mp00122: Dyck paths —Elizalde-Deutsch bijection⟶ Dyck paths
St000340: Dyck paths ⟶ ℤ
Values
[1,0] => [1,0] => [1,0] => 0
[1,0,1,0] => [1,1,0,0] => [1,0,1,0] => 0
[1,1,0,0] => [1,0,1,0] => [1,1,0,0] => 1
[1,0,1,0,1,0] => [1,1,1,0,0,0] => [1,0,1,0,1,0] => 0
[1,0,1,1,0,0] => [1,1,0,0,1,0] => [1,1,1,0,0,0] => 1
[1,1,0,0,1,0] => [1,0,1,1,0,0] => [1,1,0,1,0,0] => 1
[1,1,0,1,0,0] => [1,0,1,0,1,0] => [1,1,0,0,1,0] => 2
[1,1,1,0,0,0] => [1,1,0,1,0,0] => [1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,0] => 1
[1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0] => 3
[1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0] => 2
[1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,0] => 2
[1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0] => 2
[1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,0] => 3
[1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 2
[1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
[1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 3
[1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 3
[1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => 4
[1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0] => 3
[1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0] => 2
[1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0] => 3
[1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0] => 2
[1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => 2
[1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,0] => 3
[1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0] => 2
[1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0] => 3
[1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,0] => 2
[1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 2
[1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => 3
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 3
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 3
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 3
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 2
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 3
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 3
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 3
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 3
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => 2
>>> Load all 1200 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => 3
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => 3
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 4
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 3
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => 3
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => 3
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 3
[1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => 3
[1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => 4
[1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 4
[1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 5
[1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => 4
[1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 3
[1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 4
[1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => 4
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 3
[1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => 3
[1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => 3
[1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 4
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 4
[1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => 3
[1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => 3
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 3
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 3
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => 4
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => 3
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 3
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 2
[1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 3
[1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 4
[1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => 3
[1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 4
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 4
[1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => 3
[1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => 3
[1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 2
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 2
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => 3
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 3
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => 3
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 3
[1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 3
[1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => 2
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => 2
[1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 3
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 3
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 4
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 3
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 3
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 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] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 3
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 4
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 3
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 3
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [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] => 3
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 3
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 4
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 3
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 3
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 4
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 4
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 5
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 4
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 3
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 4
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 4
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 3
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 3
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 4
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 3
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 3
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 3
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 3
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 3
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 3
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 3
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 3
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 4
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 3
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 3
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 3
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 4
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 4
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 4
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 3
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 3
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 3
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 3
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 3
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 3
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 3
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 4
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 3
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 3
[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] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 3
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 3
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 4
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 5
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 4
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 3
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 4
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 4
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 3
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 4
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 3
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 3
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 3
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 3
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 3
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 4
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 4
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 5
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 4
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 3
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 4
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 4
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 5
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 4
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 4
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 5
[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] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 5
[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] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 6
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 5
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 4
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 5
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 5
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 4
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 3
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 4
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 4
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 5
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 4
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 4
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 5
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 5
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 4
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 3
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 4
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 2
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 3
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 4
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 4
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 5
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 4
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 4
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 3
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 4
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 4
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 5
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 4
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 4
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 5
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 5
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 4
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 3
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 4
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 4
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 4
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 3
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 3
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 3
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 4
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 3
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 3
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 4
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 3
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 3
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 4
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 4
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 4
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 3
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 3
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 3
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 3
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 4
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 3
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 3
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 3
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 3
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 4
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 5
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 4
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 4
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 4
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 3
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 4
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 4
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 4
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 3
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 3
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 3
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 4
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 3
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 4
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 4
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 5
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 4
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 3
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 4
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 4
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 5
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 4
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 4
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 5
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 5
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 4
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 3
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 4
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 4
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 4
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 3
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 3
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 3
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 4
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 4
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 3
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [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] => 3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 4
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 4
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 4
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 3
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 3
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 3
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 3
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 2
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 3
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 3
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 4
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 3
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 3
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 3
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 3
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 4
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 3
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 4
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 4
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 3
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 3
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 3
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 4
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 3
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 4
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 4
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 3
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 4
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 4
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 4
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 3
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 3
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 3
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 3
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 3
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 3
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 3
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [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] => 3
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 3
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 2
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 4
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 3
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 3
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 3
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 3
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 3
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 3
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 4
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 3
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 2
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 3
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 3
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 3
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 4
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 3
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 4
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 4
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 5
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 4
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 4
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 4
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 3
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 3
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 4
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 3
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 4
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 4
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 3
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 3
