Identifier
-
Mp00123:
Dyck paths
—Barnabei-Castronuovo involution⟶
Dyck paths
St000052: Dyck paths ⟶ ℤ
Values
[1,0] => [1,0] => 0
[1,0,1,0] => [1,0,1,0] => 0
[1,1,0,0] => [1,1,0,0] => 0
[1,0,1,0,1,0] => [1,1,0,1,0,0] => 1
[1,0,1,1,0,0] => [1,1,0,0,1,0] => 0
[1,1,0,0,1,0] => [1,0,1,1,0,0] => 0
[1,1,0,1,0,0] => [1,0,1,0,1,0] => 0
[1,1,1,0,0,0] => [1,1,1,0,0,0] => 0
[1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0] => 0
[1,0,1,1,0,0,1,0] => [1,1,1,0,1,0,0,0] => 1
[1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,0] => 1
[1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0] => 0
[1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0] => 0
[1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0] => 2
[1,1,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,1,0,0] => [1,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,0] => 0
[1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,0] => 2
[1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0] => 0
[1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => 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] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 3
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 2
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 2
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => 0
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 3
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => 3
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => 2
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => 2
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
>>> Load all 954 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 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] => 0
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 3
[1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => 3
[1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 3
[1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => 2
[1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 3
[1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => 2
[1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => 2
[1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 2
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => 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] => 1
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 2
[1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 5
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 4
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 4
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 4
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 3
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 4
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 3
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 3
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 3
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 3
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 3
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2
[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] => 3
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 3
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 3
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 2
[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] => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 3
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 3
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 1
[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] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 3
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 2
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 3
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 2
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 2
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 3
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 3
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 3
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 2
[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] => 2
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 4
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 3
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 3
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 3
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 3
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 3
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 3
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 3
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 2
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 3
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 2
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 3
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 4
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 3
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 4
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 4
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 3
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 3
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 3
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 2
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 3
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 3
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 4
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 3
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 4
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 4
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 3
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 3
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 3
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 2
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 3
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 2
[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] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 2
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 0
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 2
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 3
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 3
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 4
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 4
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 3
[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
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 3
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 3
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 2
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 2
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 3
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 3
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 2
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 0
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 3
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 2
[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] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 5
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => 4
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 5
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => 5
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 4
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => 3
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => 3
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => 3
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => 3
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => 2
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 4
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => 5
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 3
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => 3
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => 3
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => 2
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 1
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 0
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => 3
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 6
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => 5
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 5
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 5
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => 4
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 5
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 3
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 4
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 4
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => 3
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => 3
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => 2
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 5
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => 4
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => 3
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 3
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => 3
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 3
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 3
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => 2
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => 2
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => 2
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => 2
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => 5
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => 5
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => 3
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 3
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 3
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => 2
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => 2
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => 2
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => 2
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 3
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 3
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => 2
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 1
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => 2
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => 2
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => 1
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => 1
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 0
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => 1
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 0
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 0
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,1,0] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 0
[1,0,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0] => 1
[] => [] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 6
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 5
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => 2
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => 2
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => 2
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => 2
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0] => [1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 7
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => 6
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 6
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 6
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 5
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 5
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 6
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 5
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 5
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 6
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 7
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 6
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 5
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0] => [1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 4
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => 4
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 7
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 6
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 6
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => 2
[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => 5
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => 5
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => 4
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => 4
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 4
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0] => 5
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => 5
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => 5
[1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0] => 5
[1,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => 5
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => 5
[1,1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,0] => [1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0] => 5
[1,1,0,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,0] => [1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0] => 5
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
4,1 8,5,1 16,17,8,1 32,49,38,12,1 64,129,141,77,17,1
$F_{1} = 1$
$F_{2} = 2$
$F_{3} = 4 + q$
$F_{4} = 8 + 5\ q + q^{2}$
$F_{5} = 16 + 17\ q + 8\ q^{2} + q^{3}$
$F_{6} = 32 + 49\ q + 38\ q^{2} + 12\ q^{3} + q^{4}$
$F_{7} = 64 + 129\ q + 141\ q^{2} + 77\ q^{3} + 17\ q^{4} + q^{5}$
Description
The number of valleys of a Dyck path not on the x-axis.
That is, the number of valleys of nonminimal height. This corresponds to the number of -1's in an inclusion of Dyck paths into alternating sign matrices.
That is, the number of valleys of nonminimal height. This corresponds to the number of -1's in an inclusion of Dyck paths into alternating sign matrices.
Map
Barnabei-Castronuovo involution
Description
The Barnabei-Castronuovo Schützenberger involution on Dyck paths.
The image of a Dyck path is obtained by reversing the canonical decompositions of the two halves of the Dyck path. More precisely, let $D_1, 1, D_2, 1, \dots$ be the canonical decomposition of the first half, then the canonical decomposition of the first half of the image is $\dots, 1, D_2, 1, D_1$.
The image of a Dyck path is obtained by reversing the canonical decompositions of the two halves of the Dyck path. More precisely, let $D_1, 1, D_2, 1, \dots$ be the canonical decomposition of the first half, then the canonical decomposition of the first half of the image is $\dots, 1, D_2, 1, D_1$.
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