Identifier
-
Mp00122:
Dyck paths
—Elizalde-Deutsch bijection⟶
Dyck paths
Mp00124: Dyck paths —Adin-Bagno-Roichman transformation⟶ Dyck paths
St000678: Dyck paths ⟶ ℤ
Values
[1,0,1,0] => [1,1,0,0] => [1,1,0,0] => 1
[1,1,0,0] => [1,0,1,0] => [1,0,1,0] => 2
[1,0,1,0,1,0] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 2
[1,0,1,1,0,0] => [1,1,0,1,0,0] => [1,0,1,1,0,0] => 1
[1,1,0,0,1,0] => [1,1,1,0,0,0] => [1,1,1,0,0,0] => 1
[1,1,0,1,0,0] => [1,0,1,1,0,0] => [1,1,0,1,0,0] => 2
[1,1,1,0,0,0] => [1,0,1,0,1,0] => [1,0,1,0,1,0] => 3
[1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0] => 3
[1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0] => 1
[1,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0] => 2
[1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,0] => 3
[1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0] => 2
[1,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,0] => [1,1,0,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0] => [1,1,1,0,1,0,0,0] => 2
[1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0] => 3
[1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => 4
[1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0] => 3
[1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 2
[1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0] => 4
[1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => 3
[1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 1
[1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
[1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0] => 2
[1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0] => 3
[1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0] => 3
[1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0] => 2
[1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,0] => 3
[1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,0] => 4
[1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,0,0] => 3
[1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 3
[1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 4
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 3
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 4
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 3
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 5
>>> Load all 1200 entries. <<<[1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 4
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 3
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 3
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 2
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 3
[1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 4
[1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => 3
[1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => 2
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 3
[1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => 2
[1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 4
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => 3
[1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 4
[1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 5
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 3
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => 3
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 3
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => 2
[1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => 2
[1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 4
[1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => 3
[1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 3
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 4
[1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 5
[1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => 3
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 3
[1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => 2
[1,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => 3
[1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 4
[1,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 5
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 3
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 4
[1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
[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] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4
[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] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3
[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] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3
[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] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2
[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] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2
[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] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2
[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] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2
[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] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[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] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1
[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] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 2
[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] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1
[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] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 1
[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] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3
[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] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2
[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] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1
[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] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4
[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] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[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] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3
[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] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2
[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] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2
[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] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2
[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] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1
[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] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1
[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] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5
[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] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4
[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] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4
[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] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3
[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] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3
[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] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3
[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] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[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] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2
[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] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2
[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] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2
[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] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[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] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1
[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] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3
[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] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3
[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] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2
[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] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2
[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] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2
[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] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1
[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] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 2
[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] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1
[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] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1
[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] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2
[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] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1
[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] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2
[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] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1
[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] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1
[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] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3
[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] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2
[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] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4
[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] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3
[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] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2
[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] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 3
[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] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2
[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] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[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] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1
[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] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4
[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] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3
[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] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5
[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] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4
[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] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3
[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] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4
[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] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3
[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] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[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] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[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] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1
[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] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[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] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 1
[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] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 2
[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] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1
[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] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2
[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] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1
[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] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 1
[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] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2
[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] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[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] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3
[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] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2
[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] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[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] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 3
[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] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2
[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] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 1
[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] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[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] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3
[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] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2
[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] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4
[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] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3
[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] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2
[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] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5
[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] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4
[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] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3
[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] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2
[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] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 4
[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] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1
[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] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 2
[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] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1
[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] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 3
[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] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2
[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] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 1
[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] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 4
[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] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3
[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] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2
[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] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 1
[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] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 5
[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] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4
[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] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[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] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[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] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6
[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] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5
[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] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4
[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] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3
[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] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3
[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] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3
[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] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2
[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] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[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] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2
[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] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[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] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2
[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] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[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] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[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] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1
[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] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[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] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[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] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1
[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] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 1
[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] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2
[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] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2
[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] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1
[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] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 1
[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] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1
[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] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3
[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] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3
[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] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2
[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] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2
[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] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 2
[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] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[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] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4
[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] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4
[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] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3
[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] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3
[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] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 3
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2
[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] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 2
[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] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[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] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[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] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 1
[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] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 1
[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] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
[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] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2
[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] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[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] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2
[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] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 2
[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] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[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] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1
[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] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1
[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] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 1
[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] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[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] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 1
[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] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1
[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] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 1
[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] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1
[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] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2
[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] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2
[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] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3
[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] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4
[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] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[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] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2
[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] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 3
[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] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2
[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] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2