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 3
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 3
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 3
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 3
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 3
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 4
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 3
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 3
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 3
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 3
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 4
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 3
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 3
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 4
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 4
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 3
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 3
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 3
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 3
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 3
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 3
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 4
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => 3
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 3
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 4
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 4
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 5
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 4
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 4
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => 4
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 3
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 4
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 5
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 4
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 4
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 5
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 5
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 6
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 5
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 4
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 5
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 5
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 4
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 4
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 5
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 5
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 5
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 4
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => 3
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 4
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 5
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 4
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 5
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 5
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 6
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 5
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 4
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 5
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 5
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 4
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 5
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 5
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 6
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 5
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 5
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 6
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 6
[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] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 7
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 6
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => 5
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 6
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 6
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 5
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 4
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 5
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => 5
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 6
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 5
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => 5
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 6
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 6
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 5
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 4
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 5
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 5
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 5
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 4
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 4
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 5
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 4
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 5
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 5
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 6
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 5
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => 4
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 5
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 5
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => 4
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 5
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 5
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 6
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 5
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 5
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 6
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 6
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 5
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => 4
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 5
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 5
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 5
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 4
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 5
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 4
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 5
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 5
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 4
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 4
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 5
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 4
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 5
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 5
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 5
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 4
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 4
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 3
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => 4
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 3
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 4
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 4
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => 4
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 4
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 4
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 3
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 3
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 3
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 4
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 3
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 3
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 3
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 4
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 5
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 4
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 4
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 4
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 3
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 3
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 3
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 4
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 3
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 3
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 3
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 3
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 3
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 4
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 4
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 5
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 4
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 3
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 4
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 4
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 5
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 4
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 4
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 5
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 5
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 6
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 5
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 4
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 5
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 5
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 4
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 3
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 4
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 4
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 5
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 4
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 4
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 5
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 5
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 4
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 3
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 4
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 3
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 4
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 4
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 5
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 4
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 4
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 3
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 4
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 4
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 5
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 4
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 4
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 5
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 5
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 4
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 3
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 4
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 4
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 4
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 3
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 3
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 3
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 4
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 3
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 3
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 4
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 3
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 3
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 4
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 4
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 4
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 3
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 3
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 3
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 3
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 3
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 3
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 4
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 3
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 3
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 3
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 3
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 4
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 5
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 4
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 3
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 4
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 4
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 3
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 3
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 4
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 3
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 4
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 4
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 3
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 3
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 3
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 4
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 3
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 4
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 4
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 5
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 4
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 3
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 4
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 4
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 5
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 4
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 4
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 5
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 5
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 4
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 3
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 4
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 4
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 4
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 3
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 3
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 3
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 4
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 4
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 3
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 3
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 4
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 4
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 4
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 3
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 3
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 3
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 3
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 4
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 3
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 3
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 3
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 4
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 3
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 4
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 4
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 3
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 3
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 3
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 4
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 3
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 4
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 4
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 3
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 4
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 4
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 4
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 3
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 3
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 3
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 3
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 3
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 3
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 3
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 3
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 2
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 2
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,3,1 1,6,6,1 1,10,20,10,1 1,15,50,50,15,1 1,21,105,175,105,21,1
$F_{1} = 1$
$F_{2} = 1 + q$
$F_{3} = 1 + 3\ q + q^{2}$
$F_{4} = 1 + 6\ q + 6\ q^{2} + q^{3}$
$F_{5} = 1 + 10\ q + 20\ q^{2} + 10\ q^{3} + q^{4}$
$F_{6} = 1 + 15\ q + 50\ q^{2} + 50\ q^{3} + 15\ q^{4} + q^{5}$
$F_{7} = 1 + 21\ q + 105\ q^{2} + 175\ q^{3} + 105\ q^{4} + 21\ q^{5} + q^{6}$
Description
The number of non-final maximal constant sub-paths of length greater than one.
This is the total number of occurrences of the patterns $110$ and $001$.
This is the total number of occurrences of the patterns $110$ and $001$.
Map
peaks-to-valleys
Description
Return the path that has a valley wherever the original path has a peak of height at least one.
More precisely, the height of a valley in the image is the height of the corresponding peak minus $2$.
This is also (the inverse of) rowmotion on Dyck paths regarded as order ideals in the triangular poset.
More precisely, the height of a valley in the image is the height of the corresponding peak minus $2$.
This is also (the inverse of) rowmotion on Dyck paths regarded as order ideals in the triangular poset.
Map
Elizalde-Deutsch bijection
Description
The Elizalde-Deutsch bijection on Dyck paths.
.Let $n$ be the length of the Dyck path. Consider the steps $1,n,2,n-1,\dots$ of $D$. When considering the $i$-th step its corresponding matching step has not yet been read, let the $i$-th step of the image of $D$ be an up step, otherwise let it be a down step.
.Let $n$ be the length of the Dyck path. Consider the steps $1,n,2,n-1,\dots$ of $D$. When considering the $i$-th step its corresponding matching step has not yet been read, let the $i$-th step of the image of $D$ be an up step, otherwise let it be a down step.
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