[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] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3
[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] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3
[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] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4
[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] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5
[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] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4
[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] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3
[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] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4
[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] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3
[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] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3
[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] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2
[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] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2
[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] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2
[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] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2
[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] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 1
[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] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 1
[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] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[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] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 1
[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] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1
[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] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 1
[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] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2
[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] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 3
[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] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2
[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] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2
[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] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 3
[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] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2
[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] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[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] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2
[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] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2
[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] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3
[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] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4
[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] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3
[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] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4
[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] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 5
[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] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 3
[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] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3
[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] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 4
[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] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3
[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] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2
[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] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 2
[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] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 1
[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] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 1
[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] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2
[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] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 3
[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] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2
[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] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 3
[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] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 4
[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] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3
[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] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2
[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] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 4
[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] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 5
[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] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4
[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] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3
[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] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2
[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] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5
[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] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 6
[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] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5
[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] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4
[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] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3
[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] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[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] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2
[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] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[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] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2
[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] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2
[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] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2
[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] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1
[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] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[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] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[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] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1
[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] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 1
[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] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1
[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] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[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] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1
[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] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 1
[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] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[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] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2
[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] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3
[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] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 3
[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] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 1
[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] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 2
[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] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 2
[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] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 2
[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] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3
[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] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3
[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] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3
[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] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4
[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] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 4
[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] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2
[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] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3
[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] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 3
[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] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 3
[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] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[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] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2
[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] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 2
[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] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 2
[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] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 2
[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] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1
[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] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 1
[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] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1
[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] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[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] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1
[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] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1
[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] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1
[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] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 2
[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] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 2
[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] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1
[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] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 2
[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] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 2
[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] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 2
[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] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2
[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] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2
[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] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2
[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] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 3
[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] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3
[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] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3
[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] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4
[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] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 5
[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] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 4
[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] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2
[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] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[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] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 4
[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] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 3
[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] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 3
[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] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1
[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] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 1
[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] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1
[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] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 2
[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] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 2
[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] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2
[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] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 3
[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] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 4
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 3
[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] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3
[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] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 4
[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] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 5
[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] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4
[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] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 3
[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] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4
[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] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 5
[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] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 6
[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] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5
[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] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4
[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] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 3
[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] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 1
[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] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1
[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] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 1
[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] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1
[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] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 2
[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] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 2
[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] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1
[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] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 2
[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] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 2
[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] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[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] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 2
[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] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 2
[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] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 2
[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] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 3
[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] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 3
[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] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2
[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] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 3
[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] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 4
[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] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 4
[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] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[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] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 2
[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] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 3
[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] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 3
[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] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 3
[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] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1
[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] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 1
[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] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1
[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] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 2
[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] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 2
[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] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1
[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] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 2
[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] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 3
[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] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 3
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 2
[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] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 3
[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] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 4
[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] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 5
[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] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 4
[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] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3
[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] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 4
[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] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 5
[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] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 6
[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] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 5
[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] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[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] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1
[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] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 1
[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] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1
[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] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 2
[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] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 2
[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] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1
[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] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 2
[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] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 3
[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] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 3
[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] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1
[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] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 2
[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] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 3
[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] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 4
[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] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 4
[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] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 2
[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] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 3
[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] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 4
[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] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 5
[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] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 6
[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] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 5
[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] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 1
[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] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 2
[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] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 3
[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] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 4
[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] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 5
[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] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 6
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 3
[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] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2
[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] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 1
[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] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 4
[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] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3
[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] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 2
[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] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 2
[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] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1
[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] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2
[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] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2
[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] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 1
[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] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 3
[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] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 4
[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] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 3
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3
[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] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2
[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] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 1
[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] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2
[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] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 3
[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] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 2
[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] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 4
[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] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3
[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] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 2
[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] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5
[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] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4
[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] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 3
[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] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 2
[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] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3
[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] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => 4
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2
[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] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 3
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1
[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] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 3
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 3
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2
[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] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[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] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2
[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] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => 3
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 5
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4
[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] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3
[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] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2
[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] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 3
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 2
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2
[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] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 4
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 4
[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] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 3
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3
[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] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 5
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3
[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] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 5
[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] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[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] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[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] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[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] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[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] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 3
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2
[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] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2
[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] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 5
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2
[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] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 5
[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] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1
[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] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 3
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 1
[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] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 4
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 1
[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] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 5
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[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] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4
[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] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 4
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 2
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3
[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] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 4
[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] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 3
[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] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 2
[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] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 2
[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] => [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 2
[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] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 2
[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] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 2
[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] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2
[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] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 3
[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] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 2
[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] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 2
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 4
[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] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3
[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] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 3
[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] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 2
[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] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 2
[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] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 2
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 5
[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] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4
[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] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 4
[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] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3
[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] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 3
[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] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 3
[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] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2
[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] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 2
[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] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 2
[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] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => 2
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2
[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] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 3
[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] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 3
[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] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 3
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[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] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 2
[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] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 2
[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] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 2
[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] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 2
[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] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1
[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] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 2
[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] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 2
[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] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 2
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2
[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] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 3
[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] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 4
[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] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[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] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 3
[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] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2
[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] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3
[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] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 4
[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] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 5
[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] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4
[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] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4
[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] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3
[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] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3
[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] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2
[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] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2
[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] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1
[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] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 2
[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] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 2
[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] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 2
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[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] => [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 2
[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] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 3
[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] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2
[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] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 3
[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] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2
[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] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2
[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] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 3
[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] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4
[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] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3
[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] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 5
[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] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4
[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] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 3
[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] => [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 4
[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] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3
[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] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2
[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] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 1
[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] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 2
[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] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 3
[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] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2
[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] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 4
[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] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3
[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] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2
[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] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 5
[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] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4
[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] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3
[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] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2
[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] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 7
[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] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 6
[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] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5
[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] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 4
[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] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3
[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] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[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] => [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[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] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[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] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2
[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] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 4
[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] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 3
[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] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 3
[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] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 5
[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] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 4
[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] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 4
[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] => [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 3
[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] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 3
[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] => [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 3
[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] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 3
[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] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 3
[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] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 4
[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] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 5
[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] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 4
[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] => [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 4
[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] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 3
[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] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 3
[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] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 3
[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] => [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 4
[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] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 3
[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] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 5
[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] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4
[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] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 3
[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] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 6
[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] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5
[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] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4
[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] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 5
[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] => [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 4
[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] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 4
[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] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 4
[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] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 5
[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] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 4
[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] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 6
[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] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 5
[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] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[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] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 5
[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] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 6
[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] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 5
[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] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 6
[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] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 8
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 2,2,1 5,5,3,1 14,14,9,4,1 42,42,28,14,5,1 132,132,90,48,20,6,1
F2=q+q2
F3=2 q+2 q2+q3
F4=5 q+5 q2+3 q3+q4
F5=14 q+14 q2+9 q3+4 q4+q5
F6=42 q+42 q2+28 q3+14 q4+5 q5+q6
F7=132 q+132 q2+90 q3+48 q4+20 q5+6 q6+q7
Description
The number of up steps after the last double rise of a Dyck path.
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,… 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,… 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.
Map
Adin-Bagno-Roichman transformation
Description
The Adin-Bagno-Roichman transformation of a Dyck path.
This is a bijection preserving the number of up steps before each peak and sending the number of returns to the number of up steps after the last double up step.
This is a bijection preserving the number of up steps before each peak and sending the number of returns to the number of up steps after the last double up step.
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